Buildings.Media.Refrigerants.R410A

Refrigerant R410A

Information

This package contains function definitions for thermodynamic properties of R410A based on data for commercial refrigerant Dupont Suva 410A. The methodology used to evaluate the isentropic exponent is taken from de Monte (2002).

References

F. de Monte. (2002). Calculation of thermodynamic properties of R407C and R410A by the Martin-Hou equation of state, part I: theoretical development. International Journal of Refrigeration. 25. 306-313.

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
dPressureVap_dSpecificVolume_Tv	Derivative of the Martin-Hou equation of state with regards to specific volume
dPressureVap_dTemperature_Tv	Derivative of the Martin-Hou equation of state with regards to temperature
dSpecificVolumeVap_pT	Function that calculates the Jacobian of specific volume R410A vapor based on pressure and temperature
enthalpySatLiq_T	Function that calculates the enthalpy of saturated liquid R410A based on temperature
enthalpySatVap_T	Function that calculates the specific enthalpy of saturated R410A vapor based on temperature
isentropicExponentVap_Tv	Function that calculates the isentropic exponent of R410A vapor based on temperature and specific volume
pressureSatVap_T	Function that calculates the pressure of saturated R410A vapor based on temperature
pressureVap_Tv	Function that calculates the pressure R410A vapor based on temperature and specific volume
specificIsobaricHeatCapacityVap_Tv	Function that calculates the specific isobaric heat capacity of R410A vapor based on temperature and specific volume
specificIsochoricHeatCapacityVap_Tv	Function that calculates the specific isochoric heat capacity of R410A vapor based on temperature and specific volume
specificVolumeVap_pT	Function that calculates the specific volume R410A vapor based on pressure and temperature
R=114.55	Gas constant for use in Martin-Hou equation of state
TCri=345.25	Critical temperature
T_min=173.15	Minimum temperature for correlated properties
pCri=4926.1e3	Critical pressure
A={-1.721781e2,2.381558e-1,-4.329207e-4,-6.241072e-7}	Coefficients A for Martin-Hou equation of state
B={1.646288e-1,-1.462803e-5,0,1.380469e-9}	Coefficients B for Martin-Hou equation of state
C={-6.293665e3,1.532461e1,0,1.604125e-4}	Coefficients C for Martin-Hou equation of state
b=4.355134e-4	Coefficient b for Martin-Hou equation of state
k=5.75	Coefficient K for Martin-Hou equation of state

Types and constants

  final constant Modelica.SIunits.SpecificEntropy R = 114.55
    "Gas constant for use in Martin-Hou equation of state";

  final constant Modelica.SIunits.Temperature TCri = 345.25
    "Critical temperature";

  final constant Modelica.SIunits.Temperature T_min = 173.15
    "Minimum temperature for correlated properties";

  final constant Modelica.SIunits.AbsolutePressure pCri = 4926.1e3
    "Critical pressure";

  final constant Real A[:] = {-1.721781e2, 2.381558e-1, -4.329207e-4, -6.241072e-7}
    "Coefficients A for Martin-Hou equation of state";

  final constant Real B[:] = {1.646288e-1, -1.462803e-5, 0, 1.380469e-9}
    "Coefficients B for Martin-Hou equation of state";

  final constant Real C[:] = {-6.293665e3, 1.532461e1, 0, 1.604125e-4}
    "Coefficients C for Martin-Hou equation of state";

  final constant Real b = 4.355134e-4
    "Coefficient b for Martin-Hou equation of state";

  final constant Real k = 5.75
    "Coefficient K for Martin-Hou equation of state";

Buildings.Media.Refrigerants.R410A.dPressureVap_dSpecificVolume_Tv

Derivative of the Martin-Hou equation of state with regards to specific volume

Information

Function that calculates the derivative of the Martin-Hou equation of for R410A state with regards to specific volume.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]
SpecificVolume	v		Specific volume of refrigerant [m3/kg]

