Conservación de Lyumjev

The refrigerant transport properties (enthalpy, specific heat, compressibility, etc) for the case studies in this thesis were determined using the subroutines from REFPROP

35 (Lemmon et al. 2013). REFPROP is a computer program developed by the National Institute of Standard and Technology (NIST). The computer program is used to determine the fluid thermodynamic and transport properties of pure fluid and mixtures. The REFPROP software uses published models to calculate the fluid thermodynamic and transport properties.

The property models are coded in Fortran language and can be accessed by other softwares via a dynamic linked library (DLL). Lemmon et al. (2013) developed DLL’s for multiple platforms such as Excel and Matlab to link the library of subroutines for the thermodynamic property models that were programmed in Fortran. The DLL for Matlab was used in this thesis to be able to calculate the mean thermodynamic properties, the gas constant (r), the mean compressibility (ζ), and the mean isentropic coefficient (γ), for each refrigerant used in this thesis. The suction, discharge and liquid line enthalpies were determined at each time step using the REFPROP and the DLL with MATLAB.

The HVAC Toolkit operates under the assumption that the refrigerant behaves as an ideal gas over the normal operation conditions within the refrigeration cycle. This allows for the use of mean thermodynamic properties of the refrigerants for vapour and liquid regions. The HVAC Toolkit provides these mean thermodynamic values for a six different refrigerants: R-12, R-134a, R-114, R-22, R-502, and R-717. The HVAC Toolkit does not include the thermodynamic properties for some other common refrigerants used currently in chillers like R-123 and R-410a.

A subroutine was developed called PROPERTYNIST that uses the methods from the HVAC Toolkit to calculate the mean thermodynamic properties using REFPROP (Lemmon et al. 2013) to develop a thermodynamic property database for the common refrigerants not included within the HVAC Toolkit. The subroutine PROPERTYNIST can calculate the mean thermodynamic properties for any refrigerant included in REFPROP software (Lemmon et al. 2013). The gas constant (r), the mean compressibility (ζ), and the mean isentropic coefficient (γ) were calculated using PROPERTYNIST to compare with the HVAC Toolkit (Table 3.10).

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Table 3.10: Comparison of mean thermodynamic properties

Refrigerant HVAC Toolkit Bourdouxhe et al. (1994) PROPERTYNIST

r ζ γ r ζ γ R-12 68.75 0.940 1.086 68.76 0.946 1.109 R-134a 81.49 0.941 1.072 81.49 0.945 1.087 R-114 48.64 0.976 1.056 48.65 0.969 1.069 R-22 96.14 0.930 1.114 96.16 0.937 1.134 R-717 488.22 0.957 1.230 488.21 0.952 1.230 R-123 - - - 54.37 0.987 1.080 R-410a - - - 114.54 0.908 1.066

Comparing the results from PROPERTYNIST to the values in the HVAC Toolkit the highest percent difference is 2.1% for the value of the mean isentropic coefficient (γ). The new subroutine is accurate below 2.1% as compared to the refrigerants used in the HVAC Toolkit and can be used to determine the thermodynamic transport properties of other refrigerants.

It is important to understand the uncertainties associated with calculation of the thermodynamic properties for a refrigerant. The uncertainties in these thermodynamic and transport property models can vary considerably depending on the fluid type, the property, and the thermodynamic state. The uncertainties of the transport properties are complicated functions of the temperature and pressure and the estimation of uncertainty from propagation of errors from the inputs to the outputs is not possible and is beyond the scope of this thesis. A global uncertainty for each of the thermodynamic properties is used in this thesis (Table 3.11 and Table 3.12). To be able to understand the uncertainty for each property it has to be determined for each fluid and each property separately due to the uncertainties generated from each thermodynamic transport property model.

Uncertainty of Refrigerant Properties

For the three case studies that are examined in this thesis two different refrigerants are used. To be able to understand the uncertainties regarding the calculation of the refrigerant properties each model used by REFPROP (Lemmon et al. 2013) needs to be examined. The uncertainty for the density (ρ), specific heat (Cp) and the vapour pressure

37 The thermodynamics properties of R-22 are modelled by Kamei et al. (1995) and used by REFPROP (Lemmon et al. 2013). The model uses the Helmholtz equation of state to determine the thermodynamics properties of R-22 with data collected from experiments. The uncertainties of this model are shown in Table 3.11, which were obtained from REFPROP (Lemmon et al. 2013).

Table 3.11: Uncertainties for the calculation of properties of refrigerant R-22

The thermodynamics properties refrigerant R-123 are modelled by Younglove et al. (1994). The model uses the Helmholtz equation of state to determine the thermodynamics properties of R-123 with data collected from experiments. The uncertainties of this model are shown in Table 3.12, which were obtained from REFPROP (Lemmon et al. 2013).

Table 3.12: Uncertainties for the calculation of properties of refrigerant R-123

Description measured variable Symbol Uncertainty

Density ρ 0.1%

Specific heat Cp 1.5%

Vapour Pressure P 0.2%

Module 2: Uncertainty Propagation due to Measurement Errors

The VFM relies on the accuracy of the measurement devices in the system, which depends on the fixed bias uncertainty of the sensors and the random uncertainties due to the physical phenomena of the system. To understand how well the VFM estimates the chilled and condenser mass flow rate, the error propagation due to the measurements errors is required to be evaluated to be used in comparing the model to the measured value. Depending on how accurate the installed sensors are, it will determine the precision of the estimate results from the VFM.

It is recommended by some standards such as ASHRAE Guideline 2-2005 that a sensor measured data (x) must be presented with the corresponding uncertainty (Ux) by a two-

digit value bearing the same dimensions as x and denoted by the symbol plus-or-minus (±). Description measured variable Symbol Uncertainty

Density ρ 0.1%

Specific heat Cp 1%

38 Unless stated otherwise, the symbol ± in this thesis refers to the uncertainty propagation of errors due to measurements.

The uncertainties from the measuring equipment will propagate through the calculations used in the VFM models to produce a final overall uncertainty of the predictions. The uncertainty of the VFM models is evaluated to understand the limitations of the model and to evaluate how well the model compares to measured data for the chilled and condenser water mass flow rates. Models A, B and C will have different uncertainties, as well as each scenario will have a different uncertainty because of the number of sensors used in each model/scenario are different. Therefore, a general uncertainty analysis is presented in this section. The case studies will highlight how this general analysis is used for each model and scenario.