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Energies 2021, 14, 8238 10 of 25 3.1. Low Pressure Receiver Numerical Model The low-pressure receiver is a device used to separate liquid from the vapour, storing excess of refrigerant mass to ensure system capacity over a wide range of operating conditions while preventing liquid flow back and consequent damage to the compressor. The submodel of the liquid-vapour separator was conceived assuming an adiabatic constant cross-sectional area; pressure was assumed to be homogeneous in the entire volume and the densities of both the liquid and vapour phase were considered homogeneous as well in their respective volumes. The average refrigerant pressure pLPR and specific enthalpy hLPR were used to compute the state of the refrigerant leaving the receiver (in the state of saturated liquid and vapour, respectively) and the percentage of liquid volume rLV inside of the receiver, which was used to determine the height of the liquid–vapor interface HLV . 3.2. Semi-Hermetic Compressor Numerical Model The semi-hermetic compressor was modelled as a fixed-displacement compressor. The parameters required as input were the value of volumetric efficiency ηvol and overall compression efficiency ηcomp, which were computed from data supplied by the compressor manufacture, the compressor’s displacement Vd, and the nominal rotatory speed n. The adherence of the nominal maps has been already discussed in Section 2.2.3, show- ing a good agreement in terms of mass flow rate and a systematic underestimation of the power consumption of 5%, which increased to 10% when the inverter was set to 60 Hz. As a complete experimental characterization of the compressors in all the working conditions is beyond the scope of this research, the nominal data were used to model the compressor, still being aware of the findings illustrated in Section 2.2.3. for the critical evaluation of the model accuracy. Given the state of the refrigerant at the inlet, the numerical model of the compressor provided the mass-flowrate developed (Equations (12) and (13)), electric power input (Equation (14)), and state of the refrigerant at the compressor outlet. In the case of the fixed speed compressor, which operated at the constant speed of 1450 rpm, the developed mass flow rate was evaluated with Equation (12). In the case of the variable speed compressor, the developed mass flow rate was evaluated with Equation (13) instead, where the value of frequency modulation between 30 and 60 Hz provided by the inverter, Inv ∈ [0, 1] was considered. m. (12) =ρ nVη 30+30Inv (13) m. =ρ nVη V,FIXED IN 60 d vol V,INV IN60 d vol 50 m. ∆h Pel,comp = V is ηcomp (14) 3.3. Heat Exchanger Numerical Model The modelling of the heat exchangers was achieved with an approximation to a simple straight tube in perfect counter flow configuration in a similar manner as discussed in Artuso et al., 2020 [22]. The equivalent tube was characterized by the hydraulic diameter of the heat exchanger (Dh = Di for the finned coil heat exchanger and internal heat exchanger and Dh = 2bpφp for the brazed-plate heat exchanger) and the equivalent length which was calculated according to Equation (15). Lpipe = AHXDh/4Ac,tot (15) The equivalent pipe was then discretized into Ndisc elements (Figure 6), which was decided with a preliminary sensitivity study where Ndisc was increased until the solution demonstrated insensitivity to the variation of number of elements, and the length of the pipe and heat transfer area were equally distributed in each element.PDF Image | Dynamic Modelling and Validation of an Air-to-Water Reversible R744
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