LIQUID VELOCITY FIELD MEASUREMENTS IN TWO-PHASE MICROCHANNEL CONVECTION

Transcription

1 3rd International Symposium on Two-Phase Flow Modelling and Experimentation Pisa, September 2004 LIQUID VELOCITY FIELD MEASUREMENTS IN TWO-PHASE MICROCHANNEL CONVECTION Evelyn N. Wang, Shankar Devasenathipathy, Carlos H. Hidrovo, David W. Fogg, Jae-Mo Koo, Juan G. Santiago, Kenneth E. Goodson, Thomas W. Kenny Stanford University, Mechanical Engineering, Terman Engineering 551 MC 4021, Stanford, CA Phone:(650) , Fax:(650) , ABSTRACT Flow visualization studies in two-phase microchannel convection quantify bubble sizes and trajectories but provide little information about liquid velocity fields. This paper reports the first liquid velocity field measurements during bubble growth in a heated microchannel using micron-resolution particle image velocimetry (µpiv). Rectangular cross-section silicon microchannels with hydraulic diameters less than 150 µm are fabricated with integrated heaters. When power is applied to the microchannel, vapor bubbles form due to heterogeneous nucleation and grow from the side walls. Surface forces in this Stokes flow regime (Re D = 0.02) prevent bubble departure from the wall. The velocity field data provide information about the liquid/vapor interface and is used to estimate various forces associated with bubble growth. A control volume analysis approach yields an excess pressure of 1630 Pa inside the vapor bubble, when the liquid inertial and drag forces are assumed to be insignificant compared to the surface tension forces. These preliminary measurements are a step towards understanding the nucleation, growth, and detachment processes at higher flowrates during forced convective boiling in microchannels, which will ultimately aid in the design of future two-phase microchannel heat sinks. INTRODUCTION Two-phase microchannel heat sinks are promising for future thermal management of integrated circuit (IC) chips. The modeling and design of these heat sinks, however, require a comprehensive understanding of the interplay between vapor bubble nucleation and growth and the associated liquid velocity field. Most of the flow visualization studies for two-phase convection in microchannels have provided qualitative observations of bubble sizes, densities, and trajectories. Jiang et al. observed local nucleate boiling in V-grooves with D H = 26 µm 53 µm with an input power of 12 W [1]. Zhang et al. observed bubble formation and growth from cavities of 4 µm - 8 µm in microchannels with D H < 150 µm [2]. Steinke et al. collected high speed video of flow boiling in D H = 207 µm and observed different flow regimes with bubbles ranging from 15 µm to 193 µm in diameter [3]. Qu et al. visually detected boiling incipience in microchannels when the first bubble was sighted growing primarily from the bottom channel wall [4]. Few studies have reported liquid velocity measurements in two-phase systems. Lindken et al. reported velocity measurements in bubbly two-phase flow where pseudo-turbulence could be characterized [5]. Grunefeld et al. showed the feasibility of measuring instantaneous velocity fields in both gaseous and liquid phases in an unsteady laminar flow system [6]. Molho reported velocity measurements around laser-induced cavitation bubbles [7]. Qiu et al. reported liquid velocity field measurements with PIV for sliding bubbles on inclined surfaces [8]. Heinzel et al. presented preliminary flow pattern measurements in a 200 µm x 200 µm heat exchanger and described particle fouling as a large problem in obtaining further velocity measurements [9]. This paper reports quantitative flow field measurements of the liquid-phase during bubble growth in a heated microchannel using micron-resolution particle image velocimetry (µpiv). These measurements are used to study the transient dynamics of bubble growth and the corresponding unsteady velocity fields in channels with D H < 150 µm. These velocity fields allow for the quantification of forces on the liquid/vapor interface and estimation of the pressure difference across the bubble interface. These forces will be helpful for the study of bubble departure. This preliminary study reports results for Re D << 1, where surface tension forces are dominant and the bubbles do not depart from the walls. However, the approach presented here establishes a methodology for future analysis of forces which can be extended to higher flowrate conditions typical in microchannel forced convection. EXPERIMENTAL SETUP AND PROCEDURE A schematic of the imaging setup is shown in Figure 1. An epi-fluorescent microscope (Nikon TE300) is used with illumination from a mercury lamp. The filter cube assembly for the microscope consists of an exciter filter which transmits wavelengths from 450 nm to 500 nm, a dichroic beam splitter, and a 500 nm long-pass barrier emission filter. Imaging of the flow is achieved through a 20 X objective lens (NA = 0.75) and a 12-bit resolution interline cooled CCD camera (Roper Scientific CoolSnapHQ). The camera has a 1300 x 1040 pixel array with square pixels of side 6.45 µm, and a continuous frame rate of 18

