A multiscale method for compressible liquid-vapor flow with surface tension

One approach recently proposed for reducing the frictional resistance to liquid flow in microchannels is the patterning of micro-ribs and cavities on the channel walls. When treated with a hydrophobic coating, the liquid flowing in the microchannel wets only the surfaces of the ribs, and does not penetrate the cavities, provided the pressure is not too high. The net result is a reduction in the surface contact area between channel walls and the flowing liquid. For micro-ribs and cavities that are aligned normal to the channel axis (principal flow direction), these micro-patterns form a repeating, periodic structure. This paper presents experimental and numerical results of a study exploring the momentum transport in a parallel plate microchannel with such microengineered walls. The liquid-vapor interface (meniscus) in the cavity regions is treated as ideal in the numerical analysis (flat). Two conditions are explored with regard to the cavity region: 1) The liquid flow at the liquid-vapor interface is treated as shear-free (vanishing viscosity in the vapor region), and 2) the liquid flow in the microchannel core and the vapor flow within the cavity are coupled through the velocity and shear stress matching at the interface. Predictions and measurements reveal that significant reductions in the frictional pressure drop can be achieved relative to the classical smooth channel Stokes flow. Reductions in the friction factor are greater as the cavity-to-rib length ratio is increased (increasing shear-free fraction) and as the channel hydraulic diameter is decreased. The results also show that the average friction factor – Reynolds number product exhibits a flow Reynolds dependence. Furthermore, the predictions reveal the impact of the vapor cavity regions on the overall frictional resistance.

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Application of an Improved Ghost Fluid Method to the Collapse of Non-Spherical Bubbles in a Compressible Liquid

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-04027 ◽

2011 ◽

Cited By ~ 3

Author(s):

Hiroyuki Takahira ◽

Yoshinori Jinbo

Keyword(s):

Surface Tension ◽

Shock Waves ◽

Thermal Diffusion ◽

Level Set ◽

Compressible Liquid ◽

Maximum Temperature ◽

Bubble Collapse ◽

Ghost Fluid Method ◽

Toroidal Bubble ◽

The Impact

The ghost fluid method (GFM) is improved to investigate violent bubble collapse in a compressible liquid, in which the adaptive mesh refinement with multigrids, the surface tension, and the thermal diffusion through the bubble interface are taken into account. The improved multigrid GFM is applied to the interaction of an incident shock wave with a bubble. The multigrid GFM captures the fine interfacial and vortex structures of the toroidal bubble when the bubble collapses violently accompanied with the penetration of the liquid jet and the formation of the shock waves. The multigrid GFM is also applied to the bubble collapse near a tissue surface in which the tissue is modeled with gelatin in order to predict the tissue damage due to the bubble collapse; the motions of three phases for the gas inside the bubble, the liquid surrounding the bubble, and the gelatin boundary are solved directly by coupling the level set method with the improved GFM. Two kinds of level set functions are utilized for distinguishing the gas-liquid interface from the liquid-gelatin interface. It is shown that the impact of the shock waves generated from the collapsing bubble on the boundary leads to the formation of depression of the boundary; the toroidal bubble penetrates into the depression. Also, the surface tension effects are successfully included in the improved GFM. The thermal effects of internal gas on the bubble collapse are also discussed by considering the thermal diffusion across the interface in the GFM. The thermal boundary layers of the toroidal bubble are captured with the method. The result shows that the smaller the initial bubble radius becomes, the lower the maximum temperature inside the bubble becomes because of the thermal diffusion across the interface.

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