Summary
Diabatic processes dominate compressible flows with phase change where the heat of condensation or vaporization causes changes of enthalpy in the flow. The equations of motion for condensing flows are given in analogy to those of reacting flows and discontinuities are discussed. The nonequilibrium process of condensation by homogeneous nucleation in the supersaturated state is singled out by examples for steady and unsteady nozzle flows, Prandtl-Meyer flow, unsteady expansions and shock waves. A selective guide to the widely dispersed literature is provided and the early history of the discovery of condensation in supersonic wind tunnels is recounted.
Zusammenfassung
Kompressible Strömungen mit Phasenänderung können behandelt werden, wenn die Kondensations- oder Verdampfungswärme eingeführt wird. Die Bewegungsgleichungen kondensierender Strömungen werden analog zu denen der reagierenden Gase angegeben und Diskontinuitäten werden diskutiert. Der Nichtgleichgewichtsprozeß der Kondensation durch Keimbildung im übersättigten Zustand wird besonders behandelt. Beispiele für stationäre und instationäre Düsenströmung, Prandtl-Meyer-Strömung, instationäre Expansionsströmung und Stoßwellen werden gegeben. Ein kritischer Führer zur Literatur und historische Bemerkungen über die Geschichte der Entdeckung der Kondensation in Überschallwindkanälen beschließen die Arbeit.
Similar content being viewed by others
References
Ackeret, J.: Windkanäle für hohe Geschwindigkeiten, 2nd ed., p. 473–523. 1940, l.c. Volta [87] Volta Reale Accademia D'Italia, Fondazione Alessandro Volta. Atti dei Convegni 5. Le Alte Velocita in Aviazone. 30 Sept. to 6 Oct. 1935—XIII, Roma. 1st ed. 1936-XIV; 2nd ed., 1940-XIX (1935).
Ackeret, J.: Discussion with author, February 26, 1973.
Andres, R. P.: Homogeneous Nucleation in a Vapor, Chap. 2, p. 69 l.c. [100].Zettlemoyer, A. C.: Ed., Nucleation. New York: Marcel Dekker. 1969.
Arthur, P. D.: Effects of Impurities on the Supersaturation of Nitrogen in a Hypersonic Wind Tunnel. Doctoral Dissertation, California Institute of Technology, Pasadena, California (1952).
Bailey, N. P.: The Thermodynamics of Air at High Velocities. J. Aero. Sci.11, 227 (1944).
Barschdorff, D.: Dichtemessungen in Wasserdampfströmungen mit einem Differentialinterferometer. Photographie und Film in Industrie und Technik III, p. 155. Darmstadt-Wien: Verlag Dr. Othmar Helwich. 1971.
Barschdorff, D.: Verlauf der Zustandsgrößen und gasdynamische Zusammenhänge bei der spontanen Kondensation reinen Wasserdampfes in Lavaldüsen. Forsch. Ing. Wes.37, 146 (1971).
Barschdorff, D., andG. A. Fillipov: Analysis of Certain Special Operating Modes of Laval Nozzles with Local Heat Supply. Energetika i Transport3, 94 (1970), Also Heat Transfer (Soviet Research)2, 76 (1970).
Barschdorff, D., W. J. Dunning, P. P. Wegener, andB. J. C. Wu: Homogeneous Nucleation in Steam Nozzle Condensation. Nature Physical Science140, 167 (1972).
Bartlmä, F.: Instationäre Strömungsvorgänge bei Überschreiten der kritischen Wärmezufuhr. Z. Flugwissenschaften11, 160 (1963).
Bartlmä, F.: Ebene Überschallströmung mit Relaxation. Appl. Mech. Proc. 11th Int. Congr., Munich, p. 1056 (1964).
Becker, E.: Chemically Reacting Flows. Ann. Rev. Fluid Mech.4, 155 (1972).
Becker, R., andW. Döring: Kinetische Behandlung der Keimbildung in übersättigten Dämpfen. Ann. Physik24, 719 (1935).
