An optimal design of thermal protection based on materials morphology

  • Margarita O. Salosina Moscow Aviation Institute
  • Oleg M. Alifanov Moscow Aviation Institute
  • Aleksey V. Nenarokomov Moscow Aviation Institute


The paper presents a methodology for the optimal design of multilayer thermal protection based on high-porosity open-cell foam, taking into account the foam morphology. The vector of design parameters includes the thicknesses of layers, porosity and cell diameter of open-cell foam and should ensure required operation temperature on the boundaries of layers and a minimum of the total mass of the system. The optimization problem is solved using a computational scheme, which combines the projected Lagrangian method with the quadratic subproblem and the penalty function method. The penalty function method provides a good initial estimate of the optimal parameters’ values for the projected Lagrangian method with excellent local convergence properties. To illustrate the implementation of the developed algorithm and the corresponding software, the problem of choosing the optimal layer thicknesses for the multilayer thermal protection of a spacecraft along with the cell diameter and porosity of foam is considered.


optimal design, multilayer thermal protection, open-cell foam,


[1] D. Baillis, M. Raynaud, J.F. Sacadura. Determination of spectral radiative properties of open cell foam: Model validation. Journal of Thermophysics and Heat Transfer, 14(2): 137–143, 2000, doi: 10.2514/2.6519.
[2] A. Yu. Bushuev, V.V. Gorskii. One approach to constructing a method for designing model heat shields. Journal of Engineering Physics, 61(3): 1150–1156, 1991, doi: 10.1007/BF00872896.
[3] A. Yu. Bushuev, V.V. Gorskii. Use of sensitivity functions in the problem of designing a multilayer heat shield. Journal of Engineering Physics, 61(6): 1548–1554, 1991, doi: 10.1007/BF00872013.
[4] R. Coquard, D. Rochais, D. Baillis. Conductive and radiative heat transfer in ceramic and metal foams at fire temperatures. Fire Technology, 48(3): 699–732, 2012, doi: 10.1007/s10694-010-0167-8.
[5] S. Cunsolo, R. Coquard, D. Baillis, N. Bianco. Radiative properties modeling of open cell solid foam: Review and new analytical law. International Journal of Thermal Sciences, 104: 122–134, 2016, doi: 10.1016/j.jqsrt.2007.05.007.
[6] S. Cunsolo, R. Coquard, D. Baillis, W.K.S. Chiu, N. Bianco. Radiative properties of irregular open cell solid foams. International Journal of Thermal Sciences, 117: 77–89, 2017, doi: 10.1016/j.ijthermalsci.2017.03.007.
[7] P.E. Gill, W. Murray, M.H. Wright. Practical Optimization. Academic Press, London, 1981.
[8] I.S. Grigoriev, E.Z. Meilikhov [Eds]. Physical Quantities: Directory [in Russian]. Energoatomizdat, Moscow, 1991.
[9] M. Loretz, R. Coquard, D. Baillis, E. Maire. Metallic foams: Radiative properties/comparison between different models. Journal of Quantitative Spectroscopy and Radiative Transfer, 109(1): 16–27, 2008, doi: 10.1016/j.jqsrt.2007.05.007.
[10] I.A. Maiorova, P.V. Prosuntsov, A.V. Zuev. Optimal thermal design of a multishield thermal protection system of a reusable space vehicles. Journal of Engineering Physics and Thermophisics, 89(2): 528–533, 2016, doi: 10.1007/s10891-016-1406-8.
[11] R.A. Meric. Finite element analysis of optimal heating of a slab with temperature-dependent thermal conductivity. International Journal Heat and Mass Transfer, 22(10): 1347–1353, 1978, doi: 10.1016/0017-9310(79)90197-2.
[12] R.A. Meric. Optimal thermal insulation by the boundary element method. Numerical Heat Transfer, 9(2): 163–182, 1986.
[13] R.A. Meric. Sensitivity analysis and optimization for Joule heating with temperature-dependent conductivities. Numerical Heat Transfer. Part B: Fundamentals, 16(2): 213–229, 1990, doi: 10.1080/10407798908944936.
[14] V.V. Mikhailov. Optimization of multilayer thermal insulation. Journal of Engineering Physics, 39(2): 880–884, 1980.
[15] A.V. Nenarokomov. Design of a system of multilayer heat insulation of minimum mass [in Russian]. TVT, 35(6): 909–916; High Temperature, 35(6): 896–903, 1997.
[16] M. Nosratollahi, M. Mortazavi, A. Adami, M. Hosseini. Multidisciplinary design optimization of a reentry vehicle using genetic algorithm. Aircraft Engineering and Aerospace Technology: An International Journal, 82(3): 194–203, 2010, doi: 10.1108/00 022661011075928.
[17] A. ¨Ochsner, G.E. Murch, M.J.S. de Lemos [Eds]. Cellular and Porous Materials: Thermal Properties Simulation and Prediction. Wiley-VCH, Weinheim, 2008.
[18] R.J. Papoular, R. Papoular. Some optical properties of graphite from IR to millimetric wavelengths. Monthly Notices of the Royal Astronomical Society, 443(4): 2974–2982, 2014, doi: 10.1093/mnras/stu1348.
[19] A. Riccio, F. Raimondo, A. Sellitto, V. Carandente, R. Scigliano, D. Tescione. Optimum design of ablative thermal protection systems for atmospheric entry vehicles. Applied Thermal Engineering, 119: 541–552, 2017, doi: 10.1016/j.applthermaleng.2017.03.053.
[20] A.A. Shmukin, R.A. Posudievskii. Optimization of multilayer fusing heat-insulating coating. Journal of Engineering Physics, 50(2): 174–178, 1986, doi: 10.1007/BF00870083.
[21] K. Svanberg. The method of moving asymptotes – a new method for structural optimization. International Journal for Numerical Methods of Engineering, 24(2): 359–373, 1987, doi: 10.1002/nme.1620240207.
[22] G. Xie, Q. Wang, B. Sunden, W. Zhang. Thermomechanical optimization of lightweight thermal protection system under aerodynamic heating. Applied Thermal Engineering, 59(1–2): 425–434, 2013, doi: 10.1016/j.applthermaleng.2013.06.002.
Oct 3, 2019
How to Cite
SALOSINA, Margarita O.; ALIFANOV, Oleg M.; NENAROKOMOV, Aleksey V.. An optimal design of thermal protection based on materials morphology. Computer Assisted Methods in Engineering and Science, [S.l.], v. 26, n. 1, p. 47-60, oct. 2019. ISSN 2956-5839. Available at: <>. Date accessed: 21 june 2024. doi: