Application of POD-RBF technique for retrieving thermal diffusivity of
anisotropic material
WP Adamczyk1, Z. Ostrowski1, Z. Bulinski1, A. Ryfa1
1
Silesian University of Technology, Institute of Thermal Technology, Gliwice, Poland
Corresponding author: [email protected]
The knowledge about thermal diffusivity is essential in wide range of applications. It is often
used as the parameters, which describe the quality of the materials or plays crucial parameter
in numerical simulations where heat transfer process is involved. Numerous books and
Internet sites contain tabulated material properties [1,2]. Most commercial simulation
packages have direct links to libraries storing material properties [3].
The method presented in this paper was developed based on the classical Parker flash
method [4] which is classified as the transient measurement technique. The idea of the flash
method is to heat the front surface of the sample by a short laser impulse, while recording the
temperature excess on the rear side of the sample. The technique, though destructive, is the
most popular method of thermal diffusivity measurement. The literature describes numerous
attempts to enhance the classic flash method for different applications. The idea of
measurement procedure is to heat up a small portion of a small sample surface by a laser
flash and record the resulting transient temperature field by an IR camera. To retrieve three
main components of the thermal diffusivity tensor of anisotropic body, the measurement
procedure needs to be applied at least for two surfaces. The test rig consists of the laser, IR
camera, sample holder, and system for controlling position of the sample. The
measurement/inverse procedure presented in this work treats the thermal diffusivity
components as decisive variables which are retrieved by minimization of the difference
between experimental and numerical data.
In presented work two calculation algorithm were involved to retrieve unknown parameters.
The first one uses the CFD model as direct solver, whereas in the second one the direct solver
was replaced by reduce order model (POD-RBF) to decrease simulation time. The later
technique uses the numerical model to generate the database containing the system response
(investigated sample) depending on decisive variables. Then, the low dimensional model of
the considered system was developed by the use of the proper orthogonal decomposition
technique (POD) extended by radial base function (RBF) for finding relations between
snapshots. The numerical simulation results were validated with experiments conducted by
the use of commercially available Parker’s flash method and analytical model [5].
ACKNOWLEDGMENTS
The research has been supported by National Science Centre within SONATA scheme under
contract Nr. 2014/15/D/ST8/02620.
[1] Washburn, E.W. 2003, International Critical Tables of Numerical Data, Physics, Chemistry and Technology
(1st Electronic Edition), Knovel, 1926 -1930;
[2] EngineeingToolBox, website www.engineeringtoolbox.com
[3] JAHM Material Properties Database, website www.jahm.com
[4] Parker, J., Jenkins, R., Butler, R., Abbott, G., 1961, J. of Appl. Phys. 32 (1961) 9, 1679-1684.
[5] Kruczek T., Adamczyk W. Białecki R., Inte. Jour. of Thermo. 34 (2013) 3, 467-485
Keywords: thermal diffusivity, invers analysis, POD-RBF