Buildings.Utilities.Psychrometrics.Functions

Information

The nomenclature used in this package is described at Buildings.UsersGuide.Conventions.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
pW_X	Water vapor pressure for given humidity ratio
pW_TDewPoi	Function to compute the water vapor partial pressure for a given dew point temperature of moist air
pW_TDewPoi_amb	Function to compute the water vapor partial pressure for a given dew point temperature of moist air
TDewPoi_pW	Function to compute the water vapor partial pressure for a given dew point temperature of moist air
TDewPoi_pW_amb	Function to compute the dew point temperature of moist air for a given water vapor partial pressure
X_pSatpphi	Humidity ratio for given water vapor pressure
X_pW	Humidity ratio for given water vapor pressure
Examples	Collection of models that illustrate model use and test models
Internal	Solve f(x, data) for x with given f
BaseClasses	Package with base classes for Buildings.Utilities.Psychrometrics.Functions

Buildings.Utilities.Psychrometrics.Functions.pW_X

Information

Function to compute the water vapor partial pressure for a given humidity ratio.

Inputs

Type	Name	Default	Description
MassFraction	X_w		Species concentration at dry bulb temperature [1]
Pressure	p	101325	Total pressure [Pa]

Outputs

Type	Name	Description
Pressure	p_w	Water vapor pressure [Pa]

Modelica definition

function pW_X "Water vapor pressure for given humidity ratio"
  annotation(derivative=BaseClasses.der_pW_X);

  input Modelica.SIunits.MassFraction X_w(
    min=0,
    max=1,
    nominal=0.01) "Species concentration at dry bulb temperature";
  input Modelica.SIunits.Pressure p=101325 "Total pressure";
  output Modelica.SIunits.Pressure p_w(displayUnit="Pa") "Water vapor pressure";

protected 
  Modelica.SIunits.MassFraction x_w(nominal=0.01) 
    "Water mass fraction per mass of dry air";
algorithm 
  x_w := X_w/(1 - X_w);
  p_w := p*x_w/(0.62198 + x_w);
end pW_X;

Buildings.Utilities.Psychrometrics.Functions.pW_TDewPoi

Information

Dew point temperature calculation for moist air above freezing temperature.

The correlation used in this model is valid for dew point temperatures between 0 degC and 200 degC. It is the correlation from 2005 ASHRAE Handbook, p. 6.2. In an earlier version of this model, the equation from Peppers has been used, but this equation yielded about 15 Kelvin lower dew point temperatures.

Inputs

Type	Name	Default	Description
Temperature	T		Dew point temperature [K]

Outputs

Type	Name	Description
Pressure	p_w	Water vapor partial pressure [Pa]

Modelica definition

function pW_TDewPoi 
  "Function to compute the water vapor partial pressure for a given dew point temperature of moist air"
  annotation(derivative=BaseClasses.der_pW_TDewPoi);

  input Modelica.SIunits.Temperature T(min=100) "Dew point temperature";
  output Modelica.SIunits.Pressure p_w(displayUnit="Pa", min=100) 
    "Water vapor partial pressure";
protected 
  constant Real C8=-5.800226E3;
  constant Real C9=1.3914993E0;
  constant Real C10=-4.8640239E-2;
  constant Real C11=4.1764768E-5;
  constant Real C12=-1.4452093E-8;
  constant Real C13=6.5459673E0;

algorithm 
  p_w := Modelica.Math.exp(C8/T + C9 + T*(C10 + T*(C11 + T*C12)) + C13*
    Modelica.Math.log(T));
end pW_TDewPoi;

Buildings.Utilities.Psychrometrics.Functions.pW_TDewPoi_amb

Information

Dew point temperature calculation for moist air between 0 degC and 30 degC.

The correlation used in this model is valid for dew point temperatures between 0 degC and 30 degC. It is an approximation to the correlation from 2005 ASHRAE Handbook, p. 6.2, which is valid in a wider range of temperatures and implemented in Buildings.Utilities.Psychrometrics.Functions.pW_TDewPoi. The approximation error of this simplified function is below 5% for a temperature of 0 degC to 30 degC. The benefit of this simpler function is that it can be inverted analytically, whereas the other function requires a numerical solution.

Extends from Buildings.Utilities.Psychrometrics.Functions.BaseClasses.pW_TDewPoi_amb (Partial function to compute the water vapor partial pressure for a given dew point temperature of moist air and its inverse).

Inputs

Type	Name	Default	Description
Temperature	T		Dew point temperature [K]

Outputs

Type	Name	Description
Pressure	p_w	Water vapor partial pressure [Pa]

Modelica definition

function pW_TDewPoi_amb 
  "Function to compute the water vapor partial pressure for a given dew point temperature of moist air"
  annotation(derivative=BaseClasses.der_pW_TDewPoi_amb);
  extends Buildings.Utilities.Psychrometrics.Functions.BaseClasses.pW_TDewPoi_amb;

  input Modelica.SIunits.Temperature T "Dew point temperature";
  output Modelica.SIunits.Pressure p_w(displayUnit="Pa", min=100) 
    "Water vapor partial pressure";

algorithm 
  p_w := Modelica.Math.exp(a1 + a2*T);
end pW_TDewPoi_amb;

Buildings.Utilities.Psychrometrics.Functions.TDewPoi_pW

Information

Dew point temperature calculation for moist air above freezing temperature.

