The Thermal Rayleigh Problem in Perfect and Ionized Gases

Citation

Navarro-Cantero, Carlos (1967) The Thermal Rayleigh Problem in Perfect and Ionized Gases. Engineer's thesis, California Institute of Technology. doi:10.7907/X3H0-7367. https://resolver.caltech.edu/CaltechETD:etd-11152005-135817

Abstract

The problem of a heated gas at rest in contact with a cold wall has applications in shock tubes when a shock wave reflects at the end wall. A boundary layer arises that can be solved for constant conditions outside the boundary layer. In this paper, this condition is relaxed and the gas is permitted to undergo variations of pressure. The equation has been derived for the boundary layer under those conditions, and a similarity solution was found for isentropic variations of a perfect gas outside the boundary layer. This solution is only valid for a temperature of the gas much greater than the temperature of the wall, unless the latter would follow a determined variation with time. Two cases were studied; one with thermal conductivity of the gas proportional to a power of the temperature, and the other with conductivity proportional to temperature. In the first case, an integral method has to be used, which gives an excellent approximation. For the second case, the solution is worked out either by similarity procedures or by series expansions. Heat transfer and temperature in the boundary layer are seen to depend on the pressure, which acts like a weighting factor on time. For ionized gases, two cases were considered; frozen and equilibrium flow. Similarity solutions do not exist for variable pressure outside the boundary layer unless the variations of pressure with time are small enough. In this case, pressure acts again like a weighting factor on time, although the variations outside the boundary layer cannot be assumed isentropic anymore. At the same time, new equations for the equilibrium boundary layer were derived, in which the excited state of ions and atoms is taken into account. The effect of the weighting factor of the pressure is applied to explain the experimental results obtained at the end wall of a shock tube, giving explanation to certain differences between experiment and theory.

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