Conclusions
In this paper, signal flow graphs are used to analyze the dynamic behavior and to establish an analytical solution to the dynamic behavior of HEN as follows: (1) The signal flow graph of the HEN is established according to the transitive relation among streams where a single heat exchanger is treated as a 4 4 MIMO system. (2) The dynamic input-output relation of the HEN is turned into a signal flow graph, including all of the transfer relationships of the temperature and flow rate in the networks. (3) Three methods are proposed to obtain the outputs of the whole network, including the outlet nodes and the intermediate nodes in the Laplace domain. (4) An analytical solution to the dynamic behavior of HEN is presented with the Laplace inverse transform. To test the effectiveness of the proposed method, a 4 5 HEN is taken as an example. Transient processes under a single disturbance and multi-disturbances are obtained. The conditions are in accordance with the practical conditions, and exact results are obtained. The simulation results obtained illustrated the advantages of the method, including high computation speed, high static and dynamic accuracy, and good adaptability for on-line control and optimal design of the networks.
