第 8 章 遷音速バンプ流れに及ぼす非平衡凝縮の影響 167
8.5 まとめ
(a) Computational grids (Unit : mm)
(b) Boundary conditions Fig. 8.1 Computational domain
(a) Experiment (φ01= 18 %) (b) Calculation (φ01= 0 %)
Fig. 8.2 Comparison between experimental and calculatedflowfields (R= 100 mm, Dry air)
(a) Experiment (φ01= 50 %) (b) Calculation (φ01= 50 %)
Fig. 8.3 Comparison between experimental and calculatedflowfields (R= 100 mm, Moist air)
(a) Experiment (φ01= 17 %) (b) Calculation (φ01= 0 %) Fig. 8.4 Comparison between experimental and calculatedflowfields (R= 200 mm, Dry air)
(a) Experiment (φ01= 50 %) (b) Calculation (φ01= 50 %)
Fig. 8.5 Comparison between experimental and calculatedflowfields (R= 200 mm, Moist air)
Fig. 8.6 Distributions of static pressure (R= 100 mm)
Fig. 8.7 Distributions of static pressure (R= 200 mm)
(a) Dry air (φ01= 0 %)
(b) Homogeneous condensation (nhet,01= 0 m−3)
(d) nhet,01= 5.0×1012 m−3
(c)nhet,01= 1.0×1011 m−3
(e)nhet,01= 1.0×1014 m−3 Fig. 8.8 Contour maps of Mach number (R= 200 mm)
(a) Homogeneous condensation (nhet,01= 0 m−3)
(c) nhet,01= 5.0×1012 m−3
(b)nhet,01= 1.0×1011 m−3
(d)nhet,01= 1.0×1014 m−3 Fig. 8.9 Contour maps of condensate mass fraction (R= 200 mm)
Fig. 8.10 Static pressure distributions (R= 200 mm)
(a) Homogeneous condensation (nhet,01= 0 m−3)
(c) nhet,01= 5.0×1012 m−3
(b)nhet,01= 1.0×1011 m−3
(d)nhet,01= 1.0×1014 m−3 Fig. 8.11 Distributions of condensation properties (R= 200 mm)
Fig. 8.12 Separation region (R= 200 mm)
Fig. 8.13 Distributions of displacement thickness (R= 200 mm)
Fig. 8.14 Distributions of total pressure loss (R= 200 mm,x/L= 0.60)
(a)t= 0/f s
(b)t= 0.167/f s
(c)t= 0.333/f s
(d)t= 0.500/f s
(e)t= 0.667/f s
(f) t= 0.833/f s Fig. 8.15 Contour maps of Mach number (φ01= 0 %,R= 100 mm)
(a) Homogeneous condensation (nhet,01= 0 m−3)
(c) nhet,01= 5.0×1012 m−3
(b)nhet,01= 1.0×1011 m−3
(d)nhet,01= 1.0×1014 m−3 Fig. 8.16 Contour maps of Mach number (R= 100 mm)
(a) Homogeneous condensation (nhet,01= 0 m−3)
(c) nhet,01= 5.0×1012 m−3
(b)nhet,01= 1.0×1011 m−3
(d)nhet,01= 1.0×1014 m−3 Fig. 8.17 Contour maps of condensate mass fraction (R= 100 mm)
(a) Homogeneous condensation (nhet,01= 0 m−3)
