Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions

functions to find the current region for given pairs of input variables

Information

Package description

Package Regions contains a large number of auxiliary functions which are neede to compute the current region of the IAPWS/IF97 for a given pair of input variables as quickly as possible. The focus of this implementation was on computational efficiency, not on compact code. Many of the function values calulated in these functions could be obtained using the fundamental functions of IAPWS/IF97, but with considerable overhead. If the region of IAPWS/IF97 is known in advance, the input variable mode can be set to the region, then the somewhat costly region checks are omitted. The checking for the phase has to be done outside the region functions because many properties are not differentiable at the region boundary. If the input phase is 2, the output region will be set to 4 immediately.

Package contents

The main 4 functions in this package are the functions returning the appropriate region for two input variables.

Function region_ph compute the region of IAPWS/IF97 for input pair pressure and specific enthalpy.
Function region_ps compute the region of IAPWS/IF97 for input pair pressure and specific entropy
Function region_dT compute the region of IAPWS/IF97 for input pair density and temperature.
Function region_pT compute the region of IAPWS/IF97 for input pair pressure and temperature (only ine phase region).

In addition, functions of the boiling and condensation curves compute the specific enthalpy, specific entropy, or density on these curves. The functions for the saturation pressure and temperature are included in the package Basic because they are part of the original IAPWS/IF97 standards document. These functions are also aliased to be used directly from package Water.

Function hl_p computes the liquid specific enthalpy as a function of pressure. For overcritical pressures, the critical specific enthalpy is returned. An approximation is used for temperatures > 623.15 K.
Function hv_p computes the vapour specific enthalpy as a function of pressure. For overcritical pressures, the critical specific enthalpy is returned. An approximation is used for temperatures > 623.15 K.
Function sl_p computes the liquid specific entropy as a function of pressure. For overcritical pressures, the critical specific entropy is returned. An approximation is used for temperatures > 623.15 K.
Function sv_p computes the vapour specific entropy as a function of pressure. For overcritical pressures, the critical specific entropyis returned. An approximation is used for temperatures > 623.15 K.
Function rhol_T computes the liquid density as a function of temperature. For overcritical temperatures, the critical density is returned. An approximation is used for temperatures > 623.15 K.
Function rhol_T computes the vapour density as a function of temperature. For overcritical temperatures, the critical density is returned. An approximation is used for temperatures > 623.15 K.

All other functions are auxiliary functions called from the region functions to check a specific boundary.

Function boundary23ofT computes the boundary pressure between regions 2 and 3 (input temperature)
Function boundary23ofp computes the boundary temperature between regions 2 and 3 (input pressure)
Function hlowerofp5 computes the lower specific enthalpy limit of region 5 (input p, T=1073.15 K)
Function hupperofp5 computes the upper specific enthalpy limit of region 5 (input p, T=2273.15 K)
Function slowerofp5 computes the lower specific entropy limit of region 5 (input p, T=1073.15 K)
Function supperofp5 computes the upper specific entropy limit of region 5 (input p, T=2273.15 K)
Function hlowerofp1 computes the lower specific enthalpy limit of region 1 (input p, T=273.15 K)
Function hupperofp1 computes the upper specific enthalpy limit of region 1 (input p, T=623.15 K)
Function slowerofp1 computes the lower specific entropy limit of region 1 (input p, T=273.15 K)
Function supperofp1 computes the upper specific entropy limit of region 1 (input p, T=623.15 K)
Function hlowerofp2 computes the lower specific enthalpy limit of region 2 (input p, T=623.15 K)
Function hupperofp2 computes the upper specific enthalpy limit of region 2 (input p, T=1073.15 K)
Function slowerofp2 computes the lower specific entropy limit of region 2 (input p, T=623.15 K)
Function supperofp2 computes the upper specific entropy limit of region 2 (input p, T=1073.15 K)
Function d1n computes the density in region 1 as function of pressure and temperature
Function d2n computes the density in region 2 as function of pressure and temperature
Function dhot1ofp computes the hot density limit of region 1 (input p, T=623.15 K)
Function dupper1ofTcomputes the high pressure density limit of region 1 (input T, p=100MPa)
Function hl_p_R4b computes a high accuracy approximation to the liquid enthalpy for temperatures > 623.15 K (input p)
Function hv_p_R4b computes a high accuracy approximation to the vapour enthalpy for temperatures > 623.15 K (input p)
Function sl_p_R4b computes a high accuracy approximation to the liquid entropy for temperatures > 623.15 K (input p)
Function sv_p_R4b computes a high accuracy approximation to the vapour entropy for temperatures > 623.15 K (input p)
Function rhol_p_R4b computes a high accuracy approximation to the liquid density for temperatures > 623.15 K (input p)
Function rhov_p_R4b computes a high accuracy approximation to the vapour density for temperatures > 623.15 K (input p)

Version Info and Revision history

First implemented: July, 2000 by Hubertus Tummescheit

Authors: Hubertus Tummescheit, Jonas Eborn and Falko Jens Wagner
Modelon AB
Ideon Science Park
SE-22370 Lund, Sweden
email: hubertus@modelon.se

Initial version: July 2000
Revised and extended for inclusion in Modelica.Thermal: December 2002

Extends from Modelica.Icons.Library (Icon for library).

Package Content

Name Description

boundary23ofT boundary function for region boundary between regions 2 and 3 (input temperature)

boundary23ofp boundary function for region boundary between regions 2 and 3 (input pressure)

hlowerofp5 explicit lower specific enthalpy limit of region 5 as function of pressure

hupperofp5 explicit upper specific enthalpy limit of region 5 as function of pressure

slowerofp5 explicit lower specific entropy limit of region 5 as function of pressure

supperofp5 explicit upper specific entropy limit of region 5 as function of pressure

hlowerofp1 explicit lower specific enthalpy limit of region 1 as function of pressure

hupperofp1 explicit upper specific enthalpy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

slowerofp1 explicit lower specific entropy limit of region 1 as function of pressure

supperofp1 explicit upper specific entropy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

hlowerofp2 explicit lower specific enthalpy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

hupperofp2 explicit upper specific enthalpy limit of region 2 as function of pressure

slowerofp2 explicit lower specific entropy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

supperofp2 explicit upper specific entropy limit of region 2 as function of pressure

d1n density in region 1 as function of p and T

d2n density in region 2 as function of p and T

dhot1ofp density at upper temperature limit of region 1

dupper1ofT density at upper pressure limit of region 1

hl_p_R4b explicit approximation of liquid specific enthalpy on the boundary between regions 4 and 3

hv_p_R4b explicit approximation of vapour specific enthalpy on the boundary between regions 4 and 3

sl_p_R4b explicit approximation of liquid specific entropy on the boundary between regions 4 and 3

sv_p_R4b explicit approximation of vapour specific entropy on the boundary between regions 4 and 3

rhol_p_R4b explicit approximation of liquid density on the boundary between regions 4 and 3

rhov_p_R4b explicit approximation of vapour density on the boundary between regions 4 and 2

boilingcurve_p properties on the boiling curve

dewcurve_p properties on the dew curve

hvl_p

hl_p liquid specific enthalpy on the boundary between regions 4 and 3 or 1

hv_p vapour specific enthalpy on the boundary between regions 4 and 3 or 2

hvl_p_der derivative function for the specific enthalpy along the phase boundary

rhovl_p

rhol_p density of saturated water

rhov_p density of saturated vapour

rhovl_p_der

sl_p liquid specific entropy on the boundary between regions 4 and 3 or 1

sv_p vapour specific entropy on the boundary between regions 4 and 3 or 2

rhol_T density of saturated water

rhov_T density of saturated vapour

region_ph return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific enthalpy

region_ps return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific entropy

region_pT return the current region (valid values: 1,2,3,5) in IF97, given pressure and temperature

region_dT return the current region (valid values: 1,2,3,4,5) in IF97, given density and temperature

hvl_dp derivative function for the specific enthalpy along the phase boundary

dhl_dp derivative of liquid specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure

dhv_dp derivative of vapour specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure

