2.1. Single phase pressure drop comparison with experiments 2.2. Thermal model of the evaporator 2.3. Liquid plug, vapor slug and liquid film dynamics 3. Parameter study 3.1. Influence of the properties of the fluid and of the tube 3.2. Influence of he,tl, he,lf and hcond on the dynamics of the system 4. Closing remarks References Chapter 6: Conclusion and future scope 1. Conclusions 2. Future scope

iii

Abstract

This work makes an attempt to explain the self-sustained thermally-induced oscillations of a two-phase system consisting of an isolated confined liquid-vapour meniscus (a single liquid plug adjoining a vapour bubble) inside a circular capillary tube, the tube length being exposed to a net temperature gradient, thereby creating a continuous cycle of evaporation and condensation. This system represents the simplest 'unit-cell' version of a Pulsating Heat Pipe (PHP). The fundamental understanding of its transport behavior leading to self-sustained oscillations is vital for building the hitherto nonexistent mathematical models of the complete PHP system. First, visualization of the oscillations of the unit-cell has been done under controlled thermal boundary conditions. Here, a unique and novel understanding of the system dynamics has been achieved by real-time synchronization of the internal pressure measurement with highspeed videography that was used to visualize and record the meniscus oscillations and the thin liquid film that is laid on the wall when the meniscus leaves the evaporator.

When the temperature difference increases between the heat source and the heat sink, different meniscus dynamics, with excellent repeatability, can be observed. The experimental results clearly demonstrated that evaporation of the liquid film is responsible for these patterns. The different components of evaporation and condensation processes were critically analysed. Two different modes of evaporation were observed inside the system: one at the triple-line and one at the liquid-vapour interface. Contrary to obvious interpretations, maximum pressure in the vapour bubble is achieved in the downward stroke, rather than the upward stroke. Thus, the system dynamics cannot be compared with gas-compression cycles; the presence of vapour coupled with transient phase-change processes give rise to singular transport phenomena. Such an interpretation of the meniscus motion and the resulting pressure cycles has not been considered by any of the existing mathematical models of PHPs.

By simple scaling arguments, it was demonstrated that there is a high probability of metastable states existing in the system, which essentially points towards considering non-equilibrium evaporation and condensation models for predicting the thermal transport. A simple transient analytical model of thermal transport in the liquid film was developed which clearly explains the observed behavior. Existence of nonequilibrium conditions and their underlying effects on system dynamics need further exploration, both experimentally as well as analytically.

A numerical model was developed for the system consisting of a vapour plug and a liquid slug oscillating in a tube closed at one end and connected to a reservoir at a constant pressure at the other end. The modeling principle had been posed in previous work. Some modifications were never the less introduced in this work to take into account the peculiarities of the new experimental set-up and to improve the liquid film evaporation model in the light of the experimental results. Also a parametric study was carried out to understand the implications of the various factors on the working of such system. The results show that the classical correlations used to calculate pressure drops inside the liquid plug are relevant in the case of an oscillating flow. The results confirm that the dynamics of the film is the most important parameter of the system and has to be modeled by taking into account the nature of the liquid but also the nature of the wall. Therefore, the heat transfer equation in the wall has to be solved and coupled to the hydrodynamic behavior of the system. Considering that no comprehensive model of PHP system is available, the conclusions and directions provided in this study are important for building a broad understanding of these devices that remain a promising option to face the future need for thermal management of heat dissipating engineering systems. Thermodynamic cycle of PHP (Groll and Khandekar [1.14]) Fig. 1.9 Liquid slug in a PHP (Khandekar et al. [1.15]) 15 Fig. 1.10 Liquid slug in a PHP Fig. 1.11 Schematic of a Unit cell PHP (single tube: single vapour plugliquid slug) Oscillations in the single bubble PHP (Das et al. [1.34]). Left: experimental measurement of the time evolution of meniscus position (x) and vapour pressure p (fig. 1.12). The meniscus position curve is cut from the bottom because the evaporator and adiabatic sections are opaque so that the meniscus is invisible there. Right: numerical modeling of the meniscus position (x) vapour pressure (p), vapour temperature (T) and film edge position (xf) x micro-channel where x=0 is at intrinsic meniscus and increasing when move towards higher values of x (Park et al. [2.4]) Fig. 2. 3 The flow patterns encountered in vertical upwards co-current flows (Collier and Thome [2.18]) Temporal variations of location of meniscus and film thickness variation calculated using the analytical model as per eq. 4.7 (at Te = 46ºC and Tc = 16ºC, 20ºC and 24ºC, respectively, and Pr = 0.5 bar).

Introduction, Motivation and Background

Since the beginning of 18 th century that can be called as "machine age" of the earth, human has been making lot of efforts in revealing secrets of nature by discovering its governing laws. In this process, we are making machines to ease down the applied effort. As a basic rule of the nature, energy can be converted from one form to another and required work can be extracted. But still human is yet to achieve the highest possible efficiency. So most of the time this lost energy is in the form of unnecessary heat dissipation. Later this heat becomes responsible for underperformance of the system and environment hazards. In the same period, electronics has also made significant growth and contribution in developing new machines. The reliability of these electronics components is a major factor in the overall reliability. Continued miniaturization of electronic systems has resulted in a dramatic increase in the amount of heat generated per unit volume. Unless properly designed and controlled, high rates of heat generation result in high operating temperatures for electronic equipment, which will affect safety and reliability. While absolute power levels in microelectronic devices are relatively modest (a few tens to a few hundred watts), heat fluxes can be significant (~50 W/cm 2 in current electronic chips; up to 2000 W/cm 2 in semiconductor lasers). Further, temperatures at the chip surface must be kept low for both performance and reliability. Today's electronic system are normally rated for operation in the 0 to 70⁰C temperature range (commercial grade), -40 to 85⁰C

(industrial grade) and -55 to 125⁰C (military grade). For certain applications, very low temperatures (even close to as 0 K) are ideal, as conductivity increases and approaches superconductivity at this temperature. For a rule of thumb and for today's electronics, "room temperature" is a good operating temperature regardless of theoretical advantages of superconductivity. Hence from above it is clear that for the reliable and safe working of electronics systems, there will always be a need to cool these electronics

Need for thermal passive management: Electronics cooling techniques

The only form of energy leaving the electronic device is the heat generated when the current flows through resistive elements; we know that the heat dissipation or cooling load of an electronic device is equal to its power consumption. We should always keep in mind that the most desirable form of cooling is natural convection cooling, since it does not require any moving parts, and thus it is inherently reliable, quiet, and, best of all.

Simple ventilation holes on the case may be all we need for the cooling of low-powerdensity electronics such as a TV or a DVD player in a room, and a fan may be adequate for the safe operation of a home computer. But the thermal control of the electronics of an aircraft will challenge thermal designers, since the environmental conditions in this case will swing from one extreme to another in a matter of minutes. Various active/passive, single-/multi-phase, single/multi-component heat transfer strategies have evolved in the last decades to cater the increased demand of thermal management for such mini/micro systems and device. The existing heat transfer mechanisms can broadly classified as single-phase natural convection, single-phase forced convection, non-phase change multiphase techniques and phase-change multiphase heat transfer techniques. Typical range of heat transfer rates achievable from these techniques is summarized in fig. 1.1 inspired by Lin et al. [1.1].

This figure clearly indicates that multiphase heat transfer process, with phase change, provides significantly higher heat transfer coefficients than the single-phase forced convection or natural convection processes. Therefore, several multiphase techniques and their variants are used as cooling solutions in contemporary times. Some applications of modern heat transfer devices are, film cooling, spray/jet impingement cooling, wicked heat pipe, pulsating heat pipe and micro-channel heat sink with flow boiling, etc. Such devices have shown better thermal performance in terms of enhanced heat transfer coefficients and maximum heat handling capacity, in comparison to the air/liquid cooled forced or natural convective counterparts. Conventional natural convection and single-phase convection have been widely studied in the past and largely understood. However, there are many open issues, which need to be explored in multiphase flow devices because of occurrence of wide variety of flow patterns, of interfaces, contact line motion etc., which result in complex flow and heat transfer physics in such systems. Keeping the area of research concentrated towards the heat pipes and more precisely towards pulsating heat pipes, first phase passive cooling technology and then we will later will move deep in to the pulsating heat pipes research Fig. 1.1: Range of heat transfer coefficients typically possible from technologies applied in contemporary thermal management systems

Two-phase passive cooling technologies

The operation of modern passive heat transfer devices is based on the combined action of three physical phenomena: phenomena are acting together but there may be some extreme conditions where capillary effects are negligible (i.e. thermosyphons) or gravity effects are less important (i.e. sintered HP). passive device is fully thermally driven: the heating power activates the evaporation/condensation process and the consequent vapour expansion, together with the capillary/gravity effect on the liquid phase, provide the "pumping power" which is needed to maintain the fluid circulation. The passive two-phase heat transfer technology gives improved heat transfer capability:

higher heat loads and higher heat fluxes (up to 200W/cm2 of radial heat flux). Also they give improved performance: low thermal resistance down to 0.01 K/W, lower mass flow rates and relatively smaller size and weight. There is no need for external pumping work. Also have smaller temperature gradients and nearly isothermal operation regardless of variations in the heat load. Different types of two-phase passive heat transfer devices can be defined as: The heat pipe, capillary pumped loop and loop heat pipe, thermosyphon and pulsating heat pipe.

In the gravity assisted thermosyphon lower end of the tube is heated which results in the liquid evaporation and the vapour to move to the cold end of the tube where it is condensed. Since condensate is returned to the hot end by gravity, the evaporator must be situated at the lowest point. In modern devices this limitation is overcome by means of a wick structure, constructed for example from a few layers of fine gauze, which is fixed to the inside surface and returns the condensate to the evaporator by capillary

Introduction, Motivation and Background Chapter 1 forces. In the heat pipe the evaporator position is not restricted and it may be used in any orientation. If, of course, the heat pipe evaporator happens to be in the lowest position, gravitational forces assist the capillary forces.

Heat pipe

A heat pipe is a heat transfer device that uses evaporation and condensation of a twophase "working fluid" to transport large quantities of heat with a very small difference in temperature between the hot and the cold interfaces. As illustrated in fig. 1.3, a typical heat pipe consists of a sealed hollow tube made of a thermo-conductive metal such as copper or aluminum this tube can be divided in three sections: an evaporator or heat addition section, an adiabatic section, and a condenser or heat rejection section.

When heat is added to the evaporator section of the heat pipe, the heat is transferred through the shell and reaches the liquid. When the liquid in the evaporator section receives enough thermal energy, the liquid vapourises. The vapour carries the thermal energy through the adiabatic section to the condenser section, where the vapour is condensed into the liquid and releases the latent heat of vaporization. The condensate is pumped back from the condenser to the evaporator by the driving force acting on the liquid. No external power is needed for a typical heat pipe. The phase-change heat transfer occurs almost in the quasi-equilibrium state. The heat pipe has a very high efficiency to transfer the thermal energy from a heat source to a heat sink. An operational heat pipe can provide an extra-high effective thermal conductivity and reach a higher level of temperature uniformity.

The thermal conductivity of heat pipes can be as high as 10,000 W/m.K, in contrast to copper, which has a thermal conductivity of around 400 W/m.K. The working fluid medium in a heat pipe can be selected from a variety of fluids, depending on the operating temperature and compatibility with the shell material. The heat pipe can be operated from a temperature lower than 4 K to a high temperature up to 3000 K.

Because the evaporator and condenser of a heat pipe function independently, the heat pipe can be made into any shape, depending on the design requirement. Due to these unique features, the heat pipe has been widely used in a wide range of applications. There are a number of limitations smooth flow of the working fluid tension cannot overcome the summation of the total occurring in the heat pipe reaches a limit known as the capillary limit. There are several other limitations disconnecting the return of the working fluid from the evaporator to the condenser or from the condenser to the evaporator. Amo limit, sonic limit, entrainment limit, and viscous limit. When the heat flux added to the evaporator is sufficiently high, nucleate boiling occurs. The bubble formed in the wick significantly increases the thermal resistance, causi be significantly reduced. More importantly, when the heat flux is so high, the bubbles block the return of the working fluid and lead to a dry limit plays a key role in a high heat flux the cross-sectional area variation of the vapo flow condition, chocked flow occurs and the vapo amount of heat added in the evapor limit is due to the frictional shear stresses caused by the vapo liquid interface. The viscous limit occurs in a low heat flux heat pipe, where the vapo pressure difference in the vapo the vapour phase. Now let us discuss PHP separately in detail.

-2015 There are a number of limitations which affect the working of a heat pipe such as of the working fluid, when the pumping pressure produced by the surface tension cannot overcome the summation of the total pressures; the heat transport occurring in the heat pipe reaches a limit known as the capillary limit. There are several other limitations disconnecting the return of the working fluid from the evaporator to the condenser or from the condenser to the evaporator. Among these are the boiling limit, sonic limit, entrainment limit, and viscous limit. When the heat flux added to the evaporator is sufficiently high, nucleate boiling occurs. The bubble formed in the wick significantly increases the thermal resistance, causing the heat-transfer performance to be significantly reduced. More importantly, when the heat flux is so high, the bubbles block the return of the working fluid and lead to a dry-out of the evaporator. The boiling limit plays a key role in a high heat flux heat pipe. When the vapour velocity is high and sectional area variation of the vapour space in a heat pipe cannot meet the flow condition, chocked flow occurs and the vapour flow rate will not respond with the amount of heat added in the evaporator. This will lead to a sonic limit. The entrainment limit is due to the frictional shear stresses caused by the vapour flow at the vapo liquid interface. The viscous limit occurs in a low heat flux heat pipe, where the vapo e vapour phase cannot overcome the vapour pressure drop in Now let us discuss PHP separately in detail.

Introduction, Motivation and Background

6

Chapter 1

a heat pipe such as hen the pumping pressure produced by the surface the heat transport occurring in the heat pipe reaches a limit known as the capillary limit. There are several other limitations disconnecting the return of the working fluid from the evaporator to ng these are the boiling limit, sonic limit, entrainment limit, and viscous limit. When the heat flux added to the evaporator is sufficiently high, nucleate boiling occurs. The bubble formed in the wick transfer performance to be significantly reduced. More importantly, when the heat flux is so high, the bubbles out of the evaporator. The boiling r velocity is high and r space in a heat pipe cannot meet the r flow rate will not respond with the ator. This will lead to a sonic limit. The entrainment r flow at the vapourliquid interface. The viscous limit occurs in a low heat flux heat pipe, where the vapour r pressure drop in Introduction, Motivation and Background Chapter 1

Pulsating heat pipes (PHPs)

Like a conventional heat pipe, a pulsating or oscillating heat pipe, in short called as PHP\OHP, is not a cooling system, but a system to transport heat from a hot source or a heat source to a cold source or heat sink. The tube forming a PHP is bent many times in a symmetrical manner so that an evaporation section, adiabatic section and condenser section are formed (fig. Due to these oscillations, a liquid slug arrives at the hot source and it partially evaporates due to overheating, which includes the pressure in the neighboring pockets of steam and pushes in turn the liquid slugs. It should be noted that this pressure can also be result of the expansion of the steam due to the contribution of sensible heat.

Thus, the oscillations of the liquid slugs and vapour pockets are maintained due to the overheating of the wall and thus the evaporation of the liquid leads to a sudden Introduction, Motivation and Background Chapter 1 expansion of the fluid to the evaporator. Statistically, the number of such instances will always bring the liquid to the evaporator. Also the condensation of the superheated vapour at the condenser will locally lead to a pressure reduction, which also helps to maintain the oscillations. No external power is required to drive the device, internal oscillations being fully driven by the thermal non-equilibrium that is sustained inside the system due to external heating and cooling. Compared to other cooling solutions, PHPs are the simplest technology, from the point of view of manufacturing as compared to the family of heat pipes and thus more reliable and cheaper.

As stated above the pulsating heat pipe (PHP) is a non-equilibrium passive two-phase heat transfer device, first of its kind PHP was found to be described in 1971 in a Russian patent filed by Smyrnov and Savchenkov [1.4]. But in the 1990s, Akachi As stated above PHP belongs to a category of wickless heat pipes, however with complex internal thermo-hydrodynamic transport processes, responsible for the self-sustained thermally driven oscillating two-phase Taylor bubble flow which in turn, leads to its unique heat transfer characteristics. However, still the technology is simple, the physics of flow and heat transfer within these systems is extremely complex and yet not completely understood. Unlike conventional heat pipes, the study of these phenomena complex because of unsteady oscillatory flow characteristics. Understanding how PHP works is not that easy due to the in capillary tubes, evaporation and with statistical instabilities are systems. To understand the PHP working and the challenges it propose discuss various terms and methodologies involved in it.

Different arrangements

The pulsating heat pipes (PHP) can be classified on the basis of how the tubes are connected to each other and how the flow of fluid takes place inside the tubes is bent back and forth parallel to itself, and the ends of the tube may be connected to one another in a closed loop, or pinched off and welded shut in an

1.6-b).
As it is evident from the name PHP is that liquid inside these tubes, in addition to this oscillatory flow, the working fluid can also be increased and the heat transfer performance of the PHP will be improved. A high specific heat will increase the amount of sensible heat transferred. Because the majority of the total heat transfer in a PHP is due to sensible heat, a fluid with a high specific heat is desirable. A low dynamic viscosity will reduce shear stress along the wall and will consequently reduce pressure drop in the tube. This will reduce the heat input required to maintain a pulsating flow. The rate of change in pressure with respect to temperature at saturated conditions (dp/dT)sat affects the rate at which bubbles grow and collapse. At a high value of (dp/dT)sat, the difference between vapour pressure in the evaporator and condenser will be increased and the performance of a PHP will be improved by enhanced oscillatory motion of liquid slugs.

The charge ratio is the volume of the liquid divided by the total internal volume of the PHP. If the charge ratio is too low, there is not enough liquid to perpetuate oscillating slug flow and the evaporator may dry out. If the charge ratio is too high, there will not be enough bubbles to pump the liquid, and the device will act as a single phase thermosyphon. Khandekar [1.3] shows that generally charge ratios ranging from 20% to 80% will allow the device to operate as a true pulsating heat pipe. The number of turns of bent tube in the PHP may affect thermal performance and may negate the effect of gravity. By increasing the number of turns, there are more distinct locations for heat to be applied. The fluid within each turn may be either liquid or vapour, the heating of which creates differences in pressure at each turn. It is these pressure differences that drive the pulsating flow. If a PHP only has a few turns, it may not operate in the horizontal or top heat modes, but a PHP with many turns can operate at any orientation because of the perturbations in each turn.

Flow regimes in PHPs

In a PHP, different flow regimes can be observed as shown by Xu et al. [1.12] [1.12]).

Thermodynamics of PHPs

Although simple in their construction, PHPs become complicated devices when one tries to fully understand their operation: the thermodynamics driving PHP operation Heat addition and rejection and the growth /extinction of vapo bubbles drive the flow in a PHP. Even though the exact features of the thermodynamic Groll and Khandekar [1.14] the evaporator and condenser are known, or can be assumed, so the state at the outlets of the evaporator and condenser are known. Starting at the evaporator inlet, the P-h ˆ diagram), the processes required to get to point B on the diagram can be simplified to heat input at a constant pressure combined with isentropic pressure increase due to bubble expansion. As one travels through the adiabatic section from the evaporator to the condenser, the pressure decreases isenthalpically. The thermodynamic process between the condenser to constant pressure condensation with negative isentropic work. An isenthalpic pressure drop in the adiabatic section completes the cycle. Because of the numerous assumptions made in this description, thermodynamic analysis is insufficient to study PHPs.

Hydrodynamics of PHPs

Fluid flow in a capillary tube consists of liquid slugs and vapour plugs moving in unison.

The slugs and plugs initially distribute themselves in the partially filled tube. The liquid slugs are able to completely bridge the tube because surface tension forces overcome gravitational forces. There is a meniscus region on either end of each slug caused by surface tension at the solid/liquid/vapour interface. Due to the capillary dimensions of the PHP tube, a train of liquid slugs and vapour bubbles having menisci on their edges is 14 Chapter 1 the evaporator and condenser are known, or can be assumed, so the state at the outlets ser are known. Starting at the evaporator inlet, (point A on , the processes required to get to point B on the diagram can be simplified to heat input at a constant pressure combined with isentropic pressure due to bubble expansion. As one travels through the adiabatic section from the evaporator to the condenser, the pressure decreases isenthalpically. The thermodynamic s inlet and outlet are complicated, but can be simplified constant pressure condensation with negative isentropic work. An isenthalpic pressure drop in the adiabatic section completes the cycle. Because of the numerous assumptions made in this description, thermodynamic analysis is insufficient to study formed due to surface tension. Usually a liquid thin film exists around the bubbles. The contact angle of menisci, liquid thin film stability and its thickness depend on the fluidsolid combination and the operating parameters. Liquid slugs and vapour bubbles move against the gravity vector, either in its direction or at an angle to it, depending on the global PHP orientation and location of slugs/ bubbles in the up-header or down-header tubes. A detailed review on hydrodynamics parameters of pulsating heat pipes has been done by Khandekar et al. [1.15], in which they show that the liquid slugs and vapour bubbles are subjected to pressure force F1 and F2 (fig. 1.9), from the adjoining slugs/bubbles. These are not only caused due to phase-change mass transfer but also due to capillary forces. The liquid slugs and vapour bubbles experience internal viscous dissipation as well as wall shear stress. Their relative magnitude decides the predominant force to be considered. Fig. 1.9: Liquid slug in a PHP (Khandekar et al. [1.15]).

1.14]).
The slugs are separated by plugs. The vapour plug is surrounded by a thin liquid film trailing from the slug. Fig. 1.10 shows the control volume for one liquid slug in a PHP and the forces acting on it Shafii et al. [1.16]. Motion of the i th liquid slug within the PHP with an inner diameter of D and cross-sectional area of A can be described by the simplified momentum equation given by Shafii et al. [1.16, 1.17

]: π - - τ
Introduction, Motivation and Background Chapter 1 transfer in a PHP can be explained when and where it taking place, like in starting nucleate boiling for the formation of the bubbles, later there will be evaporation and condensation at the film. Heat transfer in thin films is a complex phenomenon and few researches have been found in this subject. In chapter 2 the terminologies and parameters affecting the thin film heat transfer will be explained.

Two research approaches for understanding of PHP working

Since the invention of PHP, several researchers have been putting efforts to understand and decode the physics involved in it. Most of the researches available on the PHPs are based on parametric studies without much explaining the physics behind it. In recent past there have been attempts to model a PHP by approximating various parameters affecting it. Recently it was also discussed that there is a need first to understand the local level physics happening in a PHP rather than directly going towards whole system modeling. In this direction unit cell approach (single tube: single vapour plug -liquid slug) for PHPs have been modeled and some of the researchers started building experiments based up on these modeling. There are also thoughts of some researchers that the unit cell approach (single tube: single vapour plug -liquid slug) is not exactly replicating the real PHP as it does not include the multiple vapour bubble -liquid slug interactions which may be the principle cause of PHP working. Let us now see how these two approaches (i) PHP studies as complete system (ii) Unit cell approach (single tube: single vapour plug -liquid slug) yields the various results and observation.

Studying PHPs as a complete system

Research on PHPs has seen an unprecedented increase during the last 15 years, almost 25 years after the system has been patented in its most popular layout by Akachi.

