Title メタンと空気の非予混合火炎への剪断速度の影響 ( 混合化学反応燃焼の流体力学 ) Author(s) 加賀, 義人 ; 横山, 直人 ; 水島, 二郎 Citation 数理解析研究所講究録 (2006), 1496: Issue Date URL htt

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1 Title メタンと空気の非予混合火炎への剪断速度の影響 ( 混合化学反応燃焼の流体力学 ) Author(s) 加賀義人 ; 横山直人 ; 水島二郎 Citation 数理解析研究所講究録 (2006) 1496: Issue Date URL Right Type Departmental Bulletin Paper Textversion publisher Kyoto University

$Mizushima) Dept Mech Eng Doshisha Univ 1 2 ( ) ( ) \sim m/s - 1 $10^{7}$ ( ) [1] ( )[2] (2004)[3] Safta et al (2002)[4] 2 Everest et al$

2 (Yoshito Kaga) Energy Conversion Center Doshisha Univ (Naoto Yokoyama) Dept Math Sci Rensselaer Polytech Inst (Jiro Mizushima) Dept Mech Eng Doshisha Univ 1 2 ( ) ( ) \sim m/s - 1 $10^{7}$ ( ) [1] ( )[2] (2004)[3] Safta et al (2002)[4] 2 Everest et al (1995)[5] 2

3 $\Omega_{\mathrm{c}}$ $=$ $+$ $\frac{1}{2}\mathrm{o}_{2}$ $=$ 86 ( ) 6 4 [6] 2 21 ( ) (02) (N2) [6] (a) C 4 $+$ $- \frac{1}{2}\mathrm{o}_{2}$ $arrow$ CO $+$ $2\mathrm{H}_{2}$ (b) CH4 $+$ H20 $arrow$ CO $+$ $3\mathrm{H}_{2}$ (c) $\mathrm{h}_{2}$ H20 (d) CO $+$ H20 $=$ CO2 $+$ H2 (a) (b) (C) (d) 6 4 (C) (d) (a)\sim (d) (Arrhenius) $\Omega_{\mathrm{a}}$ $\Omega_{\mathrm{b}}$ (1) $=$ $A_{\mathrm{a}}\exp(-E_{\mathrm{a}}/R^{0}T)[\mathrm{C}\mathrm{H}_{4}]^{1/2}[\mathrm{O}_{2}]^{5/4}$ (2) $=$ $\mathrm{a}_{\mathrm{b}}\exp(-\mathrm{e}_{\mathrm{b}}/\text{ }\mathrm{t})[\mathrm{c}\mathrm{h}_{4}][\mathrm{h}_{2}0]$ $\{$ $A_{\mathrm{c}\mathrm{w}\mathrm{r}}\exp(-E_{\mathrm{c}\mathrm{w}\mathrm{r}}/R^{0}T)[\mathrm{H}_{2}]^{1/2}[\mathrm{O}_{2}]^{9/4}[\mathrm{H}_{2}\mathrm{O}]^{-1}T^{-1}$ $([\mathrm{h}_{2}\mathrm{o}]>10^{-6}\mathrm{k}\mathrm{m}\mathrm{o}1/\mathrm{m}^{3})$ $A_{\mathrm{c}\mathrm{w}1}\exp(-E_{\mathrm{c}\mathrm{w}1}/R^{0}T)[\mathrm{H}_{2}]^{1/4}[\mathrm{O}_{2}]^{3/2}T^{-1}$ $([\mathrm{h}_{2}\mathrm{o}]\leq 10^{-6}\mathrm{k}\mathrm{m}\mathrm{o}1/\mathrm{m}^{3})$ $(3)$ $\Omega_{\mathrm{d}}$ $=$ $A_{\mathrm{d}}\exp(-E_{\mathrm{d}}/R^{0}T)[\mathrm{C}\mathrm{O}][\mathrm{H}_{2}\mathrm{O}]$ (4) [A] $A_{j}$ $(j=\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d})$ $R^{0}=8314\mathrm{J}/\mathrm{k}\mathrm{m}\mathrm{o}\mathrm{l}\cdot \mathrm{k}$ A $i$ 1 $\mathrm{c}\mathrm{h}_{4}$ $\mathrm{c}\mathrm{o}$ 6 ( O2 H2 H20 $\mathrm{c}\mathrm{o}_{2}$) (N2) $i$ i $W_{1}$ (Lewis number) Le: $i$ $\omega_{i}$ $\omega:=w_{i}\sum_{j}\nu_{ij}\omega_{j}$ $\nu_{ij}$ $j$