drhovl_dp

drhol_dp derivative of density of saturated water w.r.t. pressure

drhov_dp derivative of density of saturated steam w.r.t. pressure

Name	Description
boundary23ofT	boundary function for region boundary between regions 2 and 3 (input temperature)
boundary23ofp	boundary function for region boundary between regions 2 and 3 (input pressure)
hlowerofp5	explicit lower specific enthalpy limit of region 5 as function of pressure
hupperofp5	explicit upper specific enthalpy limit of region 5 as function of pressure
slowerofp5	explicit lower specific entropy limit of region 5 as function of pressure
supperofp5	explicit upper specific entropy limit of region 5 as function of pressure
hlowerofp1	explicit lower specific enthalpy limit of region 1 as function of pressure
hupperofp1	explicit upper specific enthalpy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
slowerofp1	explicit lower specific entropy limit of region 1 as function of pressure
supperofp1	explicit upper specific entropy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
hlowerofp2	explicit lower specific enthalpy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
hupperofp2	explicit upper specific enthalpy limit of region 2 as function of pressure
slowerofp2	explicit lower specific entropy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
supperofp2	explicit upper specific entropy limit of region 2 as function of pressure
d1n	density in region 1 as function of p and T
d2n	density in region 2 as function of p and T
dhot1ofp	density at upper temperature limit of region 1
dupper1ofT	density at upper pressure limit of region 1
hl_p_R4b	explicit approximation of liquid specific enthalpy on the boundary between regions 4 and 3
hv_p_R4b	explicit approximation of vapour specific enthalpy on the boundary between regions 4 and 3
sl_p_R4b	explicit approximation of liquid specific entropy on the boundary between regions 4 and 3
sv_p_R4b	explicit approximation of vapour specific entropy on the boundary between regions 4 and 3
rhol_p_R4b	explicit approximation of liquid density on the boundary between regions 4 and 3
rhov_p_R4b	explicit approximation of vapour density on the boundary between regions 4 and 2
boilingcurve_p	properties on the boiling curve
dewcurve_p	properties on the dew curve
hvl_p
hl_p	liquid specific enthalpy on the boundary between regions 4 and 3 or 1
hv_p	vapour specific enthalpy on the boundary between regions 4 and 3 or 2
hvl_p_der	derivative function for the specific enthalpy along the phase boundary
rhovl_p
rhol_p	density of saturated water
rhov_p	density of saturated vapour
rhovl_p_der
sl_p	liquid specific entropy on the boundary between regions 4 and 3 or 1
sv_p	vapour specific entropy on the boundary between regions 4 and 3 or 2
rhol_T	density of saturated water
rhov_T	density of saturated vapour
region_ph	return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific enthalpy
region_ps	return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific entropy
region_pT	return the current region (valid values: 1,2,3,5) in IF97, given pressure and temperature
region_dT	return the current region (valid values: 1,2,3,4,5) in IF97, given density and temperature
hvl_dp	derivative function for the specific enthalpy along the phase boundary
dhl_dp	derivative of liquid specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure
dhv_dp	derivative of vapour specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure
drhovl_dp
drhol_dp	derivative of density of saturated water w.r.t. pressure
drhov_dp	derivative of density of saturated steam w.r.t. pressure

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.boundary23ofT

boundary function for region boundary between regions 2 and 3 (input temperature)

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Temperature t temperature (K) [K]

Type	Name	Default	Description
Temperature	t		temperature (K) [K]

Outputs

Type Name Description

Pressure p pressure [Pa]

Type	Name	Description
Pressure	p	pressure [Pa]

Modelica definition

function boundary23ofT 
  "boundary function for region boundary between regions 2 and 3 (input temperature)"

  extends Modelica.Icons.Function;
  input SI.Temperature t "temperature (K)";
  output SI.Pressure p "pressure";
protected 
  constant Real[5] n=data.n;
algorithm 
  p := 1.0e6*(n[1] + t*(n[2] + t*n[3]));
end boundary23ofT;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.boundary23ofp

boundary function for region boundary between regions 2 and 3 (input pressure)

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

Temperature t temperature (K) [K]

Type	Name	Description
Temperature	t	temperature (K) [K]

Modelica definition

function boundary23ofp 
  "boundary function for region boundary between regions 2 and 3 (input pressure)"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.Temperature t "temperature (K)";
protected 
  constant Real[5] n=data.n;
  Real pi "dimensionless pressure";
algorithm 
  pi := p/1.0e6;
  assert(p > triple.ptriple,
    "IF97 medium function boundary23ofp called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  t := n[4] + ((pi - n[5])/n[3])^0.5;
end boundary23ofp;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hlowerofp5

explicit lower specific enthalpy limit of region 5 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hlowerofp5 
  "explicit lower specific enthalpy limit of region 5 as function of pressure"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real pi "dimensionless pressure";
algorithm 
  pi := p/data.PSTAR5;
  assert(p > triple.ptriple,
    "IF97 medium function hlowerofp5 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  h := 461526.*(9.01505286876203 + pi*(-0.00979043490246092 + (-0.0000203245575263501
     + 3.36540214679088e-7*pi)*pi));
end hlowerofp5;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hupperofp5

explicit upper specific enthalpy limit of region 5 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hupperofp5 
  "explicit upper specific enthalpy limit of region 5 as function of pressure"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real pi "dimensionless pressure";
algorithm 
  pi := p/data.PSTAR5;
  assert(p > triple.ptriple,
    "IF97 medium function hupperofp5 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  h := 461526.*(15.9838891400332 + pi*(-0.000489898813722568 + (-5.01510211858761e-8
     + 7.5006972718273e-8*pi)*pi));
end hupperofp5;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.slowerofp5

explicit lower specific entropy limit of region 5 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	specific entropy [J/(kg.K)]

Modelica definition

function slowerofp5 
  "explicit lower specific entropy limit of region 5 as function of pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  Real pi "dimensionless pressure";
algorithm 
  pi := p/data.PSTAR5;
  assert(p > triple.ptriple,
    "IF97 medium function slowerofp5 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  s := 461.526*(18.4296209980112 + pi*(-0.00730911805860036 + (-0.0000168348072093888
     + 2.09066899426354e-7*pi)*pi) - Modelica.Math.log(pi));
end slowerofp5;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.supperofp5

explicit upper specific entropy limit of region 5 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	specific entropy [J/(kg.K)]

Modelica definition

function supperofp5 
  "explicit upper specific entropy limit of region 5 as function of pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  Real pi "dimensionless pressure";
algorithm 
  pi := p/data.PSTAR5;
  assert(p > triple.ptriple,
    "IF97 medium function supperofp5 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  s := 461.526*(22.7281531474243 + pi*(-0.000656650220627603 + (-1.96109739782049e-8
     + 2.19979537113031e-8*pi)*pi) - Modelica.Math.log(pi));
end supperofp5;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hlowerofp1

explicit lower specific enthalpy limit of region 1 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hlowerofp1 
  "explicit lower specific enthalpy limit of region 1 as function of pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real pi1 "dimensionless pressure";
  Real[3] o "vector of auxiliary variables";
algorithm 
  pi1 := 7.1 - p/data.PSTAR1;
  assert(p > triple.ptriple,
    "IF97 medium function hlowerofp1 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  o[1] := pi1*pi1;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];

  h := 639675.036*(0.173379420894777 + pi1*(-0.022914084306349 + pi1*(-0.00017146768241932
     + pi1*(-4.18695814670391e-6 + pi1*(-2.41630417490008e-7 + pi1*(
    1.73545618580828e-11 + o[1]*pi1*(8.43755552264362e-14 + o[2]*o[3]*pi1
    *(5.35429206228374e-35 + o[1]*(-8.12140581014818e-38 + o[1]*o[2]*(-1.43870236842915e-44
     + pi1*(1.73894459122923e-45 + (-7.06381628462585e-47 +
    9.64504638626269e-49*pi1)*pi1)))))))))));
end hlowerofp1;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hupperofp1

explicit upper specific enthalpy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hupperofp1 
  "explicit upper specific enthalpy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real pi1 "dimensionless pressure";
  Real[3] o "vector of auxiliary variables";
algorithm 
  pi1 := 7.1 - p/data.PSTAR1;
  assert(p > triple.ptriple,
    "IF97 medium function hupperofp1 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  o[1] := pi1*pi1;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  h := 639675.036*(2.42896927729349 + pi1*(-0.00141131225285294 + pi1*(
    0.00143759406818289 + pi1*(0.000125338925082983 + pi1*(
    0.0000123617764767172 + pi1*(3.17834967400818e-6 + o[1]*pi1*(
    1.46754947271665e-8 + o[2]*o[3]*pi1*(1.86779322717506e-17 + o[1]*(-4.18568363667416e-19
     + o[1]*o[2]*(-9.19148577641497e-22 + pi1*(4.27026404402408e-22 + (-6.66749357417962e-23
     + 3.49930466305574e-24*pi1)*pi1)))))))))));
end hupperofp1;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.slowerofp1

explicit lower specific entropy limit of region 1 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	specific entropy [J/(kg.K)]

Modelica definition

function slowerofp1 
  "explicit lower specific entropy limit of region 1 as function of pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  Real pi1 "dimensionless pressure";
  Real[3] o "vector of auxiliary variables";
algorithm 
  pi1 := 7.1 - p/data.PSTAR1;
  assert(p > triple.ptriple,
    "IF97 medium function slowerofp1 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  o[1] := pi1*pi1;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  s := 461.526*(-0.0268080988194267 + pi1*(0.00834795890110168 + pi1*(-0.000486470924668433
     + pi1*(-0.0000154902045012264 + pi1*(-1.07631751351358e-6 + pi1*(
    9.64159058957115e-11 + o[1]*pi1*(4.81921078863103e-13 + o[2]*o[3]*pi1
    *(2.7879623870968e-34 + o[1]*(-4.22182957646226e-37 + o[1]*o[2]*(-7.44601427465175e-44
     + pi1*(8.99540001407168e-45 + (-3.65230274480299e-46 +
    4.98464639687285e-48*pi1)*pi1)))))))))));
end slowerofp1;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.supperofp1

explicit upper specific entropy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	specific entropy [J/(kg.K)]