2 frames/s with 2 x 2 binning. The fluid flow was driven by a constant hydrostatic head maintained by a liquid column in a graduated cylinder. The working fluid (deionized water) was seeded with 0.7 µm fluorescent particles to a volume density of %. The particles (Duke Scientific) have a peak excitation wavelength in the blue (λ = 468 nm) and have a peak emission wavelength in the green (λ = 508 nm). Triton-X surfactant (Sigma Corporation) at a concentration of 0.1% was added to the particle solution to prevent particles from sticking to the channel walls. Low flowrates of ml/min were used in this study to facilitate experiments using a continuous illumination source and the limited frame rate of the camera. Future work at more representative flowrates for microchannel convection requires the use of a pulsed laser as the illumination source and may require a high speed CCD camera. Figure 1 Schematic of experimental setup. (a) Front side of microchannel device. inlet inlet mercury lamp microchannel surfboard heater power supply microchannel CCD objective filter cube outlet 1 mm outlet 1 mm (b) Back side of microchannel device. Figure 2 Image of the fabricated silicon microchannel. The silicon microchannels have integrated aluminum heaters fabricated using standard micromachining technology. The channel is anodically bonded to a 500 µm thick Pyrex (7740) glass slide to seal the channel and to allow for optical access. The rectangular channels have dimensions 1 mm of 270 µm x 95 µm (D H = 140 µm) and 130 µm x 95 µm (D H = 97 µm). Figure 2(a) shows the front side of the test device with a 2 mm long channel and inlet and outlet reservoirs. The back side of the chip has a uniformly distributed aluminum heater along the channel as shown in Figure 2(b). The channel region is suspended such that a constant heat flux is applied to the channel. Wire bonds electrically connect the aluminum heater to the surfboard, where the input voltage can be applied and controlled by an external power supply. Fluidic inlet and outlet ports are glued to the backside of the chip. Liquid velocity fields surrounding vapor bubbles during two-phase microchannel convection can be determined by micron resolution particle image velocimetry (µpiv). A PIV algorithm developed by Meinhart et al. [10] was used to interrogate the images and determine time-averaged velocity fields using the average correlation method, such that the signal-to-noise ratio of correlation functions can be significantly improved. The measurement depth defined as the depth at which the particle-image intensity is sufficiently low such that it will not significantly influence the velocity measurement for the 20 X (NA = 0.75) objective was found to be 4.7 µm. All measurements were taken 10 µm from the glass wall of the microchannel to reduce noise from the out of plane particles. Two quantifiable sources of uncertainty in these measurements are those due to (1) Brownian motion of the seed particles, and (2) errors associated with identifying the center of cross-correlation peaks [11]. The normalized uncertainty, ε, due to Brownian motion in a two-dimensional measurement of the particle velocity can be quantified as ε = ± 2σ s Δr where Δr = sδt is the mean (deterministic) displacement of the particle and s is the in-plane velocity magnitude. The standard deviation displacement from Brownian motion in the twodimensional plane of the image is σ s = (4DΔt) 0.5, where Δt is the time between images and D = kt/6πµa is the translational diffusion coefficient. Equation (1) yields ε = 6.3% for typical velocity magnitudes in our experiment. The particle image diameters of our setup correspond to 3 to 4 pixels, and so the center of the cross correlation peak can be determined to within approximately one-tenth of the particle-image diameter [12]. Due to diffraction, the effective particle diameter in the object plane is 1.1 µm, which corresponds to a normalized measurement uncertainty of 110 nm or 2 %. The total uncertainty from these two uncorrelated sources is therefore estimated to be 6.6%. EXPERIMENTAL RESULTS To validate the experimental methods and PIV algorithm, single-phase velocity fields are initially obtained at room temperature in a D H = 97 µm channel, as shown in Figure 3. The steady state profile shows the curvature expected from this low Reynolds number flow, with a maximum velocity of 150 µm/s, corresponding to Re D = Figure 4 compares the theoretical prediction of the fully developed velocity profile in a rectangular duct [13] to the experimental data. The pressure drop across the channel is estimated from theory to be approximately 150 Pa. (1)

