<p>This study investigates the transient phase of the morphing shock control bump (SCB) over a flat plate using various velocities and accelerations. Specifically, five morphing profiles are tested, namely linear, parabolic, half-parabolic, reversed parabolic, and half-reversed parabolic morphing. The objective of this research is to numerically determine the optimal velocity profile, out of the tested ones, that reduces entropy losses, lag effect, and response time while presenting a dynamic shock system map. The simulations were conducted to solve the 2D supersonic unsteady flow with different free-stream Mach numbers (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1218_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$M_{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>). The Reynolds number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2025_1218_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="118" /> </InlineMediaObject> <EquationSource Format="TEX">$\textrm{Re}_{\infty }=6.6 \times 10^7$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>Re</mtext> <mi>∞</mi> </msub> <mo>=</mo> <mn>6.6</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>7</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> based on the bump’s length is used. The investigation is achieved by comparing the lag effect, entropy losses, and time response. The study results indicate that the optimal speed to morph with is the one that results in neither a remarkable lag effect in the shock system nor high losses in the entropy deviation from the stationary steady-state case. Additionally, the reversed parabolic motion is the most suitable profile due to its short response time, small lag effect, and low losses. This is because the generated shock system from the appearance of SCB is initially weak, allowing for relatively fast motion. However, near the end of the morphing process, the opposite occurs, requiring relatively slow motion.</p>

Dynamic shock wave investigations for an unsteady supersonic flow with a morphing bump over a flat plate

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2025年4月12日

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A. A. Hamada,
L. Margha,
M. M. AbdelRahman,
A. Guaily

摘要

This study investigates the transient phase of the morphing shock control bump (SCB) over a flat plate using various velocities and accelerations. Specifically, five morphing profiles are tested, namely linear, parabolic, half-parabolic, reversed parabolic, and half-reversed parabolic morphing. The objective of this research is to numerically determine the optimal velocity profile, out of the tested ones, that reduces entropy losses, lag effect, and response time while presenting a dynamic shock system map. The simulations were conducted to solve the 2D supersonic unsteady flow with different free-stream Mach numbers ( $M_{\infty }$ $M_{\infty}$ ). The Reynolds number $\textrm{Re}_{\infty }=6.6 \times 10^7$ ${Re}_{\infty} = 6.6 \times 10^{7}$ based on the bump’s length is used. The investigation is achieved by comparing the lag effect, entropy losses, and time response. The study results indicate that the optimal speed to morph with is the one that results in neither a remarkable lag effect in the shock system nor high losses in the entropy deviation from the stationary steady-state case. Additionally, the reversed parabolic motion is the most suitable profile due to its short response time, small lag effect, and low losses. This is because the generated shock system from the appearance of SCB is initially weak, allowing for relatively fast motion. However, near the end of the morphing process, the opposite occurs, requiring relatively slow motion.