Cyril Pistoresi

Yilin Fan

Lingai Luo
email: lingai.luo@univ-nantes.fr

Numerical study on the improvement of flow distribution uniformity among parallel mini-channels

Keywords: Process intensification, Mini-channels, Flow maldistribution, Shape optimization, Distributor

Parallel micro or mini-channels are widely used in various devices of process and energy engineering including micro-reactors, compact heat exchangers and fuel cells. Nevertheless, the flow maldistribution due to the improper design of distributor/collector is usually observed, leading to globally poor performances of these devices. The objective of this study is to optimize the shape of the distributor/collector pipes so as to achieve a uniform flow distribution among an array of parallel minichannels. A Z-type ladder fluid network with 10 mini-channels in parallel having square section is introduced and investigated. Two methods are used to optimize the shape of distributor/collector pipes: an optimized discrete stairway shape and a continuous tapered shape with an inclined angle varying from 0° to 30°. 3D-CFD simulations are carried out using the ANSYS FLUENT code. Numerical results obtained show that a relatively uniform flow distribution may be reached by the discrete stairway shape or by the continuous tapered shape distributor/collector under very low flow-rate conditions. Larger inclined angle or fewer channels in parallel are favorable for more uniform flow distribution under higher flow-rate 2 conditions. Nevertheless the distributor and the collector pipes occupy a large volume so that the entire device is less compact.

INTRODUCTION

Chemical industries and process engineering are undergoing rapid changes in the 21 st century facing the challenges of climate change and energy shortage. Process Intensification (PI) that leads to smaller, less costly, cleaner, safer, higher productivity and more energy efficient technologies is proposed as a new paradigm of process engineering [START_REF] Stankiewicz | Process Intensification[END_REF]. Particularly, the innovative design of high yield processes or compact equipments has become one of the pressing industrial needs in recent years [START_REF] Commenge | Methodological framework for choice of intensified equipment and development of innovative technologies[END_REF].

One of the routes to PI is the use of equipments with locally miniaturized structures, i.e. micro or mini-channels [START_REF] Charpentier | Process intensification by miniaturization[END_REF][START_REF] Luo | Heat & Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach[END_REF][START_REF] Commenge | Methodological framework for choice of intensified equipment and development of innovative technologies[END_REF], because of their enhanced heat and mass transfer properties. Miniaturized process and energy equipments can either be heat exchangers (e.g. Fan and Luo, 2008;Fan et al., 2008;[START_REF] Khan | A review on microchannel heat exchangers and potential applicaions[END_REF], chemical mixers or reactors (e.g. [START_REF] Hessel | Micromixers-a review on passive and active mixing principles[END_REF][START_REF] Illg | Flow chemistry using milli-and microstructured reactors-From conventional to novel process windows[END_REF][START_REF] Guo | Mixing performance assessment of a multi-channel mini heat exchanger reactor with arborescent distributor and collector[END_REF], fuel cells (e.g. [START_REF] Sung | Optimization of a fuel-cell manifold[END_REF][START_REF] Jackson | Discrete geometry optimization for reducing flow non-uniformity, asymetry, and parasitic minor loss pressure drops in Z-type configurations of fuel cells[END_REF] or integrated multifunctional systems (e.g. [START_REF] Anxionnaz | Heat exchanger/reactors[END_REF][START_REF] Guo | Multi-channel heat exchanger-reactor using arborescent distributors: A characterization study of fluid distribution, heat exchange performance and exothermic reaction[END_REF]. Nevertheless, to obtain a comparable productivity with that of conventional equipment, a number of micro/mini-channels should be installed in parallel. This so-called numbering-up process is the key issue for large-scale industrial applications of these miniaturized devices [START_REF] Al-Rawashdeh | Numberedup gas-liquid micro/milli channels reactor with modular flow distributor[END_REF][START_REF] Luo | Heat & Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach[END_REF]. Therefore, the fluid distribution uniformity among the parallel channels may play an important role on the global performance improvement of multi-channel equipments. This is particularly true when multi-scale ladder-type fluid networks (Figure 1a) are involved [START_REF] Saber | Microreactor numbering-up in multi-scale networks for industrial-scale applications: Impact of flow maldistribution on the reactor performances[END_REF][START_REF] Commenge | Methodology for multi-scale design of isothermal laminar flow networks[END_REF]. In order to achieve uniform flow distribution among all parallel channels in the network, the first and essential step is the design of an optimized two-scale elementary Z-type ladder circuit, as shown in Figure 1b. In this elementary fluidic circuit, the single inlet port and single outlet port are located on opposite sides of the bundle of parallel cross-channels, meaning that the flow direction is the same in the distributor and the collector pipes. All cross-channels are assumed to have the same geometrical characteristics so that the passage-to-passage maldistribution may be considered as negligible [START_REF] Rebrov | Single-phase fluid flow distribution and heat transfer in microstructured reactors[END_REF]. On the contrary, the improper design of fluid distributor/collector pipes is the main cause of flow maldistribution among the parallel cross-channels. Many studies have then been focused on how to improve the flow distribution uniformity of the elemental Z-type ladder circuit. It is reported that a relatively uniform distribution may only be approached by making the hydraulic resistance of cross-channels much larger than that of the distributor and collector pipes if the latter have a uniform profile (e.g. [START_REF] Saber | Rapid design of channel multi-scale networks with minimum flow maldistribution[END_REF]Tondeur et al., 2011a). This usually implies that the distributor and collector pipes are large and encumbering, which is clearly unfavorable for miniaturized devices. Instead of the uniform profile (rectangular or cylinder shape) of the distributor and collector, alternative shapes were proposed, such as triangular or trapezoidal-type (e.g. Kim et al., 1995;[START_REF] Commenge | Optimal design for flow uniformity in microchannel reactors[END_REF][START_REF] Pan | CFD-based study of velocity distribution among multiple parallel microchannels[END_REF]Renault et al., 2011) or curvatured shape (e.g. [START_REF] Pan | Optimal design of complex manifold geometries for uniform flow distribution between micochannels[END_REF][START_REF] Cho | Modeling and simulation on the mass flow distribuion in microchannel heat sinks with non-uniform heat flux conditions[END_REF][START_REF] Jackson | Discrete geometry optimization for reducing flow non-uniformity, asymetry, and parasitic minor loss pressure drops in Z-type configurations of fuel cells[END_REF]. In particular, Tondeur et al. (2011b) proposed to "taper'' the profile of distributor and collector pipes in a discrete stairway so that the flow resistances vary linearly with position, which may offer a uniform flow distribution among the parallel cross-channels. Analytical scaling relations were established based on the assumptions of Poiseuille flow and negligible singular losses (pressure losses due to divergent/convergent branching). However, no numerical or experimental work has been performed to evaluate the validity and the effective range of this analytical model. The sensitivity of the flow distribution characteristics subjected to different working conditions (e.g. different flow-rate) has not yet been reported.

