Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses

Information

Package description

Package contents

• Function fixdT constrains density and temperature to allowed region
• Function dofp13 computes d as a function of p at boundary between regions 1 and 3
• Function dofp23 computes d as a function of p at boundary between regions 2 and 3
• Function dofpt3 iteration to compute d as a function of p and T in region 3
• Function dtofph3 iteration to compute d and T as a function of p and h in region 3
• Function dtofps3 iteration to compute d and T as a function of p and s in region 3
• Function dtofpsdt3 iteration to compute d and T as a function of p and s in region 3, with initial guesses
• Function pofdt125 iteration to compute p as a function of p and T in regions 1, 2 and 5
• Function tofph5 iteration to compute T as a function of p and h in region 5
• Function tofps5 iteration to compute T as a function of p and s in region 5
• Function tofpst5 iteration to compute T as a function of p and s in region 5, with initial guess in T
• Function

Version Info and Revision history

• First implemented: July, 2000 by Hubertus Tummescheit

• Initial version: July 2000
• Documentation added: December 2002

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

Package Content

Name	Description
fixdT	region limits for inverse iteration in region 3
dofp13	density at the boundary between regions 1 and 3
dofp23	density at the boundary between regions 2 and 3
dofpt3	inverse iteration in region 3: (d) = f(p,T)
dtofph3	inverse iteration in region 3: (d,T) = f(p,h)
dtofps3	inverse iteration in region 3: (d,T) = f(p,s)
dtofpsdt3	inverse iteration in region 3: (d,T) = f(p,s)
pofdt125	inverse iteration in region 1,2 and 5: p = g(d,T)
tofph5	inverse iteration in region 5: (p,T) = f(p,h)
tofps5	inverse iteration in region 5: (p,T) = f(p,s)
tofpst5	inverse iteration in region 5: (p,T) = f(p,s)

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.fixdT

Information

Inputs

Type	Name	Default	Description
Density	din		density [kg/m3]
Temperature	Tin		temperature [K]

Outputs

Type	Name	Description
Density	dout	density [kg/m3]
Temperature	Tout	temperature [K]

Modelica definition

function fixdT "region limits for inverse iteration in region 3"

  extends Modelica.Icons.Function;
  input SI.Density din "density";
  input SI.Temperature Tin "temperature";
  output SI.Density dout "density";
  output SI.Temperature Tout "temperature";
protected 
  SI.Temperature Tmin "approximation of minimum temperature";
  SI.Temperature Tmax "approximation of maximum temperature";
algorithm 
  if (din > 765.0) then
    dout := 765.0;
  elseif (din < 110.0) then
    dout := 110.0;
  else
    dout := din;
  end if;
  if (dout < 390.0) then
    Tmax := 554.3557377 + dout*0.809344262;
  else
    Tmax := 1116.85 - dout*0.632948717;
  end if;
  if (dout < data.DCRIT) then
    Tmin := data.TCRIT*(1.0 - (dout - data.DCRIT)*(dout - data.DCRIT)/
      1.0e6);
  else
    Tmin := data.TCRIT*(1.0 - (dout - data.DCRIT)*(dout - data.DCRIT)/
      1.44e6);
  end if;
  if (Tin < Tmin) then
    Tout := Tmin;
  elseif (Tin > Tmax) then
    Tout := Tmax;
  else
    Tout := Tin;
  end if;
end fixdT;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.dofp13

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type	Name	Description
Density	d	density [kg/m3]

Modelica definition

function dofp13 "density at the boundary between regions 1 and 3"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.Density d "density";
protected 
  Real p2 "auxiliary variable";
  Real[3] o "vector of auxiliary variables";
algorithm 
  p2 := 7.1 - 6.04960677555959e-8*p;
  o[1] := p2*p2;
  o[2] := o[1]*o[1];
  o[3] := o[2]*o[2];
  d := 57.4756752485113/(0.0737412153522555 + p2*(0.00145092247736023 +
    p2*(0.000102697173772229 + p2*(0.0000114683182476084 + p2*(
    1.99080616601101e-6 + o[1]*p2*(1.13217858826367e-8 + o[2]*o[3]*p2*(
    1.35549330686006e-17 + o[1]*(-3.11228834832975e-19 + o[1]*o[2]*(-7.02987180039442e-22
     + p2*(3.29199117056433e-22 + (-5.17859076694812e-23 +
    2.73712834080283e-24*p2)*p2))))))))));

end dofp13;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.dofp23

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]

Outputs

Type	Name	Description
Density	d	density [kg/m3]

Modelica definition

function dofp23 "density at the boundary between regions 2 and 3"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  output SI.Density d "density";
protected 
  SI.Temperature T;
  Real[13] o "vector of auxiliary variables";
  Real taug "auxiliary variable";
  Real pi "dimensionless pressure";
  Real gpi23 
    "derivative of g w.r.t. pi on the boundary between regions 2 and 3";
algorithm 
  pi := p/data.PSTAR2;
  T := 572.54459862746 + 31.3220101646784*(-13.91883977887 + pi)^0.5;
  o[1] := (-13.91883977887 + pi)^0.5;
  taug := -0.5 + 540.0/(572.54459862746 + 31.3220101646784*o[1]);
  o[2] := taug*taug;
  o[3] := o[2]*taug;
  o[4] := o[2]*o[2];
  o[5] := o[4]*o[4];
  o[6] := o[5]*o[5];
  o[7] := o[4]*o[5]*o[6]*taug;
  o[8] := o[4]*o[5]*taug;
  o[9] := o[2]*o[4]*o[5];
  o[10] := pi*pi;
  o[11] := o[10]*o[10];
  o[12] := o[4]*o[6]*taug;
  o[13] := o[6]*o[6];

  gpi23 := (1.0 + pi*(-0.0017731742473213 + taug*(-0.017834862292358 +
    taug*(-0.045996013696365 + (-0.057581259083432 - 0.05032527872793*o[3])
    *taug)) + pi*(taug*(-0.000066065283340406 + (-0.0003789797503263 + o[
    2]*(-0.007878555448671 + o[3]*(-0.087594591301146 -
    0.000053349095828174*o[7])))*taug) + pi*(6.1445213076927e-8 + (
    1.31612001853305e-6 + o[2]*(-0.00009683303171571 + o[3]*(-0.0045101773626444
     - 0.122004760687947*o[7])))*taug + pi*(taug*(-3.15389238237468e-9 +
    (5.116287140914e-8 + 1.92901490874028e-6*taug)*taug) + pi*(
    0.0000114610381688305*o[2]*o[4]*taug + pi*(o[3]*(-1.00288598706366e-10
     + o[8]*(-0.012702883392813 - 143.374451604624*o[2]*o[6]*taug)) + pi*
    (-4.1341695026989e-17 + o[2]*o[5]*(-8.8352662293707e-6 -
    0.272627897050173*o[9])*taug + pi*(o[5]*(9.0049690883672e-11 -
    65.8490727183984*o[4]*o[5]*o[6]) + pi*(1.78287415218792e-7*o[8] + pi*
    (o[4]*(1.0406965210174e-18 + o[2]*(-1.0234747095929e-12 -
    1.0018179379511e-8*o[4])*o[4]) + o[10]*o[11]*((-1.29412653835176e-9
     + 1.71088510070544*o[12])*o[7] + o[10]*(-6.05920510335078*o[13]*o[5]
    *o[6]*taug + o[10]*(o[4]*o[6]*(1.78371690710842e-23 + o[2]*o[4]*o[5]*
    (6.1258633752464e-12 - 0.000084004935396416*o[8])*taug) + pi*(-1.24017662339842e-24
    *o[12] + pi*(0.0000832192847496054*o[13]*o[4]*o[6]*taug + pi*(o[2]*o[
    5]*o[6]*(1.75410265428146e-27 + (1.32995316841867e-15 -
    0.0000226487297378904*o[2]*o[6])*o[9])*pi - 2.93678005497663e-14*o[13]
    *o[2]*o[4]*taug)))))))))))))))))/pi;
  d := p/(data.RH2O*T*pi*gpi23);
end dofp23;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.dofpt3

