flow boiling stability in microchannels

Copyright (c) 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

AIAA 2002-2781

FLOW BOILING STABILITY IN MICROCHANNELS D. Brutin

L. Tadrist

Ecole Polytechnique Universitaire de Marseille : Laboratoire I.U.S.T.I. U.M.R. 6595 Technopˆ ole de Chˆ ateau Gombert - 5, Rue Enrico Fermi - 13453 Marseille Cedex 13 - FRANCE Tel: +33 (0) 4 91 10 68 94 Fax: +33 (0) 4 91 10 69 69 E-mail: [email protected]

Abstract In this paper is studied convective boiling in a rectangular microchannel with hydraulic diameter of 889 µm. We performed a pressure drop analysis by ranging several mass flow rates for a chosen heat flux provided to the channel. Two kinds of upstream conditions have been investigated on the thermohydraulic behavior. Unsteady and Steady zones are delimited on a graphical representation. The upstream condition is modified by adding a buffer tank and the procedure is repeated. The pressure loss variation with the inlet Reynolds number exhibits an N-Shape. The unsteady behaviors appear in the first increasing part of the curve whatever are the inlet conditions.

1

Introduction

Recent industrial developments of microsystems (micro-heat-exchanger, micro-fluidheater, micro-reactors) imply a focus of research on micro heat and mass transfer in such confined geometries. The understanding of flow behavior on a microscale has not followed the fast development of microsystems. On such small scales, interfacial phenomena which are often negligible in classical flows become dominant. When a phase change occurs small hydraulic diameter may influence the bubble growth and evolution. On convective boiling in microchannels, only limited studies exist. This field is at present under investigation [6, 7]. Many types of instabilities can develop in flow boiling: flow excursion is the most common one explained in classical channel diameter by a criterion [8]. Kew & al. [13] highlighted an appearance threshold of the instability phenomena when the starting diameter of the bubble approaches the hydraulic diameter of the channel. The authors proposed a model of pressure fluctuation within cylindrical channels, based on the displacement of a liquid slug surrounded by expanding vapor [14]. In 1998, Aligoodarz & al. [15] observed temperature fluctuations of the same order as the

average overheating of the wall in channels of various sizes. Peng & al. [17] conducted singlephase and flow boiling experiments of some fluids and mixtures in rectangular microchannels of hydraulic diameter from 343 µm to 133 µm and triangular microchannels ranging from 600 to 200 µm. Unusual phase-change transport phenomena were observed by the authors. They tried to explain such behavior throught two new concepts of ”evaporating space” and fictitious boiling”. They deduced from their experiments that ”nucleate boiling in microchannels having dimensions from several hundred to less than one micrometer is almost impossible”. Jiang & al. [18] devised a transparent microchannel heat sink system to visualize the flow pattern and take temperature measurements during flow boiling. For the low power supplied to the fluid flow, they observed that local nucleation was possible but difficult to generate even for 40 µm hydraulic diameter channels. For intermediate power slugs flow develop and for high power supplied a steady annular flow mode was noticed. Yu & al. [16] realized single and two-phase flow experiments in microtubes diameters of 19, 52 and 102 µm. They observed for laminar flow a lower value of Poiseuille number (P o = λ ∗ Re) of 53 instead of 64 for laminar flow and similar lower behavior for turbulent one. The experimental Nusselt number was also enhanced to compare with predicted values. The upstream and downstream conditions influence on flow boiling stability were rarely studied for our knowledge. Authors only indicate the injection device: pressurized tank, peristaltic pump, syringe without taking care of tubing and other intermediate disposal compliance. The aim of this paper is to analyze the stability range and two-phase flow behavior for two different upstream conditions. The experimental set-up and the procedure will be described. The objective is to acquire better knowledge of the boundary conditions influence on flow stability. The different boiling states observed and their behaviors will be presented and explained through pressure loss analysis.

1 American Institute of Aeronautics and Astronautics

Figure 1: Experimental set-up.