Outputs

Type	Name	Description
Real	dpdv	Derivative of pressure with regards to specific volume [Pa.kg/m3]

Modelica definition

function dPressureVap_dSpecificVolume_Tv "Derivative of the Martin-Hou equation of state with regards to specific volume" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; input Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; output Real dpdv( final unit="Pa.kg/m3") "Derivative of pressure with regards to specific volume"; protected Modelica.SIunits.SpecificVolume v_abs "Smoothed specific volume"; algorithm v_abs := Buildings.Utilities.Math.Functions.smoothMax(v, 1.01*b, 0.01*b); dpdv := -R*T/(v_abs-b)^2; for i in 1:size(A, 1) loop dpdv := dpdv - (i+1)*(A[i] + B[i]*T + C[i]*Modelica.Math.exp(-k*T/TCri))/(v_abs - b)^(i+2); end for; end dPressureVap_dSpecificVolume_Tv;

Buildings.Media.Refrigerants.R410A.dPressureVap_dTemperature_Tv

Derivative of the Martin-Hou equation of state with regards to temperature

Information

Function that calculates the derivative of the Martin-Hou equation of for R410A state with regards to temperature.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]
SpecificVolume	v		Specific volume of refrigerant [m3/kg]

Outputs

Type	Name	Description
Real	dpdT	Derivative of pressure with regards to temperature [Pa/K]

Modelica definition

function dPressureVap_dTemperature_Tv "Derivative of the Martin-Hou equation of state with regards to temperature" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; input Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; output Real dpdT( final unit="Pa/K") "Derivative of pressure with regards to temperature"; protected Modelica.SIunits.SpecificVolume v_abs "Smoothed specific volume"; algorithm v_abs := Buildings.Utilities.Math.Functions.smoothMax(v, 1.01*b, 0.01*b); dpdT := R/(v_abs-b); for i in 1:size(A, 1) loop dpdT := dpdT + (B[i] - C[i]*k/TCri*Modelica.Math.exp(-k*T/TCri))/(v_abs - b)^(i+1); end for; end dPressureVap_dTemperature_Tv;

Buildings.Media.Refrigerants.R410A.dSpecificVolumeVap_pT

Function that calculates the Jacobian of specific volume R410A vapor based on pressure and temperature

Information

Function that calculates the derivatives of Buildings.Media.Refrigerants.R410A.specificVolumeVap_pT

Inputs

Type	Name	Description
AbsolutePressure	p	Pressure of refrigerant vapor [Pa]
Temperature	T	Temperature of refrigerant [K]
Real	dp	Delta of pressure of refrigerant vapor [Pa/s]
Real	dT	Delta of temperature of refrigerant [K/s]

Outputs

Type	Name	Description
Real	dv	Delta of specific volume of refrigerant [m3/(kg.s)]

Modelica definition

function dSpecificVolumeVap_pT "Function that calculates the Jacobian of specific volume R410A vapor based on pressure and temperature" input Modelica.SIunits.AbsolutePressure p "Pressure of refrigerant vapor"; input Modelica.SIunits.Temperature T "Temperature of refrigerant"; input Real dp( final unit="Pa/s") "Delta of pressure of refrigerant vapor"; input Real dT( final unit="K/s") "Delta of temperature of refrigerant"; output Real dv( final unit="m3/(kg.s)") "Delta of specific volume of refrigerant"; protected Real dpdT( final unit="Pa/K") "Derivative of pressure with regards to temperature"; Real dpdv( final unit="Pa.kg/m3") "Derivative of pressure with regards to specific volume"; Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; algorithm v := Buildings.Media.Refrigerants.R410A.specificVolumeVap_pT(p, T); dpdT := Buildings.Media.Refrigerants.R410A.dPressureVap_dTemperature_Tv(T, v); dpdv := Buildings.Media.Refrigerants.R410A.dPressureVap_dSpecificVolume_Tv(T, v); dv := dp/dpdv + dT*(dpdT/dpdv); end dSpecificVolumeVap_pT;

