Skip to main content
SpringerLink
Log in

Streamlines behind curved shock waves in axisymmetric flow fields

  • Original Article
  • Published:
Shock Waves Aims and scope Submit manuscript

Abstract

Streamlines behind axisymmetric curved shock waves were used to predict the internal surfaces that produced them. Axisymmetric ring wedge models with varying internal radii of curvature and leading-edge angles were used to produce numerical results. Said numerical simulations were validated using experimental shadowgraph results for a series of ring wedge test pieces. The streamlines behind curved shock waves for lower leading-edge angles are examined at Mach 3.4, whereas the highest leading-edge angle cases are explored at Mach 2.8 and 3.4. Numerical and theoretical streamlines are compared for the highest leading-edge angle cases at Mach 3.6. It was found that wall-bounding theoretical streamlines did not match the internal curved surface. This was due to extreme streamline curvature curving the streamlines when the shock angle approached the Mach angle at lower leading-edge angles. Increased Mach number and internal radius of curvature produced more reasonable results. Very good agreement was found between the theoretical and numerical streamlines at lower curvatures before the influence of the trailing edge expansion fan.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. Note that the signs on the abscissa of the corresponding figure in [1] should be reversed (corrected) to agree with Fig. 3.

Abbreviations

M :

Mach number

\(\theta \) :

Shock angle

D :

Streamline curvature

\(\varGamma \) :

Normalised vorticity

J :

Normalised pressure gradient influence coefficient

K :

Streamline curvature influence coefficient

P :

Normalised streamwise pressure gradient

\(S_a\) :

Flow plane shock curvature

\(S_b\) :

Flow-normal plane shock curvature

\(\omega \) :

Vorticity

\(x_\mathrm {s}\) :

Streamline starting point x coordinate on the shock

y :

Distance from the axis of symmetry

\(y_\mathrm {s}\) :

Streamline starting point y coordinate on the shock

\(\alpha \) :

Leading-edge angle

\(L_\mathrm {w}\) :

Normalised ring wedge length

\(R_\mathrm {c}\) :

Normalised internal radius of curvature

\(R_\mathrm {le}\) :

Leading-edge radius

References

  1. Mölder, S.: Curved shock theory. Shock Waves 26, 337–353 (2016). https://doi.org/10.1007/s00193-015-0589-9

    Article  Google Scholar 

  2. Mölder, S., Timofeev, E., Emanuel, G.: Flow behind a concave hyperbolic shock. In: 28th International Symposium on Shock Waves Conference Proceeding, pp. 593–598 (2012). https://doi.org/10.1007/978-3-642-25685-1_94

  3. Mölder, S.: Flow behind concave shock waves. Shock Waves 27, 721–730 (2017). https://doi.org/10.1007/s00193-017-0713-0

    Article  Google Scholar 

  4. Filippi, A.A., Skews, B.W.: Characterisation of curved axisymmetric internal shock waves. In: 31th International Symposium on Shock Waves Conference Proceeding. Springer (2017, In Press)

Download references

Author information

Authors and Affiliations

  1. Flow Research Unit, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, 2050, South Africa

    A. A. Filippi & B. W. Skews

Authors
  1. A. A. Filippi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. W. Skews
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. W. Skews.

Additional information

Communicated by A. Higgins.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Filippi, A.A., Skews, B.W. Streamlines behind curved shock waves in axisymmetric flow fields. Shock Waves 28, 785–793 (2018). https://doi.org/10.1007/s00193-017-0783-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00193-017-0783-z

Keywords

Search

Navigation