Method of parametric identification of heat transfer capacity of thermal accumulators

Аuthors

Borschev N. O.

,

e-mail: www.moriarty93@mail.ru

Abstract

This paper presents a method for the parametric identification of the effective thermal conductivity coefficient of palmitic acid used as a heat transfer fluid in a thermal energy storage system operating on the melting-solidification principle. The thermal conductivity coefficient is sought as the product of its parameterized value and a corresponding piecewise linear continuous basis function that accounts for its temperature dependence.

The identification problem for the studied quantity is solved in an extreme formulation based on minimizing the mean squared error between the theoretical and experimental temperature fields at the locations of the temperature sensors. Prior to this, it is necessary to first define the formulation of the “direct” heat transfer problem inside the device, as well as the initial value of the parameterized thermal conductivity coefficient in each temperature basis block. This problem formulation is solved using an implicit finite-difference scheme with linearization of the nonlinear boundary conditions relative to the temperature taken from the previous time step, as well as the heat and mass transfer coefficients.

Subsequently, the mean squared error between the theoretical and experimental temperatures at the sensor locations is compiled and minimized. The conjugate directions method was chosen as the numerical optimization technique due to its high accuracy as a first-order convergence method, ensuring convergence in a minimal number of iterative approximations. To implement this optimization method, the descent step and the component of the gradient of the residual functional are first determined. The des-cent step is found based on the minimum of the studied functional at each calculation iteration. The component of the gradient of the residual functional is found by differentiating the sought heat exchange problem formulation with respect to the parameterized value of the thermal conductivity coefficient and is subsequently solved similarly to the direct heat exchange problem, given the a priori known temperature values at the nodes of the finite-difference grid.

If the difference between the identified values of the parameterized thermal conductivity coefficient is less than the systematic error of the temperature sensor, the iterative identification process is considered complete; otherwise, the aforementioned sequence is repeated until the required calculation accuracy is achieved.

Keywords:

thermal energy storage, palmitic acid, conjugate directions method, iterative regularization method, inverse heat conduction problem

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