On a model for internal waves in rotating fluids

AbstractIn this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the dispersion balance. The physical regime of validation is discussed and mathematical properties of the new system, concerning well-posedness, conservation laws and existence of solitary-wave solutions, are analyzed.

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The well-posedness of incompressible one-dimensional two-fluid model

International Journal of Heat and Mass Transfer ◽

10.1016/s0017-9310(99)00287-2 ◽

2000 ◽

Vol 43 (12) ◽

pp. 2221-2231 ◽

Cited By ~ 18

Author(s):

Jin Ho Song ◽

M. Ishii

Keyword(s):

Fluid Model ◽

Well Posedness ◽

One Dimensional ◽

Two Fluid Model ◽

Two Fluid

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Interfacial Pressure Coefficient for Ellipsoids and Its Effect on the Two-Fluid Model Eigenvalues

Journal of Fluids Engineering ◽

10.1115/1.4032755 ◽

2016 ◽

Vol 138 (8) ◽

Cited By ~ 7

Author(s):

Avinash Vaidheeswaran ◽

Martin Lopez de Bertodano

Keyword(s):

Fluid Model ◽

Pressure Coefficient ◽

Well Posedness ◽

Virtual Mass ◽

Two Phase Flows ◽

Two Phase ◽

Pressure Coefficients ◽

Interfacial Pressure ◽

Two Fluid Model ◽

Two Fluid

Analytical expressions for interfacial pressure coefficients are obtained based on the geometry of the bubbles occurring in two-phase flows. It is known that the shape of the bubbles affects the virtual mass and interfacial pressure coefficients, which in turn determines the cutoff void fraction for the well-posedness of two-fluid model (TFM). The coefficient used in the interfacial pressure difference correlation is derived assuming potential flow around a perfect sphere. In reality, the bubbles seen in two-phase flows get deformed, and hence, it is required to estimate the coefficients for nonspherical geometries. Oblate and prolate ellipsoids are considered, and their respective coefficients are determined. It is seen that the well-posedness limit of the TFM is determined by the combination of virtual mass and interfacial pressure coefficient used. The effect of flow separation on the coefficient values is also analyzed.

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Comparison of well-posedness criteria of two-fluid models for numerical simulation of gas-liquid two-phase flows in vertical pipes

Thermal Science ◽

10.2298/tsci200420158f ◽

2021 ◽

pp. 158-158

Author(s):

Naghibi Falahati ◽

V. Shokri ◽

A. Majidian

Keyword(s):

Fluid Model ◽

Well Posedness ◽

Fluid Models ◽

Vertical Pipe ◽

Numerical Diffusion ◽

Solution Field ◽

Two Fluid Model ◽

Two Phases ◽

Well Posed ◽

Two Fluid

The purpose of the present study is to compare the well-posedness criteria of the free-pressure two-fluid model, single-pressure two-fluid model, and two-pressure two-fluid model in a vertical pipe. Two-fluid models were solved using the Conservative Shock Capturing Method. A water faucet case is used to compare two-fluid models. The free pressure two-fluid model can accurately predict discontinuities in the solution field if the problem's initial condition satisfies the Kelvin Helmholtz instability conditions. The single-pressure two-fluid model can accurately predict the behavior of flows in which the two phases are poorly coupled. The two-pressure two-fluid model is an unconditionally well-posed one; if in the free-pressure two-fluid model and single-pressure two-fluid model, the range of velocity difference of two phases exceeds certain limits, the models will be ill-posed. The two-pressure two-fluid model produces more numerical diffusion than the free-pressure two-fluid and single-pressure two-fluid models in the solution field. High numerical diffusion of two-pressure two-fluid models leads to failure to better comply with the problem's analytical solution. Results show that a single-pressure model is a powerful model for numerical modeling of gas-liquid two-fluid flows in the vertical pipe due to a broader range of well-posed than free-pressure models and less numerical diffusion than the two-pressure model.

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