Modelica definition

function supperofp1 
  "explicit upper specific entropy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  Real pi1 "dimensionless pressure";
  Real[3] o "vector of auxiliary variables";
algorithm 
  pi1 := 7.1 - p/data.PSTAR1;
  assert(p > triple.ptriple,
    "IF97 medium function supperofp1 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  o[1] := pi1*pi1;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  s := 461.526*(7.28316418503422 + pi1*(0.070602197808399 + pi1*(
    0.0039229343647356 + pi1*(0.000313009170788845 + pi1*(
    0.0000303619398631619 + pi1*(7.46739440045781e-6 + o[1]*pi1*(
    3.40562176858676e-8 + o[2]*o[3]*pi1*(4.21886233340801e-17 + o[1]*(-9.44504571473549e-19
     + o[1]*o[2]*(-2.06859611434475e-21 + pi1*(9.60758422254987e-22 + (-1.49967810652241e-22
     + 7.86863124555783e-24*pi1)*pi1)))))))))));
end supperofp1;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hlowerofp2

explicit lower specific enthalpy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hlowerofp2 
  "explicit lower specific enthalpy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real pi "dimensionless pressure";
  Real q1 "auxiliary variable";
  Real q2 "auxiliary variable";
  Real[18] o "vector of auxiliary variables";
algorithm 
  pi := p/data.PSTAR2;
  assert(p > triple.ptriple,
    "IF97 medium function hlowerofp2 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  q1 := 572.54459862746 + 31.3220101646784*(-13.91883977887 + pi)^0.5;
  q2 := -0.5 + 540./q1;
  o[1] := q1*q1;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  o[4] := pi*pi;
  o[5] := o[4]*o[4];
  o[6] := q2*q2;
  o[7] := o[6]*o[6];
  o[8] := o[6]*o[7];
  o[9] := o[5]*o[5];
  o[10] := o[7]*o[7];
  o[11] := o[9]*o[9];
  o[12] := o[10]*o[10];
  o[13] := o[12]*o[12];
  o[14] := o[7]*q2;
  o[15] := o[6]*q2;
  o[16] := o[10]*o[6];
  o[17] := o[13]*o[6];
  o[18] := o[13]*o[6]*q2;
  h := (4.63697573303507e9 + 3.74686560065793*o[2] + 3.57966647812489e-6*
    o[1]*o[2] + 2.81881548488163e-13*o[3] - 7.64652332452145e7*q1 -
    0.00450789338787835*o[2]*q1 - 1.55131504410292e-9*o[1]*o[2]*q1 + o[1]
    *(2.51383707870341e6 - 4.78198198764471e6*o[10]*o[11]*o[12]*o[13]*o[4]
     + 49.9651389369988*o[11]*o[12]*o[13]*o[4]*o[5]*o[7] + o[15]*o[4]*(
    1.03746636552761e-13 - 0.00349547959376899*o[16] -
    2.55074501962569e-7*o[8])*o[9] + (-242662.235426958*o[10]*o[12] -
    3.46022402653609*o[16])*o[4]*o[5]*pi + o[4]*(0.109336249381227 -
    2248.08924686956*o[14] - 354742.725841972*o[17] - 24.1331193696374*o[
    6])*pi - 3.09081828396912e-19*o[11]*o[12]*o[5]*o[7]*pi -
    1.24107527851371e-8*o[11]*o[13]*o[4]*o[5]*o[6]*o[7]*pi +
    3.99891272904219*o[5]*o[8]*pi + 0.0641817365250892*o[10]*o[7]*o[9]*pi
     + pi*(-4444.87643334512 - 75253.6156722047*o[14] - 43051.9020511789*
    o[6] - 22926.6247146068*q2) + o[4]*(-8.23252840892034 -
    3927.0508365636*o[15] - 239.325789467604*o[18] - 76407.3727417716*o[8]
     - 94.4508644545118*q2) + 0.360567666582363*o[5]*(-0.0161221195808321
     + q2)*(0.0338039844460968 + q2) + o[11]*(-0.000584580992538624*o[10]
    *o[12]*o[7] + 1.33248030241755e6*o[12]*o[13]*q2) + o[9]*(-7.38502736990986e7
    *o[18] + 0.0000224425477627799*o[6]*o[7]*q2) + o[4]*o[5]*(-2.08438767026518e8
    *o[17] - 0.0000124971648677697*o[6] - 8442.30378348203*o[10]*o[6]*o[7]
    *q2) + o[11]*o[9]*(4.73594929247646e-22*o[10]*o[12]*q2 -
    13.6411358215175*o[10]*o[12]*o[13]*q2 + 5.52427169406836e-10*o[13]*o[
    6]*o[7]*q2) + o[11]*o[5]*(2.67174673301715e-6*o[17] +
    4.44545133805865e-18*o[12]*o[6]*q2 - 50.2465185106411*o[10]*o[13]*o[6]
    *o[7]*q2)))/o[1];
end hlowerofp2;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hupperofp2

explicit upper specific enthalpy limit of region 2 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hupperofp2 
  "explicit upper specific enthalpy limit of region 2 as function of pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real pi "dimensionless pressure";
  Real[2] o "vector of auxiliary variables";
algorithm 
  pi := p/data.PSTAR2;
  assert(p > triple.ptriple,
    "IF97 medium function hupperofp2 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  o[1] := pi*pi;
  o[2] := o[1]*o[1]*o[1];
  h := 4.16066337647071e6 + pi*(-4518.48617188327 + pi*(-8.53409968320258
     + pi*(0.109090430596056 + pi*(-0.000172486052272327 + pi*(
    4.2261295097284e-15 + pi*(-1.27295130636232e-10 + pi*(-3.79407294691742e-25
     + pi*(7.56960433802525e-23 + pi*(7.16825117265975e-32 + pi*(
    3.37267475986401e-21 + (-7.5656940729795e-74 + o[1]*(-8.00969737237617e-134
     + (1.6746290980312e-65 + pi*(-3.71600586812966e-69 + pi*(
    8.06630589170884e-129 + (-1.76117969553159e-103 +
    1.88543121025106e-84*pi)*pi)))*o[1]))*o[2]))))))))));
end hupperofp2;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.slowerofp2

explicit lower specific entropy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	specific entropy [J/(kg.K)]

Modelica definition

function slowerofp2 
  "explicit lower specific entropy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  Real pi "dimensionless pressure";
  Real q1 "auxiliary variable";
  Real q2 "auxiliary variable";
  Real[40] o "vector of auxiliary variables";
algorithm 
  pi := p/data.PSTAR2;
  assert(p > triple.ptriple,
    "IF97 medium function slowerofp2 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  q1 := 572.54459862746 + 31.3220101646784*(-13.91883977887 + pi)^0.5;
  q2 := -0.5 + 540.0/q1;
  o[1] := pi*pi;
  o[2] := o[1]*pi;
  o[3] := o[1]*o[1];
  o[4] := o[1]*o[3]*pi;
  o[5] := q1*q1;
  o[6] := o[5]*q1;
  o[7] := 1/o[5];
  o[8] := 1/q1;
  o[9] := o[5]*o[5];
  o[10] := o[9]*q1;
  o[11] := q2*q2;
  o[12] := o[11]*q2;
  o[13] := o[1]*o[3];
  o[14] := o[11]*o[11];
  o[15] := o[3]*o[3];
  o[16] := o[1]*o[15];
  o[17] := o[11]*o[14];
  o[18] := o[11]*o[14]*q2;
  o[19] := o[3]*pi;
  o[20] := o[14]*o[14];
  o[21] := o[11]*o[20];
  o[22] := o[15]*pi;
  o[23] := o[14]*o[20]*q2;
  o[24] := o[20]*o[20];
  o[25] := o[15]*o[15];
  o[26] := o[25]*o[3];
  o[27] := o[14]*o[24];
  o[28] := o[25]*o[3]*pi;
  o[29] := o[20]*o[24]*q2;
  o[30] := o[15]*o[25];
  o[31] := o[24]*o[24];
  o[32] := o[11]*o[31]*q2;
  o[33] := o[14]*o[31];
  o[34] := o[1]*o[25]*o[3]*pi;
  o[35] := o[11]*o[14]*o[31]*q2;
  o[36] := o[1]*o[25]*o[3];
  o[37] := o[1]*o[25];
  o[38] := o[20]*o[24]*o[31]*q2;
  o[39] := o[14]*q2;
  o[40] := o[11]*o[31];