4 87 1: $\frac{\text{ }R\text{ _{}\grave{\mathrm{b}}}\gamma\backslash \text{ }A_{j}E_{j}(\mathrm{J}/\mathrm{k}\mathrm{m}\mathrm{o}1)}{(\mathrm{a})44\cross 10^{11}126\cross 10^{8}}$ (a) (b) $30\cross 10^{8}$ $126\cross 10^{8}$ (c) Water Rich $25\cross 10^{16}$ $167\cross 10^{8}$ Water Lean $68\cross 10^{15}$ $167\cross 10^{8}$ (d) $27\bm{5}\cross 10^{9}$ $838\cross 10^{8}$ $i$ $i$ $c_{p_{1}}$: $h_{i}$ $T$ CHEMKINI $= \sum_{i}\mathrm{y}_{i}c_{\mathrm{p}i}$ $\overline{h}=\sum_{i}y_{1}h_{i}$ $)$ 2: $=l\mathrm{b}\text{ }\mathrm{c}\mathrm{h}_{4}\mathrm{o}_{2}\mathrm{h}_{2}\mathrm{h}_{2}\mathrm{o}\mathrm{c}\mathrm{o}\mathrm{c}\mathrm{o}_{2}\mathrm{n}_{2}w_{i}^{\backslash } \mathit{8}$ $Le_{i}$ (Soret) (Dufour) \rho $u$ $T$ $i$ $\mathrm{y}_{i}$ [7] $\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho \mathrm{u})=0$ (5) $\frac{\partial(\rho u)}{\partial t}+\nabla\cdot(\rho \mathrm{u}u)=-\nabla p+\nabla\cdot\tau$ (6) $\frac{\partial(\rho T)}{\partial t}+\nabla\cdot(\rho u\tau)-=^{\nabla\cdot(\lambda\nabla T)Q}c_{p}c_{p}11==$ (7) $\frac{\partial(\rho \mathrm{y}_{i})}{\partial t}+\nabla\cdot(\rho u\mathrm{y}_{i})-\nabla\cdot(\rho D_{\mathfrak{i}}\nabla \mathrm{y}_{i})=\omega_{i}$ (8) $\tau=\mu[\nabla u+(\nabla u)^{t}-(2/3)(\nabla\cdot u)i]$ $\mu$ $I$ $T_{\rfloor}$ p $p= \rho tt\sum_{i}\mathrm{y}_{i}/w_{2}\text{ }$ \mbox{\boldmath $\lambda$} $Q=- \sum_{i}h_{i}\omega_{1}\text{ }$ D i Smooke $et$ al[8] \mbox{\boldmath $\lambda$}/ $=A(T/T_{0})^{07}$ \mu =Pr\mbox{\boldmath $\lambda$}/ $\rho D_{i}=Le_{i}^{-1}\lambda/\overline{c_{p}}$ $T_{0}=29815\mathrm{K}$ $A$ $A=258\cross 10^{-5}\mathrm{k}\mathrm{g}/\mathrm{m}\cdot\sec$ $Pr=075$ 1CHEMKIN Sandia National Laboratories

$88 23 ( ) l(a) 1(a) l(bb) 100% 2 1 ( 1 ) $p_{0}=\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{m}$ ( $1013$ Pa) $\mathrm{x}10^{5}$ $T_{0}$ $(Y_{O_{2}0}=0232 Y_{\mathrm{N}_{2}\mathit{0}}= 0768)$$

