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supercritical pressures, b) with any degree of superheat- ing, c) with or without internal recuperator and d) with and without preheater. The methodology can be divided into three parts: a flexible ORC process model, a set of weights to confine the solutions and a genetic algorithm to find the optimum solutions. 2.1. Process Modelling the Rankine cycle was done with Matlab R2010b using systems of equations representing each com- ponent in the cycle while using equations of state (EOS) procedures from NIST Refprop 9.0 [13] to obtain thermo- dynamic states. All fluid candidates and their full chemical names can be found in the appendix. A sketch of the pro- cess is shown in Figure 1. As mentioned, the recuperator is optional depending on the fluid properties. Table 1: Modelling conditions Property Value Unit Heat source outlet temperature Polytropic efficiency, expander Isentropic efficiency, pump Evaporator min. temperature difference Superheater approach (minimum) Recuperator min. temperature difference Condenser outlet temperature Minimum vapour quality, expander 129 ◦C 0.80 - 0.80 - 10 ◦C 20 ◦C 15 ◦C 25 ◦C 1.00 - Heat Expander Condenser lower limit did not however lead to higher efficiencies or other significantly changed results in general. In order to optimise the process layout for the individ- ual fluids, a degree of freedom for the superheater approach (∆Tsh) was included. The ∆Tsh was defined as the differ- ence between temperatures of the heat source at the inlet to the boiler and the working fluid at the outlet (before the expander). This enables the optimisation of the pinch points (PP) in the boiler with four possible outcomes in terms of the limiting factor in the optimisation of the cy- cle: A) the PP is at evaporator inlet being at the minimum allowable temperature difference, B) the minimum allow- able superheater approach is reached, C) the recuperator minimum temperature difference is met, or D) none of the above in which case it is the minimum expander vapour quality which limits further optimisation. By investigating the net work output of the process ver- sus the pinch point temperature difference (∆Tpp), it was found that the optimum work output was not synonymous with having the lowest allowable ∆Tpp. Thus an optimi- sation of the ∆Tpp for each individual case was justified to find the true optimum in the large solution domain. 2.2. Governing equations In this subsection are described the main equation sys- tems of the methodology. The expander was modelled using the assumed polytropic efficiency, expander inlet en- thalpy (hi) and pressure at inlet (Pi) and outlet (Po). Due to the very wide range of expander pressure ratios inves- tigated using the optimisation algorithm, it was chosen to use a polytropic efficiency in order to have a compa- rable level of cost and technology of the expander. The outlet enthalpy was found by dividing the expander into an adequate number of stages (500) such that the result- ing isentropic efficiency was independent of the number of stages. In order to make sure that solutions were limited to ones with acceptable vapour quality in the expander, the quality (x) was tested at all stages in the expander us- ing EOS calls x = x(h, p). The pump was modelled using an assumed isentropic efficiency. A polytropic efficiency would be preferred, but to reduce computational time and since this margin is of minor influence on the cycle effi- ciency, this simplification was accepted. In the recuperator there are two temperature differ- ences which may limit the heat transfer from the stream Boiler Recuperator Pump Figure 1: Sketch of the ORC process Heat is delivered to the boiler with a heat transfer fluid called DOWthermQ, which is heated by exhaust gas from a large marine engine. This precaution is taken to avoid fire hazards in the boiler. DOWthermQ was modelled us- ing a polynomial function which reproduces the properties of the fluid as in Ref. [14]. The working fluid is (pos- sibly) preheated, evaporated and (possibly) superheated in the boiler at high pressure and is then injected in the expander. After the expander the hot low pressure fluid enters an internal heat exchanger (Recuperator) to heat up the cooler fluid from the pump. In the case the recupera- tor can heat the working fluid to reach a two-phase state, there is an elimination of the preheater heat exchanger. This is inherent in the equation systems. After the re- cuperator, the fluid is condensed in the condenser before entering the pump. Table 1 lists the process conditions used. The heat source outlet temperature was defined to prevent conden- sation of sulphuric acid in the exhaust gas to heat transfer fluid heat exchanger. A temperature of 129◦C of the heat transfer fluid is adequate to cool the exhaust gas down to 160◦C. No liquid was allowed in the expander, to ensure long life and low service requirements of this component. It is stated by Chen et al. [4] that some liquid can be allowed in the expander hence investigations were also made where vapour qualities down to 85% were allowed. Allowing this 3PDF Image | organic Rankine cycles for waste heat recovery in marine settings
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