On the effect of term in multiphase mechanics

Sha, W.T.; Soo, S. L.

doi:10.1016/0301-9322(79)90044-2

Cited by 35 publications

(11 citation statements)

References 4 publications

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“…Sha and Soo [201] dealt with essentially the same problem from a more physical angle. Their discussion focuses on what form the ∇(α k p k V k ) term in the momentum equation should take.…”

Section: Mathematical Model Formulation Aspectsmentioning

confidence: 95%

“…Those who favor (2) retaining a part of it as a stabilizing force. Sha and Soo [201] argued that the physical effect of the p k V k ∇α k term is to spread the dispersed phase which has an initial concentration gradient. They proposed to replace the term by:…”

Section: Mathematical Model Formulation Aspectsmentioning

confidence: 99%

“…Travis et al [234] considered viscous stresses, Lahey et al [143] considered the added mass force, Prosperetti and Wijngaarden [180] considered compressibility effects. Trapp [233] considered Reynolds stresses, while Stuhmiller [227], Bourè [24], Pauchon and Banerjee [173,174], Sha and Soo [201], Prosperetti and Jones [181] and Holm and Kupershmidt [115] have put their main focus on the adoption and interpretation of the interfacial pressure forces (see Sects. 3.5.1 and 3.5.6).…”

Section: Mathematical Model Formulation Aspectsmentioning

confidence: 99%

See 2 more Smart Citations

Multiphase Flow

Jakobsen

2014

Chemical Reactor Modeling

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In this chapter the pertinent multiphase modeling concepts established in fluid mechanics are examined. The modeling framework constituting the basis for the next generation of chemical reactor models is presented. The average multi-fluid model represents a trade-off between accuracy and computational efforts. This concept is a direct multi-dimensional extension of the conventional reactor models with the addition of the momentum equations. The multi-fluid model is actually the only approach that can be used analyzing chemical reactive systems on industrial scales considering both inherent physics and feasible computational efforts. The remaining sections of the chapter are devoted to the derivation of the two-fluid and multi-fluid models, and to the description of the averaging procedures commonly used in multiphase flow analysis.

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Section: Mathematical Model Formulation Aspectsmentioning

confidence: 95%

Section: Mathematical Model Formulation Aspectsmentioning

confidence: 99%

Section: Mathematical Model Formulation Aspectsmentioning

confidence: 99%

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Multiphase Flow

Jakobsen

2014

Chemical Reactor Modeling

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“…Various remedies have been proposed in order to make the equations purely hyperbolic and the system eigenvalues real. Addition of the virtual mass [3] or interfacial pressure terms [4] to the governing equations has proved efficient in improving the stability. Another interesting approach is to use the surface tension force terms, as proposed by Lee et al [5] and Chung et al [6].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Two-Fluid Two-Phase Flows by HLL Scheme Using an Approximate Jacobian Matrix

Yeom

Chang

2006

Numerical Heat Transfer, Part B: Fundamentals

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A compressible two-fluid two-phase flow model based on two sets of governing equations is formulated. We solve, using the second-order Harten, Lax, and van Leer (HLL) scheme, five disparate two-phase benchmark problems such as shock propagation in the two-phase medium, the cavitating flow, and the gravity-induced phase separation. In the conventional HLL scheme, the simple sonic speeds evaluated from the two single phases are used in lieu of the fastest speeds in the two phases, since their accurate estimation is difficult. To improve the method, we here propose utilization of the analytic eigenvalues from the temporary 6 Â 6 Jacobian matrix, reduced by dropping the interfacial transfer terms. The total sound speed of the two-phase flow evaluated by these eigenvalues agrees very well with the existing experimental data. The second-order HLL scheme using these analytic eigenvalues is proved efficient, robust, and accurate in comparison with other available methods.

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“…Compression of the gas phase depends on the predicted interfacial pressure term from both kinetic energy and continuity equations (Sha and Soo [8]). Cross-phase interactions arising from internal circulation affect the momentum exchange within the dispersed phase.…”

Section: Introductionmentioning

confidence: 99%