Compressible and immiscible fluids with arbitrary density ratio
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911397703581696 |
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| author | Wang, Fei |
| author_facet | Wang, Fei |
| contents | For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density $ρ$ within the water-air interface is assumed to be a constant based on the Boussinesq approximation namely $ρ(\mathrm{d} \mathbf u/\mathrm{d} t)$, which does not account for the true momentum evolution $\mathrm{d} (ρ\mathbf u)/\mathrm{d} t$ ($\mathbf u$-fluid velocity). Here, we present an alternative theory for the density evolution equations of immiscible fluids in computational fluid dynamics, differing from the concept of Navier-Stokes and Euler equations. Our derivation is built upon the physical principle of energy minimization from the aspect of thermodynamics. The present results provide a generalization of Bernoulli's principle for energy conservation and a general formulation for the sound speed. The present model can be applied for immiscible fluids with arbitrarily high density ratios, thereby, opening a new window for computational fluid dynamics both for compressible and incompressible fluids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compressible and immiscible fluids with arbitrary density ratio Wang, Fei Fluid Dynamics For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density $ρ$ within the water-air interface is assumed to be a constant based on the Boussinesq approximation namely $ρ(\mathrm{d} \mathbf u/\mathrm{d} t)$, which does not account for the true momentum evolution $\mathrm{d} (ρ\mathbf u)/\mathrm{d} t$ ($\mathbf u$-fluid velocity). Here, we present an alternative theory for the density evolution equations of immiscible fluids in computational fluid dynamics, differing from the concept of Navier-Stokes and Euler equations. Our derivation is built upon the physical principle of energy minimization from the aspect of thermodynamics. The present results provide a generalization of Bernoulli's principle for energy conservation and a general formulation for the sound speed. The present model can be applied for immiscible fluids with arbitrarily high density ratios, thereby, opening a new window for computational fluid dynamics both for compressible and incompressible fluids. |
| title | Compressible and immiscible fluids with arbitrary density ratio |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2406.19786 |