Implementation and testing of a model for the calculation of equilibrium between components of a refrigeration installation Marco Alexandre Onofre Dias This paper presents a model that was implemented with the objective of calculating the working conditions of real components from a refrigeration installation. With that objective parameters were calculated for sets of components from different suppliers to represent their behaviour. For compressors, the global efficiency and a parameter m from the volumetric efficiency was correlated as a function of the pressure ratio, and similar behaviour was observed for different suppliers and fluids. For evaporators and condensers values of the heat transfer capacity AU were determined and found to be well correlated with air velocity. The numerical model implemented in a VBA macro in Excel calculates the evaporation and condensing temperatures that match the capacity of the components in the refrigeration cycle. Then all the parameters from the cycle can be calculated. The model is tested with data measured in three installations and a good agreement is obtained for all variables, with differences in absorbed power below 3% and temperature differences below 2ºC except for the evaporation temperature in one case and the main effects for this mismatch are analysed. Key Words: Refrigeration; Compression cycle; Numerical model; 1 - Introduction The dimensioning of refrigeration systems is based on the assessment of the most critical conditions and usually a margin is given to allow for defrost periods and variations in loads. The actual operation conditions of the system change along time depending on the storage room and ambient conditions. The selection of components for a given refrigeration installation is considered from different suppliers and they are specified for standard conditions that are not met when they are combined. Therefore it is interesting to consider a methodology to match the working conditions of different components. Stoecker (2004) suggest that the characteristics of the compressors should be correlated by the suppliers by polynomials as a function of the evaporation and condensation temperature. The coefficients for these functions are supplied e.g. by the Bitzer (2011) software and a graphical analysis is suggested by Green and Perry (2007) to determine the equilibrium between components as shown in figure 1. The figure represents the cooling capacity as a function of the evaporation temperature from the condenser-compressor and the evaporator characteristics. The intersection point determines the operation point for those equipments. This analysis however are based on the components characteristics for assumed conditions e.g. from EN12900 with an admission temperature of 20ºC.
Figure 1 Cooling capacity as a function of the evaporation temperature from the condensercompressor and the evaporator and the determination of equilibrium (Green and Perry, 2007) The calculation of refrigeration cycles require the use of suitable models for the properties of the refrigerant fluids that are based on the fluid properties that are nowadays supplied by the refrigerant suppliers, e.g. Solvay (2011) or from research labs, e.g. NIST (2009) who distribute REFPROP. The development of models based on these packages for properties is available for simple cycles based on the definition of the evaporation and condensation temperatures. CoolPack is a software developed by DTU (2011) using EES (Engineering Equation Solver) that solves a large range of non-linear equations representing a refrigeration cycle. This program includes an option to specify the capacity of heat exchangers (AU) and the compressor global and volumetric efficiencies to determine the performance of a cycle. The values however are considered as constant and to insert specific data from a supplier previous calculations are required. Based on the scarce tools available the present work was carried out to implement a model in a readily accessible program, Excel, including characteristics from different suppliers enabling the analysis of the choice of different components in a refrigeration cycle. Following this introduction, the next section describes the models used for the components and the determination of their parameters for different suppliers. This section also includes a brief description of the algorithm developed. Section 3 presents the results obtained from simulations for three different installations and the comparison with measured values. The final conclusions are summarized in the last section.