In the present work, the flow distribution properties on a typical Z-type elemental ladder circuit are systematically investigated. We will first describe the design of a mini-channel array with integrated discrete stairway shape distributor and collector pipes based on the scaling relations proposed by Tondeur et al. (2011b). In addition, a continuous model with progressive dimension reduction (or increase) for the distributor pipe (or the collector pipe) is also introduced for comparison. Then, computational fluid dynamics (CFD) simulation results for both models will be reported, under a variety of flow-rate conditions. After that influences of some design parameters including the inclined angle and the number of parallel channels will also be discussed. Finally, main conclusions and perspectives will be summarized.

GEOMETRY AND NUMERICAL PARAMETERS

In this section, the design of parallel mini-channel array with integrated distributor/collector pipes based on two models, i.e. the discrete stairway model and the continuous tapered model will be briefly described. The CFD simulation tool and the controlling parameters will be introduced as well.

Geometry of the tested mini-channel array

Figure 2 shows a representative schematic view of Z-type elemental ladder fluid circuit. The 3D fluid domain consists of 3 sections: inlet distributor pipe, parallel mini-channel array, and outlet collector pipe. This Z-type elemental ladder network is widely used in different applications such as catalytic reactors, solar receivers, heat exchanger plates, elements of fuel cells, electrochemical microreactors, cooling network of heat sinks, or other process components. For the convenience of potential fabrication, the entire fluidic circuit has the identical channel depth (e=1 mm). There are 10 parallel straight channels (N=10) of identical length (Lch=20 mm), width (wch=1 mm) and depth (e=1 mm).

They are evenly spaced (lx=2 mm) between the axis of one channel and another. Square cross-section is used for the channels because it is adapted for future experimental visualization of the internal flow using digital camera and optical tracers. Here we introduced a millimetric design (hydraulic diameter of channels being 1 mm) because it may have comparable mixing or heat transfer performances with respect to micro-channels but with higher throughput and lower pressure loss [START_REF] Luo | Heat exchanger: from micro to multi-scale design optimization[END_REF][START_REF] Guo | Mixing performance assessment of a multi-channel mini heat exchanger reactor with arborescent distributor and collector[END_REF]. For the convenience of description, these mini-channels are indexed by k from 1 to N from left to right. When a pressure difference is applied between inlet and outlet to cause flow, it will passes through the distributor pipe, the parallel channels and the collector pipe subsequently to reach the outlet. The flow-rate in kth mini-channel is notated as qk.

q q k k - = σ (1) 2 1 1 1 MF ∑ =         - - = N k k q q q N (2) 6
where q is the mean flow-rate between parallel outlet channels.

N q q

N k k ∑ = = 1 (3)
The value of σk indicates the departure of the flow-rate in an individual channel k from the mean value whereas the value of MF indicates the overall flow maldistribution of the whole fluidic network.

Uniform flow distribution is achieved when values of σk and MF approach 0.

Discrete stairway model versus continuous tapered model

In this subsection, we will firstly describe in detail the design of discrete stairway distributor/collector based on the scaling relations proposed by Tondeur et al. (2011b). The continuous tapered model will also be introduced in the end for comparison. Tondeur et al. (2011b) proposed that uniform flow distribution may be approached by properly arranging the flow resistances on the segments of the distributor/collector pipes. A scaling relation was then established based on the assumption of linear flow/pressure behavior: pure Poiseuille flow, neglecting the inertial terms, neglecting or linearizing the singular effects (Tondeur et al. 2011b)

. 1 , , + - = k N k R R k c k d with k=1…N (4)
where Rd,k and Rc,k are the flow resistance of kth segment of the distributor pipe or the collector pipe, respectively. Using this scaling relation, a Z-type fluid circuit with uniform cross-flow distribution can be designed. One possible example is schematically shown in Figure 3, where the subscripts d, c, and ch represent the distributor, the collector and the cross-channel, respectively. The mass and pressure conservations can be easily verified while keeping the cross flow-rate all equal (qk=qch). The dimension of each segment of distributor/collector pipes can then be determined by supposing

R c,N =R c,1 /N q out =(N+1) q ch q in =(N+1) q ch q k =q ch q d,1 =Nq ch R d,1 =R d,N /N q c,1 =q ch R c,1 =R d,N q d,N =q ch R d,N =R c,1 q c,N =Nq ch q d,k =(N-k+1)q ch R d,k =R d,N /(N-k+1) q c,k =kq ch R c,k =R c
Poisseuille flow in straight channel with rectangular cross-section. The flow resistance in kth segment of the distributor pipe Rd,k may be expressed as [START_REF] White | Fluid Mechanics[END_REF]:

k d k d k h k d k d k d u ew D L f R , , , , , , 2 1 ρ = (5)
where ρ is the density of fluid, Ld,k the length of kth segment, e the depth of channels (1 mm), wd,k the width of kth segment to be determined and ud,k the fluid velocity in the kth segment. Dh,k is the hydraulic diameter for rectangular cross-section and fd,k the friction factor for a straight channel.

k d k d k h w e ew D , , , 2 + = (6) k h k d k d k d k d k d D u F F f , , , , , , Re ρ µ = = (7)
where Re is the Reynolds number, μ the viscosity of the fluid and Fd,k the form factor. The values of Fd,k for rectangular cross-section channels depend on the ratio of channel depth and width (e/wd,k). Eq. ( 8) presents the polynomial fitting correlation for Fd,k, based on the data provided from [START_REF] White | Fluid Mechanics[END_REF]

+         -         +         - = k d k d k d k d w e w e w e F (8)
Regrouping Eqs.5-7, one may obtain:

( ) 3 ; 3 2 , , , , 8 k d k d k d k d k d w e w e L F R + = µ (9)
It may be verified that the flow resistances for segments of collector pipe share the same expression as Eq. 9, by replacing the subscript d with c. By letting wd,N=wc,1=wch=1 mm, the other values of wd,k and wc,k can then be derived using Eqs. 4, 8 and 9, as listed in Table 1. Figure 2b illustrates the discrete stairway model of the Z-type ladder fluidic circuit, designed according to the morphology presented in Figure 3. Note that a continuous tapered model may also be designed, as shown in Figure 2c, by replacing the stairs by linear profiles from point to point. It may be observed that the linearization leads to an approximate trapezoidal shape for the distributor and collector, with an inclined angle (θ) of about 11.3°. This value is close to the theoretical optimal angle (10.46°) proposed by the model of [START_REF] Renault | Design and optimization of electrochemical microreactors for continuous electrosynthesis[END_REF]. The comparison between two models, i.e. the discrete stairway model and the continuous tapered model on their flow distribution properties and the related pressure drop is interesting but never attempted. Numerical tests were then performed for both models for comparison.

