液相化学反応を伴う乱流拡散の研究名城大学理工学部研究報告 No.5 21 R 6 R S 1) B 6 2 M =1 Nozzle ID =1.2 OD = x mm 6 mm 6 mm 2 mm M = 1 mm mm 1.5 mm x 1 x = 1 m
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1 1) A Study on Turbulent Diffusion with Chemical Reaction in Liquid Takashi KUBO 1) Abstract Turbulent diffusion with chemical reactions is of practical importance in many engineering and environmental elds. A diffusion eld with a one-step reaction (R + B S) in a liquid grid-turbulence has been experimentally investigated. The instantaneous concentrations of two species R and S are measured simultaneously by the light absorption spectrometric method, while the concentration of species B is determined by the conservation law. The statistics of reactive scalar elds are compared with the nonreactive scalar ones. It is ascertained that the mean concentrations of reactants R and B decrease while that of product S increases in the downstream direction because of the chemical reaction. With regard to the scalar uctuations, it is also observed that the r.m.s. values for species R become smaller than those in the nonreactive case under the present experimental conditions, whereas the r.m.s. values for species B become larger. Furthermore, the correlation coefficient between species R and B is negative and varies from.9 to.95 in the present measurement region. The present data give very important information for the modeling of the concentration correlation and chemical source term in a turbulent reactive ow. 1. 1) 2) 3) NO + O 3 NO 2 + O 2 Komori 4) 5, 6) DNS Schmidt Batchelor Kolmogorov DNS LES Bennani 7) Mehta 8) R + B k S (1) R B S k Bourne 9) B 1) 1) Department of Mechanical Engineering 44
2 液相化学反応を伴う乱流拡散の研究名城大学理工学部研究報告 No.5 21 R 6 R S 1) B 6 2 M =1 Nozzle ID =1.2 OD = x mm 6 mm 6 mm 2 mm M = 1 mm mm 1.5 mm x 1 x = 1 mm 11) (11) 2.2 Reynolds Re M = UM/ν = 9 U U =.11 m/s ν 1.5 R B Γ R = 12 mol/m 3 Γ B =.2 mol/m 3 k =.9 m 3 /(mol s) Fig. 1 Species R U Species B x Species R Schematic of diffusion eld and turbulence grid R S Γ R Γ S B Γ B Γ B = (1 F)Γ B Γ S (2) F mixture fraction F = Γ R + Γ S Γ R (3) (2) (3) Γ R Γ R + Γ B Γ B + Γ S Γ S = 1 (4) Γ S = Γ R Γ B /(Γ R + Γ B ) 1, 11) k Γ () R = FΓ R (5a) Γ () B = (1 F)Γ B (5b) () 45
3 液相化学反応を伴う乱流拡散の研究名城大学理工学部研究報告 No.5 21 (u'/u) 2, (v'/u) (u'/u) 2 (v'/u) 2 (γ '/Γ ) 2, (γ ' R () /ΓR () ) Noreaction (x + x )/M Fig. 2 Decay of turbulent intensities Fig. 3 Decay of concentration uctuation intensities for nonreactive scalar LDV 2 u v r.m.s. (x + x ) M 5 < (x + x )/M < 3 u 2 x + x =.84 U M v 2 x + x =.463 U M (6a) (6b) Reynolds Re λ 15 < Re λ < 25 Reynolds R B C.I. Direct Red 31; C.I. 291 Γ Γ Γ/Γ.15 3 γ r.m.s. x M γ 2 x.857 = 2.18 (7) Γ M (3) (5a) Γ () R γ R() r.m.s. 2 46
4 液相化学反応を伴う乱流拡散の研究名城大学理工学部研究報告 No.5 21 Γ R / Γ R (a) Species R R γ ' R / Γ R (a) Species R R Γ B / Γ B Γ S / Γ S (b) Species B B (c) Species S S γ ' S / Γ S γ ' B / Γ B (b) Species B (c) Species S B S Fig. 4 Downstream variations of the mean concentrations of reactive species Fig. 5 Downstream variations of the r.m.s. values of concentration uctuation of reactive species Γ i Γ i M 4 (a) (b) R B R B 4 (c) S r.m.s. 5 r.m.s. γi Γ i M R B R r.m.s. B r.m.s. 5) Γ R = Γ R /Γ R Γ B = Γ R /Γ B (4) w RB = Γ R Γ B w RB = Γ R Γ B = Γ R (1 Γ S Γ R ) = Γ B (1 Γ S Γ B ) w RB Γ S Γ R Γ B w RB Γ R Γ R = Γ B Γ B = Γ R = 1 Γ S Γ B = 1 Γ S Γ R Γ B 6 Γ R < Γ B R R r.m.s. B B r.m.s. S r.m.s. 47
