Filippo Pagnoni

Vincent Ayel
email: vincent.ayel@ensma.fr

Yves Bertin

Jerome Coulloux

Maxime Zebian

Loop Heat Pipe for thermal management of aircraft engine equipment

According to recent aircraft engine development trends, the performance enhancement of the propulsion plants is accompanied by both an increase of the overall pressure ratio and a decrease of the fan pressure ratio. Projections for the next decade show that equipment within the engine compartments can exceed their temperature thresholds, mining aircraft safety.

Loop heat pipes (LHP) represent highly appealing solution that could be employed as part of future passive cooling architectures, replacing or enhancing the heat transfer capabilities of currently adopted mono-phase solutions. To meet the compatibility, safety and environmental constraints, a titanium-water LHP was designed, manufactured and tested for the thermal management of aircraft engine equipment. The results encouraged the use of this technology providing clues for the development of other prototypes. The sintered titanium wick showed an excellent mechanical resistance to repeated cycles of water freeze/thaw, providing that the LHP could be potentially exposed to cold environment with limited risk to undergo structural failures. Experimental data suggests that a passivation process occurred in the first hours of operation, modifying wick wettability and improving LHP performance. This was accompanied by the generation of non-condensable gas. The impact on LHP behavior was 1 PhD, FTC -Fluid dynamics, thermal science and combustion department.

carefully analyzed, together with the influence of heat transfer on the liquid line and the cold source temperature variations. reduction and the design of more electric aircrafts (MEA) [START_REF] Rosero | Moving towards a more electric aircraft[END_REF]. As a result, thermal management is gaining increased attention as it could become one of the major issues in the upcoming generation of aircrafts. An example comes from the nacelle compartments where near future predictions based on aircraft engine's evolution trends show that integrated equipment will be subjected to increasing thermal loads [START_REF] Verseux | New challenges for engine nacelle compartments pressure and thermal loads management with aircraft engine evolution[END_REF]. As represented in Fig. 1, the turbofan nacelle contains three main compartments between the external cowl and the engine casing:

1) FAN: confined between the nacelle outer cowl and the secondary flow;

2) Intermediate compressor: between the primary and secondary flows, near the low-pressure compressor stages (LPC);

3) Core: between the primary and secondary flows, between the intermediate pressure compressor stages (IPC)

and the exhaust nozzle.

N

These regions are considered as fire or flammable fluid leakage zones: hence, specific sealing and fire extinguish systems are implemented for safety reasons. Each compartment contains a certain amount of equipment that must be maintained at an acceptable temperature to ensure the aircraft's reliability [START_REF] Verseux | New challenges for engine nacelle compartments pressure and thermal loads management with aircraft engine evolution[END_REF]. To do so, compartments are ventilated by means of a colder airflow. In the FAN compartment, fresh air from the external environment is used from specific picking points on the outer cowl. Differently, the core compartment uses air from the secondary flux (by-pass stream).

This colder air is sucked into holes drilled along the compartment and oriented toward the most critical items. Among nacelle compartments, the core is surely the most critical one in terms of thermal boundary conditions. Indeed, this relatively narrow volume confined between the carter (engine casing) and the IFS (nacelle thrust reverser inner fixed structure) is congested with several dissipative equipment and it is interested by the large heat leak coming from the engine carter, as illustrated in Fig. 1. In fact, carter's skin temperatures can easily exceed 600˚C in the hottest spots located downstream providing that radiative heat transfer can significantly impact the compartment thermal environment. As argued by Verseux et al. [START_REF] Verseux | New challenges for engine nacelle compartments pressure and thermal loads management with aircraft engine evolution[END_REF], recent engine development trends are expected to lower the fan pressure ratio of 25% and to increase the overall pressure ratio of 5 times in 2030 compared to 1995. With the former, ventilation heat transfer capabilities will be considerably reduced. As the secondary airflow will be less pressurized, the mass flow rate sucked into the compartment will be lower. Moreover, the higher overall pressure ratio will further increase the engine casing temperatures; predictions estimate a gain of 100˚C in 2030 with respect to 1995. It now becomes apparent that, in such scenario, equipment thermal protection will require a different approach in the near future. Indeed, under specific flight conditions, some of the sub-system hardware currently integrated in the engine's nacelle are already experiencing the maximum recommended temperature level.

In response to this challenge, heat pipes are claiming increased attention from the aerospace industry since the last two decades. Appealing characteristics of heat pipes for aerospace applications are: their capacity to drain and efficiently transport heat over significant distances in a fully passive manner, their long-life reliability without maintenance.

Among two-phase passive devices, loop heat pipes (LHPs) are particularly promising for aerospace applications since they have a higher flexibility than conventional heat pipes and less sensitivity to gravity [START_REF] Maydanik | Loop heat pipes[END_REF] and accelerations [START_REF] Fleming | Titanium-water loop heat pipe operating characteristics under standard and elevated acceleration fields[END_REF]. LHPs are two-phase passive thermocapillary driven heat transfer devices with a confined porous wick. As shown in Fig. 2, a conventional LHP consists of an evaporator, provided with a capillary wick and an integrated compensation chamber (hereafter called reservoir), a condenser and transport lines. To operate properly, the LHP must be perfectly sealed, previously vacuumed and then partially filled with a working fluid.

According to Fig. 2, heat is drained from the evaporator wall and reaches the liquid-vapor interface within the capillary structure, where local evaporation generates a vapor mass flow. The capillary pressure developed across the menisci forces the vapor to flow into the vapor line up to the condenser, where it is condensed and then subcooled.

Finally, the subcooled liquid flows through the liquid line into the reservoir. The reservoir is thermally and hydraulically coupled with the evaporator and it generally contains liquid and vapor at saturation conditions. The reservoir stores or releases the excess of liquid depending on the mass flow rate and provides liquid to the capillary wick. The liquid rewets the porous structure and the cycle restarts. A more detailed explanation of the LHP fundamentals and thermodynamics can be found in [START_REF] Maydanik | Loop heat pipes[END_REF].

Nowadays two aeronautical applications for loop heat pipes seems viable and they are well documented: avionics thermal management [START_REF] Baldassarre | Loop Heat Pipe for Avionics Thermal Control[END_REF][START_REF] Park | Design optimization of a loop heat pipe to cool a lithium ion battery onboard a military aircraft[END_REF] and anti-icing [START_REF] Su | A review of Loop heat pipes for anti-icing applications[END_REF]. The main unsolved issues for the use of LHPs within aircraft engine's compartments are the practical integration and the working fluid-material selection. Moreover, a LHP employed in this specific context should be able to operate under severe thermal conditions, meeting specific fire resistance requirements in line with aeronautical standards and providing long life service reliability without maintenance. The present paper deals with these aspects in two steps. First, an insight of the LHP design process deployed for this specific context is discussed. Then, the results of a multi-parametric experimental study conducted on ground under controlled boundary conditions are presented and analyzed. The goal is to provide useful information for future development of LHP dedicated to engine's compartment thermal management.

II.Loop Heat Pipe design for engine compartments applications

A. Thermal requirements Thermal environment of turbofan engine compartments is heterogeneous and characterized by large temperature variations and different ventilation conditions with respect to both axial and radial location. As a result, the present study refers to the core compartment which is, according to previous considerations, the most critical one. In particular, the targeted equipment are those located near the combustion chamber, as shown in Fig. 1. In this case, the use of a loop heat pipe would make dedicated ventilation unnecessary, since the excess of heat would be drained and transported in suitable colder spots located elsewhere. It is worth noting that the presented approach applies to other integrated items located in different compartments and, eventually, to different types of aircraft engines.

The LHP design requirements are the following: an average and maximum evaporator heat powers of 0.2 kW and 0.5 kW, respectively, a maximum heat flux to dissipate of 20 W•cm -2 together with a maximum item's skin temperature of 250˚C. The device must withstand large temperature variations across the different flight phases and taxi periods of the aircraft. It can be reasonably assumed that a component integrated within the engine's nacelle can be surrounded by an air temperature ranging from -70˚C up to +160˚C.

B. Condenser

The first step of the LHP design consists in the identification of suitable cold spot for the condenser integration and a prior estimation of its dimensions. This information is needed for preliminary sizing of the LHP (transport line path and length, according to integration constraints, reservoir volume and optimization of the evaporator block). To simplify the effective integration, keeping a general approach in the present study, an air-cooled spreader is considered.

As a result, since this component is expected to provide the highest mass fraction of the entire LHP, Aluminum 6061 is selected as building material for the spreader part only (not in direct contact with the working fluid), due to its suitable properties (𝜌 = 2.7 g•cm -3 , 𝜆 = 167 W•m -1 K -1 ) and the excellent workability. As for the heat sink geometry, a simple flat plate is considered. Indeed, although a finned surface (plate or annular) would result in a substantially greater efficiency, the flat plate gives a conservative spreader size estimation and it is particularly suitable for test purposes, allowing an easier control of the cold source temperature.

In spreader size optimization, one should first seek for those nacelle spots having the most suitable thermal boundary conditions (high heat transfer coefficients and low ambient temperatures). Then, compare these spots with local available space and integration constraints. Hence, it could be useful to plot the equivalent spreader surface needed at different compartment locations, to obtain a first selection of suitable spots. This can be done by solving a simple 1D heat conduction problem based on a nodal network like the one presented in Fig. 3 and Eq. [START_REF] Rosero | Moving towards a more electric aircraft[END_REF].

At this stage, the heat transfer between the LHP working fluid and the spreader is neglected. Instead, an equivalent heat power Q generated at the symmetry plane (with surface area Ap) is considered. In the nodal network of Fig. 3a and Eq. ( 1), hamb and Tamb are local values of air temperature and heat transfer coefficient, whilst Rplate and Ramb are the equivalent 1D thermal resistances related to the wall heat conduction and convection (on the outer surfaces), respectively. The maximum inner plate temperature Ti,p is considered to be equal to the average condenser flow temperature. To get a reasonable estimation of the spreader surface (limiting subcooling) and minimize the heat transfer on the liquid line, Ti,p is supposed equal to the air temperature surrounding the targeted equipment on the evaporator side. Since Rplate and Ramb are both functions of Ap, one can easily compute the plate surface finding the root of Eq [START_REF] Rosero | Moving towards a more electric aircraft[END_REF]. Results are reported in Fig. 3b which shows the evolution of the condenser size throughout the core compartment. The blue and red curves represent, respectively, the minimum and maximum values of Ap at different axial distances from the compartment intake. This accounts for the variation of the boundary conditions in the annulus with respect to the angular coordinate (at a fixed axial position). The values of Ap are provided in terms of dimensionless ratios with respect to the maximum allowable condenser size (from integration perspective).

