Space-Time Correlation Structure of Hypersonic Boundary Layers

Abstract

A at low speeds, the study of turbulence space-time correlations in hypersonic boundary layers affords a much better description of the flow structure than do single point measurements, from which time autocorrelations are the only means of deducing the turbulence parameters. The geographic features of eddies and their method of convection at low speeds is well understood from the work of Favre.' The only high-speed counterpart of Favre's work can be found in preliminary data reported by Horstman and Owen in transitional boundary layers at Mach 7. The rate of decay and the overall convection speed of turbulence were found unexpectedly low in these tests, especially in view of Favre's earlier results. Since the convection speed is central to the time-space transformation by which turbulence structure is deduced from Eulerian data, a closer second look at the space-time correlations of the hypersonic boundary layer was felt justified. The present experiment was carried out on the test section wall of the 21-in. Hypersonic Wind Tunnel of the Jet Propulsion Laboratory. Edge Mach number Me was 9.37, momentum Reynolds number Re was 36,$00, and the temperature ratio TW/T0 in the steady state was 0.38. The 10-cmthick boundary layer was free of longitudinal and lateral pressure gradients, and had a maximum turbulence Reynolds number of 5,000 and sublayer thickness 5S equal to 3% of the rms boundary-layer thickness. The present space-time correlation measurements were preceded by detailed surveys of the mean, intermittent, and turbulent flow.Correlation measurements were done by two hot-wire anemometers held by an actuator immersed in the flow,. While one of the two wires was held fixed, the other could be traversed along the coordinates x (the stream direction), y (normal to the wall), or z. The entire arrangement could be positioned at will at any distance y above the wall. With an adjustable delay electronic correlator, space-time correlations could thus be obtained along the three principal directions *, y, z for any arbitrarily large number of inter-probe separations x', y', and z' and time delays. The use of electronically compensated 0.00001 in. diam wires ensured adequate frequency response. Aerodynamic interference seriously hampered the measurement of the longitudinal correlations, along jc, which require two probes to lie on the same mean streamline. Care to design minimum drag support fixtures was successful in decreasing, but not alleviating, spurious signals from the downstream probe caused by the wake of its upstream companion. Fortunately, the interference effect was evident only in the outer half of the boundary layer (y>0.56). The central problem of this type of measurement lies, instead, in deducing the correlation tensor of the velocity fluctuations separately from that of the pressure or temperature fluctuations. This hot-wire signal splitting is impossible to do formally when all turbulence modes are active. A formal technique is available for separating the velocity from the temperature correlations when the pressure fluctuations p' are insignificant (p' < <u, T') but was not applied in this work. However, sufficient results were obtained using the \2 = 0.101 MA