Figure 2: Microchannel mechanical configuration.


Table 1: n-pentane liquid and vapor physical properties Conditions

Sigle

Value

Unit

25 ◦ C

σ

13.12 10−2

N.m−1

µL

2.23 10−4

P a.s

%L

621

Kg.m−3

CpL

2142

J.Kg −1 .K −1

%V

2.57

Kg.m−3

µV

6.78 10−6

P a.s

CpV

1717

J.Kg −1 .K −1

1010 hP a

TSAT

36

36 ◦ C

LV

382450

25 ◦ C

36 ◦ C

2

Experimental set-up

The main component of the loop is a microchannel heated by three faces, through which an upward fluid flow passes (Fig.1). The heated liquid is n-pentane; the physical properties are presented in Tab.1. Several openings are located along the main flow axis to allow pressure and temperature measurement through the front face. Thermocouples with 0.5 mm in diameter placed 1 mm below the heated surface of the channel evaluate the temperature profile along the main flow axis neat the wall. All the measured data (temperature, pressure and mass flow rate) are simultaneously acquired. As the Biot number (Eq.1) is quite small (Bi 1), the surface temperature measured is assumed to be the temperature given by the thermocouple placed 1 mm below the surface where h is an average coefficient of the heat transfer to the fluid flow and k is the thermal conductivity of the aluminum rod). Bi =

he k

(1)

The experimental device (Fig.1) is composed of three parts: the microchannel with the heating system, the condensor devices and an injection device which is a two-way syringe. A rigid tube containing a fixed starting level of n-pentane can be connected to the loop and will constitute a compliance source called buffer tank (BT). The entire loop is instrumented in such a way as to allow the control of the fluid flow (flow rate) and the heating parameters (inlet temperature, heat

◦

C

J.Kg −1

power supplied). The test cell is a rectangular channels of dimensions: (e, l, L) = 0.5 X 4 X 200 mm3 . The channel is hollowed out of aluminum r plates blocks covered with poly − carbonate (Fig.2). An electrical heater ensures the heating of the channel’s rear and sides faces while the transparent front face (fixed with thin calibrated adhesive tape) allows the observation of the flow patterns. The fluid inside the loop is heated to obtain boiling nucleation during few minutes to eliminate the non-condensable gas throught an opening valve in the loop. The fluid is returned to standard conditions. The experiments are then carried out using an established procedure: for a fixed heat flux several mass flow rates are provided to investigate the three possible states in the microchannel (liquid, biphasic, vapor) temperature and pressure measurements are permanently taken at different scanning frequencies (100 to 500 Hz) according to the observed phenomena dynamics. The heating power is stepped up then the new state is investigated. All acquired data are post-processed. When the stationary state is reached for each running condition (mass flow rate, heat flux) the time averages of temperature and pressure are calculated. The vapor quality, the pressure drop and the local superheating are deduced. The dynamics of the parameters are then analyzed (temperature and pressure). For each experimental condition, the frequency and amplitude fluctuations are deduced.


Table 2: Comparaison for two typical unsteady behaviors with buffer tank connected and not connected influence on respectively the average pressure loss (∆P ), the oscillation frequency (F 0 ) and the oscillation amplitude (δP ) Heat flux Inlet Reynolds number With compliance Without compliance

15.6 W.cm−2 ∆P (kPa) 5.2 4.5

382 F0 (Hz) 4 6.6

δP (kPa) 45 20

∆P (kPa) 9.4 14.3

1336 F0 (Hz) 3.8 17.4

δP (kPa) 11 1.6

Average pressure loss (Pa)

25000

20000

15000

10000

Buffer connected - Steady Buffer connected - Unsteady Buffer not connected - Steady Buffer not connected - Unsteady

5000

0 0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Reynolds number

Figure 3: Average pressure loss versus inlet Reynolds number for buffer connect and not connected to the loop (Heat flux of 15.6 W.cm−2 )

3

Results n

3.1

Pressure drop variation

As detailed in the previous section, we investigated for a heat flux several inlet Reynolds numbers. The microchannel pressure loss measured (Eq.2) is plotted as a function of the inlet Reynolds number (Eq.2) for one heat flux (15.6 W.cm−2 ) in Fig.3 for both cases without and with buffer tank. All the values measured are reported in Tab.2.