  s := 461.526*(9.692768600217 + 1.22151969114703e-16*o[10] +
    0.00018948987516315*o[1]*o[11] + 1.6714766451061e-11*o[12]*o[13] +
    0.0039392777243355*o[1]*o[14] - 1.0406965210174e-19*o[14]*o[16] +
    0.043797295650573*o[1]*o[18] - 2.2922076337661e-6*o[18]*o[19] -
    2.0481737692309e-8*o[2] + 0.00003227767723857*o[12]*o[2] +
    0.0015033924542148*o[17]*o[2] - 1.1256211360459e-11*o[15]*o[20] +
    1.0018179379511e-9*o[11]*o[14]*o[16]*o[20] + 1.0234747095929e-13*o[16]
    *o[21] - 1.9809712802088e-8*o[22]*o[23] + 0.0021171472321355*o[13]*o[
    24] - 8.9185845355421e-25*o[26]*o[27] - 1.2790717852285e-8*o[11]*o[3]
     - 4.8225372718507e-7*o[12]*o[3] - 7.3087610595061e-29*o[11]*o[20]*o[
    24]*o[30] - 0.10693031879409*o[11]*o[24]*o[25]*o[31] +
    4.2002467698208e-6*o[24]*o[26]*o[31] - 5.5414715350778e-17*o[20]*o[30]
    *o[31] + 9.436970724121e-7*o[11]*o[20]*o[24]*o[30]*o[31] +
    23.895741934104*o[13]*o[32] + 0.040668253562649*o[2]*o[32] -
    3.0629316876232e-13*o[26]*o[32] + 0.000026674547914087*o[1]*o[33] +
    8.2311340897998*o[15]*o[33] + 1.2768608934681e-15*o[34]*o[35] +
    0.33662250574171*o[37]*o[38] + 5.905956432427e-18*o[4] +
    0.038946842435739*o[29]*o[4] - 4.88368302964335e-6*o[5] -
    3.34901734177133e6/o[6] + 2.58538448402683e-9*o[6] + 82839.5726841115
    *o[7] - 5446.7940672972*o[8] - 8.40318337484194e-13*o[9] +
    0.0017731742473213*pi + 0.045996013696365*o[11]*pi +
    0.057581259083432*o[12]*pi + 0.05032527872793*o[17]*pi + o[8]*pi*(
    9.63082563787332 - 0.008917431146179*q1) + 0.00811842799898148*q1 +
    0.000033032641670203*o[1]*q2 - 4.3870667284435e-7*o[2]*q2 +
    8.0882908646985e-11*o[14]*o[20]*o[24]*o[25]*q2 + 5.9056029685639e-26*
    o[14]*o[24]*o[28]*q2 + 7.8847309559367e-10*o[3]*q2 -
    3.7826947613457e-6*o[14]*o[24]*o[31]*o[36]*q2 + 1.2621808899101e-6*o[
    11]*o[20]*o[4]*q2 + 540.*o[8]*(10.08665568018 - 0.000033032641670203*
    o[1] - 6.2245802776607e-15*o[10] - 0.015757110897342*o[1]*o[12] -
    5.0144299353183e-11*o[11]*o[13] + 4.1627860840696e-19*o[12]*o[16] -
    0.306581069554011*o[1]*o[17] + 9.0049690883672e-11*o[15]*o[18] +
    0.0000160454534363627*o[17]*o[19] + 4.3870667284435e-7*o[2] -
    0.00009683303171571*o[11]*o[2] + 2.57526266427144e-7*o[14]*o[20]*o[22]
     - 1.40254511313154e-8*o[16]*o[23] - 2.34560435076256e-9*o[14]*o[20]*
    o[24]*o[25] - 1.24017662339842e-24*o[27]*o[28] - 7.8847309559367e-10*
    o[3] + 1.44676118155521e-6*o[11]*o[3] + 1.90027787547159e-27*o[29]*o[
    30] - 0.000960283724907132*o[1]*o[32] - 296.320827232793*o[15]*o[32]
     - 4.97975748452559e-14*o[11]*o[14]*o[31]*o[34] +
    2.21658861403112e-15*o[30]*o[35] + 0.000200482822351322*o[14]*o[24]*o[
    31]*o[36] - 19.1874828272775*o[20]*o[24]*o[31]*o[37] -
    0.0000547344301999018*o[30]*o[38] - 0.0090203547252888*o[2]*o[39] -
    0.0000138839897890111*o[21]*o[4] - 0.973671060893475*o[20]*o[24]*o[4]
     - 836.35096769364*o[13]*o[40] - 1.42338887469272*o[2]*o[40] +
    1.07202609066812e-11*o[26]*o[40] + 0.0000150341259240398*o[5] -
    1.8087714924605e-8*o[6] + 18605.6518987296*o[7] - 306.813232163376*o[
    8] + 1.43632471334824e-11*o[9] + 1.13103675106207e-18*o[5]*o[9] -
    0.017834862292358*pi - 0.172743777250296*o[11]*pi - 0.30195167236758*
    o[39]*pi + o[8]*pi*(-49.6756947920742 + 0.045996013696365*q1) -
    0.0003789797503263*o[1]*q2 - 0.033874355714168*o[11]*o[13]*o[14]*o[20]
    *q2 - 1.0234747095929e-12*o[16]*o[20]*q2 + 1.78371690710842e-23*o[11]
    *o[24]*o[26]*q2 + 2.558143570457e-8*o[3]*q2 + 5.3465159397045*o[24]*o[
    25]*o[31]*q2 - 0.000201611844951398*o[11]*o[14]*o[20]*o[26]*o[31]*q2)
     - Modelica.Math.log(pi));
end slowerofp2;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.supperofp2

explicit upper specific entropy limit of region 2 as function of pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	specific entropy [J/(kg.K)]

Modelica definition

function supperofp2 
  "explicit upper specific entropy limit of region 2 as function of pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  Real pi "dimensionless pressure";
  Real[2] o "vector of auxiliary variables";
algorithm 
  pi := p/data.PSTAR2;
  assert(p > triple.ptriple,
    "IF97 medium function supperofp2 called with too low pressure\n" +
    "p = " + String(p) + " Pa <= " + String(triple.ptriple) + " Pa (triple point pressure)");
  o[1] := pi*pi;
  o[2] := o[1]*o[1]*o[1];
  s := 8505.73409708683 - 461.526*Modelica.Math.log(pi) + pi*(-3.36563543302584
     + pi*(-0.00790283552165338 + pi*(0.0000915558349202221 + pi*(-1.59634706513e-7
     + pi*(3.93449217595397e-18 + pi*(-1.18367426347994e-13 + pi*(
    2.72575244843195e-15 + pi*(7.04803892603536e-26 + pi*(
    6.67637687381772e-35 + pi*(3.1377970315132e-24 + (-7.04844558482265e-77
     + o[1]*(-7.46289531275314e-137 + (1.55998511254305e-68 + pi*(-3.46166288915497e-72
     + pi*(7.51557618628583e-132 + (-1.64086406733212e-106 +
    1.75648443097063e-87*pi)*pi)))*o[1]))*o[2]*o[2]))))))))));
end supperofp2;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.d1n

density in region 1 as function of p and T

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Temperature T temperature (K) [K]

Type	Name	Default	Description
Pressure	p		pressure [Pa]
Temperature	T		temperature (K) [K]

Outputs

Type Name Description

Density d density [kg/m3]

Type	Name	Description
Density	d	density [kg/m3]

Modelica definition

function d1n "density in region 1 as function of p and T"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.Temperature T "temperature (K)";
  output SI.Density d "density";
protected 
  Real pi "dimensionless pressure";
  Real pi1 "dimensionless pressure";
  Real tau "dimensionless temperature";
  Real tau1 "dimensionless temperature";
  Real gpi "dimensionless Gibbs-derivative w.r.t. pi";
  Real[11] o "auxiliary variables";
algorithm 
  pi := p/data.PSTAR1;
  tau := data.TSTAR1/T;
  pi1 := 7.1 - pi;
  tau1 := tau - 1.222;
  o[1] := tau1*tau1;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  o[4] := o[1]*o[2];
  o[5] := o[1]*tau1;
  o[6] := o[2]*tau1;
  o[7] := pi1*pi1;
  o[8] := o[7]*o[7];
  o[9] := o[8]*o[8];
  o[10] := o[3]*o[3];
  o[11] := o[10]*o[10];
  gpi := pi1*(pi1*((0.000095038934535162 + o[2]*(8.4812393955936e-6 +
    2.55615384360309e-9*o[4]))/o[2] + pi1*((8.9701127632e-6 + (
    2.60684891582404e-6 + 5.7366919751696e-13*o[2]*o[3])*o[5])/o[6] + pi1
    *(2.02584984300585e-6/o[3] + o[7]*pi1*(o[8]*o[9]*pi1*(o[7]*(o[7]*o[8]
    *(-7.63737668221055e-22/(o[1]*o[11]*o[2]) + pi1*(pi1*(-5.65070932023524e-23
    /(o[11]*o[3]) + (2.99318679335866e-24*pi1)/(o[11]*o[3]*tau1)) +
    3.5842867920213e-22/(o[1]*o[11]*o[2]*tau1))) - 3.33001080055983e-19/(
    o[1]*o[10]*o[2]*o[3]*tau1)) + 1.44400475720615e-17/(o[10]*o[2]*o[3]*
    tau1)) + (1.01874413933128e-8 + 1.39398969845072e-9*o[6])/(o[1]*o[3]*
    tau1))))) + (0.00094368642146534 + o[5]*(0.00060003561586052 + (-0.000095322787813974
     + o[1]*(8.8283690661692e-6 + 1.45389992595188e-15*o[1]*o[2]*o[3]))*
    tau1))/o[5]) + (-0.00028319080123804 + o[1]*(0.00060706301565874 + o[
    4]*(0.018990068218419 + tau1*(0.032529748770505 + (0.021841717175414
     + 0.00005283835796993*o[1])*tau1))))/(o[3]*tau1);
  d := p/(data.RH2O*T*pi*gpi);
end d1n;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.d2n

density in region 2 as function of p and T

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Temperature T temperature (K) [K]

Type	Name	Default	Description
Pressure	p		pressure [Pa]
Temperature	T		temperature (K) [K]

Outputs

Type Name Description

Density d density [kg/m3]

Type	Name	Description
Density	d	density [kg/m3]

