Viscous interaction over concave and convex surfaces at hypersonic speeds

Abstract

The growth of hypersonic boundary layers over both concave and convex surfaces is described, the strong-viscous-interaction equation due to Cheng et al. (1961) for curved surfaces with sharp leading edges being solved asymptotically for small and large arguments. Both the asymptotic solution for large arguments and a numerical integration predict an oscillatory behaviour of the boundary-layer thickness on concave surfaces. A modification of Cheng's theory, as suggested by Sullivan (1968) and Stollery (1970), is also examined and compared with experimental data reported here. The experiments were conducted in air using a hypersonic gun tunnel under cold wall conditions at M∞ = 12·25. They included measurement of surface pressure, heat-transfer distributions and schlieren studies for concave and convex models.

Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers

“…The collapse of the heat transfer data in the present study supports this conclusion, even in the case of an adverse pressure gradient with strong boundary layer distortion, when the external pressure distribution is calculated using the method of characteristics. The scaling obtained in the present study was compared with available data from a previous study by Mohammadian 14 ( Figure 12(a)). In that study, heat transfer was measured over a ramp with a cubic surface equation in a Mach 12.25 flow in a hypersonic gun tunnel.…”

“…The boundary layer initially grows over the flat plate portion of the model, then just after the beginning of curvature, there is an inflection point in the visual boundary layer thickness and it begins to thin. Mohammadian 14 found that for surface geometries with the form y ∼ x n , for values of n > 3/2 the boundary layer will be supercritical (i.e., with increasing pressure, the boundary layer thickness will decrease). For supercritical conditions, the outer, supersonic layer of the boundary layer is thinning faster than the subsonic streamtube near the surface is thickening due to the pressure gradient.…”

“…With the modified Cheng method, Stollery obtained good agreement between predictions and pressure measurements over a cubic concave ramp in a hypersonic gun tunnel. This method was again tested by Mohammadian 14 and compared with schlieren, surface pressure, and heat transfer data for a Mach 12.25 flow over a cubic ramp with cold wall. Near the leading edge, the modified Cheng method predictions agreed closely with heat transfer measurements, but by 4 in.…”

Reattachment heating upstream of short compression ramps in hypersonic flow

“…Different Reynolds number conditions Re ∞ are achieved by changing the total pressure in the driver, with the test flow in the tube set at atmospheric pressure prior to all runs. The free stream conditions used here correspond to selected nominal conditions that have been consolidated over a number of previous studies, with early calibrations dating to Needham (1963) and Mohammadian (1972), respectively, for Mach 8.2 and Mach 12.3 flows. At the datum conditions of M ∞ = 8.2 and Re ∞ /m = 9.35 × 10 6 (highest P o and hence Re ∞ ), the total Fig.…”

Yip-08 Hypervelocity Boundary Layer Studies for Axisymmetric Engine Flowpaths

“…Two other studies were found whose data could be analyzed to see if they showed the same link between surface curvature and heat transfer distribution. Mohammadian [56] took experimental data over a cubic compression surface for use in comparison with a numerical solution he had developed based on the method of Chang [57]. Figure 65 shows the results of the experimental study, with the curve fit which best describes the data, compared to the data from the Curved16 and Cubic1 models.…”