3 interface as well as particles coalescing at the interface as the vapor bubble is growing. Figure 3 Velocity field measurements in a D H = 97 µm channel at room temperature. (a) t = 7.2 s, P = 0.98 W Figure 4 Comparison of steady state velocity profile for experiments and theory in a rectangular duct with D H = 97 µm. 50 µm 50 µm (a) t = 7.2 s, P = 0.98 W (b) t = 21 s, P = 1.4 W Figure 5 Images of the growth of a bubble in a D H = 140µm microchannel. In two-phase flow conditions, the vapor bubble growth process was studied in the microchannel as a function of increasing power. Liquid dryout within the microchannel was observed for an input power of 1.5 W at a flowrate of ml/min. Bubbles were present after the initial occurrence of liquid dryout. Images of the bubble growth process on the side wall of a 140 µm hydraulic diameter microchannel are shown in Figure 5. These bubbles originate mainly in the channel via heterogeneous nucleation due to defect sites on the walls. The average bubble diameter growth rate is 4 µm/s and the size of the bubble can be controlled by regulating the heater power. Surface tension effects dominate in this Stokes flow regime (Re D = 0.02), and bubbles do not depart from the wall. The intensity at the liquid/vapor interface in the images is significantly greater than the rest of the image, which can be attributed to diffraction at the (b) t = 21 s, P = 1.4 W Figure 6 Velocity fields surrounding a growing bubble corresponding to images in Figure 5. Figure 6 shows instantaneous velocity vector fields at t = 7.2 s and t = 21 s with applied powers of 0.98 W and 1.4 W, respectively. The particles track the profile of the bubble due to the low Reynolds numbers (<<1) and as expected, there is no separation of flow downstream of the bubble. As the vapor bubble grows with increasing heat input, the local fluid velocity increases over the bubble due to a decrease in the effective channel crosssection, corresponding to maximum velocities of 250 µm/s and 420 µm/s in Figures 6(a) and 6(b), respectively. Figure 7 shows the increase in the local streamwise velocity component, u, corresponding to locations x = 36 µm and x = 284 µm in the velocity field shown in Figure 6(b). The u- velocity profile, at x = 36 µm shows minimal influence of the bubble and has a maximum velocity of 196 µm/s. The velocity doubles to 396 µm/s at x = 284 µm due to the presence of a 160 µm diameter vapor bubble in the channel. The u-velocity component for y = 255 µm location of the data in Figure 6(b) is plotted in Figure 8. A maximum velocity of 413 µm/s is observed at x = 263 µm due to the presence of the vapor bubble and decreases to 220 µm/s downstream of the bubble at x = 408 µm. The symmetry of the streamwise velocity profile along the streamwise direction about the center of the bubble suggests that the bubble center is approximately stationary and expanding in a

4 symmetric fashion. This is typical of the low flowrates used in the current study. µpiv are the two-dimensional velocity components projected onto the measurement plane. 50 µm 50 µm (a) Front interface at P=1.5 W. (b) Rear interface at P=1.8W. Figure 9 Images of a liquid vapor interface with a vapor slug occupying the entire channel width. Figure 7 Velocities varying in the streamwise direction corresponding to Figure 6(b) at x = 36 µm and x= 284 µm. (a) Front interface at P=1.5 W. Figure 8 Velocities varying in the streamwise direction corresponding to Figure 6(b) at y=255 µm. As power is further increased to 1.5 W, the expanding bubble occupies the entire width of the channel and an elongated vapor slug is formed. An image of the windward-interface of this vapor slug is shown in Figure 9(a). As power is increased further, the vapor slug oscillates. At a power level of 1.9 W, the leeward interface of the vapor slug was captured in the stationary field of view as shown in Figure 9(b). The velocity fields obtained in the liquid regions immediately adjacent to the front and rear interface particle images are shown in Figure 10(a) and 10(b), respectively. At the front interface shown in Figure 10(a), the fluid accelerates near the top and bottom of the bubble. In contrast, at the rear interface, the liquid exits primarily from the top of the vapor slug. This demonstrates that the flow near the bubble surface is strongly three-dimensional and the flow fields captured with (b) Rear interface at P=1.8 W. Figure 10 Velocity fields surrounding the liquid vapor bubble interface corresponding to images in Figure 9. DISCUSSION AND ANALYSIS Preliminary instantaneous velocity measurements in an integrated silicon microchannel are presented in this paper. The velocity fields obtained from these measurements help determine the forces on bubbles after nucleation and during growth, and can eventually provide insight into the mechanisms governing bubble departure. We apply a control volume approach similar to that