Unfortunately, major part of the literature does not provide universally applicable generic knowledge base on these systems; it generally focuses on one particular PHP structure or type, designed for a specific application. In these type of works, the PHP is usually characterized by the temperature difference measured between the condenser and the evaporator for a given applied heat flux. Nevertheless, each PHP has its own geometrical and thermo-physical properties (inner and outer diameters, length, closed

Introduction, Motivation and Background Chapter 1

or open-loop devices, evaporator, condenser and adiabatic lengths, number of turns, material of the tube, etc.) and is filled with a specific working fluid having also its own thermo-physical properties (latent heat, wettability and for both vapour and liquid phases: thermal conductivity and capacity, density, viscosity, etc.), and is tested in specific experimental conditions (heat load at the evaporator, ambient and condenser temperatures). A detailed review on advanced and unsolved issues in pulsating heat pipes has been done by Zhang and Faghri [1.18]. It was shown that there were several attempts to develop correlations for the overall Nusselt number in terms of nondimensional groups of parameters. However, they all have a quite narrow range of applicability and fail if applied to other PHP prototypes. The number of relevant parameters to characterize a PHP is therefore so large that it is difficult to explicitly discriminate the effect of one parameter among the others in this type of experiments.

As a result, one can find several research papers dealing with the same parameter and having conflicting conclusions. To overcome these difficulties, some authors developed non-dimensional expressions based on different numbers like the Jacob, the Karman, the Prandtl or the Kutateladze numbers and taking into account the number of turns (All these numbers are defined in Appendix-A). This occurs because the dynamic behavior of the PHPs may change strongly at slight variation of its parameters.

Systematic studies of the multi-bubble multi-turn PHPs are rare and concern mostly the qualitative description of its regimes. Nevertheless, this approach has also failed so far to provide a universal understanding of the PHP because the basic physical phenomena and the extent of parameters responsible for system dynamics are not yet well understood. More detailed quantitative information on the local measurement that would concern the menisci and film dynamics inside the PHP is lacking. Regarding the heat transfer in PHPs as a system, there have been various efforts taken by the researchers; here we are mentioning some of the important of them. Vapour mass quality is an additional independent variable for convective boiling.

Lee et al. [1.20] conducted a visual study of the flow in a closed-loop oscillation heatpipe with ethanol by varying in the inclination angles, filling ratios and working temperatures. They reported that oscillations of the bubble caused by nucleate boiling and vapour oscillation, and departure of small bubbles are considered as the representative flow pattern at the evaporator and adiabatic section, respectively.

Qu and Ma [1.21] did a theoretical analysis to determine the primary factors affecting the startup characteristics of a pulsating heat pipe. They found that the wall surface condition, evaporation in the heating section, superheat, bubble growth, and vapour bubbles trapped in cavities at the capillary inner wall affect the startup of oscillating motion in the pulsating heat pipe. Based on their experimental visualization they concluded that when the nucleate boiling occurs at the capillary inner wall, a large amount of vapour is produced. Bhuwakietkumjohn and Rittidech [1.22] Introduction, Motivation and Background Chapter 1

PHP local level approach ("unit-cell" approach)

Researchers agree that the oscillations are driven by an instability that appears due to coupling of the adiabatic vapour compression and evaporation/condensation mass exchange. Changing the nature of the fluid or the condenser temperature brought into focus a very wide range of behaviors that could not be explained in the absence of the general understanding of phenomena that occur inside the PHP. Indeed, the instability that causes the oscillations is yet to be studied. One has to begin with a system of a minimal complexity which is a straight capillary heated from one and cooled from the other end containing a single oscillating bubble fig. 1.11. This can be an important research effort dealt with systems of the reduced complexity with only one vapour bubble and/or liquid plug.

Although such a system seems to be simple, it contains the main phenomena involved in the multi-bubble PHP. One can mention evaporation/condensation of liquid continuous menisci and wetting films, motion of menisci and contact lines (film edges), viscous friction during the bubble motion among other phenomena that govern the PHP dynamics. Some of them have been extensively studied for stationary case. For example, evaporation of stationary liquid menisci in capillaries was studied in relation with the conventional heat pipes. On the other hand, the motion of constrained bubbles in capillaries (Taylor bubbles) is well studied under isothermal conditions (e.g. Reinelt [1.23] and Bico and Quéré [1.24]). It has been discovered that the viscous dissipation inside the wetting films left on the tube walls behind the moving liquid meniscus makes an important contribution to the overall pressure drop. Furthermore, the dissipation (and the pressure drop) is larger when the meniscus advances along the dry wall with respect to the wall with already deposed wetting film Bico and Quéré [1.24]. This shows the importance of the contact lines, the number of which might be large in the multibubble PHP. The evaporation at the contact lines and in the thin films (Nikolayev [1.25]). The evaporation in the constrained bubble geometry is studied in the domain of convective boiling also considered (Callegari et

Introduction, Motivation and Background

Unit cell PHP (single tube: single vapour plug -

The evaporation at the contact lines and in the thin films has been actively studied

The evaporation in the constrained bubble geometry is studied in the domain of convective boiling (Thome et al. [1.26]). The dewetting in capillaries Callegari et al. [1.27]). The oscillation of bubbles at isothermal by Lips and Bonjour [1.28] and the heat transfer in the system. In recent past researchers have done significant work to understand the basic governing physics of such simplified single branch systems. There are many researchers tried to model and performed experiments on such systems. Most of the system level models for PHPs are developed by using an average value of heat transfer coefficient (constant over time) to predict the convective heat transfer regime inside the evaporator. But in miniature unsteady devices, the fluiddynamic conditions quickly change over time and the heat transfer coefficient can be strongly influenced by this transient, especially in the boiling regime. In next section we will discuss various modeling and experimental approaches taken by researchers.

Single branch modeling

From a modeling perspective, this approach was initiated by Zhang and Faghri [1.37, 1.38] and Dobson [1.39, 1.40], who studied theoretically the governing mechanisms of a single branch of the PHP, consisting of one vapour bubble and one liquid slug.

Das et al. [1.34] developed a similar approach including the two phase equilibrium that occurs locally at the liquid vapour-interface, especially along the time-varying wetting thin film which gets laid down by the liquid plug during its journey from the evaporator towards the condenser and through which the major part of the heat and mass transfer occurs. This film was shown to be responsible for the large flow oscillations observed in the system. In this work, an instability analysis of this system was also performed. The evaporation rate was assumed to be proportional to the difference of the temperatures of the vapour and the walls in contact with it. In the vapour bubble evolution equation this leads to terms analogous to those of sensible heat transfer between the vapour and the tube walls. It is well known from general considerations of thermal resistance that during the meniscus evaporation, an important contribution to the heat and mass transfer comes from thin liquid films that may cover the interior of the capillary. The local two-phase equilibrium exists at the interface of microscopically thin films Quéré et al. [1.29] so that the interface is at saturation or very close to it. This effect was completely neglected in the above mentioned works. Dobson [1.39,1.40] has included a film in his single bubble PHP model. He introduced a lumped description of the liquidvapour meniscus and the wetting films. However the film mass exchange was not related to the liquid-vapour equilibrium and the mass exchange was proportional to the difference of temperatures of the vapo did not treat the films at all. The single taken a step forward by rigorously showing that exchange occurs via the films in the PHP. The shape of the curved meniscus including the film has been calculated. It is felt that to understand the working of the unit cell PHP it is eminent to understand the thin film behavior in two phase heat and mass transport systems. Globally, the existing models describe oscillations of small amplitude these oscillations, the meniscus is located mostly in the condenser section. Continuing on these lines, Mehta and Khandekar [1.50] recently studied the heat transfer characteristics of pulsating Taylor bubble-train flow in square mini-channels using IRT, the frequency of imposed flow fluctuations similar to those encountered in PHPs. The main objective of the study was to observe the effects of externally imposed pulsations on local heat transfer taking place in a unit cell, comprising of a Taylor liquid slug trapped between two adjacent gas bubbles. The controlling parameter of the study was liquid and gas flow rates and imposed flow frequencies. The study indicated that liquid slug distribution is one of the important parameter for improving thermal performance of PHPs. Perturbing the Taylor bubble-train flow with imposed frequencies may conditionally lead to enhancement in the heat transfer in comparison to steady continuous Taylor bubble-train. The sensible heating/cooling transport capability of the liquid slugs can be altered by controlling the wake generated by the adjoining Taylor bubbles. Interfacial slip created by intermittent flow conditions, was the major cause for heat transfer enhancement. A similar experiment performed in cryogenic conditions was presented by Bonnet et al. [1.51, 1.52] in 2011 and in 2013 respectively. Compared to the previous experiment, their system was totally opaque; a thin micro-thermocouple was used to measure the time varying temperature of the vapour, which showed that the vapour plug tended to be superheated in this single branch PHP experiment. This is a major result as this hypothesis had never earlier by Khandekar [1.3].

In the similar lines the work had been started by al. [1.34] presented the first experimental data of the simplest 'unit pulsating heat pipe consisting of one liquid plug and one vapour bubble. Their experimental setup was close to a real previously studied by Dobson end and connected to a reservoir at a constant pressure at the other end single liquid plug adjoining a vapour bubble made to thermally auto tube, which was heated on one side and cooled down on the other side, thereby creating a continuous cycle of evaporation and condensation. The movement of the men recorded in the cooled section of the tube, while the heated section, made of copper, was opaque. The vapour pressure was also measured during the oscillations. Introduction, Motivation and Background was used to measure the time varying temperature of the vapour, which showed that the vapour plug tended to be superheated in this single branch PHP experiment. This is a major result as this hypothesis had never been verified before, although it was proposed had been started by our group at CETHIL. I presented the first experimental data of the simplest 'unit-cell' version of a pulsating heat pipe consisting of one liquid plug and one vapour bubble. Their experimental setup was close to a real-PHP and also the theoretical configuration Dobson [1.39,1.40]. It consisted of a capillary tube closed at one end and connected to a reservoir at a constant pressure at the other end single liquid plug adjoining a vapour bubble made to thermally auto-oscillate inside this tube, which was heated on one side and cooled down on the other side, thereby creating a continuous cycle of evaporation and condensation. The movement of the men recorded in the cooled section of the tube, while the heated section, made of copper, was opaque. The vapour pressure was also measured during the oscillations.

Closing remarks, motivation of work and thesis chapter plan

As we have seen above, many efforts have been put recently on the topic of PHPs and the associated fundamental knowledge, but still the progress is very slow. The main reason for the slowness of the progress is the following. A large majority of the experimental studies of the PHP available in the literature concern the multi-bubble prototypes. However, it is technically impossible performing measurements (of pressure, temperature, etc.) for each individual bubble because both its ends move. For

Introduction, Motivation and Background Chapter 1

the multi-bubble case, the measurements are thus limited to averaged over all bubbles values which cannot provide enough information necessary to understand the PHP functioning. In addition, the oscillations are much less chaotic than in the multi-bubble case, so that a smaller meniscus visualization area is sufficient. As explained previously, CETHIL (Das et al. [1.34]) had started experimenting single branch PHP. Some important experimental limitations were present in the work of Das et al. [1.34]. The experimental setup was not fully transparent, except the condenser section as indicated earlier, and therefore the internal hydrodynamic phenomena could not be observed in totality. Besides, the connection between the opaque metal evaporator and the glass condenser section was to induce some flow perturbations having potential impact on the smooth meniscus movement to a certain extent.

Furthermore, experiments were done without any synchronization of the internal pressure measurements with the videography.

Das et al. [1.34] geometry where a single vapour bubble or liquid plug will travel along the capillary. In these experiments it is interesting to observe (i) the behavior of the wetting films, in particular their thickness and length, (ii) the viscous dissipation (pressure drop) during the oscillating bubble motion, and (iii) the vapour thermodynamics.

Looking in to the above discussion it is thought that a predictive modeling of the PHP is impossible without availability of reliable information on these phenomena. There is need to understand this combined system (solid-liquid-vapour system in a single branch PHP constituted of a channel wall, liquid meniscus and vapour plug) locally for finding the parameters affecting their thermo-hydrodynamics. It is visible that the thin film laid by the liquid on the channel walls plays an important role in working of PHP. Therefore it is required to understand the hydrodynamics and heat transfer characteristics of this Introduction, Motivation and Background Chapter 1 region which consists of thin film, solid wall and vapour, which in general is referred to as extended meniscus region.

In this respect as there are hardly any open literature available for thin films and their influence on working of PHPs, in chapter 2 we will be discussing the thermohydrodynamic and heat transfer features of combined solid-liquid-vapour system or extended meniscus with available literature. The chapter 2 will give us the directions to move ahead. Based up on the outcomes of chapter 1 and chapter 2, a methodology will be designed to solve the problem for which later in chapter 3, the experimental setup design and data processing will be presented. Chapter 4 will include detail analysis of experimental results and comparison of the experimental results with the available numerical models. In chapter 5 the numerical model developed will be illustrated and the results will be compared with the experiments. Chapter 6 will illustrate the conclusion of the thesis and future scope of work.

Introduction, Motivation and Background Chapter 1

Thermo-physical parameters in a single branch PHP -The extended meniscus region

As we saw capillary dimensions of the PHP tube, a liquid slug and vapour bubble having meniscus on their edge is formed due to surface tension. Usually, a liquid thin film exists around the bubble. The interfacial interactions of menisci, liquid thin film stability and its thickness depend on the fluid-solid combination and the operating parameters. It is widely accepted and observed in a PHP that the thin film is let on the wall when the meniscus moves from its extreme position in the evaporator towards the Literature review Chapter 2 condenser. Some experimental results clearly show that evaporation of the thin film is responsible for the oscillation observed experimentally in PHP studies. The films in PHP are thicker than in capillary heat pipes and are extensively of hydrodynamic origin; their thickness depends on the meniscus velocity. The heat transfer depends however on the contact line effects that define the film length. To the best of our knowledge, there are no explicit studies available in open literature related to pulsating thin film evaporation.

In general this problem can be tackled using the available knowledge on thermohydrodynamics for the so called extended meniscus by keeping in virtue our main goal of understanding the working of self-sustained thermally driven oscillating Taylor bubble flows for single plug and meniscus pulsating heat pipe system (single branch PHP).

As it is shown in chapter 1, the thin film region is responsible for high heat transfer rates because of very low thermal resistance across the liquid film. Some liquid also get adsorbed in the solid wall, but the very small scales involved in this adsorbed region is not of much interest while studying the PHP functioning. Most of the studies available for this region are in the colloidal science theory and hardly gives any help in solving our PHP problem as an engineering point of view. So this state of art will mostly focus on 'Intrinsic meniscus region (bulk liquid)' and 'Thin film region'. This thin film region and intrinsic meniscus region in combined can be called as extended meniscus region.

In other words "extended meniscus" stands for a region of space that extends from the bulk liquid to the vapour around the liquid-vapour interface and triple line. We found that most of the researches are based upon the steady film evaporations, which give the general physics behind the static film evaporation and hardly talks about its engineering applications. To add in to it, thermally induced pulsations in meniscus and vapour system which are typically found in a PHP, will only complicate the solution. By generalising the problem to the basic level, it can be compared and evaluated using standard solutions given by researchers for static thin film heat transfer. This may help us in understanding and solving the thin film heat transfer problem in unit cell PHPs. So it is evident that the meniscus and thin film region is the driving factor and should be the area of interest to understand the happenings at local level of a single branch PHP δ ′ -Literature review Chapter 2 electrons of another molecule (Wee et al. [2.3]). This is the weakest of the van der Waals forces but nevertheless given the size scale involving in the extended meniscus region, these van der Waals forces will play a significant role in analyzing such systems.

Fundamentals of extended meniscus region

To understand the construction of the extended meniscus region, let us first go through the different aspects of this region. When a liquid wets a solid wall in a tube, the meniscus is formed. Subsequently this region can further be divided in to three sub regions, as shown in fig. 2.2, (i) An adsorbed or non evaporating region, here liquid is adsorbed on the tube wall where the capillary forces are negligible and disjoining pressure plays a predominant role (ii) An evaporating thin film or transition region where effects of long-range molecular forces (disjoining pressure) as well as capillary forces are felt; (iii) An intrinsic meniscus region where capillary forces dominate and there is no influence of disjoining pressure.

Looking the historical developments in the understanding of above mentioned sub regions, Derjaguin et al. [2.1] developed an analytical theory and showed that the rate of evaporation from a capillary does not depend on the vapour diffusion through the gas only but also on the transport of liquid through the film caused by the film thickness gradient and near the adsorbed region, the disjoining pressure is dominant. According to him, the disjoining action could explain the deviation from the laws of hydrostatics that exists in the thin wetting film. Transitioning towards the bulk region or intrinsic meniscus, there is a changeover of dominance as disjoining pressure diminishes and capillary pressure is more prominent.

Potash and Wayner [2.2] studied the transport processes occurring in a twodimensional evaporating extended meniscus where the fluid flow results from both capillarity and disjoining pressure. They found that, the pressure gradient for fluid flow includes the effect of disjoining pressure and the presence of an adsorbed superheated film results in a smooth transition between the evaporating and non-evaporating portions of the extended meniscus. Literature review Chapter 2 phases is actually continuous, and the values of the properties in this region are generally different from those in the bulk phase. For a pure vapour in contact with solid wall, attraction between solid and vapour molecules can thus increase the density of vapour molecules in the interface region near solid surface. The excess vapour density above bulk value is the amount said to be adsorbed onto the surface. Taking in to account the size and scale of this region, it is mainly characterized by the supremacy of van der Waals forces between the liquid and solid wall (Wee et al. [2.3]). This leads to the inability of the superheated liquid molecules to evaporate within the adsorbed region, as they are restrained by these overwhelming adhesive forces (Wee et al. [2.3] and Stephane [2.5]). It is these adhesive forces that prevent evaporation that allow the region to be considered of uniform thickness δad (fig. 2.2) and of unspecified length 5-2.9]. This thickness however is temperature dependent. It is thus concluded that the imposed curvature value within the adsorbed region is almost zero. The thickness of the adsorbed region is sometimes given a constant value estimated from the size scale of the problem, (Park et al. [2.4, 2.10]).

[2.
However, it is now known that minor changes to the adsorbed film thickness can result in large changes in thin-film flow and evaporation rate (Lin and Faghri [2.11]). Wayner [2.12] showed that the adsorbed film thickness varies with temperature and concludes that using a constant value will miscalculate the total heat transport through the thinfilm. A final best guess is valid that within the adsorbed layer, considering the size and scale of this region, it is understood that the fluid temperature is identical to that of the solid wall [2.3, 2.9, 2.13].

Intrinsic meniscus region

The intrinsic meniscus region as shown in fig. 2.2, is the bulk region can be the best identifiable part of the liquid vapour interface, and can be seen with the bare eye, whether it is observed as a graduated cylinder or a bucket. In the many prior representations, it is like a concave meniscus. The capillary pressure is dominant, with an insignificant contribution of disjoining pressure [2.3, 2.4, 2.8]. It is for this reason that the bulk region is governed by the Young-Laplace equation (explained in section 3

Literature review Chapter 2 of this chapter) and is often considered to have a constant curvature (Stephan [2.5]). This constant curvature is often used as a far-field boundary condition when determining the transition from the thin-film region to the bulk meniscus (Stephan [2.5]). The concavity of a meniscus is determined by the cohesive interaction of the liquid with the substrate (Polansky [2.14]). In a concave meniscus, the liquid molecules have a greater affinity for the solid substrate than the bulk liquid. The evaporative mass flux contribution in intrinsic meniscus region is tiny as compared to that of the thin-film region. This has been distinguished in several works of (Wang et al. [2.13] and Buffone et al. [2.15]).

Thin film or transition region

Referring to thin film region (fig. 2.2), Potash and Wayner [2.2] studied the transport processes occurring in a two-dimensional evaporating region, where the fluid flow resulted from both capillarity and disjoining pressure. Wee et al. [2.3] also endorsed this concept. As mentioned in the intrinsic meniscus section constant curvature was found for that region and the termination of this constant curvature can be called as the beginning of the thin-film region. Defining the beginning of the thin-film region can also be done with confidence, as it transitions to the adsorbed region when curvature is zero Wee et al. [2.3] and Wang et al. [2.8]. Wang et al. [2.16,2.17] defined the thin-film region as ending at a location when the disjoining pressure drops to 1/2000th of Pdis-ad, the disjoining pressure in the non evaporating or adsorbed region. Thin-film heat transfer is seen to increase with an increase in disjoining pressure, and decrease with increasing liquid viscosity.

The road ahead -The meniscus region

However slope and curvature dependences of the disjoining pressure may in fact lead to enhanced values of the heat transfer coefficient close to the adsorbed film region and reduced values of the same for axial locations progressively towards the intrinsic meniscus, as compared to the predictions from the more traditional considerations. Such considerations may be potentially important for a more precise and improved design of cooling strategies for thermal management of electronic devices with the aid of Literature review Chapter 2 micro-scale heat pipes. The suggested modifications in the theoretical treatment become progressively more significant as the disjoining pressure becomes more and more significant, as compared to the standard capillary pressure. This is indeed the case in the thin film region, especially towards the vanishingly thin limit of the meniscus profile.

The heat transfer is greatly influenced by hydrodynamic and thermodynamic characteristics of contact line or triple line (three phase contact line) where liquidvapour interface joins the tube wall. In the case of evaporation in capillaries (PHPs) a similar situation with a stationary or moving three phase contact line appears that is governing the liquid-vapour meniscus evaporation. Very strong shear is required to make these thin films flow. The flow exists only near meniscus and near contact line.

Keeping in mind the proposed analytical solutions for the typical static thin films heat transfers, to improve or validate them for a unit cell heat transfer problem along with coupling of heat transfer with the Taylor bubble hydrodynamics. The discussion can majorly be divided in 2 parts;

(a) Hydrodynamics transport features of extended meniscus.

(b) Heat transfer characteristics of extended meniscus.

Hydrodynamic transport features of extended meniscus

As discussed earlier, this extended meniscus region normally begins with the thin film generation in two phase flows in capillaries. To understand the phenomenon happening at the extended meniscus region, first we need to know the origin of it and parameters affecting the hydrodynamics of this region. We need to go through two phase flows in capillaries. Later we will discuss the major factors involved in understanding hydrodynamics of such flows in relation to the extended meniscus. These factors arise from the solid-liquid mutual interactions and governing physics of this combined liquidsolid system. These interactions are in the form of interfacial tensions and their resulting behavior. Majorly saying in understanding hydrodynamics of an extended meniscus, entire boundary phenomena involved in these interfacial interaction are important like contact angle, contact line statics and dynamics. Also the contact line motion and pressure drops occurring due to these interactions, will also influence the Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - study of the extended meniscus and further to the overall local level understanding of single branch PHP system.

Two phase flows in capillaries

When a liquid phase and a vapour or

Taylor bubble flows

Taylor slug flow conditions are typically characterized by a sequence of long bubbles which are trapped in between liquid plugs.

nearly comparable to the pipe diameter while their axial length scale can be several times the pipe diameter. A thin liquid film always separates the bubbles from the channel wall. The thickness of this film varies from millimeter scale to micro scale

Taylor bubble flows

Taylor slug flow conditions are typically characterized by a sequence of long bubbles which are trapped in between liquid plugs. The diametrical size of these bubbles is nearly comparable to the pipe diameter while their axial length scale can be several imes the pipe diameter. A thin liquid film always separates the bubbles from the channel wall. The thickness of this film varies from millimeter scale to micro scale Literature review Chapter 2 depending upon the dimensions, geometry, flow velocity, orientation of the channel and the thermo-physical properties of the fluid, channel used and heat flux if the channel is heated. The intermittent liquid plugs may also have small diameter bubbles (much smaller than the pipe diameter) entrapped inside them (Khandekar et al. [2.19]), this tendency reduces as the Bond number decreases. Taylor bubbles are characterized by strong geometric constraints. Bretherton [2.20] observed that a Taylor bubble does not raise spontaneously in water-filled vertical capillary under the effect of gravity for Bo < 1.8; this value can also be used to define small channels. Khandekar et al. [2.19] stated that the presence of the film that separates the bubble from the wall is responsible for the bubble velocity but is different than the liquid velocity. The recirculation patterns within the liquid slugs improve heat and mass transfer from liquid to wall and interfacial mass transfer from gas/vapour to liquid. Thus, Taylor flow offers many advantages for carrying out heat mass and momentum transfer operations compared with other patterns and with single-phase laminar flow.

