Skip to main content
SpringerLink
Log in

Wall pressure fluctuations over a bulbous heat shield of a satellite launch vehicle

  • Original Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

Unsteady compressible Reynolds-averaged Navier-Stokes equations are solved for computing the flowfield over a bulbous heat shield of a satellite launch vehicle at free stream Mach number of 0.95 and 1.20 and at zero angle of incidence. A time-dependent computation is carried out employing a multistage Runge-Kutta time-stepping in conjunction with a finite volume discretization. Closure of these equations is achieved using the Baldwin-Lomax turbulence model. Comparisons are made with the experimental results such as schlieren picture and surface pressure distribution. They are found in good agreement. Numerical analysis is used to determine the characteristics of the fluctuating surface pressure at transonic and supersonic speeds. Standard deviations, higher moments, histograms, and spectrum of pressure and sound pressure level of fluctuating pressure are analyzed in the separated region of the boattail of the heat shield. High frequency components of pressure amplitude and sound pressure levels are found to be dominate at supersonic Mach number as compared to transonic Mach number.

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

Similar content being viewed by others

Abbreviations

A :

area of the computational cell

C p :

specific heat at constant pressure

C p :

static pressure coefficient

C v :

specific heat at constant volume

D :

payload shroud diameter

D :

artificial dissipation vector

e :

specific energy

F, G :

inviscid flux vector

H :

source vector

K CP :

kurtosis coefficient

M:

Mach number

p :

static pressure

<p>:

pressure fluctuation

Pr :

Prandtl number

q :

heat flux

Re:

Reynolds number

R, S :

viscous flux vector

S CP :

skewness coefficient

t :

time

u, v :

velocity components

W :

conservative variables in vector form

x, r :

coordinate directions

β:

stretching factor

γ:

ratio of specific heats

μ:

molecular viscosity

ϱ:

density

σ:

stress vector

σ CP :

standard deviation

t :

turbulent

∞:

free stream condition

ω:

wall

References

  1. Bourgine, A.: Etude des fluctuations de pression pariétales, en écoulement transonique, sur ensemble cone-cylinder présentant un retreint. ONERA TP No 942, 1971.

  2. Mehta, R. C.: Transonic flow simulation for a bulbous heat shield. J. Spacecraft Rockets34, 561–564 (1997).

    Google Scholar 

  3. Doerffer, P., Zierep, J.: An experimental investigation of the Reynolds number effect on a normal shock wave-turbulent boundary layer interaction on a curved wall. Acta Mech.73, 77–93 (1988).

    Google Scholar 

  4. Lighthill, M. J.: On sound generated aerodynamically. Proc. R. Soc. London Ser.A 211, 564–587 (1952).

    Google Scholar 

  5. hayden, R. E., Kadman, Y., Bliss, D. B., Afrik, S. A.: Diagnostic calculations of airframeradia noise. Prog. Astron. Aeron.45, 179–201 (1976).

    Google Scholar 

  6. Karamcheti, K.: Airframe and airfoil noise-panel discussion. Prog. Astron. Aeron.45, 441–443 (1976).

    Google Scholar 

  7. Kistler, A. L.: Fluctuating wall pressure under a separated supersonic flow. J. Acoust. Soc. Am.36, 543–550 (1964).

    Google Scholar 

  8. Dolling, D. S., Bogdonoff, S. M.: An experimental investigation of the unsteady behaviour of blunt fin-induced shock wave turbulent boundary layer interaction. AIAA paper 81-1287, 1981.

  9. Hayashi, M., Aso, S., Tam, A.: Fluctuations of wall pressure in the interacting region of oblique shock wave and turbulent boundary layer. Techn. Rep. Kyushu Univ.59, 75–82 (1986).

    Google Scholar 

  10. Dolling, D. S.: Fluctuating loads in shock wave/turbulent boundary layer interaction. AIAA paper 93-0284, 1993.

  11. Buffeting during atmospheric ascent. NASA Special Vehicle Design Criteria, NASA SP 8001, 1970.

  12. Coe, C. F.: The effects of some variations in launch-vehicle nose shape on steady and fluctuating pressure at transonic speeds. NASA TM X-646, 1962.

  13. Purohit, S. C.: A Navier-Stokes solution for bulbous payload shroud. J. Spacecraft Rockets23, 590–596 (1986).

    Google Scholar 

  14. Baldwin, B. S., Lomax, H.: Thin layer approximation and algebraic model for separated turbulent flows. AIAA paper 78-257, 1978.

  15. Purohit, S. C., Shang, J. S., Hankey, W. L.: Effect of suction on the wave structure of a three dimensional turret. AIAA paper 83-1738, 1983.

  16. Peyret, R., Viviand, H.: Computational methods for fluid flow, pp. 109–111. Berlin Heidelberg New York Tokyo: Springer 1993.

    Google Scholar 

  17. Jameson, A., Schmidt, W., Turkel, E.: Numerical solution of Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA paper 81-1259, 1981.

  18. Mehta, R. C.: Finite element with homotopy scheme for quasi-three-dimensional grid generation. Comm. Num. Meth. Eng. (submitted).

  19. Ahmed, S.: Flow visualization studies at transonic speeds on heat shield configurations. National Aeronautical Laboratories. Bangalore, NAL-TWT-1-36, 1984.

    Google Scholar 

  20. Mehta, R. C.: Numerical studies over a bulbous payload shroud in transonic and low supersonic Mach number. AIAA paper 97-2256, 1997.

  21. MATLAB User's Guide, pp. 2.47–2.51. The Math Works Inc. USA, 1992.

Download references

Author information

Author notes

  1. R. C. Mehta

    Present address: Aerodynamics Division, Vikram sarabhai Space Centre, 695022, Trivandrum, India

Authors and Affiliations

    Authors
    1. R. C. Mehta
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Mehta, R.C. Wall pressure fluctuations over a bulbous heat shield of a satellite launch vehicle. Acta Mechanica 137, 13–31 (1999). https://doi.org/10.1007/BF01313141

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01313141

    Keywords

    Search

    Navigation