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IF97_Utilities.mo
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IF97_Utilities.mo
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within Modelica.Media.Water;
package IF97_Utilities
"Low level and utility computation for high accuracy water properties according to the IAPWS/IF97 standard"
extends Modelica.Icons.UtilitiesPackage;
package BaseIF97
"Modelica Physical Property Model: the new industrial formulation IAPWS-IF97"
extends Modelica.Icons.Package;
record IterationData "Constants for iterations internal to some functions"
extends Modelica.Icons.Record;
constant Integer IMAX=50
"Maximum number of iterations for inverse functions";
constant Real DELP=1.0e-6 "Maximum iteration error in pressure, Pa";
constant Real DELS=1.0e-8
"Maximum iteration error in specific entropy, J/{kg.K}";
constant Real DELH=1.0e-8
"Maximum iteration error in specific enthalpy, J/kg";
constant Real DELD=1.0e-8 "Maximum iteration error in density, kg/m^3";
end IterationData;
//===================================================================
// Constant declarations
//===================================================================
record data "Constant IF97 data and region limits"
extends Modelica.Icons.Record;
constant SI.SpecificHeatCapacity RH2O=461.526
"Specific gas constant of water vapour";
constant SI.MolarMass MH2O=0.01801528 "Molar weight of water";
constant SI.Temperature TSTAR1=1386.0
"Normalization temperature for region 1 IF97";
constant SI.Pressure PSTAR1=16.53e6
"Normalization pressure for region 1 IF97";
constant SI.Temperature TSTAR2=540.0
"Normalization temperature for region 2 IF97";
constant SI.Pressure PSTAR2=1.0e6
"Normalization pressure for region 2 IF97";
constant SI.Temperature TSTAR5=1000.0
"Normalization temperature for region 5 IF97";
constant SI.Pressure PSTAR5=1.0e6
"Normalization pressure for region 5 IF97";
constant SI.SpecificEnthalpy HSTAR1=2.5e6
"Normalization specific enthalpy for region 1 IF97";
constant Real IPSTAR=1.0e-6
"Normalization pressure for inverse function in region 2 IF97";
constant Real IHSTAR=5.0e-7
"Normalization specific enthalpy for inverse function in region 2 IF97";
constant SI.Temperature TLIMIT1=623.15
"Temperature limit between regions 1 and 3";
constant SI.Temperature TLIMIT2=1073.15
"Temperature limit between regions 2 and 5";
constant SI.Temperature TLIMIT5=2273.15 "Upper temperature limit of 5";
constant SI.Pressure PLIMIT1=100.0e6
"Upper pressure limit for regions 1, 2 and 3";
constant SI.Pressure PLIMIT4A=16.5292e6
"Pressure limit between regions 1 and 2, important for two-phase (region 4)";
constant SI.Pressure PLIMIT5=10.0e6
"Upper limit of valid pressure in region 5";
constant SI.Pressure PCRIT=22064000.0 "The critical pressure";
constant SI.Temperature TCRIT=647.096 "The critical temperature";
constant SI.Density DCRIT=322.0 "The critical density";
constant SI.SpecificEntropy SCRIT=4412.02148223476
"The calculated specific entropy at the critical point";
constant SI.SpecificEnthalpy HCRIT=2087546.84511715
"The calculated specific enthalpy at the critical point";
constant Real[5] n=array(
0.34805185628969e3,
-0.11671859879975e1,
0.10192970039326e-2,
0.57254459862746e3,
0.13918839778870e2)
"Polynomial coefficients for boundary between regions 2 and 3";
annotation (Documentation(info="<html>
<h4>Record description</h4>
<p>Constants needed in the international steam properties IF97.
SCRIT and HCRIT are calculated from Helmholtz function for region 3.</p>
<h4>Version Info and Revision history</h4>
<ul>
<li>
First implemented: <em>July, 2000</em>
by Hubertus Tummescheit
</li>
</ul>
<address>
Author: Hubertus Tummescheit,<br>
Modelon AB<br>
Ideon Science Park<br>
SE-22370 Lund, Sweden<br>
email: hubertus@modelon.se
</address>
<ul>
<li>Initial version: July 2000</li>
<li>Documentation added: December 2002</li>
</ul>
</html>"));
end data;
function getTstar "Get normalization temperature for region 1, 2 or 5"
extends Modelica.Icons.Function;
input Integer region "IF 97 region";
output SI.Temperature Tstar "Normalization temperature";
algorithm
if region == 1 then
Tstar := data.TSTAR1;
elseif region == 2 then
Tstar := data.TSTAR2;
else
Tstar := data.TSTAR5;
end if;
end getTstar;
function getpstar "Get normalization pressure for region 1, 2 or 5"
extends Modelica.Icons.Function;
input Integer region "IF 97 region";
output SI.Pressure pstar "Normalization pressure";
algorithm
if region == 1 then
pstar := data.PSTAR1;
elseif region == 2 then
pstar := data.PSTAR2;
else
pstar := data.PSTAR5;
end if;
end getpstar;
record critical "Critical point data"
extends Modelica.Icons.Record;
constant SI.Pressure PCRIT=22064000.0 "The critical pressure";
constant SI.Temperature TCRIT=647.096 "The critical temperature";
constant SI.Density DCRIT=322.0 "The critical density";
constant SI.SpecificEnthalpy HCRIT=2087546.84511715
"The calculated specific enthalpy at the critical point";
constant SI.SpecificEntropy SCRIT=4412.02148223476
"The calculated specific entropy at the critical point";
annotation (Documentation(info="<html>
<h4>Record description</h4>
<p>
Critical point data for IF97 steam properties. SCRIT and HCRIT are calculated from Helmholtz function for region 3.
