Study on the rapid pressure–strain rate in the second-moment closure for turbulent flows undergoing strong compression and large distortion

To clarify applicability of the existing models for the rapid pressure–strain correlation in the Reynolds-stress closures, modifications accounting for the nonzero divergence of the mean velocity have been set into five turbulence models. These are two models of Launder et al. (LRR1 and LRR2), model of Speziale et al. (SSG), model of Johansson et al. and model of Lee. Computations have been carried out with these models for compression process in the cylinder of an internal combustion engine. The calculation results of the mean turbulent kinetic energy, the anisotropic tensor of Reynolds stress and rapid pressure–strain have been compared with the analytical solutions of rapid distortion theory in order to identify a suitable model for turbulent flows undergoing strong compressions as in the engines. The results demonstrate that the linear model of Lee which includes the history effect of the total strain can even give the same accurate predictions as those of the Johansson's nonlinear models up to fourth order in the Reynolds-stress-anisotropic tensor.