DYNAMIC SIMULATION OF A COUNTERCURRENT HEAT-EXCHANGER MODELING-START-UP AND FREQUENCY-RESPONSE

A numerical model-'Cinematic' model-utilising analytical solutions, has been developed to simulate the dynamic behaviour of an ideal, liquid-liquid, concentric pipe, countercurrent heat exchanger. This numerical model is capable of providing time domain solution directly. The details of the numerical model is presented including the frequency-response testing of the model. Frequency of disturbance is varied over a wide range (0.1 cycle/min to 50 cycles/min) and the results are compared with analytically obtained frequency-responses using Laplace transforms and trial function approaches. The following interesting features of the asymptotic behaviour of the amplitude ratios, strictly valid only when the overall number of transfer units in both streams are equal, obtained by analytical methods (Laplace transforms and trial function approaches) are also observed from the results of the 'Cinematic' model. These checks provide a good means to validate the dynamics predicted by the 'Cinematic' model. (i) The sum of the limiting amplitude ratios (omega --> 0), calculated based on the response at the outlets of the annulus and the pipe to the disturbance, equals unity. (ii) The above equality is also valid at half the length of the exchanger. (iii) The difference between the limiting amplitude ratios (omega --> 0), calculated as the response of the two liquids at any position to the disturbance, is (l/l+a) where 'a' is the number of transfer units referred to either of the fluids. (iv) Resonance phenomena usually thought of as a feature of the frequency response of second order systems is not observed. This is a new result.