Comparative Analysis of Different Methods in Mathematical Modelling of the Recuperative Heat Exchangers

 

Dalibor Stević

 

The heat exchangers are frequently used as constructive elements in various plants and their dynamics is very important. Heat exchangers are used in military aircraft of all sizes, flying different missions, in many different aircraft systems Their operation is usually controlled by manipulating inlet fluid temperatures or mass flow rates. On the basis of the accepted and critically clarified assumptions, a linearized mathematical model of the cross-flow heat exchanger has been derived, taking into account the wall dynamics. The model is based on the fundamental law of energy conservation, covers all heat accumulation storages in the process, and leads to the set of partial differential equations (PDE), the solution of which is not possible in a closed form. In order to overcome the solution difficulties, this paper analyses different methods for modeling the heat exchanger: the approach based on the Laplace transform, the approximation of partial differential equations based on the finite difference method, the method of physical discretization and the transport approach. Specifying the input temperatures and output variables, under constant initial conditions, the step transient responses have been simulated and presented in a graphic form in order to compare the results for the four characteristic methods considered in this paper and to analyze their practical significance.

Key words: heat exchanger, mathematical model, comparative analysis, Laplace transform, finite difference method, discretization method.