Simulation parameters

In this study, geometries and meshes were generated using different modules of ANSYS Workbench 12.1. Note that due to symmetrical character of the network in the direction of the depth, half of the body had been considered in the analysis. Fluent code V.12.1.4 was used to solve Navier-Stokes equations by finite volume methods. The equation for conservation of mass or continuity is:

( ) 0 u t ρ ρ ∂ + ∇ ⋅ = ∂  (10)
The momentum conservation equation:

( ) ( ) ( ) u uu p g F t ρ ρ ρ ∂ + ∇ ⋅ = -∇ + ∇ ⋅ ∏ + + ∂     (11)
where u  is the velocity, p is the static pressure, g ρ  and F  are the gravitational body force and external body forces, ∏ is the stress tensor which is given by: ( )

T 2 3 u u uI µ   ∏ = ∇ + ∇ -∇ ⋅        ( 12
)
where μ is the molecular viscosity, I is the unit tensor.

Pure water at constant temperature of 293 K was chosen as working fluid (density ρ=998.29 kg.m -3 and viscosity µ=1.003×10 -3 kg.m -1 .s -1 ). The operational pressure was fixed at 101325 Pa. In this study, simulations were performed under steady state, incompressible and isothermal condition without heat transfer. For simplification, gravity effect and viscous heating were neglected.

Velocity inlet normal to the surface was set as the boundary condition for the inlet. Four inlet velocity conditions (Uin) were tested: 1.25×10 -3 m.s -1 ; 1.25×10 -2 m.s -1 ; 1.25×10 -1 m.s -1 and 1.25 m.s -1 , corresponding to a value of mean channel Reynolds number (Rech) of 1.25, 1.25×10 1 , 1.25×10 2 and 1.25×10 3 , respectively. The boundary condition of outlet was set as pressure-outlet with zero static pressure. Adiabatic wall condition was applied and no slip occurred at the wall.

Laminar flow model was used under very low velocity conditions while k-ε Re-Normalized Group (k-ε RNG) was used for higher velocity conditions because micro turbulences and local vortex may exist.

For the pressure-velocity coupling, standard SIMPLE method was used. For discretization, standard method was chosen for pressure and first-order upwind differentiation for momentum. The solution was considered to be converged when the flow-rate at each channel and the inlet static pressure were constant from one iteration to the next (less than 0.5% variation) and the normalized residuals of all monitoring parameters were lower than the order of magnitude of 10 -6 .

Grid independence study

A grid independence study was performed using three structured meshes with different resolutions:

coarse mesh (10 segments per millimeter; 0.18 million elements); medium mesh (20 segments per millimeter; 1.65 million elements) and refined mesh (30 segments per millimeter; 5.28 million elements). Simulation results with an inlet velocity of 1.25×10 -1 m.s -1 (mean Rech=1.25×10 2 ) indicated a difference of 3.7% on the inlet pressure between the coarse mesh and the refined mesh, and of 0.9% between medium mesh and refined mesh. Mass flow-rates in each mini-channel were also compared,

showing a maximum difference of 2.6% between the coarse mesh and the refined mesh, and of 1.3%

between the medium mesh and the refined mesh. Hence, the medium mesh was selected as a compromise between the calculation time and the precision. and Uin=1.25 m.s -1 ; mean Rech=1.25×10 3 ), flow maldistribution among parallel channels is obvious, as shown on Figure 4c and4d. This is mainly due to the stronger inertial force at the higher velocity so that the fluid enters the right most channels preferentially. Dead volumes may easily be observed at the entrance zone and outside the exit port of each cross-channel. Small vortex and micro-turbulences may also be observed and the velocity profiles in the distributor and in the collector pipes are no longer symmetrical. These results indicate that more appropriate scaling relations should be developed, taking the internal terms and the singular effects into account. Some recent efforts may be found in references [START_REF] Midoux | The theory of parallel channels manifolds (Ladder networks) Revisited Part 1: Discrete mesoscopic modelling[END_REF]2015) for U-type ladder circuits. The increase of flow maldistribution with the increasing inlet velocity may be quantitatively shown in Figure 5, which presents the relative flow-rate deviation σ of each channel for different inlet velocity conditions. For inlet velocity Uin=1.25×10 -2 m.s -1 (mean Rech=1.25×10 1 ), the maximum flow-rate deviation is about 0.098 and 0.117 for discrete stairway model and for continuous tapered model, respectively, implying an acceptable flow distribution uniformity. However, the maximum value of σ rapidly increases to 0.78 (stairway model) and 0.84 (continuous model) for inlet velocity Uin=1.25 m.s - 1 (mean Rech=1.25×10 3 ), implying significant flow maldistribution.

SIMULATION RESULTS

Table 2 gives a comparison on the flow distribution uniformity and inlet/outlet pressure loss of the circuit between the discrete stairway model and the continuous tapered model, for different inlet velocity conditions. Very similar performances may be observed. For the same inlet velocity condition, the discrete stairway model may provide slightly better flow distribution uniformity with respect to the continuous tapered model, but generate higher pressure losses. Especially for inlet velocity Uin=1.25 m.s -1 (mean Rech=1.25×10 3 ), the value of pressure loss is 5.46 kPa for the discrete stairway model, 14.5% higher than that of the continuous tapered model (4.61 kPa) while the values of MF are almost the same (0.387 vs. 0.395).

