Applied Mathematics and Mechanics

, Volume 37, Issue 12, pp 1615–1630 | Cite as

Interpretation of gas-film cooling against aero-thermal heating for high-speed vehicles

  • Ming DongEmail author


The possible application of the film-cooling technique against aero-thermal heating for surfaces of high-speed flying vehicles is discussed. The technique has been widely used in the heat protection of gas turbine blades. It is shown in this paper that, by applying this technique to high-speed flying vehicles, the working principle is fundamentally different. Numerical simulations for two model problems are performed to support the argument. Besides the heat protection, the appreciable drag reduction is found to be another favorable effect. For the second model problem, i.e., the gas cooling for an optical window on a sphere cone, the hydrodynamic instability of the film is studied by the linear stability analysis to observe possible occurrence of laminar-turbulent transition.

Key words

film cooling aero-thermal heating numerical simulation laminar-turbulent transition linear stability analysis 


(x, y)

Catersian coordinate system

u, v

streamwise and wall-normal velocities








sound speed


coefficient of dynamic viscosity


shear stress


specific heat of constant volume


ratio of specific heats, 1.4


width of injection slot


dimensional quantities


quantities of oncoming flow


quantities at injection slot


quantities at interface between oncoming flow and injected gas


Mach number of oncoming flow, u e/a e


dimensional displacement thickness of Blasius boundary layer at location of injection slot in Section 2, m


dimensional radius of nose of sphere cone in Section 3, m


Reynolds number, ρe L*u e/µ e, where L* ≡ δ* in Section 2 and L* = r* in Section 3


total temperature


adiabatic wall temperature


drag force

(ξ, η)

body-fitted coordinate system to analyse boundary layer on sphere cone


semi-cone angle, (°)


perturbation of quantity F, with F representing u, v, T, and ρ

eigenfunction of perturbation F'


amplitude of instability mode




wavenumber of instability mode


frequency of instability mode


amplification factor of instability mode

Chinese Library Classification

O354.4 O357.4 

2010 Mathematics Subject Classification

76E09 76K05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Estrin, Y., Dyskin, A. V., Pasternak, E., Khor, H. C., and Kanel-Belov, A. J. Topological interlocking of protective tiles for the space shuttle. Philosophical Magazine Letters, 83, 351–355 (2003)CrossRefGoogle Scholar
  2. [2]
    Hingst, U. and Korber, S. IR window design for hypersonic missile seekers: thermal shock and cooling systems. Aerospace/Defense Sensing, Simulation and Controls, International Society for Optics and Photonics, Cardiff, 662–672 (2001)Google Scholar
  3. [3]
    Bunker, R. S. A review of shaped hole turbine film-cooling technology. Journal of Heat Transfer, 127, 441–453 (2005)CrossRefGoogle Scholar
  4. [4]
    Gao, Z., Narzary, D. P., and Han, J. C. Film cooling on a gas turbine blade pressure side or suction side with axial shaped holes. International Journal of Heat and Mass Transfer, 51, 2139–2152 (2008)CrossRefGoogle Scholar
  5. [5]
    Li, X. Y., Ren, J., and Jiang, H. D. Film cooling effectiveness distribution of cylindrical hole injections at different locations on a vane endwall. International Journal of Heat and Mass Transfer, 90, 1–14 (2015)CrossRefGoogle Scholar
  6. [6]
    Sriram, R. and Jagadeesh, G. Film cooling at hypersonic Mach numbers using forward facing array of micro-jets. International Journal of Heat and Mass Transfer, 52, 3654–3664 (2009)CrossRefGoogle Scholar
  7. [7]
    Yang, C. S., Lin, C. L., and Gau, C. Film-cooling performance and heat transfer over an inclined film-cooled surface. Journal of Thermophysics and Heat Transfer, 22, 485–492 (2008)CrossRefGoogle Scholar
  8. [8]
    Dong, M. and Wu, X. S. Local scattering theory and the role of an abrupt change on boundarylayer instability and acoustic radiation. 46th AIAA Fluid Dynamics Conference, The American Institute of Aeronautics and Astronautics, Washington, D.C. (2016)Google Scholar
  9. [9]
    Dong, M., Zhang, Y. M., and Zhou, H. A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers—–PSE plus DNS. Applied Mathematics and Mechanics (English Edition), 29, 1527–1534 (2008) DOI 10.1007/s10483-008-1201-zCrossRefzbMATHGoogle Scholar
  10. [10]
    Dong, M. and Zhou, H. A simulation on bypass transition and its key mechanism. Science China Physics Mechanics and Astronomy, 56, 775–784 (2013)CrossRefGoogle Scholar
  11. [11]
    Qin, H. and Dong, M. Boundary-layer disturbances subjected to free-stream turbulence and simulation on bypass transition. Applied Mathematics and Mechanics (English Edition), 37, 967–986 (2016) DOI 10.1007/s10483-016-2111-8CrossRefGoogle Scholar
  12. [12]
    Zhang, H. X. and Zhuang, F. G. NND schemes and their application to numerical simulation of two and three dimensional flows. Advances in Applied Mechanics, 29, 193–256 (1992)CrossRefzbMATHGoogle Scholar
  13. [13]
    Schmid, P. and Henningson, D. Stability and Transition in Shear Flows, Springer, New York (2001)CrossRefzbMATHGoogle Scholar
  14. [14]
    Su, C. H. and Zhou, H. Transition prediction of a hypersonic boundary layer over a cone at small angle of attack with the improvement of eN method. Science China Physics Mechanics and Astronomy, 52, 115–123 (2009)CrossRefGoogle Scholar
  15. [15]
    Su, C. H. The reliability of the improved eN method for the transition prediction of boundary layer on a flat plate. Science China Physics Mechanics and Astronomy, 55, 837–843 (2012)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MechanicsTianjin UniversityTianjinChina
  2. 2.Tianjin Key Laboratory of Modern Engineering MechanicsTianjinChina

Personalised recommendations