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A Method for Solving Non-Linear Thermal Problems in Re-entry of Space Vehicles

Published online by Cambridge University Press:  07 June 2016

Luigi Broglio
Luigi Broglio*
Affiliation:
Rome University
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Summary

The paper considers a body, or space vehicle, of arbitrary shape, with conductivity K and specific heat c. It is first assumed that K and c are invariant with time and the body, with a given initial temperature, is assumed to be heated by a distribution of heat sources that varies with space co-ordinates and time. It is shown that a rigorous analytical solution to the problem is possible, provided that the distribution function satisfies prescribed regularity conditions.

The same problem is then considered, but with a heat-source distribution which is also a function of temperature. In this case the problem can be reduced to a Volterra-type integral equation amenable to step-by-step solution. Convective heating and radiation are specific examples of this second case.

The third case considered is that of a body whose geometry and thermal coefficients K and c are all time-dependent, and this problem is reduced to the fixed-geometry case by the addition of a hypothetical heat-source distribution which is a function of the velocity of ablation, of temperature and of its time derivative; an integral equation of Volterra type again results.

Finally, an example is given of the application of the analysis to the ablation of a conductive spherical shell.

Type
Research Article
Information
Aeronautical Quarterly , Volume 13 , Issue 4 , November 1962 , pp. 291 - 300
Copyright
Copyright © Royal Aeronautical Society. 1962

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References

1. Broglio, L. Some Contributions to the Heat Conduction and Thermal Stresses Analysis in Aircraft and Missile Structures. Proceedings of the First I.C.A.S. Congress, Madrid, 1958, Vol. 1. Pergamon, 1959.Google Scholar
2. Broglio, L. Transient Temperatures and Thermal Vibrations in Space Structures. Proceedings of Durand Centennial Congress, Stanford University, August 1959.Google Scholar
3. Abarbanel, S. S. On Some Problems in Radiative Heat Transfer, Massachusetts Institute of Technology, Fluid Dynamics Research Group, Report 59-1 (AFOSR TN 59-31), April 1959.Google Scholar
4. Broglio, L. Heat Conduction in Solids at Hypersonic Speed. AGARD Report 209, 1958.Google Scholar
5. Broglio, L. Similar Solutions in Re-Entry Lifting Trajectories. From the book Space Research, Proceedings of the First International Space Science Symposium, p. 564, North Holland Publishing Company, Amsterdam, 1960.Google Scholar