Element contents
Mach Wave and Acoustical Wave Structure in Nonequilibrium Gas-Particle Flows
Published online by Cambridge University Press: 08 September 2021
Summary
In this Element, the gas-particle flow problem is formulated with momentum and thermal slip that introduces two relaxation times. Starting from acoustical propagation in a medium in equilibrium, the relaxation-wave equation in airfoil coordinates is derived though a Galilean transformation for uniform flow. Steady planar small perturbation supersonic flow is studied in detail according to Whitham's higher-order waves. The signals owing to wall boundary conditions are damped along the frozen-Mach wave, and are both damped and diffusive along an effective-intermediate Mach wave and diffusive along the equilibrium Mach wave where the bulk of the disturbance propagates. The surface pressure coefficient is obtained exactly for small-disturbance theory, but it is considerably simplified for the small particle-to-gas mass loading approximation, equivalent to a simple-wave approximation. Other relaxation-wave problems are discussed. Martian dust-storm properties in terms of gas-particle flow parameters are estimated.
Information
- Type
- Element
- Information
- Online ISBN: 9781108990585Publisher: Cambridge University PressPrint publication: 07 October 2021
References
Ackeret, J. 1925. Luftkrafte auf Flugel, die mit grosserer als Schallgeschwindigkeit bewegt warden. Z. Flugtech. u. Motorluftschiffahrt 16, 72–74 (Transl. in NACA Tech. Memo. 317).Google Scholar
Anderson, T. B., and Jackson, R. 1969. A fluid mechanical description of fluidized beds: Comparison of theory and experiment. Ind. Engng. Chem. Fundam. 8, 137–144.CrossRefGoogle Scholar
Brenan, C. E. 2005. Fundamentals of Multiphase Flow. Cambridge: Cambridge University Press.Google Scholar
Busemann, A. 1935. Aerodynamischer Auftrieb Uberschallgeschwindigkeit. In Atti del Convegno della Fundazione Alessandro Volta. pp. 328–360. (Transl. in British R, T.P. Translation No. 2844).Google Scholar
Carrier, G. F. 1953. Boundary layer problems in applied mechanics. Advances in Applied Mechanics, vol. 3, 1–19 (von Mises, R. and von Kármán, Th, eds.). New York: Academic Press.Google Scholar
Carrier, G. F. 1954. Boundary layer problems in applied mathematics. Comm. Pure Appl. Math. 7, 11–17.Google Scholar
Carslaw, H. S., and Jaeger, J. C. 1948. Operational Methods in Applied Mathematics, 2nd ed. Oxford: Clarendon (New York: Dover, 1963).Google Scholar
Carslaw, H. S., and Jaeger, J. C. 1959. Conduction of Heat in Solids, 2nd ed. Oxford: Clarendon.Google Scholar
Cheng, P. 1965. Study of the flow of a radiating gas by a differential approximation. PhD dissertation, Stanford University.Google Scholar
Chu, B. T. 1957. Wave propagation and the method of characteristics in reacting gas mixtures with applications to hypersonic flow. Brown University, Division of Engineering Report WADC TN-57-213, AD 118350.Google Scholar
Chu, B. T., and Parlange, Y. 1962. A macroscopic theory of two-phase flow with mass, momentum, and energy exchange. Brown University, Division of Engineering Report DA–4761/4.Google Scholar
Culick, F. E. C., and Yang, V. 1992. Prediction of the stability of unsteady motions in solid propellant of rocket motors. Chapter 18 in Nonsteady Burning and Combustion Stability Solid Propellants (L. DeLuca and M. Summerfeld, eds.), Prog. Astron. Aeronau. 143, 719–779.Google Scholar
Erdelyi, A., Magnus, W., Oberthettinger, F., and Tricomi, F. G., eds. 1954. Tables of Integral Transforms, vol. I. Bateman Manuscript Project, California Institute of Technology. New York: McGraw-Hill.Google Scholar
Esposito, F., Colangeli, L., Della Corte, V., Molfese, C., Palumbo, P., Ventura, S., Merrison, J., Nørnberg, P., Rodriguez-Gomez, J. F., Lopez-Moreno, J. J., del Moral, B., Jerónimo, J. M., Morales, R., Battistelli, E., Gueli, S., Paolinetti, R., and International MEDUSA Team. 2011. MEDUSA: Observation of atmospheric dust and water vapor close to the surface of Mars. Mars 6, 1–12. (doi: 10.1555/mars.2011.0001).Google Scholar
