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mass based derivatives (I think) plus test

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referenced in https://github.com/CoolProp/CoolProp/issues/177

Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-10-15 23:09:13 +02:00
parent 1727771411
commit c8fedbbf30
2 changed files with 58 additions and 2 deletions
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42
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
View File

@@ -1313,6 +1313,8 @@ void get_dT_drho(HelmholtzEOSMixtureBackend *HEOS, parameters index, long double
dT = 1; drho = 0; break;
case iDmolar:
dT = 0; drho = 1; break;
case iDmass:
dT = 0; drho = HEOS->molar_mass(); break;
case iP:
{
// dp/drho|T
@@ -1321,30 +1323,51 @@ void get_dT_drho(HelmholtzEOSMixtureBackend *HEOS, parameters index, long double
dT = rho*R*(1+delta*HEOS->dalphar_dDelta() - tau*delta*HEOS->d2alphar_dDelta_dTau());
break;
}
case iHmass:
case iHmolar:
{
// dh/dT|rho
dT = R*(-pow(tau,2)*(HEOS->d2alpha0_dTau2()+HEOS->d2alphar_dTau2()) + (1+delta*HEOS->dalphar_dDelta()-tau*delta*HEOS->d2alphar_dDelta_dTau()));
// dh/drho|T
// dh/drhomolar|T
drho = T*R/rho*(tau*delta*HEOS->d2alphar_dDelta_dTau()+delta*HEOS->dalphar_dDelta()+pow(delta,2)*HEOS->d2alphar_dDelta2());
if (index == iHmass){
// dh/drho|T * drhomass/drhomolar where drhomass/drhomolar = mole mass
drho *= HEOS->molar_mass();
}
break;
}
case iSmass:
case iSmolar:
{
// ds/dT|rho
dT = R/T*(-pow(tau,2)*(HEOS->d2alpha0_dTau2()+HEOS->d2alphar_dTau2()));
// ds/drho|T
drho = R/rho*(-(1+delta*HEOS->dalphar_dDelta()-tau*delta*HEOS->d2alphar_dDelta_dTau()));
if (index == iSmass){
// ds/drho|T * drhomass/drhomolar where drhomass/drhomolar = mole mass
drho *= HEOS->molar_mass();
}
break;
}
case iUmass:
case iUmolar:
{
// du/dT|rho
dT = R*(-pow(tau,2)*(HEOS->d2alpha0_dTau2()+HEOS->d2alphar_dTau2()));
// du/drho|T
drho = HEOS->T()*R/rho*(tau*delta*HEOS->d2alphar_dDelta_dTau());
if (index == iUmass){
// du/drho|T * drhomass/drhomolar where drhomass/drhomolar = mole mass
drho *= HEOS->molar_mass();
}
break;
}
case iTau:
dT = 1/dT_dtau; drho = 0; break;
case iDelta:
dT = 0; drho = 1/rhor; break;
default:
throw ValueError(format("input to get_dtau_ddelta[%s] is invalid",get_parameter_information(index,"short").c_str()));
throw ValueError(format("input to get_dT_drho[%s] is invalid",get_parameter_information(index,"short").c_str()));
}
}
void get_dT_drho_second_derivatives(HelmholtzEOSMixtureBackend *HEOS, int index, long double &dT2, long double &drho_dT, long double &drho2)
@@ -1385,6 +1408,7 @@ void get_dT_drho_second_derivatives(HelmholtzEOSMixtureBackend *HEOS, int index,
drho_dT = R*(1+2*delta*derivs.dalphar_ddelta +pow(delta,2)*derivs.d2alphar_ddelta2 - 2*delta*tau*derivs.d2alphar_ddelta_dtau - tau*pow(delta, 2)*derivs.d3alphar_ddelta2_dtau);
break;
}
case iHmass:
case iHmolar:
{
// d2h/drho2|T
@@ -1393,8 +1417,13 @@ void get_dT_drho_second_derivatives(HelmholtzEOSMixtureBackend *HEOS, int index,
dT2 = R/T*pow(tau, 2)*(tau*(HEOS->d3alpha0_dTau3()+derivs.d3alphar_dtau3) + 2*(HEOS->d2alpha0_dTau2()+derivs.d2alphar_dtau2) + delta*derivs.d3alphar_ddelta_dtau2);
// d2h/drho/dT
drho_dT = R/rho*delta*(delta*derivs.d2alphar_ddelta2 - pow(tau,2)*derivs.d3alphar_ddelta_dtau2 + derivs.dalphar_ddelta - tau*delta*derivs.d3alphar_ddelta2_dtau - tau*derivs.d2alphar_ddelta_dtau);
if (index == iHmass){
drho2 *= POW2(HEOS->molar_mass());
drho_dT *= HEOS->molar_mass();
}
break;
}
case iSmass:
case iSmolar:
{
// d2s/rho2|T
@@ -1403,8 +1432,13 @@ void get_dT_drho_second_derivatives(HelmholtzEOSMixtureBackend *HEOS, int index,
dT2 = R*pow(tau/T, 2)*(tau*(HEOS->d3alpha0_dTau3()+derivs.d3alphar_dtau3)+3*(HEOS->d2alpha0_dTau2()+derivs.d2alphar_dtau2));
// d2s/drho/dT
drho_dT = R/(T*rho)*(-pow(tau,2)*delta*derivs.d3alphar_ddelta_dtau2);
if (index == iSmass){
drho2 *= POW2(HEOS->molar_mass());
drho_dT *= HEOS->molar_mass();
}
break;
}
case iUmass:
case iUmolar:
{
// d2u/rho2|T
@@ -1413,6 +1447,10 @@ void get_dT_drho_second_derivatives(HelmholtzEOSMixtureBackend *HEOS, int index,
dT2 = R/T*pow(tau, 2)*(tau*(HEOS->d3alpha0_dTau3()+derivs.d3alphar_dtau3)+2*(HEOS->d2alpha0_dTau2()+derivs.d2alphar_dtau2));
// d2u/drho/dT
drho_dT = R/rho*(-pow(tau,2)*delta*derivs.d3alphar_ddelta_dtau2);
if (index == iUmass){
drho2 *= POW2(HEOS->molar_mass());
drho_dT *= HEOS->molar_mass();
}
break;
}
default:

