The probabilty density function (PDF) of the mixture fraction is of integral importance to a large number of combustion models. Here, a novel modelling approach for the PDF of the mixture fraction is proposed which employs dissipation elements. While being restricted to the commonly used mean and variance of the mixture fraction, this model approach individually considers contributions of the laminar regions as well as the turbulent core and the turbulent/non-turbulent interface region. The later region poses a highly intermittent part of the flow which is of high relevance to the non-premixed combustion of pure hydrocarbon fuels. The model assumptions are justified by means of the gradient trajectory based analysis of high fidelity direct numerical simulation (DNS) datasets of two turbulent inert configurations and a turbulent non-premixed jet flame. The new dissipation element based model is validated against the DNS datasets and a comparison with the beta PDF is presented.
- Combustion modeling
- Direct numerical simulations
- High Reynolds numbers
- Turbulent non-premixed flames