Analysis of Markers for Combustion Mode and Heat Release in MILD Combustion Using DNS Data

Figures & data

Figure 1. Schematic illustration of the DNS steps followed for the non-premixed MILD combustion of methane and air diluted with recirculated exhaust gases (from Doan et al. (2018)).

Table 1. Oxidizer composition for the initial MILD mixture.

Case	$X_{{\mathrm{O}}_2,ox}$	$X_{{\mathrm{H}}_{2}O,ox}$	$X_{\mathrm{C}{O}_2,ox}$	$X_{{\mathrm{N}}_2,ox}$
AZ1-2	0.035	0.134	0.067	0.764
BZ1	0.020	0.46	0.073	0.761

Table 2. MILD combustion DNS initial conditions.

Case	${\mathrm{\Lambda }}_0/{\mathrm{\ell }}_Z$	$⟨X_{{\mathrm{O}}_2}⟩$	$X_{{\mathrm{O}}_2}^{\mathrm{m}\mathrm{a}\mathrm{x}}$	${\mathrm{\ell }}_c/{\mathrm{\ell }}_Z$	$⟨Z⟩$	$Z_{st}$	${\sigma }_Z^2$	$⟨c⟩$	${\sigma }_c^2$
AZ1	0.60	0.0270	0.035	0.77	0.008	0.010	0.00007	0.56	0.068
AZ2	0.79	0.0285	0.035	0.99	0.008	0.010	0.00011	0.56	0.078
BZ1	0.60	0.0160	0.020	0.77	0.0046	0.0058	0.00003	0.56	0.068

Table 3. Conditions of additional DNS data used for numerical schlieren analysis.

Case	$u^{\prime }/s_L$	ϕ	${\mathrm{\Lambda }}_0/{\delta }_{th}$	$Re{}_t$	$Da$	$Ka$	Ref.
P1	2.19	0.8	2.11	38.5	0.97	2.22	Case C of Minamoto and Swaminathan (2014)
P2	11.25	1.0	3.75	110.0	0.33	19.5	Case K of Gao et al. (2014)
P3	9.88	0.8	1.15	96.1	0.69	11.9	Case B of Minamoto and Swaminathan (2014)

Figure 2. Volume rendered temperature field of (a) conventional turbulent premixed combustion, Case P1, and (b) MILD combustion of Case AZ1.

Figure 3. Contours of (a) heat release rate, (b) $\mathrm{T}\mathrm{C}\mathrm{I}\mathrm{M}\mathrm{\_}\mathrm{A}\mathrm{\_}1610575$ and (c) $\mathrm{\Delta }{Y}_{\mathrm{O}\mathrm{H}}$ in the mid $x$–$y$ plane at $t={\tau }_f$ in case AZ1.

Figure 4. Pdf of $\mathrm{\Delta }{Y}_{\mathrm{O}\mathrm{H}}=Y_{\mathrm{O}\mathrm{H}}^{\mathrm{R}}-Y_{\mathrm{O}\mathrm{H}}^{\mathrm{C}\mathrm{D}}$ from Case AZ1 at $t={\tau }_f$.

Figure 5. Contours of (a) $\tilde{\dot{Q}}$, (b) $\widetilde{S_{\mathrm{O}\mathrm{H}}}$, (c) $\tilde{S_{\mathrm{C}{\mathrm{H}}_2\mathrm{O}}}$, (d) $\widetilde{S_{\mathrm{H}}}$, (e) $\widetilde{S_{\mathrm{H}\mathrm{C}\mathrm{O}}}$ and (f) $\tilde{S_{\mathrm{O}\mathrm{H}}\times S_{\mathrm{C}{\mathrm{H}}_2\mathrm{O}}}$ in the mid $x$–$y$ plane for case AZ1 at $t=1.5{\tau }_f$. Dark to light gray lines are for iso-contours of values 0.1, 0.2, .., 0.9.