The film surrounding the bubbles is the only bridge between two successive slugs, and mostly, its thickness is very small in comparison with the tube diameter. For practical estimation of mass transfer coefficients across the boundaries, properties such as thickness of film that surrounds the bubbles, bubble shape and velocity, bubble and slug length, flow patterns in the liquid slug, and pressure drop, are some of the primary focus of interest. The flow and heat transfer are influenced by the dynamics of a very small group of bubbles or typically, isolated slug bubbles, rather than the averaged behavior of a large population of bubbles. This, in principle, improves the prospects of developing mechanistic models. Such development needs to be facilitated by localized experimental observations of slug-bubble systems with synchronized measurements of the resulting fluctuations in local conditions such as temperature, pressure and wall heat flux. Mass transfer characteristics are also affected by the local hydrodynamic properties of the flow. The main forces acting on slug-bubble system are due to surface tension, viscosity, inertia, gravity (body forces), applied tangential shear stress and the force associated with the disjoining pressure at the molecular level. This gives rise to primary nondimensional numbers. For details please refer to Appendix-A.

Literature review Chapter 2 It has also been found that the surface energy (surface wetting capability) of the wall may have great impact on the interfacial film dynamics when a confined bubble is flowing along with liquid in a mini /microchannel (Aussilous and Quéré [2.21]).

Modeling multi-phase fluid flow at the micro-scale with the assumption of simple disjoining pressure and liquid surface tension may not be accurate (Akbar and Ghiaasiaan [2.22]). To predict the shape, length and pressure drop under Taylor bubble flows, it is important to understand the basic physics of governing the interfacial region.

In this regard now we will discuss the various parameters involved in defining the interfacial region.

Interfacial contact line and affecting parameters

When a gas or vapour phase is introduced in a liquid phase, a chance of formation of three-phase contact lines between the parent fluid, the dispersed phase and the solid channel/duct (where fluid is in contact). These three-phase contact lines are in addition to the gas-liquid two-phase interfaces. Possibility of formation of three-phase contact lines in a PHP is high, especially in the evaporator section where bubble formation and growth of confined bubbles takes place. Elsewhere in the PHP, the Taylor bubbles usually travel with a liquid film around them. In the case of unit cell approach of the single liquid slug and single vapour slug in a single branch PHP, there is a strong chance of formation of three phase contact line. The understanding of statics and dynamics of three phase contact line will give us chance to look it in more insight of the problem.

Three-phase contact lines: Statics

Three-phase triple contact lines are said to be formed when materials in different phases, e.g. solid, liquid and gas (or vapour) intersect. Common examples are a liquid droplet spreading on a solid surface or a liquid meniscus in a capillary tube. The angle between the tangents at the liquid /gas interface and the liquid /solid interface is known as the contact angle θ of the liquid on the solid surface.

Typically, when a liquid spreads on a solid surface in the presence of the third phase (gas or vapour), several equilibrium states can be achieved from non-wetting state to

θ σ - σ - σ σ - π - σ θ σ σ - σ π σ - θ σ σ σ - σ σ σ - σ
Literature review Chapter 2 always lower than the former because of adsorption of gas/vapour molecules which lowers the surface tension of the solid. Thus, Si is always larger than Seq.

For the cases where equilibrium is not reached and Si is negative (which means that Seq is also more negative), the contact line will display a finite static contact angle θst which will not be the same as the earlier defined contact angle θ. When Si is positive, although the droplet will spread and tend to flatten, there is no surety whether Seq will necessarily be zero or negative. Thus, the drop may initially spread and if enough time is given for achieving true equilibrium, it may either become a case of complete wetting (Seq = 0) or it may retract back to a case of partial wetting (Seq < 0). In general, though, if Si is large and positive, the equilibrium state is usually characterized by Seq = 0, however there can be exceptions when Seq < 0. It is difficult to get values of Seq and even more difficult to estimate Si; careful experiments are the only meaningful alternatives for engineering applications.

Consequently, the contact angle depends not only on the thermo-physical properties of the liquid, but also on the physico-chemical structure of the solid substrate. If all the respective interfacial tensions are known, the equilibrium static contact angle can thus be estimated. But the SV (Solid-Vapour) and SL (Solid-Liquid) tensions are not only difficult to estimate but predictive theories are also weak. Also, validity of eq. 2.2 is restricted to ideal surfaces, which are rarely found in engineering practices. This makes the Young's equation eq. 2.2 rather impractical and, frequently careful experiments are needed to estimate the 'static equilibrium contact angle θeq'. It must be noted that true 'thermodynamic' equilibrium (mechanical, chemical and thermal) may be extremely difficult to achieve, especially for non-volatile fluids; at least, mechanical equilibrium (force balance) is mandatory in the definition of θeq. It is in this light that Young's equation eq. 2.2 is best derived by considering a reversible change in contact position, using global energetic arguments, i.e. the nature of the contact line region, over which intermolecular forces are acting, is not considered. Accordingly, θeq is understood to be measured macroscopically, on a scale above that of long range Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - intermolecular forces. Depending on this equilibrium contact angle, solid substrates, for a given fluid, may behave as in table 2. We know that the PHPs are surfaces, both physically and chemically heterogeneous. Therefore, efforts are needed to restore to systematic experimental work to get the real picture of actual contact angles.

In doing such experiments and subsequent post more related issues which need careful consideration (i) 'Apparent' nature of the contact angle and its hysteresis, and, (ii) pinning of contact lines.

The scale at which we look at the three in our perception of the contact angle, which the liquid liquid-solid interface. This is explained in macroscopic viewpoint, wherein the length scale is of the order of capillary radius (or the droplet radius, in case of spreading droplets), the angle which the liquid interface makes with the liquid We know that the PHPs are also made up of tubes which are real time engineering both physically and chemically heterogeneous. Therefore, efforts are needed to restore to systematic experimental work to get the real picture of actual contact angles.

In doing such experiments and subsequent post-processing of the data, there are two re related issues which need careful consideration (i) 'Apparent' nature of the contact angle and its hysteresis, and, (ii) pinning of contact lines.

The scale at which we look at the three-phase contact line manifests a dramatic change f the contact angle, which the liquid-gas interface makes with the his is explained in fig.

θ θ σ μ π μ ≈ π σ ≈ ≈ σ μ ≈ θ
Literature review Chapter 2 These equations inform us that the advancing contact angle is larger than the static contact angle and a receding contact angle is smaller than the static contact angle. This observation has been frequently reported qualitatively in the context of PHPs also.

Initial film thickness

Characteristics of the liquid film in micro-scale two phase flows are not fully understood, and thus designing two-phase flow systems still remains as a difficult task.

It is reported that the thickness of the liquid film is one of the most important parameters for predicting two phase flow heat transfer in micro tubes, Thome et al. [2.30]; Kenning et al. [2.31]; Qu and Mudawar [2.32]. The thin film thickness is of particular interest as most of the heat transfer that takes place in PHP is believed to occur in this region. When gas bubble displaces a wetting fluid in a capillary, a liquid film is deposited on the capillary between the gas bubble and the inside wall as shown in the pioneering work of Fairbrother and Stubbs [2.33]. To find the initial thickness of this laid film is still an issue of debate between scientific communities. Many researches have been conducted to investigate the characteristics of liquid film both experimentally and theoretically. The classical Landau-Levich problem of dip coating, in which an immersed plate is dragged out slowly to allow deposition of thin film of coating, has been a long studied and understood phenomena since its inception in 1942. Since then, various aspects of it has been investigated and well understood. Predicting the instability of the film formed, knowing the thickness of the coating as a function of capillary number, effects of surface tension, and many more critical aspects of dip coating have been well researched and documented. This has paved way to numerous industrial application of dip coating process. In this background, the idea of extending the dip coating predictions to flow in a capillary tube is attempted here.

Early on it was known that the film thickness follows the scaling (δ/R) ~ Ca 1/2 for Ca ranging from 10 -5 to 10 -1 . Seminal analytical work, with some simplified assumptions by Bretherton [2.20] established the scaling as (δ/R) ~ Ca 2/3 , the theory being valid for creeping flows at low Ca ranging from 10 -3 to 10 -2 and bubble Weber number much lower than 1. Although, the theory is based on low Ca assumption, it under-predicts the Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France -2015 [START_REF] Dasgupta | Use of the augmented Young-Laplace equation to model equilibrium and evaporating extended meniscus[END_REF] Literature review Chapter 2 film thickness at the lower range of Ca. This discrepancy has been explained by various mechanistic models and arguments (Goldsmith and Mason [2.34]; Schwartz et al. [2.35]), the most convincing being the effect of variable surface tension in the film and the bubble cap region, which in turn increases the film thickness at low Ca (Ratulowski and Chang [2.36]). Many experiments have confirmed the scalings, some results being close to Bretherton's theory while some more closely following that proposed by Fairbrother and Stubbs [2.33]. Various numerical studies, especially at high Ca, have been done in the context of Taylor bubbles not only to predict the bubble film thickness but also the Taylor bubble shape (Edvinsson and Irandoust [2.37]; Giavedoni and Saita [2.38]; Heil [2.39]). The effect of inertia (average flow Reynolds number) is also felt on the bubble shape and film thickness; it is non-monotonic but not profound. With increasing Reynolds number, the film thickness first decreases slightly and then somewhat increases. In addition, ripples and capillary waves can be seen on the interface. Moreover, the Froude number also affects the bubble shape as the significance of body forces increase; this is especially true while comparing upward and downward Taylor bubble flows. Increasing Ca also leads the shape of the back of the Taylor bubble to change from convex to concave (Taha and Cui [2.40]).

For low bubble velocities as in the case of very viscous fluids as in Bretherton [2.20], the deposited film thickness is governed by momentum balance between viscous and capillary forces. For the fluids with low viscosity which we use in pulsating heat pipes like water, ethanol and FC72, we need to take in account higher fluid velocities so as to take inertial forces in to account in momentum balance. Keeping in this view, Aussilous and Quéré [2.21] have taken two systems with regard to viscosity and fluid velocity range: a visco-capillary regime for fluids with low velocity and high viscosity, using empirical Taylor's law: δ/R ≈ Ca 2/3 /( 1+Ca 2/3 ), applicable up to Ca = 1; and a viscoinertial regime, corresponding to higher fluid velocities with non negligible inertial effects in the film deposition mechanisms. They introduced a correcting factor taking into account the inertial effects by introducing the Weber number.

Recently Han and Shikazono [2.41] have performed a large experimental study of liquid film thickness measurements for bubbles in steady motion and under acceleration. By of menisci also brought to the fore the importance of dynamic contact angle in the Taylor bubble flows and the dissymmetry between the advancing and receding contact angles. Along with the contact line motions an important role in the heat transfer of the thin film that for the stationary meniscus, the contact angle is almost independent of the wall superheat. In the case of a moving meniscus, as the surface velocity increases, the receding contact angle was found to vary whereas the advancing contact angle found to remain almost constant. Mukherjee [2. meniscus on a moving heated wall in two dimensions. More than 99% of the evaporation is found to take place through the receding interface as compared to the advancing interface. The local wall heat transfer varies significantly along the meniscus base. The advancing contact region shows the highest heat transfer due to transient conduction in the liquid from the heated wall. The wall heat transfer coefficient is found to increase with increase in wall velocity and the advancing contact angle but remains -2015

Literature review

It was seen that the advancing contact angle was more than for the stationary meniscus, the contact angle is almost independent of the wall superheat. In the case of a moving meniscus, as the surface velocity increases, the found to vary whereas the advancing contact angle found to Mukherjee [2.49] numerically simulated a steady evaporating meniscus on a moving heated wall in two dimensions. More than 99% of the evaporation is found to take place through the receding interface as compared to the . [2.48] showed for the stationary meniscus, the contact angle is almost independent of the wall superheat. In the case of a moving meniscus, as the surface velocity increases, the found to vary whereas the advancing contact angle found to numerically simulated a steady evaporating meniscus on a moving heated wall in two dimensions. More than 99% of the evaporation is found to take place through the receding interface as compared to the e. The local wall heat transfer varies significantly along the meniscus base. The advancing contact region shows the highest heat transfer due to transient conduction in the liquid from the heated wall. The wall heat transfer coefficient is found se with increase in wall velocity and the advancing contact angle but remains Literature review Chapter 2 unaffected with changes in wall superheat or the receding contact angle. Conclusive

evidence is yet to arrive for the PHP studies for the meniscus motion inside the capillaries.

Pressure drop in oscillating flows

The pressure drop inside a single unit cell oscillating meniscus can be studied as the pressure drop in Taylor bubble train flows. The common models for pressure drop in

Taylor bubble train flows are because of two primary reasons (i) dominance of surface tension in slug flows, which is neglected in these models (ii) additional and unique flow field attributes in terms of velocity patterns in the liquid slug and vapour bubbles, which is also ignored in conventional models. Chen et al. [2.50] have shown that even after the inclusion of surface tension effects in terms of Bond number and Weber number, all the available experimental data sets on pressure drop in slug flows cannot be comprehensively predicted. This necessarily means that improved models should not only include the effect of surface tension but should also address to resolve the effect of flow fields in the unit cell on the overall pressure drop. Khandekar [2.19] showed that all mathematical models for pulsating heat pipes use extremely simplistic pressure drop correlations, typically the Hagen-Poiseuille model. Further, the statistical measure of bubble/liquid slug lengths in the adiabatic section of the pulsating heat pipe is not yet fully resolved vis-à-vis the operating boundary conditions. Unless these issues are studied, proper pressure drop estimation in the adiabatic section of the device cannot be achieved. The fact that the Taylor bubble flow is also oscillating, further complicates the estimation. Very little information is available on oscillating Taylor bubble flows, and extensive experimentation is required to incorporate the pressure drop due to oscillating flows in the proposed models of the PHPs.

The brief state of the art we have brought in this section indicates that the friction of Taylor slug flows like in an extended meniscus of PHP may strongly depend on the wall property, effective dynamic contact angles and hysteresis in a mini /microchannel (Berthier [2.28] and Taha and Cui, [2.51]). The former will depend on the interactions between the fluid, gas/vapour, and the surface properties of the wall. Furthermore, due

Literature review Chapter 2 to the complexities of micro scale thermal capillary effects and the aspect ratio of the mini/micro channel, the relationship between the interfacial liquid film thickness, velocity profiles, friction, plug/slug menisci shape, dynamic contact angle hysteresis, is also not well understood Chamarthy [2.52].

Heat transfer characteristics of extended meniscus

In Literature review Chapter 2 It is well known that during phase-change heat transfer across menisci, an important contribution comes from the extended meniscus covering the interior of the capillary.

This was primarily shown by Potash and Wayner [2.2], who studied that heat flux profile and demonstrated that, the heat flux reached a maximum in the evaporating thin-film portion. Wayner et al. [2.55] showed that heat-transfer coefficient at interline region of an adsorption controlled wetting film varies from zero at interline to a value equal to the liquid-vapour interfacial heat-transfer coefficient over a relatively short distance. Later numerous investigations [2.8, 2.56, 2.57] indicate that it is within this region that high heat transfer rates occur as a result of small conductive resistance and fluid flow driven by the capillary and disjoining pressure gradients.

Hence, Taha and Cui [2.40] stated that this liquid film formed between confined vapour bubble and tube wall plays an important role in heat exchange, since local heat and mass transfer is effectively enhanced at the thin liquid film region. This also justifies the increasing thin-film thickness δ(x) (refer fig. 2.2) as compared to adsorbed region. It is this increasing film thickness that allows sufficient evaporation, resulting from the decay of disjoining pressure (Polansky [2.14]). Solving the resulting interface profile is an important point in studying thin films. The total heat transfer resistance is composed of the diffusional resistance of the liquid film and evaporation at vapour-liquid interface.

There are very few experimental studies available on heat transfers in thin film for such cases. In most of the available studies, the thin film evaporation model is solved analytically or numerically. Due to lack of experimentation, concrete conclusion is yet to arrive. Let us now see the available solution techniques for evaluating thin film heat transfer and how we can correlate these solutions for our extended meniscus problem.

Young-Laplace Equation

The Young-Laplace equation comes about when performing a thermodynamic analysis of interfacial tension effects. The equation can be derived from the consideration of two fluids (I and II) in equilibrium separated by a planar (fixed shape) interface region. If this fixed shape restriction is relaxed and deformation of the interface is allowed, both σ σκ σ --Literature review Chapter 2 Schonberg et al. [2.58] used a concept of augmented Young-Laplace model for an evaporating meniscus in a microchannel. It was found that the heat flux is a function of the long range Van-Der-Waals dispersion force. The apparent contact angle, which represents viscous losses near the contact line, has a large effect on the heat flow rate because of its effect on capillary suction and the area of the meniscus. The liquid pressure differs from the pressure of the vapour phase due to capillarity and long-range Van-Der-Waals dispersion forces, which are relevant in the ultrathin film formed at the leading edge of the meniscus. Important pressure gradients in the thin film cause a substantial apparent contact angle for a completely wetting system.

Vaporization and condensation interfacial resistances

Our primary interest is to calculate the local evaporation/condensation mass flux associated with interfacial temperature and pressure jump that occurs across a liquidvapour interface. This problem can be solved when we look the problem at molecular level. Due to motion of vapour molecules near the liquid-vapour interface plays a significant role in heat flux limitations of vaporization and condensation processes. For such cases, one classical approach is the use of an accommodation coefficient, which attempts to quantify the molecular behaviour at an interface. Accommodation coefficient came in to picture when molecular transport at the liquid-vapour interface was analysed as an extension of kinetic theory of gases (Carey [2.23]).

Using Maxwell's velocity distribution from kinetic theory of gases and obtaining a relationship for the fraction of the molecules with speeds in a specified range, regardless of direction using a simple cubical geometry (fig. 2.11 considering the motion of molecules). We will find the flux of molecules passing through assumed surface of S* per unit area and per unit time in such cube. A molecule with a y-component velocity (v) and any u and w must lie within distance v∆t of the surface at the beginning of the time interval in order to pass through it. The fraction of molecules having a y-component of velocity between some value v and v+dv and having any u and w is found by integrating over all possible values of u and w, obtains the following relation:

- π Δ Δ π π π π - - π - π - - γ γ γ γ γ γ γ γ γ → γ → γ - γ - γ - γ π γ γ γ γ γ γ γ γ γ γ
Literature review Chapter 2 do not equate, there would still be a net mass flux at the interface. This assumption is generally accepted in the absence of the knowledge of the individual accommodation coefficients. However as Schrage [2.59] states, this assumption is suspect. Furthermore, little experimental work has been done in quantifying accommodation coefficients given the molecular nature of the problem. Some authors also reported that in cases of extreme fluid purity, accommodation coefficient should tend to unity.

Experimental and modeling approaches for analyzing extended meniscus evaporation

The bulk transport mechanisms of liquid-vapour system in a capillary tube needs understanding of localized experimental observations of such systems, with synchronized measurements of the resulting fluctuations in local conditions such as temperature, pressure and wall heat flux. Very few experimental and numerical studies are available for heat transfer in extended meniscus region. The measurement of temperature gradient near the thin film region is always a challenging task. In such cases to predict the liquid-vapour thermodynamics inside such systems, require the precise dynamic measurement of the liquid-vapour temperature, which is still challenging due to its vibrant nature and also due to the unavailability 2 of the reliable temperature measurement techniques in such small microscopic systems. In addition, for predicting the dynamics of the liquid-vapour system in such cases of single branch PHP, the issue of dependence of thermal response and sensitivity of the temperature sensor will arise due to induced oscillating motion. There is strong need to develop appropriate temperature measuring techniques for liquid-vapour system to fasten the understanding. There are many experimental/numerical observations available for static extended meniscus evaporation problem, but there is a strong need to extend these studies to the moving meniscus. Let us now go through some of the experimental/numerical approaches and observations applied to the static extended meniscus evaporation. 2 The most of the temperature measurement techniques are intrusive in nature and may influence the system functioning.

Literature review Chapter 2 Most of the time, it was assumed that the vapour near the extended meniscus region is having uniform saturated temperature corresponding to the vapour pressure.

Stephan

and Busse [2.61] developed a model for the radial heat transfer of a grooved heat pipe evaporator. They showed that the common assumption of an interface temperature equal to the saturation temperature of the vapour can lead to a large over prediction of the heat transfer coefficient and there is presence of an inverse pressure gradient in the liquid phase, which is necessary for transporting the liquid in the micro region to the evaporating surface. These in turn lead to a significant decrease of the volatility of the liquid and a corresponding rise of the interface temperature above Tsat. They also observed that the temperature in the micro-region drastically drops and a high heat transfer is obtained at that region; up to 50 % of evaporation takes place in this small region. The length of the micro-region depends on the wetting characteristic which is represented by the local apparent contact angle. Thus, the dynamic apparent contact angle is a very important process parameter. The resulting adhesion forces cause a steady transition of the evaporating meniscus into a flat non evaporating film of microscopic thickness, which is adsorbed on the 'dry' part. Several authors [2. 56-2.58] numerically computed thickness profiles of a heptane meniscus on silicon and compared that with the experimental data. They concluded that significant resistance to heat transfer was present in the contact line region due to conduction, interfacial forces and viscous stresses.

Hoffman and Stephan [2.62] measured temperatures beneath an evaporating meniscus using thermochromic liquid crystals. They found significant temperature drop near the micro-region 3 due to presence of a high evaporative heat flux. Fig. 2.13 illustrates their experimental setup and the temperatures at various regions of extended meniscus. The wall temperature increase to a higher value in the adsorbed film region is due to decreased heat transfer. 3 this "micro region" corresponds to the thin film region described in section 1.2 of this chapter.

Literature review Chapter 2

Gully et al. [2.70] studied this problem in a unit branch PHP aiming at measuring and calculating the vapour state in a horizontal single branch PHP. The experimental setup uses oxygen at cryogenic state as operating fluid. Microscopic thermocouples were employed for the direct vapour temperature measurement. The vapour was found superheated and the vapour temperature oscillates around the evaporator temperature.

As this temperature measurement technique is intrinsic in nature, it may influence the system behavior and also the issue of dependence of thermal response and sensitivity of the sensor will arise due to induced oscillating motion of meniscus and vapour. Fig. 2.18

shows their schematics of experimental setup and the vapour temperature as compared to the saturation temperature.

Chauris et al. [2.71] studied an experimental analysis of the heat and mass transfers involved in evaporation of a thin liquid film deposited downstream a semi-infinite slug flow in a heated capillary tube (Copper tube of 200 mm length and 2 mm inner and 2.4 mm outer diameters) using water as working fluid keeping the target of understanding working of pulsating heat pipe (fig.

2.19-a).

They have done temperature measurements on the outer wall of the tube by infrared thermography, which is used to determine the meniscus location during its passage through the heated test section, so as to ensure that the triple line followed the thin film.

They found that the transfers through the thin liquid film are mainly driven by heat conduction through film thickness and evaporation at its interface. Also compared to thin film length, the meniscus radius remains very small. As a result, the cumulated heat transfers in this zone are low (up to 10% of overall heat transfers) compared to those of the thin liquid film (fig.

2.19-b). Experimental identification of the thin liquid length

subjected to evaporation confirmed that the latter is a primary function of heat flux density at the inner wall (including the stored heat) and of the deposited thin film initial thickness (through the capillary number). They also generated a generic correlation (for water) of first-order evaluation of the thin liquid film length as function of heat flux density at the wall, initial deposited film thickness and fluid properties.

Closing remarks

Looking in to the above literature it is strongly believed that a focused effort is needed to move towards a better understanding of the ultimately real PHPs. Here we are points of course of action.

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Literature review

Experimental setup schematics (b) Experimental results for wall temperature and % of heat transfer at various regions (Chauris et al. [2.71] There are hardly any experimental studies those directly focused on extended meniscus without which the complete understanding of the pulsating condensing systems is quite difficult. Measurement of vapour dynamics inside the unit cell PHP system is a challenge and unfolding of such phenomenon will lead to better understanding of the systems like PHPs.