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]
Temperature	T		temperature (K) [K]
Pressure	delp		iteration converged if (p-pre(p) < delp) [Pa]

Outputs

Type	Name	Description
Density	d	density [kg/m3]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function dofpt3 "inverse iteration in region 3: (d) = f(p,T)"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.Temperature T "temperature (K)";
  input SI.Pressure delp "iteration converged if (p-pre(p) < delp)";
  output SI.Density d "density";
  output Integer error=0 "error flag: iteration failed if different from 0";
protected 
  SI.Density dguess "guess density";
  Integer i=0 "loop counter";
  Real dp "pressure difference";
  SI.Density deld "density step";
  Modelica.Media.Common.HelmholtzDerivs f 
    "dimensionless Helmholtz function and dervatives w.r.t. delta and tau";
  Modelica.Media.Common.NewtonDerivatives_pT nDerivs 
    "derivatives needed in Newton iteration";
  Boolean found=false "flag for iteration success";
  Boolean supercritical "flag, true for supercritical states";
  Boolean liquid "flag, true for liquid states";
  SI.Density dmin "lower density limit";
  SI.Density dmax "upper density limit";
  SI.Temperature Tmax "maximum temperature";
algorithm 
  assert(p >= data.PLIMIT4A,
    "BaseIF97.dofpt3: function called outside of region 3! p too low\n" +
    "p = " + String(p) + " Pa < " + String(data.PLIMIT4A) + " Pa");
  assert(T >= data.TLIMIT1,
    "BaseIF97.dofpt3: function called outside of region 3! T too low\n" +
    "T = " + String(T) + " K < " + String(data.TLIMIT1) + " K");
  assert(p >= Regions.boundary23ofT(T),
    "BaseIF97.dofpt3: function called outside of region 3! T too high\n" +
    "p = " + String(p) + " Pa, T = " + String(T) + " K");
  supercritical := p > data.PCRIT;
  dmax := dofp13(p);
  dmin := dofp23(p);
  Tmax := Regions.boundary23ofp(p);
  if supercritical then
    dguess := dmin + (T - data.TLIMIT1)/(data.TLIMIT1 - Tmax)*(dmax -
      dmin);
    //this may need improvement!!
  else
    liquid := T < Basic.tsat(p);
    if liquid then
      dguess := 0.5*(Regions.rhol_p_R4b(p) + dmax);
    else
      dguess := 0.5*(Regions.rhov_p_R4b(p) + dmin);
    end if;
  end if;
  while ((i < IterationData.IMAX) and not found) loop
    d := dguess;
    f := Basic.f3(d, T);
    nDerivs := Modelica.Media.Common.Helmholtz_pT(f);
    dp := nDerivs.p - p;
    if (abs(dp/p) <= delp) then
      found := true;
    end if;
    deld := dp/nDerivs.pd;
    d := d - deld;
    if d > dmin and d < dmax then
      dguess := d;
    else
      if d > dmax then
        dguess := dmax - sqrt(Modelica.Constants.eps);
          // put it on the correct spot just inside the boundary here instead
      else
        dguess := dmin + sqrt(Modelica.Constants.eps);
      end if;
    end if;
    i := i + 1;
  end while;
  if not found then
    error := 1;
  end if;
  assert(error <> 1, "error in inverse function dofpt3: iteration failed");
end dofpt3;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.dtofph3

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]
SpecificEnthalpy	h		specific enthalpy [J/kg]
Pressure	delp		iteration accuracy [Pa]
SpecificEnthalpy	delh		iteration accuracy [J/kg]