The correlation used in this model is valid for dew point temperatures between 0 degC and 200 degC. It is the correlation from 2005 ASHRAE Handbook, p. 6.2. In an earlier version of this model, the equation from Peppers has been used, but this equation yielded about 15 Kelvin lower dew point temperatures.

Inputs

Type	Name	Default	Description
Pressure	p_w		Water vapor partial pressure [Pa]

Outputs

Type	Name	Description
Temperature	T	Dew point temperature [K]

Modelica definition

function TDewPoi_pW 
  "Function to compute the water vapor partial pressure for a given dew point temperature of moist air"

  input Modelica.SIunits.Pressure p_w(displayUnit="Pa", min=200) 
    "Water vapor partial pressure";
  output Modelica.SIunits.Temperature T "Dew point temperature";

algorithm 
  T := Internal.solve(
    y_zero=p_w,
    x_min=200,
    x_max=400);
end TDewPoi_pW;

Buildings.Utilities.Psychrometrics.Functions.TDewPoi_pW_amb

Information

Dew point temperature calculation for moist air between 0 degC and 30 degC with partial pressure of water vapor as an input.

The correlation used in this model is valid for dew point temperatures between 0 degC and 30 degC. It is an approximation to the correlation from 2005 ASHRAE Handbook, p. 6.2, which is valid in a wider range of temperatures and implemented in Buildings.Utilities.Psychrometrics.Functions.pW_TDewPoi. The approximation error of this simplified function is below 5% for a temperature of 0 degC to 30 degC. The benefit of this simpler function is that it can be inverted analytically, whereas the other function requires a numerical solution.

Extends from Buildings.Utilities.Psychrometrics.Functions.BaseClasses.pW_TDewPoi_amb (Partial function to compute the water vapor partial pressure for a given dew point temperature of moist air and its inverse).

Inputs

Type	Name	Default	Description
Pressure	p_w		Water vapor partial pressure [Pa]

Outputs

Type	Name	Description
Temperature	T	Dew point temperature [K]

Modelica definition

function TDewPoi_pW_amb 
  "Function to compute the dew point temperature of moist air for a given water vapor partial pressure"
  annotation(derivative=BaseClasses.der_TDewPoi_pW_amb);
  extends Buildings.Utilities.Psychrometrics.Functions.BaseClasses.pW_TDewPoi_amb;

  input Modelica.SIunits.Pressure p_w(displayUnit="Pa", min=100) 
    "Water vapor partial pressure";
  output Modelica.SIunits.Temperature T "Dew point temperature";

algorithm 
  T := (Modelica.Math.log(p_w) - a1)/a2;
end TDewPoi_pW_amb;

Buildings.Utilities.Psychrometrics.Functions.X_pSatpphi

Information

Function to compute the water vapor concentration based on saturation pressure, absolute pressure and relative humidity.

Inputs

Type	Name	Default	Description
AbsolutePressure	pSat		Saturation pressure [Pa]
Pressure	p		Pressure of the fluid [Pa]
Real	phi		Relative humidity

Outputs

Type	Name	Description
MassFraction	X_w	Water vapor concentration per total mass of air [1]

Modelica definition

function X_pSatpphi "Humidity ratio for given water vapor pressure"
  input Modelica.SIunits.AbsolutePressure pSat "Saturation pressure";
  input Modelica.SIunits.Pressure p "Pressure of the fluid";
  input Real phi(min=0, max=1) "Relative humidity";
  output Modelica.SIunits.MassFraction X_w(
    min=0,
    max=1,
    nominal=0.01) "Water vapor concentration per total mass of air";

protected 
  constant Real k = 0.621964713077499 "Ratio of molar masses";
algorithm 
  X_w := phi*k/(k*phi+p/pSat-phi);

end X_pSatpphi;

Buildings.Utilities.Psychrometrics.Functions.X_pW

Information

Function to compute the humidity ratio for a given water vapor partial pressure.

Inputs

Type	Name	Default	Description
Pressure	p_w		Water vapor pressure [Pa]
Pressure	p	101325	Total pressure [Pa]

Outputs

Type	Name	Description
MassFraction	X_w	Species concentration at dry bulb temperature [1]

Modelica definition

function X_pW "Humidity ratio for given water vapor pressure"

  input Modelica.SIunits.Pressure p_w(displayUnit="Pa") "Water vapor pressure";
  input Modelica.SIunits.Pressure p=101325 "Total pressure";
  output Modelica.SIunits.MassFraction X_w(
    min=0,
    max=1,
    nominal=0.01) "Species concentration at dry bulb temperature";

protected 
  Modelica.SIunits.MassFraction x_w(nominal=0.01) 
    "Water mass fraction per mass of dry air";
algorithm 
  x_w := 0.62198*p_w/(p - p_w);
  X_w := x_w/(1 + x_w);
end X_pW;