Modelica definition

function d2n "density in region 2  as function of p and T"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.Temperature T "temperature (K)";
  output SI.Density d "density";
protected 
  Real pi "dimensionless pressure";
  Real tau "dimensionless temperature";
  Real tau2 "dimensionless temperature";
  Real gpi "dimensionless Gibbs-derivative w.r.t. pi";
  Real[12] o "auxiliary variables";
algorithm 
  pi := p/data.PSTAR2;
  tau := data.TSTAR2/T;
  tau2 := tau - 0.5;
  o[1] := tau2*tau2;
  o[2] := o[1]*tau2;
  o[3] := o[1]*o[1];
  o[4] := o[3]*o[3];
  o[5] := o[4]*o[4];
  o[6] := o[3]*o[4]*o[5]*tau2;
  o[7] := o[3]*o[4]*tau2;
  o[8] := o[1]*o[3]*o[4];
  o[9] := pi*pi;
  o[10] := o[9]*o[9];
  o[11] := o[3]*o[5]*tau2;
  o[12] := o[5]*o[5];
  gpi := (1. + pi*(-0.0017731742473213 + tau2*(-0.017834862292358 + tau2*
    (-0.045996013696365 + (-0.057581259083432 - 0.05032527872793*o[2])*
    tau2)) + pi*(tau2*(-0.000066065283340406 + (-0.0003789797503263 + o[1]
    *(-0.007878555448671 + o[2]*(-0.087594591301146 -
    0.000053349095828174*o[6])))*tau2) + pi*(6.1445213076927e-8 + (
    1.31612001853305e-6 + o[1]*(-0.00009683303171571 + o[2]*(-0.0045101773626444
     - 0.122004760687947*o[6])))*tau2 + pi*(tau2*(-3.15389238237468e-9 +
    (5.116287140914e-8 + 1.92901490874028e-6*tau2)*tau2) + pi*(
    0.0000114610381688305*o[1]*o[3]*tau2 + pi*(o[2]*(-1.00288598706366e-10
     + o[7]*(-0.012702883392813 - 143.374451604624*o[1]*o[5]*tau2)) + pi*
    (-4.1341695026989e-17 + o[1]*o[4]*(-8.8352662293707e-6 -
    0.272627897050173*o[8])*tau2 + pi*(o[4]*(9.0049690883672e-11 -
    65.8490727183984*o[3]*o[4]*o[5]) + pi*(1.78287415218792e-7*o[7] + pi*
    (o[3]*(1.0406965210174e-18 + o[1]*(-1.0234747095929e-12 -
    1.0018179379511e-8*o[3])*o[3]) + o[10]*o[9]*((-1.29412653835176e-9 +
    1.71088510070544*o[11])*o[6] + o[9]*(-6.05920510335078*o[12]*o[4]*o[5]
    *tau2 + o[9]*(o[3]*o[5]*(1.78371690710842e-23 + o[1]*o[3]*o[4]*(
    6.1258633752464e-12 - 0.000084004935396416*o[7])*tau2) + pi*(-1.24017662339842e-24
    *o[11] + pi*(0.0000832192847496054*o[12]*o[3]*o[5]*tau2 + pi*(o[1]*o[
    4]*o[5]*(1.75410265428146e-27 + (1.32995316841867e-15 -
    0.0000226487297378904*o[1]*o[5])*o[8])*pi - 2.93678005497663e-14*o[1]
    *o[12]*o[3]*tau2)))))))))))))))))/pi;
  d := p/(data.RH2O*T*pi*gpi);
end d2n;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.dhot1ofp

density at upper temperature limit of region 1

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

Density d density [kg/m3]

Type	Name	Description
Density	d	density [kg/m3]

Modelica definition

function dhot1ofp "density at upper temperature limit of region 1"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.Density d "density";
protected 
  Real pi "dimensionless pressure";
  Real pi1 "dimensionless pressure";
  Real[4] o "auxiliary variables";
algorithm 
  pi := p/data.PSTAR1;
  pi1 := 7.1 - pi;
  o[1] := pi1*pi1;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  o[4] := o[3]*o[3];
  d := 57.4756752485113/(0.0737412153522555 + 0.000102697173772229*o[1]
     + 1.99080616601101e-6*o[2] + 1.35549330686006e-17*o[2]*o[4] -
    3.11228834832975e-19*o[1]*o[2]*o[4] - 7.02987180039442e-22*o[2]*o[3]*
    o[4] - 5.17859076694812e-23*o[1]*o[2]*o[3]*o[4] + 0.00145092247736023
    *pi1 + 0.0000114683182476084*o[1]*pi1 + 1.13217858826367e-8*o[1]*o[2]
    *pi1 + 3.29199117056433e-22*o[2]*o[3]*o[4]*pi1 + 2.73712834080283e-24
    *o[1]*o[2]*o[3]*o[4]*pi1);
end dhot1ofp;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.dupper1ofT

density at upper pressure limit of region 1

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Temperature T temperature (K) [K]

Type	Name	Default	Description
Temperature	T		temperature (K) [K]

Outputs

Type Name Description

Density d density [kg/m3]

Type	Name	Description
Density	d	density [kg/m3]

Modelica definition

function dupper1ofT "density at upper pressure limit of region 1"
  extends Modelica.Icons.Function;
  input SI.Temperature T "temperature (K)";
  output SI.Density d "density";
protected 
  Real tau "dimensionless temperature";
  Real[4] o "auxiliary variables";
algorithm 
  tau := 1386.0/T;
  o[1] := tau*tau;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  o[4] := o[3]*o[3];
  d := 57.4756752485113/(2.24144616859917 + 40.9288231166229*o[1] +
    106.47246463213*o[2] + 88.4481480270751*o[1]*o[2] + 31.3207272417546*
    o[3] + 5.47811738891798*o[1]*o[3] + 0.515626225030717*o[2]*o[3] +
    0.0274905057899089*o[1]*o[2]*o[3] + 0.000853742979250503*o[4] +
    0.0000155932210492199*o[1]*o[4] + 1.6621051480279e-7*o[2]*o[4] +
    1.00606771839976e-9*o[1]*o[2]*o[4] + 3.27598951831994e-12*o[3]*o[4]
     + 5.20162317530099e-15*o[1]*o[3]*o[4] + 3.33501889800275e-18*o[2]*o[
    3]*o[4] + 5.50656040141221e-22*o[1]*o[2]*o[3]*o[4] - 13.5354267762204
    *tau - 78.3629702507642*o[1]*tau - 109.374479648652*o[2]*tau -
    57.9035658513312*o[1]*o[2]*tau - 14.215347150565*o[3]*tau -
    1.80906759985501*o[1]*o[3]*tau - 0.127542214693871*o[2]*o[3]*tau -
    0.0051779458313163*o[1]*o[2]*o[3]*tau - 0.000123304142684848*o[4]*tau
     - 1.72405791469972e-6*o[1]*o[4]*tau - 1.39155695911655e-8*o[2]*o[4]*
    tau - 6.23333356847138e-11*o[1]*o[2]*o[4]*tau - 1.44056015732082e-13*
    o[3]*o[4]*tau - 1.50201626932938e-16*o[1]*o[3]*o[4]*tau -
    5.34588682252967e-20*o[2]*o[3]*o[4]*tau - 2.73712834080283e-24*o[1]*o[
    2]*o[3]*o[4]*tau);
end dupper1ofT;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hl_p_R4b

explicit approximation of liquid specific enthalpy on the boundary between regions 4 and 3

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hl_p_R4b 
  "explicit approximation of liquid specific enthalpy on the boundary between regions 4 and 3"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real x "auxiliary variable";
algorithm 
    // documentation of accuray in notebook ~hubertus/props/IAPWS/R3Approx.nb
  // boundary between region IVa and III
  x := Modelica.Math.acos(p/data.PCRIT);
  h := (1 + x*(-0.4945586958175176 + x*(1.346800016564904 + x*(-3.889388153209752
     + x*(6.679385472887931 + x*(-6.75820241066552 + x*(3.558919744656498
     + (-0.7179818554978939 - 0.0001152032945617821*x)*x)))))))*data.
    HCRIT;
end hl_p_R4b;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hv_p_R4b

explicit approximation of vapour specific enthalpy on the boundary between regions 4 and 3

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Type	Name	Description
SpecificEnthalpy	h	specific enthalpy [J/kg]

Modelica definition

function hv_p_R4b 
  "explicit approximation of vapour specific enthalpy on the boundary between regions 4 and 3"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
protected 
  Real x "auxiliary variable";
algorithm 
  // boundary between region IVa and III
  x := Modelica.Math.acos(p/data.PCRIT);
  h := (1 + x*(0.4880153718655694 + x*(0.2079670746250689 + x*(-6.084122698421623
     + x*(25.08887602293532 + x*(-48.38215180269516 + x*(
    45.66489164833212 + (-16.98555442961553 + 0.0006616936460057691*x)*x)))))))
    *data.HCRIT;
end hv_p_R4b;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.sl_p_R4b

explicit approximation of liquid specific entropy on the boundary between regions 4 and 3

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	specific entropy [J/(kg.K)]

Modelica definition

function sl_p_R4b 
  "explicit approximation of liquid specific entropy on the boundary between regions 4 and 3"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  Real x "auxiliary variable";
algorithm 
  // boundary between region IVa and III
  x := Modelica.Math.acos(p/data.PCRIT);
  s := (1 + x*(-0.36160692245648063 + x*(0.9962778630486647 + x*(-2.8595548144171103
     + x*(4.906301159555333 + x*(-4.974092309614206 + x*(
    2.6249651699204457 + (-0.5319954375299023 - 0.00008064497431880644*x)
    *x)))))))*data.SCRIT;
end sl_p_R4b;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.sv_p_R4b

explicit approximation of vapour specific entropy on the boundary between regions 4 and 3

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s [J/(kg.K)]

Type	Name	Description
SpecificEntropy	s	[J/(kg.K)]

Modelica definition

function sv_p_R4b 
  "explicit approximation of vapour specific entropy on the boundary between regions 4 and 3"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s;
protected 
  Real x "auxiliary variable";
algorithm 

    // documentation of accuray in notebook ~hubertus/props/IAPWS/R3Approx.nb
  // boundary between region IVa and III
  x := Modelica.Math.acos(p/data.PCRIT);
  s := (1 + x*(0.35682641826674344 + x*(0.1642457027815487 + x*(-4.425350377422446
     + x*(18.324477859983133 + x*(-35.338631625948665 + x*(
    33.36181025816282 + (-12.408711490585757 + 0.0004810049834109226*x)*x)))))))
    *data.SCRIT;
end sv_p_R4b;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhol_p_R4b

explicit approximation of liquid density on the boundary between regions 4 and 3

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

Density dl liquid density [kg/m3]

