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
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.Package (Icon for standard packages).
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 |
boundary function for region boundary between regions 2 and 3 (input temperature)
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | t | | temperature (K) [K] |
Outputs
| 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;
boundary function for region boundary between regions 2 and 3 (input pressure)
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit lower specific enthalpy limit of region 5 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit upper specific enthalpy limit of region 5 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit lower specific entropy limit of region 5 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit upper specific entropy limit of region 5 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit lower specific enthalpy limit of region 1 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
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 functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit lower specific entropy limit of region 1 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
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 functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
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 functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit upper specific enthalpy limit of region 2 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
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 functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit upper specific entropy limit of region 2 as function of pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
density in region 1 as function of p and T
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
| 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;
density in region 2 as function of p and T
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
| 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;
density at upper temperature limit of region 1
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
| 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;
density at upper pressure limit of region 1
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | T | | temperature (K) [K] |
Outputs
| 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;
explicit approximation of liquid specific enthalpy on the boundary between regions 4 and 3
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit approximation of vapour specific enthalpy on the boundary between regions 4 and 3
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit approximation of liquid specific entropy on the boundary between regions 4 and 3
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit approximation of vapour specific entropy on the boundary between regions 4 and 3
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
explicit approximation of liquid density on the boundary between regions 4 and 3
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
| 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;
explicit approximation of vapour density on the boundary between regions 4 and 2
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
| 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;
properties on the boiling curve
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
properties on the dew curve
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
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;
liquid specific enthalpy on the boundary between regions 4 and 3 or 1
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
vapour specific enthalpy on the boundary between regions 4 and 3 or 2
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
derivative function for the specific enthalpy along the phase boundary
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
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;
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
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;
density of saturated water
Information
Extends from Modelica.Icons.Function (Icon for functions).
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;
density of saturated vapour
Information
Extends from Modelica.Icons.Function (Icon for functions).
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;
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
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;
liquid specific entropy on the boundary between regions 4 and 3 or 1
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
vapour specific entropy on the boundary between regions 4 and 3 or 2
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
density of saturated water
Information
Extends from Modelica.Icons.Function (Icon for functions).
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;
density of saturated vapour
Information
Extends from Modelica.Icons.Function (Icon for functions).
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;
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 functions).
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;
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 functions).
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;
return the current region (valid values: 1,2,3,5) in IF97, given pressure and temperature
Information
Extends from Modelica.Icons.Function (Icon for functions).
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;
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 functions).
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;
derivative function for the specific enthalpy along the phase boundary
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
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;
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 functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
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 functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p | | pressure [Pa] |
Outputs
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;
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
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;
derivative of density of saturated water w.r.t. pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
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;
derivative of density of saturated steam w.r.t. pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
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;
Automatically generated Fri Nov 12 16:31:38 2010.
Modelica.Media.Water.IF97_Utilities.BaseIF97.Regions.boundary23ofT