Buildings.Media.Refrigerants.R410A.enthalpySatLiq_T

Function that calculates the enthalpy of saturated liquid R410A based on temperature

Information

Function that calculates the enthalpy of saturated liquid R410A based on temperature.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]

Outputs

Type	Name	Description
SpecificEnthalpy	h	Specific enthalpy of saturated liquid refrigerant [J/kg]

Modelica definition

function enthalpySatLiq_T "Function that calculates the enthalpy of saturated liquid R410A based on temperature" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; output Modelica.SIunits.SpecificEnthalpy h "Specific enthalpy of saturated liquid refrigerant"; protected final constant Real a[:] = {221.1749, -514.9668, -631.625, -262.2749, 1052.0, 1596.0} "Coefficients for polynomial equation"; final constant Real x0 = 0.5541498 "x0 for saturation pressure of liquid refrigerant"; Real x "Independent variable"; algorithm // Independent variable x := Buildings.Utilities.Math.Functions.smoothMax(1-T/TCri, 1e-4, 5e-3)^(1/3) - x0; // Pressure of saturated liquid refrigerant h := 1000*Buildings.Utilities.Math.Functions.polynomial(a = a, x = x); end enthalpySatLiq_T;

Buildings.Media.Refrigerants.R410A.enthalpySatVap_T

Function that calculates the specific enthalpy of saturated R410A vapor based on temperature

Information

Function that calculates the specific enthalpy of saturated R410A vapor based on temperature.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]

Outputs

Type	Name	Description
SpecificEnthalpy	h	Specific enthalpy of saturated liquid refrigerant [J/kg]

Modelica definition

function enthalpySatVap_T "Function that calculates the specific enthalpy of saturated R410A vapor based on temperature" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; output Modelica.SIunits.SpecificEnthalpy h "Specific enthalpy of saturated liquid refrigerant"; protected final constant Real a[:] = {406.0598, -34.78156, 262.8079, 223.8549, -1162.627, 570.6635} "Coefficients for polynomial equation"; Real x "Independent variable"; algorithm // Independent variable x := Buildings.Utilities.Math.Functions.smoothMax(1-T/TCri, 1e-4, 5e-3)^(1/3); // Pressure of saturated liquid refrigerant h := 1000*Buildings.Utilities.Math.Functions.polynomial(a = a, x = x); end enthalpySatVap_T;

Buildings.Media.Refrigerants.R410A.isentropicExponentVap_Tv

Function that calculates the isentropic exponent of R410A vapor based on temperature and specific volume

Information

Function that calculates the isentropic exponent of R410A vapor based on temperature and specific volume. The isentropic exponent is equal to the ratio of specific heat capacities:

k = c_p/c_v

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]
SpecificVolume	v		Specific volume of refrigerant [m3/kg]

Outputs

Type	Name	Description
IsentropicExponent	k	Specific isobaric heat capacity [1]

Modelica definition

function isentropicExponentVap_Tv "Function that calculates the isentropic exponent of R410A vapor based on temperature and specific volume" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; input Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; output Modelica.SIunits.IsentropicExponent k "Specific isobaric heat capacity"; protected Modelica.SIunits.SpecificHeatCapacity cp "Specific isobaric heat capacity"; Modelica.SIunits.SpecificHeatCapacity cv "Specific isochoric heat capacity"; algorithm // Evaluate the specific isobaric and isochoric heat capacities cp := Buildings.Media.Refrigerants.R410A.specificIsobaricHeatCapacityVap_Tv(T, v); cv := Buildings.Media.Refrigerants.R410A.specificIsochoricHeatCapacityVap_Tv(T, v); k := cp / cv; end isentropicExponentVap_Tv;

Buildings.Media.Refrigerants.R410A.pressureSatVap_T

Function that calculates the pressure of saturated R410A vapor based on temperature

Information

Function that calculates the pressure of saturated R410A vapor based on temperature.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]

Outputs

Type	Name	Description
AbsolutePressure	p	Pressure of saturated refrigerant vapor [Pa]

