Differential-Discrete Mathematical Model of the Recuperative Counter-Flow Heat Exchanger

The heat exchangers are always constructive elements of nuclear power plants and their dynamics is very important since they introduce a significant time lag in control actions. That’s why their dynamics cannot be ignored. On the basis of the accepted and critically clarified assumptions, a linearized mathematical model of the recuperative counter 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, which solution is not possible in closed form. In order to overcome the solution difficulties, the procedure of differential discrete modelling is applied, leading to the set of ordinary differential equations of a rather high order. These equations are transformed into the state space form suitable for the Matlab environment. The experimental investigations were made, putting some different typical input variables. Specifying the input temperatures and output variables, under the constant initial conditions, the step transient responses have been simulated and presented in graphic form for the particular positions in the heat exchanger in order to compare these results with the experimental data collected from the real process.