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David W. Fogg

Creare Inc, P.O. Box 71, Hanover, NH 03755 e-mail:

Kenneth E. Goodson

Department of Mechanical Engineering, Stanford University, Building 530, Room 224, Stanford, CA 94305

Bubble-Induced Water Hammer and Cavitation in Microchannel Flow Boiling

While microchannel flow boiling has received much research attention, past work has not considered the impact of acoustic waves generated by rapidly nucleating bubbles. The present work provides a theoretical framework for these pressure waves, which resembles classical “water hammer” theory and predicts a strong influence on bubble nucleation rates and effective convection coefficients. These pressure waves result directly from confinement in microchannel geometries, reflect from geometrical transitions, and super- impose to create large transients in the static liquid pressure. Feedback from the pressure waves inhibits bubble growth rates, reducing the effective heat transfer. Pressure depres- sions generated by the propagating pressure pulses can cause other bubbles to grow at lower than expected wall temperatures. The additional nucleation enhances heat transfer over short times but increased flow instability may inhibit heat transfer over longer periods. The limited quantitative measurements available in the literature indicate con- fined bubble growth rates in microchannels are significantly lower than those predicted by the classical Rayleigh–Plesset equation. The present model predicts confined bubble growth rates to within 20%. A nondimensional number indicative of the relative mag- nitude of the water hammer pressure to bubble pressure is proposed to characterize the transitions from conventional to microchannel flow boiling. DOI: 10.1115/1.3216381

Keywords: microchannel, flow boiling, confinement, two-phase heat transfer, bubble acoustics, water hammer

1 Introduction

The semiconductor industry continues to increase the total number, number density, and power density of transistors in mi- croprocessors. The resulting trend in device design is leading to highly nonuniform heat generation and increasing power con- sumption by the chips 1 . In the near future, forced air convection will be replaced by liquid microchannel cooling technologies in an effort to drive the resistance of the chip package down and allow larger heat exchangers to be located remotely in the com- puter chassis. Two-phase microchannel cooling promises in- creased performance by further reducing the package resistance while still allowing a remote exchanger to reject the waste heat to the environment.

Notwithstanding the concentrated research effort in this field, fundamental challenges in controlling the pressure and tempera- ture fluctuations remain, preventing accurate predictions of perfor- mance and reliability. Oscillations in temperature and pressure have been observed in both single channels 2 and multichannel arrays 3,4 . Qu and Mudawar 3 observed pressure drop and parallel channel instabilities in an array of 21 231 712 m2 rectangular channels. The pressure drop instability is a result of the flow rate response of the flow delivery system to pressure changes in the test section. Frequencies are usually very low on the order of 0.1 Hz. In the parallel channel instability, the flow redistributes itself in response to an increased pressure drop in a few channels due to nonuniform vapor generation. Peles 4 also observed parallel channel and pressure drop instabilities in 13 channel arrays of 50–200 m triangular channels. A flow excur- sion instability resulting from flow regime transitions and a com- pound relaxation instability from rapid bubble growth were also observed. Peles 4 noted that the instabilities were more pro-

Contributed by the Heat Transfer Division of ASME for publication in the JOUR- NAL OF HEAT TRANSFER. Manuscript received February 13, 2008; final manuscript received October 7, 2008; published online October 15, 2009.

nounced in the microchannels than they are for large channels. Zhang et al. 2 observed pressure oscillations and periodic vapor generation in single rectangular microchannels measuring 44 m and 113 m in hydraulic diameter under constant applied heat flux and constant inlet velocity boundary conditions. The resulting oscillations were classified a compound relaxation instability similar to bumping and geysering and was associated with the rapid vapor generation characteristic of microchannels. For de- tailed descriptions of two-phase flow instabilities refer to Boure et al. 5 or Carey 6 .

Understanding the dynamic behavior of microchannel flow boiling is a major challenge, as the metrology and modeling for these flows are still in their infancy relative to larger scale sys- tems. Due to the spatial constraints of the system, measurements have been limited to inlet and outlet pressures from commercial pressure taps, flow rates with commercial flow meters, wall tem- peratures with IR thermometry or microfabricated thermistors, and high speed video imaging 2,3,7–10 . The inability to directly measure flow parameters in the channel itself leads to a great deal of uncertainty as it forces assumptions to be made in order to interpolate local values from those measured externally. Research is ongoing to identify techniques to measure parameters such as void fraction 11,12 and local liquid temperature 12 but further work is required before they can be applied to obtain reliable quantitative values.

Numerical and analytical studies can provide insight into these flows in the absence of direct experimental evidence. To date, the bulk of microchannel two-phase research has been experimental, but several analytical and numerical studies have been performed. Chavan et al. 13 analytically examined the stability of two-phase forced convection in microchannels using a homogeneous flow linear stability model. This model was previously applied to mac- roscale flows. The model predicts the pressure response for a single channel to perturbations in inlet velocity and Chavan con- cludes that microchannel forced convective boiling is only stable for low subcooling and low applied heat fluxes. Consequently,

Journal of Heat Transfer Copyright © 2009 by ASME DECEMBER 2009, Vol. 131 / 121006-1 Downloaded 14 Apr 2010 to Redistribution subject to ASME license or copyright; see

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