In the present study, a robust and conservative numerical scheme is proposed to simulate the violent two-phase flows with high-density ratios. In this method, the mass conservation equation and the momentum equation are solved in a consistent manner. The tangent of hyperbola for interface capturing scheme is extended for the computation of the mass flux by which the sharpness and conservation property of density field is preserved. Compared with other recently proposed methods, no geometrical computation is involved in deriving the mass flux and the spurious velocity in the interfacial region can be completely avoided. To improve the computational efficiency, the present method is implemented on a parallel block-structured adaptive mesh refinement method with a staggered layout of variables. High-fidelity numerical simulation of plunging jet through the liquid surface is performed. A bubble detection algorithm is developed to track bubbles generated in air entrainment process. The evolution of the bubble cloud, air concentration, bubble-size, and bubble-velocity distributions are predicted and compared quantitatively with the experiment. Numerical results show the air entrainment and penetration depth are highly correlated with the upstream disturbance. The growing interfacial roughness of the jet yields more entrained air in the final stage of jet impingement. It is found that when the initial perturbation is introduced, the overall size of the equivalent bubble radius will expand, and the penetration depth of the bubble cloud will decrease, while a larger volume of air is entrained.
The Tangent of Hyperbola for INterface Capturing (THINC) scheme allows a jump‐like reconstruction and brings about a significant improvement in resolving the discontinuous part of the numerical solutions. However, it is found that the original THINC scheme loses accuracy when working on the stretched, curvilinear or highly‐skewed grid. In this study, we propose a simple strategy to determine the jump thickness parameter in the THINC function, so as to effectively suppress the unphysical oscillation. A Boundary Variation Diminishing (BVD) guideline is introduced to make options between the Weighted Essentially Non‐Oscillatory (WENO) scheme and the modified THINC scheme, thus both the smooth and discontinuous solutions can be reconstructed properly avoiding distortion of grids. Numerical validations indicate that the improved WENO‐THINC‐BVD approach maintains high resolution and is more robust on various types of non‐uniform meshes. The present method is further extended to validate the low‐dissipation property in resolving higher wave numbers portions by simulating an isotropic turbulence decay problem. Finally, we perform the direct numerical simulation (DNS) of a spatially evolving adiabatic flat plate boundary‐layer flow problem at a supersonic Mach number (). Numerical results show the predicted mean flow variables and the normalized shear stress agree well with the experimental data, significant improvements are found in the resolution of the small‐scale vortices, especially in the transition process.
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