(c) nhet,01= 5.0×1012 m−3
(b)nhet,01= 1.0×1011 m−3
(d)nhet,01= 1.0×1014 m−3 Fig. 8.18 Distributions of condensation properties (R= 100 mm)
Fig. 8.19 Separation region (R= 100 mm)
Fig. 8.20 Distributions of displacement thickness (R= 100 mm)
Fig. 8.21 Distributions of total pressure loss (R= 100 mm,x/L= 0.60)
第 9 章 結 論
湿り空気を用いた均一，および非均一凝縮に関して，衝撃波管内を伝ぱする非定常膨張波によって誘 起される流れ，先細末広円弧ノズルを有する下流膜方式ルトビーク管内流れ，および定常と非定常の 衝撃波を伴う遷音速バンプ流れを対象とした数値解析を行った．本研究で得られた主な結果を要約す ると，以下のとおりである．
(1) 衝撃波管内流れについて
1.非均一凝縮が生ずる場合の圧力の過渡的変化と液相の質量比や凝縮核との関係を調べ，均一凝縮 が生ずる場合との違いを明らかにした．
2.管内で非均一凝縮が生ずる場合，破膜直後に隔膜近傍において生ずる凝縮は均一凝縮の影響が支 配的であるが，時間の経過とともに非定常膨張波内で生ずる凝縮は非均一凝縮の影響が支配的に なる．
3.非定常膨張波内で非均一凝縮が生ずる場合の過飽和度は，高圧室の固体微粒子の初期数密度の増 加に伴い小さくなる．
4.管内で非均一凝縮が生ずる場合，高圧室における初期相対湿度や固体微粒子の初期数密度の増加 に伴い，非定常膨張波背後の圧力は増加し，低圧室側へ伝播する衝撃波のマッハ数は増加する．
(2) 先細末広円弧ノズルを有する下流膜方式ルトビーク管内流れについて
1.管内で均一凝縮が生ずる場合，ノズル入口より上流側における凝縮核と液相の発生の有無および 圧力変動の有無の観点から，管内で生ずる凝縮を伴う流れ場は3つに分類できる．
2.ノズル入口より上流側で均一凝縮，および非均一凝縮が生じない場合，高圧室の初期状態におけ る相対湿度の僅かな変化が全圧損失に大きな影響を与える．
3.管内で非均一凝縮が生じず，ノズル入口より上流側で均一凝縮が生ずる場合，全圧損失はノズル スロート高さの増加とともに小さくなる．
4.管内で非均一凝縮が生じず，ノズル内で均一凝縮による流れ場の周期的な振動が生ずる場合，ノ ズル入口より上流側で非均一凝縮を生じさせることで，流れ場の振動の発生を完全に抑制するこ とができる．
5.ノズル入口より上流側で凝縮が生ずる場合，均一，および非均一凝縮の違いに関わらず，ノズル 入口より上流側から始動衝撃波までの圧力や液相の質量比などの分布はほぼ同様となる．
6.高圧室の初期相対湿度の増加に伴い，始動衝撃波の上流における流れの全圧損失は増加し，均一 や非均一の凝縮に関わらず一定の値に漸近する．
7.非均一凝縮が生ずる場合の流れの全圧損失は，均一凝縮が生ずる場合よりも小さくなる．
(3) 遷音速バンプ流れについて
1.流れ場で均一凝縮が生ずると，バンプモデル上の定常な衝撃波の強さは凝縮が生じない場合と比 較して弱くなり，衝撃波と境界層の干渉による流れのはく離領域は小さくなる．また，非均一凝 縮が生ずる場合には，固体微粒子の初期数密度の増加に伴い衝撃波はさらに弱くなり，流れのは く離領域も小さくなる．
2.非定常な衝撃波の発生により流れ場が周期的に振動する場合，均一や非均一凝縮の違いに関わら ず，振動を抑制することができる．
3.均一凝縮が生ずる場合のバンプモデル下流側における流れの全圧損失は，凝縮が生じない場合と 比較して小さくなる．
4.バンプモデル下流側における流れの全圧損失は，固体微粒子の初期数密度に強く依存し，流れ場 の全圧損失を最小にする初期数密度の適正な値が存在する．
謝 辞
佐賀大学大学院工学系研究科瀬戸口俊明教授には，筆者が学部の頃から多大な 御指導と御鞭撻を賜り，さらに本研究を行うにあたって始終懇切丁寧なる御指導 をいただきました．衷心より深く感謝申し上げます．
また，佐賀大学大学院工学系研究科金子賢二教授,瀬戸邦聰教授，松尾繁教授に は，本論文をまとめるにあたって，貴重な御意見，御教示をいただきました．心 より感謝いたします．
そして，研究生活の様々な面で御指導いただいた佐賀大学理工学部機械システ ム工学科の木上洋一助教授，中野智弘講師，塩見憲正助手，並びに杉町等技官を はじめ機械実習工場の技官の方々に深く御礼申し上げます．
さらに，研究室にあって種々の便宜を与えていただいた佐賀大学理工学部機械 システム工学科環境流動システム学講座の皆様に御礼申し上げます．
平成18年3月23日
関連図書
[1] Stodola, A., Steam and Gas Turbine, (1927), McGraw-Hill.
