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Research Papers: Multiphase Flows

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

[+] Author and Article Information
Avinash Vaidheeswaran

School of Nuclear Engineering,
Purdue University,
400 Central Drive,
West Lafayette, IN 47906
e-mail: avaidhee@purdue.edu

Martin Lopez de Bertodano

Mem. ASME
School of Nuclear Engineering,
Purdue University,
400 Central Drive,
West Lafayette, IN 47906
e-mail: bertodan@purdue.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 14, 2015; final manuscript received January 31, 2016; published online April 22, 2016. Assoc. Editor: Alfredo Soldati.

J. Fluids Eng 138(8), 081302 (Apr 22, 2016) (7 pages) Paper No: FE-15-1664; doi: 10.1115/1.4032755 History: Received September 14, 2015; Revised January 31, 2016

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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References

Figures

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Fig. 2

Oblate ellipsoid geometry

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Fig. 1

Eigenvalues with Cp = 0.25 and CVM = 0.5

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Fig. 3

Prolate ellipsoid geometry

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Fig. 4

Variation of coefficients for oblate ellipsoid (top) and prolate ellipsoid (bottom)

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Fig. 5

Eigenvalues for oblate ellipsoid (top) and prolate ellipsoid (bottom)

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