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Effect of thermal radiation on the propagation of plane acoustic waves

Published online by Cambridge University Press:  28 March 2006

Walter G. Vincenti  and
Barrett S. Baldwin
Walter G. Vincenti
Affiliation:
Department of Aeronautical Engineering, Stanford University, Stanford, California
Barrett S. Baldwin
Affiliation:
Department of Aeronautical Engineering, Stanford University and Ames Research Center, NASA, Moffett Field, California
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Abstract

A study is made of the propagation of acoustic waves in a semi-infinite expanse of radiating gas on one side of an infinite, plane, radiating wall. A solution is found, in particular, for the case of sinusoidal oscillations in both position and temperature of the wall. The solution is based on a single linear integro-differential equation that plays the same role here as does the classical wave equation in equilibrium acoustic theory. The solution is applicable throughout the range from a completely transparent to a completely opaque gas and from very low to very high temperatures. The solution appears, in general, as the sum of two types of travelling waves: (1) an essentially classical sound-wave, but with a slightly altered speed and a small amount of damping and (2) a radiation-induced wave whose speed and damping may be either large or small, depending on the temperature and absorptivity of the gas. Since the waves are coupled, both types will usually be present together, even in the special cases of pure motion or pure temperature variation of the wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 12 , Issue 3 , March 1962 , pp. 449 - 477
Copyright
© 1962 Cambridge University Press

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References

Adrianov, V. N. & Shorin, S. N. 1958 Radiant heat transfer in the flow of a radiating medium. Isvest. Akad. Nauk SSSR, O.T.N. 5, 46 (in Russian).Google Scholar
Broer, L. J. F. 1958 Characteristics of the equations of motion of a reacting gas. J. Fluid Mech. 4, 276.Google Scholar
Chandrasekhar, S. 1950 Radiative Transfer. Oxford University Press.
Clarke, J. F. 1958 The flow of chemically reacting gas mixtures. College of Aeronautics, Cranfield, Rep. no. 117.Google Scholar
Deresiewicz, H. 1957 Plane waves in a thermoelastic solid. J. Acoust. Soc. Amer. 29, 204.Google Scholar
Goulard, R. 1959a The coupling of radiation and convection in detached shock layers. Bendix Products Div., Appl. Sci. Lab., South Bend, Indiana.
Goulard, R. 1959b Fluxes and non-dimensional parameters in radiant gases. Purdue Univ. Rep. no. A-59–8.Google Scholar
Goulard, R. & Goulard, M. 1959 Energy transfer in the Couette flow of a radiant and chemically reacting gas. Heat Trans. and Fluid Mech. Inst., Stanford University Press.
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. New York: Wiley.
Kourganoff, V. 1952 Basic Methods in Transfer Problems. Oxford University Press.
Lighthill, M. J. 1960 Dynamics of a dissociating gas. Part 2. Quasi-equilibrium transfer theory. J. Fluid Mech. 8, 161.Google Scholar
Moore, F. K. 1958 Propagation of weak waves in a dissociated gas. J. Aero. Sci. 25, 279.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York: McGraw-Hill.
Prokofyev, V. A. 1957 Weak waves in a compressible fluid with radiation effects. Prikl. Mat. i Mekh. 21, 775 (in Russian).Google Scholar
Prokofyev, V. A. 1960 Propagation of forced plane compression waves of small amplitude in a viscous gas when radiation is taken into account. Isvest. Akad. Nauk SSSR, Mekh. i Mash. 2, 17 (in Russian). (Available as trans. in ARS J., Russian Suppl., 1961, 31, 988.)Google Scholar
Rayleigh, Lord 1945 Theory of Sound, 2nd ed. New York: Dover Publications.
Rosseland, S. 1936 Theoretical Astrophysics. Oxford University Press.
Stokes, G. G. 1851 An examination of the possible effect of the radiation of heat on the propagation of sound. Phil. Mag. 1, 305.Google Scholar
Tellep, D. M. & Edwards, D. K. 1960 Radiant-energy transfer in gaseous flows. Lockheed Missiles and Space Div. Rep. no. LMSD-288203.Google Scholar
Truesdell, C. 1953 Precise theory of the absorption and dispersion of forced plane infinitesimal waves according to the Navier-Stokes equations. J. Rat. Mech. Anal. 2, 643.Google Scholar
Unsöld, A. 1955 Physik der Sternatmosphären. Berlin: Springer.
Vincenti, W. G. 1959 Non-equilibrium flow over a wavy wall. J. Fluid Mech. 6, 481.Google Scholar