Type	Name	Description
Density	dl	liquid density [kg/m3]

Modelica definition

function rhol_p_R4b 
  "explicit approximation of liquid density on the boundary between regions 4 and 3"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.Density dl "liquid density";
protected 
  Real x "auxiliary variable";
algorithm 
  if (p < data.PCRIT) then
    x := Modelica.Math.acos(p/data.PCRIT);
    dl := (1 + x*(1.903224079094824 + x*(-2.5314861802401123 + x*(-8.191449323843552
       + x*(94.34196116778385 + x*(-369.3676833623383 + x*(
      796.6627910598293 + x*(-994.5385383600702 + x*(673.2581177021598 +
      (-191.43077336405156 + 0.00052536560808895*x)*x)))))))))*data.DCRIT;
  else
    dl := data.DCRIT;
  end if;
end rhol_p_R4b;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhov_p_R4b

explicit approximation of vapour density on the boundary between regions 4 and 2

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

Density dv vapour density [kg/m3]

Type	Name	Description
Density	dv	vapour density [kg/m3]

Modelica definition

function rhov_p_R4b 
  "explicit approximation of vapour density on the boundary between regions 4 and 2"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.Density dv "vapour density";
protected 
  Real x "auxiliary variable";
algorithm 
  if (p < data.PCRIT) then
    x := Modelica.Math.acos(p/data.PCRIT);
    dv := (1 + x*(-1.8463850803362596 + x*(-1.1447872718878493 + x*(
      59.18702203076563 + x*(-403.5391431811611 + x*(1437.2007245332388
       + x*(-3015.853540307519 + x*(3740.5790348670057 + x*(-2537.375817253895
       + (725.8761975803782 - 0.0011151111658332337*x)*x)))))))))*data.
      DCRIT;
  else
    dv := data.DCRIT;
  end if;
end rhov_p_R4b;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.boilingcurve_p

properties on the boiling curve

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type Name Description

IF97PhaseBoundaryProperties bpro property record

Modelica definition

function boilingcurve_p "properties on the boiling curve"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output Common.IF97PhaseBoundaryProperties bpro "property record";
protected 
  Common.GibbsDerivs g "dimensionless Gibbs funcion and dervatives";
  Common.HelmholtzDerivs f "dimensionless Helmholtz function and dervatives";
  SI.Pressure plim=min(p, data.PCRIT-1e-7) 
    "pressure limited to critical pressure - epsilon";
algorithm 
  bpro.R := data.RH2O;
  bpro.T := Basic.tsat(plim);
  bpro.dpT := Basic.dptofT(bpro.T);
  bpro.region3boundary := bpro.T > data.TLIMIT1;
  if not bpro.region3boundary then
    g := Basic.g1(p, bpro.T);
    bpro.d := p/(bpro.R*bpro.T*g.pi*g.gpi);
    bpro.h := if p > plim then data.HCRIT else bpro.R*bpro.T*g.tau*g.gtau;
    bpro.s := g.R*(g.tau*g.gtau - g.g);
    bpro.cp := -bpro.R*g.tau*g.tau*g.gtautau;
    bpro.vt := bpro.R/p*(g.pi*g.gpi - g.tau*g.pi*g.gtaupi);
    bpro.vp := bpro.R*bpro.T/(p*p)*g.pi*g.pi*g.gpipi;
    bpro.pt := -p/bpro.T*(g.gpi - g.tau*g.gtaupi)/(g.gpipi*g.pi);
    bpro.pd := -bpro.R*bpro.T*g.gpi*g.gpi/(g.gpipi);
  else
    bpro.d := rhol_p_R4b(plim);
    f := Basic.f3(bpro.d, bpro.T);
    bpro.h := hl_p_R4b(plim);
    // bpro.R*bpro.T*(f.tau*f.ftau + f.delta*f.fdelta);
    bpro.s := f.R*(f.tau*f.ftau - f.f);
    bpro.cv := bpro.R*(-f.tau*f.tau*f.ftautau);
    bpro.pt := bpro.R*bpro.d*f.delta*(f.fdelta - f.tau*f.fdeltatau);
    bpro.pd := bpro.R*bpro.T*f.delta*(2.0*f.fdelta + f.delta*f.fdeltadelta);
  end if;
end boilingcurve_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.dewcurve_p

properties on the dew curve

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Outputs

Type Name Description

IF97PhaseBoundaryProperties bpro property record

Modelica definition

function dewcurve_p "properties on the dew curve"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output Common.IF97PhaseBoundaryProperties bpro "property record";
protected 
  Common.GibbsDerivs g "dimensionless Gibbs funcion and dervatives";
  Common.HelmholtzDerivs f "dimensionless Helmholtz function and dervatives";
  SI.Pressure plim=min(p, data.PCRIT-1e-7) 
    "pressure limited to critical pressure - epsilon";
algorithm 
  bpro.R := data.RH2O;
  bpro.T := Basic.tsat(plim);
  bpro.dpT := Basic.dptofT(bpro.T);
  bpro.region3boundary := bpro.T > data.TLIMIT1;
  if not bpro.region3boundary then
    g := Basic.g2(p, bpro.T);
    bpro.d := p/(bpro.R*bpro.T*g.pi*g.gpi);
    bpro.h := if p > plim then data.HCRIT else bpro.R*bpro.T*g.tau*g.gtau;
    bpro.s := g.R*(g.tau*g.gtau - g.g);
    bpro.cp := -bpro.R*g.tau*g.tau*g.gtautau;
    bpro.vt := bpro.R/p*(g.pi*g.gpi - g.tau*g.pi*g.gtaupi);
    bpro.vp := bpro.R*bpro.T/(p*p)*g.pi*g.pi*g.gpipi;
    bpro.pt := -p/bpro.T*(g.gpi - g.tau*g.gtaupi)/(g.gpipi*g.pi);
    bpro.pd := -bpro.R*bpro.T*g.gpi*g.gpi/(g.gpipi);
  else
    bpro.d := rhov_p_R4b(plim);
    f := Basic.f3(bpro.d, bpro.T);
    bpro.h := hv_p_R4b(plim);
    // bpro.R*bpro.T*(f.tau*f.ftau + f.delta*f.fdelta);
    bpro.s := f.R*(f.tau*f.ftau - f.f);
    bpro.cv := bpro.R*(-f.tau*f.tau*f.ftautau);
    bpro.pt := bpro.R*bpro.d*f.delta*(f.fdelta - f.tau*f.fdeltatau);
    bpro.pd := bpro.R*bpro.T*f.delta*(2.0*f.fdelta + f.delta*f.fdeltadelta);
  end if;
end dewcurve_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hvl_p

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

IF97PhaseBoundaryProperties bpro property record

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Modelica definition

function hvl_p
  annotation(derivative=hvl_p_der);
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input Common.IF97PhaseBoundaryProperties bpro "property record";
  output SI.SpecificEnthalpy h "specific enthalpy";
algorithm 
  h := bpro.h;
end hvl_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hl_p

liquid specific enthalpy on the boundary between regions 4 and 3 or 1

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Modelica definition

function hl_p 
  "liquid specific enthalpy on the boundary between regions 4 and 3 or 1"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
algorithm 
  h := hvl_p(p, boilingcurve_p(p));
end hl_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hv_p

vapour specific enthalpy on the boundary between regions 4 and 3 or 2

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Outputs

Type Name Description

SpecificEnthalpy h specific enthalpy [J/kg]

Modelica definition

function hv_p 
  "vapour specific enthalpy on the boundary between regions 4 and 3 or 2"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEnthalpy h "specific enthalpy";
algorithm 
  h := hvl_p(p, dewcurve_p(p));
end hv_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hvl_p_der

derivative function for the specific enthalpy along the phase boundary

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

IF97PhaseBoundaryProperties bpro property record

Real p_der derivative of pressure

Outputs

Type Name Description

Real h_der time derivative of specific enthalpy along the phase boundary

Modelica definition

function hvl_p_der 
  "derivative function for the specific enthalpy along the phase boundary"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input Common.IF97PhaseBoundaryProperties bpro "property record";
  input Real p_der "derivative of pressure";
  output Real h_der 
    "time derivative of specific enthalpy along the phase boundary";
algorithm 
  if bpro.region3boundary then
    h_der := ((bpro.d*bpro.pd - bpro.T*bpro.pt)*p_der + (bpro.T*bpro.pt*
      bpro.pt + bpro.d*bpro.d*bpro.pd*bpro.cv)/bpro.dpT*p_der)/(bpro.pd*
      bpro.d*bpro.d);
  else
    h_der := (1/bpro.d - bpro.T*bpro.vt)*p_der + bpro.cp/bpro.dpT*p_der;
  end if;
end hvl_p_der;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhovl_p

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

IF97PhaseBoundaryProperties bpro property record

Outputs

Type Name Description

Density rho density [kg/m3]

Modelica definition

function rhovl_p
  annotation(derivative=rhovl_p_der);
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input Common.IF97PhaseBoundaryProperties bpro "property record";
  output SI.Density rho "density";
algorithm 
  rho := bpro.d;
end rhovl_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhol_p

density of saturated water

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p saturation pressure [Pa]

Outputs

Type Name Description

Density rho density of steam at the condensation point [kg/m3]

Modelica definition

function rhol_p "density of saturated water"
  extends Modelica.Icons.Function;
  input SI.Pressure p "saturation pressure";
  output SI.Density rho "density of steam at the condensation point";
algorithm 
  rho := rhovl_p(p, boilingcurve_p(p));
end rhol_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhov_p

density of saturated vapour

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p saturation pressure [Pa]