Looking in to the above literature it is strongly believed that a focused effort is needed to move towards a better understanding of the functioning of the single branch we are giving the outcome of the literature survey 81 Chapter 2 results for wall

Chauris et al. [2.71]).

extended meniscus without which the complete understanding of the pulsatingcondensing systems is quite difficult. Measurement of vapour dynamics inside the unit cell PHP system is a challenge and unfolding of such phenomenon will Looking in to the above literature it is strongly believed that a focused effort is needed to single branch PHPs and giving the outcome of the literature survey and salient

Literature review Chapter 2 The evaporation/condensation dynamics plays a key role in the oscillations. It is clear that the major part of mass transfer occurs via the wetting film (if it exists) or in the vicinity of the triple vapour-liquid-wall contact line when the film is evaporated.

The evaporation rate depends strongly on the film area. However, the film dynamics during the oscillations is poorly understood, only a preliminary study is available.

The pressure drop in the PHP appears due to three sources of viscous dissipation in the liquid: (i) liquid-wall shear stress (ii) the viscous dissipation at the meniscus (wetting films and contact lines) and (iii) effect of the tube exhaust in the reservoir and tube bends. While the first source is well studied, two others are not understood deeply enough. The information on the second source is very scarce while the third is studied only at stationary flow. However, the liquid motion is oscillating in the PHP and the inertial effects play important role.

The vapour thermodynamic state is a very important but yet not studied for understanding the oscillation mechanism of a PHP. In some modeling approaches the vapour is allowed to be overheated due to its compression. It is assumed in the others to be at saturation temperature corresponding to its pressure, which is a behavior analogous to that observed (there are many cases of non-equilibrium) in conventional heat pipes. We think that while the vapour-liquid interface is at saturation, the temperature of the vapour bulk can be higher than the saturation temperature due to the compression. The strong temperature gradients in the vapour domain may get formed near its boundaries due to the weakness of the heat diffusion in vapour. If the vapour thermodynamic state was always at saturation curve, it could not be compressed and thus would not play the role of a spring providing the return force for the oscillation. The vapour compression would simply cause the condensation. The vapour states (both its pressure and temperature) need to be measured experimentally to verify this hypothesis.

Another important parameter is the oscillatory instability which causes oscillations and has not been yet understood. This issue is however critical because if the system Chapter 3

Experimental setups and data processing

As discussed in the Chapter 1 and 2, for better understanding of PHPs it is necessary to quantify the physical phenomena happening inside a single branch PHP using unit-cell approach. We can divide this problem keeping two main objectives in focuses, which need to be studied, and for which we developed two experimental setups: Experimental setups and data processing Chapter 3 auto-oscillations in such a 'unit-cell' system under a definite range of operating experimental conditions. Their experimental setup was close to the theoretical configuration previously studied by Dobson [3.2,3.3]. Temporal variation of vapour pressure was recorded. The passive thermally-driven auto-oscillations of the liquid plug were observed; however, the visualization was restricted to only the condenser section.

There were some important limitations with the approach of Das et al. [3.1], which are listed herein:

(i) Experiments were done without any synchronization of the internal pressure measurements with the videography. As will be discussed subsequently, this led to serious shortcomings in the interpretation of the results.

(ii) The experimental setup was not fully transparent. The evaporator, made of copper, was opaque, and therefore the internal hydrodynamic phenomena could not be observed in totality; only, the condenser section was visible. This restricted data interpretation.

(iii) The connection between the opaque metal evaporator and the adiabatic section/condenser which was made of glass, presented several flow perturbations that might have disturbed the smooth meniscus movement to a certain extent.

(iv) For modeling the internal oscillatory phenomena of the meniscus existing between the vapour bubble and the liquid plug, they introduced an improved and coherent 'evaporation/ condensation' model, as against the earlier simplified 'superheated vapour models' [3. 2-3.5]. While this improvement could indeed predict the large amplitude oscillations observed in their experiments, the possibility of metastable conditions and/or non-equilibrium heat transfer of the liquid thin film were not considered by them.

In this background, here we developed a novel experimental setup which is an improved version of the test bench, as was originally proposed by Das et al. [3.1], overcoming all its limitations listed above. As we know the primary objective of this study is to enhance the fundamental understanding of the phenomena guiding the self-sustained thermally-Experimental setups and data processing Chapter 3 induced two-phase oscillatory flows in the capillary tube of PHPs. Compared to the previous setup of Das et al. [3.1], the new design of the experimental bench is;

(i) Entirely transparent made up of glass in order to comprehensively observe the liquid film dynamics not only in the condenser, but also in the evaporator section too.

(ii)

The capillary tube is placed in a vertical heater-up position, intentionally providing the most unfavorable and demanding conditions for PHPs to operate.

(iii) The setup utilizes a seamless tube connection between the condenser and the evaporator sections, thus completely avoiding any flow perturbations due to geometrical or constructional singularities.

(iv) It is also possible to observe a thin film lay inside the evaporator in some cases of experiments. Furthermore an additional high speed camera is used in experimental setup for the definite understanding of dynamics of thin film with synchronize visualization for thin film movement inside the tube, meniscus movement and vapour pressure measurement.

(v)

The vapour pressure measurements are now fully synchronized in real-time with the high speed videography camera.

These singular improvements of the setup has led to a drastic improvement in the overall understanding of the complex thin-film evaporation and ensuing pressure fluctuations inside the unit-cell. In fact, as will be explained later, some of the interpretations are so unique that it is likely to catalyze a new perspective in mathematical description of the phenomena.

Details of the experimental setup

The experimental setup consists of a basic single branch PHP with one liquid plug and one vapour bubble in a vertical capillary tube of circular cross-section. The transparent capillary tube, made of glass, is closed at one end and connected to a reservoir maintained at a constant pressure at the other end. Its inner diameter is

Experimental setups and data processing Chapter 3 2 mm. The liquid plug oscillates between a heat source (evaporator section length = 200 mm) located near the closed side and a heat sink (condenser section length = 200 mm) located near the reservoir. In between, an adiabatic section separates the condenser and the evaporator (length = 10 mm). Thermal insulations are provided at desired places to avoid heat losses. In the following, the heat source and the heat sink will often be termed 'evaporator' and 'condenser' from an analogy with conventional heat pipes. One should however be aware that strictly speaking, this terminology is not fully adequate in the present system, since condensation can also occur in the evaporator. The basic schematic of the experimental setup with all the instrumentation is shown in the fig. 3.1 and the details of the instruments used in the will be discussed in next section.

Referring to the fig. properties of these fluids are given below in Table 3.

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Experimental setups and data processing These fluids are also chosen as they can be used in future cooling systems which require

The fundamental physical

Experimental setups and data processing Chapter 3 Dynamic Viscosity µ at 20⁰C 0.24x10 -3 0.64x10 -3 1.074x10 -3 0.8796x10 -3 Pa.s

Kinematic Viscosity υ at 20⁰C

0.33x10 -6 0.38x10 -6 1.4x10 As discussed earlier the evaporator and condenser sections are made transparent to track the meniscus and thin film movement. These evaporator and condenser which act as heat exchangers are made up of high quality borosilicate glass with suitable connections to accommodate the capillary tube. These two evaporator and condenser are identical in dimensions and shape. Evaporator and condenser are joined to each other using a specially made adiabatic section which holds these two along with the capillary tube. This adiabatic section is made up of Plexiglas and thus provides desired insulation from heat transfer interactions between evaporator and condenser. The Experimental setups and data processing Chapter 3

The reservoir used for our experiments is specially designed to store the working fluid of the PHP and also an internal jacket is integrated in it for heating and cooling of working fluid. All the parts, tubing and capillary tubes are assembled using leak proof vacuum fittings made of Teflon (can work in range of -50 °C to 150 °C). Fig. 3.3 gives the dimensions of the important parts and actual photographs of evaporator, condenser and adiabatic section.

Experimental procedure

All the parts are thoroughly cleaned and assembled, then vacuum tightness of the complete assembly is ensured. Before the experiments starts, the system is completely evacuated to remove the non condensable gases using a vacuum pump (< 10 -5 mbar).

The reservoir is then filled with the working fluid. After filling the liquid, all the non condensable gases present inside are removed. The volume of the reservoir is huge compared to that of the tube so that the oscillations inside the tube have negligible effects on the pressure within it. The capillary tube is always dipped inside the liquid irrespective of level of liquid in it. The changing in level affects the hydrostatic pressure at the exhaust of the tube, but in 3 rd place of decimal, since the height of liquid above the exhaust of the tube is greater than 100 mm. Two high speed cameras, vapour pressure sensor and vapour temperature sensor are then verified for the synchronization.

There is some volume which is present inside the system which is not contributing to the PHP phenomenon but actually affecting its performance. This volume exists there due to the connections of pressure and temperature sensors at the vapour space at the end of capillary as shown in fig. 3.2 by T junction. This volume we termed as the dead volume.

To measure this dead volume, the empty weight of the connections (T junction) which is used to connect the thermocouple and the pressure transducer was measured, with help of a highly precise mass balance of METTLER TOLEDO. Then, the system is filled with water and the total weight measured again. The difference of weights was then divided by density of water to get the dead volume inside this T junction. This process was repeated several times to minimize the error. This dead volume was then found to be equal to 2.83 x 10-6 m 3 (± 5%).

Experimental setups and data processing Chapter 3

To get acquainted to the overall behavior of the experimental setup, it was necessary to determine the appropriate boundary conditions such as evaporator temperature, condenser temperature and reservoir pressure combination in which the self sustained thermally driven oscillations are obtained. It was observed that meniscus oscillates inside the capillary tube for certain combinations of above mentioned boundary conditions; these oscillations are sometimes regular, irregular, repetitive or random in nature. In some of the cases little external excitation is needed to start the first oscillation and in some cases it is automatically started. As we know that due to instabilities involved in the PHPs in general, several experiments were performed by varying the condenser/ evaporator temperature and reservoir pressure combinations.

Due to imposed thermal gradient, meniscus oscillations of various shapes and size are observed. Out of these various experimental observations it is later on found that only a few with regular and repetitive patterns are useful to reach on logical conclusion.

With the help of vapour pressure/ temperature sensors and two high speed cameras, vapour pressure, vapour temperature, meniscus movement and triple line movement (if visible) are recorded in synchronization with each other. Also the respective reservoir pressure, condenser temperature and evaporator temperature are noted. The measurements recorded by these two cameras are in the form of B/W images. The meniscus is clearly observable in these images. Also when the thin film is observed its motion is observed by tracking the triple line motion, this motion is clearly distinguished by difference in the contrasts in the raw images. To get an accurate and reliable measurement we recorded 1000 data points per second. Although it is difficult to represent the image of the triple line here, using the appropriate image processing technique it i contrasts of various regions (thin film, vapour and liquid).

To summarize, the outcomes of the experimental measurements are the combination of following items shown in Table 3.

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Experimental setups and data processing Although it is difficult to represent the image of the triple line here, using the appropriate image processing technique it is possible to distinguish between the contrasts of various regions (thin film, vapour and liquid).

the outcomes of the experimental measurements are the combination of following items shown in Table 3.2. Although it is difficult to represent the image of the triple line here, using the s possible to distinguish between the the outcomes of the experimental measurements are the combination of Experimental setups and data processing Chapter 3 completely derived. This part of the data processing will be discussed during the detail discussion about the meniscus dynamics and thin film dynamics in the chapter 4.

Experimental setup 2: Hydrodynamics of the meniscus inside the capillary (adiabatic experiments)

As discussed earlier in chapter 1 and 2, the singularities and friction play an important role in modeling the single branch PHPs. To overcome these problems, ideal solution is to obtain two-phase frictional pressure drop for a single branch PHP. But as tt is quite difficult to build such experimental system to measure two phase pressure drop, also at same time modeling is also quite difficult as discussed in section 2.3.5 of chapter 2.

Keeping this in mind, Das et al. [3.1] have incorporated the single phase frictional pressure drop for the oscillating flow inside the capillary tube in their model. Hence it will be interesting to verify this approximation using frictional pressure drop experiments for single phase oscillating fluids. The key is to develop an experimental setup which has similar in dimensions to setup 1 (as discussed in section 1 of this chapter) and then measuring the pressure drop in adiabatic conditions for oscillating fluid within similar frequency range. This verification will give clues either to verify the assumptions used in the model developed by Das et al. [3.1] or may lead to totally new findings. Also it will be interesting to see the contact line behaviour of the thin film laid by the fluids (if visible) during the oscillations inside the capillary tube (as discussed in section 2.3.4 of chapter 2).

Details of the experimental setup

Keeping above objectives in focus we built a new experimental setup using the same dimensions as of setup 1, as discussed in the previous section. The size of the capillary tubes is kept 2 mm internal diameter and 6 mm outer diameter. The length of this capillary tube taken as 700 mm. This tube is dipped inside the same reservoir used in the setup 1 described above.

A KELLER made (model PD23 measuring up to 1000 mbar with accuracy of 0.1% of full scale) differential pressure transducer is connected at one end of the capillary tube and

Experimental setups and data processing Chapter 3 other end to the reservoir, so as to measure the pressure difference during the oscillations of the meniscus. This differential pressure transducer is capable of measuring the dynamic signal with a maximum output capturing frequency of 1000 Hz.

The differential pressure transducer requires an external power supply of appropriate DC voltage. Experiments have been done in vertical orientation as to see influence of this pressure drop on the results obtained from experimental setup 1.

The liquid inside the reservoir-capillary tube system is externally excited using a pressure function generator (made by Elveflow model AF1) connected at the reservoir to move the meniscus in desired oscillating pattern. Elveflow® provides the microfluidic flow control system using piezo technology and enables a blazing fast flow change in our system. It gives a stable and pulse less flow while remaining extremely reactive. The exit of the Elveflow pressure function generator is connected to the reservoir tank in which the capillary tube is dipped, the connection (tubing) from Elveflow to the reservoir is kept long enough to obtain smooth pulse. These external excitation to the liquid, generated similar conditions of meniscus oscillations of the thermally induced oscillations inside the capillary tube similar to as we find a typical single branch PHP.

Teflon vacuum fittings are used to connect all the tubing's of the experimental setup.

Similarly to previous experiments a high speed camera (SA-3) is simultaneously used to track the meniscus displacement. Also a DC powered light source is used along with this camera for the better illumination to capture the clear images during meniscus movement.

A GRAPHTEC data acquisition system is used for recording the data. This data acquisition device also has inbuilt standard noise filtering algorithms to filter the unnecessary noise. The pressure measurements are synchronized with the video camera with external trigger in the data acquisition system. The schematic of the actual setup is shown in fig. 3.6. These experiments are done in adiabatic conditions and without evaporator and condensers to facilitate the better view of the meniscus and thin film.

Data processing

The differential pressure measured is then converted to calculate the actual differential pressure across the two ends of the capillary tube (as the other end of differential pressure transducer were connected to the reservoir) using suitable calculations.

Camera used for capturing the capillary tube for meniscus movement tracking and for tracking thin film movement by observing the triple line (if visible) movement gives the B/W images. These images are processed with code developed in MATLab using image processing tools. The method is similar to as discussed in section 1.2 of this chapter. The detail data processing of this part will be discussed further in chapter 5 while analyzing

Experimental setups and data processing Chapter 3

the results as it involves some acquaintance with the terminologies involved in modeling such phenomenon.

Closing remarks

These experimental setups leads us to encouraging results which we feel are helpful to enhance the understanding of the singe branch PHP, are discussed in chapter 4 and 5.

Uncertainties involved and calibration of some of the instruments in these experiments are discussed separately in the Appendix-C.

Chapter 4 Results and discussions -Single branch PHP experimentation and thin film dynamics

The scientific objectives of this work are to investigate the main physical effects that govern oscillations of a meniscus in both theoretical and experimental approach of a single branch PHP. Energy is supplied to the system mainly via evaporation/condensation, which occurs mainly through the wetting films. In this context a holly collaboration of CETHIL, France and IIT Kanpur, India with the help of CEFIPRA1 came in to existence a few years ago to contribute the march towards decoding the physics of a PHP. This work is also a part of such journey. The film dynamics is studied in two different ways viz. first by experiments and then second by the theoretical modeling. In this sense, chapter 4 compromise of mainly two parts;

(i) In the first section, we will be discussing the experimental results obtained using setup 1 and setup 2 as explained in the section 1 and section 2 of the chapter 3. This will give an opportunity to discuss the overall thermo-hydrodynamics involved in the studied systems of a single branch PHP.

(ii) In second section a simplified theoretical analysis of unsteady heat transfer in the liquid thin film in context of single branch PHPs will be performed using analytical models.

The results presented here are already published (Rao et al. [4.1,4.2]) in peer reviewed journal in previous years.

Experimental results of single branch PHP

As discussed in chapter 1 and 2 self-sustained thermally-induced oscillations of a meniscus in a two-phase system consisting of a liquid plug and a vapour bubble in a

Results and discussion Chapter 4 capillary tube are needed to be studied to understand the working of single branch PHP and ultimately, of full scale PHP. In this respect as explained in chapter 3 we developed two experimental setups. In this section we will be discussing the heat transfer mechanism inside the single branch PHP along with present our overview on thin film contribution to working of a single branch PHP.

Experimental boundary conditions

As discussed in chapter 3, the experiments are performed using various fluids (De-ionized water, Ethanol, FC72 and Pentane). The exact starting conditions of such systems cannot be determined using the available knowledge. Therefore for all of the fluids, we have tried various combinations of reservoir pressure, evaporator temperature and condenser temperature to find the correct combination of above three for obtaining self-sustained-thermally induced oscillations of the working fluid inside the system. We were successfully able to find such suitable combination for the FC72 and pentane but with de-ionized water and ethanol, we were not able to find any combination of reservoir pressure (0.2 to 1 bar), evaporator temperature (-10 to 120⁰C) and condenser temperature (-10 to 120⁰C) that would result in visible oscillations. Later on, analyzing the results for FC72, we found that the thin film laid by the meniscus on evaporator wall during receding motion towards the condenser plays an important role in maintaining the oscillations (refer section 1.4 below). So the non functioning of our system with de-ionized water and ethanol can be due to the phenomenon assumed by -2015

Results and discussion

triple line is shown by red colour which doesn't move at all with respect to the meniscus and believed to be pinned to the wall. For no pinning case the triple shown by green colour moves along with the meniscus and hence have zero relative velocity meniscus movement. In the case of partial pinning which is represented by blue line the triple line movement behaviour will lay in the zone in between green and red dotted lines. The slope of this blue dotted line will depend upon the interfacial and solid.

Schematics of the various possible cases of contact line behaviour

To verify this hypothesis we have done the experiments in adiabatic conditions to observe the relative film motion with meniscus. It is found it possible to observe the motion of triple line in the case of de-ionized water.

adiabatic experimental results of the motion of the triple line with motion in a capillary and thus corresponds to the partial pinning of Tripathi et al. [4.3]. Looking into fig. 4.1 we can say that the contact line is not pinned and also the de-pinning rate is not that high. So this can be a 109 Chapter 4 triple line is shown by red colour which doesn't move at all with respect to the meniscus and believed to be pinned to the wall. For no pinning case the triple shown by green colour moves along with the meniscus and hence have zero relative velocity meniscus movement. In the case of partial pinning which is represented by blue line the triple line movement behaviour will lay in the zone in between green and red dotted lines. The slope of this blue dotted line will depend upon the interfacial Schematics of the various possible cases of contact line behaviour.

To verify this hypothesis we have done the experiments in adiabatic conditions (refer meniscus. It is found ionized water. We believe that this movement of the contact line sustainable oscillations in the case of de experiments of the FC72, Ethanol and Pentane it is not able to visualize the triple line movement; hence it will be difficult to comment on fluids. But as in the heat transfer experiments we saw the motion of the triple line for the FC72 (refer section 1.2 below), so we feel it is can be a case of full pinning, and also although the movement of triple line but it sustains thermally-induced oscillations, hence it may be a case of full pinning. As we described earlier that neither obtained for the Ethanol, nor we experiments, so it can be a case of partial pinning or no pinning. This invisibility of the triple line movement (thin film) in the case of Ethanol the very thin film formation which is not is not favorable to capture.

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Results and discussion

: Represents the adiabatic experimental results for de-ionized water, the triple line with respect to meniscus motion in a capillary and thus corresponds to the partial pinning of contact line.

We believe that this movement of the contact line may be responsible for the non sustainable oscillations in the case of de-ionized water. Similarly in the adiabatic experiments of the FC72, Ethanol and Pentane it is not able to visualize the triple line movement; hence it will be difficult to comment on the contact line behaviour of these fluids. But as in the heat transfer experiments we saw the motion of the triple line for efer section 1.2 below), so we feel it is can be a case of full pinning, and also although the movement of triple line is not visible for Pentane heat transfer experi induced oscillations, hence it may be a case of full pinning. As neither the self-sustained thermally-induced oscillations are nor we able to see its triple line movement in adiabatic experiments, so it can be a case of partial pinning or no pinning. This invisibility of the triple line movement (thin film) in the case of Ethanol and Pentane may be due to either the very thin film formation which is not observable using the camera or refractive index experiments, so it can be a case of partial pinning or no pinning. This invisibility of the and Pentane may be due to either using the camera or refractive index Chapter 4 Although this contact line behaviour may not be the only cause of non self-sustained thermally-induced oscillations, it may be affected by physical properties, interfacial behaviour or tube material in the case of water and ethanol. In this respect a model is developed and solved to incorporate such parameters to know their relative influence on oscillations, which will be discussed in chapter 5.

Results and discussion

So here onwards only results of FC72 will be discussed for a set of parameters to understand the governing mechanism of the single branch PHP. Similar kinds of results are also obtained for the Pentane but without the recording of the thin film location, these results are presented in the Appendix-D for the purpose of archival.

In the following, experimental results are discussed for various operating boundary conditions of FC72 as working fluid. The reservoir is maintained at a constant pressure of 0.5 bar, corresponding to a saturation temperature of 37.2ºC. The evaporator temperature Te is kept constant at 46ºC while the condenser temperature Tc is varied from 0ºC to 32ºC. It is observed that when Tc is kept below 16ºC (large temperature difference between the evaporator and condenser) or above 28ºC (low temperature difference between the evaporator and condenser) the meniscus moves rather randomly and hence, it is very hard to obtain repeatability in such results. For the condenser temperature in between 16ºC to 28ºC systematic repeatable oscillations of vapour pressure and meniscus movement and thin film movement are observed. Therefore, the results presented in the next sections are taken in this range to arrive at meaningful conclusions which can contribute in attaining the objectives of this research.

Note: For the figures (fig. 4.3 to 4.8) presented in this section, the location X = 0 corresponds to the bottom of the adiabatic section. Locations defined by X > La are in the evaporator section (represented by red line on primary Y-axis) while those defined by X < 0 are in the condenser section (represented by blue line on primary Y-axis).

Results and discussion Chapter 4

Meniscus oscillation with pressure variation

Fig. 4.3 shows the temporal variation of vapour pressure in the vapour bubble, along with the location of the meniscus and the triple-line, for four cases of the experimentally applied boundary conditions (Te = 46ºC and Tc = 16ºC, 20ºC, 24ºC and 28ºC, respectively). Three complete meniscus motion cycles are presented for each condenser temperature. It is observed that meniscus movement and pressure variation are quasiperiodic and nicely repeatable for all of the cases. When the meniscus moves towards the condenser (downward motion), a thin liquid film gets drained or laid on the tube wall. As it will be explained later, this film drainage by the moving meniscus is responsible for the large amount of vapour generation at the evaporator, which, in turn, leads to the oscillation of the liquid plug. By looking at the video of meniscus motion, it is possible to distinctly observe three different zones inside the tube: a dark zone corresponding to the liquid plug, a clear zone corresponding to the vapour slug, and an in-between zone where the contrast is neither dark nor clear that corresponds to this thin liquid film, which gets laid down during meniscus downward motion.

