Purdue University Graduate School
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Measurements of Transition near the Corner Formed by a Highly-Swept Fin and a Cone at Mach 6

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posted on 2021-12-20, 13:59 authored by Franklin D TurbevilleFranklin D Turbeville
A 7° half-angle cone with a highly-swept fin was tested in the Boeing/AFOSR Mach-6 Quiet Tunnel at 0.0° angle of attack. Previous measurements of the surface heat transfer using temperature sensitive paint revealed heating streaks on the cone surface related to streamwise vortices generated by the fin shock. High-frequency measurements of the cone-surface pressure fluctuations revealed that transition occurs in the streak region at sufficiently-high freestream unit Reynolds numbers under quiet flow. In this work, high-resolution measurements of the surface heat transfer are obtained using infrared thermography and a polyether-ether-ketone wind-tunnel model. In addition, a novel model design made it possible to measure pressure fluctuations throughout the streak region on the cone surface.

A slender cone with a sharp nosetip and a fin swept back 75° with a 3.18 mm leading-edge radius served as the primary geometry for this work. Two laminar heating streaks
were measured on the cone surface. These travel along a line of nearly-constant azimuth. A hot spot develops in the streak farthest from the fin, which then moves upstream with increasing freestream Reynolds number. Downstream of this hot spot, the streaks begin to spread in azimuth. The heat transfer along the outer streak shows a threefold increase near the hot spot before decreasing back to nearly two times the laminar streak heating. The amplitude of the pressure fluctuations increases simultaneously with the heat transfer, reaching a peak of nearly 9% of the Taylor-Maccoll pressure for a 7° straight cone. Power spectral densities calculated from these fluctuations demonstrate spectral broadening, which is indicative of boundary-layer transition. Using surface-pressure-fluctuation and heat-flux measurements, transition onset was estimated to occur at an axial length Reynolds number of 2.2×106. Pressure sensors that were rotated through the streak region showed that multiple instabilities amplify between the heating streaks, upstream of the transition onset location. Downstream of transition onset, the highest-amplitude instabilities are localized to the hot spot in the outer streak. The effect of freestream noise on transition was also investigated with this geometry. Under conventional noise levels, transition onset was estimated to occur at an axial length Reynolds number of 0.93×106, and only one instability was measured in the streak region with a frequency similar to the second-mode instability.

Four configurations were tested to investigate the effect of fin sweep and nosetip bluntness under quiet flow. Fins with 70° and 75° sweep were each tested with nominally sharp and 1-mm-radius nosetips. Increasing fin sweep was shown to move the heating streaks on the cone closer to the fin and to decrease the peak-to-peak spacing of the streaks. In addition, transition onset occurred at lower freestream unit Reynolds numbers for the 70° sweep case. Increasing nosetip radius had little effect on the heating streaks, other than to delay the transition location. A blunt nosetip was shown to delay transition more for the 75° sweep fin as compared to the 70° fin. Similar instabilities were measured for all four of the configurations in this work. The frequency of the instabilities appears to be correlated with the peak-to-peak distance of the heating streaks, which can be viewed as an indirect measurement of the vortex diameter.

Lastly, the first quantitative measurements of heat transfer on the fin were made using the infrared thermography apparatus. Peak heating on the fin, not including the leading edge, is lower than peak heating rates on the cone. One broad heating streak was measured close to the corner, and smaller low-heating streaks were measured farther outboard. The heating within the streak closest to the corner was shown to agree well with a fully-laminar computed basic state, indicating that the flow on the fin is laminar up to at least 6.31×106 m−1. Using miniaturized Kulite sensors, pressure fluctuations were measured at twelve locations on the fin surface. No obvious conclusions could be drawn from these Kulite measurements, and there is no clear indication that transition occurs on the fin within the maximum quiet
freestream conditions.


Towards a Mechanism-Based Procedure for Predicting Boundary-Layer Transition on Slender Models with Highly Swept Fins: Further Mach-6 Quiet-Tunnel Measurements

United States Department of the Navy

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Degree Type

  • Doctor of Philosophy


  • Aeronautics and Astronautics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Steven Schneider

Additional Committee Member 2

Joseph Jewell

Additional Committee Member 3

Jonathan Poggie

Additional Committee Member 4

Neal Bitter

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