Modelica definition

function pressureSatVap_T "Function that calculates the pressure of saturated R410A vapor based on temperature" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; output Modelica.SIunits.AbsolutePressure p "Pressure of saturated refrigerant vapor"; protected final Real a[:] = {-1.440004, -6.865265, -0.5354309, -3.749023, -3.521484, -7.75} "Coefficients for polynomial equation"; final Real x0 = 0.2086902 "x0 for saturation pressure of refrigerant vapor"; Real x "Independent variable"; algorithm // Independent variable x := Buildings.Utilities.Math.Functions.smoothMax(1-T/TCri, 1e-4, 5e-3) - x0; // Pressure of saturated refrigerant vapor p := pCri*Modelica.Math.exp(TCri/T*Buildings.Utilities.Math.Functions.polynomial(a = a, x = x)); end pressureSatVap_T;

Buildings.Media.Refrigerants.R410A.pressureVap_Tv

Function that calculates the pressure R410A vapor based on temperature and specific volume

Information

Function that calculates the pressure R410A vapor based on temperature and specific volume. The pressure is calculated from the Martin-Hou equation of state.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]
SpecificVolume	v		Specific volume of refrigerant [m3/kg]

Outputs

Type	Name	Description
AbsolutePressure	p	Pressure of refrigerant vapor [Pa]

Modelica definition

function pressureVap_Tv "Function that calculates the pressure R410A vapor based on temperature and specific volume" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; input Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; output Modelica.SIunits.AbsolutePressure p "Pressure of refrigerant vapor"; protected Modelica.SIunits.SpecificVolume v_abs "Smoothed specific volume"; algorithm v_abs := Buildings.Utilities.Math.Functions.smoothMax(v, 1.01*b, 0.01*b); p := R*T/(v_abs-b); for i in 1:size(A, 1) loop p := p + (A[i] + B[i]*T + C[i]*Modelica.Math.exp(-k*T/TCri))/(v_abs - b)^(i+1); end for; end pressureVap_Tv;

Buildings.Media.Refrigerants.R410A.specificIsobaricHeatCapacityVap_Tv

Function that calculates the specific isobaric heat capacity of R410A vapor based on temperature and specific volume

Information

Function that calculates the specific isobaric heat capacity (c_p) of R410A vapor based on temperature and specific volume.

The specific isobaric heat capacity is evaluated from the partial derivatives of the Martin-Hou equation of state.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]
SpecificVolume	v		Specific volume of refrigerant [m3/kg]

Outputs

Type	Name	Description
SpecificHeatCapacity	cp	Specific isobaric heat capacity [J/(kg.K)]

Modelica definition

function specificIsobaricHeatCapacityVap_Tv "Function that calculates the specific isobaric heat capacity of R410A vapor based on temperature and specific volume" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; input Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; output Modelica.SIunits.SpecificHeatCapacity cp "Specific isobaric heat capacity"; protected Real dpdT "First derivative w.r.t. temperature of the Martin-Hou equation"; Real dpdv "First derivative w.r.t. specific volume of the Martin-Hou equation"; Modelica.SIunits.SpecificHeatCapacity cv "Specific isochoric heat capacity"; algorithm cv := Buildings.Media.Refrigerants.R410A.specificIsochoricHeatCapacityVap_Tv(T, v); dpdT := Buildings.Media.Refrigerants.R410A.dPressureVap_dTemperature_Tv(T, v); dpdv := Buildings.Media.Refrigerants.R410A.dPressureVap_dSpecificVolume_Tv(T, v); cp := cv - T * dpdT^2 / dpdv; end specificIsobaricHeatCapacityVap_Tv;

Buildings.Media.Refrigerants.R410A.specificIsochoricHeatCapacityVap_Tv

Function that calculates the specific isochoric heat capacity of R410A vapor based on temperature and specific volume

Information

Function that calculates the specific isochoric heat capacity (c_v) of R410A vapor based on temperature and specific volume.