Outputs

Type	Name	Description
Density	d	density [kg/m3]
Temperature	T	temperature (K) [K]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function dtofph3 "inverse iteration in region 3: (d,T) = f(p,h)"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.SpecificEnthalpy h "specific enthalpy";
  input SI.Pressure delp "iteration accuracy";
  input SI.SpecificEnthalpy delh "iteration accuracy";
  output SI.Density d "density";
  output SI.Temperature T "temperature (K)";
  output Integer error "error flag: iteration failed if different from 0";
protected 
  SI.Temperature Tguess "initial temperature";
  SI.Density dguess "initial density";
  Integer i "iteration counter";
  Real dh "Newton-error in h-direction";
  Real dp "Newton-error in p-direction";
  Real det "determinant of directional derivatives";
  Real deld "Newton-step in d-direction";
  Real delt "Newton-step in T-direction";
  Modelica.Media.Common.HelmholtzDerivs f 
    "dimensionless Helmholtz function and dervatives w.r.t. delta and tau";
  Modelica.Media.Common.NewtonDerivatives_ph nDerivs 
    "derivatives needed in Newton iteration";
  Boolean found "flag for iteration success";
  Integer subregion "1 for subregion 3a, 2 for subregion 3b";
algorithm 
  if p < data.PCRIT then
    // allow a 10 J margin inside the (well approximated) phase boundary
    subregion := if h < (Regions.hl_p(p) + 10.0) then 1 else 
      if h > (Regions.hv_p(p) - 10.0) then 2 else 0;
    assert(subregion <> 0,"inverse iteration of dt from ph called in 2 phase region: this can not work");
  else
    //supercritical
    subregion := if h < Basic.h3ab_p(p) then 1 else 2;
  end if;
  T := if subregion == 1 then Basic.T3a_ph(p,h) else Basic.T3b_ph(p,h);
  d := if subregion == 1 then 1/Basic.v3a_ph(p,h) else 1/Basic.v3b_ph(p,h);
  i := 0;
  error := 0;
  while ((i < IterationData.IMAX) and not found) loop
    f := Basic.f3(d, T);
    nDerivs := Modelica.Media.Common.Helmholtz_ph(f);
    dh := nDerivs.h - h;
    dp := nDerivs.p - p;
    if ((abs(dh/h) <= delh) and (abs(dp/p) <= delp)) then
      found := true;
    end if;
    det := nDerivs.ht*nDerivs.pd - nDerivs.pt*nDerivs.hd;
    delt := (nDerivs.pd*dh - nDerivs.hd*dp)/det;
    deld := (nDerivs.ht*dp - nDerivs.pt*dh)/det;
    T := T - delt;
    d := d - deld;
    dguess := d;
    Tguess := T;
    i := i + 1;
    (d,T) := fixdT(dguess, Tguess);
  end while;
  if not found then
    error := 1;
  end if;
  assert(error <> 1,
    "error in inverse function dtofph3: iteration failed");
end dtofph3;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.dtofps3

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]
SpecificEntropy	s		specific entropy [J/(kg.K)]
Pressure	delp		iteration accuracy [Pa]
SpecificEntropy	dels		iteration accuracy [J/(kg.K)]

Outputs

Type	Name	Description
Density	d	density [kg/m3]
Temperature	T	temperature (K) [K]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function dtofps3 "inverse iteration in region 3: (d,T) = f(p,s)"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.SpecificEntropy s "specific entropy";
  input SI.Pressure delp "iteration accuracy";
  input SI.SpecificEntropy dels "iteration accuracy";
  output SI.Density d "density";
  output SI.Temperature T "temperature (K)";
  output Integer error "error flag: iteration failed if different from 0";
protected 
  SI.Temperature Tguess "initial temperature";
  SI.Density dguess "initial density";
  Integer i "iteration counter";
  Real ds "Newton-error in s-direction";
  Real dp "Newton-error in p-direction";
  Real det "determinant of directional derivatives";
  Real deld "Newton-step in d-direction";
  Real delt "Newton-step in T-direction";
  Modelica.Media.Common.HelmholtzDerivs f 
    "dimensionless Helmholtz function and dervatives w.r.t. delta and tau";
  Modelica.Media.Common.NewtonDerivatives_ps nDerivs 
    "derivatives needed in Newton iteration";
  Boolean found "flag for iteration success";
  Integer subregion "1 for subregion 3a, 2 for subregion 3b";
algorithm 
  i := 0;
  error := 0;
  found := false;
  if p < data.PCRIT then
    // allow a 1 J/K margin inside the (well approximated) phase boundary
    subregion := if s < (Regions.sl_p(p) + 10.0) then 1 else 
      if s > (Regions.sv_p(p) - 10.0) then 2 else 0;
    assert(subregion <> 0,"inverse iteration of dt from ps called in 2 phase region: this is illegal!");
  else
    subregion := if s < data.SCRIT then 1 else 2;
  end if;
  T := if subregion == 1 then Basic.T3a_ps(p,s) else Basic.T3b_ps(p,s);
  d := if subregion == 1 then 1/Basic.v3a_ps(p,s) else 1/Basic.v3b_ps(p,s);
  while ((i < IterationData.IMAX) and not found) loop
    f := Basic.f3(d, T);
    nDerivs := Modelica.Media.Common.Helmholtz_ps(f);
    ds := nDerivs.s - s;
    dp := nDerivs.p - p;
    if ((abs(ds/s) <= dels) and (abs(dp/p) <= delp)) then
      found := true;
    end if;
    det := nDerivs.st*nDerivs.pd - nDerivs.pt*nDerivs.sd;
    delt := (nDerivs.pd*ds - nDerivs.sd*dp)/det;
    deld := (nDerivs.st*dp - nDerivs.pt*ds)/det;
    T := T - delt;
    d := d - deld;
    dguess := d;
    Tguess := T;
    i := i + 1;
    (d,T) := fixdT(dguess, Tguess);
  end while;
  if not found then
    error := 1;
  end if;
  assert(error <> 1,
    "error in inverse function dtofps3: iteration failed");
end dtofps3;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.dtofpsdt3

