Second-order curved shock theory

Shi, Chongguang; Han, Wei‐Qiang; Deiterding, Ralf; Zhu, Chengxiang; You, Yancheng

doi:10.1017/jfm.2020.158

Cited by 19 publications

(10 citation statements)

References 16 publications

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“…The curved shock equations were originally derived by Mölder (2016), and then developed into second-order form by Shi et al. (2020). For clarity, curved shock theory is introduced before the equations of MOCC are derived.…”

Section: Methods Of Curved-shock Characteristicsmentioning

confidence: 99%

“…Furthermore, taking the derivative with respect to of both sides of each of the first-order curved shock equations gives the second-order curved shock equations: Details of the derivation of the second-order curved shock equations and their coefficients have been given by Shi et al. (2020).…”

Section: Methods Of Curved-shock Characteristicsmentioning

confidence: 99%

“…Shi et al. (2020) then derived the second-order curved shock equations and applied them to flowfield calculations. The results were more accurate than the first-order curved shock equations proposed by Mölder (2016).…”

Section: Introductionmentioning

confidence: 99%

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Method of curved-shock characteristics with application to inverse design of supersonic flowfields

et al. 2021

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Section: Methods Of Curved-shock Characteristicsmentioning

confidence: 99%

Section: Methods Of Curved-shock Characteristicsmentioning

confidence: 99%

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Method of curved-shock characteristics with application to inverse design of supersonic flowfields

et al. 2021

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“…Emanuel (2019) and Shi et al. (2020) further developed the theory to higher dimensions and orders, respectively. Shi et al.…”

Section: Introductionmentioning

confidence: 99%

Reflection and transition of planar curved shock waves

Zhang

Shi

et al. 2023

J. Fluid Mech.

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In this paper, the reflection of curved shock waves over a symmetry plane in planar supersonic flow is studied. This includes stable Mach reflection (MR) and the regular reflection (RR) to MR transition process. Curved shock theory (CST) is applied to derive the high-order parameters in front of and behind the shock wave. The method of curved shock characteristics is used to establish an analytical model to predict the wave configurations. The shock structures provided by the proposed model agree well with the numerical results. Flow structures, such as the height of the Mach stem and the shape of the shock wave and slip line, are studied by applying the analytical model. Isentropic waves generated from a curved wall are found to significantly influence the flow patterns. It appears that the compression waves obstruct the formation of the sonic throat and increase the Mach-stem height. The expansion waves have the opposite effect. The evolution mechanism of the Mach stem is found in conjunction with the RR-to-MR transition process. The CST is extended to a moving frame and used to model the transition. The time history of the moving triple point illustrates the effects of the incident shock angle and isentropic waves on the transition process.

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“…Recently, Shi et al. (2020) developed the second-order CST, which improves the accuracy in describing the flow behind axisymmetric curved shocks. Shi et al.…”

Section: Introductionmentioning

confidence: 99%

Intensification of non-uniformity in convergent near-conical hypersonic flow

Zhang

et al. 2021

J. Fluid Mech.

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The inevitable formation of a Mach disk at the central axis of a convergent conical shock wave may suffer from fundamental changes when the flow deviates from the axisymmetric condition. In this paper, the behaviours of near-conical shocks, which are generated by a circular ring wedge of $10^{\circ }$ at typical angles of attack (AoAs), are investigated at a free stream Mach number of 6 in a shock tunnel. To reveal the characteristics and mechanism of the flow, numerical analyses are carried out under the same conditions. The results indicate that when the flow deviates from axial symmetry, the circumferential non-uniformity is remarkably intensified as the shock converges downstream. The converging centre shifts against the inclination of the incoming flow and moves to the leeward side. For a sufficiently small AoA, the formation of a Mach disk remains similar to that in the axisymmetric case, although the Mach disk shrinks in size and is slightly flattened. As the circumferential non-uniformity of the shock increases at an AoA of approximately $3^{\circ }$ , a pair of kinks separate the shock surface into two discontinuous segments with the stronger shock segment on the windward side and the weaker shock segment on the leeward side. When the AoA increases further, the shrinkage of the Mach disk continuously occurs, and the Mach disk is eventually replaced by a regular reflection. The discontinuity of a convergent shock with flattening on the separated shock segments and the insufficient strength increase during the subsequent convergence are responsible for the appearance of regular reflection.

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Second-order curved shock theory

Cited by 19 publications

References 16 publications

Method of curved-shock characteristics with application to inverse design of supersonic flowfields

Method of curved-shock characteristics with application to inverse design of supersonic flowfields

Reflection and transition of planar curved shock waves

Intensification of non-uniformity in convergent near-conical hypersonic flow

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