Furthermore, under proper lighting conditions and controlled focus, it is also possible to clearly observe the liquid film vanishing with time, i.e., evaporation of the film from the glass surface is unmistakably recorded. The movement of the triple-line towards the condenser is also clearly observable. We consider that the liquid film vanishes when the contrast value observed on the video is similar to the contrast value due to the vapour.

However, as the contrast depends on the thickness of the liquid film, the sensitivity of the camera is probably not able to distinguish film-remnants which are extremely thin.

Therefore, subsequent analysis is based till the location where the difference of contrast is just vanishing. However, one should keep in mind that the absence of explicit quantitative data points does not mean with certainty that the liquid film has indeed totally vanished; a few monolayers of liquid may still be remaining. Nevertheless, the recorded information certainly enables to bring some essential information for qualitative interpretations. c), the meniscus cycle consists of one full stroke inside the evaporator followed by two smaller strokes in the condenser section. During the downward stroke of the meniscus, as noted earlier, it ass to the vapour space and helps in increasing the vapour pressure. Until the time the liquid film laid down by the downward moving meniscus is completely evaporated, the meniscus is not able to reo the condenser. Thus, two strokes are seen to occur in the condenser section. The meniscus re-enters the evaporator section, after the second stroke in the condenser is over, and then the quasihe meniscus inside the = 80 mm for the different condenser temperatures. This tends to suggest that the amount of vapour generated during one Chapter 4 cycle at the evaporator is rather constant, since it is proportional to the length of the liquid film drained by the meniscus in the evaporator.

Results and discussion

Conversely, the maximum level reached by the meniscus inside the condenser increases with the increase of Tc during the first stroke inside the meniscus. Indeed, for smaller condenser temperatures (larger temperature difference), a smaller heat exchange surface area is necessary to condense the vapour generated by the evaporation of the liquid film. The second stroke in the condenser is always shorter than the first one, which can be explained by a smaller amount of vapour generated in the evaporator (the last remnant of the disappearing liquid film), as the remaining liquid film length is much smaller at the end of a cycle. One can also observe that the cycle time-period slightly increases with the increase of Tc.

The qualitative behaviour of the meniscus oscillatory motion is quite different for Tc = 28ºC; the meniscus oscillation cycle consisting of a single to-fro stroke in the evaporator (fig. 4.3-d), followed by one stroke in the condenser section. Therefore, the net time period of one oscillation cycle is also smaller than for the other condenser temperatures. One can also observe that the amplitude of the signal is much smaller in both the condenser and the evaporator. Above a condenser temperature of 28°C, the energy of the system is not sufficient to maintain the oscillations. It was not possible to distinguish clearly the triple-line evaporation in that case because the length of the film formed due to drainage was very short, compared to other condenser temperatures.

Lastly, comparing the pressure signal for the four graphs (fig.

Results and discussion Chapter 4

From points A to E, the meniscus is moving upwards in the evaporator and is in the process of approaching the top-most position in the evaporator. During that stage, the vapour space is getting compressed and the pressure of the vapour bubble is simultaneously increasing. At point E, the meniscus reaches the topmost position of evaporator and dwells there for a very short time. This dwelling can be observed both in meniscus location and pressure variations (fig. 4.4-b). After point E, the meniscus starts its downward journey. It is observed that a film of liquid is laid on the wall of the tube and the triple-line location coincides with point E. As the meniscus starts moving downwards, this triple-line also starts following it but with a different speed. At point J, the meniscus is about to exit from the evaporator, as it enters the condenser section. It is clearly visible in the figure that at this stage the liquid film still exists in the evaporator section. The maximum value of vapour space pressure is not reached when the meniscus is at its topmost location in the tube, but just before it enters into the condenser. Indeed, the evaporation of the liquid film during the downward movement of the meniscus towards the condenser contributes to the increase of the pressure during the descent of the plug. From points K to M, the meniscus keeps on moving downwards in the condenser and the pressure begins to decrease, due to both, expansion of the vapour bubble and simultaneous condensation. At point M, the meniscus reaches the first bottom-most point in the condenser. The liquid film, albeit thinner, is still in the evaporator. From point N to point P, the vapour-pressure stills decreases, and the meniscus moves towards the evaporator.

During this upward motion of the meniscus in the condenser section, the pressure increases again, clearly indicating that the rate of vapour condensation process is not sufficient to overcome the mass addition rate due to the evaporation of the remaining liquid film. Therefore, the meniscus is not able to reach the adiabatic section, but changes its direction to move downwards again instead of entering the evaporator. This, as explained, happens due to the continued presence of the liquid film in evaporator, which is still continuously evaporating, thus restricting the upward motion of the meniscus. From points P to R the meniscus again re-travels till the bottom-most point of the condenser and very quickly thereafter, the vapour pressure decreases again.

Meanwhile, no sooner the liquid film vanishes in between point R to T in the evaporator, Chapter 4 subsequent variation of the mass of vapour is only due to condensation and therefore the pressure of the vapour decreases until a very low value that enables the meniscus to be pulled up into the evaporator section yet again. This process then repeats itself, starting from A to T, with regular repeatable cyclic oscillations.

Results and discussion

As has been appreciated, during one complete cycle of meniscus motion, the variation of the vapour pressure is due to both, evaporation and condensation of the fluid and compression or expansion phenomena of the vapour. During the ascent of the meniscus in the evaporator (upward stroke), no thin liquid film is present ahead of the meniscus.

Hence during this part of the motion, there is practically no mass addition to the vapour space due to evaporation and the pressure change is directly attributable to compression effect, which results in a small variation of the pressure during that stage. This result undoubtedly highlights the importance of the thin film evaporation and vapour condensation phenomena in the ensuing meniscus oscillations, as compared the purely compression and expansion effects. behind the meniscus and takes finite time to evaporate. However, as mentioned earlier, it was not possible to record the variation of liquid film thickness until the very end of the evaporation process, due to photographic limitations. Nevertheless, it is clear that the film lifespan in the evaporator is rather long as compared to the total time period of the oscillation.

Therefore, until the meniscus completes the first part of the cycle of travelling through to the bottom-most point of condenser again coming back to the entrance of evaporator, remnants of the evaporating liquid film still exists in evaporator, thereby restricting the entry of the meniscus into evaporator and pushes it back to the condenser. This behaviour of the meniscus movement is responsible for small and big amplitude oscillations, respectively. As soon as the liquid film completely disappears from the Chapter 4 evaporator, the meniscus is able to re-enter the evaporator again during its return motion from condenser. In this way, regular and repeatable self-sustained thermally driven oscillations go on in the tube at the imposed thermal gradient. With reference to the fig. 4.3, it can be said that the film life, i.e., the time period between the film appearing and subsequently completely getting evaporated and vanishing, is of the order of typically between 1.0 s to 1.4 s.

Results and discussion

1.3

Actual vapour temperature versus the vapour saturated temperature Fig. 4.5 presents temporal variations of vapour pressure and temperature in the vapour bubble depicting several cases of the experimentally applied boundary conditions (Te = 46ºC and Tc = 16ºC, 20ºC, 24ºC and 28ºC). The saturation temperature of the working fluid corresponding to the measured pressure is also plotted along with the measured vapour temperature. The measurement of temperature by this micro-thermocouple is critical and requires close scrutiny. Indeed, even if the size of the thermocouple is rather small (bead diameter is 80 µm), its frequency response, although much faster than the oscillating frequency of the system, is still finite and non-zero. Furthermore, the microthermocouple also exchanges heat by thermal radiation with the inner wall of the capillary tube (although emissivity of both the surfaces is expected to be quite low), which will introduce a non-vanishing bias in the temperature measurement. The precision of the temperature sensor would be lower than ± 0.5 K if it was only based on a calibration process, but the previous described experimental biases increase this uncertainty and make it difficult to estimate properly. However, even with these limitations, the temperature information given by this micro-thermocouple provides some very useful information for qualitative interpretations of the system dynamics.

Secondly, and more strikingly, one major conclusion is that the vapour temperature is always higher than the saturated temperature derived from corresponding vapour pressure measurement, which corroborates the recent results obtained by Gully et al. [4.4] in cryogenic conditions. Their study also brings out the existence of superheated conditions of the vapour space during meniscus motion. This is a quite an important conclusion for the proposed modeling of the unit-cell PHP system. The fact that vapour Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - is seen to be always superheated throughout the cycle of meniscus oscillation provides the first-order justification for using space, in conjunction with the film dynamics in the evaporator and film condensation the condenser; the latter two models providing the respective sources and sinks for vapour mass, corresponding to the evaporation and condensation rates, respectively. In the subsequent section, this idealization is used to find the temporal mass variat the system, and as will be demonstrated, this exercise does provide important insights into the thermal-fluidic behaviour of self meniscus motion. Firstly, it is seen that the measured vapour temperature is somewhat lower than the maintained evaporator temperature. The variation is extremely small, which can be due to the dampening of the signal due to the non -2015

Results and discussion

seen to be always superheated throughout the cycle of meniscus oscillation provides order justification for using the ideal gas equation for modeling the vapour space, in conjunction with the film dynamics in the evaporator and film condensation the condenser; the latter two models providing the respective sources and sinks for vapour mass, corresponding to the evaporation and condensation rates, respectively. In the subsequent section, this idealization is used to find the temporal mass variat the system, and as will be demonstrated, this exercise does provide important insights fluidic behaviour of self-sustained thermally driven oscillatory : Temporal variations of pressure (right ordinate axis) along with temperature in the vapour bubble and saturation temperature Tsat = f(Pv), for experimental boundary = 46ºC and Tc = 16ºC, 20ºC, 24ºC, 28ºC, respectively and P rstly, it is seen that the measured vapour temperature is somewhat lower than the maintained evaporator temperature. The variation is extremely small, which can be due to the dampening of the signal due to the non-zero time response of the system.

119 Chapter 4 seen to be always superheated throughout the cycle of meniscus oscillation provides ling the vapour space, in conjunction with the film dynamics in the evaporator and film condensation in the condenser; the latter two models providing the respective sources and sinks for vapour mass, corresponding to the evaporation and condensation rates, respectively. In the subsequent section, this idealization is used to find the temporal mass variation in the system, and as will be demonstrated, this exercise does provide important insights sustained thermally driven oscillatory : Temporal variations of pressure (right ordinate axis) along with temperature in ), for experimental boundary and Pr = 0.5 bar.

rstly, it is seen that the measured vapour temperature is somewhat lower than the maintained evaporator temperature. The variation is extremely small, which can be due zero time response of the system.

Results and discussion Chapter 4

Dynamics of the liquid film

The vapour mass dynamics can be estimated using simple assumption of ideal gas equation and the different measurements made via the sensors placed in the vapour space. This information, coupled to the temporal movement of the triple-line, enables to estimate the time-dependent changes of the liquid film thickness. Finally, a simple mass balance equation in the evaporator provides an estimation of the initial thickness of the film. Hence, the dynamics of the film in the evaporator can be completely derived; this procedure is detailed below.

Experimental estimation of the vapour mass dynamics

As discussed in data processing section 1.3 of chapter 3, instantaneous mass of the vapour can be calculated using the following equation.

m t = P t × V t R × T t × M 4.1
Where, R is the universal gas constant and M = 338 / , the molecular weight of FC72.

Fig. 4.6 shows the temporal variations of meniscus location and triple-line locations, respectively, along with the mass of vapour calculated using ideal gas, eq. 4.1, depicting several cases of the applied boundary conditions (Te = 46ºC and Tc = 16ºC, 20ºC and 24ºC). Vapour mass variation inside the system is a combined effect of evaporation and condensation, respectively, which may be occurring simultaneously. Therefore, any combination of evaporation and condensation rates can produce this variation of vapour mass. One has to develop a heat transfer model to extract these parameters from the experimental data. It is also observed in fig. 4.6-d that even a ± 10ºC variation in vapour temperature measurement affects only ±3% of instantaneous vapour mass calculations.

Therefore, even if the temperature measurement by the micro-thermocouple is not highly accurate, the validity of the estimation of the vapour mass certainly remains rather reasonable. The mean estimated initial liquid film thickness is estimated to be equal to 75 µm, 69 µm and 67 µm for Tc equal 16ºC, 20ºC and 24ºC, respectively. The thickness is nearly constant in Zone #2, while at the same time, the triple condenser; this clearly indicates that two different processes of evaporation occur inside the system, one at the triple liquid film. In Zone #3, the liquid film thickness in the evaporator section decrea rapidly as the meniscus recedes deep into the condenser section towards the reservoir.

When the meniscus reaches back to the evaporator section during its first upwards journey, a small increase of the film thickness is observed in some conditions, whi attributed to condensation of compressed vapour on the film. In Zone #4, the thickness -2015

Results and discussion

: Temporal variations of location of meniscus and film thickness variation calculated using the analytical model as per eq. 4.7 (at Te = 46ºC and Tc and 24ºC, respectively, and Pr = 0.5 bar).

The mean estimated initial liquid film thickness is estimated to be equal to 75 µm, 69 equal 16ºC, 20ºC and 24ºC, respectively. The thickness is nearly constant in Zone #2, while at the same time, the triple-line moves towards the nser; this clearly indicates that two different processes of evaporation occur inside the system, one at the triple-line and the other at the liquid-vapour interface of the liquid film. In Zone #3, the liquid film thickness in the evaporator section decrea rapidly as the meniscus recedes deep into the condenser section towards the reservoir.

When the meniscus reaches back to the evaporator section during its first upwards journey, a small increase of the film thickness is observed in some conditions, whi attributed to condensation of compressed vapour on the film. In Zone #4, the thickness The mean estimated initial liquid film thickness is estimated to be equal to 75 µm, 69 equal 16ºC, 20ºC and 24ºC, respectively. The thickness is nearly line moves towards the nser; this clearly indicates that two different processes of evaporation occur inside vapour interface of the liquid film. In Zone #3, the liquid film thickness in the evaporator section decreases rapidly as the meniscus recedes deep into the condenser section towards the reservoir.

When the meniscus reaches back to the evaporator section during its first upwards journey, a small increase of the film thickness is observed in some conditions, which is attributed to condensation of compressed vapour on the film. In Zone #4, the thickness reasonable estimates of the initial film thickness can be independently verified, as can be clearly seen in Table 4.1.

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Results and discussion

Results and discussion

Comparison of the empirical scaling correlations for predicting the initial film lay down by a moving meniscus inside a tube presents the four different explicit contributions to the vapour mass variation Te = 46°C and Tc = 16°C). Qualitatively similar results are obtained for the other boundary conditions also. The mass due to condensation on the meniscus region is varying nearly linearly because the vapour saturation temperature, which exists on the meniscus, does not vary much during the experiment and therefore, and Tc remains nearly constant (eq. 4.2). In any case, the amount of condensation on the meniscus is negligible compared to the amount of condensation on the liquid film. This latter component of condensation, which is due to the large variation of the liquid film length in the condenser, is much more critical and important. When the condenser section is full of liquid, its contribution is equal to zero 129 Chapter 4 Comparison of the empirical scaling correlations for predicting the initial film presents the four different explicit contributions to the vapour mass variation = 16°C). Qualitatively similar results are obtained for the other boundary conditions also. The mass due to condensation on the meniscus region is varying nearly linearly because the vapour saturation temperature, ry much during the experiment and therefore, 2). In any case, the amount of condensation on the meniscus is negligible compared to the amount of component of condensation, which is due to the large variation of the liquid film length in the condenser, is much more critical and important. When the condenser section is full of liquid, its contribution is equal to zero, Chapter 4 while it is maximum, when the meniscus is at the bottom of the condenser section. The evaporation process is more complicated. Fig. 4.10 shows that the amount of vapour generated at the triple-line is significant and equal to more than 1/3 of the contribution of the liquid film evaporation. Furthermore, the evaporation rate at the triple-line can almost be considered as constant during the entire life of the liquid film while the evaporation on the liquid film is highly dependent on the location of the meniscus inside the tube. The net evaporation rate is maximum when the meniscus is at the bottom of the condenser, while it tends to zero or become slightly negative (i.e., condensation occurs on it) when the vapour is being compressed by the upward moving meniscus. Results and discussion Chapter 4 [ 4.17]). Statistically speaking, given the fact that the local thermodynamic quantities are changing continuously at this characteristic frequency at any given spatial location inside a PHP, the pertinent question to ask is, how different sub-constituents of the unit-cell respond to these changing thermodynamic conditions?

Results and discussion

Scaling arguments

To answer this question, consider a typical PHP made up of copper tube of inside The thermal response of a material to a change in temperature is indicated by its compares the thermal conductivity to thermal diffusivity for a wide range of materials on a log-log scale (Salazar [4.20]). The data points noted as condensed matter (liquids and solids) can be described as being near a straight

As it can be noted, with respect to thermal diffusivity, gases are quite different as compared to the condensed matter. With respect to the transient nature of heat transfer in a PHP, it is worthwhile to note that all the three phases, viz. vapour

Results and discussion

scales of these three interacting sub-systems of the unit-cell will be of interest. Table 4 Salazar [4.20]).

nal thermal change imposed on the boundary of these elements exceeds the respective characteristic frequency of the element under consideration, such perturbation information will, in principle, remain largely isolated cell. Considering the fact that typical PHPs Khandekar et al. [4.17]).

× × × × • • • • •
Results and discussion Chapter 4 the characteristic time-scales of the constituents of the unit cell. For example, in a typical journey from the evaporator to the condenser, while the vapour will quickly respond to the change in temperature of its new colder surroundings, the liquid plug adjoining the vapour bubble will be much slower in loosing the sensible heat. From a thermodynamic standpoint, this essentially means that the probability of a temperature difference occurring between the liquid plug and the vapour bubble is quite high. In addition, there is considerable difference between the time response of the vapour and the surrounding liquid film. Thus, the very premise of the assumption of thermodynamic 'equilibrium', in the context of PHPs is rather misleading and inappropriate. In spite of the fact that explicit experimental evidence of non-equilibrium in PHP systems is yet to appear, the arguments presented above clearly indicate that the very nature of PHP heat transfer is guided by this inherent non-equilibrium existing between the vapour bubbles and adjoining liquid plugs.

The system always tries to come to equilibrium locally by either exchanging heat/mass with the wall, or by exchanging heat/mass with the surrounding elements of the unitcell with which a temperature difference exists so as to rearrange the respective chemical potentials of the two phases. Any change in the respective specific Gibbs free energy, due to a temperature or a pressure imbalance at the interface will lead to a driving potential for local phase-change. Moreover, change in temperature of the vapour can also take place by compression of its volume experienced via the movement of the adjoining liquid plugs. This local compression of a particular unit-cell can be an outcome of events taking place at other locations in the device. If such an event takes place in the adiabatic zone, the temperature of the vapour bubble will rise, depending on the adiabatic index of compression. In such a situation, if the process is fast enough, then there is more likelihood of the liquid film responding to the change in the vapour temperature than the adjoining bulk phase of the liquid plugs.

Considering the fact that non-equilibrium conditions exist inside the system, it is worthwhile to compare the heat transfer resistances experienced by the liquid film surrounding the bubble in getting the required heat of evaporation (or vice-versa). In general, the liquid thin-film essentially interacts with two elements, the vapour bubble Chapter 4 and the tube wall. In the adiabatic zone, it can exchange heat/mass to/from the vapour bubble. Inside the evaporator and the condenser, transport of heat can occur either with the wall or with the vapour bubble. As pointed out earlier, possibility of vapour bubble to have a higher temperature than the tube wall exists due to compression of its volume by the adjoining liquid plugs. In an analogous way, the vapour bubble can become cooler than the adjoining wall due to expansion 3 . This discussion suggests that, a situation where in a gradient between the wall temperature Tw and the vapour temperature Tv is generated, with the liquid film existing at a different temperature Tlf, should be occurring routinely in the transient operation of the PHP system.

Results and discussion

Thermal response time of liquid thin film

Let us consider the temperature in a cross-section of the tube between point states E and I (fig. Let us assume that the initial temperature of this film is equal to the temperature of the meniscus, which, in turn, can be considered as equal to the condenser temperature Tc as a first approximation, since the time response of the liquid slug is very small compared to the frequency of the meniscus motion. At this very first moment, the liquid film is bounded by the wall at temperature Tw and the vapour at temperature Tv. From the wall side, the liquid film is heated by thermal diffusion due to the strong temperature gradient between the wall and the liquid film. This diffusional heating is not instantaneous, but depends on the thermophysical properties of the liquid film and is guided by the unsteady heat diffusion equation. On the other side of the liquid film, the strong temperature gradient expected between the vapour and the liquid is likely to 3 While in the adiabatic zone, the adiabatic index of compression and expansion can be assumed to be valid for the vapor, it is not possible to ascertain the index of compression under diabatic conditions, in the evaporator or the condenser, wherein compression and/or expansion can take place simultaneously with heat addition/removal. Chapter 4 of the model. It has to be noted that the model can also be used in the condenser area to estimate the time scale of condensation. In that case, the temperature of the wall Tw is equal to Tc.

- π Δ γ γ ′ ′ ∂ ∂ ∂ ∂ α ρ Δ - - - π π α - ∞ π - π π - ρ Δ - π π ρ π α - ∞

Results and discussion

Film thickness variation during phase-change

In this section, we present simulations obtained with the analytical model presented above for the experimental conditions, namely Te = 55 °C, Tc = -3 °C and Pr = 0.42 bar, with FC72 as the working fluid in experimental setup as described in section 1 of chapter 3. Let us assume that the pressure of the vapour is equal to Pr as a first approximation.

In reality, the vapour pressure fluctuates around this value during one cycle (fig. 4

.4).

There are two main unknowns in the model: the initial thickness of the liquid film and the temperature of the vapour Tv, which is needed to calculate the liquid-vapour interface temperature Tlv. Let us assume that Tv ranges between Tw and Tsat (Pv). Within this range of vapour temperature, the interface temperature Tlv (eq. 4.10) is ranging between 33.2°C and 34°C. Thus, the superheating of the vapour does not have a strong influence on Tlv and we assume that Tv is equal to Tw in the following. Let us also assume that the temperature of the wall is equal to the temperature of the evaporator; the wall poses no thermal resistance. Fig. 4.13 presents the temperature field of the liquid film at different times assuming an initial film thickness equal to 50 µm. The vapour initially condensates until time t = 24 ms, after which the temperature gradient inside the film becomes negative enabling the evaporation of the liquid thin film to begin. Till that time, the thickness of the film has increased to 58 µm due to mass addition due to condensation of vapour. At time t = 93 ms, the thickness of the film reaches the initial thickness again, as a result of evaporation. Thus, a time delay of about 100 ms is necessary before the net evaporation of the film begins. This is not at all negligible since it represents 1/5th of the meniscus oscillation period. The liquid film gets totally evaporated at time t = 0.25 s, which represents about one half of the period. The results show that when the thickness of the film is doubled, the delay is multiplied by four. Thus, a very precise estimation of the initial liquid film thickness is required to accurately modeling the PHP behavior.

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Results and discussion

Temporal variation of liquid film thickness (δlf,i = 50 µm) at the conditions existing in the evaporator section of the present experiment for FC72 (Te °C and Pr = 0.42 bar).

shows the major influence of the film thickness on the time required to evaporate the film. Three initial liquid film thicknesses are compared: δ = 100 µm. Obviously, the time required to evaporate the film increases with the increase of δlf,i. The time period for which the initial phase of condensation prevails is equal to 24 ms, 54 ms and 100 ms, and the time period before is equal to 93 ms, 210 ms and 390 ms for initial film thickness = 75 µm and δlf,i = 100 µm, respectively. For the two last film thicknesses, the delay induced by the condensation is not compatible with the present = 55 °C, Tc = -3 °C and Pr = 0.42 bar) as the frequency is equal to 2 Hz. The next meniscus cycle will commence before the liquid film fully evaporates.

