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Experiments in Fluids

, Volume 52, Issue 2, pp 273–287 | Cite as

Behaviour of a shock train under the influence of boundary-layer suction by a normal slot

  • A. Weiss
  • H. Olivier
Research Article

Abstract

The interaction of a shock train with a normal suction slot is presented. It was found that when the pressure in the suction slot is smaller or equal to the static pressure of the incoming supersonic flow, the pressure gradient across the primary shock is sufficient to push some part of the near wall boundary layer through the suction slot. Due to the suction stabilized primary shock foot, the back pressure of the shock train can be increased until the shock train gradually changes into a single normal shock. During the experiments, the total pressure and therewith the Reynolds number of the flow were varied. The structure and pressure recovery within the shock train is analysed by means of Schlieren images and wall pressure measurements. Because the boundary layer is most important for the formation of a shock train, it has been measured by a Pitot probe. Additionally, computational fluid dynamics is used to investigate the shock boundary-layer interaction. Based on the experimental and numerical results, a simplified flow model is derived which explains the phenomenology of the transition of a shock train into a single shock and derives distinct criteria to maintain a suction enhanced normal shock. This flow model also yields the required suction mass flow in order to obtain a single normal shock in a viscous nozzle flow. Furthermore, it allows computation of the total pressure losses across a normal shock under the influence of boundary-layer suction.

Keywords

Mach Number Normal Shock Total Pressure Loss Schlieren Image Nozzle Wall 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a

Speed of sound (m/s)

\( A^{*} \)

Nozzle throat area (mm²)

b

Half width of the shock-wave reactor (mm)

\( h^{*} \)

Half height of the nozzle throat (mm)

h

Half duct height (mm)

hs

Thickness of boundary-layer upstream of the suction slot (mm)

H

Duct height (mm)

Ma1

Mach number upstream of the suction slot

Ma2

Mach number downstream of the primary shock

Ma3

Mach number downstream of reflected shocks at the nozzle centre line

\( \dot{m}_{\text{s}} /\dot{m}_{1} \)

Relative mass flow through suction system

p0

Total pressure (bar)

p1

Static pressure upstream of the shock (bar)

p2

Static pressure downstream of the shock (bar)

p3

Static pressure downstream of the suction slot (bar)

pc

Static pressure in the suction cavity (bar)

q

Suction mass flow per span (kg/s m)

R

Specific gas constant (J/kg K)

S

Slot width (mm)

T0

Total temperature (K)

X

Distance of suction slot from first nozzle throat (mm)

Greek symbols

σ

Shock-wave angle (°)

δ

Boundary-layer thickness (mm)

\( \delta^{*} \)

Boundary-layer displacement thickness (mm)

θ

Boundary-layer momentum thickness for undisturbed flow (mm)

β

Deflection angle (°)

γ

Isentropic exponent

Notes

Acknowledgments

The research reported in this paper was funded by the DFG (German research foundation) PAK 75/1. The author also wishes to acknowledge the efforts of Wolfgang Bauer to prepare and carry out the experiments presented herein. Also, thanks to Andreas Grzona for the productive cooperation.

References

  1. Billig F (1993) Research on supersonic combustion. J Propuls Power 9(4):499–514CrossRefGoogle Scholar
  2. Chyu WJ, Rimlinger MJ, Shih TI-P (1995) Control of shock-wave/boundary-layer interactions by bleed. AIAA J 33(7):1239–1247CrossRefGoogle Scholar
  3. Crocco L (1958) One-dimensional treatment of steady gas dynamics. In: Emmons HW (ed) Fundamentals of gas dynamics. Princeton University Press, Princeton, pp 110–130Google Scholar
  4. Davis OD, Willis BP, Hinges WR (1995) Flowfield measurements inside a boundary-layer bleed slot. AIAA J 34(10):1977–1983CrossRefGoogle Scholar
  5. Grzona A, Weiss A, Olivier H et al. (2007) Gas-phase synthesis of non-agglomerated nanoparticles by fast gas dynamic heating and cooling. In: Hannemann K, Seiler F (eds) Shock waves. Proceedings of the 26th international symposium on shock waves, vol 2. Göttingen, Germany, pp 857–862Google Scholar
  6. Hamed A, Yeuan JJ, Shi SH (1995) Shock-wave/boundary layer interaction with bleed part 1: effect of slot angle. J Propuls Power 11(6):1231–1235CrossRefGoogle Scholar
  7. Matsuo K, Miyazato Y, Kim HD (1999) Shock train and pseudo-shock phenomena in internal gas flows. Prog Aerosp Sci 35:33–100CrossRefGoogle Scholar
  8. Schulte D, Henckels A, Wepler U (1998) Reduction of shock induced boundary layer. Aerosp Sci Technol 4:231–239CrossRefGoogle Scholar
  9. Seddon J, Goldsmith EL (1999) Intake aerodynamics. Blackwell Science, OxfordGoogle Scholar
  10. Stanewsky E, Délery J, Fulker J, Geißler W (eds) (1997) Euroshock: drag reduction by passive shock control. Vieweg, WiesbadenzbMATHGoogle Scholar
  11. Stanewsky E, Délery J, Fulker J, de Matteis P (eds) (2002) Euroshock II: drag reduction by shock boundary layer control. Springer, BerlinzbMATHGoogle Scholar
  12. Thompson PA (1972) Compressible-fluid dynamics. McGraw-Hill, New YorkzbMATHGoogle Scholar
  13. Truckenbrodt E (1980) Fluidmechanik, band 1. Springer, BerlinzbMATHGoogle Scholar
  14. Weise A (1943) The separation of flow due to compressibility shock, NACA TM No. 1152, translated from ‘Über die Strömungsablösung durch Verdichtungsstöße’ Technische Berichte, Band 10, Heft 2, pp 59–61Google Scholar
  15. Weiss A, Grzona A, Olivier H (2010) Behavior of shock trains in a diverging duct. Exp Fluids 49(2):355–366CrossRefGoogle Scholar
  16. Wong WF (1974) The application of boundary layer suction to suppress strong shock-induces separation in supersonic inlets. AIAA Paper 74-1063Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Shock Wave LaboratoryRWTH Aachen UniversityAachenGermany

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