Spherical expansion of a binary gas mixture into a flooded space

Abstract

i0. J. P. Parker,"Rotational and vibrational relaxation in diatomic gases," Phys. Fluids, 2, No. 4 (1959). ii. C. F. Hansen and W. E. Pearson, "Three-dimensional model of collision-induced vibra- tional transitions in homonuclear diatomic molecules," J. Chem. Phys., 53, No. 9 (1970) o 12. E.H. Carnevale, C. Carey, and G. Larson, "Ultrasonic determination of rotational colli- sion numbers and vibrational relaxation times of poiyatomic gases at high temperatures, ~' J. Chem. Phys., 47, No. 8 (1967). SPHERICAL EXPANSION OF A BINARY GAS MIXTURE INTO A FLOODED SPACE V. N. Gusev and V. V. Ryabov UDC 533.6.011,,8:532.525.2 INTRODUT ION An increasing interest in the study of jet flows in connection with their possible use in the separation of isotopes or gas mixtures has recently been noted. Direct observations of the separation of mixtures during the penetration of the ambient gas into the jet (see [I], for example) serve as the basis for this. One-dimensional flow from a source can become a good theoretical model for the study of separation processes in jet flows. The properties of the spherical expansion of a viscous heat-conducting gas into a flooded space have been studied in detail on the example of this flow using the Navier--Stokes equations (see the bibliography of [2]). In the investigation of separation effects one must allow for diffusional processes in addition to viscosity and heat conduction. In theoretical investigations great attention has been paid to this ques- tion in the study of the structure of a piane shock wave in a binary gas mixture. The pres- ent investigation was undertaken for the purpose of clarifying the role of diffusional pro- cesses in one-dimensional flow from a spherical source. The spherical shock wave, in which the complete separation of the components of a mixture is possible in the presence of a small counterpressure, as shown in the report, is studied in detail. Asymptotic solutions are obtained in the transonic and hypersonic regions of flow. The results of n~unerical cal~ culations are presented for argon-helium mixtures at different initial concentrations. w Let us consider the established supersonic flow of a gas mixture escaping from a spherical source of radius n, with the velocity of sound (Mach number M, = i) into a space with a constant pressure p=. The flow will occur along radii from points of the sphere with the center at the origin of coordinates and will consist of two regions, inner supersonic (r, < r < r+) and outer subsonic, separated by some transitional region. In the case of an ideal gas the flow is described by the Euler equations and r+ is the coordinate of the shock wave; in the presence of viscosity r+ is the coordinate where the flow parameters are extre- mal. Following [3], we write the system of one-dimensional Navier--Stokes equations for a one- temperature gas mixture in the case of spherical symmetry: