Skip to main content
SpringerLink
Log in

Computation of turbulent flow in a mixed compression intake

  • Published:
International Journal of Advances in Engineering Sciences and Applied Mathematics Aims and scope Submit manuscript

Abstract

Turbulent flow in a mixed compression intake is investigated. The unsteady compressible Navier–Stokes equations are solved using a stabilized finite element method with 6-noded triangular element. The Spalart–Allmaras model is used for turbulence closure. For comparison, the laminar flow is studied as well. A bleed of 6 % is utilized to overcome the start-up problem of the intake. The effect of back pressure on the performance of the intake is studied via the total pressure recovery and distortion index. Total pressure recovery is relatively lower while distortion index is higher for turbulent flow compared to laminar flow. The critical back pressure ratio, for unstart of the intake, for turbulent flow is higher compared to laminar flow. The effect of bleed on the performance of the intake is studied.

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Abbreviations

\(p_b/p_i\) :

Back pressure ratio

\(\rho \) :

Density

DI:

Distortion index, (\(p_{0max} - p_{0min})\)/\(\bar{p}_{0}\)

\(\mu \) :

Dynamic viscosity

\({\nu }\) :

Kinematic viscosity

\(\tilde{\nu }\) :

Kinetic eddy viscosity

M:

Mach number

\(\dot{m}\) :

Mass flow rate

Re:

Reynolds number

p:

Static pressure

\(\theta \) :

Static temperature

TPR:

Total pressure recovery, \(\bar{p}_{0}\)/\(p_{0i}\)

\(\mu _t\) :

Turbulent viscosity

\(\infty \) :

Free-stream

i:

Inflow

cowl:

Lower cowl wall

ramp:

Ramp wall

t:

Throat

0:

Total/stagnation

\(\sim \) :

Favre-mass averaging

–:

Reynolds averaging

\({''}\) :

Unsteady fluctuation

References

  1. Hill, P.G., Peterson, C.R.: Mechanics and Thermodynamics of Propulsion, vol. 1. Addison-Wesley Publishing Co., Reading (1992)

    Google Scholar 

  2. Seddon, J., Goldsmith, E.L.: Intake Aerodynamics, vol. 2. Blackwell science, London (1999)

    Google Scholar 

  3. Oswatitsch, K.: Pressure Recovery in Missiles with Reaction Propulsion at High Supersonic Speeds. NACA TM-1140. National Advisory Committee for Aeronautics, Washington (1947)

  4. Ferri, A., Nucci, R.: The Origin of Aerodynamic Instability of Supersonic Inlets at Subcritical Conditions. NACA RM-L50K30. National Advisory Committee for Aeronautics, Washington (1951)

  5. Trimpi, R.: A Theory for Stability and Buzz Pulsation Amplitude in Ram Jets and an Experimental Investigation Inducing Scale Effects. NACA Report-1265. National Advisory Committee for Aeronautics, Washington (1953)

  6. Dailey, C.L.: Supersonic diffuser instability. J. Aeronaut. Sci. 22, 733–749 (1955)

    Article  Google Scholar 

  7. Fisher, S., Neale, M., Brooks, A.: On the Sub-Critical Stability of Variable Ramp Intakes at Mach Numbers Around 2. National Gas Turbine Establishment, ARC R. & M. no.3711 (1970)

  8. Herrmann, D., Gülhan, A.: Experimental analyses of inlet characteristics of an airbreathing missile with boundary-layer bleed. J. Propuls. Power 23, 1–10 (2014).

    Google Scholar 

  9. Newsome, R.W.: Numerical simulation of near-critical and unsteady, subcritical inlet flow. AIAA J. 22(10), 1375–1379 (1984)

    Article  MATH  Google Scholar 

  10. Shigematsu, J., Yamamoto, K., Shiraishi, K., Tanaka, A.: A numerical investigation of supersonic inlet using implicit TVD scheme. AIAA Paper 2135 (1990)

  11. Lu, P.J., Jain, L.T.: Numerical investigation of inlet buzz flow. J. Propuls. Power 14(1), 90–100 (1998)

    Article  Google Scholar 

  12. Trapier, S., Duveau, P., Deck, S.: Experimental study of supersonic inlet buzz. AIAA J. 44(10), 2354–2365 (2006)

    Article  Google Scholar 

  13. Lee, H.J., Lee, B.J., Kim, S.D., Jeung, I.S.: Flow characteristics of small-sized supersonic inlets. J. Propuls. Power 27(2), 306–318 (2011)

    Article  Google Scholar 

  14. Knight, D.D.: Improved calculation of high speed inlet flows. part II: results. AIAA J. 19(2), 172–179 (1981)

    Article  Google Scholar 

  15. Knight, D.: Calculation of a Simulated 3-D High Speed Inlet Using the Navier–Stokes Equations. AIAA Paper (83-1165) (1983)

  16. Chan, J.J., Liang, S.M.: Numerical investigation of supersonic mixed-compression inlet using an implicit upwind scheme. J. Propuls. Power 8(1), 158–167 (1992)

    Article  Google Scholar 

  17. Anderson, W.E., Wong, N.D.: Experimental Investigation of a Large Scale, Two-Dimensional, Mixed-Compression Inlet System: Performance at Design Conditions, \({M}_{\infty }=3.0\). NASA TM X-2016 (1970)

