Hyperbolic models for two-phase (or two-material) flow
For some time it has been known that many of the two-phase flow models lead to ill-posed problems unless viscous stresses are included. The inclusion of viscous stresses changes the character of the equations from hyperbolic to parabolic. A continuing problem has been to find a well-posed hyperbolic system of equations which provide a reasonable model for two-phase flow, or to show that no such model exists. Another outstanding problem has been to understand why the derivation procedures for microstructural models produce models with the peculiar defect of being unstable. A careful investigation of the derivation procedures for the simple case of stratified flow suggests that the equal-pressures assumption is most likely the assumption leading to instability. Consideration of the alternative assumption suggests a model, namely the Unequal-Pressures Model, which is expressed by a first order system of partial differential equations with real characteristics. Thus the problem of complex characteristics (or sound speeds) which lead to the instability in the equal-pressures models is obviated. The form that the analysis takes suggests a technique for categorizing models according to the evolution equations for their internal state variables in order to aid model builders in quickly determining which models will lead to complex characteristics. Also a model with real characteristics for the two-phase flow of a bubbly liquid arises from an extension of the Unequal-Pressures model for single-layered flow to multi-layered flow. This Unequal-Pressures model has real characteristics fo all physically acceptable states and has a complete set of eigenvectors except for a set of measure zero in state space and therefore is hyperbolic in state space. Also this Unequal-Pressures model is stable in the sense of von Neumann a.e. in state space.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 5969038
- Report Number(s):
- SAND-81-0253; ON: DE82000807
- Country of Publication:
- United States
- Language:
- English
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