[2] Oswatitsch, K., Kondensationserscheinungenn in Ueberschallduesen, Z. angew. Math. Mech., 22(1942), 1-14.
[3] Wegener, P. P., Water Vapor Condensation Process in Supersonic Nozzle, J.Appl.Phys., 25-12, (1954), 1485-1491.
[4] Hill, P.G., Condensaton of water vapor during supersonic expansion in nozzle, J.Fluid Mech., 25-3, (1966), 593-620.
[5] P. P.Wegener, Acta mechanica, 21, (1975), 65.
[6] Wegener, P.P., and Mach, L.M., Condensation in Supersonic and Hypersonic Wind Tunnels, Adv. in Appl. Mech., 5, (1958), 307-447, Academic Press.
[7] Wegener, P.P., and Pouring, A.A., Experiments on Condensation of Water Vapour by Ho-mogeneous Nucleation in Nozzles, Phys. Fluid, 7-3, (1964), 352-361.
[8] Pouring, A.A., Thermal Choking and Condensation in Nozzles, Phys. Fluid, 8-10, (1965), 1802-181.
[9] Volmer, M., Kinetik der Phasenbildung, (1945), Edwards Brothers.
[10] Frenkel, J., Kinetic Theory of Liquids, (1946), Oxford University Press.
[11] Abraham, F.F., On the time-Dependent Structure of Currents in Non-Steady-State Nucle-ation Kinetics, J.Chem.Phys., 54-9, (1971), 3874-3875.
[12] Abraham, F.F., and Dave, J.V., Thermodynamics of Microcrystallites and Its Ration to Nucleation Theory, J. Chem. Phys., 55-4, (1971), 4817-4821.
[13] Katz, J.L., Comdensation of a Supersaturated Vaper.I.The Homogeneous Nucleation on the n-Alkanes, J. Chem. Phys., 52-9, (1970), 4733-4748.
[14] Dorfeld, W.G., and Hudson, J.B., Condensation in CO2 Free Jet Expansions.I.Dimer Forma-tion, J. Chem. Pys., 59-3, (1973), 1253-1260.
[15] Schmidt, B., Jahrbuch WGLR, (1962), 160.
[16] Zierep, J., and Lin, S., Bestimmung des Kondensationsbeginns bei Entspannung feuchter Luft in Ueberschallduesen, Forsh. Ing.-Wes., 33, (1967), 169-172.
[17] Wegener, P.P., and Cagliostro, D.J., Combustion Science and Technology, 6, (1973), 269-277． [18] Barschdorff, D., and Fillipov, G.A., Heat Transfer-Societ Research, 2-5, (1970), 76-87.
[19] Saltanov, G.A., and Tkalenko, R.A., J. Appl. Mech. Tech. Phys., 16-6, (1975), 875-878.
[20] White, A.J., and Young, J/B., J. Propulsion Power, 9, (1993), 579-587.
[21] Adam, S., and Schnerr, G.H., Instabilities and bifurcation of non-equilibrium two-phaseflows, J. Fluid Mech., 348, (1997), 1-28.
[22] Zierep, J., Stroemungen mit Energiezufuhr, 2, (1990), Aufl., G. Braun, Karlsruhe.
[23] Schnerr, G.H., Homogene Kondensation in Stationaeren Transsonischen Stroemungen durch Laval-duesen und um Profile, (1986), Hab. schrift, Universitaet Karlsruhe.
[24] Schnerr, G.H., and Dohrmann, U., Transonic Flow Around Airfoils wiht Relaxation and Energy Supply by Homogeneous Condensation, AIAA J., 28-7, (1990), 1187-1193.
[25] Young, J.B., Nonequilibrium wet-steam calculations for nozzles and turbin cascades, J.Turbomachinery, 114, (1992), 569-579.
[26] Matsuo, K., Kawagoe, S., Setoguchi, T., and Sonoda, K., Condensation Shock and Examples, Machine Study, 36-1, (1984), 73-79.
[27] Matsuo, K., Kawagoe, S., Sonoda, K., and Sakao, T., Study on Condensation Shock Waves (Part 1, Mechanism of their Formation), Bull. JSME, 28-241, (1985), 1416-1422.