Figure 6. Scatter plots of normalized heat release rate vs (a) $\widetilde{[\mathrm{O}{\mathrm{H}}^{\ast }]}$, (b) $\widetilde{S_{\mathrm{O}\mathrm{H}}}$, (c) $\tilde{S_{\mathrm{C}{\mathrm{H}}_2\mathrm{O}}}$, (d) $\widetilde{S_{\mathrm{H}}}$, (e) $\widetilde{S_{\mathrm{H}\mathrm{C}\mathrm{O}}}$ and (f) $\tilde{S_{\mathrm{O}\mathrm{H}}\times S_{\mathrm{C}{\mathrm{H}}_2\mathrm{O}}}$ for case AZ1 obtained using the data shown in Figure 5. Points are colored by their streamwise locations.

Table 4. Pearson correlation coefficients for the $\tilde{\dot{Q}}$-$\widetilde{S_{\alpha }}$ scatter plots.

Case	$\widetilde{[\mathrm{O}{\mathrm{H}}^{\ast }]}$	$\widetilde{S_{\mathrm{O}\mathrm{H}}}$	$\tilde{S_{\mathrm{C}{\mathrm{H}}_2\mathrm{O}}}$	$\widetilde{S_{\mathrm{H}}}$	$\widetilde{S_{\mathrm{H}\mathrm{C}\mathrm{O}}}$	$\tilde{S_{\mathrm{O}\mathrm{H}}\times S_{\mathrm{C}{\mathrm{H}}_2\mathrm{O}}}$	$\tilde{S_{\mathrm{H}}\times S_{\mathrm{C}{\mathrm{H}}_2\mathrm{O}}}$
AZ1	0.9153	−0.4835	0.5407	−0.1454	0.9447	0.9543	0.9549
AZ2	0.9431	0.0134	0.0890	0.3532	0.9511	0.9557	0.9306
BZ1	0.9458	0.2023	0.1091	0.4009	0.9529	0.9555	0.9279

Figure 7. Volume rendered images of normalized (a) heat release rate, $\tilde{\dot{Q}}$, and (b) $\widetilde{[\mathrm{O}{\mathrm{H}}^{\ast }]}$ for the case AZ1.

Figure 8. Variations of $\mathrm{F}\mathrm{I}$ (in a,c) and $\mathrm{C}\mathrm{M}$ (b,d) in the mid $x$–$y$ plane for cases AZ1 (a,b) and BZ1 (c,d) at $t=1.5{\tau }_f$. The results are shown for regions with ${\dot{Q}}^{+}\ge 1.0$.

Figure 9. Joint-pdf of ($\mathrm{C}\mathrm{M}$, $\mathrm{F}\mathrm{I}$) in regions with ${\dot{Q}}^{+}\ge 1.0$ and $\mathrm{C}\mathrm{M}<0$ for cases (a) AZ1 and (b) BZ1 using samples collected in the mid $x$–$y$ plane at $t=1.5{\tau }_f$ shown in Figure 8.

Figure 10. Numerical schlieren for the premixed cases (a) P1 and (b) P2, (c) premixed MILD combustion case P3 and the non-premixed MILD combustion cases (d) AZ1, (e) AZ2 and (f) BZ1. Axes for cases P1 and P2 are normalized by their respective laminar flame thicknesses.

Figure 11. Numerical schlieren image for the data in the mid $x$–$y$ plane of the (a) MILD combustion case AZ1 and (b) premixed combustion case P2. The iso-lines show the normalized heat release rate (white dotted line is for 0.2, dashed line is for 0.5, dash-dotted line is for 0.7 and solid line is for 0.9).

Doan, N.A.K., Swaminathan, N., and Minamoto, Y. 2018. DNS of MILD combustion with mixture fraction variations. Combust. Flame, 189, 173–189. doi:10.1016/j.combustflame.2017.10.030

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Minamoto, Y., and Swaminathan, N. 2014. Scalar gradient behaviour in MILD combustion. Combust. Flame, 161(4), 1063–1075. doi:10.1016/j.combustflame.2013.10.005

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Gao, Y., Chakraborty, N., and Swaminathan, N. 2014. Algebraic closure of scalar dissipation rate for large eddy simulations of turbulent premixed combustion. Combust. Sci. Technol., 186(10–11), 1309–1337. doi:10.1080/00102202.2014.934581

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