5 presented by Kandlikar and Stumm [14] to determine the excess pressure inside the vapor bubble before departure. Figure 11 shows the chosen control volume (CV1) that encloses the region just upstream of the windward half of the bubble. The depth of the control volume is defined by the channel depth. CV1 liquid β Side wall The force balance in the x-direction for CV1 can be expressed as F σ,1,x + F σ,2,x + F D,CV1,x + F P,CV1,x = M out,x M in,x (2) where the M & out, x is the momentum efflux, M & in, x is the momentum influx, F σ,1,x is the x-component of the bubbleedge surface tension on the side wall, F σ,2,x is the surface tension acting along the edge of CV1, F D,CV1,x is the drag force, and F P,CV1,x is the net pressure force acting on the control volume, all acting in the x-direction. The above force balance assumes that the bubble is growing slowly, such that the liquid experiences negligible changes in velocity due to bubble growth compared to the externally imposed velocity field in the channel. Surface tension forces are given by π / 2 F σ,1,x = 2σr s cosβ cosγdγ (3) 0 β F σ,2, x = 2σπrb (1 ) (4) π where σ is the surface tension, r s is the radius of the bubble base, β is the contact angle, and γ is the angle between the radial lines. The contact angle, β, is estimated to be 50 degrees from the recorded images, which also show symmetry on the upstream and downstream sides of the bubble. This suggests that fluid inertial and drag forces are small, a result that will be confirmed by analyzing the terms in equation (2). The total drag force for a pure vapor bubble subjected to a uniform liquid flow around it κ F D = Re b 1+ κ vapor ρu2 2 x F σ,1 y r b F σ,2 Figure 11 Force analysis on the front control volume of the bubble. F P r s β A p (5) was recommended by Clift et al. [15] where κ=µ v/ µ f is the viscosity ratio, ρ is the density of the fluid, u is the liquid velocity, Re b is the bubble Reynolds number, and A P is the projected area. From calculating the drag force around a vapor bubble, the total drag is found to be very small compared to the other forces. Since the drag for CV1 in the x-direction is a fraction of the total drag, this term can be ignored in the analysis. A better estimate of the drag on CV1 can be derived from the velocity field measurements. However, to obtain the shear stress at the side wall shown in Figure 11 requires high resolution velocity measurements such that the viscous boundary layer can be resolved. The bubble diameters used in this analysis are comparable to or larger than the channel depth normal to Figure 11, which strongly suggests that the bubble fills the channel in the depth direction. Therefore, in the analysis, the bubble is assumed to be cylindrical. The data in Figure 6 are taken at a depth of approximately 10 µm from the glass, which is significantly less than the total channel depth of 100 µm. As a result, the flow fields observed here will be somewhat less than those in the middle of the channel. In the present work, detailed study of three dimensional flow fields was limited by noise considerations as discussed in the experimental section. Future work will aim to bring the issue of bubble shape into the force analysis developed here. To obtain a more accurate estimate of the momentum fluxes on the right control surface requires obtaining velocity fields at various channel depths. By evaluating these momentum fluxes at different depths, the significance of the three-dimensional effects can be better quantified. The excess pressure, Δp excess, acting on the control volume is given by Δp excess = F P A p (6) where F P is the pressure force acting on the projected area, A P. From the velocity fields shown in Figure 6(b), the momentum influx and outflux were calculated to be 1.5x10-13 N and 3x10-13 N, respectively, and the drag force was estimated to be 9x10-11 N. These terms were neglected compared to the total surface tension force of 24x10-6 N acting on the control volume. Therefore, a static force balance between the surface tension and excess pressure force was performed, and an excess pressure difference of 1630 Pa was determined. When liquid velocities reach approximately 250 mm/s, liquid inertial and drag forces will be comparable to the surface tension force, and will have a significant effect on the force balance. The bubbles in these current experiments do not detach from the walls. However, when the bubbles do detach at higher flowrates, these excess pressure estimates will aid in determining bubble departure conditions. From prescribing a control volume around the vapor bubble, a static force balance of the surface tension, excess pressure, and viscous forces will determine bubble departure criteria. Quantifying these viscous forces at the bubble interface from these velocity fields are currently underway. The low flowrates used in the current experiments are not practical for microchannel cooling. However, these preliminary velocity measurements confirm the applicability of obtaining velocity fields surrounding vapor bubbles in two-phase microchannel convection. High flow rate conditions should be addressable using a faster frame rate camera and pulsed laser