This approach is very simple and effective for the early design phase; parametric analyses can be easily conducted, considering different heat sink types (finned plate, annular fins spreaders…), different materials and asymmetric boundary conditions. According to Fig. 3b, the spreader size is minimum in local spots close to compartment inlet;

this is due to the presence of the compartment air intake (secondary flow) and the lower carter temperatures with respect to the regions downstream (closer to exhaust nozzle). Beyond the second half of the compartment, the spreader surface becomes too large and integration is not possible. Once suitable spots are identified, the best one is selected by pursuing the criteria of transport lines lengths minimization, according to integration constraints. In the present case, the best spot has the following characteristics: Ap,max/Ap = 1.1, relative distance between evaporator and condenser of 1.6 m, relative elevation close to zero (LHP can be considered as horizontal). Consequently, to meet integration requirements and space constraints, the transport line lengths range between 3.3 and 3.6 m (more details in section F). The procedure mentioned above allows to perform a prior estimation of the main LHP dimensions, according to the guidelines presented in the next sections. Then, condenser geometry is optimized and validated with a 2D condenser model coupled with a LHP solver implemented in Matlab®; for more details the reader is invited to consult reference [START_REF] Pagnoni | Effects of loop heat pipe condenser design on the overall thermal performance[END_REF]. As a result, the final geometry consists of a 1 m pipe arranged in a serpentine manner, sandwiched between the internal grooves of two 326 x 146 x 5 mm 3 aluminum plates, as shown in Fig. 3c. Pipe's dimensions and characteristics will be provided in section II.F.

𝑄 = , = , ⁄ ⁄ (1)

C. Working fluid and construction material selection

In heat pipes design, the choice of the working fluid and material pair is of primary importance for both performances and reliability. Since titanium and common titanium alloys are widely used in aeronautics, as well as in engine's compartments, they are considered as building materials for the LHP prototype. As for the working fluid, appealing characteristics for potential candidates are:

1) Good thermophysical properties (high surface tension, liquid density and latent heat, low viscosity);

2) Freezing point below the minimum ambient and cooling temperatures;

3) Useful temperature range (UTR [START_REF] Faghri | Heat Pipes: Review, Opportunities and Challenges[END_REF]) superimposed to the LHP operating one; 4) Compatible with the lightweight alloys used in the aeronautical environment (titanium/titanium alloys); 5) Low flammability risk and toxicity.

Fig. 4 contains a list of working fluids with respect to the thermal requirements of section II.A, degree of potential risk and availability of compatibility data [START_REF] Faghri | Heat Pipes: Review, Opportunities and Challenges[END_REF][START_REF] Hall | Rules of Thumbs for Chemical Engineers[END_REF][START_REF] Mishkinis | Loop Heat Pipes working fluids for intermediate temperature range: from -40˚C to 125˚C[END_REF][START_REF] Anderson | Evaluation of Heat Pipe Working Fluids in The Temperature Range 450 to 700K[END_REF]. As reported in Fig. 4, only few fluids can withstand the large temperature excursion that interests the different nacelle's regions. However, most of them have a high level of hazard and their use for aeronautical applications is already prohibited (ammonia, pentane, methanol, toluene, naphthalene, Dowtherm A) or it might be restricted or banned in the near future (organic, synthetic and silicon-based fluids).

Moreover, most of these fluids are proprietary; relevant information about their thermophysical properties (like surface tension variation with temperature), chemical compatibility, thermal degradation and stability in two-phase closed systems is not provided. Hence, these fluids are discarded from the list of potential candidates (at least as long as their data are insufficient). As a result, despite its freezing point at 0°C, water is the only fluid of the list with excellent thermophysical properties, perfect UTR, not flammable, hazardous free and successfully tested in long-life tests with titanium and titanium alloys [START_REF] Anderson | Evaluation of Heat Pipe Working Fluids in The Temperature Range 450 to 700K[END_REF][START_REF] Anderson | High Temperature Water Heat Pipe Life Tests[END_REF]. Indeed, in their life tests, Anderson et al. [START_REF] Anderson | High Temperature Water Heat Pipe Life Tests[END_REF] analyzed the chemical compatibility between water and titanium in several wicked heat pipes made up of commercially pure (CP) titanium and some of the most common alloys (Grade 5, 7 and 9) from a minimum of 8000 up to 20000 hours at 277˚C. They argued that, despite initial gas generation during the passivation process, water and titanium alloys showed an acceptable compatibility. Indeed, a limited amount of non-condensable gas (NCG) was produced in all the tested samples showing an asymptotic evolution. Titanium alloys and CP titanium heat pipes provided different NCG generation rates during the tests. According to Anderson et al. [START_REF] Anderson | Intermediate Temperature Fluids Life Tests -Experiments[END_REF], the NCG generation is strongly related to operating temperature and might also depend of the operating time. Limited information on NCG generation in titanium-water

LHPs is available in the literature. In some of the manufactured CP-Ti LHPs [START_REF] Hartensine | Titanium Loop Heat Pipe for Nuclear Power System[END_REF][START_REF] Fleming | Titanium-Water Loop Heat Pipe Operating Characteristics Under Standard and Elevated Acceleration Fields[END_REF], the authors mention an initial device processing at low heat powers, followed by a purge and refill with the working fluid. Details about the operating temperatures and gas generation rate inside the devices are not provided. Moreover, according to the literature (an example in [START_REF] Maydanik | Loop heat pipes[END_REF]), a controversial aspect in using water below its freezing point is the atypical volume expansion upon solidification which can lead to startup failure or, in the worst case, to serious structural damages of LHP components. This is actually one of the major issues that has prevented from the use of water as working fluids for several heat pipe applications, including aerospace ones. However, there is a serious lack of data on this topic and the limited number of available studies concern heat pipes made of mold materials like copper [START_REF] Stein | Quality Assurance in solar and thermal heating and cooling technology, keeping track with recent and upcoming developments (QUAIST) -Summary report: freeze resistance test of heat pipe evacuated tube collectors[END_REF]. Hence, there is a strong need of experimental researches to clarify this aspect using stiffer materials like titanium for both the envelope and capillary wick. In the present paper, a resistance test of water freezing in a CP titanium wick is presented in section II.E. A wide discussion on NCG generation in the titanium water prototype is proposed in section IV. For the present LHP, CP-2 Ti is selected for both the evaporator envelope and the porous wick, whereas condenser and transport lines pipes are made in Grade 9 Ti (standard pipes used and certified for core compartment's fire zones). The use of these materials prevents the LHP from encountering differential thermal expansion problems and reducing the risk of Galvanic corrosion.

D. Evaporator and reservoir

The LHP evaporator and reservoir are both hydraulically and thermally coupled: a careful design must be carried out to ensure the liquid supply in the porous wick while keeping a low heat leak from both the porous wick and the evaporator wall to the reservoir. Here, a flat opposite replenishment evaporator with an inverted meniscus and a diskshaped capillary structure is selected. The integrated reservoir has a cylindrical shape and belongs to the same titanium block of the evaporator case. The reservoir is sized according to the internal volumes of the LHPs while accommodating the swing of the liquid density between the cold and hot cases [START_REF] Ku | Operating Characteristics of Loop Heat Pipes[END_REF], as shown in Eq. ( 2) and (3), respectively. In the latter, the terms Vll, Vvl, Vcond, Vw and Vw,gr represent the internal volumes of: liquid line (ll), vapor line (vl), condenser pipe (cond), empty portion of the porous wick (w) and vapor grooves (w,gr). The reservoir volume V R is sized by setting its void fractions values for the hot and cold cases (𝛼 and 𝛽, respectively) simplifying the expression of the total fluid mass M in Eq. (2-3). As shown in Fig. 5, the reservoir is closed by means of a flat disk welded at one edge, where a long bayonet is inserted to facilitate wick rewetting. The porous wick is wedged by means of a tightening part (yellow component in Fig. 5) screwed in the inner wall of the reservoir. The tightening element has an annular fin of triangular section, inserted in one circumferential groove engraved on one side of the wick. This configuration aims to provide a uniform pressure all along the outer perimeter of the wick, ensuring a good thermal contact between the wick and evaporator wall and an effective sealing between the evaporator wall and the reservoir.

The latter aspect is crucial for a correct LHP operation (vapor flows back to reservoir must be avoided).

M=𝜌 l,cold V ll +V vl +V cond +V w +V w,gr +𝜌 v,cold (1-𝛽)V R

(2)

M=𝜌 l,hot (V ll +V w +(1-𝛼)V R )+𝜌 v,hot V w,gr +V vl +V cond +𝛼V R (3)
Finally, the evaporator wall thickness is sized on the base of a tradeoff between the minimum value of the thermal resistance associated to wall heat conduction and the minimum impact on wall deformation, estimated as in Eq. ( 4)

from static elasticity theory. At 250˚C, saturated water pressure is almost 40 bar; this can be considered as the design specification from the mechanical point of view (worst case scenario). Similar considerations can be done for the reservoir walls: the reduction of the parasitic heat leak via the evaporator wall requires a smaller cross section (thin walls) to the detriment of mechanical deformation. In Eq. ( 4) wmax is the maximum displacement at the center of the disk with an imposed pressure difference between each side, r being the disk radius and e its thickness, E at denominator is the Young's modulus and υ the Poisson's ratio.

w max = ΔP 1-υ 2 r 4 (4)
The main geometrical parameters are resumed in Fig. 5: the evaporator and reservoir are obtained from a single CP-2 titanium block. Choosing 𝛼 = 0 and 𝛽 = 1 in Eq. (2-3), from the geometrical characteristics of the transport lines (see section F) and porous wick (see section E), the resulting height of the reservoir is 75 mm. The straight bayonet tube is screwed on the upper plug and has an outer diameter of 3 mm and an inner one of 2 mm.

