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Added more tests for second derivatives

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Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-08-24 20:45:07 +02:00
parent 799422fe40
commit c398ea91a7
2 changed files with 94 additions and 3 deletions
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4
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
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@@ -1323,7 +1323,7 @@ void get_dT_drho_second_derivatives(HelmholtzEOSMixtureBackend *HEOS, int index,
drho_dT = 0;
break;
case iTau:
dT2 = 0; drho_dT = 0; drho2 = 0; break;
dT2 = 2*Tr/pow(T,3); drho_dT = 0; drho2 = 0; break;
case iDelta:
dT2 = 0; drho_dT = 0; drho2 = 0; break;
case iP:
@@ -1336,7 +1336,7 @@ void get_dT_drho_second_derivatives(HelmholtzEOSMixtureBackend *HEOS, int index,
case iHmolar:
{
// d2h/drho2|T
drho2 = R*T/pow(rho, 2)*pow(delta,2)*(tau*HEOS->d3alpha0_dDelta2_dTau() + 2*derivs.d2alphar_ddelta2 + delta*derivs.d2alphar_ddelta2);
drho2 = R*T*pow(delta/rho,2)*(tau*derivs.d3alphar_ddelta2_dtau + 2*derivs.d2alphar_ddelta2 + delta*derivs.d3alphar_ddelta3);
// d2h/dT2|rho
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