Outputs

Type Name Description

Density rho density of steam at the condensation point [kg/m3]

Modelica definition

function rhov_p "density of saturated vapour"
  extends Modelica.Icons.Function;
  input SI.Pressure p "saturation pressure";
  output SI.Density rho "density of steam at the condensation point";
algorithm 
  rho := rhovl_p(p, dewcurve_p(p));
end rhov_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhovl_p_der

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p saturation pressure [Pa]

IF97PhaseBoundaryProperties bpro property record

Real p_der derivative of pressure

Outputs

Type Name Description

Real d_der time derivative of density along the phase boundary

Modelica definition

function rhovl_p_der
  extends Modelica.Icons.Function;
  input SI.Pressure p "saturation pressure";
  input Common.IF97PhaseBoundaryProperties bpro "property record";
  input Real p_der "derivative of pressure";
  output Real d_der "time derivative of density along the phase boundary";
algorithm 
  d_der := if bpro.region3boundary then (p_der - bpro.pt*p_der/bpro.dpT)/
    bpro.pd else -bpro.d*bpro.d*(bpro.vp + bpro.vt/bpro.dpT)*p_der;
end rhovl_p_der;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.sl_p

liquid specific entropy on the boundary between regions 4 and 3 or 1

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Modelica definition

function sl_p 
  "liquid specific entropy on the boundary between regions 4 and 3 or 1"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  SI.Temperature Tsat "saturation temperature";
  SI.SpecificEnthalpy h "specific enthalpy";
algorithm 
  if (p < data.PLIMIT4A) then
    Tsat := Basic.tsat(p);
    (h,s) := Isentropic.handsofpT1(p, Tsat);
  elseif (p < data.PCRIT) then
    s := sl_p_R4b(p);
  else
    s := data.SCRIT;
  end if;
end sl_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.sv_p

vapour specific entropy on the boundary between regions 4 and 3 or 2

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Outputs

Type Name Description

SpecificEntropy s specific entropy [J/(kg.K)]

Modelica definition

function sv_p 
  "vapour specific entropy on the boundary between regions 4 and 3 or 2"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.SpecificEntropy s "specific entropy";
protected 
  SI.Temperature Tsat "saturation temperature";
  SI.SpecificEnthalpy h "specific enthalpy";
algorithm 
  if (p < data.PLIMIT4A) then
    Tsat := Basic.tsat(p);
    (h,s) := Isentropic.handsofpT2(p, Tsat);
  elseif (p < data.PCRIT) then
    s := sv_p_R4b(p);
  else
    s := data.SCRIT;
  end if;
end sv_p;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhol_T

density of saturated water

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Temperature T temperature [K]

Outputs

Type Name Description

Density d density of water at the boiling point [kg/m3]

Modelica definition

function rhol_T "density of saturated water"
  extends Modelica.Icons.Function;
  input SI.Temperature T "temperature";
  output SI.Density d "density of water at the boiling point";
protected 
  SI.Pressure p "saturation pressure";
algorithm 
  p := Basic.psat(T);
  if T < data.TLIMIT1 then
    d := d1n(p, T);
  elseif T < data.TCRIT then
    d := rhol_p_R4b(p);
  else
    d := data.DCRIT;
  end if;
end rhol_T;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.rhov_T

density of saturated vapour

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Temperature T temperature [K]

Outputs

Type Name Description

Density d density of steam at the condensation point [kg/m3]

Modelica definition

function rhov_T "density of saturated vapour"
  extends Modelica.Icons.Function;
  input SI.Temperature T "temperature";
  output SI.Density d "density of steam at the condensation point";
protected 
  SI.Pressure p "saturation pressure";
algorithm 

    // assert(T <= data.TCRIT,"input temperature has to be below the critical temperature");
  p := Basic.psat(T);
  if T < data.TLIMIT1 then
    d := d2n(p, T);
  elseif T < data.TCRIT then
    d := rhov_p_R4b(p);
  else
    d := data.DCRIT;
  end if;
end rhov_T;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.region_ph

return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific enthalpy

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

SpecificEnthalpy h specific enthalpy [J/kg]

Integer phase 0 phase: 2 for two-phase, 1 for one phase, 0 if not known

Integer mode 0 mode: 0 means check, otherwise assume region=mode

Outputs

Type Name Description

Integer region region (valid values: 1,2,3,4,5) in IF97

Modelica definition

function region_ph 
  "return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific enthalpy"
  extends Modelica.Icons.Function;
 input SI.Pressure p "pressure";
 input SI.SpecificEnthalpy h "specific enthalpy";
 input Integer phase=0 
    "phase: 2 for two-phase, 1 for one phase, 0 if not known";
 input Integer mode=0 "mode: 0 means check, otherwise assume region=mode";
  output Integer region "region (valid values: 1,2,3,4,5) in IF97";
  // If mode is different from 0, no checking for the region is done and
  // the mode is assumed to be the correct region. This can be used to
  // implement e.g. water-only steamtables when mode == 1
protected 
  Boolean hsubcrit;
  SI.Temperature Ttest;
  constant Real[5] n=data.n;
  SI.SpecificEnthalpy hl "bubble enthalpy";
  SI.SpecificEnthalpy hv "dew enthalpy";
algorithm 
  if (mode <> 0) then
    region := mode;
  else
    // check for regions 1, 2, 3 and 4
    hl := hl_p(p);
    hv := hv_p(p);
    if (phase == 2) then
      region := 4;
    else
      // phase == 1 or 0, now check if we are in the legal area
      if 
        (p < triple.ptriple) or (p > data.PLIMIT1) or (h < hlowerofp1(p)) or 
        ((p < 10.0e6) and (h > hupperofp5(p)))
        or ((p >= 10.0e6) and (h > hupperofp2(p))) then
        // outside of valid range
        region := -1;
      else
        //region 5 and -1 check complete
        hsubcrit := (h < data.HCRIT);
        // simple precheck: very simple if pressure < PLIMIT4A
        if (p < data.PLIMIT4A) then
          // we can never be in region 3, so test for others
          if hsubcrit then
            if (phase == 1) then
              region := 1;
            else
              if (h < Isentropic.hofpT1(p,Basic.tsat(p))) then
                region := 1;
              else
                region := 4;
              end if;
            end if;
            // external or internal phase check
          else
            if (h > hlowerofp5(p)) then
              // check for region 5
              if ((p < data.PLIMIT5) and (h < hupperofp5(p))) then
                region := 5;
              else
                region := -2;
                // pressure and specific enthalpy too high, but this should
              end if;
              // never happen
            else
              if (phase == 1) then
                region := 2;
              else
                if (h > Isentropic.hofpT2(p,Basic.tsat(p))) then
                  region := 2;
                else
                  region := 4;
                end if;
              end if;  // external or internal phase check
            end if;
            // tests for region 2 or 5
          end if;
          // tests for sub or supercritical
        else
          // the pressure is over data.PLIMIT4A
          if hsubcrit then
            // region 1 or 3 or 4
            if h < hupperofp1(p) then
              region := 1;
            else
              if h < hl  or p > data.PCRIT then
                region := 3;
              else
                region :=4;
              end if;
            end if;
            // enf of test for region 1, 3 or 4
          else
            // region 2, 3 or 4
            if (h > hlowerofp2(p)) then
              region := 2;
            else
              if h > hv  or p > data.PCRIT then
                region := 3;
              else
                region := 4;
              end if;
            end if;
            // test for 2 and 3
          end if;
          // tests above PLIMIT4A
        end if;
        // above or below PLIMIT4A
      end if;
      // check for grand limits of p and h
    end if;
    // all tests with phase == 1
  end if;
  // mode was == 0
  // assert(region > 0,"IF97 function called outside the valid range!");
end region_ph;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.region_ps

return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific entropy

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

SpecificEntropy s specific entropy [J/(kg.K)]