As a result, the evaporator -reservoir cylindrical body has a total height of 90 mm and an outer diameter of 50 mm. The evaporator wall has a squared shape, for an easier fixation to the dissipating item. The reservoir wall thickness is 1 mm, whilst the evaporator wall one is 2 mm.

E. Porous wick

The disk-shape porous wick is the most important component of the LHP that ensures the fluid circulation inside the loop by means of the capillary pressure. The wick, manufactured by the Atherm® company, is obtained from a standard > 98.4% CP titanium powder, pressureless sintered and without previous compacting. The pore radius is minimized, according to manufacturing capabilities, keeping a reasonable value of wick porosity and permeability.

Hence, the average pore radius is 4.25 µm and the permeability, measured by mercurial porous meter on a wick sample, is 1.5•10 -13 m 2 . According to the Young-Laplace Equation (see Eq. ( 5): 𝜎 being the liquid surface tension, 𝜃 the working fluid wetting angle within the porous structure and 𝑟 the pore radius), the capillary pressure using water as working fluid ranges from 5 to 25 kPa between 100˚C and 200˚C, considering 𝜃 values between 0˚ and 75˚.

Based on Atherm® company experience and know-how on flat evaporator LHPs, a fishbone shape geometry for vapor grooves is considered for wick vapor grooves. These are machined on one side of the wick, collecting vapor from the smaller grooves into the thicker one in the center up to the vapor line, as shown in Fig. 5 (right hand side).

With such configuration, the vapor pressure drop in the transition from smaller grooves to central collector is reduced, with respect to a 90˚ configuration (grooves perpendicular to vapor collector). The optimum grooves size is obtained fitting data collected from other LHPs manufactured by the Atherm® company: the smaller grooves have a squared cross section of 1 mm width, whilst the central one has a conic shape with a variable width ranging from 1.5 mm up to 2.8 mm. The contact area between the wick and the evaporator wall is approximately 55% of the total evaporator's wall surface. The porous wick thickness impacts both the heat leak to the reservoir by convective-conduction heat transfers [START_REF] Launay | Analytical Model for Characterization of Loop Heat Pipes[END_REF], as shown in Eq. ( 6). In the latter, the terms ew and Aw represent the wick thickness and cross section area, respectively, whilst λ w,eff the effective wick thermal conductivity (estimated through semi-empirical correlations for sintered wicks [START_REF] Hamdan | Steady-State Model of a Loop Heat Pipe (LHP) with Coherent Porous Silicon (CPS) Wick in the Evaporator[END_REF]) and the flow pressure drop within the wick (evaluated from the Fick law, as in Eq. ( 7), where Kw is the wick permeability). From equations ( 6) and ( 7) it becomes apparent that an increase of the wick thickness ew increases exponentially the thermal resistance and linearly the pressure drop. Even in this case, the best solution is a tradeoff of these two aspects; here, a wick thickness of 10 mm and an outer diameter of 45 mm is selected.

∆𝑃 = 𝑐𝑜𝑠𝜃 (5)
∆P w = μ l ṁe w K w ρ l A w (6)
As previously discussed, it is important to verify the effective wick mechanical resistance to repeated water freeze/thaw cycles. To do so, the porous wick was embedded into an open cylinder, representing the reservoir wall, and then sank into a pure distilled water bath. The temperature of the bath was changed from +10˚C to -10˚C every two hours, so that the liquid had enough time to freeze and thaw completely during each cycle. Three porous wicks were tested in parallel: after more than 1500 cycles, any sign of structural damage was detected neither residuals of the sintered powder in the water bath were found. This encouraging result may come from the relatively low porosity and the small dimensions of the pores that confer good mechanical strength (high containment). For the purposes of the present work, we consider that a proven resistance over ~1k cycles represents a satisfying result which confirms the choice of water as working fluid for our design. Nonetheless, more R&D efforts are necessary to cover real qualification tests on the entire water LHP subjected to freeze/thaw, frozen startup etc… This in order to certify this technology for aircraft engine applications.

F. Transport lines

Depending on the heat sink location with respect to the heat source, the transport lines can be up to few meters long. During normal operation, the engine vibration can lead to dangerous resonance phenomena on the transport lines that must be avoided to ensure the structural integrity of the LHP. It is important to support the pipe in a proper number of points and to use pipes with suitable characteristics. Hence, standard tubes of CP-Ti Grade 9 having external and internal diameters of 6.35 mm and 5.05 mm, respectively, are considered. These pipes are currently in use in pressurized hydraulic loops inside the core compartment: they can resist to high pressures up to 300 bar at 70˚C.

The LHP prototype designed in the present paper has vapor and liquid lines of 3.3 m and 3.6 m, respectively.

These strictly depends on the cold source and evaporator locations inside the compartment. As for the condenser, the same pipe is used to avoid compatibility issues.

III.Experimental set up

A schematic view of the LHP is shown in Fig. 6. The device is integrated on a test rig and attached to two heat sources (primary and secondary heaters) and a heat sink. The linear distance between evaporator and condenser is 1.6 m, according to the results presented in section II.B. The bends in transport lines are consequent to the practical integration of the LHP on the test rig. Preserving the linear distance between the evaporator and condenser is useful to investigate the LHP operation at variable inclinations with respect to gravity (relative height between hot and cold source). However, these results are not presented in the paper since they go beyond the scope of the presented application.

The device is mounted on a test rig and attached to two heat sources (primary and secondary heaters) and a heat sink. The primary heater is attached to the evaporator wall; it consists of a single squared copper matrix of 50 x 50 x 15 mm 3 with two embedded cartridge heaters (2 x 300 W max, outer diameter: 8 mm, length: 50 mm). To account for the liquid line heat transfers inside the different engine's compartments (see Fig. 1), the secondary heater is fixed on the pipe, near the reservoir inlet. This consists of a 50 x 50 x 15 mm 3 copper matrix equipped with a cartridge heater (125 W max, outer diameter: 6.35 mm, length: 64 mm). A modulate heat power is delivered to both heaters by means of remote DC Power Supplies (EA Model PS-9360).

The heat sink is a 326 x 146 x 15 mm 3 304L stainless steel cold plate; the Dowtherm® A coolant (i.e. the secondary working fluid) flows at a controlled temperature by means of a remote chiller (Huber 385 Unistat). To enhance the thermal contact between the heat sources/sink and the LHP, a graphite sheet is used at the evaporator side (eGraf 1220:

e = 0.5 mm, λ ~ 10 W•m -1 •K -1
), whilst a gap filler is used at the condenser one (Laird Technologies Tflex™ 500; e = 0.5 mm, λ ~ 2.8 W•m -1 •K -1 ).

To minimize the heat leaks through the test fixture and with the external environment, the LHP rests on several thin PTFE rods (λ ~ 0.25, > 6 cm long, W•m -1 •K -1 ) and is covered with multiple layers of mineral wool (~ 0.07 W•m - 1 •K -1 ). Before the test, the LHP was vacuumed and the connection sealing verified with a Helium leak detector system (ASM Graph 142). During the filling operations, the working fluid was degassed through repetitive freezing/vaporization cycles in a dedicated tank, pumping away the excess of mass and the eventual presence of noncondensable gases (NCG). From the working fluid inventory evaluated from Eq. (1-2), the LHP is charged with a water mass of 186.7 g.

IV.Results and discussions

The test campaign has consisted in analyzing the influence of several operating parameters on the LHP operation:

variable heat power inputs supplied to the primary and secondary heaters and secondary working fluid temperatures.

However, from the early tests immediately after the first filling with pure water, a significative deviation from the saturation condition was observed via the pressure sensors, providing that a non-negligible amount of NCG was generated inside the device. The impact of NCG on LHP behavior and thermal performance represents a key factor that must be carefully analyzed for the present application. Indeed, even low gas generation rates can produce a significant amount of gas in the timespan of the engine's service life. Hence, the LHP was cycled at different heat power inputs until the pressure recorded at the beginning of each test (when the device was at a homogeneous temperature) did not change with respect to previous days (according to sensors' accuracy), providing that the NCG amount inside the LHP was stable. This coincides with the observations of Singh et al. [START_REF] Singh | Operational characteristics of the miniature loop heat pipe with non-condensable gases[END_REF] who studied the influence of NCG generated in a copper/water mini LHP during the first days of tests. Indeed, they noticed that the constant generation of NCG inside their device finally slowed down until was practically ceased. They argued that the major amount of NCG is produced during the initial test runs of the loop heat pipe. In the present study, once all the tests with a stable amount of NCG were completed, the LHP was purged, refilled and the tests repeated.

