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Energies 2021, 14, 8238 14 of 25 Equation (28) was used in the model in order to predict the correlation between the lift and the entrainment ratio for values other than the nominal ones: φnom(pMN, TMN,pSN,TSN) φEj1 pMN,TMN,pSN,TSN,∆pliftnom φ= φVEJ1 pMN, TMN,pSN,TSN,∆plift (28) This extrapolation was accurate only when the equilibrium point of the system was close to the nominal point, and decreased as the actual working condition differed from the nominal. This will be discussed in the Results and Validation session. Given the entrainment ratio from Equation (28) and the motive mass flow rate, the suction nozzle mass flow rate was given by Equation (29). The mass flow rate and spe- cific enthalpy at the diffuser were given by Equations (30) and (31), which enforce the conservation of the mass and the energy: m. = φ m. SN (29) 1+φ 3.6. Boundary Conditions and Control Systems Due to the model being a dynamic one, each boundary condition had to be stated as a function of time. For stationary tests, inputs were maintained as constants. The required inputs were the water inlet conditions on both high and low pressure sides, the air inlet conditions at the finned coil heat exchanger, the compressors’ status (ON/OFF and, in case, the inverter status), and the mass flow circulating in the natural circulation flooded evaporator. In the validation phase, these inputs were set according to the corresponding experi- mental values. 3.7. Solver To evaluate the numerical solution, the software Simcenter AMESim employed a default optimized solver, based on an optimized variable integration method. When the nu- merical solution was evaluated, to examine its accuracy, a tolerance equal to tol = 10−7 was chosen; after each computation step, the software integrator checked for the convergence and estimated the error: for each state, variable yi, the error must satisfy the conditions εi < tol(1 + yi). When the iterations converged, an error test was applied to determine if the results were accurate enough, however if either of these tests failed, the integration step was replaced with a smaller step size. 4. Results and Validation The numerical model was intended to investigate the thermal performance of the refrigerating system operating according to heat pump configuration and chiller config- uration and to extend the results coming from the experimental campaign. In order to obtain the model validation, the results obtained from the model were compared against experimental data. 4.1. Validation of the Heat Pump Configuration The validation of the numerical model was provided in both steady state and transient operation. The inputs given to the numerical model were the state of the air and the m. = (1 + φ) m. DIFF water, which were collected experimentally during the test, which were m. IN = 25.2 kgs−1, IN◦IN .−1air◦ Tair =8.7 C, φair =67% for the air and mwater,1 =2kgs , Twater,1 = 23.9 C for the water. MN (30) hDIFF = hMN + φhSN (31) MNPDF Image | Dynamic Modelling and Validation of an Air-to-Water Reversible R744
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