<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">$4.56 \times 10^{6}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4.56</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> per meter. Two ramp angles of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$15^\circ $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>15</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$18^\circ $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>18</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$15\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>15</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> as the plate length increased by <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">$\approx 80\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≈</mo> <mn>80</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">$\approx 0.6 U_{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≈</mo> <mn>0.6</mn> <msub> <mi>U</mi> <mi>∞</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>. The peak value of the Stanton number is found to be <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq7.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\approx $</EquationSource> <EquationSource Format="MATHML"><math> <mo>≈</mo> </math></EquationSource> </InlineEquation> 15–27% higher than the time and span-averaged value for the 15P3 and 18P3 cases, highlighting a strong effect of downwash due to streamwise vortices on the wall heating rate distribution. The unsteady data also reveal a negative correlation between the flow reattachment location and the Stanton number close to the reattachment point. An earlier reattachment is shown to increase the Stanton number and vice versa resulting in a <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1239_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">$\approx 40\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≈</mo> <mn>40</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

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2025年6月17日

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K. Dixit,
R. R. Kumar,
N. R. Vadlamani,
N. Tsuboi

摘要

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 $4.56 \times 10^{6}$ $4.56 \times 10^{6}$ per meter. Two ramp angles of $15^\circ $ $15^{\circ}$ and $18^\circ $ $18^{\circ}$ 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 $15\%$ $15 %$ as the plate length increased by $\approx 80\%$ $\approx 80 %$ 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 $\approx 0.6 U_{\infty }$ $\approx 0.6 U_{\infty}$ . The peak value of the Stanton number is found to be $\approx $ $\approx$ 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 $\approx 40\%$ $\approx 40 %$ 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.