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Energies 2021, 14, 8238 12 of 25 All the empirical correlations utilized in the refrigerant, air side, and water side in the heat exchangers of the system are listed in Tables 4–6. Table 4. Empirical correlation utilized in the case of finned coil heat exchanger. Applied Region Air side Refrigerant side: evaporation Refrigerant side: gas-cooling/condensation Items Heat transfer coefficient Heat transfer coefficient Pressure drop Heat transfer coefficient Pressure drop Correlation Colburn j-factor [24] Two-phase: VDI for horizontal tube, 1992 [25] Single phase: Gnielinski, 1976 [26] Friedel, 1979 [27] Transcritical: Gnielinski, 1976 [26] Subcritical: Shash, 1979 [28] Friedel, 1979 [27] Applied Region Water side Refrigerant side: evaporation Refrigerant side: gas-cooling/condensation Items Heat transfer coefficient Pressure drop Heat transfer coefficient Pressure drop Heat transfer coefficient Pressure drop Correlation Sieder and Tate, 1936 [29] Friedel, 1979 [27] Two-phase: Sieder and Tate, 1936 [29] Single phase: Sieder and Tate, 1936 [29] Friedel, 1979 [27] Transcritical: Sieder and Tate, 1936 [29] Subcritical: Sieder and Tate, 1936 [29] Friedel, 1979 [27] Table 5. Empirical correlation utilized in the case of brazed-plate heat exchanger. Table 6. Empirical correlation utilized in the case of internal heat exchanger. Applied Region Refrigerant side: gas-cooling/condensation Items Heat transfer coefficient Pressure drop Correlation Transcritical: Sieder and Tate, 1936 [29] Subcritical: Sieder and Tate, 1936 [29] Friedel, 1979 [27] The inputs required by the submodel were the geometric dimensions of the heat exchanger, and the state of the two fluids, i.e., refrigerant and air/water, at the inlet. The model evaluated, for each discretized element: the state of the refrigerant (T(j), p(j), h(j)), rrr the state of air/water (T(j), p(j), h(j)), the heat flow rate Q. (j), and the respective pressure aaa hx loss ∆p(j). The total heat flow rate and pressure losses were then evaluated with Equations (21) and (22): 3.4. Expansion Device Numerical Model . (TOT) Ndisc . (j) Qhx = ∑ Qhx (21) j=1 Ndisc ∆p(TOT) = ∑ ∆p(j) (22) j=1 The expansion devices of the system are the back-pressure valve, performing the expansion after the gas cooler, and the expansion valves located between the low pressure receiver and the evaporators. The throttling process was considered isenthalpic, while the effect of choked flow was neglected. The mass flow rate through the throttle was determined by the flow coefficient Cq, the actual cross flow area Aop, the inlet density, and the pressure difference across the valve ∆pVALVE, according to Equation (23): m. = CqAopρin∆pVALVE (23)PDF Image | Dynamic Modelling and Validation of an Air-to-Water Reversible R744
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