[28] Matsuo, K., Kawagoe, S., Sonoda, K., and Setoguchi, T., Oscillations of Laval Nozzle Flow with Condensation (Part 1, on the Range of Oscillations and Their Frequencies), Bulletin of JSME, Vol.26, No.219, 1983, 1556-1562.
[29] Matsuo, K., Kawagoe, S., Sonoda, K., Kwon, S. B., Yamamoto, H., and Sugiyama, E.,Studies of Condensation Shocks (2nd Report, Relation between Condensation Shock Wave and Con-densation Zone), Bull. JSME, 29-248, (1986), 439-443.
[30] Kawata, H., and Mori, Y., Study on Gasdynamics of Condensation in a Shock Tube, Trans.
Jpn. Soc. Mech. Eng. 38, (1972), 2843-2853.
[31] Sislian, J.P., Condensation of Water Vapor with or without a Carrier Gas in a Shock Tube, UTIAS Rep., 201, (1975).
[32] Kotake, S., and Glass, I.I., Condensation of Water Vapour on Heterogeneous Nucleation in a Shock Tube, UTIAS Report, No.207, 1976.
[33] Turnbull, D., Progress in Solid State Physics, Vol.3, Academic Peress, New York, (1956).
[34] Hirth, J.P., and Pound, G.M., Condensation and Evaporation, Nucleation and Growth Ki-netics, Pergamon Press, Oxford, (1963).
[35] Walton, D., Nucleation of Vapor Deposits, J. Chem. Physics, Vol.37, 2182, (1962).
[36] Fletcher, N.H., Size Effect in Heterogeneous Nucleation, The Journal of Chemical Physics, Vol.29, No.3, (1958), 572-576.
[37] Buckle, E.R., and Pouring, A.A., Effects of Seeding on the Condensation of Atmospheric Moisture in Nozzles, Nature, Vol.208, No.5008, (1965), 367-369.
[38] Pouring, A.A., Effects of Heterogeneous Nucleation of Water Vapor in Nozzles, Transactions of the ASME, Journal of Basic Engineering, (1970), 689-693.
[39] Winkler, G., and Schnerr, G.H., Nucleating Unsteady Flows in Low Pressure Steam Turbine Stages, 4th European Conference on Turbomachinery, (2001), 793-802.
[40] Yamamoto, S., Onset of Condensation in Vortical Flow over Sharp-Edged Delta Wing, A Collection of the 15th AIAA Computational Fluid Dynamics Conference and Exhibit, Vol.2, (2001), 852-861.
[41] Abe, K., and Kameda, M., Condensation on Droplets in Moist Air by Heterogeneous Nucle-ation, Computational Fluid Dynamics Journal, Special Issue, 12(2):36, (2003), 295-308.
[42] Courtney, W.G., Condensation in a Rarefaction Wave, ONR Technical Report, NOnr, 4154(00), (1965).
[43] Barschdorff, D., Carrier Gas Effects on Homogeneous Nucleation of Water Vapor in a Shock Tube, The Physics of Fluids 18, (1975), 529-536.
[44] Matsuo, K., et al., Relation between Condensation and Thermal Choking in an Unsteady Subsonic Flow, Bulletin of the JSME, 25, (1981), 744-751.
[45] Studzinski, W., et al., Unsteady Expansion Flow with Binary Nucleation and Condensation in a Shock Tube, Proc. of the 14 Int. Symp. On Shock Tubes and Shock Waves, (1983), 421-428.
[46] Matsuo, S., Tanaka, M., Setoguchi, T., and Kim, H.D., Shock Tube Flows with Non-Equilibrium Condensation in Rarefaction Wave, Proc. of the 14 Int. Symp. On Shock Tubes and Shock Waves, (1983), 421-428.
[47] Ludwieg, H., Der Rohrwindkanal, Zeitschrift f¨ur Flugwissenschaften, Vol.3, No.7, (1955), 206-216.
[48] Cable, A.J., and Cox, R.N., The Ludwieg Pressure Tube Supersonic Wind Tunnel, The AeronauticalQuarterly, Vol.14, No.2, (1963), 143-157. (1963)
[49] Friehmelt, H., Koppenwaller, G., and M¨uller-Eigner, R., Calibration and First Results of a Redesigned Ludwieg Expansion Tube, AIAA/DGLR Fifth International Aerospace Planes and Hypersonics Technologies Conference, AIAA-93(5001), (1993).
