A parametric analysis of streamwise vortices on a compression ramp at Mach 4

Abstract Large-eddy simulations are conducted to investigate supersonic flow over a compression ramp at a free stream Mach number of 4.0 and a unit Reynolds number of $$4.56 \times 10^{6}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4.56</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> per meter. Two ramp angles of $$15^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>15</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> and $$18^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>18</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> are considered along with three different ramp positions (P1, P2, and P3) from the plate leading edge, with the plate length increasing progressively from P1 to P3. Simulations reveal that with an increase in the plate length and ramp angle, the separation point shifts downstream, accompanied by an extended separation length. Furthermore, with an increase in the ramp angle and plate length, a higher Görtler number is observed upstream of the reattachment indicating a greater likelihood of Görtler instability. In particular, no streamwise vortices were observed for the 15P1 and 15P2 cases, while for the 18P3 case, increased instability resulted in the breakdown of streamwise vortices, driving the transition to turbulence. The wavelength of streamwise streaks decreased by approximately $$15\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>15</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> as the plate length increased by $$\approx 80\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>80</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> from 18P1 to 18P3. Unsteady analysis revealed the role of spanwise secondary instabilities over these vortices, that trigger turbulent spots that propagate at a speed of $$\approx 0.6 U_{\infty }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>0.6</mml:mn> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:mrow> </mml:math> . The peak value of the Stanton number is found to be $$\approx $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>≈</mml:mo> </mml:math> 15–27% higher than the time and span-averaged value for the 15P3 and 18P3 cases, highlighting a strong effect of downwash due to streamwise vortices on the wall heating rate distribution. The unsteady data also reveal a negative correlation between the flow reattachment location and the Stanton number close to the reattachment point. An earlier reattachment is shown to increase the Stanton number and vice versa resulting in a $$\approx 40\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>40</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> variation compared to the time-averaged value. The results from this study underscore the critical influence of plate length on the formation of streamwise vortices, with significant implications for wall heating rate distribution and flow transition dynamics.