Far wake behavior of hypersonic spheres.

The behavior of the far wake of hypersonic spherical bodies (traveling at speeds between 19,000 and 23,000 fps) has been studied with schlieren techniques in the free-flight range. Measurements were made of the distance to the first appearance of viscous wake turbulence outside the inviscid wake, an occurrence that was denoted "breakthrough." Viscous damping in the viscous wake is believed to account for the rapid movement of breakthrough back in the wake at lower Reynolds numbers (near 105). At the lowest Reynolds numbers studied breakthrough no longer occurred, presumably because of critical viscous damping, and the inviscid wake as a whole developed instabilities. In all cases the far wake growth approached the classical one-third power variation with distance. The importance of the presence of a well-marked inviscid wake in hypersonic flows is discussed in detail. The effects of body size and the effects of an ablating surface material on the measurements are presented. I. Introduction C ONFLICTING results have been reported recently concerning the appearance of tubulence in the wakes of spherical hypersonic bodies. The majority of studies (e.g., Refs. 1-3) indicates that turbulence onset, or transition, occurs within 10 body diam behind the body at Reynolds numbers (Rem, &) greater than 105, where Re^, D = U^D/v^ is determined by ambient kinematic viscosity vmj flight speed Um, and body diameter D. In another report, however, turbulence was first detected some 50 to 100 diam behind the body at these Reynolds numbers.4 This long distance to transition appears inconsistent, even with previous reports by the same authors,2 and it has been suggested that the phenomenon was not transition but, rather, fully developed turbulence, earlier turbulence having been masked by inadequate instrument sensitivity.1'4 The studies reported here were undertaken, in part, to attempt to resolve these discrepancies and uncertainties by performing schlieren studies of the wake development behind models in free flight in the ballistic range, and in part to aid in understanding the radar backscatter and radiation studies of the wake already under way in the ballistic range. The chemical processes governing the production and removal of emitting species and ionized species are, to a large extent, controlled by the turbulent mixing and, hence, by the turbulent wake development. Consequently, in much of what follows, fluid mechanical phenomena are discussed with their relationship to radiation and radar observations in mind. (Data on radiation and radar observations will be published elsewhere.5'6) At hypersonic speeds, the shock-generated wake appears as a well-defined column, having much the same appearance as the boundary-layer-generated wake in schlieren photographs.1 The different origins of the two wakes account for their designations as the viscous (inner) wake, generated by viscous interaction with the body, and the inviscid (outer) wake, generated by shock-heating in an essentially inviscid portion of the flowfield. A more descriptive designation for the shockgenerated wake might be "entropy wake" since it results from entropy change at the bow shock. The viscous wake structure within the hot, low-density wake of a spherical hypersonic body is difficult to "see" using schlieren devices, because their sensitivity is proportional to the fluid density gradients. The inviscid wake boundaries, however, are clearly marked at high flight speeds, their sharp-edged appearance accentuated by the axial symmetry of the wake flow. In fact, the inviscid wake is so well defined at re-entry speeds that it has been erroneously identified by others as a viscous wake.4 At lower speeds the inviscid gradients lessen, and no inviscid wake can be defined; and at subsonic speeds, with the disappearance of the bow shock, no inviscid, shock-heated wake can exist. Thus the concept of an inviscid wake appears to apply only to near-re-entry conditions. At relatively high Reynolds numbers (Re^, D above 105) the viscous wake will be unstable, and transition to turbulence will occur some distance behind the body. This turbulent, viscous wake grows more rapidly than the surrounding inviscid wake, entraining the shock-heated gases. At some point the inviscid wake is completely filled by the viscous