2 Models for components and equilibrium This section presents simple models that are used to fit parameters to represent the main components of a refrigeration cycle: compressor, evaporator and condenser. The equilibrium calculation to be carried out should represent the effect of operational variables such as the temperatures of the storage rooms, ambient and admission in the compressor, so thermodynamic and heat transfer models are required to relate these with the evaporation and condensation pressure (and temperatures). The thermodynamic cycle considered is a simple one as represented in figure 2. Figure 2 Thermodynamic cycle of refrigeration systems. Evaporator (40), Heating in admission line (01) that is included in reference cycle (EN12900), Compressor (12), Condenser (23), Expansion valve (34). 2.1 - Compressor The compressor is the component of the cycle that defines the refrigerant flow section presents simple models that are used to fit parameters to represent the main components of a refrigeration cycle: compressor, evaporator and condenser. The equilibrium calculation to be carried out should represent the effect of operational variables such as the temperatures of the storage rooms, ambient and admission in the compressor, so thermodynamic and heat transfer models are required to relate these with the evaporation and condensation conditions. The reciprocating compressor considered in the present work is a positive displacement machine so the main characteristics are the volumetric displacement, the volumetric efficiency and the global efficiency. There are models in the literature that consider several processes within the compressor case that includes the electrical engine and transmissions. Navarro et al (2007) present such a detailed model from which they derive the variation of the global and volumetric efficiencies. For the volumetric efficiency there are contributions from the theoretical volumetric efficiency and effects from leaks and condensation/re-vaporisation. In the present model in the absence of detailed data about the compressors the volumetric efficiency η Vol is modelled as a function of the pressure ratio (r P ) by:
1 1 n 1 Vol m r P (1) where the parameter m in theory corresponds to the ratio between the residual and the displaced volume. In the results of Navarro it was found that when no condensation/revaporization effects were considered, the values of m obtained are larger than the geometrical factors. The other parameter that arises in the volumetric efficiency model above is the n index of the polytropic evolution in the compressor. In the present work data from compressors was used to calculate the refrigerant fluid mass flow rate from the energy balance: Q0refrig m ( h 1 h 4 ) (2) where Q0 refrig is the refrigeration capacity provided by the compressor and the enthalpy difference in the denominator is the refrigeration effect from a standard cycle used to define the compressor performance. The actual volumetric efficiency is defined with the mass flow rate, the inlet density into the compressor (ρ 1 ) and the volumetric displacement flow of the compressor V from the definition: Vol m (3) V 1 The other main parameter that characterizes the compressor is its global efficiency that can be defined as the ratio of the power consumption from an isentropic evolution in comparison to the actual power consumption: Comp m ( h2 s h1 ) W (4) Comp Based on this value the actual discharge conditions from the compressor can be estimated considering that it is adiabatic. This is approximately true for hermetic compressors where the heat loss from electrical motor inefficiency and mechanical dissipation heats the refrigerant fluid. Based on the calculated discharge conditions, the polytropic index n can be obtained: P2 P 1 v v 2 n ln( P2 P1 ) n ln( v / v ) 1 (5) 1 2 Using the values of the actual volumetric efficiency and the polytropic index n, the parameter m of the volumetric efficiency can be estimated and has been correlated as a function of the pressure ratio for compressors from the same suppliers for different fluids, as indicated in figure 3, for the case of Bitzer compressors.
Compressor efficiency M 0,14 M -BITZER 0,12 0,1 0,08 0,06 y = 5,7518E-04x 2-1,1721E-02x + 1,1591E-01 R 2 = 3,4429E-01 y = 3,5723E-04x 2-8,8710E-03x + 1,0059E-01 R 2 = 2,8253E-01 y = 7,5825E-04x 2-1,5666E-02x + 1,2730E-01 R 2 = 6,9142E-01 r404a r22 r134a r404arp>5 R22RP>5 R134aRP>5 0,04 0,02 0 y = -2,6572E-03x 2 + 1,5362E-02x + 6,0938E-02 R 2 = 1,4211E-01 y = -2,1630E-03x 2 + 6,1811E-03x + 8,6811E-02 R 2 = 5,9140E-02 y = 2,1308E-03x 2-2,9021E-02x + 1,6010E-01 R 2 = 6,1249E-01 0 2 4 6 8 10 12 14 16 RP Figure 3 Correlations for the parameter m from the volumetric efficiency as a function of the pressure ratio. It can be observed that the values are not constant as would be expected by the simple theory but there is a reasonable representation as a function of the pressure ratio r P. The global efficiency has also been correlated with this variable with the results presented in figure 4. Compressor efficiency BITZER 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 y = 5,0786E-03x 2-4,3000E-02x + 7,3109E-01 R 2 = 1,1184E-03 y = 6,5925E-02x 2-5,0973E-01x + 1,5779E+00 R 2 = 6,1653E-01 y = -1,1388E-02x 2 + 1,0667E-01x + 3,6741E-01 R 2 = 6,9007E-01 y = -1,5565E-03x 2 + 1,1890E-02x + 6,1931E-01 R 2 = 2,6541E-01 y = -1,2704E-03x 2 + 1,6799E-02x + 5,9308E-01 R 2 = 2,3546E-01 y = -1,1982E-03x 2 + 1,8923E-02x + 5,5384E-01 R 2 = 7,0834E-02 0 0 2 4 6 8 10 12 14 16 RP r404a r22 r134a r404arp>5 R22RP>5 R134aRP>5 Figure 4 Correlations of the global compressor efficiency as a function of the pressure ratio. Based on the definition of the correlations presented in the figures, it was possible to build a model to represent the performance of the compressors as a function of the operating conditions that is evaporation and condensation temperatures. The model can also be used to represent variations in the admission temperature. Figure 5 presents a comparison of the values calculated for a Bitzer compressor as a function of the evaporation temperature using different approximations for the correlations. The values from figures 3 and 4 correspond to the best approach but the other approaches also provide reasonable results, where a single set of values is used irrespectively of the pressure ratio and the refrigerant.
