A mathematical description of temperature-dependent boundary conditions is crucial in manifold model-based control or prototyping applications, where accurate thermal simulation results are required. Estimation of boundary condition coefficients for complex geometries in complicated or unknown environments is a challenging task and often does not fulfill given accuracy limits without multiple manual adaptions and experiments. This paper aims to describe an efficient method to identify thermal boundary conditions from measurement data using model order reduction.
An optimization problem is formulated to minimize temperature deviation over time between simulation data and available temperature sensors. Convection and radiation effects are expressed as a combined heat flux per surface, resulting in multiple temperature-dependent film coefficient functions. These functions are approximated by a polynomial function or splines, to generate identifiable parameters. A formulated reduced order system description preserves these parameters to perform an identification. Experiments are conducted with a test-bench to verify identification results with radiation, natural and forced convection.
The generated model can approximate a nonlinear transient finite element analysis (FEA) simulation with a maximum deviation of 0.3 K. For the simulation of a 500 min cyclic cooling and heating process, FEA takes a computation time of up to 13 h whereas the reduced model takes only 7-11 s, using time steps of 2 s. These low computation times allow for an identification, which is verified with an error below 3 K. When film coefficient estimation from literature is difficult due to complex geometries or turbulent air flows, identification is a promising approach to still achieve accurate results.
A well parametrized model can be further used for model-based control approaches or in observer structures. To the knowledge of the authors, no other methodology enables model-based identification of thermal parameters by physically preserving them through model order reduction and therefore derive it from a FEA description. This method can be applied to much more complex geometries and has been used in an industrial environment to increase product quality, due to accurate monitoring of cooling processes.
Frank, T., Wieting, S., Wielitzka, M., Bosselmann, S. and Ortmaier, T. (2019), "Identification of temperature-dependent boundary conditions using MOR", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 2, pp. 1009-1022. https://doi.org/10.1108/HFF-05-2019-0404
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