A. LHP passivation: operation in presence of NCG Fig. 7 reports a comparison between the LHP evaporator wall (average TCs 1-3), vapor line inlet (TC 11) and reservoir temperatures (average TCs 4-7) during steady-state operations, recorded in horizontal position at different heat power steps Qin after 8, 80 and 300 hours of operation and constant secondary fluid temperature of 50°C. One can observe that LHP thermal performance has evolved considerably within this time interval. In fact, after an initial improvement between 8 and 80 hours of operations, a clear degradation has occurred between 80 and 300 hours. The latter was due to NCG generation, as suggested by the translation along the vertical axis of both temperatures and pressures curves. Differently, values recorded after 8 hours seem not correlated to those of other tests. Indeed, evaporator wall temperatures are remarkably higher and the difference between the vapor line inlet and reservoir temperatures is much lower compared to successive tests, although the NCG amount was lower. This evidence seems to contradict what is reported in the literature [START_REF] Singh | Operational characteristics of the miniature loop heat pipe with non-condensable gases[END_REF][START_REF] Prado-Montes | Effects of non condensable gas in an ammonia loop heat pipe operating up to 125°C[END_REF][START_REF] He | Effects of non-condensable gas on the operation of a loop heat pipe[END_REF][START_REF] He | Effects of non-condensable gas on the startup of a loop heat pipe[END_REF][START_REF] Wang | Effect of evaporator tilt on a loop heat pipe with non-condensable gas[END_REF]. Indeed, the presence of NCG is usually accompanied by a degradation of the overall thermal performance of loop heat pipes. This is generally characterized by an increase of the evaporator temperature [START_REF] Singh | Operational characteristics of the miniature loop heat pipe with non-condensable gases[END_REF][START_REF] He | Effects of non-condensable gas on the operation of a loop heat pipe[END_REF][START_REF] Wang | Effect of evaporator tilt on a loop heat pipe with non-condensable gas[END_REF] or a decrease of the reservoir/condenser's ones since the system is controlled to keep constant evaporator's temperature [START_REF] Prado-Montes | Effects of non condensable gas in an ammonia loop heat pipe operating up to 125°C[END_REF], particularly at low temperatures and low heat power levels. However, except the work of Singh et al. [START_REF] Singh | Operational characteristics of the miniature loop heat pipe with non-condensable gases[END_REF], all other studies [START_REF] Prado-Montes | Effects of non condensable gas in an ammonia loop heat pipe operating up to 125°C[END_REF][START_REF] He | Effects of non-condensable gas on the operation of a loop heat pipe[END_REF][START_REF] He | Effects of non-condensable gas on the startup of a loop heat pipe[END_REF][START_REF] Wang | Effect of evaporator tilt on a loop heat pipe with non-condensable gas[END_REF] concern the influence of a controlled amount of inert gas (nitrogen) injected in the loop. In the latter cases, the influence of NCG is purely thermodynamic and the NCG accumulated in the reservoir (mixture of NCG and saturated working fluid) leads to different P-T conditions for the operating points. The working fluid temperature corresponds to a pressure higher than the theoretical corresponding saturation pressure [START_REF] Prado-Montes | Effects of non condensable gas in an ammonia loop heat pipe operating up to 125°C[END_REF]. The higher temperature difference between evaporator and reservoir leads to an increase of the parasitic heat flux from evaporator to reservoir. Hence, a higher liquid subcooling becomes necessary to compensate the parasitic heat leak. However, in the present case, the situation is more complex. In view of Figure 7a, the difference between evaporator and reservoir temperatures first decreases significantly between 8h and 80h of tests, then increases again after 300h but to lower values than initially.

Concerning the generated NCG studied by Singh et al. [START_REF] Singh | Operational characteristics of the miniature loop heat pipe with non-condensable gases[END_REF], they observed an accumulation of oxidized regions on the inner wall of the reservoir as well as on the liquid absorbing face of the wick due to the gas absorption at these The heat transfer on the transport lines deserves careful attention for this specific application. Indeed, the heat radiation from the engine's carter and the natural/forced convection within the compartment could play a remarkable role on LHP operation. As the most critical conditions occur when the subcooled liquid is heated up in the liquid line, the goal of this analysis is to investigate the LHP behavior under different secondary controlled heat loads delivered to the liquid line. Results are presented in Fig. 10, for the following operating conditions: horizontal orientation, TII = 130˚C and Qin = 200 W (grey dashed line, "Primary heater"). Six steps are delivered to the liquid line (red dashed line, "Secondary heater") between 20 W and 58 W. One can observe that, without secondary heating, the liquid line temperatures (TC 10, 12 and 13, see Fig. 6 as reference) are well below the condenser's outlet one (TC 17). Increasing the heat load on the secondary heater, the liquid flow in TC 10 is progressively heated up but always in single phase, as it does not reach the saturation conditions (TCs 4-7, reservoir). Increasing the power on the liquid line leads to a decrease of subcooling rate and an increase of the resulting temperature in the reservoir, together with the evaporator wall and the vapor temperatures. The thermodynamic cycle is thus shifted upwards along the saturation curve.

However, when the secondary heat power supplied exceeds 49 W, the liquid line temperature increases sharply (red dotted areas), exceeding the reservoir's one (TC 12), followed by a slight increase of temperature oscillation amplitudes. Even in this case, the LHP operation remains robust and the situation quickly stabilizes, with a smooth increase of the reservoir (TCs 4-7), vapor line inlet (TC 11) and evaporator wall (TCs 1-3) temperatures. A similar behavior is observed for the highest heat power step of 58 W. At this point the heat flux is sufficient to create some nucleation spots, vapor bubbles are generated together with some instability phenomenon like the slight condenser's outlet temperature drop (TC 17), due to a quick back flow in the liquid line. However, flow entering the reservoir is fully re-condensed, providing that TC 10 is well below TCs 4-7. It is interesting to observe an abrupt temperature drop of ~20˚C recorded from TC 13 at 49 W. It is difficult to explain this behavior from the available data. However, this looks like a local effect, with no remarkable impact on other parts of the LHP, thus not relevant from the LHP operational perspective. As a conclusion, despite a smooth increase of temperatures any remarkable consequence on the LHP operation is observed by delivering a heat power to the liquid line up to 30% of the heat power supplied to the evaporator. This result is important for the LHP pre-design in severe thermal environments like the engine's nacelle. those of the reservoir. Hence, excluding a Cold Shock, the cause of this observed behavior remains unclear and deserves further investigations, although it seems clear that this transient instability is localized in the porous wick. Another instability occurred in this test at low heat power (110 W); the flow reversal (Fig. 11). The available documentation on this phenomenon is really limited and usually attributed to the vapor bubble formation within the capillary structure [START_REF] Fleming | Titanium-Water Loop Heat Pipe Operating Characteristics Under Standard and Elevated Acceleration Fields[END_REF]. However, in the present case, the appearance of flow reversal seems to be related to the reservoir's inlet flow conditions, in particular, on the role of the heat losses in the liquid line at low heat power inputs. Before the flow reversal, the LHP operation is unusual: two-phase condensing flow is present in a significant portion of the liquid line, as suggested by temperature TC 14 The latter is indeed close to vapor line temperatures (TCs 11, 16 and 18), as shown in left-hand zoomed view of Fig. 11. Hence, we can conclude that condensation ends in the second half of the liquid line, where the flow is also subcooled (TCs 10, 12 and 13); this behavior occurs also with the first heat power step of 30 W. In this situation, the LHP behavior is driven by the heat losses between the transport lines and the external environment (at ~ 20˚C), regardless the heat sink conditions. Meantime, the reservoir slowly heats up (TCs 4-9). Once it get close enough to vapor temperatures (TCs 11, 16 and 18), the flow reversal appears: a quick ejection of fluid from the reservoir into the liquid line causes a sharp increase of TC 10, followed by TCs 12 and 13. The long liquid plug flows backwards in the liquid line, entering the condenser. Then, flow circulation restarts normally, condensation front moves inside the condenser and spreader plate temperatures increase slightly (TCs 25-30). TC 17 now decreases below the saturation point, providing that flow at condenser's exit is now subcooled. Finally, vapor, reservoir and evaporator temperatures increase smoothly and asymptotically. From now on, the LHP shows a normal steady operation and the heat sink drives the operating temperature. The role of the heat losses in the liquid line becomes less important. The situation does not change at higher heat power steps. It becomes apparent that, in absence of NCG, the LHP operation was affected by instability phenomena occurring mostly during the transient phase and that deserve further investigation. Comparing equivalent tests with and without NCG, it was observed that the LHP with NCG has a larger operation spectrum over a wider range of heat powers. However, looking at Fig. 12, the steady thermal performance is remarkably degraded compared to the case without NCG, especially at lower heat powers. One can observe that also the shape of the operating curve is different. The presence of NCG extends the heat load range in the variable conduction mode [START_REF] He | Effects of non-condensable gas on the operation of a loop heat pipe[END_REF]. NGC has also a remarkable impact on the condenser. In fact, since in this case the vapor temperature is higher at the condenser inlet, for the same TII, the condensation length can be remarkably lower.

V.Conclusions

In this study, a Loop Heat Pipe was conceived, manufactured and tested for the thermal management of the aircraft nacelle equipment. The minimization of the condenser size was actually a multi-objective problem that concerned the evaluation of suitable thermal environment, the minimization of the transport lines length and the integration constraints. Water was selected as working fluid, CP titanium and Grade 9 titanium alloys were selected as materials for their relatively low density, chemical compatibility with water and proven feasibility for both aeronautical and heat pipes applications. A flat evaporator and a disk-shaped capillary structure were chosen, with vapor grooves machined on one side of the porous wick and arranged in a fishbone shape. The sintered porous wick has shown a satisfying mechanical stiffness that allowed to resist to more than 1500 cycles of water freezing/thaw within the porous structure itself. During the first tests, an important amount of non-condensable gases was generated. The LHP was cycled and the NGC amount became stable; this required approximately 300 hours of tests and the major contribution to this generation came from the porous structure. The passivation had also significantly increased the wettability of the porous media, providing that LHP performances improved despite the initial gas generation. This has also outlined the importance of fluid/solid wettability of the porous wick. A decrease of the secondary working fluid temperature increased the transition heat power thresholds between the variable and fixed conductance modes, changing the concavity of the operating curves. A secondary heater attached to the liquid line have allowed to investigate the effects of a heat gain on the liquid line, to simulate the heat transfer within the engine nacelle. The tests were successful and the LHP has shown a robust operation and self-adaptability when the returning subcooled liquid was heated up. The maximum heat power supplied to the secondary heater was up to 30 % of the evaporator one. Finally, the LHP was vacuumed, re-filled with the same amount of water and tests were repeated. This time, the steady state thermal performances improved considerably, but instability phenomena occurred. At low secondary fluid temperature, the transient phases were characterized by large and long temperature overshoots. Their origin remains unclear. Moreover, local episodes of flow reversal were also observed. When comparing the LHP performances with and without NCG, important differences were found, especially at lower heat power levels. As a conclusion, results show that titaniumwater LHPs are promising and efficient solutions for the thermal control of engine integrated equipment. Although more efforts are needed for the characterization of these devices in the nacelle environment, this study has outlined some important clues that encourage further investigations in the field.

  owadays, R&D efforts in civil aviation are mainly oriented towards fuel consumption optimization for CO2

Fig. 1

 1 Fig. 1 Schematic view of the engine's compartments (left) and illustration of the heat transfer on a single integrated item (right).

Fig. 2

 2 Fig. 2 Schematic of a conventional loop heat pipe with flat evaporator: typical liquid vapor distribution during normal operation.

