27 1: Lewis $Le_{i}$ $\mathrm{c}\mathrm{h}_{4}$ CO $\mathrm{c}\mathrm{o}_{2}$ $\mathrm{h}_{2}$ $\mathrm{h}_{2}\mathrm{o}$ $\mathrm{n}_{2}$ O2 $Le_{i}$

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1 (Naoto YOKOYAMA)1 (Kana SAITO) (Jiro MIZUSHIMA) 1 (Peters 1984) (Kida and Goto 2002) (Donbar et al 2001) ( 2002) Navier-Stokes (Nada et al 2004) Everest et al (1995) Rayleigh - 2 (1998) Skeletal (2004) / - $k-\epsilon$ Large Eddy Simulation 6 4 l nyokoyam@maildoshishaacjp

$Skeletal (2004) / - $k-\epsilon$ Large Eddy Simulation 6 4$

2 27 1: Lewis $Le_{i}$ $\mathrm{c}\mathrm{h}_{4}$ CO $\mathrm{c}\mathrm{o}_{2}$ $\mathrm{h}_{2}$ $\mathrm{h}_{2}\mathrm{o}$ $\mathrm{n}_{2}$ O2 $Le_{i}$ Dufour ( ) Soret ( ) $\rho$ $u$ $T$ $Y_{i}$ $\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho u)=0$ (1a) $\frac{\partial(\rho u)}{\partial t}+\nabla\cdot(\rho uu)=-\nabla p+\nabla\cdot\tau$ (1b) $\frac{\partial(\rho T)}{\partial t}+\nabla\cdot(\rho ut)-\nabla\cdot(\lambda\nabla T)=-\sum_{i}1\underline{1}h_{i}\omega_{i}\overline{\overline{c_{p}}}\overline{c_{\mathrm{p}}}$ (1c) $\frac{\partial(\rho Y_{i})}{\partial t}+\nabla\cdot(\rho uy_{i})-\nabla\cdot(\rho D_{i}\nabla Y_{i})=\omega_{i}$ $(1\mathrm{d})$ $p$ $R$ $W_{i}$ $p=$ $\tau$ $\rho RT\sum_{i}Y_{i}/W_{i}$ $I$ $\tau=\mu(\nabla u+$ $(\nabla u)^{t}-2/3(\nabla\cdot u)i)$ $= \sum_{i}y_{i}c_{\mathrm{p}i}$ $h_{i}$ $h_{i}=h_{i}^{0}+ \int_{t^{0}}^{t}c_{pi}(t)dt$ $\omega_{i}$ CHEMKIN(Kee et al 1996) $\lambda$ $D_{i}$ $\mu$ (Smooke et al 1991) $=A(T/T_{0})^{07}$ $\rho D_{i}=Le_{i}^{-1}(\lambda/\overline{\%})$ $\mu=pr(\lambda/\overline{c_{p}})$ V $A=258\cross 10^{-5}\mathrm{k}\mathrm{g}/(\mathrm{m}\cdot\sec)$ Prandtl $Pr=075$ Lewis 1 $Le_{i}$ 6 4 (Jones and Lindstedt 1988) $\mathrm{c}\mathrm{h}_{4}+\frac{1}{2}\mathrm{o}_{2}arrow \mathrm{c}\mathrm{o}+2\mathrm{h}_{2}$ $\mathrm{c}\mathrm{h}_{4}+\mathrm{h}_{2}\mathrm{o}arrow \mathrm{c}\mathrm{o}+3\mathrm{h}_{2}$ (2a) (2b) $\mathrm{h}_{2}+\frac{1}{2}\mathrm{o}_{2}=\mathrm{h}_{2}\mathrm{o}$ (2c) $\mathrm{c}\mathrm{o}+\mathrm{h}_{2}\mathrm{o}=\mathrm{c}\mathrm{o}_{2}+\mathrm{h}_{2}$ $(2\mathrm{d})$

$T)}{\partial t}+\nabla\cdot(\rho ut)-\nabla\cdot(\lambda\nabla T)=-\sum_{i}1\underline{1}h_{i}\omega_{i}\overline{\overline{c_{p}}}\overline{c_{\mathrm{p}}}$ (1c) $\frac{\partial(\rho$