The results show that when the thickness of the film is doubled, the delay is multiplied hus, a very precise estimation of the initial liquid film thickness is required to accurately modeling the PHP behavior. shows the major influence of the film thickness on the time required to evaporate the film. Three initial liquid film thicknesses are compared: δlf,i = 50 µm, = 100 µm. Obviously, the time required to evaporate the film . The time period for which the initial phase of condensation prevails is equal to 24 ms, 54 ms and 100 ms, and the time period before is equal to 93 ms, 210 ms and 390 ms for initial film thickness = 100 µm, respectively. For the two last film thicknesses, the delay induced by the condensation is not compatible with the present as the frequency is equal to 2 Hz. The next meniscus cycle will commence before the liquid film fully evaporates.

The results show that when the thickness of the film is doubled, the delay is multiplied hus, a very precise estimation of the initial liquid film thickness is required to The physical mechanisms that control the thickness of the liquid film are similar to that encountered into dip coating problems, in whi to deposit a liquid film. In the case of a PHP, the tube is stable and the liquid moves but the principles are similar. These kinds of films are described as the Landau (Mayer et al. [4.22]) from the na problem in 1942. It has been shown that the thickness of the film depends on several non-dimensional numbers like the capillary number and the capillary length al. [4.22]). The geometry of the substrate as well as its wettability is also important parameters. Dip coating problems are still an active field of research nowadays. This is the literature that has to be explored to increase the knowledge on such films inside a PHP, but this is beyond the scoop of the present work.

The model presented in section phenomena at the condenser. In that case, the temperature of the wall is set to the condenser temperature (e.g.

-2015

Results and discussion

Influence of the initial thickness of the liquid film on its evolution from initial condition to the final state of complete evaporation. During the initial period the film becomes thicker as it experiences condensation of vapour on it The physical mechanisms that control the thickness of the liquid film are similar to that encountered into dip coating problems, in which a substrate is withdrawn from a bath, to deposit a liquid film. In the case of a PHP, the tube is stable and the liquid moves but the principles are similar. These kinds of films are described as the Landau from the names of the two authors who first reported on this problem in 1942. It has been shown that the thickness of the film depends on several dimensional numbers like the capillary number and the capillary length

The geometry of the substrate as well as its wettability is also important parameters. Dip coating problems are still an active field of research nowadays. This is the literature that has to be explored to increase the knowledge on such films inside a , but this is beyond the scoop of the present work.

The model presented in section 1.4.3 can also be used to study the heat transfer phenomena at the condenser. In that case, the temperature of the wall is set to the condenser temperature (e.g. -3°C in the conditions of the experiment).

144 Chapter 4 Influence of the initial thickness of the liquid film on its evolution from initial complete evaporation. During the initial period the film on it.

The physical mechanisms that control the thickness of the liquid film are similar to that ch a substrate is withdrawn from a bath, to deposit a liquid film. In the case of a PHP, the tube is stable and the liquid moves but the principles are similar. These kinds of films are described as the Landau-Levich flows mes of the two authors who first reported on this problem in 1942. It has been shown that the thickness of the film depends on several dimensional numbers like the capillary number and the capillary length (Mayer et The geometry of the substrate as well as its wettability is also important parameters. Dip coating problems are still an active field of research nowadays. This is the literature that has to be explored to increase the knowledge on such films inside a can also be used to study the heat transfer phenomena at the condenser. In that case, the temperature of the wall is set to the e conditions of the experiment). Fig. 4.16 Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - presents the temperature of the film for different times assuming an initial thickness of 50 µm. One can clearly see that the condensation rate is intense in the early stages and decreases subsequently as the film film increases, the condensation rate is lower than the evaporation rate. Nevertheless, as there is no delay at the condenser, at time needed to evaporate a film of thickness 50 µm), the increase of the film thickness is equal to 50 µm at the condenser. Thus, the mean rate of condensation is equal to the mean rate of evaporation, but the dynamics of both heat transfer processes are different, condensation process being more regular. This simple analysis can obviously not describe the entirety of the complex process of heat and mass exchange during the cycle of the an operating PHP. For instance, the above analysis tends to show that during any portion of the cycle, when the meniscus is in the evaporator, the thinnest portion of the liquid film is subject to evaporation while the thickest portion of the film is -2015

Results and discussion

presents the temperature of the film for different times assuming an initial thickness of 50 µm. One can clearly see that the condensation rate is intense in the early stages and decreases subsequently as the film thickness increases. As the thermal resistance of the film increases, the condensation rate is lower than the evaporation rate. Nevertheless, as there is no delay at the condenser, at time t = 0.25 s (which corresponds to the time lm of thickness 50 µm), the increase of the film thickness is equal to 50 µm at the condenser. Thus, the mean rate of condensation is equal to the mean rate of evaporation, but the dynamics of both heat transfer processes are different, s being more regular.

Temperature of the liquid film (δlf,i= 50 µm) at different time in the conditions of the experiment at the condenser. This simple analysis can obviously not describe the entirety of the complex process of heat and mass exchange during the cycle of the vapour bubble -liquid slug interface in an operating PHP. For instance, the above analysis tends to show that during any portion of the cycle, when the meniscus is in the evaporator, the thinnest portion of the liquid film is subject to evaporation while the thickest portion of the film is 145 Chapter 4 presents the temperature of the film for different times assuming an initial thickness of 50 µm. One can clearly see that the condensation rate is intense in the early stages and thickness increases. As the thermal resistance of the film increases, the condensation rate is lower than the evaporation rate. Nevertheless, as = 0.25 s (which corresponds to the time lm of thickness 50 µm), the increase of the film thickness is equal to 50 µm at the condenser. Thus, the mean rate of condensation is equal to the mean rate of evaporation, but the dynamics of both heat transfer processes are different, = 50 µm) at different time in the This simple analysis can obviously not describe the entirety of the complex process of liquid slug interface in an operating PHP. For instance, the above analysis tends to show that during any portion of the cycle, when the meniscus is in the evaporator, the thinnest portion of the liquid film is subject to evaporation while the thickest portion of the film is Chapter 4 simultaneously subjected to condensation (from the vapour) and evaporation (due to the heat flowing from the wall) that eventually results in net evaporation. Taking this observation into account, and the thermally thick character of the liquid film, it is imperative that a comprehensive treatment of the unit-cell is required for deeper understanding of the involved spatio-temporal phenomena. Alternately, just considering evaporation of the film is not sufficient, as part of the film may also be experiencing condensation due to the local spatial thermal non-equilibrium. From an experimental viewpoint, it is now clear that at least two new parameters should be measured as a function of time to describe quantitatively the mechanisms involved in the studied system: the time evolution of the vapour temperature and either the film shape/size or the time required for its evaporation. Proper video-recording could allow characterizing the film geometry and its time-dependant evolution, but measuring the vapour temperature with high time-resolution and with minimal perturbation certainly remains a challenge to be addressed in the future.

Results and discussion

Closing remarks

Self-sustained thermally-driven oscillations of a single meniscus can be obtained and efficiently sustained inside a capillary tube over long periods of time by maintaining a step thermal gradient over its length. Associated phase-change processes lead to thermo-mechanical instability in the system which generates continuous autooscillations of the meniscus. The amplitude of the oscillations not only depends on the temperature difference between the condenser and the evaporator, but also on their absolute temperature levels. Oscillations are quasi-periodic in nature for a range of imposed temperature gradients; they become more regular and periodic as this gradient decreases. In line with the recent literature (by this group of authors and others), maximum pressure in the vapour space does not occur when the liquid meniscus is at top of evaporator section; it occurs when the meniscus reaches the adiabatic section in the downward stoke while going from the evaporator to the condenser. During this downward motion of the meniscus, a liquid film is laid down on the tube wall and the very high net evaporation rate of this film contributes to rapid increase of the pressure in the vapour space.

The two processes of evaporation and condensation of vapour to/from the liquid film Chapter 4 and the meniscus respectively, may occur simultaneously during parts of the cycle.

Results and discussion

Net vapour mass flux is determined from the dominant mechanism out of these two.

Condensation of vapour mostly occurs on the liquid film inside the condenser section. A small amount of condensation is also observed on the moving meniscus.

For a given boundary condition, the film thickness and its length at a given time determines the overall dynamics of the meniscus. The results show that evaporation takes place at both, the triple-line and the liquid film interface, the continuation of the former mechanism being somewhat higher than the latter. The amount of vapour generated at the triple-line is significant and equal to more than 1/3 of the contribution of the liquid film evaporation. At the triple-line, the evaporation rate is nearly constant during one complete cycle while it depends strongly on the location of the meniscus inside the system for the liquid film evaporation. With average value of Capillary and Bond numbers, the initial film thickness estimated by Han and Shikazono [4.8], is in the range 80 µm to 90 µm. This is in reasonable agreement with the range predicted by our model (65 µm to 75 µm).

Most of the existing mathematical models fall short of predicting the entire thermohydrodynamics of pulsating heat pipes. While some do not include evaporation and condensation processes, others do not appreciate the dominant role of the liquid film in obtaining self-sustained oscillations. The intricate dependency of the net vapour pressure on simultaneous occurrence of evaporation and condensation is also not included by any of the models reported till date. Too, the occurrence of superheated vapour and the possibility of the existence of metastable phase behaviour need further exploration. The experiments reported here helps in understanding these critical issues and will contributed towards improved mathematical modelling of the entire PHP systems. Nevertheless, a predictive theoretical model of both the triple line and thin film evaporation is not easy to develop. It has to include the thermal inertia effects in both the wall and the liquid film, since the thermal problem is highly non stationary. Furthermore, the physics of the triple line -that has been widely studied in the literature -includes several unknown parameters that have to be taken into account (accommodation coefficient, disjoining pressure, contact angle).

The evaporation mass flux experienced in the vapour space is not only due to the Modeling of single branch PHP Chapter 5

Tube, evaporator and condenser

In the model of Das et al. [5.1], the tube is supposed to be a perfect thermal conductor and the evaporator and the condenser are considered as two perfect heat sources having a constant temperature Te and Tc. Therefore, the temperature of the tube is supposed to be constant in both the evaporator and the condenser and equal to the temperatures of the heat sources.

In the experiment, the temperatures at the evaporator and at the condenser are Modeling of single branch PHP eq. 5.2 and then merging it with eq. 5.3-5.7, it is possible to instantaneous differential pressure between reservoir pressure P pressure above the liquid slug in capillary P(t). The time required to evaporate the liquid film is equal to 3.2 s, while it lasts about 1.2 s during the experiment. Nonetheless, in the experiments, the film also evaporates at the triple line, which increases the amount of evaporation. Furthermore, one can see that the effect of hHS on the evaporation period is important. Yet, in the condition of the experiment, hHS varies all along the tube. It is higher at the bottom part of the evaporator, close to the adiabatic section than at the top of the evaporator. Indeed, in the experiments, the heating liquid arriving from the thermostatic bath enters into the evaporator heat exchanger perpendicularly to the tube, at the bottom of the evaporator. Therefore, at this location, the heat transfer coefficient is probably much higher than 200 W/m².K. Then, the liquid goes through the heat exchanger in parallel with the tube towards the top of the evaporator and as a consequence, the heat transfer coefficient decreases. Therefore, the liquid film evaporation is more efficient near the adiabatic section than inside the evaporator. One can conclude from this section that an accurate modeling of the liquid film requires a complete 2D modeling of the thermal system, taking into account the heat transfer between the heating fluid in the evaporator heat exchanger and the tube, and the heat diffusion in the tube and the liquid film. Indeed, both the thermal diffusivity of the tube and the heat transfer coefficient between the heat exchanger and the tube have an influence on the dynamics of the liquid film. In a real PHP, usually made of copper, the thermal diffusivity ( and in relation also the effusivity) of the tube would be much higher, leading to a different behavior as it will be explained in section 3 of this chapter.

Anyway, in the next section, the model of the liquid film is simplified using eq. 5.14 to reach some conclusions on the liquid plug, vapour slug and liquid film dynamics. The wall is supposed to be at a constant temperature Te with a constant heat transfer coefficient between the heat source and the saturation temperature of the vapour.

Liquid plug, vapour slug and liquid film dynamics

In this section, eq. 5.1, 5.2, 5.8, 5.11, 5.13 and 5.15 are solved and the results compared to the measurements of the vapour pressure, the meniscus oscillation and the liquid film dynamics presented in chapter four. The unknown heat transfer coefficients he,tl and he,lf are chosen so that the dynamics of the liquid film thickness and length fits with the experimental data presented in chapter 4. The sensitivity of the model to these parameters is important, as it will be shown in the parametric study. -2015

Modeling of single branch PHP

experimentally. This temperature is also the mean temperature of the wall calculated with the thermal model, which confirms the conclusions reached with this model.

Meniscus movement depending on the evaporator temperature.

omparison of meniscus and triple line dynamics and vapour = 37.5⁰C and the measurements. There is a good agreement he experimental and numerical results for both the liquid film and oscillation

The mean vapour pressure on one cycle is similar numerically and experimentally but the time variations are slightly different, which can be explained by the very simple modelling of the dynamics of the liquid film. For example, the numerical vapour pressure increases abruptly as soon as the liquid film is deposited on the wall, while experimentally this growth is smoother. This can be explained by the modelling of the liquid film evaporation. Numerically, evaporation of the liquid film begins as soon as the film is deposited on the wall, while the thermal model shows that there is a delay during which condensation on the film occurs. Therefore, during this delay, evaporation at the triple line is counterbalanced by this condensation phenomenon, which explains why the pressure does not increase so sharply in the experiments. Modeling of single branch PHP agreement between the numerical and experimental results. It is clearly visible that the heated conditions and the hypothesis of using ideal gas equation is within reasonable limits (this holds well as at given Pv, it is very less than the we also have moderate ∆P and ∆T).

present the temporal variation of the meniscus pressure for three cases of Tc (Tc = 16 °C, Tc = 20 °C and T for the sake of comparison with the experimental data presented in

The unknown heat transfer coefficients he,tl and he,lf are chosen so that the dynamic the liquid film thickness and length fit with the experimental data. One can observe the same behavior as in the experimental data: the amplitude of the oscillation in the condenser and the frequency of the oscillation increase with the increase of T As it was not possible to record the liquid film evaporation in the case of the The black curve is the meniscus oscillation calculated with heat transfer coefficients (he,tl = 8.638×10 6 W/m²K; he,lf = 3.212×10 3 W/m²K) chosen so that the dynamics of the liquid film thickness and length fits with the experimental data presented in chapter 4.

Influence of he,tl and he,lf and hc on the dynamics of the system

The blue and red curves are the meniscus oscillations obtained nullifying he,lf and he,tl, respectively. Therefore, the effect of each component on the shape of the oscillation can be evaluated. One can see that each phenomenon taken individually leads to an oscillation shape totally different with a frequency two times lower than the black curve.

This result shows that the dynamics of the film fully controls the oscillation parameters.

For the triple line, the heat transfer coefficient is huge. It however corresponds to standard values available in the literature (Stephan and Busse [5.2]). The heat transfer coefficient for the liquid film is twice the one calculated using the liquid film thermal conductance (he,lf ~ 1600 W/m²K with equation 5.21). It has to be noted that it is not possible to fit the experimental data using a smaller heat transfer coefficient for the Modeling of single branch PHP Chapter 5 liquid film. This result can be explained by the temperature of the wall which is probably underestimated. With a wall temperature Te = 38.4 °C, the same pattern (fig. 5.17) as with Te = 37.5 °C is obtained but the heat transfer coefficients are lower (h e,tl = 5.579×10 6 W/m²K; h e,lf = 1.605×10 3 W/m²K) and more coherent with the heat transfer model. A higher wall temperature leads to a smaller heat transfer coefficient. he,lf = 3.212×10 3 W/m²K; hc =800 W/m²K. Fig. 5.18 shows that it is possible to find another pair of heat transfer coefficients (he,tl = 7.348×10 6 W/m²K; he,lf = 7.273×10 3 W/m²K) that fit with the experimental data.

By comparison with fig 5.16, the shape of the oscillation is similar, but the heat transfer at the triple line is lower to compensate for the higher value of the heat transfer coefficient for the liquid film. This result also shows the complexity of the model.

Closing remarks

In this last chapter, numerical simulations have brought some new insights of the fundamental nature on the single branch Pulsating Heat Pipe, especially following:

The results show that the classical correlations used to calculate pressure drops inside the liquid plug in the model are relevant in the case of an oscillating flow.

The results confirm that the dynamics of the film is the most important parameter of the system and has to be modeled by taking into account the nature of the liquid but also the nature of the wall. Therefore, the heat transfer equation in the wall has to be solved and coupled to the hydrodynamic behavior of the system.

  vi

3. 1 .Fig. 1 . 2 Fig. 1 . 3

 11213 Fig. 1.2 Heat transfer coefficient attainable with natural convection, single-phase liquid forced convection and boiling for different coolants (Lasance [1.2]) Fig. 1.3 Typical heat pipe schematic Fig. 1.4 Schematic of typical pulsating heat pipe (Khandekar [1.3]) Fig. 1.5 Prototypes proposed by Akachi et al. [1.8] Fig. 1.6 Different configurations of PHP, (a) Closed end (b) Closed loop (c) Closed loop with check valve (d) PHP with open ends Fig. 1.7 Different flow regimes of PHP (Xu et al. [1.12]) Fig. 1.8 Thermodynamic cycle of PHP (Groll and Khandekar [1.14]) Fig. 1.9 Liquid slug in a PHP (Khandekar et al. [1.15]) 15 Fig. 1.10 Liquid slug in a PHP Fig. 1.11 Schematic of a Unit cell PHP (single tube: single vapour plugliquid slug)

Fig. 1 .

 1 Fig. 1.12 Lumped meniscus/wetting film model for the single-bubble PHP [1.34, 1.39, 1.40] and its key geometrical and physical parameters. The pressure at the right open end of the tube is imposed to the value Pext by connecting the tube to a large reservoir Fig. 1.13 Das et al. Setup in 2010 [1.34] Fig. 1.14Oscillations in the single bubble PHP (Das et al.[1.34]). Left: experimental measurement of the time evolution of meniscus position (x) and vapour pressure p (fig.1.12). The meniscus position curve is cut from the bottom because the evaporator and adiabatic sections are opaque so that the meniscus is invisible there. Right: numerical modeling of the meniscus position (x) vapour pressure (p), vapour temperature (T) and film edge position (xf)

1

 1 Fig. 2.2 (a) Schematics of an extended meniscus in unit cell PHP (b) A typical comparison of capillary and disjoing pressure obtained by numerical simulation for meniscus formed by water in a

Fig. 2 . 4 60 Fig. 2 .Fig. 2 .Fig. 2 . 77 Fig. 2 .Fig. 2 .experimental setup 1 -Fig. 3 . 2 Fig. 3 . 3 FigFig. 4 . 2 Fig. 4 . 6

 24602227722132334246 Fig. 2.4 Liquid slug in a PHP (Khandekar et al. [2.19]) Fig. 2.5 (a) Contact angle of a fluid on solid substrate (b) The moving meniscus seen on three different length scales (Khandekar et al. [2.19]) Fig. 2.6 (a) Contact angle hysteresis, (b) continuously varying physical and chemical in-homogeneity, and (c) sharp physical or chemical discontinuities at the surface (Khandekar et al. [2.19]) Fig. 2.7 Variation of apparent contact angle with Ca as per Tanner's law. Inset shows experimental data by Kavehpour et al. [2.29] Fig. 2.8 Variation of film thickness with Capillary number, as per five correlations mentioned therein Fig. 2.9 Possible configurations of the plugs/ meniscus under oscillatory motion (Tripathi et al. [2.44]) 60Fig. 2.10 Contact angle data superimposed on meniscus velocity, U, vs. time graph at an oscillating frequency of 0.5 Hz Shekhawat et al. [2.45] Fig. 2.11 Nomenclature and geometry used in molecular flux derivation (Carey [2.23]) Fig. 2.12 Modeling S* with regards to thin-film setup (Carey [2.23]) Fig. 2.13 (a) Experimental setup (top view) and details of capillary slot (b) Temperature distribution at the micro-region (Hoffman and Stephan [2.62]) Fig. 2.14 (a) Schematic representation of the experimental set-up of the VCVB heat exchanger, cross-sectional view of the top-corner of the cuvette showing liquid meniscus and the adsorbed thin film region and schematic of the micro-region (b) Evaporative heat flux profile at the liquid-vapour interface of the evaporating meniscus region, The solid-liquid and liquid-vapour interface temperature profiles in the evaporating meniscus region as a function of the meniscus length and surface tension variation with the evaporating meniscus region (Panchamgam et al. [2.63]) Fig. 2.15 (a) Experimental setup schematics (b) Infrared temperature maps of Ttop and Tbottom at a heat flux of 1190 W/m 2 and different evaporation rates for Image of heptane meniscus on

Fig. 4 . 8 Fig. 4 .Fig. 4 .

 4844 Fig. 4.8 Variation of Capillary number of the meniscus motion during one complete oscillation cycle Fig. 4.9 Comparison of the empirical scaling correlations for predicting the initial film thickness lay down by a moving meniscus inside a tube Fig. 4.10 Cumulated variation of vapour mass during one cycle separating four different contributions: Evaporation on the triple-line or on the liquid film in the evaporator and condensation on the liquid film or on the meniscus in the condenser (Te = 46ºC and Tc = 16ºC, first cycle) Fig. 4.11 Unit cell of single branch PHP Fig. 4.12 Thermal conductivity versus thermal diffusivity for a wide

Fig. 4 .Fig. 5 . 3 Fig. 5 . 5 Fig. 5 .Fig. 5 .Fig. 5 .Fig. 5 .Fig. 5 .Fig. 5 .

 45355555555 Fig. 4.15 Influence of the initial thickness of the liquid film on its evolution from initial condition to the final state of complete evaporation. During the initial period the film becomes thicker as it experiences condensation of vapour on it Fig. 4.16 Temperature of the liquid film (δlf,i= 50 µm) at different time in the conditions of the experiment at the condenser

Fig. 1 . 2 3 Chapter 1 phase

 1231 shows a function of the attainable heat transfer in terms of the heat transfer coefficient. A -2015 Introduction, Motivation and Background phase convection have been widely studied in the past and largely understood. However, there are many open issues, which need to be explored in multiphase flow devices because of occurrence of wide variety of flow patterns, of interfaces, contact line motion etc., which result in complex flow and heat transfer Keeping the area of research concentrated towards the heat pipes and more precisely towards pulsating heat pipes, first we will briefl phase passive cooling technology and then we will describe heat pipes in general and will move deep in to the pulsating heat pipes research history and challenges Range of heat transfer coefficients typically possible from various cooling technologies applied in contemporary thermal management systems (Lin et al. phase passive cooling technologies he operation of modern passive heat transfer devices is based on the combined action of three physical phenomena: phase-change, gravity and capillarity. phenomena are acting together but there may be some extreme conditions where capillary effects are negligible (i.e. thermosyphons) or gravity effects are less important shows a comparison of various cooling techniques as a function of the attainable heat transfer in terms of the heat transfer coefficient. A convection have been widely studied in the past and largely understood. However, there are many open issues, which need to be explored in multiphase flow devices because of occurrence of wide variety of flow patterns, presence of interfaces, contact line motion etc., which result in complex flow and heat transfer Keeping the area of research concentrated towards the heat will briefly discuss two describe heat pipes in general and challenges. various cooling Lin et al. [1.1]). he operation of modern passive heat transfer devices is based on the combined action change, gravity and capillarity. These three phenomena are acting together but there may be some extreme conditions where capillary effects are negligible (i.e. thermosyphons) or gravity effects are less important comparison of various cooling techniques as a function of the attainable heat transfer in terms of the heat transfer coefficient. A Introduction, Motivation and Background Chapter 1

Fig. 1 . 2 :

 12 Fig. 1.2: Heat transfer coefficient attainable with natural convection, single-phase liquid forced convection and boiling for different coolants (Lasance [1.2]).

