An experimental investigation of heat transfer from a highly cooled turbulent boundary layer.

Abstract

Shock-tube measurements of turbulent heat transfer in supersonic, dissociated air and in the presence of a zero pressure gradient are presented for incident shock velocities from 3 to 6 mm//zsec and initial driven tube pressures of 5, 8, 10, and 20 mm Hg. These data were obtained using platinum calorimeter gages positioned on the inside surface of a sharp leadingedge hollow cylinder with its axis aligned parallel to the frees tream flow. The range of conditions included Reynolds numbers from approximately 10 5 to 1.4 X 10 6 , total enthalpies simulating flight velocities up to 8 km/sec, and wall-to-adiabatic-wall enthalpy ratios from 0.01 to 0.04. Two-dimensional roughness elements were used to trip the boundary layer. The data obtained are compared with a number of existing techniques for the prediction of turbulent heating. Although the data was obtained at conditions outside of the range on which the method of Spalding and Chi is based, reasonable agreement with this method is shown to exist. Comparisons of existing methods of prediction are also made with other experimental data available from the literature. Nomenclature Cf= skin-friction coefficient Cfi = skin-friction coefficient for incompressible flow c/o = skin-friction coefficient for compressible flow with zero dissociation C H = Stanton number Fc, FR = correlation parameters of Spalding and Chi, Eqs.(6) and (7) h = static enthalpy M = Mach number PI = initial shock-tube driven pressure q -surface heat-transfer rate Re' = Reynolds number per unit length based on local freestream conditions, p e u e /^e Re x = Reynolds number based on local freestream conditions and the effective x distance, p e u e x/ij,e Ree = Reynolds number based on momentum thickness and local freestream conditions, p e u<@/v e (R = ratio of incident normal shock chemical relaxation time to the available test time T = gas temperature u -flow velocity in streamwise direction U 8 = incident shock-wave velocity x = effective streamwise distance; either measured from leading edge or from boundary-layer trip as noted a = percent dissociation, atom mass fraction fj, = gas viscosity p = gas density T C =F characteristic chemical reaction time Tf = characteristic flow residence time (u e /x}~1 Subscripts aw = adiabatic wall condition e = local condition at edge of boundary layer Presented as Paper 68-43 at the AIAA 6th Aerospace Sciences

A Comparison of Four Simple Calculation Methods for the Compressible Turbulent Boundary Layer on a Flat Plate

“…For the conditions of the tests of Ref. 6, the Eckert and phi-methods give the largest estimates, with Eckert's method giving a slightly higher estimate than the pfi-method. The adiabatic wall reference enthalpy method gives the next lowest estimate, and finally the Spalding and Chi method gives the lowest.…”