Blythe, P. A., andC. J. Shih: Weak Condensation Shocks and the High Activation Limit. Tech. Report No. CAM-110-26 (BRL CR NO. 90) (1973). (Available as AD-758277 from the National Technical Information Service, Springfield, Va. 22151.)
Bray, K. N. C.: Atomic Recombination in a Hypersonic Wind-Tunnel Nozzle. J. Fluid Mech.6, 1 (1959).
Brodkey, R. S.: The Phenomena of Fluid Motions. Reading, Mass.: Addison-Wesley Publishing Co. 1967.
Broer, L. J. F.: On the Influence of Acoustic Relaxation on Compressible Flow. Appl. Sci. Res.A 2, 447 (1951).
Buhler, R. D.: Condensation of Air Components in Hypersonic Wind Tunnels. Theoretical Calculations and Comparison with Experiment. Doctoral Dissertation, California Institute of Technology, Pasadena, California (1952).
Burgers, J. M.: Address at the Dedication of the Naval Ordnance Laboratory, Aeroballistic Research Facilities. U.S. Naval Ordnance Report 1130, p. 20 (1949).
Busemann, A.: Private communication March 19, 1971, and discussion with author November 1972.
Cagliostro, D. J.: Periodic Compressible Nozzle Flow Caused by Heat Addition due to Condensation. Doctoral Dissertation, Yale University, New Haven, Connecticut (1972).
Charyk, J. F.: Condensation Phenomena in Supersonic Flows. Doctoral Dissertation, California Institute of Technology, Pasadena, California (1946).
Clumpner, J. A.: Light Scattering from Ethyl Alcohol Droplets Formed by Homogeneous Nucleation. J. Chem. Phys.55, 5042 (1971).
Courant, R., andK. O. Friedrichs: Supersonic Flow and Shock Waves. New York: Interscience. 1948.
Daum, F. L., andG. Gyarmathy: Condensation of Air and Nitrogen in Hypersonic Wind Tunnels. AIAA J.6, 458 (1968).
Davydov, L. M.: Study of Nonequilibrium Condensation in Supersonic Nozzles and Jets. Mekhanika Zhidkosti i Gaza3, 66 (1971). Also Fluid Mechanics (Soviet Research)1, 90 (1972).
Deych, M. Ye., G. A. Saltanov, V. F. Stepanchuk, andV. M. Orlova: Study of Energy Losses in Condensation Discontinuities and Shocks in Flow of Wet Steam. Energetika i Transport5, 93 (1968). Also Heat Transfer (Soviet Research)1, 135 (1969).
Deych, M. Ye., G. A. Kurshakov, G. A. Saltanov, andI. A. Yatcheni: A Study of the Structure of Two-Phase Flow Behind a Condensation Shock in Supersonic Nozzles. Energetika i Transport2 (1968). Also Heat Transfer (Soviet Research)1, 95 (1969).
Dunning, W. J.: General and Theoretical Introduction, Chap. 1, p. 1, l.c. [100].Zettlemoyer, A. C.: Ed., Nucleation. New York: Marcel Dekker. 1969.
Eber, G: Private communication September 4, 1972.
Eber, G., andK. H. Gruenewald: Schlieren-Photography of Condensation Disturbances in the 40×40 cm Peenemünde Supersonic Wind Tunnels. Private Communication (1941/42).
Feder, J., K. C. Russell, J. Lothe, andG. M. Pound: Homogeneous Nucleation and Growth of Droplets in Vapors. Adv. Phys. (Suppl. Phil. Mag.)15, 111 (1966).
Glass, I. I., andG. N. Patterson: A Theoretical and Experimental Study of Shock Tube Flows, J. Aeronaut, Sci.22, 73 (1955). Also Private communication to Heybey and Reed (1955).
Gyarmathy, G.: Kondensationsstoß-Diagramme für Wasserdampfströmungen. Forsch. Ing. Wes.29, 105 (1963).
