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Thermodynamic efficiency of thermoacoustic mixture separation
1.G. W. Swift, “Thermoacoustic engines,” J. Acoust. Soc. Am. 84, 1145–1180 (1988).
2.G. W. Swift and P. S. Spoor, “Thermal diffusion and mixture separation in the acoustic boundary layer,” J. Acoust. Soc. Am. 106, 1794–1800 (1999);
2.G. W. Swift and P. S. Spoor, J. Acoust. Soc. Am. 107, 2299(E) (2000);
2.G. W. Swift and P. S. Spoor, J. Acoust. Soc. Am. 109, 1261(E) (2001).
3.P. S. Spoor and G. W. Swift, “Thermoacoustic separation of a He–Ar mixture,” Phys. Rev. Lett. 85, 1646–1649 (2000).
4.D. A. Geller and G. W. Swift, “Saturation of thermoacoustic mixture separation,” J. Acoust. Soc. Am. 111, 1675–1684 (2002).
5.L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1982), Eq. (57.3).
6.The hydraulic radius of a duct is defined as the ratio of the cross-sectional area to the perimeter. For a right circular cylinder, the hydraulic radius is equal to one half of the cylinder radius.
7.E. J. Watson, “Diffusion in oscillating pipe flow,” J. Fluid Mech. 133, 233–244 (1983).
8.Note that in the above expression, the enter only in ratios. The mass diffusion coefficient the kinematic viscosity ν, and the thermal diffusivity κ are all proportional to and therefore to Furthermore, each of these parameters has approximately the same weak power-law dependence on temperature; in the simplest mean-free-path theory for a dilute gas of rigid spheres, this power law is Thus, ratios of the such as σ and are essentially independent of pressure and roughly independent of temperature in the regime that the gases in the mixture can be considered ideal. See Ref. 23.
9.In general, can be a function of both temperature and pressure. The temperature dependence typically exhibits a maximum value (at fixed pressure), and for the room-temperature He–Ar mixtures of our previous experiments, is 0.8 of its maximum value at atmospheric pressure. The experimentally measured may either increase or decrease with pressure, but this effect is due to the nonidealities in the equations of state of the gases. See K. E. Grew and T. L. Ibbs, Thermal Diffusion in Gases (Cambridge University Press, Cambridge, 1952), Chaps. 4–5. Nonideal gas behavior is beyond the scope of our treatment.
10.N. Rott, “Damped and thermally driven oscillations in wide and narrow tubes,” Z. Angew. Math. Phys. 20, 230–243 (1969), and
10.N. Rott, “Thermally driven oscillations. III. Second-order heat flux,” Z. Angew. Math. Phys. 26, 43–49 (1975).
11.R. Raspet, C. J. Hickey, and J. M. Sabatier, “The effect of evaporation-condensation on sound propagation in cylindrical tubes using the low reduced frequency approximation,” J. Acoust. Soc. Am. 105, 65–73 (1999);
11.W. V. Slaton and R. Raspet, “Wet-walled thermoacoustics,” J. Acoust. Soc. Am. 110, 2677 (2001);
11.William V. Slaton, “Inert gas–vapor mixtures in thermoacoustics,” Ph.D. thesis, University of Mississippi, 2001.
12.A. Bejan, Advanced Engineering Thermodynamics, 2nd ed. (Wiley, New York, 1997).
13.G. W. Swift, Thermoacoustics: A Unifying Perspective for Some Engines and Refrigerators, Chap. 6 (Acoustical Society of America, 2002)
14.This can be found in many introductory thermodynamics texts. For example, see Eqs. (4.128) and (4.139) in Ref. 12.
15.H. London, Separation of Isotopes (Newnes, London, 1961).
16.S. Villani, Isotope Separation (American Nuclear Society, La Grange Park, IL, 1976).
17.Encyclopedia of Separation Technology, edited by D. M. Ruthven (Wiley, New York, 1997), Vol. 1.
18.Gaseous diffusion describes effusion, or the molecular flow of a gas through narrow pores into vacuum. In mass diffusion, the mixture is separated by the difference in the components’ rates of diffusion through a carrier gas (preferably one which is easily stripped from the product). See Ref. 16 for details of these methods.
19.For an account of the theoretical discovery by Enskog and Chapman separately, and the experimental confirmation by Chapman and Dootson, see the review by R. Clark Jones, and W. H. Furry, “The separation of isotopes by thermal diffusion,” Rev. Mod. Phys. 18, 151–224 (1946).
20.K. Clusius and G. Dickel, “Neues Verfahren zur Gasentmischung und Isotopentrennung,” Naturwissenschaften 26, 546(L) (1938).
21.D. Massignon, in Topics in Applied Physics: Uranium Enrichment, edited by S. Villani (Springer, New York, 1979), Vol. 35, pp. 55–56.
22.L. Onsager, “Separation of gas (isotope) mixtures by irreversible processes,” Phys. Rev. 55, 1137(A) (1939).
23.J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
24.Anthony V. Nero, Guidebook to Nuclear Reactors (University of California Press, Berkeley, 1979); see also the Uranium Information Centre at www.uic.com.au.
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