A further note on shock-tube measurements of end-wall radiative heattransfer in air

Abstract

Fig. 2 Upwash interference at the plane of wing in rectangular tunnels with solid side walls of eight-to-width ratio 0.667. and (3). At the plane of the wing, x = y = z = 0, the expression may be simplified to = (sT k /2bh){Re(k) (15) yhere Be(k) = J7i»(*) = -+ + X + '} n-l L-i(2nk) = Modified Struve functionThe real and imaginary parts of the upwash interference relationship, Eq. (15), are plotted against reduced frequency for tunnels of height-to-width ratio X = 0.667 in Fig. 2. The results of the static case derived in Ref. 1 may be obtained by taking the limit k -> 0 in Eq. (15). Concluding RemarksResults are given here for incompressible flow and all frequencies; however, they may be used for low frequencies in subsonic compressible flow with a minor modification, as in Eq. (5). All results are obtained for a small-wing model on the centerline of the tunnel. The expression for a model with an off-centerline position may be derived in a similar manner. Within the assumptions of linearized theory, solutions of any wing configuration may be obtained by superposition since it may be regarded as made up of "small wings/ 7 that is, lifting elements of area. The over-all corrections to forces and moments in wind tunnels as for general wings may be calculated 7 by the utilization of the upwash interference.By examining the curves of the exact solutions given here, the validity of the approximation solution 2 in a power series of frequency up to the first order is within a rather narrow range of small values frequency, if the solution is extended to a slotted-wall tunnel.The present results for slotted-wall tunnels provide information that will assist in choosing a tunnel wall configuration. For example, the optimum slot parameter of a circular cross section is about P = 0.6 from Fig. 1. For rectangular tunnel of height-to-width rat'o of 0.667 (Fig. 2), the optimum slot parameter s in the range of 0.4 <P h < 0.6. S HOCK-tube measurements of the end-wall radiative heat transfer behind reflected shock waves in air have been previously reported in Ref. 1. These measurements were carried out at an initial shock-tube driven pressure of 1 mm Hg and at shock velocities ranging from 6.5 to 9.5 km/sec. A thinfilm heat-transfer gage mounted behind a sapphire window located in the end wall of an arc-driven shock tube was used to measure the radiation in the wavelength region 0.17-6 /z. In Ref. 1, comparisons were made between the experimental data and end-wall heat-transfer predictions based upon numerical solutions for the flowfield behind reflected shock waves in air. These equilibrium air solutions used several different models to account for radiative emission and absorption. Included were models for a gray gas as well as for a nongray gas. In the latter case, a two-step absorption co-