A general pressure equation based method for incompressible two-phase flows

We present a fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure equation. In addition, the volume-of-fluid approach is used for interface capturing under the operator-split methodology. Our method is fully-explicit and stable with simple local spatial discretization, and hence, it is easy to implement. Several two- and three-dimensional canonical two-phase flows are simulated. The qualitative and quantitative results prove that our method is capable of accurately handling problems involving a range of density and viscosity ratios and surface tension effects

Numerical simulation of weakly compressible multiphase flows with a baer-nunziato type model

We present the results of the simulation of two-phase CO2 flows at low-Mach number, obtained through a pressure-based Baer-Nunziato type model. The underlying full non-equilibrium model enables the description of each phase with its own thermodynamic model, so it circumvents the requirement of the definition of the speed of sound of the vapor-liquid mixture. The primitive formulation, combined with a special pressure scaling to correctly capture the behavior in the zero-Mach limit, is well-suited to model weakly compressible flows, and makes easier the use of arbitrary thermodynamic models. At the interfaces, the phasic velocity and pressure are driven toward the equilibrium by means of relaxation processes, whose velocities are controlled by user-defined parameters. The set of seven partial differential equations describing the flow evolution is discretized through a finite-volume scheme in space and an hybrid implicit-explicit time discretization, to avoid the stringent time step limitation imposed by the acoustics. We compare the results of a shock-tube problem, initially containing saturated CO2, obtained according to the stiffened gas model and to the Peng-Robinson equation of state. 1 INTRODUCTION Among the technologies able to contrast the global warning, carbon capture and storage (CCS) is regarded as a crucial and effective approach. Consequently, the numerical investigation of carbon dioxide (CO2) flows under the different conditions we can encounter within the CCS framework is becoming more and more important. In this work, we focus in particular in unsteady weakly compressible twophase flows. Such kind of flows may occur in the transport pipelines, because of fluctuating in the CO2 supply, impurities, or during transient events, such as start-up, shut-down or depressurization [1]. From a numerical point of view, these flows present different challenging aspects. First of all, the weak compressibility—that is the condition where the flow velocity is considerably smaller than the speed of sound but compressibility effects cannot be neglected—makes inefficient and inaccurate the standard compressible solvers. Second, the multitude of spatial scales and the presence of dynamic interfaces that separate the different phases call for an effective modeling that avoids the full resolution of the flow field but takes into consideration the relevant flow features. Third, a flexible implementation of the thermodynamic modeling for the CO2 is recommended to be able to customize it according to the different applications

Velocity and energy relaxation in two-phase flows

In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model assumes each phase to possess its own velocity and energy variables. Despite recent advances, the six equations model remains computationally expensive for many practical applications. Moreover, its advection operator may be non-hyperbolic which poses additional theoretical difficulties to construct robust numerical schemes |Ghidaglia et al, 2001]. In order to simplify this system, we complete momentum and energy conservation equations by relaxation terms. When relaxation characteristic time tends to zero, velocities and energies are constrained to tend to common values for both phases. As a result, we obtain a simple two-phase model which was recently proposed for simulation of violent aerated flows [Dias et al, 2010]. The preservation of invariant regions and incompressible limit of the simplified model are also discussed. Finally, several numerical results are presented.Comment: 37 pages, 10 figures. Other authors papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

An implicit-explicit solver for a two-fluid single-temperature model

We present an implicit-explicit finite volume scheme for two-fluid single-temperature flow in all Mach number regimes which is based on a symmetric hyperbolic thermodynamically compatible description of the fluid flow. The scheme is stable for large time steps controlled by the interface transport and is computational efficient due to a linear implicit character. The latter is achieved by linearizing along constant reference states given by the asymptotic analysis of the single-temperature model. Thus, the use of a stiffly accurate IMEX Runge Kutta time integration and the centered treatment of pressure based quantities provably guarantee the asymptotic preserving property of the scheme for weakly compressible Euler equations with variable volume fraction. The properties of the first and second order scheme are validated by several numerical test cases