Toward robust prediction of crossflow-wave instability in hypersonic boundary layers

Traveling and stationary crossflow-wave instabilities in a laminar Mach 6 boundary layer are investigated on a 38.1% scale model of the Fifth Hypersonic International Flight Research Experiment (HIFiRE-5) elliptic cone at zero angle of attack and yaw. The Langley Stability and Transition Analysis Code (LASTRAC) was used to analyze the crossflow dominated boundary layer in the mid-span region near the downstream end of the model. Disturbance growth rates, wave angles, and phase speeds are computed with LASTRAC using quasi-parallel Linear Stability Theory (LST), Linear Parabolized StabilityEquations (LPSE), and two-plane or surface marching LPSE (2pLPSE). The predicted wave angles and phase speeds are validated using experimental data, and are found to be in better agreement than previous computations. Further numerical analysis is conducted using the Spatial BiGlobal technique (SBG), which simultaneously accounts for wall-normal and spanwise gradients in the mean boundary layer at a particular axial station. For the first time in the literature, a comparison is made between crossflow wave growth rates computed using LST, LPSE, and 2pLPSE and those computed using SBG, accounting for curvature and geometric divergence of the elliptic cone. The agreement between LST, LPSE, and SBG is fair at best, but excellent agreement is realized between 2pLPSE and SBG. This result constitutes a co-verification of the LASTRAC and SBG stability codes, and provides evidence that 2pLPSE accurately models the physics of the traveling-crossflow instability.