X ¯ = 1 ∆Pi ∆P n i=1

Re =

%L Uin DH µL

(2)

For both situations that is both inlet conditions, an N-Shaped curve is observed and corresponds to the two-phase flow length variation inside the channel. For very high Reynolds numbers (Re > 7000), the flow in the channel is solely liquid and the pressure drop curve corresponds to the curve of a liquid flow whereas, for very small Reynolds numbers (Re < 100), the channel is virtually wholly vapor, thus the pressure drop curve is that of a vapor flow. In-between, the N-Shape is


1300 1200

Inlet pressure Outlet pressure

6000

(a)

3.8 Hz

1100

900

2000 0 -2000 -4000

800 700 600 500 400 300 200

-6000

100 0

-8000 2,30 2,35 2,40 2,45 2,50 2,55 2,60 2,65 2,70 2,75 2,80 2,85 2,90

0

10

20

30

40

50

60

Frequency (Hz)

Time (s)

8000

40

6000

35

(c)

(d)

17.4 Hz 4000

30

Amplitude (rms(Pa ²))

Pressure fluctuating component (Pa)

(b)

1000

4000

Amplitude (rms(Pa ²))

Pressure fluctuating component (Pa)

8000

2000

0

-2000

-4000

25

20

15

10

Inlet pressure Outlet pressure

-6000

5

-8000

0

3,1

3,2

3,3

3,4

3,5

3,6

3,7

3,8

3,9

Time (s)

4,0

0

10

20

30

40

50

60

Frequency (Hz)

Figure 4: For a Reynolds number of 1336: Inlet and outlet pressure evolution with (a) BT connected and (c) BT not connected. Average pressure drop FFT with (b) BT connected and (d) BT not connected.

due to the two-phase flow pressure loss. In fact, three zones exist: liquid, two-phase and vapor zone. The length of these zones vary according to the mass and heat fluxes leading to this typical N-Shape. In addition, two regimes are found. A first one where temperature and pressure measured in the channel are steady. For a given heat flux, this regime corresponds to Reynolds numbers higher than a critical one (ReC is here around 1800). A second one where the temperatures and pressures are unsteady. The measured variables fluctuate in time with a specific amplitude and frequency. For both cases, the average pressure losses are found identical in the first increasing part of curve (i.e. Re < 1800) while for Re > 1800 two distinct curves are obtained. This shift is still not elucidated. For the first case with the buffer tank connected, the mass flow rate is provided to be constant at the syringe exit. In the graph presented in Fig. 3, the unsteady behaviors are found to be in the range where the pressure drop increases with the inlet Reynolds numbers. The unsteady behavior points confirmed by spectral analysis of the pres-

sure drop signal are reported. A typical pressure drop variations in such an unsteady zone is presented in Fig.(4a) for a Reynolds number of 1336. Only the fluctuating component of the pressure loss signal evolution is presented. In Fig.(4a) the inlet and outlet pressure signals fluctuates at 3.8 Hz with an average oscillation amplitude of 11 kPa. The signal is centered on the average pressure loss of 9.4 kPa. In Fig.(4a), the fluctuation might be due to the formation of a partial vapor slug. This assumptions must be confirmed by imaging. For the second case without buffer tank, the mass flux at the bottom of the channel is provided to be constant. Also, two types of behavior may be observed according to the operating conditions. For increasing inlet Reynolds numbers, when the maximum pressure loss exceeds at a critical Reynolds number a steady behavior is observed. For lower Reynolds number, an unsteady behavior is found. Typical signals are presented in Fig.(4c) for a Reynolds number of 1336, the pressure loss fluctuates at a much higher frequency (17.4 Hz) with a smaller average fluctuation amplitude of 1.6 kPa; the signal is also centered on the average pressure loss.


