Design Optimization for Early Natural Transition Over High-Speed Axisymmetric Configurations

Supersonic and hypersonic quiet tunnels provide a test environment representative of atmospheric flight conditions by maintaining a laminar boundary layer over the nozzle wall. However, natural boundary-layer transition (BLT) under quiet conditions is commonly not observed due to the limitations on realizable Reynolds numbers of the currently operational quiet tunnels. Adjoint-based shape optimization with integrated computational fluid dynamics (CFD) and transition prediction based on the N-factor method is proposed to modify the profile of a circular cone at zero degrees angle of attack to promote flight-realistic BLT at supersonic and hypersonic conditions representative of the flow in the NASA Langley Mach 3.5 Supersonic Low Disturbance Tunnel (SLDT) and the Purdue University Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT). The maximum N-factor values at the selected Mach 3.5 SLDT and Mach 6 BAM6QT conditions for a nominally sharp, 7-degree half-angle, circular cone with a length of L=0.5 m are N~10.5 and N~7, respectively. Based on correlations with experiments, transition onset is expected where the Mack's first-mode waves reach NT=10 or the Mack's second-mode waves reach NT=15 for the supersonic and hypersonic cases, respectively. Shape optimization is performed to minimize the transition location xT with fully attached flow. For the supersonic configuration, the predicted transition onset is shifted from xT/L=0.861 to 0.647. The design iterations at the hypersonic condition converge to an optimized geometry with a minimum xT/L=0.435. The proposed adjoint-based design optimization approach is demonstrated to provide optimized geometries for early BLT at nominal, high-speed, quiet wind-tunnel conditions.