5 88 23 ( ) l(a) 1(a) l(bb) 100% 2 1 ( 1 ) $p_{0}=\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{m}$ ( $1013$ Pa) $\mathrm{x}10^{5}$ $T_{0}$ $(Y_{O_{2}0}=0232 Y_{\mathrm{N}_{2}\mathit{0}}= 0768)$ $(Y\mathrm{c}\mathrm{H}_{4}0=1)$ $T_{1}=2000\mathrm{K}$ $-(\mathit{8})$ (5) $50\cross 10^{-3}\sec$ l(b) x $L_{x}=10^{-2}\mathrm{m}$ $y$ $L_{\mathrm{y}}=2\cross 10^{-2}\mathrm{m}$ x y 2 1(b) 2 $\alpha$ 22 $\alpha=0^{\mathrm{o}}$ $5^{\mathrm{o}}$ $1\mathit{8}0^{\mathrm{o}}$ 8 x : $u_{x\epsilon}$ $=$ $-F_{s}(xy)A_{s}\sin\alpha(x\cos(-\alpha)-y\sin(-\alpha))$ (9) $u_{y\epsilon}$ $=$ $+F_{s}(x y)a_{\mathit{8}}\sin\alpha(x\sin(-\alpha)+y\mathrm{c}o\mathrm{s}(-\alpha))$ (10) $A_{s}$ $A_{\theta}=4000$ $F_{s}(xy)$ $x$ $r=\sqrt{x^{2}+y^{2}}$ 1 $(2r/L_{x}\leq 05)$ $F_{s}(x y)=\{$ $\cos^{2}(\pi\frac{2r/l_{x}-05}{08-05})$ $(05<2r/L_{x}<08)-$ (11) $0$ $(2r/L_{x}\geq 0\mathit{8}0)$ 6 4 (Runge-Kutta method) $x$ $2\cross 10^{-6}\mathrm{m}$ $y$ (CFL condition) $(\Delta t\approx 2\cross 10^{-\epsilon_{\sec}})$ $c$ $c=\sqrt{\kappa p}/\rho$ $\kappa=_{\mathit{5}}/$($\text{ }$ -R) R=RO\Sigma iyi/wi x

6 89 $y$ (NSCBC Navier-Stokes characteristic boundary conditions) (a) (b) 1: (a) (b) 3 8 $Z[9]$ : $Z= \frac{2y_{\mathrm{c}\mathrm{h}_{4}}/w_{\mathrm{c}\mathrm{h}_{4}}+(\mathrm{y}_{\mathrm{o}_{2}0}-\mathrm{y}_{\mathrm{o}_{2}})/w_{\mathrm{o}_{2}}+(\mathrm{y}\mathrm{c}\mathrm{o}/w_{\mathrm{c}\mathrm{o}}+\mathrm{y}_{\mathrm{h}_{2}}/w_{\mathrm{h}_{2}})/2}{2\mathrm{y}_{\mathrm{c}\mathrm{h}_{4}0}/w_{\mathrm{c}\mathrm{h}_{4}}+y_{\mathrm{o}_{2}0}/w_{\mathrm{o}_{2}}}$ (12) ( 2) $Z$ $0$ 1 $Z_{\mathrm{s}\mathrm{t}}=$ q 2 $(\mathrm{y}\mathrm{o}_{2}0/w_{\mathrm{o}_{2}})/(2\mathrm{y}_{\mathrm{c}\mathrm{h}_{4}0}/w_{\mathrm{c}\mathrm{h}_{4}}+\mathrm{y}_{\mathrm{o}_{2}0}/w_{o_{2}})$ $Z_{\mathrm{s}\mathrm{t}}\approx 0055$ (Burke-Schumann s solution) $Le_{j}$ 1 2(a) Z $(Y_{\mathrm{C}\mathrm{H}_{4}} \mathrm{y}_{\mathrm{o}_{2}})$ (T-To) 1 $Z>Z_{\mathrm{s}\mathrm{t}}$ 2 Ol<Z<07 4