  18. Jain, M.K., Mittal, S.: Euler flow in a supersonic mixed-compression inlet. Int. J. Numer. Methods Fluids 50, 1405–1423 (2006)

    Article  MATH  Google Scholar 

  19. Kotteda, V.M.K., Mittal, S.: Viscous flow in a mixed compression intake. Int. J. Numur. Methods Fluids 67, 1393–1417 (2011)

    Article  MATH  Google Scholar 

  20. Vivek, P., Mittal, S.: Buzz instability in a mixed-compression air intake. J. Propuls. Power 25, 819–822 (2009)

    Article  Google Scholar 

  21. Trapier, S., Deck, S., Duveau, P.: Delayed detached-eddy simulation and analysis of supersonic inlet buzz. AIAA J. 46(1), 118–131 (2008)

    Article  Google Scholar 

  22. Hughes, T.J., Brooks, A.: A multidimensional upwind scheme with no crosswind diffusion. Finite Elem. Methods Convect. Domin. Flows AMD 34, 19–35 (1979)

    MathSciNet  Google Scholar 

  23. Brooks, A.N., Hughes, T.J.R.: Streamline Upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 32, 199–259 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  24. Tezduyar, T., Hughes, T.: Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: Proceedings of AIAA 21st Aerospace Sciences Meeting, AIAA Paper, vol. 83, p. 0125 (1983)

  25. Le Beau, G.J., Tezduyar, T.E.: Finite element computation of compressible flows with the SUPG formulation. In: Dhaubhadel, M., Engelman, M.S., Reddy, J.N. (eds.) American Society of Mechanical Engineers, vol. 123, pp. 21–27. Fluids Engineering Division (Publication) FED, Portland (1991)

    Google Scholar 

  26. Mittal, S.: Finite element computation of unsteady viscous compressible flows. Comput. Methods Appl. Mech. Eng. 157, 151–175 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  27. Mittal, S.: Finite element computation of unsteady viscous transonic flows past stationary airfoils. Comput. Mech. 21, 172–188 (1998)

    Article  MATH  Google Scholar 

  28. Kotteda, V.M.K., Mittal, S.: Stabilized finite-element computation of compressible flow with linear and quadratic interpolation functions. Int. J. Numer. Methods Fluids 75(4), 273–294 (2014)

    Article  MathSciNet  Google Scholar 

  29. Spalart, P.R., Allmaras, S.R.: One-Equation Turbulence Model for Aerodynamic Flows. AIAA-92-0439 (1992)

  30. Wervaecke, C., Beaugendre, H., Nkonga, B.: A fully coupled RANS Spalart–Allmaras SUPG formulation for turbulent compressible flows on stretched–unstructured grids. Comput. Methods Appl. Mech. Eng. 233, 109–122 (2012)

    Article  MathSciNet  Google Scholar 

  31. Gacherieu, C., Weber, C., Coriolis, G.: Assessment of Algebraic and One-Equation Turbulence Models for the Transonic Turbulent Flow Around a Full Aircraft Configuration, pp. 98–32457. AIAA paper (1998)

  32. Rogers, S., Roth, K., Nash, S., Baker, M., Slotnick, J., Cao, H., Whitlock, M.: Advances in Overset CFD Processes Applied to Subsonic High-Lift Aircraft. AIAA paper 2000-4216 (2000)

  33. Deck, S., Duveau, P., d’Espiney, P., Guillen, P.: Development and application of Spalart–Allmaras one equation turbulence model to three-dimensional supersonic complex configurations. Aerosp. Sci. Technol. 6(3), 171–183 (2002)

    Article  MATH  Google Scholar 

  34. Launder, B.E., Sandham, N.D.: Closure Strategies for Turbulent and Transitional Flows. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  35. Mizukami, A.: An implementation of the Streamline-Upwind/Petrov–Galerkin method for linear triangular elements. Comput. Methods Appl. Mech. Eng. 49, 357–364 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  36. Hughes, T.J.R., Mallet, M., Mizukami, A.: A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput. Methods Appl. Mech. Eng. 54, 341–355 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  37. Tezduyar, T.E.: Adaptive determination of the finite element stabilization parameters. In: Proceedings of the ECCOMAS Computational Fluid Dynamics Conference. Swansea, Wales (2001)

  38. Mittal, S., Kumar, B.: Flow past a rotating cylinder. J. Fluid Mech. 476, 303–334 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  39. Akin, J.E., Tezduyar, T., Ungor, M., Mittal, S.: Stabilization parameters and Smagorinsky turbulence model. J. Appl. Mech. Trans. ASME 70, 2–9 (2003)

    Article  MATH  Google Scholar 

  40. Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, 208 016, UP, India

    V. M. Krushnarao Kotteda & Sanjay Mittal

Authors
  1. V. M. Krushnarao Kotteda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjay Mittal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanjay Mittal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kotteda, V.M.K., Mittal, S. Computation of turbulent flow in a mixed compression intake. Int J Adv Eng Sci Appl Math 6, 126–141 (2014). https://doi.org/10.1007/s12572-014-0115-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12572-014-0115-9

Keywords

Search

Navigation