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Chapter 5 Starting from the same computing environment that is used for the steady-state model, the available multi-objective optimizer runs by first acquiring the array of the parameters and of the upper and lower bounds for the vector of the optimization variables X ̄, which in the case at hand reads X ̄ = [P6, ∆Trec, ∆TOTB, T11, DOTB,in, tOTB, lOTB, uexh, Drec,in, trec, lrec, prec, lrec,b], (5.7) where P6 is the turbine inlet pressure, ∆Trec = T8 − T2 the minimum temperature difference in the recuperator, and ∆TOTB the temperature difference between the two streams in the once-through boiler, at the location where the ORC fluid is in saturated liquid condition. Note that this does not necessarily correspond to the so-called pinch-point of the heat exchanger, since the minimum temperature difference between the two streams in the OTB might also be located at its inlet. T11 is the lower temperature reached by the exhaust, see Fig. 5.1. The variables uexh, DOTB,in, tOTB and lOTB are the velocity of the exhaust gases, the inner diameter, the thickness and the length of the tubes of the once-through boiler. Similarly, Drec,in, trec, and lrec refer to the same quantities in the recuperator, while prec is the tubes pitch. The variable lrec,b indicates the baffle spacing given as a percentage of the shell diameter. The objective functions chosen in the present analysis are collected in the array J ̄, i.e. J ̄ = [−W ̇ net,ORC, VOTB + Vrec], (5.8) where W ̇ net,ORC is the net power output of the ORC power unit, and the second metric accounts for the total ORC module volume which is determined by the more bulky components, i.e. the heat exchangers. The first term is selected in order to maximize the power output of the combined cycle plant while the latter term is added to the objective function since compactness represents a crucial design requirement in the considered application. The integration of dynamic simulations into the the automated design procedure allows to discard unfeasible designs. Since the dynamics of the condenser can be neglected for the reasons explained in §5.4.2, the volume of the condenser is not included in the second term of the objective function, see Equation 5.8. The multi-objective optimization uses a controlled elitist genetic algorithm (GA) to search for solutions which minimize simultaneously the two objective functions [34]. Compared to gradient- based methods, a GA is less prone to converge to local minima of the problem. This typically comes at the cost of an increased computational cost, due to the large number of evaluations of the objective functions [34]. The GA parameters are specified as follows: population size equal to 200, generation size equal to 100, crossover fraction equal to 0.8, and migration fraction equal to 0.2. These numerical values are selected in order to ensure the repeatability of the solution when different simulations are performed, and are selected as suggested in Ref. [34]. Table 5.3 lists the upper and lower bounds utilized for the optimization variables, according to the limits reported in Ref. [16]. As the SGT-500 engine can operate on a wide range of both liquid and gas fuels, the limit temperature of the flue gas at the outlet of the OTB is set to 140 ◦C, in order to prevent the condensation of corrosive compounds. Supercritical cycle configurations are not considered here, and the upper bound for the turbine inlet pressure is thus set equal to 90% of the critical pressure of cyclopentane. Table 5.4 lists the parameters which are kept constant during the multi-objective optimization. The fin profile and the configuration of the once-through boiler and of the recuperator are retrieved from Refs. [16, 33]. The condensing pressure of the working fluid is fixed to 1 bar, corresponding to a temperature of 50 ◦C, in order to avoid inward air leakage into the condenser. Referring to Fig. 5.7, the calculation loop regarding the ORC module determines the ther- modynamic states at the inlet and at the outlet of each component, as detailed in Ref. [10]. The pressure drops in the heat exchangers are initially set to zero. At this point the design procedure 136PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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