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Hypersonic reattachment flow usually causes extremely high wall heat flux, which is of great concern in engineering. The flow can be modeled as a high-speed shear layer impinging on a wall at a certain angle, which forms an oblique stagnation-point flow in the vicinity of the stagnation point, including stagnation-component and shear-component. Previous work focused on incompressible oblique stagnation-point flow, while in the present study a semi-analytical-semi-numeric solution is given via the self-similar method for compressible oblique stagnation-point flow. Through the comparison and validation with the numerical results, it is found that the flow model can well simulate the heat transfer near the wall in the flow of uniform shear layer impinging on the wall caused by hypersonic reattachment. With the analysis of the contribution of the energy transport and the heat production in the flow model, it is found that the compression effect and dissipation effect are mainly caused by the shear-component, leading to a significant convective heat transfer in the flow direction, which is different from the case of the classic boundary layer. Then the temperature of the flow near the wall rises rapidly after reattachment, resulting in a high heat flux to the wall. Parameter analysis indicates that the wall heat-transfer coefficient is related to the dimensionless wall temperature gradient and the thickness of the boundary layer. The former is mainly controlled by the shear-component parameter
$H_{\zeta}$ , and the latter is negatively correlated with the stagnation-component parameter$H_{\beta}$ . Further analysis shows that the wall heat-transfer coefficient has a linear relationship with$H_{\zeta}$ and is proportional to$\sqrt{H_{\beta}}$ when$H_{\beta}$ is small. This work provides a theoretical basis and solution for studying on the hypersonic reattachment flow, and it is also an extension of the asymmetric stagnation boundary layer theory.-
Keywords:
- oblique stagnation-point/
- reattachment/
- shear layer/
- heat transfer
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Case No. $ M_\infty $ $ {Re}_L / 10^4 $ $ \theta /(^{\circ}) $ $ T_\infty $/K $ T_{\rm{w}} $/K L/m A1 9 1 25 60 300 1 B1 9 2 25 60 300 1 B2 11 2 25 60 300 1 C1 9 5 25 60 300 1 C2 11 5 25 60 300 1 C3 13 5 25 60 300 1 C4 15 5 25 60 300 1 D1 13 10 25 60 300 1 D2 15 10 25 60 300 1 E1 11 5 21 60 297 1 E2 11 5 24 60 297 1 E3 11 5 27 60 297 1 E4 11 5 30 60 297 1 F1 15 2 30 60 300 1 G1 15 5 24 60 300 1 G2 15 5 27 60 300 1 H1 11 2 25 100 300 1 H2 11 2 25 150 300 1 H3 11 2 25 200 300 1 H4 11 2 25 250 300 1 I1 11 5 25 60 100 1 I2 11 5 25 60 200 1 I3 11 5 25 60 250 1 I4 11 5 25 60 350 1 I5 11 5 25 60 450 1 
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Case No. $ M_{\rm{e}} $ $ H_{\beta} \times 10^4 $ $ H_{\zeta} \times 10^3 $ $ D_{\rm{e}} $ $ {\bar T}_{\rm{w}} $ $ \theta $ A1 4.82 1.79 12.25 15.2 1.64 13.6 B1 4.60 1.60 10.27 16.4 1.51 14.0 B2 5.57 1.16 6.45 19.9 1.43 15.0 C1 4.69 0.97 5.21 23.1 1.57 15.3 C2 5.44 0.78 3.89 25.6 1.37 15.8 C3 6.15 0.66 3.22 27.5 1.23 16.0 C4 6.55 0.68 3.10 27.7 1.04 16.5 D1 6.00 0.51 2.32 32.4 1.18 16.6 D2 6.28 0.51 2.17 32.9 0.96 17.0 E1 5.90 0.57 4.93 23.0 1.56 12.1 E2 5.60 0.71 4.07 25.1 1.42 14.8 E3 5.18 0.93 3.86 25.4 1.25 17.2 E4 4.71 1.28 3.99 24.5 1.07 19.7 F1 5.71 1.75 5.17 21.0 0.82 20.2 G1 7.05 0.50 2.61 30.4 1.19 15.5 G2 5.99 0.90 3.40 26.1 0.88 18.0 H1 5.48 1.17 6.40 18.9 0.83 15.1 H2 5.38 1.22 6.52 18.2 0.54 15.3 H3 5.46 1.12 5.90 18.9 0.41 15.4 H4 5.08 1.36 7.29 16.8 0.36 15.3 I1 5.35 0.90 3.88 23.4 0.45 16.9 I2 5.50 0.78 3.53 25.7 0.93 16.6 I3 5.50 0.75 3.57 26.1 1.17 16.2 I4 5.43 0.80 4.10 25.5 1.59 15.6 I5 5.45 0.73 4.06 27.1 2.07 15.0 DownLoad:
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