18
src/Tests/CoolProp-Tests.cpp
View File

@@ -972,6 +972,24 @@ TEST_CASE("Test first partial derivatives using PropsSI", "[derivatives]")
CHECK(rel_err_exact < 1e-7);
CHECK(rel_err_approx < 1e-7);
}
SECTION("Check dpdrho|T 3 ways for water using mass based","")
{
T = 80+273.15;
shared_ptr<CoolProp::AbstractState> AS(CoolProp::AbstractState::factory("HEOS", "Water"));
AS->update(CoolProp::PT_INPUTS, 101325, T);
long double rhomass = AS->rhomass();
double dpdrhomass__T_AbstractState = AS->first_partial_deriv(CoolProp::iP, CoolProp::iDmass, CoolProp::iT);
double dpdrhomass__T_PropsSI_num = (PropsSI("P","T",T,"Dmass",rhomass+1e-3,"Water") - PropsSI("P","T",T,"Dmass",rhomass-1e-3,"Water"))/(2*1e-3);
double dpdrhomass__T_PropsSI = PropsSI("d(P)/d(Dmass)|T","T",T,"P",101325,"Water");
CAPTURE(rhomass);
CAPTURE(dpdrhomass__T_AbstractState);
CAPTURE(dpdrhomass__T_PropsSI_num);
CAPTURE(dpdrhomass__T_PropsSI);
double rel_err_exact = std::abs((dpdrhomass__T_AbstractState-dpdrhomass__T_PropsSI)/dpdrhomass__T_PropsSI);
double rel_err_approx = std::abs((dpdrhomass__T_PropsSI_num-dpdrhomass__T_PropsSI)/dpdrhomass__T_PropsSI);
CHECK(rel_err_exact < 1e-7);
CHECK(rel_err_approx < 1e-7);
}
SECTION("Invalid first partial derivatives","")
{
CHECK(!ValidNumber(PropsSI("d()/d(P)|T","T",300,"P",101325,"n-Propane")));