7 $\mathrm{h}_{2}\mathrm{o}$ $(Z_{\mathrm{e}\mathrm{t}})$ $\Omega_{\mathrm{c}}$ $\Omega_{\mathrm{d}}$ 90 2: (a) ( ) (b) (c) (d) Z>4t (b) (d) 2(d) Peters (2000)[9] 2(b) Z\leq Ol $(\mathrm{y}_{\mathrm{c}\mathrm{h}_{4}} \mathrm{y}_{\mathrm{o}_{2}} \mathrm{y}_{\mathrm{h}_{2}\mathrm{o}})$ $(\mathrm{y}_{\mathrm{h}_{2}})$ t $Z=0$ $Z_{\mathrm{s}\mathrm{t}}$ $Z>Z_{\mathrm{s}\mathrm{t}}$ 1 $Z>Z_{\mathrm{s}\mathrm{t}}$ ( $2(\mathrm{c})$) 2(c) (Zst) (Z<Z8t) $Z=005$ (a) (b) Z_{\mathrm{s}\mathrm{t}}$ $Z\geq (a) (b) $Z<Z_{\mathrm{s}\mathrm{t}}$ $\Omega_{\mathrm{b}}$ (\Omega a \Omega d) 2(d) $Z>Z_{\mathrm{s}\mathrm{t}}$ (a) (b) \Omega $\mathrm{h}_{2}\mathrm{o}$ $Z\sim 0062$ (d) (C) \Omega Z\sim 005

8 $\frac{\partial u_{i}}{\partial x_{j}}=\frac{1}{2}$ ( $\frac{\partial u_{j}}{\partial x_{\dot{*}}})+\frac{1}{2}(\frac{\partial u_{1}}{\partial x_{j}}-\frac{\partial u_{j}}{\partial x_{i}})$ $\alpha$ 91 4 Z Zst (c) Zst $(\nabla Z\cdot\nabla Q)/ \nabla Z \nabla Q =0$ for $Q\gg 1$ (13) 2 3: {sij}\equiv {\partial uj/ } : (14) {sij} 3 $e:(i=123)$ $\lambda_{i}(i=123;\lambda_{1}>\lambda_{2}>\lambda_{3})$ 2 $\lambda_{1}>0$ $\lambda_{2}=0$ \mbox{\boldmath $\lambda$}3<0 Z $(e\mathrm{a})$ $\theta_{3\nabla Z}=\cos^{-1}(e_{3}/ e_{3} \cdot\nabla Z/ \nabla Z )$ ( 3) ( 1(b) ) 22 $\alpha=0^{\mathrm{o}}$ $5^{\mathrm{o}}$ 1575o 8 8 $\theta_{3\nabla Z}=\cos^{-1}(e_{3}/ e_{3} \cdot\nabla Z/ \nabla Z )$ 2

$$\circ$ $\circ$ $\circ$ $\circ$ 92 4 4(a) 4(h) (13) (i) (vi) 40\mu sec l(b) 25mm 4(a) \alpha =0 4(b) $\alpha=225^{\text{ }}$ $\alpha$ 4(h) 225 3 $e_{3}$ ( ) $\text{ }\theta_{3\nabla z\text{ }}$ Q$

