Hyperbolic two-pressure models for two-phase flow

Journal Article · Sun Jan 01 04:00:00 EST 1984 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(84)90056-1· OSTI ID:5133421

Ransom, V H; Hicks, D L

For some time it has been known that many of the two-phase flow models lead to ill-posed Cauchy problems because they have complex characteristic values. A necessary condition (at least in the linear case) for the Cauchy problem to be well-posed is that it be stable in the sense of von Neumann. For systems of partial differential equations of first order, stability in the sense of von Neumann is essentially equivalent to the condition that the model be hyperbolic (all real characteristic values and complete set of characteristic vectors). Herein models are developed which have real characteristic values for all physically acceptable stgates (state space) and except for a set of measure zero have a complete set of characteristic vectors in state space. Therefore, these models are hyperbolic a.e. (almost everywhere) in state space. Also, they are stable in the sense of von Neumann a.e. in state space even without inclusion of viscosity terms. The models discussed herein are developed for the case of two-phase separated planar flow and include transverse momentum considerations. These models are referred to as ''two-pressure'' models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase; the pressure fields are related through momentum considerations. Numerical results on a steady-state problem show good agreement with existing steady-state results. Numerical results on a transient problem agree with a single-pressure model until the onset of numerical instability in the single-pressure model. Compared to the single-pressure (hydrostatic) model, the two-pressure model approximates additional physical features and is shown to be viable approach for the case of separated flow.

• Research Organization: EG and G Idaho, Inc., Idaho Falls, Idaho 83415
• DOE Contract Number: AC07-76ID01570
• OSTI ID: 5133421
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 53:1; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
640410 -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
FLUID FLOW
LINEAR MOMENTUM
MATHEMATICAL MODELS
ONE-DIMENSIONAL CALCULATIONS
STEADY-STATE CONDITIONS
TRANSVERSE MOMENTUM
TWO-PHASE FLOW