Influence of thermal expansion on fluid dynamics of turbulent premixed combustion and its modelling implications

The purpose of this paper is to demonstrate the effects of thermal expansion, as a result of heat release arising from exothermic chemical reactions, on the underlying turbulent fluid dynamics and its modelling in the case of turbulent premixed combustion. The thermal expansion due to heat release gives rise to predominantly positive values of dilatation rate within turbulent premixed flames, which has been shown to have significant implications on the flow topology distributions, and turbulent kinetic energy and enstrophy evolutions. It has been demonstrated that the magnitude of predominantly positive dilatation rate provides the measure of the strength of thermal expansion. The influence of thermal expansion on fluid turbulence has been shown to strengthen with decreasing values of Karlovitz number and characteristic Lewis number, and with increasing density ratio between unburned and burned gases. This is reflected in the weakening of the contributions of flow topologies, which are obtained only for positive values of dilatation rate, with increasing Karlovitz number. The thermal expansion within premixed turbulent flames not only induces mostly positive dilatation rate but also induces a flame-induced pressure gradient due to flame normal acceleration. The correlation between the pressure and dilatation fluctuations, and the vector product between density and pressure gradients significantly affect the evolutions of turbulent kinetic energy and enstrophy within turbulent premixed flames through pressure-dilatation and baroclinic torque terms, respectively. The relative contributions of pressure-dilatation and baroclinic torque in comparison to the magnitudes of the other terms in the turbulent kinetic energy and enstrophy transport equations, respectively strengthen with decreasing values of Karlovitz and characteristic Lewis numbers. This leads to significant augmentations of turbulent kinetic energy and enstrophy within the flame brush for small values of Karlovitz and characteristic Lewis numbers, but both turbulent kinetic energy and enstrophy decay from the unburned to the burned gas side of the flame brush for large values of Karlovitz and characteristic Lewis numbers. The heat release within premixed flames also induces significant anisotropy of sub-grid stresses and affects their alignments with resolved strain rates. This anisotropy plays a key role in the modelling of sub-grid stresses and the explicit closure of the isotropic part of the sub-grid stress has been demonstrated to improve the performance of sub-grid stress and turbulent kinetic energy closures. Moreover, the usual dynamic modelling techniques, which are used for non-reacting turbulent flows, have been shown to not be suitable for turbulent premixed flames. Furthermore, the velocity increase across the flame due to flame normal acceleration may induce counter-gradient transport for turbulent kinetic energy, reactive scalars, scalar gradients and scalar variances in premixed turbulent flames under some conditions. The propensity of counter-gradient transport increases with decreasing values of root-mean-square turbulent velocity and characteristic Lewis number. It has been found that vorticity aligns predominantly with the intermediate principal strain rate eigendirection but the relative extents of alignment of vorticity with the most extensive and the most compressive principal strain rate eigendirections change in response to the strength of thermal expansion. It has been found that dilatation rate almost equates to the most extensive strain rate for small sub-unity Lewis numbers and for the combination of large Damkohler and small Karlovitz numbers, and under these conditions vorticity shows no alignment with the most extensive principal strain rate eigendirection but an increased collinear alignment with the most compressive principal strain rate eigendirection is obtained. By contrast, for the combination of high Karlovitz number and low Damkohler number in the flames with Lewis number close to unity, vorticity shows an increased collinear alignment with the most extensive principal direction in the reaction zone where the effects of heat release are strong. The strengthening of flame normal acceleration in comparison to turbulent straining with increasing values of density ratio, Damkohler number and decreasing Lewis number makes the reactive scalar gradient align preferentially with the most extensive principal strain rate eigendirection, which is in contrast to preferential collinear alignment of the passive scalar gradient with the most compressive principal strain rate eigendirection. For high Karlovitz number, the reactive scalar gradient alignment starts to resemble the behaviour observed in the case of passive scalar mixing. The influence of thermal expansion on the alignment characteristics of vorticity and reactive scalar gradient with local principal strain rate eigendirections dictates the statistics of vortex-stretching term in the enstrophy transport equation and normal strain rate contributions in the scalar dissipation rate and flame surface density transport equations, respectively. Based on the aforementioned fundamental physical information regarding the thermal expansion effects on fluid turbulence in premixed combustion, it has been argued that turbulence and combustion modelling are closely interlinked in turbulent premixed combustion. Therefore, it might be necessary to alter and adapt both turbulence and combustion modelling strategies while moving from one combustion regime to the other.