Mesh Independence and Adaptive Mesh Refinement For Advanced Engine Spray Simulations

Computational fluid dynamic (CFD) analysis of in-cylinder events in the automotive industry is heavily dependent on spray simulations for almost all advanced engine concepts. As the upper bound of efficiency in these engines is pursued, the accurate prediction of sprays is critical, since the mixture preparation and ignition, whether by spark or auto-ignition, needs to be precisely controlled. While most of the spray literature closely examines various drop processes, especially breakup, comparatively less attention has been focused on the momentum coupling between the liquid and the gas phases, in particular the numerical aspects. In fact, adjusting models for the evolution of drop size has been one of the dominant means of controlling predictions of spray shape and liquid penetration. However, this approach breaks down when the drop sizes (and their spatial evolution) required for correct spray penetration and shape deviate significantly from actual values and lead to inaccurate predictions. Such inaccuracies prohibit correct prediction, e.g., of vapor distribution and wall deposition. This study shows a methodology for momentum coupling that can be applied to meshes of arbitrary structure, shape, and topology. It utilizes a least-squares based interpolation scheme for gas-to-liquid coupling and a kernel smoothing scheme for liquid-to-gas coupling that together are effective, even for coarse meshes, in eliminating grid artifacts in the spray shape. The key elements of the momentum coupling are also formulated to be second-order accurate. While second-order accuracy cannot be definitively proven with the current results, improved convergence behavior is demonstrated. Adaptive mesh refinement enables significantly greater resolution of the spray liquid-gas interaction while incurring only a small increase in overall grid size and is demonstrated to be equivalent in accuracy to a mesh that is globally refined. The combination of these numerical techniques result in significant strides in spray simulation accuracy with little penalty in computational cost.