Table 2. Comparison of pressure loss (Δp) and maldistribution factor (MF) between two models

ΔP [Pa] MF [-] Inlet velocity [m.s -1 ] Mean Rech [-] Stairway Continuous Stairway Continuous 1.25×10 -3 1.25 9.20×10 -1 8.80×10 -1 1.82×10 -2 2.99×10 -2
1.25×10 -2 1.25×10 1 9.48 9.05 4.11×10 -2 5.44×10 -2

1.25×10 -1 1.25×10 2 1.29×10 2 1.19×10 2 2.33×10 -1 2.43×10 -1 1.25 1.25×10 3 5.46×10 3 4.61×10 3 3.87×10 -1 3.95×10 -1

As a short conclusion, the discrete stairway model could provide relatively uniform flow distribution only under low flow-rate conditions (e.g. Uin<1.25×10 -2 m.s -1 ; mean Rech<1.25×10 1 ). The flow maldistribution observed at higher flow-rate conditions is mainly due to the departure from the ideal flow pattern (pure Poiseuille flow, neglecting the inertial terms, neglecting the singular effects). The continuous tapered model shows comparable performances to discrete stairway model, but may be more favorable in terms of lower pressure loss under higher flow-rate conditions. However, uniform flow distribution can no longer be guaranteed.

EFFECTS OF DESIGN PARAMETERS

In this section, the effects of some design parameters on the flow distribution uniformity will be tested and reported. We focus on the continuous tapered model because it may provide comparable flow distribution uniformity with respect to the discrete stairway model but with relatively lower pressure loss and easier to be fabricated. Two design parameters will be studied: the inclined angle (θ) of the distributor/collector pipes and the total number (N) of parallel mini-channels.

Effects of the inclined angle

Numerical simulations were performed for the Z-type ladder circuit with the inclined angle (θ) for the distributor/collector pipes varying from 0° to 30°, under four different inlet velocity conditions (mean Rech varying between 1.25 and 1.25×10 3 ). The inclined angle θ=0° shows a classic rectangular shape of distributor/collector pipes while other values of θ implies a trapezoidal or near triangular shape.

Other geometrical dimensions are kept as the same as the one tested in the above section.

Figure 6 shows the velocity profiles in the Z-type ladder circuit with different inclined angles for the distributor/collector pipes, for Uin=1.25×10 -2 m.s -1 (mean Rech=1.25×10 1 ). It may be observed that the flow always goes preferentially into the rightmost channels of the circuit, implying that at this inlet velocity, the inertial effect of fluid flow is already significant. It may also be observed that the higher the value of θ, the more uniform flow distribution may be achieved. However, this implies that the entire flow circuit becomes less compact, i.e. the distributor and collector pipes occupy a large volume.

Influence of the number of mini-channels

3D-CFD simulations were realized on Z-type ladder circuit with number of mini-channels of 5, 10 and 20, while the inclined angle of the distributor/collector pipes was fixed at 30°, as shown in Figure 8. This is for the purpose of highlighting the influence of the number of mini-channels on the flow distribution uniformity. Figure 9 shows the evolution of maldistribution factor (MF) as a function of the number of minichannels under four inlet velocity conditions studied. It may be observed that the difference on the flow distribution uniformity for different N cases is relatively very small under low inlet velocity conditions (e.g. Uin<1.25×10 -2 m.s -1 ; mean Rech=1.25×10 1 ). However, the value of MF increases rapidly with increasing N number under high velocity conditions. For a inlet velocity Uin=1.25 m.s -1 (mean Rech=1.25×10 3 ), the value of the MF increases from 0.100 for 5 channels case, to 0.217 for 10 channels case, and finally reaches 0.229 for 20 channels case. Generally speaking, it will be easier to achieve uniform flow distribution when fewer sub-streams should be formed (small N).

CONCLUSION AND PERSPECTIVES

This paper presents a numerical study on the flow distribution characteristics of a Z-type ladder circuit having 10 mini-channels in parallel. The validity and the effective range of the discrete stairway model and the continuous tapered model for the design of distributor/collector pipes are discussed. The effects of inclined angle and the number of parallel mini-channels on the distribution uniformity are also analyzed. Based on the results presented above, the following conclusions may be reached.

• The discrete stairway model could provide relatively uniform flow distribution under low flow-rate conditions (e.g. Uin<1.25×10 -2 m.s -1 ; mean Rech<1.25×10 1 ). For higher flow-rate conditions, significant flow maldistribution seems inevitable.

• The continuous tapered model by linearizing the stairways may provide comparable flow distribution uniformity regarding the discrete stairway model, but may be more favorable in terms of lower pressure loss under higher flow-rate conditions.

• Increasing the inclined angle and decreasing the number of parallel channels are favorable for more uniform flow distribution. However, the compactness of the network may then be lost.

It should be noted that both models could provide relatively uniform flow distribution under very low flow-rate conditions. The potential applications could be for fuel cells where the flow velocity in parallel channel is small, with the aim of process intensification. Another direction of application is to construct a multi-scale fluidic network such as shown in Figure 1a, so that the working load for each elemental Z-type circuit could be relatively small.

Our ongoing works are focused on the development of more appropriate scaling relations and evolutionary algorithms [START_REF] Wang | Heuristic optimality criterion algorithm for shape design of fluid flow[END_REF]2014;[START_REF] Luo | Heuristic shape of optimization of baffled fluid distributor for uniform flow distribution[END_REF] for more subtle modifications of the distributor/collector shape, in order to reach uniform flow distribution with small increase of pressure loss. Numerical and experimental investigations on the hydraulic and thermal characteristics of a multi-scale ladder network are also the directions of our future work.

ACKNOWLEDGEMENT

The authors would like to thank the "Region Pays de la Loire" for the project "Nouvelle équipe de recherche" and its financial support to the PhD study of M. Cyril Pistoresi.

NOMENCLATURE

Figure 1 .

 1 Figure 1. Multi-scale fluidic network (a) and elementary Z-type ladder circuit (b).

Figure 2 .

 2 Figure 2. Geometry of the tested Z-type ladder. (a) mini-channel array; (b) discrete stairway type distributor/collector; (c) continuous tapered distributor/collector

  q

Figure 3 .

 3 Figure 3. Flow resistance distribution for uniform flow distribution among parallel channels. Modified from Tondeur et al. (2011b)

Figure 4

 4 Figure 4 shows the contour of velocity magnitude on the mid-depth surface (symmetry) of the Z-type ladder circuit, under different inlet velocity conditions. Simulation results for the discrete stairway model are presented on the left side of Figure 4 while those for the continuous tapered model are shown on the right side. It can be observed on Figure4aand 4b that for relatively low inlet velocity conditions (Uin=1.25×10 -3 m.s -1 ; mean Rech=1.25 and Uin=1.25×10 -2 m.s -1 ; mean Rech=1.25×10 1 ), both models could provide a relatively uniform flow distribution among the 10 parallel mini-channels. It seems that the velocity profiles in the distributor pipe and in the collector pipe are regular and symmetric, implying that the flow patterns are rather laminar. The impact of singularity losses in converging or diverging bifurcations on the flow distribution uniformity is not significant.