Gyarmathy, G., andH. Meyer: Spontane Kondensation (VDI Forsch.-Heft 508). Düsseldorf: VDI Verlag. 1965.
Hall, N. A.: Thermodynamics of Fluid Flow. New York: Prentice Hall. 1951.
Hermann, R.: Der Kondensationsstoß in Überschall-Windkanaldüsen. Luftfahrtforsch.19, 183 (1942).
Heybey, W.: Analytische Behandlung des geraden Kondensationsstoßes. Heeresversuchsstelle Peenemünde, Archiv. Nr. 66/72 (1942). Also: NACA TM 1174 (1947).
Heybey, W.: Private communications October 31 and December 9, 1972.
Heybey, W. H., andS. G. Reed, Jr. Weak Detonations and Condensation Shocks. J. Appl. Phys.26, 969 (1955).
Hill, P. G.: Condensation of Water Vapor During Supersonic Expansion in Nozzles. J. Fluid Mech.25, 593 (1966).
Homer, J. B., I. R. Hurle, andP. J. Swain: Shock-Tube Study of the Nucleation of Lead Vapour. Nature229, 251 (1971).
Homer, J. B., andI. R. Hurle: Shock-Tube Studies on the Decomposition of Tetramethyl-Lead and the Formation of Lead Oxide Particles. Proc. R. Soc. Lond.A 327 61 (1972).
Jungclaus, G., andO. van Raay: Brechnung der Strömung in Lavaldüsen mit beliebig verteilter Wärmezufuhr. Ing. Arch.36, 226 (1967).
Kawada, H., andY. Mori: A Shock Tube Study of Condensation Kinetics. Bull. Jap. Soc. Mech. Eng.16, 1053 (1973).
Kung, R. T. V., andS. H. Bauer: Nucleation Rates in Fe Vapor: Condensation to Liquid in Shock Tube Flow. Proc. Eighth Int. Shock Tube Symp. London, Paper No 61. (Stollery, J. L., A. G. Gaydon, andP. R. Owen, eds.). London: Chapman and Hall. 1971.
Kyrchakov, A. V., G. A. Saltanov, andR. A. Tkalenko: Analytical and Experimental Analysis of Condensation in a Centered Rarefaction Wave (in Russian), P.M.T.F. No. 5, 117 (1971).
Lee, J. H., R. I. Soloukhin andA. K. Oppenheim: Current Views on Gaseous Detonation. Astronautica Acta14, 565 (1969).
Liepmann, H. W., andA. Roshko: Elements of Gasdynamics. New York: J. Wiley. 1957.
Lothe, J., andG. M. Pound: Statistical Mechanics of Nucleation. Chap. 3, p. 109, l.c. [100].Zettlemoyer, A. C.: Ed., Nucleation. New York: Marcel Dekker. 1969.
Lukasiewicz, J., andJ. K. Royle: Effects of Air Humidity in Supersonic Wind Tunnels. Aeronaut. Res. Council, Repts. and Mem. No. 2563 (1948).
Marble, F. E.: Some Gasdynamic Problems in the Flow of Condensing Vapors. Astronautica Acta14, 585 (1969).
Marble, F. E.: Dynamics of Dusty Gases. Ann. Rev. Fluid Mech.2, 397 (1970).
Oppenheim, A. K., E. A. Lundstrom, A. L. Kuhl, andM. M. Kamel: A Systematic Exposition of the Conservation Equations for Blast Waves. Trans. ASME, J. Appl. Mech. Ser. E,38, 783 (1971).
Oswatitsch, K.: Die Dispersion und Absorption des Schalles in Wolken. Phys. Z.42 365 (1941).
Oswatitsch, K.: Die Nebelbildung in Windkanälen und ihr Einfluß auf Modellversuche. Jahrbuch der deutschen Luftfahrtforsch. I, 692 (1941).