Fig. 3

 3 Fig. 3 Condenser design steps: a) 1D spreader approximation (Q = 200 W), b) spreader plate surfaces for different core compartment regions and c) optimized geometry (all lengths are in mm).

Fig. 4

 4 Fig. 4 Common, organic, synthetic and silicon-based fluids utilized in heat pipe technology and heat transfer applications: useful temperature range, freezing, boiling -flash points and limitations.

Fig. 5

 5 Fig. 5 Half-sectional view of the evaporator -reservoir (left) and a detailed view of both upper and bottom surfaces of the porous wick (right).

Fig. 6

 6 Fig. 6 Schematic view of the LHP prototype equipped with the heating blocks and the cold plate with an illustration of temperature and pressure sensors arrangement.

Fig. 7 a

 7 Fig. 7 a) Evaporator wall, vapor line and reservoir temperatures, and b) vapor pressure as functions of Qin for several operating hours (horizontal, TII = 50˚C).

Fig. 8 Fig. 8 Fig. 9

 889 Fig.8reports the temperatures and pressure signals recorded during a test in horizontal orientation with increasing and decreasing heat power inputs and a constant secondary fluid temperature of 110˚C. Once the first 40 W heat power step is supplied, the evaporator and reservoir temperatures increased sharply and almost simultaneously. This may be due to the presence of liquid in the vapor grooves and vapor in the evaporator core, respectively[START_REF] Ku | Loop Heat Pipe Startup Behaviors[END_REF][START_REF] He | Effects of non-condensable gas on the startup of a loop heat pipe[END_REF]. In this situation (one of the most critical according to He et al.[START_REF] He | Effects of non-condensable gas on the startup of a loop heat pipe[END_REF]), the loop startup requires evaporator superheating. Once nucleation started, vapor begins to flow and, like a piston, pushes the long liquid plug away from the vapor line, bringing the excess of liquid into the reservoir. During this transient phase of approximately 1100 seconds, high amplitude temperature oscillations occur, in particular in the vapor line at condenser inlet (TC 18, yellow curve) as well as in the liquid line at the reservoir inlet (TC 10, green curve), at 100 W. This was also one of the additional effects related to the presence of NCG in loop heat pipes already observed by Prado-Montes et al.[START_REF] Prado-Montes | Effects of non condensable gas in an ammonia loop heat pipe operating up to 125°C[END_REF], with the largest amounts of NCG and lowest heat power levels. Oscillations in LHP temperatures are linked to unstable operation, probably due to a significant degradation of the LHP overall conductance.

Fig. 10

 10 Fig. 10 Transient response of the LHP with increasing liquid line secondary heater power (horizontal, TII = 130˚C, Qin = 200 W).

Fig. 11

 11 Fig. 11 Transient response of the LHP without NCGs (horizontal, TII = 50˚C).

Fig. 12

 12 Fig. 12 Effects of NCGs on evaporator and reservoir steady-state temperatures (horizontal, TII = 50˚C).

Beyond 200 W, the LHP provides a smooth and robust operation. The values measured by the vapor line thermocouples (TCs 11,[START_REF] Fleming | Titanium-Water Loop Heat Pipe Operating Characteristics Under Standard and Elevated Acceleration Fields[END_REF] are well close to each other (average difference less than 2˚C over 1.6 m); this suggests that vapor superheating is negligible at the evaporator's outlet. The apparent temperature drop measured by TC 18 below saturation point is due to a thermal interaction between the pipe wall and the condenser. The reservoir temperatures measured in the middle of the cylindrical wall (TCs 4-7) are substantially higher than those placed on the disk above (TCs 8, 9). Here, the temperature difference is caused by the presence of NCG accumulated in the upper part of the reservoir, where they are normally trapped during LHP operation in horizontal position. Indeed, Fig. 8b shows that pressures values recorded during the test at the reservoir inlet far exceed the saturation level corresponding to the measured temperatures (𝑃 , = 𝑃 (𝑇𝐶𝑠 (4 -7)), computed via the Clausius-Clapeyron equation).

Surprisingly, condenser's outlet temperature TC 17 is below the heat sink one of 110˚C; this may be due to a thermal interaction with the filling branch pipe (Fig. 6), not insulated. Although the LHP was thermally insulated, heat losses occur in the transport lines, as suggested by the temperature drop in the liquid line (TC 17-14-13-12-10), caused by a sensible heat leak ranging between 5% and 13% of Qin. A little temperature hysteresis is observed between the increasing and decreasing heat power routines.

Finally, a temperature gradient is observed at the interface between the heating matrix and the LHP evaporator wall (TC1-3, red in Fig. 8a): their relative differences at a fixed heat power input of 400 W dropped of 12˚C between 8 and 300 hours of operation. This may be due to a change in the porous wick characteristics during its passivation process, as previously discussed.

B. Influence of the secondary fluid temperature

As shown in Fig. 9, the secondary fluid temperature has a remarkable impact on the LHP operation. Indeed, a change of the secondary working fluid temperature modifies both the concavity and the relative minimum of the LHP operating curves (Fig. 9a). A high secondary working fluid temperature (150°C) provides higher liquid temperatures at condenser outlet (TC 17), as shown in Fig. 9b. At low heat powers, the mass flow rate is rather small and the liquid within the liquid line approaches the ambient temperature, due to the heat losses in the transport line (even with the thermal insulation), regardless the heat sink conditions, which is typical of U-shape operating curves of LHPs. Hence, the operating temperatures curves are closer to each other in the range between 100 W and 150 W, providing that the

D. LHP operation without NCG

Once the NCG generation rate inside the LHP became negligible, the device was vacuumed and refilled with pure water. Then, tests were repeated, carefully checking the reservoir temperatures and pressures. Fig. 11 shows the temperatures recorded during a horizontal test, at TII = 50˚C. One can observe that reservoir temperatures (TCs 4-7 and 8-9) are now well superimposed, whatever the heat power applied, proving the absence of NGC (also confirmed by the pressure curves, not presented here). In this case, the LHP steady-state temperatures are significantly lower compared to the equivalent tests with NCG, as shown in Fig. 12. However, the LHP operation present large temperature overshoots during the transient phase at high heat power steps. These appeared only with a lower secondary working fluid temperature (in the test of Fig. 11, TII = 50˚C) and for high heat powers supplied at the evaporator. As shown in Fig. 11, when the heat power increases above 200 W, the evaporator wall temperatures in particular are interested by high peaks and longer transient periods. This evidence suggests that three-phase contact line recedes within the porous wick, vapor penetrates in the empty spaces of the wick providing an effective insulation between the evaporator wall and the saturating flow. As a result, the evaporator wall temperatures are increased until the liquid-vapor front advances again retaking its original configuration. It is difficult to clearly understand the origin of this transient behavior from the available data. The slight undershoot of reservoir temperatures immediately after the heat power increase (see the right-hand zoomed view of Fig. 11) reminds the "Cold Shock"; a phenomenon observed in large LHPs undergoing high heat power transitions and documented by Nikitkin et al. [START_REF] Nikitkin | High Power Cold Shock Phenomena in Loop Heat Pipes[END_REF]. During a Cold Shock, as the mass flow rate increases with the input heat power, at high heat power steps there is a rapid injection of cold liquid into the reservoir. This could slow down the temperature growth rate of the reservoir with respect to the evaporator one. A pressure difference is generated across the wick. This additional pressure difference, together with the hydraulic losses through the LHP may exceed the wick pumping capability, causing a temporary evaporator dry out, terminating the flow circulation with a sharp temperature rise in evaporator and reservoir [START_REF] Prado-Montes | Effects of non condensable gas in an ammonia loop heat pipe operating up to 125°C[END_REF]. In the tests performed in the present work, any sign of flow circulation shut-off was detected. Moreover, up to 330 W, the vapor and the reservoir temperatures are well superimposed, excluding the possibility of an additional pressure difference across the wick to be counterbalanced by the porous media. The same considerations can be extended to the case of 398 W, where the vapor is clearly superheated (TC 11) but the saturation conditions of the vapor are really close to

Aknowledgments

The authors wish to deeply thank the French Civil Aviation Authority (DGAC) for the financial support in the context of the OPTIMA project.


Maksym Slobodeniuk
email: maksym.slobodeniuk@ensma.fr

Remi Bertossi

Vincent Ayel

Rajalakshmi Ravichandran

Karthik Thyagarajan

Cyril Romestant

Yves Bertin

Ensma

Experimental study of the flat plate pulsating heat pipe operation during dry-out and flow reactivation periods under microgravity conditions

Keywords: Flat plate pulsating heat pipe, Microgravity, Flow regime, Re-activation, Transition velocity

An investigation of thermal performances of the flat plate pulsating heat pipe (FPPHP) and liquid-vapor interfaces oscillation influence on the flow pattern inside FPPHP for microgravity conditions have been performed. Tested pulsating heat pipe represents a seven U-turns closed-looped FPPHP made of molybdenum base (200×80×3 mm 3 ) and sapphire cover plate (200×80×5 mm 3 ) and designed for 69 th ESA Parabolic Flight Campaign. Serpentine channel with depth of 2.5 mm and width of 3 mm is engraved in molybdenum base that with following gluing of sapphire plate on the base gives 3×3 mm 2 square channel (0.5 mm of the glue thickness). Ethanol is chosen as working fluid with volumetric filling ratio of 40%. Experimental tests are performed for heat loads range from 100 W to 150 W. Microgravity periods are mostly characterized by the significant temperature augmentation in the evaporator zone (temperature rise up to 36 K for 150 W of applied power). This temperature rise is a result of fluid accumulation in the condenser and dry-out of evaporatorheat transfer only by the FPPHP body conduction. Flow reactivation, accompanied by the flow pattern change from slug-plug to semi-annular and temperature drop, was observed only for few cases during microgravity phases. Video post-processing was done to define flow parameters influencing flow transition for microgravity conditions, as well as to determine liquid plugs velocities and accelerations for both phases. Most used criteria of the slug-plug flow definition are validated for this case: obtained average Weber number value is almost the same that reference value (Weref = 4) and average Garimella number is most of the ten times higher than reference (Gaexp = 1980, Garef = 160). The magnitude of driving pressures are in the range of 50-630 Pa with average value of 360 Pa.

