Investigation of Reactive Scalar Mixing in Transported PDF Simulations of Turbulent Premixed Methane-Air Bunsen Flames

Abstract

Transported probability density function (TPDF) simulations have been performed in conjunction with DNS data to investigate the mixing characteristics of reactive scalars in two turbulent lean premixed methane-air Bunsen flames with Case A being close to the corrugated flamelet regime and Case C being close to the broken reaction zones regime. The study shows that with an accurate mixing timescale of progress variable being provided, TPDF simulations using the EMST mixing model predict scalar mixing and flame characteristics reasonably well. Modeling reactive scalar mixing rate remains one key challenge. For turbulent flames close to the flamelet regime, i.e. Case A, the turbulent flame structure represented by the scatter of OH, as well as the resemblance of the flame induced dissipation rate to the actual dissipation rate, highlights the necessity to account for flame structure when modeling reactive scalar mixing in flamelet region. A posteriori tests show that the hybrid mixing timescale model, which accounts for both turbulence and flame structure effects on the scalar mixing timescale, yields better performance than the constant mechanical-to-scalar timescale model for turbulent premixed flames close to the flamelet regime. Moreover, the hybrid model shows potential for modeling differential mixing rates of intermediate species featuring their own characteristic timescales. The effects of progress variable definition and turbulence modeling on the computed flame characteristics are investigated, and the significance of turbulence modeling in RANS-TPDF simulation is illustrated.

Appendix: Convergence studies with respect to grid resolution, ISAT error tolerance and the number of particles per cell

Figure 22 shows the RANS-TPDF simulations of Case A from two set of grids. The base grid resolution is 144×48 in streamwise (x) and spanwise (y) direction, while the fine grid resolution is 720×90. Note that the full 3D DNS simulation has 720×400×180 grids in streamwise, crosswise and spanwise direction, respectively. The RANS-TPDF simulation exploits the statistical homogeneity along the crosswise direction and the symmetry at y = 0. Therefore, the fine grid essentially has the same grid resolution with DNS on x-y plane. As shown, the simulation with the fine grid yields almost the same mean and rms radial profiles as the base case at all the plotted locations. As far as the computational cost is concerned, the RANS-TPDF simulation with 30 computational particles per cell takes around 300 CPU hours on the base grid and around 4000 CPU hours on the find grid.

Fig. 22

Spanwise profiles of mean axial velocity $\overset{\sim }{U}$, mean progress variable $\overset{\sim }{c}$, its rms $\sqrt{\overset{\sim }{c{"}^2}}$, and mean mass fractions ${\overset{\sim }{Y}}_{CO}$ and ${\overset{\sim }{Y}}_{OH}$ for Case A. Dashed red: base grid (144×48); Dot-dashed blue: fine grid (720×90); Solid black: DNS

Numerical tests on the effect of ISAT error tolerance on the predictions have been carried out with error tolerances of 10⁻³, 10⁻⁴ and 5 × 10⁻⁵, respectively. Figure 23 shows that the differences from the different error tolerances are negligible for the prediction of the mean and rms quantities.

Fig. 23

Spanwise profiles of mean axial velocity $\overset{\sim }{U}$, mean progress variable $\overset{\sim }{c}$, its rms $\sqrt{\overset{\sim }{c{"}^2}}$, and mean mass fractions ${\overset{\sim }{Y}}_{CO}$ and ${\overset{\sim }{Y}}_{OH}$ for Case A. Dashed red: ISAT error tolerance 10⁻³; Dot-dashed blue: ISAT error tolerance 10⁻⁴; Dotted black: ISAT error tolerance 5 × 10⁻⁵

Convergence tests on the number of particles per cell (N_pc) have been carried out with N_pc=30 and 80, respectively. Figure 24 shows that differences between N_pc=30 and 80 are negligible for the prediction of the mean and rms quantities.

Fig. 24

Spanwise profiles of mean axial velocity $\overset{\sim }{U}$, mean progress variable $\overset{\sim }{c}$, its rms $\sqrt{\overset{\sim }{c{"}^2}}$, and mean mass fractions ${\overset{\sim }{Y}}_{CO}$ and ${\overset{\sim }{Y}}_{OH}$ for Case A. Dashed red: N_pc=30; Dot-dashed blue: N_pc=80