Fan, L.-S., and Zhu, C. 1998. Principles of Gas-Solid Flows. Cambridge: Cambridge University Press.Google Scholar
Ganser, G. H., and Drew, D. A. 1987. Nonlinear periodic waves in a two-phase flow model. SIAM J. Appl. Math. 47, 726–736.Google Scholar
Gelder, G. F., Smyers, W. H., and Glahn, U. von. 1956. Experimental droplet impingement on several two-dimensional air-foils with thickness ratios of 6 to 16 percent. NACA TN 3839.Google Scholar
Glauert, H. 1928. The effect of compressibility on the lift of an airfoil. Proc. Roy. Soc. A 118, 113–119.Google Scholar
Glauert, M. 1940. A method of constructing the paths of rain-drops of different diameters moving in the neighborhood of (1) a circular cylinder, and (2) an airfoil, placed in a uniform stream of air; and the determination of deposit of drops on the surface and the percentage of drops caught. British Ministry of Supply, ARC RM 2025.Google Scholar
Guazzelli, E., and Morris, J. F. 2012. A Physical Introduction to Suspension Dynamics. Cambridge: Cambridge University Press.Google Scholar
Hinze, J. O. 1962. Momentum and mechanical-energy balance equations for a flowing homogeneous suspension with slip between the two phases. Appl. Sci. Res. A 11, 33–46.Google Scholar
Hoglund, R. F. 1962. Recent advances in gas-particle nozzle flows. J. American Rocket Soc. 32, 662–671.Google Scholar
Homsy, G. M., El-Kaissy, M. M., and Didwania, A. 1980. Instability waves and the origin of bubbles in fluidized beds. Part II. Comparison with theory. Int. J. Multiphase Flow 6, 305–318.Google Scholar
Jackson, R. 1971. Fluid mechanical theory. In Fluidization (Davidson, J. F. and Harrison, D., eds.). London: Academic Press.Google Scholar
Jackson, R. 2000. The Dynamics of Fluidized Particles. Cambridge: Cambridge University Press.Google Scholar
Kármán, Th. von 1935. The problem of resistance in compressible fluids. In Atti del Convegno della Fundazione Alessandro Volta. 222–277. Also in Collected Works 2, 179–221. London: Butterworth (1956).Google Scholar
Kármán, Th. von 1941. Compressibility effects in aerodynamics. J. Aeron. Sci. 8, 337–356.Google Scholar
Kármán, Th. von 1947a. Sand ripples in the desert. Technicon Yearbook, 52–54. Also in Collected Works 3, 352–356. London: Butterworth (1956).Google Scholar
Kármán, Th. von 1947b. Supersonic aerodynamics: Principles and applications. J. Aeron. Sci. 14, 373–409. Also in Collected Works. London: Butterworth (1956).Google Scholar
Kármán, Th. von 1959. Some significance developments in aerodynamics since 1946. J. Aero/Space Sci. 26, 129–144. Also in Collected Works. London: Butterworth (1956).Google Scholar
Kármán, Th. Von, and Moore, N. B. 1932. Resistance of slender bodies moving with supersonic velocities. Trans .A. S. M. E. 54, 303–310. Also in Collected Works 2, 376–393. London: Butterworth (1956).Google Scholar
Kiely, D. H. 1959. The irreversible thermodynamics of particulate systems. Eng. D. thesis, Yale University.Google Scholar
Kluwick, A. 1983. Small-amplitude finite-rate waves in suspensions of particles in fluids. ZAMM 63, 161–171. (presented at EUROMECH 1944: Mech. Sedimentation and Fluidized Beds. Tech. Univ. Vienna, 1981).Google Scholar
Lagerstrom, P. A. 1996. Laminar Flow Theory. Princeton, NJ: Princeton University Press.Google Scholar
Levine, J. S., and Winterhalter, D., conveners. 2017. Dust in the Atmosphere of Mars and Its Impact on Human Exploration. Lunar Planetary Institute, Houston. L. P. I. Contribution No. 1966, (abstracts in www.hou.usra.edu>meetings>marsdust2017).Google Scholar
Lewis, W., and Brun, R. J. 1956. Impingement of water droplets on a rectangular half-body in a two-dimensional incompressible flow field. NACA TN 3658.Google Scholar
Lighthill, M. J. 1949. A technique for rendering approximate solutions to physical problems uniformly valid. Phil. Mag. 40, 1719–1201. doi: 10.1080/14786444908561410Google Scholar
