Stagnation-point convective heat transfer in frozen boundary layers.

Abstract

An experimental investigation of the heat transfer to surfaces having widely differing catalytic activity in dissociated and partially ionized flows is described. The theory of Goulard is used to show that large deviations in heating rate from the fully catalytic prediction can occur when the product of the body nose radius and stagnation-point pressure (Rp s ) is small. The experimental data agree with Goulard's theory for dissociated flows when the boundarylayer properties and surface catalytic activity are known. Heating-rate measurements in dissociated flows are used with the theory to estimate the catalytic activity of eight surfaces in both nitrogen and air. Heating-rate measurements obtained in partially ionized flows were below those predicted by Fay and Kemp for an equilibrium boundary layer and for a fully catalytic surface in a frozen boundary layer. A theory is not presently available for heat transfer to finite catalytic or noncatalytic surfaces in nonequilibrium ionized flows. NomenclatureA = area of test model surface on which heating rates were measured, m 2 c p -specific heat at constant pressure, Mjoule/kg °K H = total enthalpy (u m 2 /2) + h, Mjoule/kg /* T h = static enthalpy, I c p dT + ahip + cfo 0 J o &D° = dissociation energy, Mjoule/kg /i/° = ionization energy, Mjoule/kg K = constant in Eq. (9) k w -catalytic reaction rate constant, cm/sec Le = Lewis number M = Mach number m = molecular weight of gas mixture, g/mole ra 0 = molecular weight of undissociated gas, g/mole p = pressure, atm q = heat-transfer rate to surf ace, kW/m 2 R = body nose radius, cm or m /£ eff = effective body nose radius, cm or m (R = universal gas constant n = base radius of body, cm or m Sc = Schmidt number T = temperature, °K u = velocity, m/sec Z = compressibility factor, 1 + a. OL = fraction of molecules dissociated 7 = isentropic exponent j w = recombination efficiency e = fraction of atoms ionized M = viscosity, g/cm sec p = density, g/cm 3 <T = Prandtl number () = average value Subscripts e = boundary-layer edge fc = fully catalytic nc = noncatalytic s = stagnation point W = wall oo = freestream

Recasting the Fay-Riddell formulae for computing the stagnation point heat flux

“…Data obtained by the silver slug calorimeter are higher than those obtained by the Gardon gauge. This agrees with the analysis by Pope [10]; i.e. a silver calorimeter involves a higher catalytic level and, therefore, higher heat fluxes in comparison with a constantan gauge (here called the Gardon gauge).…”

“…The dissociation and vibration Damkoeler numbers, both for tests in air and in nitrogen, are of the order of 10 À4 ; gas in the HEBDAF can be considered to be frozen. Extending, approximately, the report by Pope [10] to the HEBDAF tests, copper and nickel involve a very low catalytic level.…”

A new concept of heat-flux probe for the Scirocco Plasma Wind Tunnel

“…For this reason we must correct the value of the slug, by means of an equivalent radius of curvature. In literature the issue has been studied by [3] and [4].…”

“…In particular in [3] it is obtained an equivalence, in terms of stagnation point heat flux, between a flat faced probe and a spherical faced probe, as The values that were measured are affected by uncertainties of measurement. The uncertainty in the assessment of heat flow of the slug, neglecting at first analysis the density and the specific heat, (as they are constants given with extreme accuracy in the literature), can be derived estimating the uncertainties on "l" and on "∆T/∆t".…”

Effects of freestream nonequilibrium on convective heat transfer to a blunt body

“…It is well known that the heat transfer to a solid surface is extremely sensitive to the wall catalycity, provided that the flow is in a nonequilibrium state and it includes dissociated atoms. 13 ' 14 Catalytic wall boundary conditions are obtained by balancing the mass flux of species with the chemical rate of production or depletion caused by surface reactions. For an impermeable wall, this balance is described by…”