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

Shi, Chongguang; Zhu, Chengxiang; You, Yancheng; Zhu, Guojun

doi:10.1017/jfm.2021.454

Cited by 15 publications

(10 citation statements)

References 29 publications

(40 reference statements)

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“…To calculate supersonic flow fields, Shi et al. (2021) derived the MOCC in (2.5) in the plane, where denotes the streamline, and denotes the characteristic coordinates from the Euler equations: …”

Section: Analytical Modelmentioning

confidence: 99%

“…Three unit algorithms (interior process, shock process and wall/parameter distribution process) are introduced by Shi et al. (2021). As shown in figure 3, the flow in region (1) is a typical internal flow with uniform inflow and known wall boundary conditions that can be solved using the interior, shock and wall processes.…”

Section: Analytical Modelmentioning

confidence: 99%

“…Shi et al. (2021) derived the method of curved shock characteristics (MOCC) for calculating the supersonic flow field behind curved shock waves based on the CST. In 2017, the CST was applied to the reflection of a curved shock by Mölder (2017).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Analytical Modelmentioning

confidence: 99%

Section: Analytical Modelmentioning

confidence: 99%

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Reflection and transition of planar curved shock waves

Zhang

Shi

et al. 2023

J. Fluid Mech.

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“…(2023) provided the shock geometries and transition criteria based on the method of curved-shock characteristics (Shi et al. 2021), where the quasi-one-dimensional assumption was also applied for calculating the height of the sonic throat.…”

Section: Introductionmentioning

confidence: 99%

“…To further improve the accuracy, Shi et al. (2021) developed a method of curved-shock characteristics (MOCC) for analysis and inverse design in supersonic flow fields. In their method, the downstream of the shock wave was precisely solved by a modified method of characteristics, where the boundary conditions were given by the gradients from CST.…”

Section: Introductionmentioning

confidence: 99%

A study of streamline geometries in subsonic and supersonic regions of compressible flow fields

Tian,

Cui

2024

J. Fluid Mech.

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The geometrical properties of streamlines, such as the curvatures, directions and positions, are studied in steady inviscid compressible flow fields via differential geometry theories and conservation laws. The influences of the streamline geometries on the flow speeds and pressures are also identified and discussed. By transforming the streamlines to fill the domain and satisfy the boundary conditions, a unified geometry-based solver, the streamline transformation method, is proposed for both subsonic and supersonic regions. The governing equations and boundary conditions along streamlines and shock waves are also derived. This method is verified by numerical results of three typical flow fields, including the subsonic channel flow, the supersonic downstream of attached shock waves and especially the subsonic/supersonic downstream of detached bow shock waves. Both two-dimensional planar and axisymmetric flow fields are considered. Compared with the results from computational fluid dynamics, good agreements are achieved by this method, while fewer computational resources, by an order of magnitude, are consumed. Features of these flow fields are also analysed from a geometrical perspective, such as flow speeds and pressures deviated by the wall curvatures, and three-dimensional effects in the after-shock flow fields. For a hyperbolic-shaped bow shock wave, the stand-off distances and the transitions from subsonic to supersonic regions are also discussed. As indicated by the accuracy, efficiency and applicability in a wide range of flow speeds, the streamline transformation method would be a potential candidate for the theoretical analysis and inverse design of high-speed flow fields, especially where the subsonic regions exist downstream of strong shock waves.

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