Supersonic Flow over Elliptic Cone with Different Ellipticity Ratio

Document Type : Regular Article


Department of Mechanical Engineering, Amrita School of Engineering, Bengaluru, Amrita Vishwa Vidyapeetham, India



This study investigates supersonic flow characteristics over circular and elliptic cones at various angles of attack. Simulations were conducted on the cones with the same base area and length-to-diameter ratio. The elliptic cones considered had axis ratios of 1.5 and 3. The angle of attack varied from 0o to 50o, with two different Mach numbers (1.97 and 2.94) employed for the analysis. The numerical results were compared with the experimental and theoretical findings from existing literature. The results revealed that increasing the ellipticity ratio of the cones resulted in higher lift generation. The pressure distributions on the windward and leeward sides of the cones were also examined. The results demonstrated that elliptic cones outperformed circular cones in terms of lift production, and this advantage increased with higher ellipticity ratios. Specifically, when the ellipticity ratio was increased from 1 to 3, the maximum increase in lift coefficient was 96% and 100% at Mach numbers 2.94 and 1.97, respectively. Additionally, by changing the ellipticity ratio from 1 to 1.5, the maximum gain in the lift-drag ratio was 16% and 22% at Mach numbers 1.97 and 2.94, respectively. Notably, an elliptic cone with an ellipticity ratio of 3 achieved a remarkable 46% gain in lift-to-drag ratio compared to a circular cone. However, as the angle of attack increased, a primary bow shock formed on the windward side of the cone, with an embedded shock appearing on the leeward side.


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