An all-Mach consistent numerical scheme for simulation of compressible multi-component fluids including surface tension, cavitation, turbulence modeling and interface sharpening on compact stencils

We present a numerical scheme valid in the range of highly to weakly compressible flows using a single-fluid four equation approach together with multi-component thermodynamic models. The approach can easily be included into existing finite volume methods on compact stencils and enables handling of compressibility of all involved phases including surface tension, cavitation and viscous effects. The mass fraction (indicator function) is sharpened in the two-phase interface region using the algebraic interface sharpening technique Tangent of Hyperbola for INterface Capturing (THINC). The cell face reconstruction procedure for mass fractions switches between an upwind-biased and a THINC-based scheme, along with proper slope limiters and a suitable compression coefficient, respectively. For additional sub-grid turbulence modeling, a fourth order central scheme is included into the switching process, along with a modified discontinuity sensor. The proposed “All-Mach” Riemann solver consistently merges the thermodynamic relationship of the components into the reconstructed thermodynamic variables (like density, internal energy), wherefore we call them All-Mach THINC-based Thermodynamic-Dependent Update (All-Mach THINC-TDU) method. Both, liquid-gas and liquid-vapor interfaces can be sharpened. Surface tension effects are taken into account by using a Continuum Surface Force (CSF) model. In order to reduce spurious oscillations at interfaces we decouple the computation of the interface curvature from the computation of the gradient of the Heaviside function. An explicit, four stage low storage Runge-Kutta method is used for time integration. The proposed methodology is validated against a series of reference cases, such as bubble oscillation/advection/deformation, shock-bubble interaction, a vapor/gas bubble collapse and a multi-component shear flow. The results of a near-critical shock/droplet interaction case are superior to those obtained by WENO3 and OWENO3 schemes and support that the proposed methodology works well with various thermodynamic relations, like the Peng-Robinson equation of state. Finally, the approach is applied to simulate the three-dimensional primary break-up of a turbulent diesel jet in a nitrogen/methane mixture including surface tension effects under typical dual-fuel conditions. The obtained results demonstrate that the methodology enables robust and accurate simulations of compressible multi-phase/multi-component flows on compact computational stencils without excessive spurious oscillations or significant numerical diffusion/dissipation.     «

We present a numerical scheme valid in the range of highly to weakly compressible flows using a single-fluid four equation approach together with multi-component thermodynamic models. The approach can easily be included into existing finite volume methods on compact stencils and enables handling of compressibility of all involved phases including surface tension, cavitation and viscous effects. The mass fraction (indicator function) is sharpened in the two-phase interface region using the algebr...     »