Oswatitsch, K.: Kondensationserscheinungen in Überschalldüsen. ZAMM22, 1 (1942).
Oswatitsch, K.: Kondensationsstöße in Lavaldüsen. Z. Ver. deutsch. Ing.86, 702 (1942).
Oswatitsch, K.: Gasdynamik. Wien: Springer. 1952.
Oswatitsch, K.: Private communication June 15, 1970.
Penner, S. S., andF. A. Williams: Detonation and Two-Phase Flow. Progress Astron. Aero.6. New York: Academic Press. 1962.
Petty, D. G., P. A. Blythe, andC. J. Shih: Near-equilibrium Nozzle Flows of a Condensible Vapor. Tech. Report No. CAM-110-25 (BRL CR NO. 85). (1972) (Available as AD-756471 from the National Technical Information Service, Springfield, VA 22151.)
Pierce, T., P. M. Shermann, D. D. McBride: Condensation of Argon in a Supersonic Stream. Astronautica Acta16, 1 (1971).
Pouring, A. A.: Thermal Choking and Condensation in Nozzles. Phys. Fluids8, 1802 (1965).
Reed, Jr., S. G.: Some Examples of Weak Detonations. J. Chem. Phys.20, 539 (1952).
Roberts, R.: A Light Scattering Investigation of Droplet Growth in Nozzle Condensation. Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, Mass. (1969).
Ross, F. W.: Propagation in a Compressible Fluid of Finite Oblique Disturbances with Energy Exchange and Change of State. J. Appl. Phys.22, 1414 (1951).
Rott, N., B. Chaix, andZ. Plaskowski: Ein Diagramm zur Beurteilung der Feuchtigkeits-Verhältnisse in rascher Luftströmung. Schweiz. Bauzeitung66 (1948).
Rudinger, G.: Relaxation in Gas-Particle Flow, Nonequilibrium Flows (Wegener, P. P., ed.), Vol. 1, Part1, p. 119. New York: Marcel Dekker. 1969.
Samaras, D. G.: The Problem of Heat Addition in Ducts. Can. J. Res.24, 272 (1946).
Schmidt, B.: Beobachtungen über das Verhalten der durch Wasserdampfkondensation ausgelösten Störungen in einer Überschall-Windkanaldüse. Jahrbuch WGLR, 160 (1962).
Shapiro, A.: The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. I. New York: Ronald Press Co. 1953.
Shapiro, A. H., andW. R. Hawthorne: The Mechanics and Thermodynamics of Steady One-Dimensional Gas Flow. J. Appl. Mech.14, A317 (1947).
Smith, L. T.: An Experimental Investigation of Two Phase Wedge and Prandtl-Meyer Flow. Doctoral Dissertation, Yale University, New Haven, Conn. (1970).
Smith, L. T.: Experimental Investigation of the Expansion of Moist Air Around a Sharp Corner. AIAA J.9, 2035 (1971).
Soo, S. L.: Fluid Dynamics of Multiphase Systems. Waltham, Mass.: Blaisdell Publishing Co. 1967.
Steffen, H. H.: Theoretical and Experimental Investigation of Two-Dimensional Flow Around a Corner with Heat Addition. (Strömungsmechanik und Strömungsmaschinen, Heft 6, S. 40.) Karlsruhe: Verlag G. Braun. 1967.
Stein, G. D., andP. P. Wegener: Experiments on the Number of Particles Formed by Homogeneous Nucleation in the Vapor Phase. J. Chem. Phys.46, 3685 (1967).
Stein, G. D.: Angular and Wavelength Dependence of the Light Scattered from a Cloud of Particles Formed by Homogeneous Nucleation. J. Chem. Phys.51, 938 (1969).
Stever, H. G.: Condensation Phenomena in High Speed Flows, Fundamentals of Gasdynamics, Vol. III (Emmons, H. W., ed.), p. 526. Princeton, N. J.: Princeton University Press. 1958.
Stodola, A.: Steam and Gas Turbines. New York: McGraw-Hill. 1927.