Power Cons. (kw) Refrigeration Capacity (kw) 20.2Y-r404a 50,00 45,00 40,00 35,00 30,00 25,00 20,00 15,00 10,00 5,00 0,00-35 -30-25 -20-15 -10-5 0 Evaporation Temperature (ºC) Catalogue 1aprox 2aprox 3aprox 20.2Y-r404a 25 20 15 10 5 0-35 -30-25 -20-15 -10-5 0 Evaporation Temperature(ºC) Catalogue 1aprox 2aprox 3aprox Figure 5 Comparison of the model results using different approximations with the values from the catalogue. a) Refrigeration capacity, b) power consumption. 2.2 Evaporators and Condensers The evaporators and condensers are considered in the same section as both are heat exchangers with phase change. Actually for non-azeotropic mixtures there is a small temperature variation associated with the phase change that is neglected. Further in both cases there is an area of the heat exchanger that is used to superheat the vapour in the evaporator and to cool the superheated vapour in the condenser. Therefore for the condenser the temperature difference in that area is larger than in the area of phase change while the opposite happens in the case of the evaporators. In both cases the heat transfer coefficient is smaller in the superheated vapour compared with the phase change zone and this effect is more important for the evaporator. To avoid the complication of considering a two zone for each equipment it is usual to define an overall heat transfer capacity based on the difference between the inlet temperature of the air crossing the heat exchanger and the phase change temperature. Based on this approach values for the global heat transfer coefficient (U) were calculated and are represented as a function of the air velocity in figure 6. In the case of the evaporator the velocity from the fans was considered, while for the condensers the average values were considered. In both cases it can be observed that the global heat transfer coefficient depends on velocity with an exponent of the order of 0.6 that is typical for heat exchangers. 2.3 Equilibrium calculations The calculation of the equilibrium situation between a given set of components: compressor, condenser and evaporator is carried out firstly by determining the condensation temperature
U (W/m 2 K) U (W/m 2 K) that balances the performance of the condenser with the compressor. This calculation is based on a pre-assumed value of the evaporation temperature that is corrected in a iterative procedure that compares the refrigeration capacity provided by the compressor and the heat transfer capacity of the evaporator. The final results of the simulation are the evaporation and condensation temperatures and all the values that can then be defined including the refrigeration capacity and the power consumption. The next section presents results from calculations for different cases and shows how the model responds to modifications in individual components. 35 30 25 20 15 Evaporator Mod. DFE y = 12,212x 0,6085 R² = 0,777 10 2,5 3 3,5 4 Air Velocity (m/s) 35 30 25 20 15 10 5 0 Condenser -Mod ACP y = 11,767x 0,6569 R² = 0,8537 1 2 3 4 Air Velocity (m/s) Figure 6 Variation of global heat transfer coefficients with typical air velocities. a) Evaporators, b) Condensers. 3 Equilibrium calculations and validation This section presents the results from the application of the model for three test cases. The first test case is based on an installation that has a condenser/compressor group for which the characteristics of the compressor were know so the heat transfer capacity of the condenser was estimated from results of that condenser in different assemblies. Figure 7 presents the measured values of pressure, represented as equivalent phase change temperatures for the refrigerant used (R404a). These values were monitored using a Testo 556 data logger coupled with pressure probes at the admission and discharge lines of the compressor. In this case the evaporation temperature decreased until reaching -15ºC that was much lower than anticipated from the model and the thermal expansion valve had to be regulated leading to an evaporating temperature of -8ºC while the chamber temperature was - 1ºC.
