Design of a Hypersonic Swept-Wing Experiment for the Study of Crossflow-Vortex/Step-Excrescense Interaction

Theoretical guidance is provided for the design of a swept-wing experiment in the University of Arizona's Mach 5 Ludwieg Tube aimed at studying crossflow-vortex/step-excrescence interaction. The success of this campaign relies on producing spanwise uniform flow, so that crossflow vortices are amplified as uniformly as possible. We propose to use a full-span, bi-convex infinite-swept wing. In this article, we fixed the chord length to 5.75 in (146 mm) and model the edge effects by tracking Mach waves from the intersection of the wing with the wind-tunnel walls: we suppose that operating in the supersonic flow in-between these Mach waves allows for the best spanwise uniformity. Furthermore, we consider an infinitely sharp nose, so that the inviscid flow can be determined with the Rankine-Hugoniot and Prandtl-Meyer equations. We use the code DEKAF to solve the boundary-layer equations and Linear Stability Theory (LST) to determine stationary-crossflow-disturbance amplification. Large amplification is found to be supported over a large chordwise portion of the wing in the considered range of sweep angles (60 to 75 degrees) and airfoil thicknesses (1 to 25 percent leading-edge-perpendicular chord). Ignoring the edge effects, the maximum amplification N-factor of 16.1 is achieved at a thickness ratio of 18% and a sweep angle of 67 degrees; larger thicknesses yield diminishing returns. Upon dropping the chordwise portion subject to edge effects, we find that large amplification (N exceeding 8) is supported for 63% of the chord upon adopting a thickness ratio of 24% and a sweep angle of 60 degrees. We realize airfoils that are this thick may cause blockage issues if the tunnel is operated with a closed test section: for this reason, amplification results are provided for a very broad range of sweep angles and airfoil thicknesses. Next to informing the design of the wind-tunnel experiment with LST calculations, we report our on-going progress on verifying an extended and newly developed stability code: a plane-marching Parabolized Stability Equations (PSE) and Harmonic Navier-Stokes (HNS) approach.