The specific isochoric heat capacity is evaluated from the partial derivatives of the Martin-Hou equation of state.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
Temperature	T		Temperature of refrigerant [K]
SpecificVolume	v		Specific volume of refrigerant [m3/kg]

Outputs

Type	Name	Description
SpecificHeatCapacity	cv	Specific isochoric heat capacity [J/(kg.K)]

Modelica definition

function specificIsochoricHeatCapacityVap_Tv "Function that calculates the specific isochoric heat capacity of R410A vapor based on temperature and specific volume" input Modelica.SIunits.Temperature T "Temperature of refrigerant"; input Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; output Modelica.SIunits.SpecificHeatCapacity cv "Specific isochoric heat capacity"; protected Real a[:] = {2.676087e-1, 2.115353e-3, -9.848184e-7, 6.493781e-11} "Coefficients for ideal gas specific isobaric heat capacity"; Real integral_of_d2pdT2 "Integral over v of the second derivative w.r.t. temperature of the Martin-Hou equation"; Modelica.SIunits.SpecificHeatCapacity cpo "Ideal gas specific isobaric heat capacity"; Modelica.SIunits.SpecificHeatCapacity cvo "Ideal gas specific isochoric heat capacity"; algorithm // Ideal gas isobaric heat capacity from polynomial equation cpo := 1.0e3*Buildings.Utilities.Math.Functions.polynomial(a = a, x = T); cvo := cpo - R; // Integral of second derivative of pressure w.r.t. temperature integral_of_d2pdT2 := (k/TCri)^2 * Modelica.Math.exp(-k*T/TCri) * sum(C[i]/(i*(v - b)^(i)) for i in 1:size(C, 1)); cv := cvo - T * integral_of_d2pdT2; end specificIsochoricHeatCapacityVap_Tv;

Buildings.Media.Refrigerants.R410A.specificVolumeVap_pT

Function that calculates the specific volume R410A vapor based on pressure and temperature

Information

Function that calculates the specific volume R410A vapor based on pressure and temperature. The specific volume is evaluated iteratively by succesive evaluations of the vapor pressure.

The initial guess is estimated by the first term in the Martin-Hou equation of state.

References

Thermodynamic properties of DuPont Suva 410A: https://www.chemours.com/Refrigerants/en_US/assets/downloads/h64423_Suva410A_thermo_prop_si.pdf

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure of refrigerant vapor [Pa]
Temperature	T		Temperature of refrigerant [K]

Outputs

Type	Name	Description
SpecificVolume	v	Specific volume of refrigerant [m3/kg]

Modelica definition

function specificVolumeVap_pT "Function that calculates the specific volume R410A vapor based on pressure and temperature" annotation(derivative=Buildings.Media.Refrigerants.R410A.dSpecificVolumeVap_pT); input Modelica.SIunits.AbsolutePressure p "Pressure of refrigerant vapor"; input Modelica.SIunits.Temperature T "Temperature of refrigerant"; output Modelica.SIunits.SpecificVolume v "Specific volume of refrigerant"; protected Modelica.SIunits.SpecificVolume dv "Error on specific volume of refrigerant"; Modelica.SIunits.Pressure dp "Error on pressure of refrigerant"; Real dpdv( final unit = "(Pa.kg)/m3") "Partial derivative dp/dv"; Integer m "Counter"; algorithm // Initial guess of specific volume v := R*T/p + b; dv := 1e99; m := 0; while abs(dv/v) > 1e-10 loop assert(m < 1E3, "Failed to converge in Buildings.Media.Refrigerants.R410A.specificVolumeVap_pT"); m := m + 1; // Evaluate first derivative of pressure w.r.t. specific volume dpdv := Buildings.Media.Refrigerants.R410A.dPressureVap_dSpecificVolume_Tv(T, v); // Error on pressure dp := p - Buildings.Media.Refrigerants.R410A.pressureVap_Tv(T, v); // Corresponding linear adjustment of specific volume dv := dp/dpdv; v := v + dv; end while; end specificVolumeVap_pT;