Figure 4 .

 4 Figure 4. Velocity profiles for the discrete stairway model and for the continuous tapered model. (a) Uin=1.25×10 -3 m.s -1 (mean Rech=1.25); (b) Uin=1.25×10 -2 m.s -1 (mean Rech=1.25×10 1 ); (c) Uin=1.25×10 -1 m.s -1 (mean Rech=1.25×10 2 ); (d) Uin=1.25 m.s -1 (mean Rech=1.25×10 3 )

Figure 5 .

 5 Figure 5. Relative flow-rate deviation (σ) of parallel channels for different inlet velocity conditions

Figure 6 .

 6 Figure 6. Velocity profiles in the Z-type ladder circuit for Uin=1.25×10 -1 m.s -1 (mean Rech=1.25×10 2 ). (a) θ=0°; (b) θ=5°; (c) θ=10°; (d) θ=20°; (e) θ=30°

Figure 7 .

 7 Figure 7. Influences of inclined angle (θ) on the flow distribution uniformity (MF) under different inlet velocity conditions

Figure 8 .

 8 Figure 8. Geometries of ladder circuit tested with different number of mini-channels in parallel

Figure 9 .

 9 Figure 9. Influences of the number of parallel channels (N) on the flow distribution uniformity (MF) under different mean Rech conditions

  External body force [kg.m.s -²] gGravitational acceleration [m.s -²]

Table 1 .

 1 Widths for the segments of distributor/collector pipes (unit: mm)

	wd,1	wd,2	wd,3	wd,4	wd,5	wd,6	wd,7	wd,8	wd,9	wd,10
	wc,10	wc,9	wc,8	wc,7	wc,6	wc,5	wc,4	wc,3	wc,2	wc,1
	4.01 3.66 3.30 2.99 2.65 2.31 1.97 1.63 1.29 1.00


Guillaume Boutin

Min Wei

Yilin Fan

Lingai Luo
email: lingai.luo@univ-nantes.fr

Experimental Measurement of Flow Distribution in a Parallel Mini-channel 1 Fluidic Network using PIV Technique 2

Keywords: Flow distribution, Fluidic network, PIV, Parallel channels, Streamline profile, CFD 27

come

Experimental measurement of flow distribution in a parallel mini-channel fluidic network using PIV technique

in the literature may be classified into two main categories: intrusive and non-intrusive 19 methods. One straightforward intrusive method is the weighting method [START_REF] Fan | Experimental investigation of the flow distribution of a 2-dimensional 25 constructal distributor[END_REF][12][13] , by weighting 20 out the mass of fluid collected from each individual channel/tube during a typical sampling 21 time when the flow-rate is stabilized. This method is relatively simple to operate by using a 22 digital balance and a stop watch, but unfortunately cannot be applied to an enclosed parallel instruments and their basic principles may be found in the books of Baker [START_REF] Baker | Flow measurement handbook: industrial designs, operation principles, performance, and 33 application[END_REF] and LaNasa and 35 Upp [15] .

36

Although the intrusive methods are relatively easy for implementation and operation, they 37 may not be suitable for flow distribution measurement in micro-or mini-channel fluidic 38 networks. Firstly, most of the flowmeters without probes may occupy a large volume 39 compared to micro-or mini-channel. For example the minimum required piping is about 10 40 mm for Venturi meter, and about 25 mm for liquid turbine meter [15] . Some micro sensors may 41 be commercially available but are either immature or very expensive [START_REF] Kuo | Micromachined thermal flow sensors-A review[END_REF] . Secondly, the 42 variation of measurement locations required for multiple channels devices is relatively 43 difficult to be realized. Thirdly, the intrusive methods will inevitably change the flow paths of To overcome aforementioned drawbacks, non-intrusive techniques become well-developed 4 which usually involve the flow visualization. Some researchers [17][18][19] tried to obtain more PIV technique may be found in relevant review articles [20][START_REF] Luo | Heat and Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach[END_REF][22][23][24][25] . A general comparison between 34 various frequently-used techniques for micro-or mini-fluidic flow measurements are 35 presented in Table 1. It can be noted that PIV is a non-intrusive, whole field method with 36 possible high resolution and precision.

37

PIV technique used in microfluidics (or called µPIV) was firstly introduced by Santiago et 38 al. [26] . In their study, the movement of particles tagged with fluorescent dye was recorded 39 under a continuous Hg-arc lamp by CCD camera. After the introduction of laser illumination 40 by Meinhart et al. [27] , abundant studies in the literature have been devoted to the improvement of PIV technique for flow field measurement. However, most of these studies were focused 42 on single channel [27][28][29][30][31][32][33] , or at best on two parallel channels [34] . A noticeable exception is the study of Wen et al. [35] which measured the flow-rate distribution among multiple outlets of an Actually, the velocity vectors on a single plane parallel to the flow direction cannot correctly 3 reflect the velocity profiles on the channel's cross-sectional surface (Fig. 4 as an example). In the rest of this paper, we shall first introduce the experimental set-up and the PIV 21 instruments used in this study. The measurement parameters, the experimental procedure and 22 the uncertainty will be discussed using a double-channels device as an example. Then, a mini-23 fluidic network having 15 parallel channels will be tested under different total inlet flow-rate 24 conditions. The flow-rate distribution among parallel channels obtained by PIV technique will 25 be compared with CFD simulation results under the same operational conditions. Finally, 26 remarks and main conclusions will be summarized. The light scattered from the particles was collected by a CCD camera (DANTEC, FlowSense) with 2048×2048 pixels. The minimum time interval between two frames was 1 µs. An 16 additional macro LAVISION lens was used to yield a magnification of about 260 pixel•mm -1 17 for double-channels device and about 230 pixel•mm -1 for 15-channels device. Therefore, the 18 view field was 7.87 mm×7.87 mm and 8.73 mm×8.73 mm, respectively. Note that the frame 19 must be recorded when the laser sheet outputs, so a synchronizer (DANTEC, 80N77) was 20 used to guarantee that the laser and the CCD camera work synchronously. A commercial 21 software FlowManager (v3.41) was used to control the PIV system and to process the data by 22 2-frame cross-correlation and Fast Fourier Transforms (FFTs). After that, the velocity vector 23 profiles could be obtained. In the current study, the size of the PIV interrogation window was 24 fixed at 16×16 pixels with an overlap of 50% after several attempts considering a compromise 25 between the measurement accuracy and the computational time. The spatial resolution of PIV 26 is determined by 2.8 times of the size of interrogation window [START_REF] Luo | Heat and Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach[END_REF] . Therefore, the physical spatial resolution was 0.17 mm for double-channels device and 0.19 mm for 15-channels 28 device, respectively.

