Theory of stagnation-point heat transfer in a partially ionized diatomic gas

Abstract

Stagnation-point heat transfer in a partially ionized diatomic gas is considered. The concept of frozen thermal conductivity is used, and a simplified "binary diffusion" model of the gas is proposed. In this model the charge-exchange cross-section for atom-ion collisions is taken t,-be infinite so there is no relative diffusion of the atoms and the ionelectron pairs. This permits the diffusion effects to be dealt with as if there were only two components, molecules and atom-ion-electron particles, and thus greatly simplifies the calculations. However, the thermodynamic and transport properties are evaluated using all four components, molecules, atoms, ions, and electrons. With this model, calculations are made for both frozen and equilibrium boundary layers in nitrogen up to about 60, 000 ft/sec, and arguments are presented for applying the resalts to air. The results show the equilibrium heat transfer rate to be progressively smaller than the frozen rate as the velocity increases above 30, 000 ft/sec, the ratio reaching Z/3 at 50, 000 ft/sec.Simple correlation formulas for the results are given.

Stagnation point heat transfer measurements in partially ionized air

“…The atom concentration peaks in the middle of the boundary layer and the molecule concentration starts to build up deep in the boundary layer as the atom concentration starts to decrease. (31) The result of combining these concentrations with the binary diffusion model is that as there are no molecules in the boundary layer in places where there are ions, and thus there is no diffusion between ions and molecules; consequently, no ionization energy can diffuse to the wall.…”

“…(31) Both equilibrium and frozen boundary layer calculations for nitrogen as the working fluid are shown for comparison with the data. The transport properties of nitrogen were expressed as simple functions of temperature and concentrations, as discussed in references (31) and (32). The data appear to follow the theoretical predictions in a general way.…”

Aerothermodynamic Analysis for Axisymmetric Projectiles at Supersonic/Hypersonic Speeds

“…Heat transfer rates at the stagnation point on a blunt-nose projectile are calculated using correlation formulae for a gas in chemical equilibrium. These formulae are given by Fancett 38 based on the work of Fay and Kemp 39 . In this formula the stagnation point heat transfer rate q n (kW/m 2 ) is computed from the freestream velocity V∞ (m/sec), the normal shock stagnation pressure p tn (atm), and the nose radius r n (cm).…”

High Enthalpy Hypersonic Boundary-Layer Flow

“…The integral transformations used were In modern high enthalpy boundary layer problems, the major interest is in heat transfer. With this in mind, Fay and Kemp (1963) suggested that the use of a density-thermal conductivity product is more appropriately used in the transformed equations of motion than the density-viscosity product.…”

“…The viscosity was calculated using Sutherland's formula. Fay and Kemp (1963) extended the work of Fay and Riddell to an ionizing diatomic gas. The density-viscosity product was replaced by a density-thermal conductivity product.…”