Lighthill, M. J. 1958. Fournier Analysis and Generalized Functions. Cambridge: Cambridge University Press.Google Scholar
Lighthill, M. J., and Whitham, G. B. 1955. On kinematic waves. I. Flood movement in long rivers. Proc. Roy. Soc. A 229, 281–316.Google Scholar
Liu, J. T. C. 1964. Problems in Particle-Fluid Mechanics, 66–138. Ph.D.Thesis, Pasadena: California Institute of Technology.Google Scholar
Liu, J. T. C. 1965. On the hydrodunamic stability of a parallel dusty gas flow. Phys. Fluids 8, 1939–1945.Google Scholar
Liu, J. T. C. 1966. Flow induced by an oscillating infinite flat plate in a dusty gas. Phys. Fluids 9, 1716–1720.Google Scholar
Liu, J. T. C. 1967. Flow induced by the impulsive motion of an infinite flat plate in a dusty gas. Astronautica Acta 13, 369–377.Google Scholar
Liu, J. T. C. 1981a. Finite-amplitude instabilities in fluidized beds. Abstract in XV Biennial Symposium on Advanced Problems in Fluid Mechanics, 80–81 (Ficzdon, W. and Herczynski, R., eds.). Warsaw: IPPT-PAN.Google Scholar
Liu, J. T. C. 1981b. Finite-amplitude instabilities in fluidized beds. Abstract in EUROMECH 1944: Mech. Sedimentation and Fluidized Beds, 43–44. (Clift, R. and Schneider, W., eds.). Vienna: Technical University of Vienna.Google Scholar
Liu, J. T. C. 1982. Note on a wave-hierarchy interpretation of fluidized bed instabilities. Proc. R. Soc. Lond. A 380, 229–239.Google Scholar
Marble, F. E. 1962. Dynamics of a gas containing small solid particles. In Proc. 5th AGARD Colloquium on Combustion and Propulsion, Braunschweig, 239–270. Oxford: Pergamon.Google Scholar
Marble, F. E. 1963. Nozzle contours for minimum particle-lag loss. AIAA J. 1, 2793–2801.CrossRefGoogle Scholar
Marble, F. E. 1969. Some gas dynamics problems in the flow of condensing vapors. Astron. Acta 14, 585–613.Google Scholar
Marble, F. E. 1970. Dynamics of dusty gases. Ann. Rev. Fluid Mech. 2, 397–446.CrossRefGoogle Scholar
Merrison, J., Jensen, J., Kinch, K., Mugford, R., and Nørnberg, P. 2004. The electrical properties of Mars analogue dust. Planet. Space Sci. 52, 279–290.CrossRefGoogle Scholar
Merrison, J. P., Gunnlaugsson, H. P., Hogg, M. R., Jensen, M., Lykke, J. M., Bo Madsen, M., Nielsen, M. B. Nørnberg, P., Ottosen, T. A., Pedersen, R. T., Pederse, S., and Sørensen, A. V. 2012. Factors affecting the electrification of wind-driven dust studied with laboratory simulations. Planet. Space Sci. 60, 328–335.Google Scholar
Metzger, S. M., Carr, J. R., Johnson, J. R., Parker, T. J., and Lemmon, M. T. 1999. Dust devil vortices seen by the Mars Pathfinder camera. J. Geophys. Res. Lett. 26, 2781–2784.Google Scholar
Michael, D. H. 1964. The stability of plane Poiseuille flow of a dusty gas. J. Fluid Mech. 18, 19–32.Google Scholar
Michael, D. H. 1965. Kelvin–Helmholtz instability of a dusty gas. Proc. Cambridge Phil. Soc. 61, 569–572.Google Scholar
Miles, J. W. 1959. Potential Theory of Unsteady Supersonic Flow. Cambridge: Cambridge University Press.Google Scholar
Miura, H. 1974. Supersonic Flow of a Dusty Gas over a slender wedge. J. Phys. Soc. Jpn. 37, 497–504.Google Scholar
Miura, H., and Glass, I. I. 1986 Oblique shock waves in a dusty gas flow over a wedge. Proc. R. Soc. A 408, 61–78.Google Scholar
Miura, H., and Glass, I. I. 1988 Supersonic expansion of a dusty gas around a sharp corner. Proc. R. Soc. A 415, 91–105.Google Scholar
Moore, F. K., and Gibson, W. E. 1960. Propagation of weak disturbances in a gas subject to relaxation effects. J. Aero/Space Sci. 27, 117–127.Google Scholar
Moroz, V. I., Petroval, E. V., and Ksanfomality, V. 1993. Spectrophotometry of Mars in the KRFM experiment of the Phobos mission: Some properties of the particles of atmospheric aerosols and the surface. Planetary and Space Science 41, 569–585.Google Scholar
Needham, D. J., and Merkin, J. H. 1983. The propagation of a voidage disturbance in a uniformly fluidized bed. J. Fluid Mech. 131, 427–454.Google Scholar
