Characteristics, stability, and short-wavelength phenomena in two-phase flow equation systems
The occurrence and significance of complex characteristics in two-phase flow equation systems are clarified by a detailed analysis of separated two-phase flow between two parallel plates. The basic system of one-dimensional, two-phase flow equations for this problem possesses complex characteristics, exhibits unbounded instabilities in the short-wavelength limit, and constitutes an improperly posed initial value problem. These difficulties have led some workers to propose major modifications to the basic equation system. The relatively minor modification of introducing surface tension is shown to be sufficient to render the characteristics real, to stabilize short-wavelength disturbances, and to produce a properly posed problem. For a given value of the surface tension, the basic equation system thus modified is shown to predict correctly the evolution of small-amplitude disturbances having wavelengths long compared to the plate spacing. A formula is given for the artificial surface tension necessary to stabilize wavelengths of the order of the mesh spacing in a finite-difference numerical calculation. A brief discussion is given concerning the expected behavior of surface tension as compared to viscosity in the nonlinear regime. The general relationship between characteristics and stability is discussed in Appendix A.
- Research Organization:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)
- DOE Contract Number:
- E(10-1)-1375
- OSTI ID:
- 7353649
- Report Number(s):
- ANCR-1272; TRN: 76-013113
- Resource Relation:
- Other Information: C52(E11*
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
42 ENGINEERING
TWO-PHASE FLOW
WATER COOLED REACTORS
DIFFERENTIAL EQUATIONS
ONE-DIMENSIONAL CALCULATIONS
PLATES
REACTOR SAFETY
STABILITY
SURFACE TENSION
VISCOSITY
EQUATIONS
FLUID FLOW
REACTORS
SAFETY
SURFACE PROPERTIES
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