Temperatura (ºC) Bruno Terroal - 2ºEnsaio tevap= -15ºC tevap= -8ºC 35,0 30,0 25,0 20,0 15,0 10,0 tevap 5,0 tcond 0,0-5,0 0 200 400 600 800 1000 1200-10,0-15,0-20,0 Tempo (s) Figure 7 Results of the measurements carried out at Bruno Terroal plant for evaporation and condensation temperatures calculated from the pressure measurements at the compressor. The calculated evaporation temperature in this case was -6.8ºC due to the large capacity of the evaporator. This is a value similar to the one obtained after regulating the thermostatic valve, showing that the regulation of the valve should impose a smaller temperature difference than the one resulting from the heat capacity of the evaporator that is considered in the equilibrium between components. The second test that is presented is for a freezed products chamber from Manjarlima. In this case the measurements were done in a cycle where the evaporation temperature decreased reaching -28.9ºC while the chamber reached -22ºC. For this case the capacity of the condenser was not exactly known as it was one sector of a larger condenser. Therefore simulations were carried out for different condensation capacities with values of the nominal capacity around 30 kw that is the correct choice for the other components. The results are presented in table 1 where the influence of the condenser capacity is obviously the modification of the condensation temperature. The power consumption and the evaporation temperature can be predicted with fair accuracy and are not strongly influenced by the assumptions. The parameter that is more strongly influenced as in the previous case is the refrigeration capacity that is not measured but has a strong influence on the efficiency of the refrigeration system and the results justify the use of the model to assess this value. Real Values Simulation Condenser Capacity (kw) 30,07 17,96 33,5 Refrig. Cap. (kw) 17,07 14,89 17,28 Power Cons.(kW) 10,43 10,59 11,39 10,51 EER 1,61 1,31 1,64 Evap. Temp (ºC) -28,9-28,01-27,21-28,09 Cond. Temp. (ºC) 35,3 34,21 42,29 33,42 Table 1 Comparison of results for the installation Manjarlima and analysis of the effect of the condenser capacity.
Temperature (ºC) The third case that is presented is for a refrigeration chamber at Toze Crispim that uses individual condenser and compressor and two similar evaporators. This case is the best known and the results of the measurements are presented in figure 8. Typical values are identified in the figure and the ambient temperature was 25 to 26ºC. The temperature at the compressor inlet was not measured but since the line is insulated it is expected to be about 2ºC as in the first case. Nevertheless a parametric test is carried out to see the influence of the heat gain in the admission compression line as presented in table 2. tcond = 37,1ºC TOZE CRISPIM tevap = -6,3ºC 50,0 40,0 30,0 20,0 10,0 0,0-10,0 0 500 1000 1500 2000-20,0-30,0-40,0-50,0 Time (s) Tevap Tcond Figure 8 Results of the measurements carried out at Tozé Crispim for evaporation and condensation temperatures calculated from the pressure measurements at the compressor. Simulation Real Values Inlet temp. (ºC) 20 10 2 Refrig. Cap. (kw) 19,82 20,53 21,15 Power Cons.(kW) 7,53 7,44 7,40 7,35 EER 2,66 2,78 2,88 Evap. Temp. (ºC) -6,3-5,31-5,50-5,67 Cond.Temp. (ºC) 37,1 35,08 35,32 35,49 Table 2 Comparison of results for the installation Tozé Crispim and analysis of the effect of the inlet temperature for the compressor. It can be seen that the influence of this parameter is strong in the refrigeration capacity but less significant in the measured variables. The level of agreement between the calculated and measured values is good and represents variations in the temperature difference in the heat exchangers below 15%. In the power consumption the deviations as in the previous cases are below 3%. 4 Conclusions The present work presents a model to evaluate the equilibrium between components of a refrigeration installation that can incorporate data from actual equipments. A procedure was developed to find model parameters and the values obtained allow for the following
conclusions. The global compression efficiency and a parameter from the volumetric efficiency can be correlated with the pressure ration in the compressor. For the heat exchangers the global coefficients present a variation with air velocity in line with heat transfer coefficients. The algorithm developed allows for the calculation of the evaporation and condensation temperature as well as the refrigeration capacity and the power consumption. It is shown that with the exception of one case the temperatures can be predicted within 2ºC and the power consumption within 3%. The reasons for the larger difference in one case was discussed. References Bitzer, 2011, Bitzer software 5.3.1,http://www.bitzer.de/eng/productservice/software/3 DTU, 2011, Coolpack software, Version 1.46, http://www.ipu.dk/english/ipu- Manufacturing/Refrigeration-and-energy-technology/Downloads/CoolPack.aspx, Department of Mechanical Engineering-Technical University of Denmark. Green, D.W. and Perry, R.H., 2007 -Chemical Engineering s Handbook, 8th Edition, Mc Graw Hill. Navarro, E., Granryd, E, Urchueguia, J.F. e Coberian, J.M., 2007 A phenomenological model for analyzing reciprocation compressors, International Journal of Refrigeration, 30: 1254-1265. NIST, 2009, REFPROP - Reference Fluid Thermodynamic and Transport Properties Database, http://www.nist.gov/srd/nist23.cfm, National Institute of Standard and Technology Solvay, 2011, http://www.solvaychemicals.com/en/products/fluor/software.aspx Stoecker, Wilbert F. 2004 Industrial Refrigeration Handbook, McGraw-Hill.