9 $\circ$ $\circ$ $\circ$ $\circ$ (a) 4(h) (13) (i) (vi) 40\mu sec l(b) 25mm 4(a) \alpha =0 4(b) $\alpha=225^{\text{ }}$ $\alpha$ 4(h) $e_{3}$ ( ) $\text{ }\theta_{3\nabla z\text{ }}$ Q \alpha \theta 3\nabla z \theta 3\nabla z - $\circ$ \theta 3\nabla Z 90 $\alpha$ $45^{\mathrm{o}}$ 4(c) 4(c) (vi) t=200\mu sec $\lambda_{p}$ $\lambda_{n}$ $\theta_{3\nabla Z}$ 5(a) $\theta_{3\nabla Z}$ $I_{\mathrm{H}_{2}}=-\nabla\cdot(\rho uy_{\mathrm{h}_{2}})$ $J_{\mathrm{H}_{2}}=\nabla\cdot(\rho D_{\mathrm{H}_{2}}\nabla \mathrm{y}_{\mathrm{h}_{2}})$ $\omega_{\mathrm{h}_{2}}$ 5(b) 5(c) $\partial\rho \mathrm{y}_{\mathrm{h}_{2}}/\partial \mathrm{t}=\mathrm{i}_{\mathrm{h}_{2}}+\mathrm{j}_{\mathrm{h}_{2}}+\omega_{\mathrm{h}_{2}}$ 5(b) 3 IH2 5(c) $I_{\mathrm{H}_{2}}$ $J_{\mathrm{H}_{2}}+\omega_{\mathrm{H}_{2}}$ $I_{\mathrm{H}_{2}}$ $\lambda_{n}$ $J_{\mathrm{H}_{2}}+\omega_{\mathrm{H}_{2}}$ $\lambda_{n}$ $\alpha$ $0^{\mathrm{o}}<\alpha<90^{\mathrm{o}}$ $\alpha$ 1 4 $\alpha=675^{\mathrm{o}}$ ( 4(d)) $\alpha=1575^{\mathrm{o}}$ ( $4(\mathrm{g})$ ) $\alpha=0$

10 $\alpha n_{\mathrm{b}\backslash }\wedge\frac{\mathrm{e}}{\vee \mathrm{x}}\ddot{\s} :_{\epsilon}$ $\mathrm{t}5$ (a) $\alpha=0$ (b) $\alpha=225^{\mathrm{o}}$ (c) $\alpha=450^{\mathrm{o}}$ 138 : 138 (d) $\alpha=675^{\mathrm{o}}$ $\mathrm{q}126$ $\not\in 200$ $7\mathrm{S}$ 90 $ $ $\theta_{3\nabla Z}( )$ 4:

11 94 5: 4(c) $t=200\mu\sec[(\mathrm{v}\mathrm{i})]$ (a) $(\mathrm{b})-(\mathrm{c})$ Z=005 ( ) 45 [1] T J Poinsot D C Haworth and G Bruneaux Difect Simuration and Modeling of Flame- Wall Interaction for Premixed Turbulent Combustion Combust Flame 95 pp $(1993\rangle$ [2] N Peters Laminar Diffusion Models in Non-Premixed Turbulent Combustion Prog Energy Combust Sci 10 pp (1984) [3] $(\mathrm{b}\text{ }) 70$ 691 pp (2004) [4] C Safta S Enachescu and C K Madnia Interaction of a Vortex Ring with a Diffusion Flame Phys Fluids 14 pp (2002)

12 95 [5] D A Everest J F Driscoll W J A Dahm and D A Feikema Images of the Temperature Field and Temperature Gradients to Quantify Mixing Rates within a Non-Premixed Turbulent Jet Flame Combust Flame 101 pp (1995) [6] W P Jones and R P Lindstedt Global Reaction Schemes for Hydrocarbon Combustion Combust Flame 73 pp (1988) [7] ( $\mathrm{p}$ 2001) 33 [8] M D Smooke et al Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames (SPringer-Verlag New York 1991) pp 1-28 [9] N Peters Turbulent Combustion (Cambridge Univ Press Cambridge 2001) pp

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 $Le_{i}$

$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}$$ 1413 2005 26-35 26 (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)

Title メタンと空気の非予混合火炎への剪断速度の影響 ( 混合 化学反応 燃焼の流体力学 ) Author(s) 加賀, 義人 ; 横山, 直人 ; 水島, 二郎 Citation 数理解析研究所講究録 (2006), 1496: Issue Date URL htt

Title メタンと空気の非予混合火炎への剪断速度の影響 ( 混合化学反応燃焼の流体力学 ) Author(s) 加賀, 義人 ; 横山, 直人 ; 水島, 二郎 Citation 数理解析研究所講究録 (2006), 1496: Issue Date URL htt