Fig. 1 .

 1 Fig. 1.

Fig. 1 . 3 :

 13 Fig. 1.3: Typical heat pipe schematic.

Fig. 1 . 4 :

 14 Fig. 1.4: Schematic of typical pulsating heat pipe (Khandekar [1.3]).

  [1.5-1.7] patent the first of its kind of working pulsating heat pipe (PHP). The prototypes of Akachi are widely accepted and up till now exploited for further research (the actual pictures with the dimensions of such PHP are given in fig. 1.5).

Fig. 1 . 5 :

 15 Fig. 1.5: Prototypes proposed by Akachi et al. [1.8].

9 Chapter 1 completely

 91 Fig. 1.6: Different configurations of PHP with check

  (fig. 1.7). If the vapour bubbles are smaller than the diameter of the tube (a, b, c), the flow is said dispersed bubble; this corresponds to a low nucleation which continues to the evaporator. There is no coalescence effect and, most often, bubbles are condensed before reaching the condenser. When these bubbles become numerous, they can coalesce and form vapour pockets (f, g, h) or long bubbles. It is then intermittent regime compound vapour pockets called as liquid and vapour phases flow randomly inducing fluctuations in pressure and velocity. The length of the vapour pockets depends on the surface tension of the fluid bounded by pocket breaking phenom any more in contact with the wall; it forms a cylindrical channel, surrounded by a liquid ring. The flow is then said annular transfer occurs by both sensible heat and latent heat. Depending on the type of flow, one or the other of these transfer modes is dominant. The transfer with phase change is favored in the annular flow while the sensible heat is predominant i Yang et al. [1.13].

Fig. 1 . 7 :

 17 Fig. 1.7: Different flow regimes of

1 ,

 1 described it in general terms using a pressure/ enthalpy diagram as seen in fig. 1.8. The temperature and vapo 13 Chapter separated by liquid slugs. The r phases flow randomly inducing fluctuations in pressure and velocity. r pockets depends on the surface tension of the fluid and is When speed becomes high, the vapour is not any more in contact with the wall; it forms a cylindrical channel, surrounded by a liquid The work in the literature shows that the heat transfer occurs by both sensible heat and latent heat. Depending on the type of flow, one or the other of these transfer modes is dominant. The transfer with phase change is Taylor Bubble flow Although simple in their construction, PHPs become complicated devices when one tries thermodynamics driving PHP operation needs extinction of vapour bubbles drive the flow in a PHP. Even though the exact features of the thermodynamic described it in general terms using . The temperature and vapour quality in Introduction, Motivation and Background

Fig. 1 . 8 :

 18 Fig. 1.8: Thermodynamic cycle of PHP

r

  plugs moving in unison. tube. The liquid slugs are able to completely bridge the tube because surface tension forces overcome gravitational forces. There is a meniscus region on either end of each slug caused by illary dimensions of r bubbles having menisci on their edges is Introduction, Motivation and Background Chapter 1

Fig. 1 . 11 :

 111 Fig. 1.11: Schematic of a Unit cell PHP (single tube: single vapour plug

Fig. 1 . 1

 11 Fig. 1.1

1. 13 :

 13 Das et al. Setup in 2010 [1.34].Das et al. [1.34] has been compared with this single bubble experiment. The working fluid is n-pentane. The temperature Tc of the condenser 25 Chapter 1 was used to measure the time varying temperature of the vapour, which showed that the vapour plug tended to be superheated in this single branch PHP experiment. This is a been verified before, although it was proposed In 2010, Das et cell' version of a pulsating heat pipe consisting of one liquid plug and one vapour bubble. Their PHP and also the theoretical configuration was It consisted of a capillary tube closed at one end and connected to a reservoir at a constant pressure at the other end (fig. 1.13). A oscillate inside this tube, which was heated on one side and cooled down on the other side, thereby creating a continuous cycle of evaporation and condensation. The movement of the meniscus was recorded in the cooled section of the tube, while the heated section, made of copper, was has been compared with this single bubble of the condenser Introduction, Motivation and Background Chapter 1 section of the tube is controlled by a transparent heat exchanger in which a coolant (water) is circulating. A vapour bubble is confined by the liquid at the closed side of the tube. The meniscus oscillations occur depending on the experimental conditions. Their frequency was about 3 Hz and the meniscus dynamics was observed in the transparent condenser with a high speed camera; the pressure of the vapour plug was also monitored (fig 1.14, left). The comparison with a theoretical model shows a reasonable agreement (fig. 1.14, right), at least regarding the orders of magnitude and the general trend.

Fig. 1 . 14 :

 114 Fig. 1.14: Oscillations in the single bubble PHP (Das et al. [1.34]). Left: experimental measurement of the time evolution of meniscus position (x) and vapour pressure p (fig.1.12). The meniscus position curve is cut from the bottom because the evaporator and adiabatic sections are opaque so that the meniscus is invisible there. Right: numerical modeling of the meniscus position (x) vapour pressure (p), vapour temperature (T) and film edge position (xf).

  developed a simplified model based on the balance equations. This model conserves the main features of the multibubble PHP, the most important of which is the existence of self-sustained oscillations. This work shows a strong sensitivity of the modeling results to several parameters (or rather physical phenomena), on which the information is not yet available in the open literature. There is strong need to perform experiments (in particular those concerning the viscous dissipation) for a

  to single branch PHPs As discussed in the previous chapter, universal thermal performance modeling of Pulsating Heat Pipes (PHP) requires local, spatio-temporally coupled, flow and heat transfer information of self-sustained thermally-driven oscillating Taylor bubble flow, under different operating conditions. Local hydrodynamic characteristics such as velocities, lengths, shapes/profiles of bubbles/slugs, their dynamic contact angles, thickness of the liquid film that surrounds the bubbles, enhanced mixing/ flow circulation within the liquid slugs and net pressure drop along the flow, etc., are needed to predict local heat transfer methodology and thus the global thermal performance. Hence it is necessary to understand first, what are the parameters which are important in studying the local level or unit cell approach in a single branch PHP. The methods to define the nature and target continuum of the problem are not well defined in available open literature. Hence here we are trying to prepare a state of the art using the related knowledge available in this field. To start with, let us go insight in the thermo-physical parameters involved in working of a single branch PHP and later we will see the issues and their solution methodologies.

Fig. 2 . 2 : 1 . 2 . 1 . 2 (

 221212 Fig. 2.2: (a) Schematics of an e comparison of capillary and disjoing pressure meniscus formed by water in a micro increasing when move towards higher values of

  distribution can take up variety particular flow pattern depends on the and heat flux if the channel is heated and mass in two-phase flow conditions phases in the channel. It is therefore successive flow patterns are appropriate to that pattern can be chosen. upwards co-current flows are shown schematically in [2.18]).

Fig. 2 . 3 :

 23 Fig. 2.3: The flow patterns encountered in vertical upwards co

Fig. 2 . 4 :

 24 Fig. 2.4: Liquid slug in a PHP

1 i

 1 .e., in the presence of the terrestrial gravity field, when the channel diameter reduce at least down to millimeters or µ meters.-2015Literature review entrapped between liquid slugs) is observed which are flow pattern found in PHPs (as shown in fig.2.4). Slug flow belongs to a class of intermittent flows that has very typical features. There is an inherent constituent for such a flow because of intermittent phase reversal which results in fluctuations of pressure and velocity. The nose of the bubble has a characteristic spherical cap and the gas in the bubble is separated from the pipe wall by a slowly descending film of liquid. The liquid flow is contained in liquid slugs which separate successive gas bubbles. These slugs may or may not contain smaller entrained gas bubbles carried in the wake of the large bubble. The length of the main gas bubble . The two-phases may be composed of an either gas component system or single component, vapour-liquid system. Capillary slug flow or is one of the sub-classes of conventional slug flow; as noted, this pattern appears when surface tension dominates over gravitational body . Due to this, capillary slug flows exist in horizontal as well as in vertical orientations. Also, flow is essentially laminar and predominantly viscous : Liquid slug in a PHP (Khandekar et al.[2.19]).

2 )

 2 i.e., in the presence of the terrestrial gravity field, when the channel diameter reduce at least down to[START_REF] Cooper | The microlayer in nucleate pool boiling[END_REF] Chapter is observed which are also . Slug flow belongs to a features. There is an inherent for such a flow because of intermittent phase reversal of the bubble has a characteristic spherical cap and the gas in the bubble is separated from the pipe wall by a slowly descending film of liquid. The liquid flow is contained in liquid slugs which t contain smaller entrained gas bubbles carried in the wake of the large bubble. The length of the main gas bubble phases may be composed of an either gas-liquid twopillary slug flow or classes of conventional slug flow; as noted, this pattern appears when surface tension dominates over gravitational body ell as in vertical orientations. Also, flow is essentially laminar and predominantly viscous (Khandekar Taylor slug flow conditions are typically characterized by a sequence of long bubbles he diametrical size of these bubbles is nearly comparable to the pipe diameter while their axial length scale can be several imes the pipe diameter. A thin liquid film always separates the bubbles from the channel wall. The thickness of this film varies from millimeter scale to micro scale i.e., in the presence of the terrestrial gravity field, when the channel diameter reduce at least down to

  2.5-b (Khandekar et al. macroscopic viewpoint, wherein the length scale is of the order of capillary radius (or the droplet radius, in case of spreading droplets), the angle which the liquid interface makes with the liquid-solid interface is termed as the apparent co 48 Chapter 2 intermolecular forces. Depending on this equilibrium contact angle, solid substrates, for range for various types of fluids Schematic also made up of tubes which are real time engineering both physically and chemically heterogeneous. Therefore, efforts are needed to restore to systematic experimental work to get the real picture of actual contact angles. processing of the data, there are two re related issues which need careful consideration (i) 'Apparent' nature of the contact ine manifests a dramatic change gas interface makes with the Khandekar et al. [2.19]). From a macroscopic viewpoint, wherein the length scale is of the order of capillary radius (or the droplet radius, in case of spreading droplets), the angle which the liquid-gas apparent contact θ θ Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0080/these.pdf © [M. Rao], [2014], INSA de Lyon, tous droits réservés

-

  Fig. 2.8: Variation of film thickness with Capillary number, as per five correlations

Fig. 2 . 9 :Fig. 2 . 10 :

 29210 Fig. 2.9: Possible configurations of the plugs/ meniscus under oscillatory motion

Fig. 2 .

 2 Fig. 2.10 represents the evaluation of the meniscus velocity and the contact angle. The contact angle and the velocity display coherent oscillations.

2

 2 e. The local wall heat transfer varies significantly along the meniscus base. The advancing contact region shows the highest heat transfer due to transient conduction in the liquid from the heated wall. The wall heat transfer coefficient is found se with increase in wall velocity and the advancing contact angle but remains 61 Chapter It was seen that the advancing contact angle was more than represents the evaluation of the meniscus velocity and the contact angle. The contact angle and the velocity display coherent oscillations. ontact angle data superimposed on meniscus velocity U vs. time graph at an on adiabatic oscillations of menisci also brought to the fore the importance of dynamic contact angle in the Taylor bubble flows and the dissymmetry between the advancing and receding contact receding meniscus plays

  order to understand the oscillatory flow pattern in PHP, it is essential to model the simultaneous phase change heat and mass transfer in Taylor-Bubble flows in small scale channels. Magnini et al.[2.53] stated that Taylor Bubble flow is efficient heat transfer mechanism because of recirculating flows within liquid slugs, evaporation of thin liquid film surrounding the bubble and presence of large interfacial area which enhance heat and mass transfer. They performed a numerical study of the hydrodynamics and heat transfer of elongated Taylor Bubble in a microchannel. Their numerical results reveal that the bubble shows an exponential time-law growth which is in agreement with theoretical models. Also, thin-film evaporation is the dominant heat transfer mechanism in the liquid film region between the wall and bubble while convection is found to strongly enhance the heat transfer in the intrinsic meniscus region. Recently the importance of Taylor bubble flows in enhancing the heat transfer characteristics is recently shown byMehta [2.54]. He found that injection of Taylor bubbles provides an efficient means of heat transfer enhancement, up to 1.2 to 2.0 times, as compared to fully developed laminar single-phase liquid flow. While in many systems, capillary flows are uni-directional in nature or are employed in this way, there are many instances where the flow is either oscillating or pulsating in nature, as in the case of PHPs. These oscillations/ pulsations may be externally controlled, thermally driven or alternatively an effect of the dynamic instabilities which are inherent part of two-phase boiling/ condensation systems. There is scarcely any work on oscillatory Taylor bubble flows. So it is important to see the factors affecting heat transfer characteristics of extended meniscus and available solution methods. While at the scale of thin films, PHPs are always governed by transient phenomena, most of the literature available is focused on single Taylor Bubble growth during flow boiling without accounting for heat transfer in the micro-layer near the liquid-gas-solid three phase contact region.

Fig. 2 . 2 Fig. 2 . 2 Fig. 2 .Fig. 2 . 2 s

 2222222 Fig. 2.13: (a) Experimental setup (top view) and details of capillary slot (b) Temperature distribution at the micro

Fig. 2 .Fig. 2 . 17 :

 2217 Fig. 2.16 shows their experimental setup and underneath the meniscus at different input heat fluxes and linear local heat flux distribution for different input heat fluxes.

Fig. 2 .

 2 Fig. 2.19: (a) Experimental setup schematics (b) temperature and % of heat transfer at various regions

( a ) 1 . Experimental setup 1 :

 a11 Thermal dynamics of the simplest version of PHP, namely the single branch PHP: The first experimental set-up is designed to give us the understanding of the heat transfer mechanism inside a single-branch PHP along with the better insight to the thermally-driven self-sustained meniscus oscillations. This insight information obtained can lead us to the dynamics of thin film and its behaviour. This will enable to move closer to the governing physics of oscillating phase change systems like PHPs. (b) Hydrodynamics of the meniscus inside the capillary: The second experimental setup is designed to obtain the hydrodynamics behavior of different oscillating fluids inside a capillary tube by controlling the flow by external pressure variations in adiabatic condition. Mainly this setup is designed to estimate single phase frictional pressure drop and to observe contact line motion in oscillating conditions for various fluids. Thermal dynamics of the simplest unit cell of PHP As discussed earlier in chapter 1, in 2010, Das et al.[3.1] presented the first experimental data of the simplest 'unit-cell' version of a pulsating heat pipe. This system consisted of a 2.0 mm ID capillary tube, heated on one end and cooled on the other end, with one liquid plug and one vapour bubble. They were able to obtain thermally-driven

3 . 1 ,Fig. 3 . 1 :

 3131 Fig. 3.1: Schematics of experimental setup 1

  Fig. 3.1: Schematics of experimental setup 1-Thermal dynamics of the simplest unit cell of PHP.

Fig. 3 . 2 : 1 Fig. 3 . 3 :

 32133 Fig. 3.2: Photograph of experimental setup 1

Fig. 3 . 4 :

 34 Fig. 3.4: (a) Typical image from camera 1 of the complete unit cell PHP with meniscus (b) Schematic image from the camera 2 of the

Fig. 3 . 4 :

 34 Fig. 3.4: (a) Typical image from camera 1 of the complete unit cell PHP with meniscus (b) Schematic image from the camera 2 of the thin liquid film and triple line

Fig. 3 . 4 :

 34 Fig. 3.4: (a) Typical image from camera 1 of the complete unit cell PHP with meniscus thin liquid film and triple line.

Fig. 3 .Fig. 3 . 6 : 3 :

 3363 Fig. 3.7 shows the actual photograph of the experimental setup. To quantify the validity of standard frictional pressure drop correlations in such case of oscillatory motion of

  Fig. 4.1 Schematics of the various possible cases of contact line behaviour

Fig. 4 . 2 :

 42 Fig. 4.2: Represents the adiabatic experimental results the triple line with respect to meniscus motion in a capillary and thus corresponds to the partial pinning of contact line

Chapter 4 ionized

 4 water, motion of the triple line with respect to meniscus motion in a capillary and thus corresponds to the responsible for the non Similarly in the adiabatic experiments of the FC72, Ethanol and Pentane it is not able to visualize the triple line the contact line behaviour of these fluids. But as in the heat transfer experiments we saw the motion of the triple line for efer section 1.2 below), so we feel it is can be a case of full pinning, and also is not visible for Pentane heat transfer experiments induced oscillations, hence it may be a case of full pinning. As induced oscillations are triple line movement in adiabatic

Fig. 4 . 3 : 4 :

 434 Fig. 4.3: Temporal variations of pressure (right ordinate axis) in the vapour bubble along with location of meniscus (left ordinate axis, solid line) and triple ordinate axis, dotted line) for experimental condition of T (b) Tc = 20ºC, (c) T

  4.3-a to d), shows the decrease of its amplitude with the decrease of the difference between Te and Tc. The maximum of amplitude varies from 0.16 bar to 0.06 bar, when Tc varies from 16ºC to 28ºC, respectively. The oscillatory behaviour of the meniscus can be directly and definitely linked with the nature of the liquid film laid by the meniscus while coming down from evaporator. This phenomenon is explained in details in fig. 4.4-a where the boundary conditions are Te = 46ºC and Tc = 20ºC. Time evolution of the meniscus from the evaporator (Stage A) as it passes towards the condenser (Stage J) and comes back to the evaporator (Stage T) Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - is shown. Fig. 4.4-b is a typical temporal variation of pressure in the vapour bubble and movement of triple-line depicting several steps of the meniscus motion along with different stages in one cycle (A to T).

Fig. 4 . 4 :

 44 Fig. 4.4: (a) Schematic explaining the events during one cycle of the meniscus motion. (b) Time evolution of the meniscus from the entrance passes towards the condenser (Stage J) and comes back to the evaporator (Stag shown. The four zones

Fig. 4 . 4 :

 44 Fig. 4.4: (a) Schematic explaining the events during one cycle of the meniscus motion. (b) Time evolution of the meniscus from the entrance in the evaporator (Stage A) as it passes towards the condenser (Stage J) and comes back to the evaporator (Stag shown. The four zones are also highlighted (will be used in section 1.4.1).

Fig. 4 .

 4 Fig. 4.4-b represents the time-evolution of the meniscus location and corresponding variation of vapour pressure during a period of 1.6 seconds. In addition, the location of the moving triple-line, i.e., the edge of the liquid film on the channel wall, is also displayed on this figure. It is clearly visible that the liquid film motion always lags

Fig. 4 . 5 :

 45 Fig. 4.5: Temporal variations of pressure (right ordinate axis) along with temperature in the vapour bubble and saturation temperature Tsat = f(P condition of Te = 46ºC and T

Fig. 4 . 6 :Fig. 4 . 7 :

 4647 Fig. 4.6: Temporal variations of location of triple-line (left ordinate axis, dotted line) and mass of vapour (right ordinate axis) calculated using ideal gas equation ( Tc = 20ºC, (c) Tc =24ºC,, and (d) the vapour tem

Chapter 4 :

 4 Temporal variations of location of meniscus and film thickness variation c = 16ºC, 20ºC

-

  Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0080/these.pdf © [M. Rao], [2014], INSA de Lyon, tous droits réservés Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - area in fig. 4.8, the average value of Ca is 0.021. With average value of Bo = 1.72 in this zone, the initial film thickness estimated by This is within reasonable range of what was earlier predicted by the model described in section 1.4.3, i.e., ~ 69 µm.

Fig. 4 . 8 :

 48 Fig. 4.8: Variation of Capillary number of the meniscus motion during

, 4 ,

 4 Fig. 4.9: Comparison of the empirical scaling correlations for predicting the initial film thickness lay

Fig. 4 . 10 : 2 .Results and discussion Chapter 4

 41024 Fig. 4.10: Cumulated variation of vapour mass during one cycle separating four different contributions: Evaporation on the triple-line or on the liquid film in the evaporator and condensation on the liquid film or on the meniscus in the condenser (Te = 46ºC and Tc = 16ºC, first cycle).

diameter 2 .Fig. 4 .

 24 Fig. 4.

  phase and the solid phase (tube material), having drastically different thermal diffusivities are interacting with each other at all times. In fact, the difference in their respective thermal response, as against the inertia of the working fluid, eventually leads to the oscillating motion inside the device. Estimating the typical characteristics time 133 Chapter 4 scale of the liquid slug (δl) and vapour , scales with the radius of the PHP tube, as a first order approximation. The vapour bubble can be . The characteristic The thermal response of a material to a change in temperature is indicated by its compares the thermal conductivity to thermal diffusivity . The data points noted as condensed matter (liquids and solids) can be described as being near a straight line. As it can be noted, with respect to thermal diffusivity, gases are quite different as compared to the condensed matter. With respect to the transient nature of heat transfer vapour phase, liquid phase and the solid phase (tube material), having drastically different thermal diffusivities are interacting with each other at all times. In fact, the difference in their id, eventually leads to the oscillating motion inside the device. Estimating the typical characteristics time Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - scales of these three interacting sub summarizes the typical values of the characteristic characteristic frequency of response of the different elements of the unit estimated for a copper tube filled with water and for the glass tube filled with FC72, as in the present experiment.

Fig. 4 . 12 :

 412 Fig. 4.12: Thermal conductivity versus thermal diffusivity for a wide variety of homogeneous materials (closed circles open squares-polymers; open circles

. 2 summarizes

 2 the typical values of the characteristic time scale and the corresponding characteristic frequency of response of the different elements of the unit estimated for a copper tube filled with water and for the glass tube filled with FC72, as in conductivity versus thermal diffusivity for a wide variety of homogeneous materials (closed circles-metals; squares-ceramics; triangles polymers; open circles-liquids; and crosses-gases) (Salazar [4. If the frequency of any external thermal change imposed on the boundary of these elements exceeds the respective characteristic frequency of the element under consideration, such perturbation information will, in principle, remain largely isolated from the concerned element of the unit-cell. Considering the fact that typical PHPs operate with dominant oscillating frequencies between 0-5 Hz (Khandekar et al. [of interest. Table 4.2 time scale and the corresponding characteristic frequency of response of the different elements of the unit-cell, as estimated for a copper tube filled with water and for the glass tube filled with FC72, as in conductivity versus thermal diffusivity for a wide variety of ceramics; triangles-glasses;

  4.4), wherein the downward motion of the meniscus has just commenced from the evaporator. As has been clearly seen in the experiments and explained in the previous section, a thin liquid film is laid down and remains on the tube wall as the meniscus moves in the downward stroke. The liquid film is bounded by the tube wall on one side and compressed vapour on the other side, as detailed in the unit-cell description of fig.4.11.

Fig. 4 . 13 : 4 =

 4134 Fig. 4.13: Temporal variation of the liquid film thickness (δ corresponding temperature at the conditions existing in the evaporator se present experiment for FC72 (T

143 Chapter 4 =

 4 50 µm) at the conditions = 55 °C, Tc = -3

Fig. 4 . 15 :

 415 Fig. 4.15: Influence of the initial thickness of the liquid film on its evolution from initial condition to the final state of becomes thicker as it experien

Fig. 4 . 16 :

 416 Fig. 4.16: Temperature of the liquid film ( conditions of

Chapter 5 Modeling

 5 This section presents the thermo vapour plug and a liquid slug oscillating in a tube closed at reservoir at a constant pressure P were already presented in Das et al.chapter to take into account the peculiarities of the new experimental set improve the liquid film evaporation model in the light of the experimental results. In particular, the equations of the model are developed for the syste orientation, while in Das et al.[5.1] discuss the results obtained using this model in comparison with the experimental results obtained in chapter 4. Also implications of the various factors on the working of such system.

