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Extrapolation-to-flight of aerodynamic heating measurements and determination of in-flight radiation-equilibrium surface temperature in hypersonic/high enthalpy flow conditions

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Abstract

The previously demonstrated success of the reference enthalpy concept in heat transfer prediction at hypersonic flow conditions is utilized herein to propose a cost-effective methodology for extrapolation-to-flight of Stanton number measurements (or baseline computational results), and the determination of radiation-equilibrium surface temperatures that develop on actual vehicle surfaces during hypersonic/high enthalpy flight conditions. The methodology couples the (analytical) generalized reference enthalpy solution with Euler computations (providing input data along the edge of thin boundary layers) and is, therefore, significantly cheaper and more efficient than the execution of full Navier–Stokes computations that are presently incorporated, particularly so in the thermo-chemically active high enthalpy flow regime. The validity of the proposed methodology is demonstrated in a first step by means of two-dimensional test cases, whereby extrapolated data accuracy is better than 20%.

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Abbreviations

b.l.:

boundary layer

C :

constant

c p :

specific heat at constant pressure

h :

enthalpy

M :

Mach number

l.e.:

leading edge

L :

body length

n :

exponent

p :

pressure

Pr :

Prandtl number

r :

recovery factor

q :

heat transfer rate

Re :

Reynolds number

St :

Stanton number

T :

temperature

u :

velocity

x (or s):

coordinate in main flow direction – effective boundary layer growth length

ε:

emissivity

μ:

viscosity

ρ:

density

e :

boundary layer edge

flt:

flight (extrapolated condition)

grad:

(velocity) gradient

L :

based on body length

main:

(velocity component) in main flow direction or resultant velocity

radeq:

radiation-equilibrium

rec:

recovery

stag:

stagnation (total)

unit:

free-stream unit (Reynolds number per meter)

w:

wall

WT:

wind tunnel (baseline condition)

∞, inf:

free-stream

*:

reference enthalpy

References

  1. Simeonides, G.: Simple formulations for convective heat transfer prediction over generic aerodynamic configurations and scaling of radiation-equilibrium wall temperature. ESA/ESTEC EWP-1860; included in ESA Working Paper EWP-1880 (1995)

  2. Simeonides G. (1998). Generalised reference enthalpy formulations and simulation of viscous effects in hypersonic flow. Shock Waves J. 8(3): 161–172

    Article  Google Scholar 

  3. Eckert, E.R.G.: Engineering relations of friction and heat transfer to surfaces in high velocity flow. J. Aeronaut. Sci. 22(8), (1955)

  4. Fay J.A., Riddell F.R. (1958). Theory of stagnation point heat transfer in dissociated air. J. Aeronaut. Sci. 25(2): 13–85

    MathSciNet  Google Scholar 

  5. Poll, D.I.A.: Heat transfer to a swept leading edge in hypersonic flow including effects of transition. Aerothermochemistry of Spacecraft and Associated Hypersonic Flows, IUTAM Symposium, Marseille (1992)

  6. Hayes, J.R., Neumann, R.D.: Introduction to aerodynamic heating analysis of supersonic missiles. In: Merendhal, M.R. (ed.) Tactical missile aerodynamics prediction methodology, AIAA Progress in Astronautics and Aeronautics, Vol. 142 (1992)

  7. Simeonides G., Haase W. (1995). Experimental and computational investigations of hypersonic flow about compression corners. J. Fluid Mech. 283: 17–42

    Article  Google Scholar 

  8. Vermeulen, J.P., Simeonides, G.: Parametric studies of shock wave boundary layer interactions over 2D compression corners at Mach 6. Von Karman Institute TN 181 (1992)

  9. Simeonides, G., Walpot, L., Netterfield, M., Tumino, G.: Evaluation of engineering heat transfer prediction methods in high enthalpy flow conditions. 31st AIAA Thermophysics Conference, New Orleans, AIAA Paper 96-1860 (1996)

  10. Simeonides G., Walpot L., Netterfield M., Tumino G. (1998). Evaluation of engineering heat transfer prediction methods in high enthalpy flow conditions. AIAA J. Spacecr. Rockets 35(1): 107–109

    Article  Google Scholar 

  11. Hirschel, E.H.: Basics of aerothermodynamics. Engineering Monograph, Springer, Berlin Heidelberg New York and Progress in Astronautics and Aeronautics, AIAA Inc, Washington DC (2004)

  12. Hirschel, E.H.: Aerothermodynamics of radiation cooled surfaces. Aerothermodynamics and propulsion Integration for Hypersonic Vehicles, AGARD FDP-VKI Special Course, AGARD-R-813, pp. 3-1–3-16 (1996)

  13. Hamilton H.H., DeJarnette F.R., Weilmuenster K.J. (1987). Application of axisymmetric analog for calculating heating in three-dimensional flows. AIAA J. Spacecr. 24(4): 296–302

    Article  Google Scholar 

  14. Zoby E.V., Moss J.N., Sutton K. (1981). Approximate convective heating equations for hypersonic flows. AIAA J. Spacecr. Rockets 18(1): 64–70

    Article  Google Scholar 

  15. Moeckel, W.E., Weston, K.C.: Composition and thermodynamic properties of air in chemical equilibrium. NACA TN 4265 (1958)

  16. Gupta, R.N., Lee, K.P., Thompson, R.A., Yos, J.M.: Calculations and curve fits of thermodynamic and transport properties for equilibrium air to 30,000 K. NASA Ref. Publ. 1260 (1991)

  17. Simeonides, G: Hypersonic shock wave boundary layer interactions over compression corners. Ph.D. Thesis, von Karman Institute/University of Bristol (1992)

  18. Simeonides, G., Gibergy, X., De La Casa, X., Charbonnier, J.M.: Combined convective heating–radiation cooling analysis for aerodynamic surfaces in hypersonic flow and experimental simulation of temperature viscous effects. In: Heat Transfer in Single Phase Flows 5, Proceedings EUROTHERM Seminar 55, National Technical University of Athens (1997)

  19. Walpot L.M.G., Simeonides G., Muylaert J., Bakker P.G. (1996). High enthalpy nozzle flow sensitivity study and effects on heat transfer. International J. Shock Waves 6(4): 197–204

    Article  Google Scholar 

  20. American Institute of Physics Handbook. McGraw Hill, New York (1957)

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Authors and Affiliations

  1. Hellenic Aerospace Industry, S.A., P.O. Box 23, 32009, Schimatari, Greece

    George A. Simeonides

  2. Department of Mechanical and Aeronautical Engineering, University of Patras, Rio Patras, Greece

    George A. Simeonides

Authors
  1. George A. Simeonides
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Correspondence to George A. Simeonides.

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Communicated by K. Takayama.

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Simeonides, G.A. Extrapolation-to-flight of aerodynamic heating measurements and determination of in-flight radiation-equilibrium surface temperature in hypersonic/high enthalpy flow conditions. Shock Waves 16, 25–34 (2006). https://doi.org/10.1007/s00193-006-0040-3

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