Introduction

Integration of high power and performance electronic devices in modern spacecraft systems with heat generation of hundreds of watts per square centimeter crucially increases needs in high performance, low weight, energy efficient and reliable thermal management systems. Due to these specific demands, twophase heat rejection devices are preferable for space applications. However, pumped cooling devices, despite their capability to remove high heat fluxes, require supplemental equipment, as well as pumping subsystem (usually consisting moving parts), extension reservoir etc., which leads to additional energy consumption, increase in weight and size and, as a consequence, reliability loose. Heat pipes, as one of the most widely used, both for terrestrial and aerospace applications, passive two-phase thermal dissipation technology, despite their reliability and development, cannot manage with extra high heat fluxes and longdistance heat transportation [START_REF] Hengeveld | Review of Modern Spacecraft Thermal Control Technologies[END_REF]. Capillary Pumped Loops (CPLs) and Loop Heat Pipes (LHPs) are devoid of these disadvantages (heat removal capability could be at least in two orders magnitude higher than for conventional heat pipes), but CPLs need exhaust and time-consuming starting process and for LHPs is not easy to achieve a steady-state temperature regime due to wick "back conduction" [START_REF] Bugby | Multievaporatorhybrid loop heat pipe for small spacecraft thermal management[END_REF]. Although existing highly efficient passive cooling solutions, the engineering society is still in search of simple, low cost, high performance and reliable heat transfer technologies.

During few last decades, research and engineering studies on a new passive two-phase heat transfer device with a simple structure, called Pulsating Heat Pipe (PHP) or Oscillating Heat Pipe (OHP), took shape. In the following, the acronym FPPHP will refer to "Flat Plate Pulsating Heat Pipe", i.e. a metallic plate in which is engraved a unique square or rectangular channel. The simple structure of the PHP is represented by a curved tube or channel (with an inner diameter of capillary dimension to ensure domination of surface tension forces compared to gravitational ones), which is folded back to make itself parallel and partially filled with liquid to reach saturation conditions [START_REF] Akachi | Pulsating heat pipes[END_REF]. The liquid is distributed inside the channels in a chaotic manner, forming alternating chains of liquid plugs and vapor bubbles. Evaporator and condenser are placed usually on the opposite sides of PHP (with an intermediate so-called adiabatic zone between them), which leads to differences in saturation conditions between two zones and, as a result, pressure driven displacement of the liquid-vapor pairs along the channels. Consequently, heat transfer process related to PHP operation, consists of both latent and sensible heat forms, which increases thermal performances. Simple design without any porous structures, moving parts and sub-systems, coupled with high heat transfer performance makes PHP a very promising technology for future exploitation onboard space apparatuses.

Recently, Ayel et al. tested a semi-transparent FPPHP (square channel dimensions of 2.5 mm with FC72 as working fluid) during the ESA 62 nd Parabolic Flight Campaign. [Ayel,18] highlighted two major periodic phenomena for large diameter channels FPPHP operating under microgravity conditions. First, the fluid spontaneously tends to a temporary dry-out at the evaporator, with liquid phase accumulated only in the cold parts of the condenser zone, pushed by the vapor produced in the evaporator zone. Secondly, isolated liquid plugs moves under the influence of even small pressure variations and flow through the hot evaporator zone, leading to strong evaporation and/or boiling, increasing the local pressure. This mechanism results in triggering a strong slug flow motion in all the interconnected channels and therefore temporarily improving the overall heat transfer, decreasing the evaporator temperatures, until a following weakening of the fluid motion causes another dry-out condition, and so on [Ayel,18].

Similarly, available data on the stable PHP operation in horizontal mode is an object of many contradictions. [Yang,09;Qu,12;Betancur,18;Winkler,[START_REF] Pietrasanta | Experimental analysis of two-phase flows in the context of Pulsating Heat Pipes for space applications[END_REF] reported an efficient PHP operation under horizontal orientation, but unstable operation with low thermal performances caused by intermittent long-term stopover phenomena (momentary stops of liquid slugs oscillation [Jun,[START_REF] Pietrasanta | Developing flow pattern maps for accelerated two-phase capillary flows[END_REF]) or even a complete stop of operation due to early dry-out of the evaporator were observed for horizontal inclination of PHP [Khandekar,02] [Chien,12] [Ayel,14] [Jun,18].

Almost all-available literature on flow visualization in PHP is about qualitative analysis of flow behavior and influence of sensible heat transfer on the overall performance of PHP, which is still contradictory [START_REF] Shafii | Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes[END_REF][START_REF] Senjaya | Oscillating Heat Pipe Simulation With Bubble Generation[END_REF]Nikolaev, 2011;[START_REF] Jo | Experimental investigations of heat transfer mechanisms of a pulsating heat pipe[END_REF][START_REF] Jung | Effect of oscillation amplitudes on heat transfer mechanisms of pulsating heat pipes[END_REF][START_REF] Kamijima | Relating the thermal properties of a micro pulsating heat pipe to the internal flow characteristics via experiments, image recognition of flow patterns and heat transfer simulations[END_REF]. Quantitative analysis of flow regimes and their transition is presented in the work of Pietrasanta et al. [START_REF] Pietrasanta | Developing flow pattern maps for accelerated two-phase capillary flows[END_REF], where the authors proposed a flow pattern characterization based on modified -commonly used-non-dimensional criteria: Bond (Bo), Weber (We) and Froude (Fr) numbers.

Related mostly to design tasks is the definition of adequate critical diameter ensuring stable liquid/vapor separation in slug/plug flow. Today, the most important non-dimensional parameters, like static criterion based on Bond number (eq. 1), considering gravitational and surface tension forces balance, a dynamic criterion, based on Weber number (eq. 2) and including both surface tension and inertial forces, or more relevant criterion, including inertial and buoyancy effects based on Garimella number (eq. 3), are widely used [START_REF] Hosoda | Meandering Closed-Loop Heat Transport Tube[END_REF][START_REF] Gu | Effects of Gravity on the Performance of Pulsating Heat Pipes[END_REF]Harirchian, 2010]. Common critical values for transitional flow from slug flow to annular flow pattern based on these three non-dimensional numbers are given below:

𝐵𝑜 𝑐𝑟𝑖𝑡 = (𝜌 𝑙 -𝜌 𝑣 )𝑔𝐷 2 𝜎 = 2
(1)

𝑊𝑒 𝑐𝑟𝑖𝑡 = 𝜌 𝑙 𝑢 2 𝐷 𝜎 = 4
(2)

𝐺𝑎 𝑐𝑟𝑖𝑡 = 𝐵𝑜 0.5 • 𝑅𝑒 = ( (𝜌 𝑙 -𝜌 𝑣 )𝑔𝐷 2 𝜎 ) 0.5 • 𝜌 𝑙 𝑢𝐷 𝜇 𝑙 = 160 (3)
where l, v, g, D, σ, v, Re, μl are liquid, and vapor, densities, gravity acceleration, channel diameter, surface tension, liquid slug velocity, Reynolds number and liquid dynamic viscosity respectively.

Andredaki et al. [Andredaki, 2021] numerically studied the break-up mechanism and flow regimes of Taylor bubbles inside capillary tubes of different diameters and fluids. Based on their numerical investigation, partial break-up of bubble happens in the range of 75 < We < 250 and full break-up for We > 250, which is much higher than the above-mentioned value 𝑊𝑒 𝑐𝑟𝑖𝑡 = 4.

Due to complicated interaction between gravitational, interfacial, inertial and viscous forces inside PHP, it becomes difficult to implement these criteria even for adequate design of PHP for terrestrial applications, or to predict flow pattern transition [START_REF] Pietrasanta | Developing flow pattern maps for accelerated two-phase capillary flows[END_REF]. In microgravity, high velocity interface motions lead to flow pattern changes from established slug/plug to annular flow, indicating inertial forces predomination on surface tension [Ayel, 2019a]. Besides, liquid velocities values during PHP operation could be much higher than the widely accepted one of 0.1 m/s.

Complex mechanisms of thermo-hydrodynamic processes inside PHP are not fully studied and any suitable design recommendations are no available, together with some contradictory assessments from researchers [START_REF] Tang | A review of recent experimental investigations and theoretical analyses for pulsating heat pipes[END_REF][START_REF] Bastakoti | An overview on the developing trend of pulsating heat pipe and its performance[END_REF] and absence of universal flow transition criteria. Misunderstandings of the relation between velocity and flow pattern need regular experimental investigations to be carried out.

Due to specific design features of flat plate pulsating heat pipes, as a plane shape which allows the installation of a transparent plate covering it, visualization studies are possible for all channels and zones without significant changes in fluid/structure interactions (besides, the base with milled channels is made from designed material).

The general objective of this work is to study the heat transfer capability of a flat plate pulsating heat pipe designed and test it under microgravity conditions. Also, characterize the flow behavior during stopover and following flow pattern transition during the reactivation phases. For these reasons, a molybdenum/sapphire FPPHP was tested during the 69 th ESA Parabolic Flight Campaign.

Experiments

Test section

The investigated flat plate pulsating heat pipe (FPPHP) with seven U-turns in the evaporation zone is shown in figure 1. It has been fabricated from a molybdenum rectangular plate (80×200×3 mm 3 ) in which a unique rectangular channel (2.5 mm deep and 3 mm large) has been milled. The plate with the milled channel is covered with a sapphire plate (80×200×5 mm 3 ) using epoxy glue to guarantee perfect sealing at the plate boards, and between adjacent channels relative to one-another. The thickness of the glue layer is set at 0.5 mm, providing to the channels a depth of 3 mm, giving them a square shape that corresponds to the chosen hydraulic diameter of 3 mm. Molybdenum as a construction material was chosen in order to have almost the same coefficient of thermal expansion (4.8 μm.K -1 ) as sapphire glass (5.2 μm.K -1 ) while maintaining a high thermal conductivity (138 W.m -1 K -1 ).

