Abstract
Abstract
Highlights
The difficulties in developing hyperbolic two-fluid models for disperse multiphase flows has been reviewed by Lhuillier, Chang & Theofanous (2013)
Numerical simulations with non-hyperbolic two-fluid models diverge under grid refinement due to the complex eigenvalues in the continuum limit
To illustrate the behaviour of the proposed two-fluid model, we develop a 1-D numerical solver for the full model written in conservative form
Summary
The difficulties in developing hyperbolic two-fluid models for disperse multiphase flows has been reviewed by Lhuillier, Chang & Theofanous (2013). We employ the same model formulation, extended to account for the added mass from particle wakes and pseudo-turbulence, to compressible fluid–particle flows with a slip velocity due, e.g. to buoyancy. Our treatment of added mass is similar to Cook & Harlow (1984) (see appendix A for more details), but generalized to a compressible fluid and a non-constant added-mass function The latter is required to handle flows wherein the particle-phase volume fraction varies significantly. The kinetic-theory derivation leads to conservation laws in the form of hyperbolic equations This has advantages over a formulation where the virtual mass is treated as an interphase force when solving the two-fluid model numerically. In the stiffened-gas model used for the fluid, Θf must be initialized such that the fluid pressure pf is positive
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