6 illumination. Such measurements should shed light on detachment physics. CONCLUSIONS AND FUTURE WORK Liquid velocity measurements during two-phase bubble nucleation and growth are presented for the first time for heated silicon microchannels with hydraulic diameters of less than 150 µm. These measurements reveal details associated with the interplay between bubble growth and detachment with the unsteady velocity field in the microchannel. A preliminary approach for understanding forces on the bubble and determining bubble departure criteria based on excess pressure is presented. Future work in obtaining velocity fields at higher flowrates with bubble growth will be used to building more detailed models for bubble detachment physics. ACKNOWLEDGMENTS The authors would like to thank Dave Huber for valuable discussions. This work is supported by the National Defense Science and Engineering Graduate Fellowship and MARCO. The project made use of the National Nanofabrication Users Network facilities funded by the National Science Foundation under award number ECS NOMENCLATURE a=radius of fluorescent sphere [m] A p =projected area [m 2 ] D=translational diffusion coefficient (D=kT/6πµa) [m 2 /s] D H =hydraulic diameter [m] F σ,1 =surface tension force due to bubble base [N] F σ,2 =surface tension force at the bubble center plane normal to wall [N] F D =drag force [N] F P =net pressure force [N] k=boltzmann constant [m 2 kg/s 2 K] M & M & in out = = momentum flux in [N] momentum flux out [N] r b =radius of bubble [m] Re b =Reynolds number based on bubble diameter Re D =Reynolds number based on hydraulic diameter r s =radius at bubble base [m] T=temperature [K] u=streamwise velocity [m/s] v=velocity perpendicular to the stream wise direction [m/s] x=coordinate axis in the direction of flow [m] y=coordinate axis normal to the flow direction [m] z=coordinate in the depthwise direction [m] β=contact angle between vapor and liquid at the wall γ=angle measured from front edge ΔP=excess pressure [N/m 2 ] Δt=time between images [s] ε= normalized uncertainty κ=viscosity ratio of vapor to liquid = µ v /µ f λ=wavelength [m] µ=viscosity of water [Ns/m 2 ] ρ L =liquid density [kg/m 3 ] ρ v =vapor density [kg/m 3 ] σ=surface tension [N/m] σ s =standard deviation displacement [N/m] τ=shear stress [N/m 2 ] REFERENCES 1. L. Jiang, M. Wong, and Y. Zohar, Phase change in microchannel heat sinks with integrated temperature sensors, Journal of MicroElectroMechanical Systems, vol. 8(4), pp , L. Zhang, E.N. Wang, J.-M. Koo, L. Jiang, K.E. Goodson, J.G. Santiago, and T.W. Kenny. Enhanced Nucleate Boiling in Microchannels, Fifteenth IEEE International Conference on Micro Electro Mechanical Systems. Las Vegas, Nevada, U.S.A, vol. pp , M. Steinke and S.G. Kandlikar. Flow Boiling and Pressure Drop in Parallel Flow Microchannels, 1st International Conference on Microchannels and Minichannels. Rochester, New York, vol. pp W. Qu, Mudawar, I., Prediction and measurement in incipient boiling heat flux in micro-channel heat sinks, International Journal of Heat and Mass Transfer, vol. 45, pp , R. Lindken and W. Merzkirch, Velocity measurements of liquid and gaseous phase for a system of bubbles rising in water, Experiments in Fluids, vol. 29, pp. S194-S201, G. Grunefeld, H. Finke, J. Bartelheimer, and S. Kruger, Probing the velocity fields of gas and liquid phase simultaneously in a two-phase flow, Experiments in Fluids, vol. 29(4), pp , J. Molho, Electrokinetic Dispersion in Microfluidic Separation Systems, in Mechanical Engineering. 2001, Stanford Unversity. p D. Qiu and V.K. Dhir, Experimental study of flow pattern and heat transfer associated with a bubble sliding on downward facing included surfaces, Experimental Thermal and Fluid Science, vol. 26, pp , V. Heinzel, A. Jianu, and H. Sauter. Flow Pattern Measurement by PIV in the Microchannels of a Heat Exchanger and Associated Problems due to Fouling, First International Conference on Microchannels and Minichannels. Rochester, New York, vol. pp , C.D. Meinhart, S.T. Wereley, and J.G. Santiago, A PIV algorithm for estimating time-averaged velocity fields, Journal of Fluids Engineering, vol. 122(2), pp S. Devasenathipathy, Santiago, J. G., Wereley, S.T., Meinhart, C.D., Takehara, K., Particle imaging techniques for microfabricated fluidic systems, Experiments in Fluids, vol. 34, pp , A.K. Prasad, R.J. Adrian, C.C. Landreth, and P.W. Offutt, Effect of resolution on the speed and accuracy of particle image velocimetry interrogation, Experiments in Fluids, vol. 13, pp , F.M. White, Viscous Fluid Flow. New York: McGraw Hill, 1991.

7 14. S.G. Kandlikar and B.J. Stumm, A Control Volume Approach for Investigating Forces on a Departing Bubble Under Subcooled Flow Boiling, Journal of Heat Transfer, vol. 117, pp , R. Clift, J.R. Grace, and M.E. Weber, Bubbles, Drops and Particles. New York: Academic Press, 1978.