エンタルピー一定条件下における高温予混合火炎の固有不安定性に関する数値シミュレーション

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1 Journal of the Combustion Society of Japan Vol.52 No.162 (2010) ORIGINAL PAPER エンタルピー一定条件下における高温予混合火炎の固有不安定性に関する数値シミュレーション Numerical Simulation on the Intrinsic Instability of High-Temperature Premixed Flames Under the Constant-Enthalpy Conditions 1 * 2 3 KADOWAKI, Satoshi 1 *, YAHATA, Masafumi 2, and KOBAYASHI, Hideaki Graduate School of Management of Technology, Nagaoka University of Technology, Nagaoka, Niigata , Japan Graduate School of Engineering, Nagaoka University of Technology, Nagaoka, Niigata , Japan Institute of Fluid Science, Tohoku University, Katahira, Aoba-ku, Sendai, Miyagi , Japan ; Received 7 May, 2010; Accepted 29 June, 2010 Abstract : The effects of the unburned-gas temperature on the intrinsic instability of high-temperature premixed flames under the constant-enthalpy conditions were studied by two-dimensional unsteady calculations of reactive flows. A sinusoidal disturbance with sufficiently small amplitude was superimposed on a planar flame to obtain the relation between the growth rate and wave number, i.e. the dispersion relation. The growth rate increased as the unburned-gas temperature became higher, which was due to the increase in burning velocity of a planar flame. The linearly most unstable wave number, i.e. the critical wave number, was almost constant, indicating that the cell size was independent of the unburned-gas temperature. To elucidate the characteristics of cellular flames induced by intrinsic instability, a sinusoidal disturbance with the critical wave number was superimposed. The superimposed disturbance evolved, and a cellular-shaped front formed. As the unburnedgas temperature became higher, the behavior of cellular flames became milder, even though the growth rate increased. This was because that the difference in temperature between burned and unburned gases decreased owing to the constant-enthalpy conditions. Key Words : High-temperature premixed flame, Intrinsic instability, Cellular flame, Numerical simulation 1. はじめに [1-2] * Corresponding author. kadowaki@mech.nagaokaut.ac.jp [3-6] [7-10] ( ) (63)

2 記号 a δ a i B δ S u0 /δ C p J/kgK c 0 D E e k k c m/s m 2 /s RT 0 p 0 1/δ 1/δ Le ( = a/d) M ( = S u0 /c 0 ) Pr ( = /a) p p 0 p u p 0 Q R p 0 Pa C p T 0 /Y 0 J/molK S cf S u0 S u S u0 S u0 m/s T T 0 T b T u T 0 t T 0 T 0 K δ/s u0 u, v S u0 x, y δ Y Y 0 Y u Y 0 a g Y 0 m 2 /s δ m ( = a/su0) l δ lc δ ν m 2 /s ρ ρ0 ρu ρ0 ρ0 kg/m 3 w Su0/δ 2. 支配方程式 ( ) x y (1) (64)

3 331 x 100 y x Tu Yu y y x (4) ai = 0.1 ai = 1.0 SGI Altix 3799Bx2 (2) 4. 結果および考察 4.1. 平面火炎 ( ) 3. 数値シミュレーション 3.93 m/s (M = 0.01) 2086 K (Tb = 7.0) [11] Le = 1.0 Pr = 1.0 g = 1.4 Q = 6.0 E = 70 Tu = ( ) (3) (3) Tu Yu 1 Tu = 1.0 & 3.0 (Yu = 1.0 & 0.67) ( = ρusu) Tu = 1.0 & 3.0 ρusu = 1.00 & () [12] Tu Yu (pu = 1.0) 4.2. 分散関係 (ai = 0.1) (65)

4 Fig.3 Dispersion relations at Tu = 1.0 & 3.0; the solid and broken lines denote the results of theoretical analyses on the dispersion relation. Fig.1 Distributions of flow variables in planar flames at Tu = 1.0 & 3.0. (k = 2p/l) 1.0 [16] 3 Tu = 1.0 & 3.0 ( 2 ) () [12] Fig.2 Burning velocities of planar flames, depending on the unburnedgas temperature; the solid line denotes the results of theoretical analyses on the burning velocity. [13-15] (5) 4.3. セル状火炎 a i = 1.0 (lc = 2p/kc) 4 Tu = 1.0 & 3.0 Tu = 3.0 T u = (66)

5 333 Fig.4 Time histories of amplitude at Tu = 1.0 & 3.0 (t = 0 through 25). Fig.6 Burning velocities of planar flames and cellular flames, depending on the unburned-gas temperature. 5. おわりに Fig.5 Shapes of flame fronts at Tu = 1.0 & 3.0 (t = 0, 10, 20,..., 50). ( = Scf - Su) Tu = 1.0 & & (Tu = Tu = ) (Tu = ) 1) 2) 3) 1.0 (67)

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