Integer phase 0 phase: 2 for two-phase, 1 for one phase, 0 if unknown

Integer mode 0 mode: 0 means check, otherwise assume region=mode

Outputs

Type Name Description

Integer region region (valid values: 1,2,3,4,5) in IF97

Modelica definition

function region_ps 
  "return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific entropy"
  extends Modelica.Icons.Function;
 input SI.Pressure p "pressure";
 input SI.SpecificEntropy s "specific entropy";
 input Integer phase=
                0 "phase: 2 for two-phase, 1 for one phase, 0 if unknown";
 input Integer mode=
               0 "mode: 0 means check, otherwise assume region=mode";
  output Integer region "region (valid values: 1,2,3,4,5) in IF97";
  //  If mode is different from 0, no checking for the region is done and
  //    the mode is assumed to be the correct region. This can be used to
  //    implement e.g. water-only steamtables when mode == 1
protected 
  Boolean ssubcrit;
  SI.Temperature Ttest;
  constant Real[5] n=data.n;
  SI.SpecificEntropy sl "bubble entropy";
  SI.SpecificEntropy sv "dew entropy";
algorithm 
  if (mode <> 0) then
    region := mode;
  else
    // check for regions 1, 2, 3, and 4
    sl := sl_p(p);
    sv := sv_p(p);
    // check all cases two-phase
    if (phase == 2) or (phase == 0 and s > sl and s < sv and p < data.PCRIT) then
      region := 4;
    else
      // phase == 1
      region := 0;
      if (p < triple.ptriple) then
        region := -2;
      end if;
      if (p > data.PLIMIT1) then
        region := -3;
      end if;
      if ((p < 10.0e6) and (s > supperofp5(p))) then
        region := -5;
      end if;
      if ((p >= 10.0e6) and (s > supperofp2(p))) then
        region := -6;
      end if;
      if region < 0 then
        assert(false, "region computation from p and s failed: function called outside the legal region");
      else
        ssubcrit := (s < data.SCRIT);
        // simple precheck: very simple if pressure < PLIMIT4A
        if (p < data.PLIMIT4A) then
          // we can never be in region 3, so test for 1 and 2
          if ssubcrit then
            region := 1;
          else
            if (s > slowerofp5(p)) then
              // check for region 5
              if ((p < data.PLIMIT5) and (s < supperofp5(p))) then
                region := 5;
              else
                region := -1;
                // pressure and specific entropy too high, should never happen!
              end if;
            else
              region := 2;
            end if;
            // tests for region 2 or 5
          end if;
          // tests for sub or supercritical
        else
          // the pressure is over data.PLIMIT4A
          if ssubcrit then
            // region 1 or 3
            if s < supperofp1(p) then
              region := 1;
            else
              if s < sl  or p > data.PCRIT then
                region := 3;
              else
                region := 4;
              end if;
            end if;
            // test for region 1, 3 or 4
          else
            // region 2, 3 or 4
            if (s > slowerofp2(p)) then
              region := 2;
            else
              if s > sv  or p > data.PCRIT then
                region := 3;
              else
                region := 4;
              end if;
            end if;
            // test for 2,3 and 4
          end if;
          // tests above PLIMIT4A
        end if;
        // above or below PLIMIT4A
      end if;
      // grand test for limits of p and s
    end if;
    // all tests with phase == 1
  end if;
  // mode was == 0
end region_ps;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.region_pT

return the current region (valid values: 1,2,3,5) in IF97, given pressure and temperature

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Temperature T temperature (K) [K]

Integer mode 0 mode: 0 means check, otherwise assume region=mode

Outputs

Type Name Description

Integer region region (valid values: 1,2,3,5) in IF97, region 4 is impossible!

Modelica definition

function region_pT 
  "return the current region (valid values: 1,2,3,5) in IF97, given pressure and temperature"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.Temperature T "temperature (K)";
  input Integer mode=0 "mode: 0 means check, otherwise assume region=mode";
  output Integer region 
    "region (valid values: 1,2,3,5) in IF97, region 4 is impossible!";
algorithm 
  if (mode <> 0) then
    region := mode;
  else
    if p < data.PLIMIT4A then
      //test for regions 1,2,5
      if T > data.TLIMIT2 then
        region := 5;
      elseif T > Basic.tsat(p) then
        region := 2;
      else
        region := 1;
      end if;
    else
      //test for regions 1,2,3
      if T < data.TLIMIT1 then
        region := 1;
      elseif T < boundary23ofp(p) then
        region := 3;
      else
        region := 2;
      end if;
    end if;
  end if;
  // mode was == 0
end region_pT;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.region_dT

return the current region (valid values: 1,2,3,4,5) in IF97, given density and temperature

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Density d density [kg/m3]

Temperature T temperature (K) [K]

Integer phase 0 phase: 2 for two-phase, 1 for one phase, 0 if not known

Integer mode 0 mode: 0 means check, otherwise assume region=mode

Outputs

Type Name Description

Integer region (valid values: 1,2,3,4,5) in IF97

Modelica definition

function region_dT 
  "return the current region (valid values: 1,2,3,4,5) in IF97, given density and temperature"
  extends Modelica.Icons.Function;
  input SI.Density d "density";
  input SI.Temperature T "temperature (K)";
  input Integer phase= 0 
    "phase: 2 for two-phase, 1 for one phase, 0 if not known";
  input Integer mode= 0 "mode: 0 means check, otherwise assume region=mode";
  output Integer region "(valid values: 1,2,3,4,5) in IF97";
protected 
  Boolean Tovercrit "flag if overcritical temperature";
  SI.Pressure p23 "pressure needed to know if region 2 or 3";
algorithm 
  Tovercrit := T > data.TCRIT;
  if (mode <> 0) then
    region := mode;
  else
    p23 := boundary23ofT(T);
    if T > data.TLIMIT2 then
      if d < 20.5655874106483 then
        // check for the density in the upper corner of validity!
        region := 5;
      else
        assert(false,"out of valid region for IF97, pressure above region 5!");
      end if;
    elseif Tovercrit then
      //check for regions 1, 2 or 3
      if d > d2n(p23, T) and T > data.TLIMIT1 then
        region := 3;
      elseif T < data.TLIMIT1 then
        region := 1;
      else // d  < d2n(p23, T) and T > data.TLIMIT1
        region := 2;
      end if;
      // below critical, check for regions 1, 2, 3 or 4
    elseif (d > rhol_T(T)) then
      // either 1 or 3
      if T < data.TLIMIT1 then
        region := 1;
      else
        region := 3;
      end if;
    elseif (d < rhov_T(T)) then
      // not liquid, not 2-phase, and not region 5, so either 2 or 3 or illegal
      if (d > d2n(p23, T) and T > data.TLIMIT1) then
        region := 3;
      else
        region := 2;
      end if;
    else
      region := 4;
    end if;
  end if;
end region_dT;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.hvl_dp

derivative function for the specific enthalpy along the phase boundary

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

IF97PhaseBoundaryProperties bpro property record

Outputs

Type Name Description

Real dh_dp derivative of specific enthalpy along the phase boundary

Modelica definition

function hvl_dp 
  "derivative function for the specific enthalpy along the phase boundary"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input Common.IF97PhaseBoundaryProperties bpro "property record";
  output Real dh_dp "derivative of specific enthalpy along the phase boundary";
algorithm 
  if bpro.region3boundary then
    dh_dp := ((bpro.d*bpro.pd - bpro.T*bpro.pt) + (bpro.T*bpro.pt*
      bpro.pt + bpro.d*bpro.d*bpro.pd*bpro.cv)/bpro.dpT)/(bpro.pd*
      bpro.d*bpro.d);
  else
    dh_dp := (1/bpro.d - bpro.T*bpro.vt) + bpro.cp/bpro.dpT;
  end if;
end hvl_dp;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.dhl_dp

derivative of liquid specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Outputs

Type Name Description

DerEnthalpyByPressure dh_dp specific enthalpy derivative w.r.t. pressure [J.m.s2/kg2]

Modelica definition

function dhl_dp 
  "derivative of liquid specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.DerEnthalpyByPressure dh_dp 
    "specific enthalpy derivative w.r.t. pressure";
algorithm 
  dh_dp := hvl_dp(p, boilingcurve_p(p));
end dhl_dp;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.dhv_dp

derivative of vapour specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p pressure [Pa]

Outputs

Type Name Description

DerEnthalpyByPressure dh_dp specific enthalpy derivative w.r.t. pressure [J.m.s2/kg2]

Modelica definition

function dhv_dp 
  "derivative of vapour specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t pressure"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.DerEnthalpyByPressure dh_dp 
    "specific enthalpy derivative w.r.t. pressure";
algorithm 
  dh_dp := hvl_dp(p, dewcurve_p(p));
end dhv_dp;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.drhovl_dp

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p saturation pressure [Pa]

IF97PhaseBoundaryProperties bpro property record

Outputs

Type Name Description

Real dd_dp derivative of density along the phase boundary [kg/(m3.Pa)]

Modelica definition

function drhovl_dp
  extends Modelica.Icons.Function;
  input SI.Pressure p "saturation pressure";
  input Common.IF97PhaseBoundaryProperties bpro "property record";
  output Real dd_dp(unit="kg/(m3.Pa)") 
    "derivative of density along the phase boundary";
algorithm 
  dd_dp := if bpro.region3boundary then (1.0 - bpro.pt/bpro.dpT)/
    bpro.pd else -bpro.d*bpro.d*(bpro.vp + bpro.vt/bpro.dpT);
end drhovl_dp;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.drhol_dp

derivative of density of saturated water w.r.t. pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p saturation pressure [Pa]

Outputs

Type Name Description

DerDensityByPressure dd_dp derivative of density of water at the boiling point [s2/m2]

Modelica definition

function drhol_dp 
  "derivative of density of saturated water w.r.t. pressure"
  extends Modelica.Icons.Function;
  input SI.Pressure p "saturation pressure";
  output SI.DerDensityByPressure dd_dp 
    "derivative of density of water at the boiling point";
algorithm 
  dd_dp := drhovl_dp(p, boilingcurve_p(p));
end drhol_dp;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.drhov_dp

derivative of density of saturated steam w.r.t. pressure

Information

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

Type Name Default Description

Pressure p saturation pressure [Pa]

Outputs

Type Name Description

DerDensityByPressure dd_dp derivative of density of water at the boiling point [s2/m2]

Modelica definition

function drhov_dp 
  "derivative of density of saturated steam w.r.t. pressure"
  extends Modelica.Icons.Function;
  input SI.Pressure p "saturation pressure";
  output SI.DerDensityByPressure dd_dp 
    "derivative of density of water at the boiling point";
algorithm 
  dd_dp := drhovl_dp(p, dewcurve_p(p));
end drhov_dp;

HTML-documentation generated by Dymola Sun Jan 17 21:12:34 2010.

Type	Name	Default	Description
Pressure	p		pressure [Pa]
IF97PhaseBoundaryProperties	bpro		property record

Type	Name	Description
Pressure	p	saturation pressure [Pa]
IF97PhaseBoundaryProperties	bpro	property record
Real	p_der	derivative of pressure