Purdue University Graduate School
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Instability and Transition on Slender Cones under Fully Quiet Mach-6 Flow

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posted on 2022-10-14, 12:14 authored by Kathryn A. GrayKathryn A. Gray

Experiments were performed in the Boeing/AFOSR Mach-6 Quiet Tunnel on sharp, slender straight cones at zero degrees angle of attack. These long models allow the second mode to grow to large amplitudes without the need for introduced perturbations and without the presence of the Gortler instability. PCB pressure sensors and global thermal imaging are used to study the development of the second-mode instability. Transition was measured on both the 2.5 degree and 3 degree half-angle cones in high-Reynolds number quiet flow, indicated by increased heating and by breakdown of the second-mode instability. 

Evidence of a flow-induced vibration on the 2.5 degree model was also measured for freestream unit Reynolds numbers between approximately 6.5 and 9.5 million per meter. These conditions produce large second-mode waves, and it is thought that the second-mode instability incites a resonance in the model near 100 kHz. The vibration interferes with measurements of the second mode. Since no such phenomenon is seen on the 3 degree cone, it was the predominant model studied.

Second-mode amplitudes on the 3 degree cone grew to a maximum amplitude before breakdown of 25.3% of the mean surface pressure. This value agreed with previous correlations between edge Mach number and the maximum second-mode amplitude that were found from measurements in conventional wind tunnels. The maximum second-mode amplitude was measured at a length-based Reynolds number of approximately 10 million. Small residual angles of attack (less than 0.1 degrees) did not significantly affect the maximum second-mode amplitude or the Reynolds number at which it was measured. 

Heat transfer was measured on the 3 degree cone using IR thermography, and the laminar-scaled Stanton number was used to estimate the beginning of transition. The heating rose above the laminar value at a length-based Reynodls number of 9.6 million, almost simultaneously with the second mode reaching the maximum amplitude. This indicates that transition begins as the second mode begins to break down. The rise in heating coincides with the appearance of streamwise heating streaks. The streaks move forward on the cone for increasing Reynolds numbers. A second set of streaks appears downstream of the primary set for higher Reynolds numbers. The maximum heating is measured near the end of transition at a length-based Reynolds number of approximately 12.4 million before the heating decreases towards the turbulent value. 

Measurements of intermittency were used to estimate the onset of transition, and good agreement was reached with the transition-onset location estimated using heat transfer. The measured intermittency compared well to the classic Narasimha-Dhawan distribution. Additionally, the intermittency indicated that the flow became always turbulent at a length-based Reynolds number of approximately 12.0 million, which is just before the maximum in heating. The ratio of the onset of transition to the end of transition for the 3 degree cone was approximately 0.85. The ratio for the Reentry F flight was approximately 0.8 and the ratio for conventional wind tunnels is typically near 0.5. These results support previous findings that the transition extent in quiet tunnels is shorter than in noisy tunnels and better approximates that seen in flight.


Degree Type

  • Doctor of Philosophy


  • Aeronautics and Astronautics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Steven Schneider

Advisor/Supervisor/Committee co-chair

Joseph Jewell

Additional Committee Member 2

Jonathan Poggie

Additional Committee Member 3

Hermann Fasel

Additional Committee Member 4

Katya Casper

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