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
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 =1.5 2. x 2.1 1 6 mm 6 mm 6 mm 2 mm M = 1 mm 25 1.2 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
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) 2 1 1-1 1-2 1-3 (u'/u) 2 (v'/u) 2 (γ '/Γ ) 2, (γ ' R () /ΓR () ) 2 1 1 1 1-1 Noreaction 1-4 1 5 1 5 1 (x + x )/M 1-2 1 1 1 1 2 Fig. 2 Decay of turbulent intensities Fig. 3 Decay of concentration uctuation intensities for nonreactive scalar 3.2 3. 3.1 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 1.12 1.6 (6a) (6b) Reynolds Re λ 15 < Re λ < 25 Reynolds 9 3.2 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
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.3.2.1 (a) Species R R γ ' R / Γ R.3.2.1 (a) Species R R Γ B / Γ B Γ S / Γ S 1.9.8.7.3.2.1 (b) Species B B (c) Species S S γ ' S / Γ S γ ' B / Γ B.15.1.5.15.1.5 (b) Species B (c) Species S B S 1 2 3 Fig. 4 Downstream variations of the mean concentrations of reactive species 1 2 3 Fig. 5 Downstream variations of the r.m.s. values of concentration uctuation of reactive species 3.3 4 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
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 1.2.4 5 15 3 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 8 6 4 2.6.7.8.9 1 Γ B / Γ B 3 2 1 (b) Species B.2.4 Γ S / Γ S Fig. 7 (c) Species S 5 5 15 15 Downstream changes of concentration PDFs 3 3 Fox 12) α = R B PDF p RB 1 5 48
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 -.6 -.7 -.8 -.9-1 Present Experiment -1.1 1 2 3 Fig. 8 Downstream variations of the concentration correlation coefficients -.2 -.4 -.6 -.8 Present Experiment -.1 1 2 3 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 1.9.8 5 1 15 = 5 = 15 = 3.7.1.2.3 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.9.95 5. 1 DNS Probability Density Function, PDF 13) PDF LES Filtered Density Function FDF 14, 15) 49
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. 211 242, 1991. 2) 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. 373 47, 1996. 3) 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. 339 372, 1996. 4) 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. 742 748, 1994. 第 64 号 第 628 号 pp. 453 461, 1998. 12) R. O. Fox: Computational Models for Turbulent Re- acting Flows, Cambridge University Press, pp. 153 156, 23. 13) S. B. Pope: PDF Method for Turbulent Reactive Flows, Progress in Energy and Combustion Science, Vol. 11, pp. 119 192, 1985. 14) 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. 499 515, 1998. 15) 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. 2321 2337, 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. 462 47, 1998. 6) 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. 214 221, 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. 1157 1166, 1985. 8) 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. 189 111, 1987. 9) 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. 293 314, 1985. 1) 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. 518 522, 199. 11) 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