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D Steady-state moving-boundaries heat exchanger model Summary. This appendix describes the practical implementation of a three- zone steady-state heat exchanger model. A formalism is set up to avoid numerical failures during the iterations of the Newton solver. When simulating steady state thermodynamic cycles with acausal equations, e.g. using "Engineering Equation Solver" (EES), non-convergence often occurs in the heat exchanger models, particularly when three-zones, moving boundaries model are used. This is particularly true in the case of low pinch point (i.e. relatively high heat transfer coefficients or exchange area): the iteration process can lead to a superposition of both temperature profiles, as illustrated in Figure 101. To avoid this issue, the iterative process should not be left to the solver, and most of the heat exchanger model should be written using causal equations, allowing conditional statements. The iteration scheme of the proposed heat exchanger model is the following: 1. The complete temperature profile is defined as an initial value. The heat transfer coefficients are set as parameters or calculated with heat transfer correlations. 2. Using these heat transfer coefficients, the required heat transfer area for each zone (liquid, two-phase, vapor) is calculated with causal equations only. This implies using the LMTD method instead of the ε−NTU method. The required total heat transfer area is then obtained by summing the computed values for each zone. Figure 101: Simulation failure due to non-physical temperature profiles during the iterations XIIIPDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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