Identification of climatic conductivity in multi-circuit thermal-hydraulic means of ensuring thermal conditions

Аuthors

^1*, Losev M. I.², Bordachev A. M.³

1. Joint Institute for High Temperatures of the Russian Academy of Sciences, 13, Izhorskaya str., Moscow, 125412, Russia
2. Moscow Institute of Physics and Technology (National Research University), 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia
3. National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya str., Moscow, 111250 Russia

*e-mail: www.moriarty93@mail.ru

Abstract

This paper presents a method for determining the specific thermal resistance of multi-loop thermohydraulic systems using the example of a recuperative heat exchanger, which serves as a heat transfer link between two or more pipelines. This heat exchange device is commonly used in thermal stabilization systems for heat-emitting energy equipment, such as heat dissipation from printed circuit boards with thermal regulation systems based on the use of hydraulic loops. This parameter is determined as a function of temperature and includes the integral conductive-convective resistance and the resistance through the wall of the recuperative heat exchanger. Linear-continuous basis functions, accounting for the dependence of specific thermal resistance on temperature, are chosen as the basis functions. The task of parametric identification of specific thermal conductivity is solved as a problem of finding the global minimum of the root mean square deviation functional between the task setup, which describes the closest heat exchange model in this system, and its simplified thermal simulation model, under assumptions of negligible thermal expansion of the structural material, isotropy of thermal properties, minor heat exchange with the environment (adiabats are specified at the boundary), as well as negligible heat transfer along the casing of the device. The considered heat exchange problems inside the recuperative device are solved numerically using the thermal balance method (lumped parameter method) with the implicit 4th-order Runge–Kutta scheme. Based on the obtained solutions for temperature fields at corresponding isothermal nodes as a function of time, the initial parameterized value of specific thermal resistance at the first computational iteration undergoes minimization of the target root mean square deviation functional. The method of conjugate gradients, well-established in solving inverse coefficient heat conduction problems, is chosen as the unconditional minimization method. This method also allows for achieving the stopping criterion of the iteration process in the minimal number of iterations, imposing a constraint on the continuity of the investigated root mean square error. The stopping criterion for the iterative process of identifying the parameterized value of specific thermal resistance is the superposition of errors that contribute to the inaccuracy in the problem setup, namely: the error in the heat exchange problem setup inside the heat exchanger, the error in the numerical method for calculating the temperature field, rounding errors, the error in determining the descent parameter in the conjugate gradient method, and so on. 

Keywords:

regenerative heat exchanger, iterative regularization method, conjugate gradient method, Runge–Kutta method, thermal balance method, root mean square deviation or mean square deviation

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