Physics – Fluid Dynamics
Scientific paper
1998-03-19
Physics
Fluid Dynamics
27 pages with 1 figure, LaTeX2e
Scientific paper
We study low-speed flows of a highly compressible, single-phase fluid in the presence of gravity, for example in a regime appropriate for modeling recent space-shuttle experiments on fluids near the liquid-vapor critical point. In the equations of motion, we include forces due to capillary stresses that arise from a contribution made by strong density gradients to the free energy. We derive formally simplified sets of equations in a low-speed limit analogous to the zero Mach number limit in combustion theory. When viscosity is neglected and gravity is weak, the simplified system includes: a hyperbolic equation for velocity, a parabolic equation for temperature, an elliptic equation related to volume expansion, an integro-differential equation for mean pressure, and an algebraic equation (the equation of state). Solutions are determined by initial values for the mean pressure, the temperature field, and the divergence-free part of the velocity field. To model multidimensional flows with strong gravity, we offer an alternative to the anelastic approximation, one which admits stratified fluids in thermodynamic equilibrium, as well as gravity waves but not acoustic waves.
Denny Diane L.
Pego Robert L.
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