The heating of the evaporator is provided via an engraved molybdenum plate (80×40×3 mm 3 , fig. 1) glued on the bottom backside of the FPPHP with a serpentine groove of 1.5×1.5 mm 2 . Stainless still coated Ni-Chrome heating wire (Thermocoax ® Type NcAc15) is crimped into the groove of the heating plate. Heat rejection from the condenser is realized via a copper block (100×80×10 mm 3 ), glued on the top back side of FPPHP, with milled rectangular shape serpentine channel through which cooling water circulates. Four T-type thermocouples (±0,8 K, precise positions are presented in fig. 1) are installed between the heating plate and FPPHP within the grooves milled inside channel ribs. Measurements of the fluid pressure at the bottom of the evaporator (connected to a hole in the middle U-turn) are realized with GE ® PTX5076-TA digital pressure sensor (±200 Pa). Leakage tests were done using Pfeiffer Vacuum® Adixen ASM 142 helium leaks detector. Previous preliminarily terrestrial tests showed that molybdenum-water pair induces an electrochemical reaction with generation of non-condensable gas and liquid/surface staining. Thus, pure ethanol was used as a working fluid. Vacuumed PHP was filled with previously degassed ethanol with 40% of volumetric filling ratio.

Experimental setup

Two dedicated experimental racks have been developed respecting specific technical requirements to provide tests during parabolic flight campaigns onboard Novespace aircraft A320. The experimental system consists of the main control rack, which provides control and maintenance of the second, confined rack dedicated to the experiments (schematic on fig. 2), in which the manufactured flat plate pulsating heat pipe was installed. A confined rack is necessary to isolate PHP and sub-systems from any impact from outside, preventing potential leakage to ambient and making possible the ambient temperature control inside. One side of the confined rack was made from a massive aluminum plate (air-cooled heat exchanger with ambience), embedded with fifteen copper heat sinks equipped with fans which are divided into three independent electrical channels to allow rough control of the cooling fluid temperature level. Aluminum plate in paring with condenser cooling block, Ismatec ® Reglo-ZS gear pump and extension reservoir create a water cooling loop sub-system for heat rejection from the condenser to the plane cabin ambient air. Canon ® EOS 100D camera is used for the recording of fluid flow motions inside PHP. Synchronization of recorded videos with other parameters was performed using a LED, directly mounted on the PHP. Temperature and pressure data, as well gravity level, were acquired via NI ® cRIO-9074 chassis with installed thermocouple and voltage inlet modules, and DC output module for synchronization procedure.

Besides thermocouples installed in the evaporation zone (T1 to T4, see figure 1), two thermocouples are set up on the inlet (Tinlet) and outlet (Toutlet) of the condenser cooling block: one is directly installed on the aluminum massive plate (Tcool), and the last one measures the confined rack ambient air temperature near the PHP (Tamb).

Fugure 2. Schematic view of the experimental system configuration Two computers are mounted into the main control rack for experimental system control, data acquisition and manipulations with camera. Developed LabVIEW ® software allows data acquisition and recording, trigger with camera for synchronization and input power regulation. Command systems also consist of an electrical power supply (ELC ® ALR3220 DC), security box (which is needed for the partial or complete shutdown of the experimental system in case of exceeding threshold temperature), self-made accelerometer and pump flow regulator. DC source is connected to the heater wire located in the heating plate. The main rack is connected to the onboard electrical system.

Parabolic flights

Nowadays, the simplest approach to reach microgravity conditions is the parabolic flight, during which an aircraft (Airbus A310 ZERO-G) flies from steady horizontal flight to following maneuvers: (a) aircraft climbs up to 50° (pull-up phase, fig. 3) for about 20 s with accelerations levels (perpendicular to the aircraft floor) between 1.8 and 2g; after, (b) power of all aircraft engines are reduced for about 20 to 25 s just for air drag compensation (parabolic free fall, i.e. microgravity phase); (c) the aircraft dives down to 42° (pullout phase) during around 20 s with 1,6-2g acceleration and (d) comes back to a steady horizontal flight [START_REF] Pletser | The First European Parabolic Flight Campaign with the Airbus A310 ZERO-G[END_REF]. All these maneuvers are combined in sequences of five parabolas with intervals of around one minute between each parabola. The duration of each sequence is of few minutes. One day of flight allows reaching thirty parabolas plus one for adjustment in the six sequences of five successive parabolas. The residual accelerations sensed by experimental set-ups attached to the aircraft floor structure are typically in the order of 0.01g during the microgravity phase.

Results and discussion

Experimental results, obtained during the 69 th ESA Parabolic Flight Campaign for molybdenum FPPHP with heat loads of 100 W, and 150 W (constant level for each set of five consecutive parabolas), are presented in the following section. FPPHP has been tested in a vertical position with bottom heat mode during normal and hyper gravity phases (position is not important for the microgravity phase). It should be noted that due to the high thermal inertia of the FPPHP and the short duration of microgravity phases, thermal regimes are not developed during these periods.

Temperature responses during parabolas

Figure 4 represents temperature and pressure variations during a series of five consecutive parabolas for respective 100 W (a) and 150 W (b) applied heat powers. The temperature and pressure profile during normal gravity remains almost stable without significant fluctuations. Whereas, hyper gravity periods are characterized by small decrease of evaporator temperature and pressure. However, with the onset of microgravity, a simultaneous temperature rise is observed for all evaporator thermocouples. This temperature increase is a consequence of liquid accumulation in the condenser zone and evaporator dry-out as a result (figure 5 (b, left)). In contrast to the temperature, pressure rises little and then stabilizes (unless during reactivation periods). For all heat loads, such temperature behavior was observed during every microgravity period. The temperature and pressure profiles for 100 W and 150 W, which are the most representative, are shown below.

Flow characterization during parabola

The presence of the whole menisci in every channel and liquid accumulation in the condenser zone is clearly visible in fig. 5b (left). Due to accumulation in the condenser zone, liquid separates in the form of plugs and vapor bubbles by the menisci, and the vapor phase remains in the adiabatic and evaporation zones and provokes dry-out and failure operation of the FPPHP. In such a configuration, evaporator wall temperatures continuously rises due to a weak heat transfer with the non-moving fluid (until t = 6221 s in fig. 5a). Unlike the dry-out case, flow re-activation leads to a spontaneous rise of menisci oscillating amplitude, menisci deformation and a uniform fluid distribution inside the FPPHP in the form of a semi-annular/annular flow pattern. Flow pattern during this period is very similar to that observed for a FPPHP tested in the bottom heating mode under normal gravity conditions with ethanol [Ayel,14]. Synchronization of videos with temperature and pressure profiles have demonstrated that the reactivation of fluid flow inside the PHP is at the origin of the observed evaporator temperature decrease. In parabola n°2 of figure 4a and 3, 4 of figure 4b, no re-activation phase have been observed and the resulting temperature curves consist of smooth temperature increase due to continuous heating and lack of cooling process.

Menisci movement and re-activation mechanism, as well stopover mechanism, will be explained in the next section.

Video post-processing tool

In this section, obtained images resulting from the recorded video during three microgravity periods (red fields in fig. 4) have been post-processed for liquid/vapor interface tracking during dry-out and re-activation phases. Interface detection and their tracking allow identifying positions of menisci at each time and, as a derivative, to calculate their velocities and accelerations up to the flow transition and re-activation, or until menisci deformation and break-up (if they still exist) do not allow to track them anymore.

To process rough images, first, they were extracted from raw videos in the form of image frames sequences and then converted to black and white. After that, feature definition and object tracking tools, available in the OpenCV® tool-set, are used for the menisci tracking. The main purpose of these tools is the manual definition of the vapor/liquid interfaces and their following automatic tracking through time (fig. 6 (top)).

One of the advantages of this approach is the possibility of defining the flow transition from slug flow to annular flow pattern, or another kindif interface cannot be defined anymore (due to highly deformed menisci). Therefore, in the following, critical velocities/acceleration values can be defined as the last values obtained before menisci "disappearance" or their deformation, corresponding to the transitional flow pattern.

Figure 6. Definition of the menisci position: (top) channel with menisci and (bottom) tracking approach validation

To validate the approach developed in the present work, available images from previous studies of tubular pulsating heat pipe [START_REF] Pietrasanta | Experimental analysis of two-phase flows in the context of Pulsating Heat Pipes for space applications[END_REF] have been used for the generation of the composite image (fig 6

(top)). Then, the image of menisci is isolated and placed over an extracted backdrop of the fluid regions in the image. The menisci are then moved with a given velocity profile (sinusoidal). The developed framework is used to determine menisci velocities from synthetic images and then allows comparing the latter with programmed velocity profile and showing great consistency in the results (fig. 6 (bottom)).

Motion of liquid plugs

For better readability of the acquired data, an extra focus will be placed on the examination of two nearby liquid plugs: LP67 and LP89, which are located in the center of the FPPHP. Figure 7 depicts these two liquid plugs, as well as the channel numbers. Dry-out/Stopover the y-axis of figure 8 (situated between 0 cm and 4 cm positions). This means that the fluid flow transition is probably not triggered by evaporation in the evaporator but in the superheated adiabatic zone. On the other hand, high menisci motion amplitudes lead to the liberation of the wall surfaces in the condenser (located between 12 cm and 20 cm in y-axis of fig. 8) and, as a result, to a higher condensation rate local pressure drop near liquid plug. Unlike cases for 150 W applied heat power, no frequent high amplitude movements of the central liquid plugs have not been observed for 100 W.

Values of maximum velocities (Vmax, see figure 9) obtained for all microgravity periods during which reactivation phases were observed, as well velocities measured just before the flow pattern transitions (Vtrans, see figure 9), are shown in figure 10. In most cases, maximum oscillation velocities correspond to the transition velocities just before the flow pattern transition/menisci deformation. Only in few cases, the maximum velocities Vmax have been reached during the period prior to transition (figure X). The average velocity of transition for all presented conditions is equal to 0.19 m/s, which is two times higher than the commonly known operating velocity of 0.1 m/s in the literature. It must be noted that, sometimes "transition velocity" corresponds to the menisci deformation, but not to their total "disappearance". However, reaching these velocities gives us a flow pattern transition represented in figure 5 (b, right).

Figure 9. Transient velocities of two following liquid plugs menisci (150 W, parabola 1).

Figure 10. Channel distribution of Vmax and Vtrans.