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]
SpecificEntropy	s		specific entropy [J/(kg.K)]
Density	dguess		guess density, e.g., from adjacent volume [kg/m3]
Temperature	Tguess		guess temperature, e.g., from adjacent volume [K]
Pressure	delp		iteration accuracy [Pa]
SpecificEntropy	dels		iteration accuracy [J/(kg.K)]

Outputs

Type	Name	Description
Density	d	density [kg/m3]
Temperature	T	temperature (K) [K]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function dtofpsdt3 "inverse iteration in region 3: (d,T) = f(p,s)"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.SpecificEntropy s "specific entropy";
  input SI.Density dguess "guess density, e.g., from adjacent volume";
  input SI.Temperature Tguess "guess temperature, e.g., from adjacent volume";
  input SI.Pressure delp "iteration accuracy";
  input SI.SpecificEntropy dels "iteration accuracy";
  output SI.Density d "density";
  output SI.Temperature T "temperature (K)";
  output Integer error "error flag: iteration failed if different from 0";
protected 
  Integer i "iteration counter";
  Real ds "Newton-error in s-direction";
  Real dp "Newton-error in p-direction";
  Real det "determinant of directional derivatives";
  Real deld "Newton-step in d-direction";
  Real delt "Newton-step in T-direction";
  Modelica.Media.Common.HelmholtzDerivs f 
    "dimensionless Helmholtz function and dervatives w.r.t. delta and tau";
  Modelica.Media.Common.NewtonDerivatives_ps nDerivs 
    "derivatives needed in Newton iteration";
  Boolean found "flag for iteration success";
  SI.Density diter "density";
  SI.Temperature Titer "temperature (K)";
algorithm 
  i := 0;
  error := 0;
  found := false;
  (diter,Titer) := fixdT(dguess, Tguess);
  while ((i < IterationData.IMAX) and not found) loop
    (d,T) := fixdT(diter, Titer);
    f := Basic.f3(d, T);
    nDerivs := Modelica.Media.Common.Helmholtz_ps(f);
    ds := nDerivs.s - s;
    dp := nDerivs.p - p;
    if ((abs(ds/s) <= dels) and (abs(dp/p) <= delp)) then
      found := true;
    end if;
    det := nDerivs.st*nDerivs.pd - nDerivs.pt*nDerivs.sd;
    delt := (nDerivs.pd*ds - nDerivs.sd*dp)/det;
    deld := (nDerivs.st*dp - nDerivs.pt*ds)/det;
    T := T - delt;
    d := d - deld;
    diter := d;
    Titer := T;
    i := i + 1;
  end while;
  if not found then
    error := 1;
  end if;
  assert(error <> 1,
    "error in inverse function dtofpsdt3: iteration failed");
end dtofpsdt3;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.pofdt125

