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Shock detachment from curved wedges

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Abstract

Curved shock theory is used to show that the flow behind attached shocks on doubly curved wedges can have either positive or negative post-shock pressure gradients depending on the freestream Mach number, the wedge angle and the two wedge curvatures. Given enough wedge length, the flow near the leading edge can choke to force the shock to detach from the wedge. This local choking can preempt both the maximum deflection and the sonic criteria for shock detachment. Analytical predictions for detachment by local choking are supported by CFD results.

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Notes

  1. Algebraic expressions for these coefficients are given in [3] where they have the following equivalents: \(a_{1} = J_{a}, a_{2} = J_{b}, b_{1} = K_{a}, b_{2} = K_{b}, d = I_{a}\).

  2. An interesting variation would be to assume a linear decrease in Mach number instead of the square of the Mach number. In this case (9) is read, \(\hbox {d}M_{2}/{\mathrm{d}{s}} = - (1 - M_2)/L^{*}\). This equation gives a different value of \(L^{*}\) by at most a factor of 2.

  3. The nature of local choking behind shocks is distinguished by the post-shock flow being either subsonic or supersonic. Hence the shocks are denoted as “subsonic” and “supersonic” in the two cases.

  4. \(L^{*}\) is normalized by the URW radius of \(y_{1}=1\).

References

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Acknowledgements

Rabi Tahir generously provided the Masterix code and much essential support in its application. Evgeny Timofeev provided advice and effort in obtaining the CFD results using the Masterix code.

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Authors and Affiliations

  1. Ryerson University, Toronto, Ontario, Canada

    S. Mölder

  2. 89 Joseph St., Port Carling, Ontario, P0B 1J0, Canada

    S. Mölder

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  1. S. Mölder
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Correspondence to S. Mölder.

Additional information

Communicated by B. W. Skews and E. Timofeev.

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Mölder, S. Shock detachment from curved wedges. Shock Waves 27, 731–745 (2017). https://doi.org/10.1007/s00193-017-0714-z

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