3 $v_{\mathrm{c}\mathrm{h}_{4}}$ $\mathrm{m}$ $\mathrm{k}\mathrm{g}$ $\mathrm{s}\mathrm{e}\mathrm{c}$ $\ovalbox{\tt\small REJECT}$ $\mathrm{m}\mathrm{o}1$ 28 2: $A_{i}$ (a) $44\cross 10^{11}$ $126\cross 10^{5}$ $(\mathrm{b})$ $3\cross 10^{8}$ $126\cross 10^{5}$ $(\mathrm{c})$ $25\cross 10^{16}$ $167\cross 10^{5}$ $(\mathrm{d})$ $275\cross 10^{9}$ $838\cross 10^{4}$ 1: $\Omega_{j}$ Arrhenius $\Omega_{\mathrm{a}}=A_{\mathrm{a}}[\mathrm{C}\mathrm{H}_{4}]^{1/2}[\mathrm{O}_{2}]^{5/4}\exp(-E_{\mathrm{a}}/RT)$ $\Omega_{\mathrm{b}}=A_{\mathrm{b}}[\mathrm{C}\mathrm{H}_{4}]$ [H20] (3a) $\exp(-e_{\mathrm{b}}/rt)$ (3b) $\Omega_{\mathrm{c}}=A_{\mathrm{c}}[\mathrm{H}_{2}]^{1/2}[\mathrm{O}_{2}]^{9/4}[\mathrm{H}_{2}\mathrm{O}]^{-1}T^{-1}\exp(-E_{\mathrm{c}}/RT)$ (3c) $\Omega_{\mathrm{d}}=A_{\mathrm{d}}[\mathrm{C}\mathrm{O}][\mathrm{H}_{2}\mathrm{O}]\exp(-E_{\mathrm{d}}/RT)$ $(3\mathrm{d})$ $[\cdot]$ $A_{i}$ $E_{i}$ l 2 $\nu_{ij}$ (2) $j$ (1) $\omega_{i}=\sum_{j}\nu_{ij}\omega_{j}$ 6 (Lele 1992) Navier- Stokes (Baum et al 1994) 1 $d=2\cross 10^{-3}\mathrm{m}$ $Y_{\mathrm{C}\mathrm{H}_{4}0}=1$ $T_{1\mathrm{o}\mathrm{w}}=300\mathrm{K}$ $T_{1\mathrm{o}\mathrm{w}}$ $v\mathrm{c}\mathrm{h}_{4}=40\mathrm{m}/\sec$ $Y_{\mathrm{O}_{2}0}=0232$ $Y_{\mathrm{N}_{2}0}=0768$ $v_{\mathrm{a}\mathrm{i}\mathrm{r}}=4\mathrm{m}/\sec$ $T_{\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}}=2000\mathrm{K}$ $t<50\cross 10^{-4}\sec$ $T_{\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}}=2250\mathrm{K}$ $T_{\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}}$ 1 $Re\sim 8\cross 10^{3}$ Reynolds Damk\"ohler $Da\sim 4\cross 10^{7}$ 4 Runge-Kutta

$Arrhenius $\Omega_{\mathrm{a}}=A_{\mathrm{a}}[\mathrm{C}\mathrm{H}_{4}]^{1/2}[\mathrm{O}_{2}]^{5/4}\exp(-E_{\mathrm{a}}/RT)$ $\Omega_{\mathrm{b}}=A_{\mathrm{b}}[\mathrm{C}\mathrm{H}_{4}]$ [H20] (3a)$