Fig. 5

 5 Fig. 5.1: Geometrical prop

  controlled by two heat exchangers connected to a thermostatic bath of controlled temperatures Te and Tc. Therefore, the real boundary condition at the outside periphery of the tube is a Fourier boundary condition between the wall and the heating fluid at temperature Te or the cooling fluid at temperature Tc. The heat transfer coefficients depend on the cooling or heating fluid properties inside the two heat exchangers as well as the heat exchanger geometry and the velocity of the fluid within it. Inside the tube, the saturation temperature is imposed at the liquid-vapour interface and the liquid film thickness and the temperature of the film are both functions of time. Therefore, the temperature field inside the tube is also a function of time and the transient heat transfer equation has to be solved to take into account both the heat transfer within the tube and the liquid film and the thermal inertia of the system.A thermal model has been developed in order to evaluate the influence of the nature of the tube and of the heat exchanger on the temperature of the tube and the rate of evaporation. This model does not take into account the triple line, but only the liquid film. It is an extension of the analytical model developed in chapter 4 for the liquid film, which takes into account the tube, the heat exchanger and a variable saturation temperature at the liquid vapour interface of the liquid film.

Fig. 5 . 3 Fig. 5 . 4 :

 5354 Fig. 5.3 shows the equivalent electrical representation of the transient thermal model of the system at time j. The tube and the liquid film are discretized in ntb and nlf nodes of temperature T j tb,z and T j lf,z respectively and are separated by equivalent thermal

  meniscus location and the experimental instantaneous differential pressure drop are plotted for FC72 (fig 5.4 (a) and (b)) and for Pentane ( (c) and (d)). On the same figure, the theoretical pressure drop including all components is also plotted. temporal variation of analytical and experimental for the single phase liquid oscillating inside a capillary tube of 2mm al , where (a) for fluid FC72 oscillating at 1 Hz (b) for fluid FC72 or fluid pentane oscillating at 1 Hz (d) for fluid pentane -axis represents the location of meniscus in capillary tube, closest location to reservoir during the oscillation) 164 Chapter 5 it is possible to find instantaneous differential pressure between reservoir pressure Pr(t) and s differential pressure drop (a) and (b)) and for Pentane (fig 5.4 drop including all components analytical and experimental pressure drop for the single phase liquid oscillating inside a capillary tube of 2mm along with the or fluid FC72 or fluid pentane axis represents the location of meniscus in capillary tube, during the oscillation). Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France - Modeling A good agreement is observed shows that classical correlations used to calculate pressure drops inside the liquid plug are relevant in the case of an oscillating flow the pressure drops adds a time and slightly increases the amplitude of the pressure variation.

Fig. 5 . 5 :ρ

 55 Fig. 5.5: Comparison of three components contributing in theoretical pressure drop across the tube length Lt (i) Instantaneous momentum of the liquid slug and (iii) Shear term (Fτ) for oscillating at 1.5 Hz (c) For fluid pentane oscillating at 1 Hz (d) For fluid pentane

Fig. 5 .

 5 Fig. 5.7 presents the flow rate of evaporation of the liquid film versus time for the three value of hHS. Initially, the liquid film thickness increases due to the condensation of the vapour on the cold liquid as it was already observed in the analytical model developed in chapter 4. Then, the evaporation of the liquid film increases with the increase of the time. This result confirms that liquid film evaporation is not a linear function of time.

Fig. 5 . 7 :

 57 Fig. 5.7: Flow rate of evaporation of the liquid film.

  Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0080/these.pdf © [M. Rao], [2014], INSA de Lyon, tous droits réservés Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France -2015 169 Modeling of single branch PHP Chapter 5

Fig. 5 . 8 Fig. 5 . 8 :

 5858 Fig. 5.8 shows the meniscus location v/s time for different temperatures of the wall: (Te = 37.5 °C, Te = 38 °C, Te = 40 °C and Te = 46 °C), the temperature of the condenser being equal to 16 °C. The fluid is FC72 and the pressure of the reservoir is equal to 0.5bar. The geometrical parameters are the same as in the experiment. The heat transfer coefficient at the condenser is supposed to be equal to 800 W/m².K, following the same assumption as in chapter 4. One can see that the oscillation pattern obtained by the model is close to that measured experimentally. Depending on the temperature of the evaporator Te, the frequency of the oscillation and its amplitude are different, both the frequency and the amplitude increasing with the increase of Te. For a temperature of the evaporator Te = 37.5 °C, the frequency and the amplitude are similar to that observed

Fig. 5 .

 5 Fig. 5.9 shows a comparison of meniscus between the model with Te = 37.5 between the experimental and numerical resultsdynamics. The mean vapour pressure on one cycle is similar numerically and experimentally but the time variations are slightly different, which can be explained by the very simple modelling of the dynamics of the vapour pressure increases abruptly as soon as the liquid film is deposited on the wall, while experimentally this growth is smoother. the liquid film evaporation. Numerically, the film is deposited on the wall, while the thermal model shows that there is a delay during which condensation on the film occurs. Therefore, during this delay, evaporation at the triple line is counterba why the pressure does not increase so sharply

(fig. 5 .ModelingFig. 5 . 9 :Fig. 5 . 10 :

 559510 Fig. 5.9: Comparison of meniscus movement, triple line movement and for Te = 37.5⁰C (in thermal model) and T Tc = 16⁰C, Pr = 0.5 bar, for similar dimensions as described in chapter 3 experimental setup 1. he,tl = 7.348×10

Fig. 5 .

 5 Fig. 5.11 to fig. 5.13 present dynamics, and vapour pressure for three cases of 24°C) for the sake of comparison with the experimental data presented in The unknown heat transfer coefficients h the liquid film thickness and length fit with the experimental data same behavior as in the experimental data: the amplitude of the oscillation in the condenser and the frequency of the oscillation increase with th

Fig. 5 . 11 :

 511 Fig. 5.11: Meniscus movement, triple li Te = 37.5 ⁰C and Tc = 16 °C,

Fig. 4 .Fig. 5 . 13 :Chapter 5 Fig. 5 .

 451355 Fig. 4.6-d, with Tc = 28 °C, it is also not possible to unknown heat transfer coefficients he,tl and he,lf using the same procedure. Nonetheless, provided in the next section to show the influence of the heat transfer coefficient on the dynamics of the system.

Fig. 5 .

 5 Fig. 5.16 presents the effect of he,tl and he,lf on the dynamics of the meniscus. The conditions are the same as in fig 5.9 (Te = 37.5⁰C; Tc = 16⁰C; Pr = 0.5 bar, fluid FC72).

Fig. 5 . 16 :

 516 Fig. 5.16: Meniscus dynamic for Te = 37.5 ⁰C and Tc = 16 ⁰C; he,tl = 8.638×10 6 W/m²K;

Fig. 5 . 17 :

 517 Fig. 5.17: Meniscus movement, triple line movement and vapour pressure with Te = 38.4 ⁰C; Tc = 16 °C; he,tl = 5.579×10 6 W/m²K; he,lf = 1.605×10 3 W/m²K; hc =800 W/m²K.

Fig 5 .

 5 Fig 5.19 shows the effect of the condensation heat transfer coefficient on the oscillation shape. Increasing the condensation heat transfer decreases the frequency and the amplitude of the oscillation inside the condenser and increases the amplitude inside the evaporator.

Fig. 5 . 19 :

 519 Fig. 5.19: Meniscus dynamic depending on the condensation heat transfer; Te = 37.5 ⁰C, Tc = 16 ⁰C; he,tl = 7.348×10 6 W/m²K; he,lf = 7.273×10 3 W/m²K.

  1 Pentane results (meniscus location cannot be tracked completely because it was beyond the range of camera)

	ext IRT	External Infra red thermography
	HS LV	Heat sink or heat source Liquid-Vapour
	hyd OD	Hydraulic Outer diameter
	i OHP	Initial Oscillating heat pipe
	int PHP	Interface Pulsating heat pipe
	l SL	Liquid Solid-Liquid
	lf SS	Liquid film Stainless steel
	lv SV	Liquid-Vapour Solid-Vapour
	max TC	Maximum Thermocouple
	meas TV	Measured Television
	mol TLC	Molecular Thermochromic liquid crystal
	p th	pressure Theoretical
	r µTC	Reservoir Micro thermocouple
	res	Residing
	reg	Regular
	s	Slug
	sl	Solid-Liquid
	so	Dry solid surface
	st	Static
	sv	Solid-Vapour
	sat	Saturated
	sens	Sensible
	sign	Singularity
	t	Total
	tb	tube
	th	Theoretical
	tl	Triple line
	v	Vapour
	w	Wall
	z	Constant
	Abbreviations
		Definition
	B/W	Black and white
	CCD	Charge-coupled device
	cond	Condensing
	CETHIL	Centre d'Energétique et de Thermique de Lyon
	CLOHP/CV	Closed loop oscillating heat pipe with checked valves
	DC	Direct current
	DVD	Digital video disk
	Diff	Differential
	eq	Equation
	HP	Heat pipe
	HS	Heat source or Heat sink
	ID	Internal diameter
	IR	Infra red
		xix xx

1 Chapter 1

Introduction, Motivation and Background Chapter 1

		Chapter 1
	-liquid slug).
	actively studied
	The evaporation in the constrained bubble geometry is studied in
	. The dewetting in capillaries is
	. The oscillation of bubbles at isothermal
	. However, the conjunction of . However, the conjunction of
	phase change and oscillating dynamics introduces new challenges. Some of them are phase change and oscillating dynamics introduces new challenges. Some of them are
	in particular with the oscillations in a capillary in isothermal in particular with the oscillations in a capillary in isothermal
	]. A first experiment of visualization of self-sustained oscillation of sustained oscillation of
	liquid meniscus in a capillary with evaporation/condensation was	performed by
	. It permitted to determine the main factors that de . It permitted to determine the main factors that determine the
	number of works dealing with the physical phenomena number of works dealing with the physical phenomena
	occurring in the PHP (with PHPs of 1-2 bubbles) has remarkably increased creased [1.32-1.36].
	This shows an acknowledgement by scientific community of the necessity of This shows an acknowledgement by scientific community of the necessity of
	fundamental studies related to the PHP. Research at the local scale (i.e. at the scale of fundamental studies related to the PHP. Research at the local scale (i.e. at the scale of
	one bubble and one liquid plug), although few, were addressed quite early, in order to one bubble and one liquid plug), although few, were addressed quite early, in order to
	augment the knowledge on basic phenomena which are responsible for the oscillations augment the knowledge on basic phenomena which are responsible for the oscillations
		21

Introduction, Motivation and Background r

  equilibrium and the mass exchange was proportional to the difference of temperatures of the vapour and the wall, just like in the other works that id not treat the films at all. The single-bubble model of Zhang and Faghri[1.

	Chapter 1 Introduction, Motivation and Background Chapter 1
	r equilibrium and the mass exchange was proportional to the scale modeling has been extended to several PHP branches with many liquid plugs and
	vapour bubbles [1.41-1.46].	r and the wall, just like in the other works that
		Zhang and Faghri [1.37] has
	taken a step forward by rigorously showing that the most part of heat and mass most part of heat and mass As was noted earlier, exhaustive mathematical modeling of the phenomena occurring
	exchange occurs via the films in the PHP. The shape of the curved meniscus including exchange occurs via the films in the PHP. The shape of the curved meniscus including inside a PHP is yet an unaccomplished task. The models which are available for pressure
	It is felt that to understand the working of the unit cell PHP It is felt that to understand the working of the unit cell PHP drop and heat transfer coefficients are indeed very much simplified; they not only ignore
	it is eminent to understand the thin film behavior in two phase heat and mass transport it is eminent to understand the thin film behavior in two phase heat and mass transport the complex physics of the 'unit-cell', but the singular characteristics of oscillating
	Globally, the existing models describe oscillations of small amplitude Globally, the existing models describe oscillations of small amplitude. During hydrodynamics of Taylor bubbles also remain completely unaddressed.
	This means these oscillations, the meniscus is located mostly in the condenser section. This means these oscillations, the meniscus is located mostly in the condenser section. This means 3.2
	basically that the evaporation in s basically that the evaporation in such models is almost inexistent, which uch models is almost inexistent, which contradicts
	most experimental results where strong amplitude meniscus oscillations ar most experimental results where strong amplitude meniscus oscillations ar most experimental results where strong amplitude meniscus oscillations are observed.
	At each oscillation the meniscus sweeps both the condenser and evaporator. These At each oscillation the meniscus sweeps both the condenser and evaporator. These At each oscillation the meniscus sweeps both the condenser and evaporator. These
	limitations have been successfully overcome within a film evaporation/condensation limitations have been successfully overcome within a film evaporation/condensation limitations have been successfully overcome within a film evaporation/condensation
	model Das et al. [1.34]. It uses the lumped meniscus geometry ( . It uses the lumped meniscus geometry (fig. 1.12 2) and accounts
	for the two-phase equilibrium at the vapo phase equilibrium at the vapour-liquid interface. It explains large liquid interface. It explains large
	amplitude oscillations. An analytical expression describing the oscillations in the single amplitude oscillations. An analytical expression describing the oscillations in the single amplitude oscillations. An analytical expression describing the oscillations in the single-
	bubble PHP in the horizontal position has been established. bubble PHP in the horizontal position has been established.
	Fig. 1.12: Lumped meniscus/wetting film model for the single Lumped meniscus/wetting film model for the single-bubble PHP bubble PHP
	[1.34, 1.39, 1.40] and its key geometrical and physical parameters. The pressure at the ] and its key geometrical and physical parameters. The pressure at the ] and its key geometrical and physical parameters. The pressure at the
	right open end of the tube is imposed to the value P right open end of the tube is imposed to the value Pext by connecting the tube to a large by connecting the tube to a large
		reservoir.
	The approach of Dobson [1.39 39, 1.40] has been extended by Shafii et al. [1. i et al. [1.16, 1.17] to
	model the PHP with multiple vapo model the PHP with multiple vapour bubbles, liquid plugs and tube bends. r bubbles, liquid plugs and tube bends. The local
	-2015	23

.2. Single branch PHP experiments

	Looking the literature related to experimental studies on PHPs, the local approach to
	study its characteristics is comparatively even scarcer. Local heat transfer
	measurements in non-boiling Taylor bubble flow, in the context of pulsating heat pipes,
	have been recently addressed. Many research groups have shown that the flow field in
	single phase liquid flows gets significantly modified by slipping Taylor bubbles of
	gas/vapour through it, which eventually leads to enhanced heat transfer [1.47-1.49].

  1.10 P.A. Kew, K. Cornwell, Correlations for the prediction of boiling heat transfer in small-diameter channels, J. Appl. Therm. Eng.,17 (1997) 705-715. 1.11 S. Khandekar, M. Groll, On the definition of pulsating heat pipes: An overview, Proceedings of 5 th Minsk International Conference, Minsk, Belarus (2003). 1.12 J.L. Xu, Y.X. Li, T.N. Wong, High speed flow visualization of a closed loop pulsating heat pipe, Int. J. Heat Mass Transfer, 48 (2005) 3338-3351. 1.13 H. Yang, S. Khandekar, M. Groll, Performance characteristics of pulsating heat pipes as integral thermal spreaders Int. J. Ther. Sci. 48/4 (2009) 815-824. 1.14 M. Groll, S. Khandekar, Pulsating Heat Pipes: Progress and prospects, Proc. International Conference on Energy and the Environment, Shanghai, China, 1 (2003) 723-730. .40 R.T. Dobson, An open oscillatory heat pipe water pump, Appl. Therm. Eng., 25(4) (2005) 603-621. 1.41 V.S. Nikolayev, A dynamic film model of the pulsating heat pipe, J. Heat Transfer, 133 (8) (2011) 081504. 1.42 V.S. Nikolayev, Towards predictive modeling of pulsating heat pipes, in: Proc. 16th International Heat Pipe Conference, INSA Lyon, Lyon, France, (2012). 1.43 M. Mameli, M. Marengo, S. Khandekar, Towards Quantitative Validation of a Closed Loop Pulsating Heat Pipe Numerical Model, invited lecture in Proc. 16th Int. Heat Pipe Conf., INSA, Lyon, France (2012). 1.44 M. Mameli, M. Marengo, S. Zinna, Numerical model of a multi-turn closed loop pulsating heat pipe: Effects of the local pressure losses due to meanderings, Int.

1.15 S. Khandekar, P.K. Panigrahi, F. Lefèvre, J. Bonjour, Local hydrodynamics of flow in a pulsating heat pipe: a review, Front. Heat Pipes, 1, 023003 (2010) 1-20. 1.16 M.B. Shafii, A. Faghri and Y. Zhang, Thermal modeling of unlooped and looped pulsating heat pipes, ASME J. Heat Transfer, 123 (2001) 1159-1171. 1.17 M.B. Shafii, A. Faghri, Y. Zhang, Analysis of heat transfer in unlooped and looped pulsating heat pipes, International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12/5, (2002) 585-609. 1.18 Y. Zhang, A. Faghri, Advances and unsolved issues in pulsating heat pipes, Heat Tran. Eng., 29(1) (2008) 20-44. 1.19 S. Khandekar, P. Charoensawan, M. Groll, P. Terdtoon, Closed loop pulsating heat pipes Part B: visualization and semi-empirical modeling, Appl. Therm. Eng. 23 (2003) 2021-2033. 1.20 W.H. Lee, H.S. Jung, J.H. Kim, J.S. Kim, Flow visualization of oscillating capillary tube heat pipe, 11th International Heat Pipe Conference, Tokyo, Japan, (1999) 131-136. 1.21 W. Qu, H.B. Ma, Theoretical analysis of startup of a pulsating heat pipe, Int. J. Heat Mass Transfer 50 (2007) 2309-2316. 1.22 N. Bhuwakietkumjohn, S. Rittidech , Internal flow patterns on heat transfer characteristics of a closed-loop oscillating heat-pipe with check valves using ethanol and a silver nano-ethanol mixture, Exp. Therm. Fluid Sci., 34 (2010) 1000-1007. 1.23 D.A. Reinelt, The rate at which a long bubble rises in a vertical tube, J. Fluid. Mech. 175 (1987) 557-565. 1.24 J.Bico, D. Quéré, Falling slugs, J. Colloid Interface Sci. 243 (2001) 262-264. Introduction, Motivation and Background Chapter 1 1J. Heat Mass Transf., 55 (2012) 1036-1047. 1.45 R. Senjaya, T. Inoue, Oscillating heat pipe simulation considering bubble generation Part I: Presentation of the model and effects of a bubble generation, Int. J. Heat Mass Transfer 60 (2013) 816-824. 1.46 V.S. Nikolayev, Dynamics of the triple contact line on a nonisothermal heater at partial wetting Phys. Fluids, 22 (2010) 082105. 1.47 A.K. Bajpai, S. Khandekar, Thermal transport behavior of a liquid Plug Moving Inside a Dry Capillary Tube, Heat Pipe Sc. Tech., 3(2-4) (2012) 97-124. 1.48 A. Majumder B. Mehta, S. Khandekar, Local nusselt number enhancement during gas-liquid Taylor bubble flow in a square mini-channel: An experimental study, Int. J. Thermal Sci., 66 (2013) 8-18. 1.49 B. Mehta, S. Khandekar, Taylor bubble-train flows and heat transfer in the context of pulsating heat pipes, Int. J. Heat Mass Transfer, 79 (2014) 279-290. 1.50 B. Mehta, S. Khandekar, Measurement of local heat transfer coefficient during gas-liquid Taylor bubble train flow by infrared thermography, Int. J. Heat Fluid Flow, 45 (2014) 41-52, 1.51 F. Bonnet, P. Gully, V.S. Nikolayev, Experimental study of a single branch cryogenic pulsating heat pipe: first results, in: Proc. Eurotherm Sem. on gravitational effects on liquid-vapour phase change, IUSTI, Hyeres, France, (2011). 1.52 F. Bonnet, P. Gully, V.S. Nikolayev, N. Luchier, T.Q. Tran, Evaluation of the vapour thermodynamic state in PHP, 17th Int. Heat Pipe Conf., October 13-17, Kanpur, India, (2013).

Table 2 . 1 :

 21 Static equilibrium contact angle θ

	Fluid type	Static equilibrium contact angle
	Hydrophilic
	Hydrophobic
	Super-hydrophobic	150°

Table 3 .

 3 1: The basic physical properties of fluids used

	Properties	Pentane	FC72 1	Ethanol	De-ionized water	Units
	Boiling pt. -1 atm	35.9	56	78.37	100	⁰C
	Density
	ρ	626	1680	789	996.8	kg/m 3
	at 20⁰C

Table 3 .

 3 2: Typical experimental measurements

	Item	Symbol
	Evaporator temperature	Te
	Condenser temperature	Tc
	Reservoir pressure	Pr
	Temporal variation of the vapour pressure	Pv (t)
	Temporal variation of the vapour temperature	Tv (t)
	Images of the meniscus for each time instance
	Images of the triple line ( if visible) for each time instance
	1.3. Data processing

The pressure and temperature data are filtered using inbuilt standard noise filtering algorithms embedded in the data acquisition system. There are two cameras used for capturing the photographs of complete capillary tubes for meniscus movement tracking (Camera 1), photographs of evaporator capillary tube for tracking thin film movement (Camera 2) by observing the triple line (if visible) movement. These images are processed with code developed in MATLab image processing tools. The code is available in Appendix-B for the purpose of archival. The outcome of this image processing is the position of meniscus inside the capillary tube in terms of pixel coordinates and later converted in actual distance by using appropriate scaling. Same is done for the case of triple line movement. which explained previously in section 1.2 of this chapter, is due to the connections of measuring instruments.

Table 3 .

 3 3: Typical experimental measurements

	Item

Table 4 .

 4

				1: Comparison of initial film thickness 2
	BC	Te (°C)	Tc (°C)	Ca	Bo	δlf,i → eq. 4.8 (µm)	δlf,i → Section 1.4.3 (µm)
	#1	46	16	0.0198 1.452	93.1	75
	#2	46	20	0.0210 1.720	90.1	69
	#3	46	24	0.0175 1.782	81.7	67

2

  Values of average Ca and Bo are calculated at mean temperature of Te and Tc.

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0080/these.pdf © [M. Rao], [2014], INSA de Lyon, tous droits réservés

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0080/these.pdf © [M. Rao], [2014], INSA de Lyon, tous droits réservés Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France -2015

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0080/these.pdf © [M. Rao], [2014], INSA de Lyon, tous droits réservés Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France -

CEFIPRA joint project between CETHIL, France and IIT Kanpur, India # 4408-1 Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0080/these.pdf © [M. Rao], [2014], INSA de Lyon, tous droits réservés Manoj RAO -PhD Thesis: CETHIL, INSA de Lyon, France -2015

Literature review Chapter 2 is globally stable at some system parameters, the PHP might stop functioning. Such failures have indeed been observed experimentally. A parametric study of the instability needs to be carried out both theoretically and experimentally (different fluids, temperatures, pressures) in order to determine the oscillation threshold. Chapter 4 heat flow by conduction from the wall to the interface, but also to the thermal nonequilibrium between the vapour and the liquid. If the vapour temperature is greater than the liquid temperature, the net mass flux of evaporation will be lower than conduction-induced evaporation mass flux, as the thermal non-equilibrium leads to condensation. Otherwise, the mass flux is due to both conduction through the film and thermal non-equilibrium.

Results and discussion

The simplified analysis of unsteady heat transfer in the liquid thin film shows the importance of measuring the time-evolution of the temperature of the vapour with a high time-resolution and a good accuracy, which remains a challenge today under such experimental conditions. While calculating the uncertainty in the mass, the uncertainty due to the meniscus tracking by high speed camera is calculated by the resolution of the image and the limitation of image processing software which could not differentiate the intensity in about 10-15 pixels around the meniscus. This in turn, contributed in uncertainty of vapour volume calculation.

Appendix

Using eq. C.3, we found that there is uncertainty of ±5% in the calculation of the vapour mass dynamics. Similarly using eq. C.4 the uncertainty in film thickness calculation is believed to be 15%. For the pressure drop calculation there is no other variable involved in estimating it, hence the accuracy of the differential pressure transducer itself depicts the uncertainty in this case.

One more important observation is that all of these calibrations are being performed in