Öpik, E. J. 1962. Atmosphere and surface properties of Mars and Venus. Prog. Aeron. Scis. 1, 261–342. (Singer, S. F., ed.) North Holland, Amsterdam.Google Scholar
Pollack, J. B., Ockert-Ball, M. E., and Shepard, M. K. 1995. Viking lander image analysis of Martian atmosphere dust. J. Geophys. Res. 100 (E3), 5235–5250.Google Scholar
Prandtl, L. 1935 Allgemeine Uberlegungen uber die stromung zusammendruckbarer flussigkeiten. Atti del Covegno della Foundazione Allessandro Volta, 169–197 (Transl. in NACA Tech. Memo 805).Google Scholar
Probstein, R. F. and Fassio, F. 1970. Dusty Hypersonic Flows. AIAA J. 8, 772–779. (doi: 10.2514/3.5755).CrossRefGoogle Scholar
Rannie, W. D. 1962. A perturbation analysis of one-dimensional heterogeneous flow in rocket nozzles. In Progress in Astronautics and Rocketry 6, 117–144 (Penner, S. S. and Williams, F. A., eds.). New York: Academic Press.Google Scholar
Rubinow, S. I., and Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459.Google Scholar
Rudinger, G. 1964. Some properties of shock relaxation in gas flows carrying small particles. Phys. Fluids 7, 658–663.Google Scholar
Saffman, P. G. 1962. On the stability of laminar flow of dusty gas. J. Fluid Mech. 13, 120–128.Google Scholar
Sears, W. R. 1954. Small perturbation theory. In General Theory of High Speed Aerodynamics, 61–121 (Sears, W. R., ed.). Princeton, NJ: Princeton University Press.Google Scholar
Serafini, J. S. 1954. Impingement of water droplets on wedges and double-wedge airfoils at supersonic speeds. NACA Report 1159.Google Scholar
Stokes, G. G. 1851. An examination of the possible effect of the radiation of heat on the propagation of sound. Phil. Mag. 1, 305–317. Also in Math and Phys. Papers 3, 142–154. Cambridge University Press (1901).Google Scholar
Tabakoff, W., and Hussein, M. F. 1971. Trajectories of particles suspended in fluid flow through cascades. J. Aircraft 8, 60–62.Google Scholar
Taylor, G. I. 1940. Notes on possible equipment and technique for experiments on icing of aircraft. Britain, Ministry of Supply, ARC RM 2029.Google Scholar
Tomasko, M. G., Doosa, L. R., Lemmom, M., Smith, P. H., and Wegryn, E. 1999. Properties of dust in Martian atmosphere from images of Mars Pathfinder. J. Geophys. Res. 104, 8987–9008.Google Scholar
Toon, O. B., Pollack, J. B., and Sagan, C. 1977. Mariner 9 spacecraft. Physical properties of the particles comprising the Martian dust storm of 1971–1972. Icarus 30, 663–696.Google Scholar
Torobin, L. B., and Gauvin, W. H. 1959. Fundamental aspect of solid-gas flow. Canadian J. Chem. Eng: Pt. I (August 1959), 121–142; Pt. II (October 1959), 167–176; Pt. III (December 1959), 224–236; Pt. IV (October 1960), 142–153; Pt. V (December 1960) 189–200.Google Scholar
Van Deemter, J. J., and Van der Laan, E. T. 1961. Momentum and energy balances for dispersed two-phase flow. Appl. Sci. Res. A 11, 102–108.Google Scholar
Vincenti, W. G. 1959. Non-equilibrium flow over a wavy wall. J. Fluid Mech. 6, 481–496.Google Scholar
Vincenti, W. G., and Kruger, C. H., Jr. 1965. Introduction to Physical Gas Dynamics. New York: Wiley.Google Scholar
Watson, G. N. 1962. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge: Cambridge University Press.Google Scholar
Wegener, P. P., and Cole, J. D. 1962. Experiments on propagation of weak disturbances in stationary supersonic nozzle flow of chemically reacting gas mixtures. In Eighth Symposium (International) on Combustion. Baltimore: Williams and Wilkins co., pp. 348–359.Google Scholar
Whitham, G. B. 1959. Some comments on wave propagation and shock wave structure with application of magnetohydrodynamics. Comm. Pure Appl. Math. 12, 113–158.Google Scholar
Accessibility standard: Unknown
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
Accessibility compliance for the HTML of this Element is currently unknown
and may be updated in the future.
- 1
- Cited by