dorsal/arxiv
View SchemaModels of low-speed flow for near-critical fluids with gravitational and capillary effects
| Authors | Diane L. Denny, Robert L. Pego |
|---|---|
| Categories | |
| ArXiv ID | physics/9803027 |
| URL | https://arxiv.org/abs/physics/9803027 |
Abstract
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.
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"abstract": "We study low-speed flows of a highly compressible, single-phase fluid in the\npresence of gravity, for example in a regime appropriate for modeling recent\nspace-shuttle experiments on fluids near the liquid-vapor critical point. In\nthe equations of motion, we include forces due to capillary stresses that arise\nfrom a contribution made by strong density gradients to the free energy. We\nderive formally simplified sets of equations in a low-speed limit analogous to\nthe zero Mach number limit in combustion theory.\n When viscosity is neglected and gravity is weak, the simplified system\nincludes: a hyperbolic equation for velocity, a parabolic equation for\ntemperature, an elliptic equation related to volume expansion, an\nintegro-differential equation for mean pressure, and an algebraic equation (the\nequation of state). Solutions are determined by initial values for the mean\npressure, the temperature field, and the divergence-free part of the velocity\nfield. To model multidimensional flows with strong gravity, we offer an\nalternative to the anelastic approximation, one which admits stratified fluids\nin thermodynamic equilibrium, as well as gravity waves but not acoustic waves.",
"arxiv_id": "physics/9803027",
"authors": [
"Diane L. Denny",
"Robert L. Pego"
],
"categories": [
"physics.flu-dyn"
],
"title": "Models of low-speed flow for near-critical fluids with gravitational and capillary effects",
"url": "https://arxiv.org/abs/physics/9803027"
},
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"variant": "snapshot-2026-03-01",
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