5 液相化学反応を伴う乱流拡散の研究名城大学理工学部研究報告 No.5 21 w RB 2 R 1 Γˆ 2 1 p R Γ R ΓˆR ΓˆB ΓˆS Γ R / Γ R (a) Species R Fig. 6 Pro le of concentration product γs /Γ S.5 7 PDF p i 4 5 r.m.s. R r.m.s. R PDF B r.m.s. B PDF S kγ R Γ B kγ R Γ B = k(γ R Γ B + γ R γ B ) 12) R B C RB = γ R γ B /(γr γ B ) 8 C RB = 1.95 < C RB <.9 9 α = γ R γ B /(Γ R Γ B ) 1 α α = α = 1 p B Γ B p S Γ S 1 B Γ B / Γ B (b) Species B.2.4 Γ S / Γ S Fig. 7 (c) Species S Downstream changes of concentration PDFs 3 3 Fox 12) α = R B PDF p RB
6 液相化学反応を伴う乱流拡散の研究名城大学理工学部研究報告 No.5 21 C RB α Present Experiment Fig. 8 Downstream variations of the concentration correlation coefficients Present Experiment Fig. 9 Downstream variations of the segregation factors PDF 8 PDF 4. R + B S R B S B R R, B S Reynolds Re M 9 (1) R B S (2) R Γ B /Γ B = 5 = 15 = Γ R /Γ R Fig. 1 Downstream changes of concentration joint PDF between species R and B r.m.s. B R B (3) R B DNS Probability Density Function, PDF 13) PDF LES Filtered Density Function FDF 14, 15) 49
7 液相化学反応を伴う乱流拡散の研究 名城大学理工学部研究報告 No.5 21 システムの有効性 日本機械学会論文集 B 編 参考文献 1) R. W. Bilger, L. R. Saetran, and L. V. Krishnamoor- thy: Reaction in a Scalar Mixing Layer, Journal of Fluid Mechanics, Vol. 233, pp , ) R. J. Brown and R. W. Bilger: An Experimen- tal Study of a Reactive Plume in Grid Turbulence, Journal of Fluid Mechanics, Vol. 312, pp , ) J. D. Li and R. W. Bilger: The Diffusion of Con- served and Reactive Scalars Behind Line Sources in Homogeneous Turbulence, Journal of Fluid Mechanics, Vol. 318, pp , ) S. Komori, T. Kanzaki, and Y. Murakami: Concen- tration Correlation in a Turbulent Mixing Layer with Chemical Reaction, Journal of Chemical Engineering of Japan, Vol. 27, No. 6, pp , 第 64 号 第 628 号 pp , ) R. O. Fox: Computational Models for Turbulent Re- acting Flows, Cambridge University Press, pp , ) S. B. Pope: PDF Method for Turbulent Reactive Flows, Progress in Energy and Combustion Science, Vol. 11, pp , ) P. J. Colucci, F. A. Jaberi, P. Givi, and S. B. Pope: Filtered Density Function for Large Eddy Simula- tion of Turbulent Reacting Flows, Physics of Fluids, Vol. 1, pp , ) M. R. H. Sheikhi, T. G. Drozda, P. Givi, and S. B. Pope: Velocity-Scalar Filtered Density Function for Large Eddy Simulation of Turbulent Flows, Physics of Fluids Vol. 15, pp , 23. 原稿受理日 平成 21 年 9 月 18 日 5) 酒井康彦 久保貴 中村育雄 化学反応を伴う乱 流噴流拡散の研究 第 2 報 反応濃度場の特性, 日本機械学会論文集 B 編 第 64 号 第 628 号 pp , ) 久保貴 酒井康彦 太田功 中村育雄 連続競争 反応を伴う乱流噴流拡散の研究 第 2 報 反応濃 度場の特性 日本機械学会論文集 B 編 第 66 号 第 648 号 pp , 2. 7) A. Bennani, J. N. Gence, and J. Mathieu: The In- uence of a Grid-Generated Turbulence on the Development of Chemical Reactions, AIChE Journal, Vol. 31, No. 7, pp , ) R. V. Mehta and J. M. Tarbell: An Experimental Study of the Effect of Turbulent Mixing on the Se- lectivity of Competing Reactions, AIChE Journal, Vol. 33, No. 7, pp , ) J. R. Bourne, C. Hilber, and G. Tovstiga: Kinetics of the Azo Coupling Reactions between 1-Naphthol and Diazotised Sulphanic Acid, Chemical Engineering Communications, Vol. 37, pp , ) 酒井康彦 中村育雄 角田博之 櫛田武広 吸光ス ペクトル法によるファイバ形多成分変動濃度計の 開発に関する研究 日本機械学会論文集 B 編 第 56 号 第 522 号 pp , ) 酒井康彦 久保貴 中村育雄 化学反応を伴う乱 流噴流拡散の研究 第 1 報 多成分変動濃度測定 5
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