Scaling Aspects of the Characteristic Time Combustion Model in the Simulation of Diesel 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.

In order to explain the scaling phenomenon, it is shown that there is a global proportionality constant which relates the spatially-averaged dissipation scale to the eddy turnover time. This constant acts as the scaling factor and depends on the turbulence integral length scale which can be estimated from the engine and injection geometries.