Numerical Study of the Effect of Surface Tension on Vapor Bubble Growth during Flow Boiling in Microchannels

Microchannel heat sinks typically consist of parallel channels connected through a common header. During flow boiling random temporal and spatial formation of vapor bubbles may lead to reversed flow in certain channels which causing an early CHF condition. Inside the microchannels the liquid surface tension forces is expected to play an important role and impact the vapor bubble growth and corresponding wall heat transfer. In the present study growth of a vapor bubble inside a microchannel during flow boiling is numerically studied by varying the surface tension but keeping the value of contact angle constant. The complete NavierStokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid-vapor interface is captured using the level set technique. The fluid properties used are of water but the surface tension value is varied systematically. The effect of surface tension on bubble growth rate and wall heat transfer is quantified. The results indicate that for the range of parameters investigated surface tension has little influence on bubble growth and wall heat transfer. INTRODUCTION Flow through microchannels is a matter of extensive study due to wide ranging applications in engineering and biological sciences. Bubble formation inside microchannels can take place if the fluid is a mixture of gas and liquid or the temperature of the liquid is above its saturation temperature corresponding to the pressure. When the bubbles are of the same size as the microchannel hydraulic diameters, they regulate the flow characteristics and if applicable the wall heat transfer. In the microscale the surface tension forces are expected to dominate relative to the gravitational forces and control the bubble dynamics. Kandlikar (2004) listed several non-dimensional groups relevant to study of two-phase in microchannels. He developed a mechanistic model of the flow boiling phenomena based on the different forces acting on a growing vapor bubble. He introduced a new non-dimensional group K2 which is the ratio of the evaporation momentum force and the surface tension force but it did not include the contact angle. He also provided a plot of K2 employed in different experimental investigations in minichannels. Mukherjee and Mudawar (2003) developed a smart pumpless loop for microchannel electronic cooling and tested it with both water and dielectric FC-72. The dielectric has much lower surface tension and contact angle values as compared to water and produced much smaller vapor bubbles. The authors concluded that bubbles formed in FC-72 provided less obstruction to the liquid flow as compared to water and hence dielectrics are more appropriate for microchannel heat exchangers. Lee et al. (2004) experimentally studied bubble dynamics in trapezoidal microchannels with hydraulic diameter of 41.3 microns and recorded bubble departure size and frequency using high speed digital camera. The bubble departure radius was found to decrease with heat flux whereas there was a mixed effect of mass flux on the bubble departure radius. The authors concluded that the bubble departure radius was primarily influenced by surface tension forces and drag due to bulk flow. Mukherjee and Dhir (2005) developed a three dimensional numerical model using the level-set method to study lateral merger of vapor bubbles during nucleate pool boiling. Mukherjee and Kandlikar (2005) extended the model to study vapor bubble growth inside a microchannel during flow boiling. The bubble growth was studied for various values of incoming liquid flow rate and temperature. The effect of gravity was found to be negligible on the bubble dynamics. The model however, used a fixed value of surface tension and the contact angle. 1 Copyright © 2006 by ASME Yang et al. (2002) simulated bubbly two phase flow in a narrow channel using a numerical code FlowLab based on the Lattice-Boltzmann method. Single or multiple twodimensional Taylor bubbles were placed in a vertical channel and their behavior was studied for different values of surface tension and body forces. No heat transfer or phase change was considered between the two phases. The authors found little effect of surface tension on the movement of the bubbles or the flow regime transition. In the present study a vapor bubble growing on a heated wall inside a microchannel during flow boiling is numerically studied. All liquid and vapor properties are kept constant except the value of surface tension which is systematically varied. The contact angle of the liquid vapor interface at the contact line region with the solid wall is also kept constant. The objective is to study the effect of surface tension without any effect of contact angle on the bubble dynamics and corresponding wall heat transfer. NOMENCLATURE A wall area Cp specific heat at constant pressure d grid spacing g gravity vector H Heaviside function h heat transfer coefficient hfg latent heat of evaporation k thermal conductivity L length of bubble L1 upstream bubble cap location L2 downstream bubble cap location l0 length scale m mass transfer rate at interface ms milliseconds Nu Nusselt number p pressure Re Reynolds number ST surface tension T temperature T ∆ temperature difference, Tw-Tsat t time t0 time scale u x direction velocity u0 velocity scale v y direction velocity w z direction velocity x distance in x direction y distance in y direction z distance in z direction T β coefficient of thermal expansion κ interfacial curvature μ dynamic viscosity ν kinematic viscosity ρ density σ surface tension τ time period φ level set function