29

A workbench which permits the subtle movements of the test-section was specially designed 30 and built. The camera may be moved in x direction whereas the platform to fix the test-section 31 is moveable in y and z directions, as shown in Fig. 2. The movements in x and y directions 32 were realized using steel orbits while the movement of the platform along z direction was 33 realized using a precise lift and a digital gauge with an accuracy of 0.01 mm. Due to the 34 different scattered light optical paths, the focus of the lens must be adjusted for each vertical 35 plane, leading to different magnification ratios which must be taken into account in the post-36 processing. It should be noted that the platform can also be rotated around z-axis to ensure a 37 fine overlap between the walls of channels and the boundaries of the PIV interrogation technique for parallel channels under multiple refractions. Each channel has a square cross-13 section of 5 mm×5 mm, the hydraulic diameter thus being 5 mm. The total channel length is 14 320 mm (the transparent part being 100 mm), longer than 20 times of its hydraulic diameter to 15 ensure the fully-developed flow [37] . The distance between the axes of two channels is 15 mm.

16

The channel closer to the laser source is named as CH1 while the other one is named as CH2.

Measuring procedure and post-processing 24

Recall that the 2D-2C PIV technique yields the flow velocity field on a certain plane. We 25 define the middle plane of channels parallel to the flow direction as the base plane (z=0) so 26 that the cross-section of channels ranges from z=-2.5 mm to z=+2.5 mm. In order to construct 27 accurate fluid flow field, the cross-section of channels was divided into 21 planes along z axis, 28 with a stepping distance of 0.25 mm to be measured. It should be noted that the laser source 29 was fixed so that the device should be moved vertically along z direction for different 30 measuring planes, using the adjustable workbench described in Section 2.2.

31

For each measuring plane, a large number of frames (200 or 375 pairs in this study) should be should be recalculated as follows:

3 U U G t ′ = ∆
(2)

4
where U′ is the flow velocity obtained by PIV post-processing under the unit of pixels/frame 5 and ∆t is the time interval between two frames. A MATLAB programme was built to handle 6 the calculation process automatically.

7

Once the unit conversions for all measuring planes were finished, a fixed physical position where U is the mean fluid velocity in a channel, µ the dynamic viscosity of water and d h the 26 hydraulic diameter of the channel calculated as:

27 4 h S d A =
(5)

28
where A is the perimeter of the channel's cross-section.

29 where m is the average mass flow-rate among 15 channels given by:

p f f Q Q Q ε - ± = ± (
2 1 M k k m m M = = ∑ (8)

22

Simulations were performed under steady state, incompressible and isothermal condition 23 without heat transfer. The gravity effect at -z direction was also taken into account.

24

A commercial code FLUENT (version 12.1.4) was used to solve the Navier-Stokes equations.

25

The fluid flow was calculated by the COUPLED method for pressure-velocity coupling, and 26 second-order upwind differential scheme was applied for discretization of momentum and 27 standard method for pressure. Laminar or standard k-ε model was used to simulate the laminar 28 or turbulent flow, respectively. Constant mass flow-rate at inlet surface was given and the 29 boundary condition of outlet was set as pressure-outlet with zero static pressure. Adiabatic 30 wall condition was applied and no slip occurred at the wall. The solution was considered to be 31 converged when 1) sums of the normalized residuals for control equations were all less than 32 1×10 -6 ; and 2) the mass flow-rate at each channel was constant from one iteration to the next 33 (less than 0.5% variation).

34

The grid density used in the study was 5 segments per millimeter (1.42 million elements in cases, a uniform distribution among parallel channels is generally required [START_REF] Lalot | Flow maldistribution in heat exchangers[END_REF][START_REF] Tondeur | Uniform flows in rectangular lattice networks[END_REF]39] , while in 1 many other cases, a target flow distribution which is non-uniform should be achieved [40][41][42] . In

23

  channels fluidic network due to the presence of the fluid collector. 24 Other intrusive methods are usually based on the establishment of relationships between the 25 flow-rate (or flow velocity) and another physical quantity which can be measured easily. For 26 example, the mean fluid velocity in a channel may be obtained by measuring the difference 27 between the static and dynamic pressures using a Pitot tube pointing directly into the fluid 28 flow and then by solving the Bernoulli's equation. Hot Wire Anemometry (HWA) is based on 29 the measurement of convective heat transfer coefficient between the heated wire and the 30 surrounding flow velocity. Due to the scalar quantity measurement, however, HWA is 31 incapable of determining the direction of fluid flow. Other intrusive flowmeters include 32 orifice plate meter, Venturi meter, variable area meter, positive displacement flowmeter, 33 turbine and related flowmeter, vortex-shedding flowmeter, etc. More details on these 34

  44the fluidic network (for example the removal of the outlet collector for the weighting method), 45 or disturb the established streamline profiles due to additional boundary conditions of the for example the insertion of different probes). Hence, intrusive 1 methods are difficult to be applied for precise measurement of flow distribution in micro-or 2 mini-channel fluidic networks.

