拡散 熱的および流体力学的不安定性のスケール効果

Transcription

1 Journal of the Combustion Society of Japan Vol.56 No.176 (2014) ORIGINAL PAPER 拡散 熱的および流体力学的不安定性のスケール効果 Scale Effects of Diffusive-thermal and Hydrodynamic Instability * SHIBAYAMA, Shimon and KUWANA, Kazunori* Yamagata University, Jonan, Yonezawa, Yamagata , Japan ; Received 20 September, 2013; Accepted 30 December, 2013 Abstract : The damage caused by an accidental gas explosion, for example the maximal blast pressure, is strongly influenced by the flame propagation velocity during the explosion. The flame propagation during an explosion is significantly affected by flame instability, and it is known that the flame propagation velocity has certain scale dependency. This study investigates scale effects of diffusive-thermal and hydrodynamic instability by numerically solving the Sivashinsky equation. The following four conditions are considered: a purely diffusive-thermally unstable flame, a purely hydrodynamically unstable flame, a flame that is diffusive-thermally stable but hydrodynamically unstable, and a flame that is unstable both diffusivethermally and hydrodynamically. It is found that diffusive-thermal instability mainly influences the flame wrinkle structure of a specific wavelength, while hydrodynamic instability influences the largest structure. Thus, hydrodynamic instability shows scale dependency. The fractal dimensions of the flames, which can be used to estimate the flame propagation velocity during an explosion, are computed by two different methods: a Fourier analysis and a method based on the scale dependency of flame propagation velocity. The both methods yield consistent results, and it is found that the fractal dimension mainly depends on the thermal expansion ratio; its dependency on the Lewis number is rather weak. Key Words : Diffusive-thermal instability, Hydrodynamic instability, Scale dependency, Fractal dimension 1. 緒言 [1-3] [1] [4] [5] * Corresponding author. kuwana@yz.yamagata-u.ac.jp (78)

2 計算モデル 2.1. 基礎方程式 [5] Sivashinsky [6] Sivashinsky Sivashinsky (1) I(F) (2) F y ε γ 2.2. パラメータ (1) ε (3) Le Lewis (Le = α/d α D ) Le0 Lewis Le > Le0 ( ε < 0) Le < Le0 ( ε > 0) (1) γ (1) (1) O(γ) γ 0.8 Sivashinsky O(γ 2 ) [7,8] [5] 0 < γ < 1 (1) γ = 0.8 (1) Sivashinsky Lewis O(1) Sivashinsky CFD 2.3. 計算条件 1 case I γ = 0 case II ε = 0 [5] case III case IV ε γ [9] [5] -l < x < l x = ±l l Table 1 The calculation conditions. (4) ρu ρb ρu > ρb 0 < γ < 1 (79)

3 Fig.1 Flame shapes for the computational domain size of 512; (a) case I, (b) case II, (c) case III, and (d) case IV. [5] [10] 3. 計算結果 3.1. 火炎形状 2l = t = y 1a case I t = Δt = 500 case I b case II t = Δt = 20 case I c case III t = Δt = 50 case I, II d case IV t = Δt = 10 case IV case II 3.2. Fourier 解析 Fourier ( 2) 2 Fˆ 2 (Fˆ Fourier ) k (80)

4 175 Fig.2 Fourier transform of function F for the computational domain size of 512; (a) case I, (b) case II, (c) case III, and (d) case IV. (1) kc 2l = 512 t = 500 Δt = 500 t = Fourier 20 Fourier 2a case I ( ) Fourier k 10-1 Fˆ 2 k k = kc Fˆ 2 2b case II ( ) Fourier 2a k = kc Fˆ 2 case II Fˆ 2 2c (case III ) k = kc Fˆ 2 2d (case IV ) k = kc 2b (case II) k k Fˆ 2 (kc ) 3.1 Fˆ 2 k Fˆ 2 ~ k -a d [11] (5) 2 case II case IV (5) a = 2.9 d = 1.05 ( γ ) ( ε ) case I case II [5] (81)

5 case I (5) 3.3. 火炎伝播速度 3 2l = V 2l t = case I ( ) case II ( ) case III ( ) 2l 200 2l 200 case I 4 case III 2l = 108 case IV ( ) case II case IV case III case II-case IV ( ε ) ( γ ) ( ) 3 [5,10] 3 case II-case IV 0.05 d d = 1.05 Fig.3 Scale dependency of flame propagation velocity. Fig.4 Flame shape for the computational domain size of 108 in case III. Fourier 2l 200 case III [5] 3 case II 0.06 t = l 2896 γ ( ) ( Lewis ) γ = 0.5 d = 1.05 γ [5] γ = 0 d = 1 d γ 4. 結言 Sivashinsky (82)

6 177 case I case II case III case IV 4 case I Fourier (kc) case II-case IV Fourier Fourier d = 1.05 case I case III case I Fourier ( ) [5] γ Lewis Sivashinsky γ CFD CFD 謝辞 JSPS References 1. Dobashi, R., Kawamura, S., Kuwana, K. and Nakayama, Y., Proceedings of the Combustion Institute 33: (2011). 2. Tomizuka, T., Kuwana, K., Shimizu, K., Mogi, T., Dobashi, R. and Koshi, M., Journal of Loss Prevention in the Process Industries 26: (2013). 3. Tomizuka, T., Kuwana, K., Mogi, T., Dobashi, R. and Koshi, M., International Journal of Hydrogen Energy 38: (2013). 4. Gostintsev, Yu. A., Istratov, A. G., and Shulenin, Yu. V., Combustion, Explosion, and Shock Waves 24: (1988). 5. Mukaiyama, K., Shibayama, S. and Kuwana, K., Combustion and Flame 160: (2013). 6. Sivashinsky, G. I., Acta Astronautrica 4: (1977). 7. Sivashinsky, G. I. and Clavin, P., Journal de Physique 48: (1987). 8. Joulin, G. and Cambray, P., Combustion Science and Technology 81: (1992). 9. Michelson, D. M. & Sivashinsky, G. I., Acta Astronautrica 4: (1977). 10. Mukaiyama, K. & Kuwana, K., Journal of Loss Prevention in the Process Industries 26: (2013). 11. Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, 2nd ed., Wiley (2003). (83)