</p>
<h4>Version Info and Revision history</h4>
<ul>
<li>
First implemented: <em>July, 2000</em>
by Hubertus Tummescheit
</li>
</ul>
<address>
Author: Hubertus Tummescheit,<br>
Modelon AB<br>
Ideon Science Park<br>
SE-22370 Lund, Sweden<br>
email: hubertus@modelon.se
</address>
<ul>
<li>Initial version: July 2000</li>
<li>Documentation added: December 2002</li>
</ul>
</html>"));
end critical;
record triple "Triple point data"
extends Modelica.Icons.Record;
constant SI.Temperature Ttriple=273.16 "The triple point temperature";
constant SI.Pressure ptriple=611.657 "The triple point pressure";
constant SI.Density dltriple=999.792520031617642
"The triple point liquid density";
constant SI.Density dvtriple=0.485457572477861372e-2
"The triple point vapour density";
annotation (Documentation(info="<html>
<h4>Record description</h4>
<p>Vapour/liquid/ice triple point data for IF97 steam properties.</p>
<h4>Version Info and Revision history</h4>
<ul>
<li>
First implemented: <em>July, 2000</em>
by Hubertus Tummescheit
</li>
</ul>
<address>
Author: Hubertus Tummescheit,<br>
Modelon AB<br>
Ideon Science Park<br>
SE-22370 Lund, Sweden<br>
email: hubertus@modelon.se
</address>
<ul>
<li>Initial version: July 2000</li>
<li>Documentation added: December 2002</li>
</ul>
</html>"));
end triple;
package Regions
"Functions to find the current region for given pairs of input variables"
extends Modelica.Icons.FunctionsPackage;
//===================================================================
// "Public" functions
//===================================================================
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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 accuracy 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;
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;
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;
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 "Specific entropy";
protected
Real x "Auxiliary variable";
algorithm
// documentation of accuracy 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;
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;
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;
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 function and derivatives";
Common.HelmholtzDerivs f
"Dimensionless Helmholtz function and derivatives";
SI.Pressure plim=min(p, data.PCRIT - 1e-7)
"Pressure limited to critical pressure - epsilon";
algorithm
bpro.R_s := 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_s*bpro.T*g.pi*g.gpi);
bpro.h := if p > plim then data.HCRIT else bpro.R_s*bpro.T*g.tau*g.gtau;
bpro.s := g.R_s*(g.tau*g.gtau - g.g);
bpro.cp := -bpro.R_s*g.tau*g.tau*g.gtautau;
bpro.vt := bpro.R_s/p*(g.pi*g.gpi - g.tau*g.pi*g.gtaupi);
bpro.vp := bpro.R_s*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_s*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_s*bpro.T*(f.tau*f.ftau + f.delta*f.fdelta);
bpro.s := f.R_s*(f.tau*f.ftau - f.f);
bpro.cv := bpro.R_s*(-f.tau*f.tau*f.ftautau);
bpro.pt := bpro.R_s*bpro.d*f.delta*(f.fdelta - f.tau*f.fdeltatau);
bpro.pd := bpro.R_s*bpro.T*f.delta*(2.0*f.fdelta + f.delta*f.fdeltadelta);
end if;
end boilingcurve_p;
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 function and derivatives";
Common.HelmholtzDerivs f
"Dimensionless Helmholtz function and derivatives";
SI.Pressure plim=min(p, data.PCRIT - 1e-7)
"Pressure limited to critical pressure - epsilon";
algorithm
bpro.R_s := 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_s*bpro.T*g.pi*g.gpi);
bpro.h := if p > plim then data.HCRIT else bpro.R_s*bpro.T*g.tau*g.gtau;
bpro.s := g.R_s*(g.tau*g.gtau - g.g);
bpro.cp := -bpro.R_s*g.tau*g.tau*g.gtautau;
bpro.vt := bpro.R_s/p*(g.pi*g.gpi - g.tau*g.pi*g.gtaupi);
bpro.vp := bpro.R_s*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_s*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_s*bpro.T*(f.tau*f.ftau + f.delta*f.fdelta);
bpro.s := f.R_s*(f.tau*f.ftau - f.f);
bpro.cv := bpro.R_s*(-f.tau*f.tau*f.ftautau);
bpro.pt := bpro.R_s*bpro.d*f.delta*(f.fdelta - f.tau*f.fdeltatau);
bpro.pd := bpro.R_s*bpro.T*f.delta*(2.0*f.fdelta + f.delta*f.fdeltadelta);
end if;
end dewcurve_p;
function hvl_p
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;
annotation (
derivative(noDerivative=bpro) = hvl_p_der,
Inline=false,
LateInline=true);
end hvl_p;
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));
annotation (Inline=true);
end hl_p;
function hv_p
"Vapour specific enthalpy on the boundary between regions 4 and 3 or 2"