3.2

Boundary condition influence

In both cases, instabilities occurs in the first increasing part of the pressure loss versus inlet Reynolds number diagram (Fig.3). In the case, we will call with compliant upstream condition (with buffer tank connected) at a constant heat flux the transition Reynolds number is lower to compare with the case not connected. The unsteady state appear for lower inlet Reynolds number to compare with the case without compliant upstream condition. The threshold is so lower when a compliance source is connected in the loop. The Ledinegg range for loop oscillation when a compliant condition in provided is the negative slope of pressure loss versus Reynolds number curve. Our experimental result do not present unsteady behavior when the buffer tank is connected in this zone where as such a configuration should provide flow excursions when it is coupled with the microchannel. However, even if the characteristic N-Shape curve is experimentally obtained; we do not observe unsteady behavior which is for flow boiling in microchannel a deviation from boiling in tubes of higher diameters. For both inlet Reynolds number investigated, the fluctuation amplitude are much more smaller when the buffer tank is disconnected. But unsteady behaviors are still present. Oscillation frequencies when the buffer tank is not connected are higher than when the buffer is connected, furthermore the Fast Fourrier Transform exhibit a characteristic frequency with a narrow band in this configuration. A typical length to characterize boiling is the capillary length (Eq.3a). This length is used in many correlations for the determination of the bubble departure diameter. Thus, the geometric confinement influence on boiling can be summarized by the ratio of the capillary length and the microchannel hydraulic diameter which constitute the confinement number (Eq.3b). When the confinement number is lower than 1, it indicates that boiling is not modified by wall proximity whereas for number higher than 1 the wall proximity influence the bubble growth and evolution in the channel. For the microchannel devised of 889 µm hydraulic diameter using n-pentane, the capillary length is 1.46 mm which gives a confinement: Co = 1.6.

Lcap =

r

σ (a) g(%L − %V )

Co =

Lc (b) (3) DH

So, it seems that for our configuration with a confinement number up to 1, the confinement effect influence boiling stability by preventing flow

oscillations in the negative slope range when upstream compliant conditions are provided. Unsteady range is limited to inlet Reynolds number down to 2300. But when a constant mass flow rate is provided at the channel entrance, unsteady behavior still exist in the two-phase at others frequencies and fluctuations amplitudes. Whatever the unsteady range is located for Reynolds numbers down to 1800.

4

Conclusion

Steady and unsteady behaviors are evidenced by the experimental results of convective boiling in a microchannel. A critical Reynolds number is found to separate steady and unsteady zones in the diagram ∆P =f(Re). Two types of unsteady behavior due to the confinement or the coupling with the buffer tank are detailed and analyzed. They show coupling effect on unsteady behavior such as fluctuation amplitude. The results obtained differ from those for flow boiling in larger tubes. Further investigations will be performed to validate this result.

Acknowledgment We tanks the ”Centre National d’Etudes Spatiales” for his financial assistance: Grant N◦ 793/2000/CNES/8308.

Nomenclature Roman letters A Area (m2 ) Bi Biot number (−) Co Confinement number (−) Cp Heat specific (J.Kg −1 .K −1 ) DH Hydraulic diameter (m) e Thickness (m) F Frequency (Hz) h Average heat transfer coefficient (W.m−2 .K −1 ) k Thermal conductivity (W.m−1 .K −1 ) l Width (m) L Length (m) LV Heat of vaporization (J.Kg −1 ) P Pressure (P a) Po Poiseuille number (P a) Re Reynolds number (−) U Velocity (m.s−1 ) T Temperature (◦ C) Greek symbols δ Fluctuation component (−)


∆ λ µ % σ Subscript C in L V

Difference (−) Friction factor (−) Dynamic viscosity (P a.s) Density (Kg.m−3 ) Surface tension (N.m−1 ) & Supperscript Critical Inlet Liquid Vapor

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