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Implemented second saturation derivatives with respect to p; Closes #238

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Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-12-19 17:39:47 -06:00
parent 132b0ab5dd
commit 884a3ff8ff
4 changed files with 73 additions and 7 deletions
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29
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
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@@ -2566,9 +2566,34 @@ long double HelmholtzEOSMixtureBackend::calc_first_saturation_deriv(parameters O
throw ValueError(format("Not possible to take first saturation derivative with respect to %s", get_parameter_information(Wrt1,"short").c_str()));
}
}
long double HelmholtzEOSMixtureBackend::calc_second_saturation_deriv(parameters Of1, parameters Wrt1)
long double HelmholtzEOSMixtureBackend::calc_second_saturation_deriv(parameters Of1, parameters Wrt1, parameters Of2, parameters Wrt2)
{
throw NotImplementedError("calc_second_saturation_deriv is not yet implemented");
if (Wrt1 == iP && Wrt2 == iP){
if (Of1 != Of2){ throw ValueError(format("Currently, only possible to take second saturation derivative of y both times (d2ydx2)"));}
long double dydT_constp = this->first_partial_deriv(Of1, iT, iP);
long double d2ydTdp = this->second_partial_deriv(Of1, iT, iP, iP, iT);
long double d2ydp2_constT = this->second_partial_deriv(Of1, iP, iT, iP, iT);
long double d2ydT2_constp = this->second_partial_deriv(Of1, iT, iP, iT, iP);
long double dTdp_along_sat = calc_first_saturation_deriv(iT, iP);
long double dvdrhoL = -1/POW2(SatL->rhomolar());
long double dvdrhoV = -1/POW2(SatV->rhomolar());
long double DELTAv = 1/SatV->rhomolar()-1/SatL->rhomolar();
long double dDELTAv_dT_constp = dvdrhoV*SatV->first_partial_deriv(iDmolar, iT, iP)-dvdrhoL*SatL->first_partial_deriv(iDmolar, iT, iP);
long double dDELTAv_dp_constT = dvdrhoV*SatV->first_partial_deriv(iDmolar, iP, iT)-dvdrhoL*SatL->first_partial_deriv(iDmolar, iP, iT);
long double DELTAh = SatV->hmolar()-SatL->hmolar();
long double dDELTAh_dT_constp = SatV->first_partial_deriv(iHmolar, iT, iP)-SatL->first_partial_deriv(iHmolar, iT, iP);
long double dDELTAh_dp_constT = SatV->first_partial_deriv(iHmolar, iP, iT)-SatL->first_partial_deriv(iHmolar, iP, iT);
long double ddT_dTdp_along_sat_constp = (DELTAh*(_T*dDELTAv_dT_constp+DELTAv)-_T*DELTAv*dDELTAh_dT_constp)/POW2(DELTAh);
long double ddp_dTdp_along_sat_constT = (DELTAh*(_T*dDELTAv_dp_constT)-_T*DELTAv*dDELTAh_dp_constT)/POW2(DELTAh);
double ddp_dydpsigma = d2ydp2_constT + dydT_constp*ddp_dTdp_along_sat_constT + d2ydTdp*dTdp_along_sat;
double ddT_dydpsigma = d2ydTdp + dydT_constp*ddT_dTdp_along_sat_constp + d2ydT2_constp*dTdp_along_sat;
return ddp_dydpsigma + ddT_dydpsigma*dTdp_along_sat;
}
else{
throw ValueError(format("Currently, only possible to take second saturation derivative w.r.t. P (both times)"));
}
}
} /* namespace CoolProp */

2
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.h
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@@ -69,7 +69,7 @@ public:
long double calc_ODP();
long double calc_first_saturation_deriv(parameters Of1, parameters Wrt1);
long double calc_second_saturation_deriv(parameters Of1, parameters Wrt1);
long double calc_second_saturation_deriv(parameters Of1, parameters Wrt1, parameters Of2, parameters Wrt2);
/// Calculate the phase once the state is fully calculated but you aren't sure if it is liquid or gas or ...
void recalculate_singlephase_phase();