3

 3

5

  detailed fluid flow characteristics through the estimation of Residence Time Distribution 6 (RTD) inside the device. Concentration meters or spectrometers are usually used to measure 7 the concentration variation of indicator at the outlet. In this case, the inevitable diffusion 8 between the indicator and the fluid flow and the theoretical mixing models used may have 9 great influences on the precision of the measurement results. 10 Another significant advance in optical-based non-intrusive flow measurement is the Laser-11 Doppler Velocimetry (LDV), which consists of laser transmitting and receiving optics and the 12 seeding particles mixed in the measured fluid flow. It is based on the Doppler effect which is 13 the linear change of laser light frequency proportional to the velocity of seeding particles. 14 LDV technique has various features, i.e., linear output signal, no calibrations required, high 15 frequency response and direct velocity measurement. When opaque fluid flow (e.g. liquid 16 slurries) is involved, Doppler Ultrasonic Velocimetry (DUV) using the ultrasound instead of 17 laser is a suitable alternative. Both LDV and DUV can offer good spatial and temporal 18 resolutions, but are limited by single point measurement. Multipoint measurement for parallel 19 channels is theoretically feasible with a combination of many measured points, but may 20 practically be prohibitive due to the heavy workload. 21 Recently, Particle Image Velocimetry (PIV) technique has undergone a rapid development 22 which benefits from the advances in laser and camera technologies. Different from LDV, PIV 23 takes the images of seeding particles suspended in the fluid flow while the local fluid velocity 24 vectors are measured by the displacement of various particles within a short time interval. 25 More precisely, the laser is introduced to illuminate the seeding particles in a plane twice in a 26 known time interval while the light scattered by the particles is recorded by a Charge Coupled 27 Device (CCD) camera equipped with a lens on a sequence of two frames. The images are then 28 digitized and transferred directly to the memory of a computer. After that, an individual image 29 is divided into a number of interrogation windows, the mean displacement of all particles in 30 each interrogation window being calculated with statistical methods (such as the cross-31 correlation) through post-processing. Finally, the whole flow field in the plane can be 32 established based on the velocity vectors of all interrogation windows. More details on the 33

44

  individual gas distributor. The distributor had a conventional dimension of 905 mm in length 45 and 154 mm in radius, with a middle inlet pipe of 176 mm in length and 200 mm in diameter. 46 41 parallel tubes with the width of 9.5 mm served as the outlets of the distributor. Although

  properties among parallel outlets were measured by PIV technique, only 1 one plane parallel to the flow direction was selected as the sampling plane for each outlet.

2

 2

4

  Consequently, noticeable measurement errors and uncertainties on the flow-rate seem 5 inevitable. Moreover, the effect of boundary layers may greatly affect the flow distribution, 6 especially in micro-or mini-channels. To the best of our knowledge, systematic and precise 7 measurement of flow distribution among multiple micro-(mini-) channels using PIV 8 technique is still lacking.

  9

Table 1 : 10 11

 110 Comparison between various frequently-used microfluidic measurementsAs a result, the present study aims at realizing PIV measurement of the flow-rates in parallel 12 channels and studying the fluid flow distribution in a multiple channels fluidic network. To do 13 this, two steps are programmed. Firstly for the precise measurement of flow-rate in a single 14 channel, standard PIV technique will be used to obtain the 2D-2C (2 dimensions, 2 15 components) velocity vectors on multiple planes parallel to the flow direction, so as to 16 reconstruct accurate velocity profiles on the cross-sectional surface taking the potential effects 17 of boundary layers into account. Secondly, such procedure will be repeated for every micro-18 (mini-) channel in the fluidic network so as to obtain the actual flow distribution properties 19 among parallel channels.

  20

Figure 1

 1 Figure1shows the schematic diagram of the experimental set-up built in the laboratory LTN

3 Standard

 3 Figure 1: Schematic diagram of experimental setup

14

 14

Figure 2 : 3 .

 23 Figure 2: Schematic view of the experimental workbench for subtle movements of the test-section

9 3 .

 3 1. Double-channels device for pre-test 10 A double-channels device was fabricated in house using Polymethyl Methacrylate (PMMA) 11 material, as shown in Fig. 3, for the purpose of confirming the feasibility of the 2D-2C PIV 12

  17

A

  static pressure probe and a valve were installed at the inlet of each channel to adjust the 18 balanced flow-rates needed in the following test.

Figure 3 :

 3 Figure 3: The geometry and dimensions of double-channels device: (a) schematic view (unit: mm); (b)

  32 captured and averaged to eliminate the random errors. Likewise, different planes were 33 measured successively to obtain the fluid flow velocity vectors in y-z plane. Note that for each 34 plane, the acquisition parameters (e.g., the focus of the lens, the time interval between two 35 laser pulses, and the laser energy) should be adjusted according to different vertical positions, 36 implying different magnifications of lens. In the post-processing, different relationships 37 between the actual length (the width of channel in this study) and the corresponding numbers 38 of pixels should be used by introducing a magnification ratio G defined as follows: the width of the channel and N is the corresponding pixel numbers in the captured 1 image. Due to non-identical values of G for different measured planes, the actual velocity U 2

8 ( 21 where

 821 for example the middle of the image) for all measuring planes was chosen as the transverse 9 surface and the fluid flow velocity profiles at y-z surface could be obtained, as an example 10 shown in Fig.4. The boundary layers near the side walls could be clearly observed while 11 those near the top and bottom walls are less obvious. That is due to the fact that the spatial 12 resolution is less accurate in vertical direction (z direction) than in horizontal direction (y 13 direction). Indeed, the horizontal spatial resolution is determined by the size of interrogation 14 window (0.17 mm in this study) while the vertical spatial resolution is limited by the stepping distance (0.25 mm) combined with the laser sheet thickness (0.11 mm). For more accurate 16 description of the top and bottom boundary layers, a smaller stepping distance could be used 17 which means more sampling x-y planes.18Based on the fluid flow velocity profiles at y-z surface (cross-section), the mass flow-rate m 19 passing through the channel can be easily obtained as follows: Q is the volume flow-rate, S is the area of the cross-section of the channel and ρ is the 22 density of water used in our study (998.2 kg•m -3 ). The channel Reynolds number is calculated

Figure 4 : 8 3. 3 .

 483 Figure 4: Example of fluid flow velocity profile at the cross-sectional surface of a channel

Table 2 : 21 22 4 .

