A pressure-based method for weakly compressible two-phase flows under a Baer-Nunziato type model with generic equations of state and pressure and velocity disequilibrium

07/26/2021
by   Barbara Re, et al.
0

Within the framework of diffuse interface methods, we derive a pressure-based Baer-Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes relaxation terms characterized by user-defined finite parameters, which drive the pressure and velocity of each phase toward the equilibrium. There is no clear notion of speed of sound, and thus, most of the classical low Mach approximation cannot easily be cast in this context. The proposed solution strategy consists of two operators: a semi-implicit finite-volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. Being the acoustic terms in the hyperbolic part integrated implicitly, the stability condition on the time step is lessened. The discretization of non-conservative terms involving the gradient of the volume fraction fulfills by construction the non-disturbance condition on pressure and velocity to avoid oscillations across the multimaterial interfaces. The developed simulation tool is validated through one-dimensional simulations of shock-tube and Riemann-problems, involving water-aluminum and water-air mixtures, vapor-liquid mixture of water and of carbon dioxide, and almost pure flows. The numerical results match analytical and reference ones, except some expected discrepancies across shocks, which however remain acceptable (errors within some percentage points). All tests were performed with acoustic CFL numbers greater than one, and no stability issues arose, even for CFL greater than 10. The effects of different values of relaxation parameters and of different amount equations of state – stiffened gas and Peng-Robinson – were investigated.

READ FULL TEXT
research
11/01/2019

Non-equilibrium Model for Weakly Compressible Multi-component Flows: the Hyperbolic Operator

We present a novel pressure-based method for weakly compressible multiph...
research
04/26/2020

A weakly non-hydrostatic shallow model for dry granular flows

A non-hydrostatic depth-averaged model for dry granular flows is propose...
research
05/17/2023

On a Doubly Reduced Model for Dynamics of Heterogeneous Mixtures of Stiffened Gases, its Regularizations and their Implementations

We deal with the reduced four-equation model for dynamics of the heterog...
research
06/02/2020

On the simulation of multicomponent and multiphase compressible flows

The following paper presents two simulation strategies for compressible ...
research
01/20/2023

A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers

We present a novel staggered semi-implicit hybrid FV/FE method for the n...
research
02/12/2020

Cahn-Hilliard Navier-Stokes Simulations for Marine Free-Surface Flows

The paper is devoted to the simulation of maritime two-phase flows of ai...

Please sign up or login with your details

Forgot password? Click here to reset