Skin-friction drag at supersonic-hypersonic speeds with transition.

Abstract

NOWLEDGE of the skin-friction drag is of primary importance in the design of advanced aircraft and/or aerospace vehicles. Considerable analytical and experimental studies have been conducted to predict the skin friction for flow conditions that are either laminar or fully turbulent. For mixed flow conditions, the total skin-friction drag coefficient will vary widely depending on the location of the transition point because of the large differences between the drag coefficients for laminar and turbulent flow at identical Reynolds numbers. When transition from laminar to turbulent flow occurs at low speed, the well-known formula of Prandtl-Schli chting1 has provided, although empirical in nature, a quick but accurate estimate of the skin-friction drag. Bertram2 has proposed a semi-empirical method for estimating the skinfriction drag on a delta wing at hypersonic speeds wherein transition is present. However, reviewing his results (Ref. 2, Fig. 15), they do not appear correct. The purpose of this note is to present a method that is similar to Bertram's but which is more rigorous and less complicated and provides numerical results of the skin-friction drag coefficient as a function of the transition on a delta wing. Consider a flat plate delta wing in a hypersonic flow at small values of angle of attack. Depending on the freestream Mach number, unit Reynolds number, leadingedge thickness, surface roughness, etc., a portion of the flow on the wing will become turbulent. For a delta wing at small angles of attack, chordwise strip theory is generally valid provided the spanwise pressure gradient induced by the leading-edge-bluntness or boundary-laye r-shock interaction is small. It may be noted that ARA has successfully obtained and correlated pressure and force data from a large (48 in. long) 70° swept blunted-leading-edge delta wing at Mach numbers 3 to 8; the data have shown that, except near the nose, chordwise strip theory is a good approximation. Not only is the theoretical treatment of the transition location difficult, but, in addition, its experimental determination is also quite illusive. It is generally accepted that the beginning and end points are determined, respectively, by the minimum and maximum locations of the axial variations of either the surface-pitot-pressure or the heat-transfer rate. There are several thoughts, however, for defining the actual transition location. For instance, some investigators define the location as the point of inflection between the minimum and maximum axial surface-pitot-pressure or heat-transfer rate; others use the end point of the transition region. At moderate supersonic speeds the streamwise distance between the minimum and maximum pressure or heat-transfer rate is