Information

Inputs

Type	Name	Default	Description
Density	d		density [kg/m3]
Temperature	T		temperature (K) [K]
Pressure	reldd		relative iteration accuracy of density [Pa]
Integer	region		region in IAPWS/IF97 in which inverse should be calculated

Outputs

Type	Name	Description
Pressure	p	pressure [Pa]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function pofdt125 "inverse iteration in region 1,2 and 5: p = g(d,T)"
  extends Modelica.Icons.Function;
  input SI.Density d "density";
  input SI.Temperature T "temperature (K)";
  input SI.Pressure reldd "relative iteration accuracy of density";
  input Integer region 
    "region in IAPWS/IF97 in which inverse should be calculated";
  output SI.Pressure p "pressure";
  output Integer error "error flag: iteration failed if different from 0";
protected 
  Integer i "counter for while-loop";
  Modelica.Media.Common.GibbsDerivs g 
    "dimensionless Gibbs funcion and dervatives w.r.t. pi and tau";
  Boolean found "flag if iteration has been successful";
  Real dd "difference between density for  guessed p and the current density";
  Real delp "step in p in Newton-iteration";
  Real relerr "relative error in d";
  SI.Pressure pguess1=1.0e6 "initial pressure guess in region 1";
  SI.Pressure pguess2 "initial pressure guess in region 2";
  constant SI.Pressure pguess5=0.5e6 "initial pressure guess in region 5";
algorithm 
  i := 0;
  error := 0;
  pguess2 := 42800*d;
  found := false;
  if region == 1 then
    p := pguess1;
  elseif region == 2 then
    p := pguess2;
  else
    p := pguess5;
  end if;
  while ((i < IterationData.IMAX) and not found) loop
    if region == 1 then
      g := Basic.g1(p, T);
    elseif region == 2 then
      g := Basic.g2(p, T);
    else
      g := Basic.g5(p, T);
    end if;
    dd := p/(data.RH2O*T*g.pi*g.gpi) - d;
    relerr := dd/d;
    if (abs(relerr) < reldd) then
      found := true;
    end if;
    delp := dd*(-p*p/(d*d*data.RH2O*T*g.pi*g.pi*g.gpipi));
    p := p - delp;
    i := i + 1;
    if not found then
      if p < triple.ptriple then
        p := 2.0*triple.ptriple;
      end if;
      if p > data.PLIMIT1 then
        p := 0.95*data.PLIMIT1;
      end if;
    end if;
  end while;

    // print("i = " + i2s(i) + ", p = " + r2s(p/1.0e5) + ", delp = " + r2s(delp*1.0e-5) + "\n");
  if not found then
    error := 1;
  end if;
  assert(error <> 1,
    "error in inverse function pofdt125: iteration failed");
end pofdt125;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.tofph5

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]
SpecificEnthalpy	h		specific enthalpy [J/kg]
SpecificEnthalpy	reldh		iteration accuracy [J/kg]

Outputs

Type	Name	Description
Temperature	T	temperature (K) [K]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function tofph5 "inverse iteration in region 5: (p,T) = f(p,h)"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.SpecificEnthalpy h "specific enthalpy";
  input SI.SpecificEnthalpy reldh "iteration accuracy";
  output SI.Temperature T "temperature (K)";
  output Integer error "error flag: iteration failed if different from 0";

protected 
  Modelica.Media.Common.GibbsDerivs g 
    "dimensionless Gibbs funcion and dervatives w.r.t. pi and tau";
  SI.SpecificEnthalpy proh "h for current guess in T";
  constant SI.Temperature Tguess=1500 "initial temperature";
  Integer i "iteration counter";
  Real relerr "relative error in h";
  Real dh "Newton-error in h-direction";
  Real dT "Newton-step in T-direction";
  Boolean found "flag for iteration success";
algorithm 
  i := 0;
  error := 0;
  T := Tguess;
  found := false;
  while ((i < IterationData.IMAX) and not found) loop
    g := Basic.g5(p, T);
    proh := data.RH2O*T*g.tau*g.gtau;
    dh := proh - h;
    relerr := dh/h;
    if (abs(relerr) < reldh) then
      found := true;
    end if;
    dT := dh/(-data.RH2O*g.tau*g.tau*g.gtautau);
    T := T - dT;
    i := i + 1;
  end while;
  if not found then
    error := 1;
  end if;
  assert(error <> 1, "error in inverse function tofph5: iteration failed");
end tofph5;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.tofps5

