An equivalent dissipation rate model for capturing history effects in non-premixed flames

The effects of strain rate history on turbulent flames have been studied in the past decades with 1D counter flow diffusion flame (CFDF) configurations subjected to oscillating strain rates. In this work, these unsteady effects are studied for complex hydrocarbon fuel surrogates at engine relevant conditions with unsteady strain rates experienced by flamelets in a typical spray flame. Tabulated combustion models are based on a steady scalar dissipation rate (SDR) assumption and hence cannot capture these unsteady strain effects; even though they can capture the unsteady chemistry. In this work, 1D CFDF with varying strain rates are simulated using two different modeling approaches: steady SDR assumption and unsteady flamelet model. Comparative studies show that the history effects due to unsteady SDR are directly proportional to the temporal gradient of the SDR. A new equivalent SDR model based on the history of a flamelet is proposed. An averaging procedure is constructed such that the most recent histories are given higher weights. This equivalent SDR is then used with the steady SDR assumption in 1D flamelets. Results show a good agreement between tabulated flamelet solution and the unsteady flamelet results. This equivalent SDR concept is further implemented and compared against 3D spray flames (Engine Combustion Network Spray A). Tabulated models based on steady SDR assumption under-predict autoignition and flame lift-off when compared with an unsteady Representative Interactive Flamelet (RIF) model. However, equivalent SDR model coupled with the tabulated model predicted autoignition and flame lift-off very close to those reported by the RIF model. This model is further validated for a range of injection pressures for Spray A flames. The new modeling framework now enables tabulated models with significantly lower computational cost to account for unsteady history effects.