Effects of Streamwise Thermal Gradients on Second-Mode Instability

The effects of experimentally feasible, patterned wall heating and cooling on the growth of the second-mode instability are considered both numerically and experimentally. The study considers both a sharp tip, 40-cm-long and a 2-mm-radius blunted tip, 1-m-long 7 degree half-angle cone at zero angle of attack. Experiments were conducted in the AFOSR–Notre Dame Large Mach-6 Quiet Tunnel under conventional noise conditions. Numerical stability analysis was conducted using the JoKHeR parabolized stability equations code. Experiments on the 40-cm-long cone showed transition without thermal control at ���� = 9.4 and 11.8 · 10^6 /m around �� = 0.37 m. Thermally modified configurations indicated little effect on transition. The 1 m experimental analysis showed little to no impact of thermal control for the ���� = 4.8 · 10^6 /m case, but changes in ��-factor as large as 1 for ���� = 7.1 · 10^6 /m. Spectra indicated that second-mode disturbance amplitudes were lowered at �� = 41, 52, 63, and 71 cm to varying degrees depending on the thermal configuration. This is corroborated by computational results, with predicted the greatest reduction of around 52% in disturbance amplitude at ���� = 7.1 · 10^6 /m. These results are a starting point for identifying the most effective wall-temperature distribution for controlling boundary-layer transition.