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]
SpecificEntropy	s		specific entropy [J/(kg.K)]
SpecificEnthalpy	relds		iteration accuracy [J/kg]

Outputs

Type	Name	Description
Temperature	T	temperature (K) [K]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function tofps5 "inverse iteration in region 5: (p,T) = f(p,s)"

  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.SpecificEntropy s "specific entropy";
  input SI.SpecificEnthalpy relds "iteration accuracy";
  output SI.Temperature T "temperature (K)";
  output Integer error "error flag: iteration failed if different from 0";

protected 
  Modelica.Media.Common.GibbsDerivs g 
    "dimensionless Gibbs funcion and dervatives w.r.t. pi and tau";
  SI.SpecificEntropy pros "s for current guess in T";
  parameter SI.Temperature Tguess=1500 "initial temperature";
  Integer i "iteration counter";
  Real relerr "relative error in s";
  Real ds "Newton-error in s-direction";
  Real dT "Newton-step in T-direction";
  Boolean found "flag for iteration success";
algorithm 
  i := 0;
  error := 0;
  T := Tguess;
  found := false;
  while ((i < IterationData.IMAX) and not found) loop
    g := Basic.g5(p, T);
    pros := data.RH2O*(g.tau*g.gtau - g.g);
    ds := pros - s;
    relerr := ds/s;
    if (abs(relerr) < relds) then
      found := true;
    end if;
    dT := ds*T/(-data.RH2O*g.tau*g.tau*g.gtautau);
    T := T - dT;
    i := i + 1;
  end while;
  if not found then
    error := 1;
  end if;
  assert(error <> 1, "error in inverse function tofps5: iteration failed");
end tofps5;

Modelica.Media.Water.IF97_Utilities.BaseIF97.Inverses.tofpst5

Information

Inputs

Type	Name	Default	Description
Pressure	p		pressure [Pa]
SpecificEntropy	s		specific entropy [J/(kg.K)]
Temperature	Tguess		guess temperature, e.g., from adjacent volume [K]
SpecificEntropy	relds		iteration accuracy [J/(kg.K)]

Outputs

Type	Name	Description
Temperature	T	temperature (K) [K]
Integer	error	error flag: iteration failed if different from 0

Modelica definition

function tofpst5 "inverse iteration in region 5: (p,T) = f(p,s)"
  extends Modelica.Icons.Function;
  input SI.Pressure p "pressure";
  input SI.SpecificEntropy s "specific entropy";
  input SI.Temperature Tguess "guess temperature, e.g., from adjacent volume";
  input SI.SpecificEntropy relds "iteration accuracy";
  output SI.Temperature T "temperature (K)";
  output Integer error "error flag: iteration failed if different from 0";

protected 
  Modelica.Media.Common.GibbsDerivs g 
    "dimensionless Gibbs funcion and dervatives w.r.t. pi and tau";
  SI.SpecificEntropy pros "s for current guess in T";
  Integer i "iteration counter";
  Real relerr "relative error in s";
  Real ds "Newton-error in s-direction";
  Real dT "Newton-step in T-direction";
  Boolean found "flag for iteration success";
algorithm 
  i := 0;
  error := 0;
  T := Tguess;
  found := false;
  while ((i < IterationData.IMAX) and not found) loop
    g := Basic.g5(p, T);
    pros := data.RH2O*(g.tau*g.gtau - g.g);
    ds := pros - s;
    relerr := ds/s;
    if (abs(relerr) < relds) then
      found := true;
    end if;
    dT := ds*T/(-data.RH2O*g.tau*g.tau*g.gtautau);
    T := T - dT;
    i := i + 1;
  end while;
  if not found then
    error := 1;
  end if;
  assert(error <> 1,
    "error in inverse function tofpst5: iteration failed");
end tofpst5;