Identification of insulating materials thermal properties by inverse method using reduced order model

Abstract The analytical models used by hot-wire type probes are no longer suitable for the characterization of insulating materials. This paper proposes a solution, which is based on a numerical reduced order technique named AROMM (Amalgamated Reduced Order Modal Method) coupled to an inverse procedure. We demonstrate that a single reduced order model provides precise results for insulated materials characterized by different thermal properties, with the advantage of computing 250 times faster than a classical finite element modelization. Such model is then tested through multiple scenarios in order to evaluate the accuracy of the proposed methodology. Results show the importance of the sensitivity of the measurement regarding the sought parameters, which later intervene during the identification process. A statistical study allows us to access a satisfying confidence interval for a common measurement noise. At last, a study on the influence of an eventual thermal contact resistance is conducted.

[1]  Hyun jun Kim,et al.  Thermal conductivity measurement of anisotropic material using photothermal deflection method , 2008 .

[2]  M. Lazard,et al.  Online Temperature Prediction Using a Branch Eigenmode Reduced Model Applied to Cutting Process , 2009 .

[3]  Adam Fic,et al.  Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element Method , 2005 .

[4]  O. Quéméner,et al.  Modal Reduction of an Advection-Diffusion Model Using a Branch Basis , 2008 .

[5]  M. E. Prado,et al.  Thermal Conductivity Measurements and Predictive Models for Frozen Guava and Passion Fruit Pulps , 2013 .

[6]  Elissa El Rassy,et al.  Unconventional flash technique for the identification of multilayer thermal diffusivity tensors , 2020 .

[7]  Günter Kargl,et al.  In situ methods for measuring thermal properties and heat flux on planetary bodies , 2011, Planetary and space science.

[8]  L. Marmoret,et al.  Limit of validity of the log-linear model for determining thermal properties of light insulation materials with cylindrical hot probe , 2017 .

[9]  In Situ Measurement of Thermal Diffusivity in Anisotropic Media , 2013 .

[10]  Juan Pou,et al.  Thermal properties measurement of slate using laser flash method , 2012 .

[11]  Maurice Clerc,et al.  L'optimisation par essaim particulaire , 2002, Techniques et sciences informatiques.

[12]  M. Akoshima,et al.  Experimental Verification to Obtain Intrinsic Thermal Diffusivity by Laser-Flash Method , 2013 .

[13]  Richard Griffiths,et al.  Analysis of thermal-probe measurements using an iterative method to give sample conductivity and diffusivity data , 2004 .

[14]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[15]  H. Park,et al.  On the solution of inverse heat transfer problem using the Karhunen–Loève Galerkin method , 1999 .

[16]  Simultaneous Estimation of the Thermal Diffusivity and Thermal Contact Resistance of Thin Solid Films and Coatings Using the Two-Dimensional Flash Method , 2003 .

[17]  Yves Jannot,et al.  Simplified estimation method for the determination of the thermal effusivity and thermal conductivity using a low cost hot strip , 2004 .

[18]  B. Bhushan,et al.  Thermal diffusivity study of aged Li-ion batteries using flash method , 2010 .

[19]  Stephen Grove,et al.  Thermal conductivity probe length to radius ratio problem when measuring building insulation materials , 2012 .

[20]  Bart Nicolai,et al.  Optimization of the temperature sensor position in a hot wire probe set up for estimation of the thermal properties of foods using optimal experimental design , 2003 .

[21]  Y. Rouizi,et al.  Numerical model reduction of 2D steady incompressible laminar flows: Application on the flow over a backward-facing step , 2009, J. Comput. Phys..

[22]  H. Beji,et al.  Assessment of long time approximation equation to determine thermal conductivity of high porous materials with NSS probe , 2016 .

[23]  E. Cueto,et al.  Proper Generalized Decomposition based dynamic data driven inverse identification , 2012, Math. Comput. Simul..

[24]  S. Nielsen,et al.  Determination of thermal properties of materials by Monte Carlo inversion of pulsed needle probe data , 2019, International Journal of Heat and Mass Transfer.

[25]  S. D. Probert,et al.  Use of the thermal-probe technique for the measurement of the apparent thermal conductivities of moist materials , 1984 .

[26]  S. Carmona,et al.  Spatio-temporal identification of heat flux density using reduced models. Application to a brake pad , 2019, International Journal of Heat and Mass Transfer.

[27]  Daniel Petit,et al.  Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step , 2010 .

[28]  W. Tao,et al.  Theoretical accuracy of anisotropic thermal conductivity determined by transient plane source method , 2017 .

[29]  S. Carmona,et al.  Estimation of heat flux by using reduced model and the adjoint method. Application to a brake disc rotating , 2018, International Journal of Thermal Sciences.

[30]  Etienne Videcoq,et al.  Heat source identification and on-line temperature control by a Branch Eigenmodes Reduced Model , 2008 .

[31]  Yves Jannot,et al.  Thermal conductivity measurement of insulating materials with a three layers device , 2009 .

[32]  J. Blackwell A Transient-Flow Method for Determination of Thermal Constants of Insulating Materials in Bulk Part I—Theory , 1954 .

[33]  Paolo Bison,et al.  Thermal conductivity measurements on wood materials with transient plane source technique , 2015 .

[34]  The generalized amalgam method for modal reduction , 2012 .

[35]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[36]  Wen-Long Cheng,et al.  Simultaneous measurement of thermal properties by thermal probe using stochastic approximation method , 2011 .

[37]  P. Fauchais,et al.  The least square method in the determination of thermal diffusivity using a flash method , 1986 .

[38]  K. Zacny,et al.  Improved data reduction algorithm for the needle probe method applied to in-situ thermal conductivity measurements of lunar and planetary regoliths , 2014 .

[39]  Retrieving thermal conductivity of the solid sample using reduced order model inverse approach , 2017 .

[40]  Jean Dumoulin,et al.  Diagnostic de structures de Génie Civil : Identification des propriétés spatiales et de la surface d’un défaut , 2014 .

[41]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[42]  Bernard Flament,et al.  Simulation de la conduction non linéaire en régime variable: décomposition sur les modes de branche , 1999 .

[43]  Chao Yang,et al.  ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods , 1998, Software, environments, tools.

[44]  J. Jaeger Conduction of Heat in an Infinite Region Bounded Internally by a Circular Cylinder of a Perfect Conductor , 1956 .

[45]  W. Adamczyk,et al.  Retrieving thermal conductivities of isotropic and orthotropic materials , 2016 .