Entropy and objectivity as constraints upon constitutive equations for two-fluid modeling of multiphase flow
In the modeling of multiphase flows, the complexity due to interfaces and the resultant discontinuities in fluid properties makes it essential to work with average parameters. This inevitably involves a loss of information regarding details of the flow. Averaging techniques do not yield the constitutive equations. These equations must be based on physical reasoning and/or experimental data. A systematic method of applying the second law of thermodynamics and the principle of objectivity to the derivation of candidate constitutive equations of multiphase flow is derived here and applied to the case of a sparsely dispersed flow of a discrete phase within a continuous phase. The local instantaneous entropy equation is first expressed as an equality. An averaged phasic entropy equation in which derivatives of entropy do not occur is then derived. A cell-model approximation for the ensemble average is derived that is capable of accounting for gradients of average flow parameters. This is used to derive hydrodynamic constitutive equations which are demonstrated to satisfy the second law of thermodynamics. Objectivity and the calculated hydrodynamic constitutive equations are used to hypothesized sets of constitutive equations for a real two-phase medium.
- Research Organization:
- Rensselaer Polytechnic Inst., Troy, NY (USA)
- OSTI ID:
- 5171963
- Country of Publication:
- United States
- Language:
- English
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