Role of the progress variable in models for partially premixed turbulent combustion

It is shown that if partially premixed combustion is described in terms of a mixture fraction and a progress variable, scalar dissipation terms appear in the transport equation for the progress variable. These terms are essential if not only the fully premixed limit but also the transport equation for a classical diffusion flame are to be recovered. The eddy breakup relationship between mean rate of reaction and scalar dissipation is extended to partially premixed combustion at high Damköhler numbers. Advantages and disadvantages of working in terms of a progress variable rather than a major species mass fraction or temperature are identified and discussed.