[50] Schneider, S.P., and Haven, C.E., Quiet-Flow Ludwieg Tube for High-Speed Transition Re-search, AIAA J., Vol.33, No.4, (1995), 688-693.
[51] Kwon, S.B., Matsuo, K., Kawagoe, S., Matsuo, S., Total Pressure Loss in Supersonic Nozzle Flows with Condensation, JSME Int. J., Vol.31, No.1, (1988), 16-21.
[52] Wegener, P.P., and Cagliostro, D. J., Periodic Nozzle Flow with Heat Addition, Combustion Sci. and Tech., Vol.6, (1973), 269-277.
[53] Matsuo, S., Setoguchi, T., Yamashita, H., Kaneko, K., Kim, H.D., and Matsuo, K., Control of Shock Wave Using Nonequilibrium Condensation of Moist Air, Proceedings of Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, (2001), 1841-1846.
[54] Shimamoto, K., Matsuo, S., Setoguchi, T., Tanaka, M., and Kaneko, K., Control of Shock Wave in Transonic Flow Field, Proceedings of the Fifth JSME-KSME Fluids Engineering Conference on Disc[CD-ROM], (2002).
[55] 松尾一泰，他3名，凝縮衝撃波の理論と実例(1)，機械の研究，36-1(1984)，73-78.
[56] 松尾一泰，他3名，凝縮衝撃波の理論と実例(3)，機械の研究，36-3(1984)，425-429.
[57] 松尾一泰，圧縮性流体力学，(1994)，理工学社.
[58] 松尾一泰，他3名，凝縮衝撃波の理論と実例(6)，機械の研究，36-6(1984)，754-758.
[59] 中間健二郎，湿り空気の非平衡凝縮が湿り空気に及ぼす影響，佐賀大学大学院修士論文，(1997).
[60] Michael, H., Instation¨are Ph¨anomene in homogen/heterogen kondensierenden Du¨usen- und Turbinenstr¨omungen, Dissertation, Fakult¨at f¨ur Maschinenbau, Universit¨at Karlsruhe(TH), Germany, (1999).
[61] Adam, S., Numerische und Experimentelle Untersuchung Instation¨arer D¨usenstr¨omungen mit Energiezufuhr durch Homogene Kondensation, Dissertation, Fukalt¨at f¨ur Maschinenbau, Universit¨at Karlsruhe (TH), Germany, (1999).
[62] 物理学辞典編集委員会，物理学辞典，(1992)，培風館.
[63] 松尾繁，超音速内部流動に及ぼす凝縮の影響に関する研究，九州大学大学院総合理工学研究科 博士論文，(1988).
[64] 藤井孝蔵，流体力学の数値計算法，(1994)，東京大学出版，123-130.
[65] Steger, J.L., Implict Finite-Differance Simulation of Flow about Arbitrary Two-Dimension Geometries,AIAA J., 16-7, (1978), 679-686.
[66] 荒川忠一，数値流体工学，(1994)，東京大学出版.
[67] 棚橋隆彦，CDF数値流体力学，(1993)，アイピーシー，647-738.
[68] 数値流体力学編集委員会編，乱流解析，(1995)，東京大学出版会.
[69] Kunz, R.F., and Lakshminaraya, B., Explicit Navier-Stokes Computation of Cascade Flow Using the k-², AIAA J., 30, (1992), 13-21.
[70] 吉澤徴，乱流モデルと圧縮性，日本航空宇宙学会誌，41-470，(1993)，2-8.
[71] 大宮司久明，山本悟，反変速度成分の圧縮性ナビエ・ストークス方程式の陰的時間進行法，航 空宇宙技術研究所特別資料，9，(1988)，77-83.
[72] Yee, H.C., A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods, NASA TM 101088, (1989).
[73] 数値流体力学編集委員会編，圧縮性流体解析，(1995)，東京大学出版会.
[74] Hirsch, C., Numerical Computation of Internal and External Flows, 2, (1998), A Wiley-Interscience Publication.
[75] Pulliam, T.H., and Chaussee, D.S., A Diagonal Form of an Implicit Approximate-Factorization Algorithm, J. Comp. Phys., 39, (1981), 347-363.