Non-dimensional analysis of flow pattern transition

The obtained transition velocities allow evaluation of commonly used criteria for confined flow prediction: Weber and Garimella numbers, as functions of the channel number are presented in fig. 11 and fig. 12 respectively. First observations show a distribution of Weber number ranging from 1 to 12, but most of the points (72%) are gathered in the zone between 3 and 5, very close to the reference value of 4. Values for the interfaces of the liquid plug 1-14 are significantly higher than other due to higher transition velocity, which could be caused by a length of this liquid plug that is higher (around 50%) than others (surrounding U-turn in the condenser zone). The applied heat power seems to have very little influence on the results.

Almost the same behavior, as shown for Weber number, is observed for Garimella number values (fig. 12).

It is interesting to note that despite the weak influence of the applied heat power on the values, it seems to affect both criteria behaviorvery similar for both parabolas for 150 W of applied power. Despite the similar behavior with Weber number, the average value of Ga number, about1980, is ten times higher than the value of 160 mentioned in the literature. Figure 12. Garimella number based on the transition velocity.

Force balance for liquid plugs motion.

The following momentum equation [START_REF] Bertossi | Motion of liquid plugs between vapor bubbles in capillary tubes: a comparison between fluid[END_REF] could be used to calculate the magnitude of the driving pressure as well as the impact of the influencing forces on the motion of liquid plugs (fig. 14):

𝑚 𝑙 𝑑𝑢 𝑙 𝑑𝑡 = 𝐹 𝑑𝑟𝑖𝑣 -𝐹 𝑣𝑖𝑠 (4)
where Fvis and Fdriv are viscous and driving forces, respectively. These forces are calculated with eq. ( 5). Gravity forces are not taken into account in this calculation due to the microgravity conditions. (5)

where ml, Lp, ul are liquid plug mass, length and velocity respectively; l is the liquid density; Acs and R are the channel cross-section area and radius respectively; ΔPv and ΔPc pressure difference between two sides of the liquid plug, and the capillary pressure respectively; and Λ=64/Re is the Darcy coefficient for viscous pressure losses for laminar flow (here, the flow is assumed to be developed laminar flow). Liquid plug mass is calculated as:

𝑚 𝑙 = 𝜌 𝑙 𝐴 𝑐𝑠 𝐿 𝑝 (6)
As shown in fig. 13, the length of liquid plug is defined from the knowledge of the positions (from top of each channel) of the two menisci located at both ends of liquid plug (xn and xn+1):

𝐿 𝑝 = 𝐿 𝑏𝑒𝑛𝑑 + 𝑥 𝑛 + 𝑥 𝑛+1 (7)
where Lbend represents the length of the U-turn. Vapor pressure difference between two ends of liquid plug is given by: Due to specific interest in flow transition and almost similar motion amplitudes and frequencies for all liquids plugs, calculated forces magnitudes just for one "surrounding" and two central liquid plugs (for channels 1-14, 6-7 and 7-9, see figure 7) are presented in figure 14.

∆𝑃 𝑣 = 𝑃 𝑣𝑟 -𝑃 𝑣𝑎 (
Left-hand side of figure 14 represents forces magnitudes, obtained from Eq. ( 4) and ( 5), for a period, representing one second before transition, for 100 W, and right-hand side for 150 W, applied powers, respectively (parabola 5). Figure 14d, where forces are negative due to the opposite direction of the liquid plug movement, is presented with reversed y-axis for better comparison. Re-activation zone characterized by the significant amplitude and frequency rise of all forces oscillations for high heat loads. Fluctuations for lower heat powers are less noticeable. It is important to note that the viscous forces are the weakest, while not being negligible for both cases during dry-out phase; but this influence comes out just before transition (as can be seen in fig. 14d, e and f). Comparing presented cases, the acceleration and driving forces values on the transition line are very close from case to case. Interesting fact is that the transition takes place not at the same time for each liquid plugs, but with short time delay, that may be due to the vapor compressibility (dash line in fig. 14).

Knowing the driving forces, the resulting values of the driving pressures ∆𝑃 𝑑𝑟𝑖𝑣 (eq. 9) are plotted in figure 15. Note that the capillary pressure drop, ∆𝑃 𝑐 , is directly included in the driving pressure term in eq. ( 9) due to the fact that its value is not estimable in these measurements. In analogy with the previous figures, driving pressures are plotted for the liquid plugs 6-7, and 8-9, in figure 15 for the periods from start of microgravity (at t = 0 s) until the re-activation phase with applied power of 100 W (fig. 15a) and 150 W (fig. 15b). In parallel, the experimental absolute pressure (Pexp), in the evaporator between these two liquid plugs, is also plotted in the same graphs. One can see that the absolute pressure shows increased instabilities during the re-activation phases, synchronously with the calculated driving pressure fluctuations from the post-processing of the image analysis. Here it can be seen that during total period until re-activation, values of driving pressure for the two liquid plugs seems to be almost similar with a slight time lag, due to the vapor compressibility (as shown previously). Amplitudes of pressure oscillations increase up to the value attained at the re-activation time and do correspond to significant absolute pressure surge between two liquid plugs. Interesting to note, that the final values of driving pressure (corresponding to the flow pattern transition) are almost similar for both values of applied heat power and are of about 350-380 Pa. However, unlike the particular case represented in figure 15, driving pressure is varying in the wide range of values from 50 to 670 Pa, as represented in figure 16. At the same time, 62% of data are in the range of ±100 Pa from the average value of 360 Pa. Note that this pressure difference is one order of magnitude higher than the maximum capillary pressure drop, from minimum receding contact angle to maximum advancing contact angle (∆𝑃 𝑐,𝑚𝑎𝑥 = 2𝜎 𝑅 ⁄ ), of about 20-28 Pa when calculated in the temperature range of figure 4. This signifies that the driving pressure difference is largely counterbalanced by the inertial and viscous forces before the rupture of the menisci at the transition between slug flow and annular flow.

Conclusions

Experimental investigation of the thermal and flow behaviors of a molybdenum flat plate pulsating heat pipe filled with ethanol and operating under microgravity conditions, is performed to characterize the stopover and flow re-activation mechanisms. Specific results for three parabolas with flow re-activation for the microgravity conditions obtained during 69 th ESA Parabolic Flight Campaign are presented. Microgravity periods, as previously reported, are accompanied by the stopover phenomena and evaporator dry-out that leads to overall thermal transport degradation. It was found that, during some parabolas, stopover periods occur and are sometimes interrupted by a flow pattern transition from slug flow to annular flow with uniform liquid distribution inside pulsating heat pipe, also called re-activation phases.

The motion of liquid/vapor interfaces, as well as the force influence on fluid flow and flow pattern change, were analyzed. Despite the different amplitude and oscillation frequencies during microgravity start and stopover periods, the values of transition velocities appear to be very close to each other.

Frequently used non-dimensional criteria, based on Weber and Garimella numbers, have been evaluated for tested FPPHP under microgravity conditions. Experimentally obtained average values of We number are identical to the reference critical value (Wecrit = 4), whereas average values of Ga number (Ga = 1980) are one magnitude higher than reference critical value (Gacrit = 160).

Most of the driving pressure values (ΔPdriv,av=360 Pa) for the transition from slug flow to annular flow, obtained from the momentum equation for liquid plugs, are one order of magnitude higher than the maximum capillary pressure drop (ΔPc,max=20-28 Pa).

Future complex studies are necessary to enhance the characterization of flow behavior and flow transition inside of FPPHP under microgravity conditions.

Figure 1 .

 1 Figure 1. Schematic representation of used FPPHP

Figure 3 .

 3 Figure 3. Parabolic flight trajectory[START_REF] Pletser | The First European Parabolic Flight Campaign with the Airbus A310 ZERO-G[END_REF]

Figure 4 .

 4 Figure 4. Temperature and pressure profiles of FPPHP during a series of five parabolas for 100 W (a) and 150 W (b) of applied power Sometimes, evaporator temperatures suddenly and arbitrarily drops during microgravity periods, as well observable instantaneous pressure rise which corresponds to some changes in flow regime and fluid

Figure 5 .

 5 Figure 5. Transient operation during microgravity phase: (a) temperatures profiles of flow reactivation during the 5 th parabola of fig. 4b; and (b) flow patterns one second before (left) and one second after fluid flow reactivation (right).

Figure 7 .Figure 8 .

 78 Figure 7. Representing liquid plugs and channels numbering As the flow dynamics directly influence the re-activation phenomena, a study of the liquid/vapor interfaces displacements is presented in the following section. Menisci displacements of the two neighboring liquid plugs in the central zone of the FPPHP, for three tested cases (one for 100 W, and two for 150 W applied heat power, respectively) are presented in figure 8. Microgravity phase turns fluid into slugs and plugs form and, once dried-out, the liquid plugs accumulated in the condenser zone are accompanied by low displacement interfaces movements (figure 8 (yellow section)) after flow stabilization due to influence of small pressure variations in the evaporator caused by vapor superheating, which was already observed in

Figure 11 .

 11 Figure 11. Weber number based on the transition velocity.

  𝐴 𝑐𝑠 . (∆𝑃 𝑣 -∆𝑃 𝑐 ) •

Figure 13 .

 13 Figure 13. Schematic diagram of liquid plug movement.

Figure 14 .

 14 Figure 14. Forces influencing the liquid plugs motion during period prior to reactivation phases: for 100 W (a) channels 1-14 ; (b) channels 6-7; (c) channels 8-9; and for 150 W (d) channels 1-14 ; (e) channels 6-7; (f) channels 8-9.

Figure 15 .

 15 Figure 15. Comparison of driving forces values for two central liquid plugs (fig. 7): (a) 100 W and (b) 150 W.

Figure 16 .

 16 Figure 16. Transitional driving pressure based on the transition velocity.

Acknowledgements

This work was supported by ESA MAP project INWIP, ESA MAP project TOPDESS and French government program "Investissements d'Avenir" (ANR-18-EURE-0010). Special thanks must be given to NOVESPACE team in Bordeaux for their assistance, to N. Melville and Dr. B. Toth from ESA.

Nomenclature

Acs

Cross-section surface, m