Skip to main content
SpringerLink
Log in

Estimation of surface heat flux for ablation and charring of thermal protection material

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

Ablation of the thermal protection material of the reentry hypersonic flight vehicle is a complex physical and chemical process. To estimate the surface heat flux from internal temperature measurement is much more complex than the conventional inverse heat conduction problem case. In the paper, by utilizing a two-layer pyrogeneration-plane ablation model to model the ablation and charring of the material, modifying the finite control volume method to suit for the numerical simulation of the heat conduction equation with variable-geometry, the CGM along with the associated adjoint problem is developed to estimate the surface heat flux. This estimation method is verified with a numerical example at first, the results show that the estimation method is feasible and robust. The larger is the measurement noise, the greater is the deviation of the estimated result from the exact value, and the measurement noise of ablated surface position has a significant and more direct influence on the estimated result of surface heat flux. Furthermore, the estimation method is used to analyze the experimental data of ablation of blunt Carbon-phenolic material Narmco4028 in an arc-heater. It is shown that the estimated surface heat flux agrees with the heating power value of the arc-heater, and the estimation method is basically effective and potential to treat the engineering heat conduction problem with ablation.

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

Similar content being viewed by others

References

  1. Jiang GQ, Liu LY (2003) Heat transfer of hypersonic gas and ablation thermal protection. National Defense Industrial Press, Beijing (In Chinese)

    Google Scholar 

  2. Beck JV, Blackwell B, Clair CRS Jr (1985) Inverse heat conduction: Ill-posed problems. Wiley, New York

    MATH  Google Scholar 

  3. Alifanov OM (1994) Inverse heat transfer problems. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Milos FS, Chen YK (2013) Ablation, thermal response, and chemistry program for analysis of thermal protection systems. J Spacecr Rockets 50(1):137–149

    Article  Google Scholar 

  5. Mahzari M, Cozmuta I, Clark I, Braun R (2011) An inverse parameter estimation methodology for the analysis of aeroheating and thermal protection system experimental data. In: 42nd AIAA thermophysics conference, pp 27–30

  6. Kanevce LP, Kanevce GH, Angelevski ZZ (1999) Comparison of two kinds of experiments for estimation of thermal properties of ablative composite. In: Inverse problems in engineering: theory and practice—3rd international conference on inverse problems in engineering, Port Ludlow, WA, USA, 13–18 June 1999

  7. Oliveira APD, Orlande HRB (2004) Estimation of the heat flux at the surface of ablating materials by using temperature and surface position measurements. Inverse Probl Sci Eng 12(5):563–577

    Article  MathSciNet  Google Scholar 

  8. Hakkaki-Fard A, Kowsary F (2008) Heat flux estimation in a charring ablator. Numer Heat Transf Part A 53:543–560

    Article  Google Scholar 

  9. He KF, Qian WQ, Zhou Y, Shao YP (2013) Estimation of surface heat flux for variable geometry heat conduction problem. In: Fudym O et al (eds) IPDO2013-4th inverse problems, design and optimization symposium, published by Ecole Des Mines d’Albi-Carmaux, France, 2013, pp 55–56

  10. Amar AJ, Blackwell BF, Edwards JR (2008) One-dimensional ablation using a full Newton’s method and finite control volume procedure. J Thermophys Heat Transf 22(1):71–82

    Article  Google Scholar 

  11. Qian WQ, Zhou Y, He KF, Yuan JY, Huang JD (2012) Estimation of surface heat flux for nonlinear inverse heat conduction problem. Acta Aerodyn Sin 30(2):145–150 (In Chinese)

    Google Scholar 

  12. Sutton K (1970) An experimental study of a carbon-phenolic ablation material. NASA-TND-5930

Download references

Acknowledgments

The authors are grateful for the support provided by the National Natural Science Foundation of China (Grant No. 11372338) and the foundation of the State Key Laboratory of Aerodynamics (Grant No. JBKY11030903).

Author information

Authors and Affiliations

  1. State Key Laboratory of Aerodynamics, Mianyang, 621000, Sichuan, China

    Wei-qi Qian, Kai-feng He & Yu Zhou

  2. China Aerodynamics Research and Development Center, Mianyang, 621000, Sichuan, China

    Wei-qi Qian, Kai-feng He & Yu Zhou

Authors
  1. Wei-qi Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai-feng He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei-qi Qian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qian, Wq., He, Kf. & Zhou, Y. Estimation of surface heat flux for ablation and charring of thermal protection material. Heat Mass Transfer 52, 1275–1281 (2016). https://doi.org/10.1007/s00231-015-1653-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-015-1653-9

Keywords

Search

Navigation