4 t=48 $\cross$ 10-3sec& \acute 2 $t=48\cross 10^{-3}\sec$ $0\leq r\leq 12\cross 10^{-2}0\leq z\leq 95\cross 10^{-2}$ $5\cross 10^{-3}\leq z_{\sim}<225\cross 10^{-2}$ $J$ $z\sim 8\cross 10^{-3}\mathrm{m}$ $\cross$ $\leq z_{\sim}<4\cross 10^{-3}$ 2 ( $2(c)-(g)$ ) - l $\backslash ^{\backslash }$ ( $2(a)(b)$ ) 32 Bilger(1988) $Z= \frac{2y_{\mathrm{c}\mathrm{h}_{4}}/w_{\mathrm{c}\mathrm{h}_{4}}+(y_{\mathrm{o}_{2}0}-y_{\mathrm{o}_{2}})/w_{\mathrm{o}_{2}}+(y_{\mathrm{c}\mathrm{o}}/w_{\mathrm{c}\mathrm{o}}+y_{\mathrm{h}_{2}}/w_{\mathrm{h}_{2}})/2}{2y_{\mathrm{c}\mathrm{h}_{4}0}/w_{\mathrm{c}\mathrm{h}_{4}}+y_{\mathrm{o}_{2}0}/w_{\mathrm{o}_{2}}}$ (4) $Z= \frac{y_{\mathrm{o}_{2}0}/w_{\mathrm{o}_{2}}}{2y_{\mathrm{c}\mathrm{h}_{4}0}/w_{\mathrm{c}\mathrm{h}_{4}}+y_{\mathrm{o}_{2}0}/w_{o_{2}}}=z_{\mathrm{s}\mathrm{t}}$ (5) b $D_{i}$ $D$ 3 $Z_{\mathrm{s}\mathrm{t}}$ $\rho\frac{\partial Z}{\partial t}+\rho u\cdot\nabla Z=\nabla\cdot(\rho D\nabla Z)$ (6) $Z=Z_{\mathrm{s}\mathrm{t}}$ (6) $\rho\frac{\partial Y_{i}}{\partial t}=\frac{\rho}{le_{i}}\frac{\chi}{2}\frac{\partial^{2}y_{i}}{\partial Z^{2}}+\omega_{i}$ (7) $\chi$ $\chi=2d \nabla Z ^{2}$ $D_{i}$ 2 (6)

5 30 2; $(t=48\cross 10^{-3})(a)$ (b) (c) (d) ) (e) (f) (g) H $z$

$10^{-3})(a)$$

6 31 3: 48 ) $\cross 10^{-3}$ $Z_{\mathrm{s}\mathrm{t}}$ $- \sum_{i}h_{i}\omega_{i}$ ) $(t=$ ( Lewis 1 Burke-Schumann $Z\leq Z_{\mathrm{s}\mathrm{t}}$ 0 $Y_{\mathrm{F}^{\backslash }}=\{$ $Y_{\mathrm{F}0}(Z-Z_{\mathrm{s}\mathrm{t}})/(1-Z_{\mathrm{s}\mathrm{t}})$ $Z>Z_{\mathrm{s}\mathrm{t}}$ $Y_{\mathrm{O}_{2}0}(1-Z/Z_{\mathrm{s}\mathrm{t}})$ $Z\leq Z_{\mathrm{s}\mathrm{t}}$ $Y_{\mathrm{O}_{2}}=\{$ 0 $Z>Z_{\mathrm{s}\mathrm{t}}$ $Z$ $Z\leq Z_{\mathrm{s}\mathrm{t}}$ $T-T_{1\mathrm{o}\mathrm{w}}\propto\{$ $1-Z$ $Z>Z_{\mathrm{s}\mathrm{t}}$ $t=48\cross 10^{-3}$ 4 Burke-Schumann Burke-Schumann l $=Z_{\mathrm{s}\mathrm{t}}$ 4 Z G 0 3

$$Y_{\mathrm{O}_{2}0}(1-Z/Z_{\mathrm{s}\mathrm{t}})$ $Z\leq Z_{\mathrm{s}\mathrm{t}}$ $Y_{\mathrm{O}_{2}}=\{$ 0 $Z>Z_{\mathrm{s}\mathrm{t}}$ $Z$ $Z\leq$

7 $\dot{\mathrm{b}}_{\tilde{\mathrm{t}}}$ $z$ $T_{:}$ $Y_{\mathrm{C}\mathrm{H}_{4}}$ $Y_{\mathrm{O}_{2}}$ 4: $Z$ Burke-Schumann $Z=Z_{\mathrm{s}\mathrm{t}}$ $(t=48\cross 10^{-3})$ $Y_{i}$ (7) $Z$ $\chi_{\mathrm{s}\mathrm{t}}$ } $=Z_{\mathrm{s}\mathrm{t}}$ 5 Z $\xi$ (a) (b) $\xi=0$ $r$ $n$ $\varphi$ $\varphi=\nabla\cdot u-n\cdot\nabla u\cdot n$ $5(a)$ $\xi\leq 8\cross 10^{-3}$ 2 3 $z_{\sim}<7\cross 10^{-3}$ $5(b)$ \mbox{\boldmath $\xi$}\sim $<8\cross 10^{-3}$ $5(a)10^{-2}<\xi\sim<\sim 25\cross 10^{-2}$ $5(b)$ 2 3 $10-2\sim\sim<z<225\cross 10^{-2}$ $5(a)$ 3 $6(a)$

$$=Z_{\mathrm{s}\mathrm{t}}$ 5 Z $\xi$ (a) (b) $\xi=0$ $r$ $n$ $\varphi$ $\varphi=\nabla\cdot u-n\cdot\nabla u\cdot n$ $5(a)$ $\xi\leq 8\cross 10^{-3}$ 2 3$