 2214 The results of different cases in pre-test Measurement of flow-rate distribution in a multi-channel fluidic network 23 After the pre-test and uncertainty analysis of the 2D-2C PIV technique using the double-24 channels device, a 15-channels device with integrated distributor and collector was fabricated 25 and tested to show the effectiveness and the validity of the experimental method. The results 26 obtained by PIV are also compared with CFD simulation results under different total flow-rate channels fluidic network consisting of 15 parallel channels, a distributor and a 30 collector was used for study, as shown in Fig. 5. The overall dimension is 242 mm in length 31 and 90 mm in width. For the convenience of fabrication, the entire fluidic network has the 32 identical channel depth (e=2 mm). The inlet and outlet channels located in diagonal position 33 have the same width of 5 mm, but different lengths (50 mm for inlet tube and 100 mm for 34 outlet tube). The length of the distributing manifold is 13 mm and the width is 90 mm. 35 Identical dimensions are used for the collecting manifold (length of 13 mm and width of 90 36 mm). There are fifteen parallel straight channels with identical width of 2 mm, length of 60 37 mm and depth of 2 mm. They are evenly spaced at 4 mm between the axis of one channel and 38 another. For the convenience of description, they are indexed by k from 1 to M from the inlet 39 side to the outlet side. By this way, the mass flow-rate in kth channel is notated as m k . The 40 flow-rate ratio σ is introduced for each channel as follows:

3 4Figure 5 :74. 2 . CFD simulation parameters 16 3D

 35216 Figure 5: The geometry and dimensions of 15-channels fluidic network. (a) Cube A; (b) Cube B (unit:

  35total) and structured mesh was generated using software ICEM (version 12.1) to build up the 36 geometry model. A grid independence study was performed with a refined mesh (8 segments 37 per millimeter; 5.49 million elements in total). Simulation results with the inlet volume flow-38 rate of 1.8 L•min -1 indicated a difference of about 3.2% on the inlet pressure. For the mass 39 flow-rate in each channel, the maximum difference was less than 4.9%. Therefore, the normal 40 mesh was used as a compromise between the calculation time and the precision while the 41 value of 4.9% was indicated as error bars for the CFD results in the following figures.

1

  Two different inlet total fluid flow-rates (Q in ) were tested in this study, i.e. high inlet flow-rate 2 of 1.8 L•min -1 and low inlet flow-rate of 0.18 L•min -1 , in order to cover both the laminar and 3 the turbulent flow patterns. The corresponding Re number at the inlet channel (Re in ) was 8500 4 and 850, respectively. The mean Re number in the parallel channels (Re ch ) was 1000 for 5 Q in =1.8 L•min -1 and 100 for Q in =0.18 L•min -1 . The numerical (CFD) and experimental (PIV) 6 results on fluid flow distribution among the 15 parallel channels are shown in Fig. 6.

7 8 Figure 6 : 10 11 37 Figure 7 : 38 mean 40 Figure 8 :7 8 among parallel channels. 9 18may be reached: 25 • 30 •

 861037738408892530 Figure 6: The flow distribution properties obtained by PIV and CFD under different inlet flow-rate

2 7 8

 7 our earlier work, an original CFD-based evolutionary algorithm has been proposed to realize 3 uniform or non-uniform fluid flow distribution among parallel channels[43][44] . The 4 experimental validation of this optimization method with the PIV technique developed in this 5 paper is our on-going work. 6 This work is financed by the BPI France and the Region Pays de la Loire, and monitored by 9 the SATT OUEST VALORISATION within the project OPTIFLUX (No. DV2054). One of 10 the authors, M. Min WEI would also like to thank the French CNRS for its partial financial 11 support to his PhD study. The authors also thank Mr. Gwenaël BIOTTEAU and Mr. Nicolas 12 LEFEVRE for their great assistances during the device fabrication and the building of the 13 experimental set-up.

  Fan Y, Luo L, Flamant G. CFD-based evolutionary algorithm for the realization of target fluid 9 flow distribution among parallel channels. Chem. Eng. Res. Des. 2015; 100: 341-352.

Figure 1 : Schematic diagram of experimental setup 13 Figure 2 : 14 Figure 3 :photo view 16 Figure 4 :Figure 5 :Figure 6 : 21 Figure 7 :Figure 8 : 8 L

 11321431645621788 Figure 1: Schematic diagram of experimental setup

  Spalding DB, Fedorov VA. Steam condensation in parallel channels with nonuniform heat 1 removal in different zones of heat-exchange surface. Int. J. Heat Mass Transfer 2012; 55: 6054-6059.

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	4	PMMA	Polymethyl Methacrylate billboard design. Sol. Energy 2013; 97: 356-368.
		PSP	Polyamid Seeding Particles
	5	RTD [42]	Residence Time Distribution Wei M, Fan Y, Luo L, Flamant G. Fluid flow distribution optimization for minimizing the peak
	6		temperature of a tubular solar receiver. Energy 2015; 91: 663-677.
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	14 15		F o F o F o
	16	Nomenclature	r r r
		A d h e G l m m M N	perimeter hydraulic diameter channel depth magnification ratio width of the channel mass flow-rate average mass flow-rate P P P number of channels pixel numbers e e r e e r e e r	m m m pixel m -1 m kg s -1 kg s -1 -pixel
	17 18	Q Re S ∆t U U U ′ Greek symbols volume flow-rate Reynolds number area of cross-section of channel time interval between two frames actual velocity mean velocity measured velocity by PIV ε deviation of PIV µ dynamics viscosity ρ density σ flow-rate ratio	R e v i e w R e v i e w R e v i e w	m 3 s -1 -m 2 s m s -1 m s -1 pixel frame -1 -Pa s kg m -3 -
		Subscripts
		ch	channel
		f	flowmeter
		in	inlet/distributor
		k	channel index
		p	PIV
	19
	20	Abbreviation
		CCD	Charge Coupled Device
		CFD	Computational Fluid Dynamics
					13 14 15

Table 1 : Comparison between various frequently-used microfluidic measurements 28Table 2 : The results of different cases in pre-test

 12

	27
	29
	30

Table 1 : Comparison between various frequently-used microfluidic measurements 1

 1

	Page 21 of 49
	Name	Intrusive/ non-intrusive	Spatial resolution	Tracer needed	Required instruments
	Weighting method	Yes	No flow field information; flow-rate measurement only	No	Container; digital balance; stop watch
	RTD	No	No flow field information; flow-rate measurement only	Yes	Tracer injector; fast camera; concentration meter or spectrometer
	HWA	Yes	Single point measurement; local scalar flow velocity	No	Hot-wire probe; analog-to-digital convertor; data processing
	LDV/DUV	No	Single point measurement; local vectorial flow velocity	Yes	Continuous laser (or Ultrasonic); beam-splitter; light collector; data processing
	PIV	No	Whole flow field measurement; velocity profiles	Yes	Double pulsed laser; CCD camera; lens; data processing
	2

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apjce Asia-Pacific Journal of Chemical Engineering

	F o
	r
	P
	e e r
	R e v i e w
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Table 2 : The results of different cases in pre-test 1 No. Case Number of frames for each plane Q f (L•min -1 ) Q p (L•min -1 )

 2

	ε	min	ε	max
	(-)		(-)

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Acknowledgements