Scalar Forcing Methodology for Direct Numerical Simulations of Turbulent Stratified Mixture Combustion

Abstract

Scalar forcing in the context of turbulent stratified flame simulations aims to maintain the fuel-air inhomogeneity in the unburned gas. With scalar forcing, stratified flame simulations have the potential to reach a statistically stationary state with a prescribed mixture fraction distribution and root-mean-square value in the unburned gas, irrespective of the turbulence intensity. The applicability of scalar forcing for Direct Numerical Simulations of stratified mixture combustion is assessed by considering a recently developed scalar forcing scheme, known as the reaction analogy method, applied to both passive scalar mixing and the imperfectly mixed unburned reactants of statistically planar stratified flames under low Mach number conditions. The newly developed method enables statistically symmetric scalar distributions between bell-shaped and bimodal to be maintained without any significant departure from the specified bounds of the scalar. Moreover, the performance of the newly proposed scalar forcing methodology has been assessed for a range of different velocity forcing schemes (Lundgren forcing and modified bandwidth forcing) and also without any velocity forcing. It has been found that the scalar forcing scheme has no adverse impact on flame-turbulence interaction and it only maintains the prescribed root-mean-square value of the scalar fluctuation, and its distribution. The scalar integral length scale evolution is shown to be unaffected by the scalar forcing scheme studied in this paper. Thus, the scalar forcing scheme has a high potential to provide a valuable computational tool to enable analysis of the effects of unburned mixture stratification on turbulent flame dynamics.

Implications of Using Scalar Forcing to Sustain Reactant Mixture Stratification in Direct Numerical Simulations of Turbulent Combustion

“…The scalar forcing methodology proposed by Daniel et al [23] and further developed by Brearley et al [24] has been adopted for this study as it can maintain a prescribed distribution (i.e., probability density function (PDF)) of a scalar field (e.g., bimodal, uniform, or bell-shaped). Consequently, the mean, root-mean-square (rms) and scalar bounds are also maintained.…”

“…A detailed description and derivation of the scalar forcing scheme used here are provided by Daniel et al [23] for the original scalar forcing scheme and details on the modified scalar forcing scheme to account for the feedback on the scalar dissipation rate to maintain the prescribed rms value of the scalar fluctuations are available in Brearley et al [24]. It should be recognised here that Daniel et al [23] originally proposed the scalar forcing methodology based on a reaction analogy to describe mixing.…”

“…where M is a hypothetical chemical species representing the mixed fluid state, E l and E u are hypothetical chemical species representing the extra concentrations of unmixed fluid towards the lower or upper bounds of the scalar respectively. Brearley et al [24] made modifications to Equation (2) to make it more robust for a chemically reacting flow. According to Daniel et al [23] K value should be chosen such that it corresponds to the desired steady state scalar dissipation rate, which controls the scalar PDF distribution.…”

“…Furthermore, it has also been shown by Brearley et al [24] that the PDF shape can be maintained for all turbulence conditions, i.e., decaying turbulence, Lundgren forcing and Modified Bandwidth forcing, without any modifications needed to the scalar forcing method. Brearley et al [24] also showed that the root-mean-square value of scalar fluctuation is faithfully maintained by the scalar forcing technique for different PDF shapes (i.e., bimodal or Gaussian). However, the influence of sustained mixture stratification on the structure and dynamics of turbulent planar flames is yet to be analysed in detail.…”

“…The development of a scalar forcing methodology that accurately captures characteristics of turbulent stratified combustion has been the subject of recent research efforts [23,24] where the effectiveness of the methodology was demonstrated mainly for passive scalar mixing. The sensitivity of the method to different turbulence and scalar conditions, including decaying turbulence and different turbulence forcing schemes (Lundgren forcing [25] and Modified Bandwidth forcing [26]) along with different scalar length scales, has been performed in the earlier work by Brearley et al [24]. It was found that the length scale of the scalar distribution at the end of simulation time is independent of the initial value specified for the scalar length scale and was only dependent on the nature of the velocity forcing scheme.…”