8 $\mathfrak{c}\backslash$ 33 $Z=Z_{\mathrm{s}\mathrm{t}}$ 5: (a) (b) $(\mathrm{x}10^{3})$ (b) ( ) 6: (a) 2 up ( )down b ( )

$$(\mathrm{x}10^{3})$ (b) ( )$

9 34 $(r z)=(28\cross 10^{-3}2088\cross 10^{-2})(\xi\sim 1499\cross 10^{-2})$ $\eta$ $\eta=0$ 3 2 $6(b)$ 2 $\chi_{\mathrm{s}\mathrm{t}}=2d \nabla Z _{\mathrm{s}\mathrm{t}}^{2}$ $(r z)=(302\cross 10^{-3}1388\cross 10^{-2})(\xi\sim 2201\cross 10^{-2})$ $\grave{\mathrm{j}}\ovalbox{\tt\small REJECT}$ Burke-Schumann $\langle$ Lagrangian (Pitsch 2000) 3 $\Delta$ Baum M Poinsot T and Th\ evenin D (1994) Accurate boundary condition for multicomponent reactive flows J Comput Phys

$2201\cross 10^{-2})$ 4 6 4 $\grave{\mathrm{j}}\ovalbox{\tt\small REJECT}$ Burke-Schumann $\langle$ Lagrangian (Pitsch$

10 ) ) 35 Bilger R (1988) The structure of turbulent nonpremixed flames In Twenty-Second Symposium (Intemational) on Combustion pp The Combustion Institute Pittsburgh Donbar J M Driscoll J F and Carter C D (2001) Strain rates measured along the wrinkled flame contour within turbulent non-premixed jet flame Cornbust Flame Everest D A Driscoll J F Dahm W J A and Feikema D A (1995) Images of the two-dimensional field and temperature gradients to quantify mixing rates within a non-premixed turbulent jet flame Combust Flame Jones W P and Lindstedt R P (1988) Global reaction schemes for hydrocarbon combustion Combust Flame Kee R J Rupley F M Meeks E and Miller J A (1996) Chemkin-III: Afortran chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics Technical Report SAND Sandia National Laboratories Kida S and Goto S (2002) Line statistics: Stretching rate of passive lines in turbulence Phys Fluids (2004) ( $\mathrm{b}$ Lele S K (1992) Compact finite difference schemes with spectral-like resolution $J$ Comput Phys Nada Y Tanahashi M and Miyauchi T (2004) Effect of turbulence characteristics on local flame structure of $\mathrm{h}_{2}$-air premixed flames J Turbulence 5 16 Peters N (1984) Laminar diffusion models in non-premixed turbulent combustion Prog Energy Combust Sci Pitsch H (2000) Unsteady flamelet modeling of differential diffusion in turbulent jet diffusion flames Combust Flame Smooke M D Wess J Ruelle D Jaffe R L and Ehlers J (Eds) (1991) Reduced $\mathrm{p}\mathrm{p}$ Kinetic Mechanisms and Asymptotic Approirnations for Methane-Air Flames $1-$ $28$ Springer-Verlag (2002) (6 ) Djamrak D (1998) 2 $\mathrm{b}$ (

(1995) Images of the two-dimensional field and temperature gradients to quantify mixing rates within a non-premixed turbulent jet flame Combust Flame 101 58-68 Jones W P and Lindstedt R P (1988)

(Mamoru Tanahashi) Department of Mechanical and Aerospaoe Engineering Tokyo Institute of Technology ,,., ,, $\sim$,,

$(Mamoru Tanahashi) Department of Mechanical and Aerospaoe Engineering Tokyo Institute of Technology ,,., ,, $\sim$,,$ 1601 2008 69-79 69 (Mamoru Tanahashi) Department of Mechanical and Aerospaoe Engineering Tokyo Institute of Technology 1 100 1950 1960 $\sim$ 1990 1) 2) 3) (DNS) 1 290 DNS DNS 8 8 $(\eta)$ 8 (ud 12 Fig