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

2016 ◽  
Vol 138 (8) ◽  
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.

Effect of Interfacial Pressure Term on Numerical Stability of a Two-Fluid Model

2014 ◽  
Author(s):  
Tomio Okawa ◽  
Yoshiro Kudo
Keyword(s):  
Numerical Stability ◽  
Two Phase Flow ◽  
Flow Boiling ◽  
Fluid Model ◽  
Phase Flow ◽  
Numerical Instability ◽  
Two Phase ◽  
Interfacial Pressure ◽  
Two Fluid Model ◽  
Two Fluid

Mathematical ill-posedness of the governing equations is one the main causes of numerical instability encountered in numerical simulation of two-phase flow using a two-fluid model. It is known that the ill-posedness can be mitigated if the difference between the average pressures of gas and liquid phases is taken into consideration appropriately. In the present work, it was investigated how the numerical stability of the one-dimensional, two-fluid model is influenced by the interfacial pressure terms that express the pressure difference between bubbles and continuous liquid phase in bubbly two-phase flow. Analyses were carried out for adiabatic air-water two-phase flow and subcooled flow boiling. It was confirmed that the interfacial pressure terms are effective to mitigate the numerical instability induced by the mathematical ill-posedness of the two-fluid model. However, the standard interfacial pressure terms deteriorated the numerical stability in some cases. It was found that the simplified model in which the spatial gradients of relative velocity and fluid density are eliminated is effective for the mitigation of numerical instability in wider analytical conditions.

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