Szczeniowski, B.: Flow of Gas Through a Tube of Constant Cross-Section with Heat Exchange Through the Tube Walls. Can. J. Res.23, 1 (1945).
Taylor, G. I.: Pitot Pressures in Moist Air. Aero. Res. Counc., Tech. Rep. for the year 1945, Reports and Memoranda No. 2248, p 180, London 1955.
Thomann, H.: Size of Ice Crystals Formed During Rapid Expansions of Humid Air. Phys. Fluids9, 896 (1966).
Tkalenko, R. A.: On Spontaneous Condensation in a Supersonic Flow Around a Corner (in Russian). Mechanika Zhyidkosti i Gasa, No. 5, 73 (1970).
Volmer, M., andA. Weber: Keimbildung in übersättigten Gebilden. Z. Phys. Chem.119, 277 (1926).
Volta Reale Accademia D'Italia, Fondazione Alessandro Volta. Atti dei Convegni 5. Le Alte Velocita in Aviazone. 30 Sept. to 6 Oct. 1935—XIII, Roma. 1st ed. 1936-XIV; 2nd ed., 1940-XIX (1935).
Wegener, P. P., andG. Lundquist: Condensation of Water Vapor in the Shock Tube Below 150°K. J. Appl. Phys.22, 233 (1951).
Wegener, P. P.: Water Vapor Condensation Process in Supersonic Nozzles. J. Appl. Phys.25, 1485 (1954).
Wegener, P. P. andL. M. Mack: Condensation in Supersonic and Hypersonic Wind Tunnels. Adv. Appl. Mech.5 p. 307. New York: Academic Press. 1958.
Wegener, P. P.: Experiments on the Departure From Chemical Equilibrium in a Supersonic Flow. ARS J.30, 322 (1960).
Wegener, P. P.: Condensation Phenomena in Nozzles, Progress Astron. Aero.15, 701. New York: Academic Press. 1964.
Wegener, P. P., andA. A. Pouring: Experiments on Condensation of Water Vapor by Homogeneous Nucleation in Nozzles. Phys. Fluids7, 352 (1964).
Wegener, P. P.: Gasdynamics of Expansion Flows with Condensation, and Homogeneous Nucleation of Water Vapor. Nonequilibrium Flows (Wegener, P. P., ed.), Vol. 1, Part 1, p. 163. New York: Marcel Dekker. 1969.
Wegener, P. P., andJ.-Y. Parlange: Condensation by Homogeneous Nucleation in the Vapor Phase. Naturwissenschaften57, 525 (1970).
Wegener, P. P., J. A. Clumpner, andB. J. C. Wu: Homogeneous Nucleation and Growth of Ethanol Drops in Supersonic Flow. Phys. Fluids15, 1869 (1972).
Wegener, P. P., andD. J. Cagliostro: Periodic Nozzle Flow with Heat Addition. Combustion Sci. and Tech.6, 269 (1973).
Willmarth, W. W., andH. T. Nagamatsu: The Condensation of Nitrogen in a Hypersonic Nozzle. J. Appl. Phys.23, 1089 (1952).
Wilson, C. T. R.: Condensation of Water Vapor in the Presence of Dust-Free Air and Other Gases, Trans. Roy. Soc. (London)189, 265 (1897).
Zettlemoyer, A. C.: Ed., Nucleation. New York: Marcel Dekker. 1969.
Zierep, J., andS. Lin: Ein Ähnlichkeitsgesetz für instationäre Kondensationsvorgänge in Lavaldüsen. Forsch. Ing. Wesen34, 97 (1968).
Zimet, E.: Yale University, Private Communication (1971).
Author information
Authors and Affiliations
Additional information
With 15 Figures
Rights and permissions
About this article
Cite this article
Wegener, P.P. Nonequilibrium flow with condensation. Acta Mechanica 21, 65–91 (1975). https://doi.org/10.1007/BF01172829
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01172829