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A correction for the turbulence dissipation, based on non-equilibrium turbulence considerations from rapid distortion theory, has been derived and implemented in combination with the RNG k - ε model in a KIVA-based code. This model correction has been tested and compared with the standard RNG k - ε model for the compression and the combustion phase of two heavy duty DI diesel engines. The turbulence behavior in the compression phase shows clear improvements over the standard RNG k - ε model computations. In particular, the macro length scale is consistent with the corresponding time scale and with the turbulent kinetic energy over the entire compression phase. The combustion computations have been performed with the characteristic time combustion model. With this dissipation correction no additional adjustments of the turbulent characteristic time model constant were necessary in order to match experimental cylinder pressures and heat release rates of the two engines.

Combustion simulations utilizing the characteristic time combustion model have been performed for four DI diesel engines ranging in size from heavy-duty to large-bore designs. It has been found that the pre-factor to the turbulent characteristic time acts as a scaling parameter between the engines. This phenomenon is explained in terms of the non-equilibrium behavior of the turbulent time and length scales, as is encountered in the rapidly distorting, spray-induced flows of DI diesel engines. In fact, the equilibrium assumption between turbulence production and dissipation, which forms the basis for the employed k-ε-type turbulence models, does not hold in these situations. For such flows, the real turbulent dissipation time scale is locally proportional to the turbulent characteristic time scale which is determined by a typical eddy turnover time.