Pressure‐based unified solver for gas‐liquid two‐phase flows where compressible and incompressible flows coexist

Abstract

Summary We propose a pressure‐based unified solver for gas‐liquid two‐phase flows where compressible and incompressible flows coexist. Unlike the original thermo–Cubic Interpolated Propagation Combined Unified Procedure (CIP‐CUP) method proposed by Himeno et al (Transactions of the Japan Society of Mechanical Engineers, Series B, 2003), we split the advection term of the governing equations into a conservation part and into the rest. The splitting of advection term has two advantages. One is the high degree of freedom in choosing discretization schemes such as central‐difference schemes, upwind schemes, and Total Variation Diminishing (TVD) schemes. The other is the ease of implementation on unstructured grids. The advantages enable the analyses of various flows such as turbulent and supersonic ones in actual complicated boundaries. Therefore, the solver is useful for practical analyses. The solver was validated on the following test cases: subsonic single‐phase flows, incompressible single‐phase turbulent flows, and incompressible gas‐liquid two‐phase flows. With unstructured grids, we obtained the equivalent results as the ones with structured grids. After the validations, subsonic jet impinging on a water pool was calculated and compared with experimental results. It was confirmed that the calculated results were consistent with the experimental ones.

A unified algorithm for interfacial flows with incompressible and compressible fluids

“…For instance, acoustic waves in the gas phase are known to promote interfacial instabilities [74], which however have a negligible influence on the behaviour of the liquid phase in subsonic flows; especially, the compressibility of the liquid does not influence the acoustics in the gas phase, as shown by the presented results. With the presented algorithm the simplification of an incompressible fluid cannot only be invoked for low-Mach flows with respect to the gas phase, as considered in previous studies [37][38][39], but practically for any flow velocity. While a compressible liquid is not a valid simplification for large liquid Mach numbers, for subsonic gas flows, for instance in subsonic fuel injection and spray atomisation processes, the presented results suggest an incompressible liquid to be a reasonable assumption.…”

“…Wadhwa et al [36] proposed a method for computing incompressible liquid drops in a compressible gas, representing the interface as a matching moving mesh and solving the flow of the incompressible fluid using the artificial compressibility method of Chorin [23]. Others proposed algorithms for compressible-incompressible flows applying the same governing equations in non-conservative form in both fluids [37][38][39] and these algorithms are, in general, only applicable to incompressible and low Mach number flows. However, the application of the governing equations in conservative form together with a conservative discretisation is a prerequisite for an accurate prediction of flows in all Mach number regimes [40], in particular shock waves, rarefaction fans and contact discontinuities.…”

Coupled Simulation of Flow and Chemical Reaction with Finite Reaction Rate for Decarburization of Molten Iron using Gas Jet of Carbon Dioxide

“…After adding mass conservation equations for chemical species to the governing equations of compressible/incompressible gas-liquid two-phase flows, 24) we obtained the following equations:…”

“…Using Eqs. ( 17) and ( 20), the following pressure equation can be obtained: The material derivative term D D g ρ * / t can be discretized as follows: 24)…”

“…Furthermore, their models were not validated under the high CO 2 concentration condition, which is considered to be the case in actual BOFs from the model experiment with combustion in opposing flows of O 2 and CO. 23) We herein propose a CFD solver, which fully couples governing continuum mechanics equations with a decarburization reaction model considering the mass transfer and the finite reaction rate on the gas-liquid interface, in order to elucidate the effects of each rate-limiting process. In this method, our pressure-based solver of mixed compressibility for two-phase flows 24) was extended to treat reactive flows. The decarburization reaction model based on the model by Nomura and Mori 25) was integrated into the CFD solver.…”