93
src/Tests/CoolProp-Tests.cpp
View File

@@ -985,7 +985,7 @@ TEST_CASE("Test first partial derivatives using PropsSI", "[derivatives]")
}
}
TEST_CASE("Test second partial derivatives using PropsSI", "[derivatives]")
TEST_CASE("Test second partial derivatives", "[derivatives]")
{
double hmolar, hmass, T = 300;
SECTION("Check d2pdrho2|T 3 ways","")
@@ -1017,6 +1017,97 @@ TEST_CASE("Test second partial derivatives using PropsSI", "[derivatives]")
CHECK(!ValidNumber(PropsSI("d(d()/d(P)|T)/d()|","T",300,"P",101325,"n-Propane")));
CHECK(!ValidNumber(PropsSI("dd(Dmolar)/d()|T)|T","T",300,"P",101325,"n-Propane")));
}
SECTION("Check derivatives with respect to T","")
{
shared_ptr<CoolProp::AbstractState> AS(CoolProp::AbstractState::factory("HEOS", "Propane"));
double rhomolar = 100, dT = 1e-1;
AS->update(CoolProp::DmolarT_INPUTS, rhomolar, T);
// base state
long double T0 = AS->T(), rhomolar0 = AS->rhomolar(), hmolar0 = AS->hmolar(), smolar0 = AS->smolar(), umolar0 = AS->umolar(), p0 = AS->p();
long double dhdT_rho_ana = AS->first_partial_deriv(CoolProp::iHmolar, CoolProp::iT, CoolProp::iDmolar);
long double d2hdT2_rho_ana = AS->second_partial_deriv(CoolProp::iHmolar, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar);
long double dsdT_rho_ana = AS->first_partial_deriv(CoolProp::iSmolar, CoolProp::iT, CoolProp::iDmolar);
long double d2sdT2_rho_ana = AS->second_partial_deriv(CoolProp::iSmolar, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar);
long double dudT_rho_ana = AS->first_partial_deriv(CoolProp::iUmolar, CoolProp::iT, CoolProp::iDmolar);
long double d2udT2_rho_ana = AS->second_partial_deriv(CoolProp::iUmolar, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar);
long double dpdT_rho_ana = AS->first_partial_deriv(CoolProp::iP, CoolProp::iT, CoolProp::iDmolar);
long double d2pdT2_rho_ana = AS->second_partial_deriv(CoolProp::iP, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar);
// increment T
AS->update(CoolProp::DmolarT_INPUTS, rhomolar, T+dT);
long double Tpt = AS->T(), rhomolarpt = AS->rhomolar(), hmolarpt = AS->hmolar(), smolarpt = AS->smolar(), umolarpt = AS->umolar(), ppt = AS->p();
// decrement T
AS->update(CoolProp::DmolarT_INPUTS, rhomolar, T-dT);
long double Tmt = AS->T(), rhomolarmt = AS->rhomolar(), hmolarmt = AS->hmolar(), smolarmt = AS->smolar(), umolarmt = AS->umolar(), pmt = AS->p();
long double dhdT_rho_num = (hmolarpt-hmolarmt)/(2*dT);
long double d2hdT2_rho_num = (hmolarpt-2*hmolar0+hmolarmt)/pow(dT,2);
long double dsdT_rho_num = (smolarpt-smolarmt)/(2*dT);
long double d2sdT2_rho_num = (smolarpt-2*smolar0+smolarmt)/pow(dT,2);
long double dudT_rho_num = (umolarpt-umolarmt)/(2*dT);
long double d2udT2_rho_num = (umolarpt-2*umolar0+umolarmt)/pow(dT,2);
long double dpdT_rho_num = (ppt-pmt)/(2*dT);
long double d2pdT2_rho_num = (ppt-2*p0+pmt)/pow(dT,2);
CAPTURE(format("%0.15Lg",d2pdT2_rho_ana).c_str());
double tol = 1e-4;
CHECK(std::abs((dhdT_rho_num-dhdT_rho_ana)/dhdT_rho_ana) < tol);
CHECK(std::abs((d2hdT2_rho_num-d2hdT2_rho_ana)/d2hdT2_rho_ana) < tol);
CHECK(std::abs((dpdT_rho_num-dpdT_rho_ana)/dpdT_rho_ana) < tol);
CHECK(std::abs((d2pdT2_rho_num-d2pdT2_rho_ana)/d2pdT2_rho_ana) < tol);
CHECK(std::abs((dsdT_rho_num-dsdT_rho_ana)/dsdT_rho_ana) < tol);
CHECK(std::abs((d2sdT2_rho_num-d2sdT2_rho_ana)/d2sdT2_rho_ana) < tol);
CHECK(std::abs((dudT_rho_num-dudT_rho_ana)/dudT_rho_ana) < tol);
CHECK(std::abs((d2udT2_rho_num-d2udT2_rho_ana)/d2udT2_rho_ana) < tol);
}
SECTION("Check derivatives with respect to rho","")
{
shared_ptr<CoolProp::AbstractState> AS(CoolProp::AbstractState::factory("HEOS", "Propane"));
double rhomolar = 100, drho = 1e-1;
AS->update(CoolProp::DmolarT_INPUTS, rhomolar, T);
// base state
long double T0 = AS->T(), rhomolar0 = AS->rhomolar(), hmolar0 = AS->hmolar(), smolar0 = AS->smolar(), umolar0 = AS->umolar(), p0 = AS->p();
long double dhdrho_T_ana = AS->first_partial_deriv(CoolProp::iHmolar, CoolProp::iDmolar, CoolProp::iT);
long double d2hdrho2_T_ana = AS->second_partial_deriv(CoolProp::iHmolar, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT);
long double dsdrho_T_ana = AS->first_partial_deriv(CoolProp::iSmolar, CoolProp::iDmolar, CoolProp::iT);
long double d2sdrho2_T_ana = AS->second_partial_deriv(CoolProp::iSmolar, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT);
long double dudrho_T_ana = AS->first_partial_deriv(CoolProp::iUmolar, CoolProp::iDmolar, CoolProp::iT);
long double d2udrho2_T_ana = AS->second_partial_deriv(CoolProp::iUmolar, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT);
long double dpdrho_T_ana = AS->first_partial_deriv(CoolProp::iP, CoolProp::iDmolar, CoolProp::iT);
long double d2pdrho2_T_ana = AS->second_partial_deriv(CoolProp::iP, CoolProp::iDmolar, CoolProp::iT, CoolProp::iDmolar, CoolProp::iT);
// increment rho
AS->update(CoolProp::DmolarT_INPUTS, rhomolar+drho, T);
long double Tpr = AS->T(), rhomolarpr = AS->rhomolar(), hmolarpr = AS->hmolar(), smolarpr = AS->smolar(), umolarpr = AS->umolar(), ppr = AS->p();
// decrement rho
AS->update(CoolProp::DmolarT_INPUTS, rhomolar-drho, T);
long double Tmr = AS->T(), rhomolarmr = AS->rhomolar(), hmolarmr = AS->hmolar(), smolarmr = AS->smolar(), umolarmr = AS->umolar(), pmr = AS->p();
long double dhdrho_T_num = (hmolarpr-hmolarmr)/(2*drho);
long double d2hdrho2_T_num = (hmolarpr-2*hmolar0+hmolarmr)/pow(drho,2);
long double dsdrho_T_num = (smolarpr-smolarmr)/(2*drho);
long double d2sdrho2_T_num = (smolarpr-2*smolar0+smolarmr)/pow(drho,2);
long double dudrho_T_num = (umolarpr-umolarmr)/(2*drho);
long double d2udrho2_T_num = (umolarpr-2*umolar0+umolarmr)/pow(drho,2);
long double dpdrho_T_num = (ppr-pmr)/(2*drho);
long double d2pdrho2_T_num = (ppr-2*p0+pmr)/pow(drho,2);
CAPTURE(format("%0.15Lg",d2pdrho2_T_ana).c_str());
double tol = 1e-4;
CHECK(std::abs((dhdrho_T_num-dhdrho_T_ana)/dhdrho_T_ana) < tol);
CHECK(std::abs((d2hdrho2_T_num-d2hdrho2_T_ana)/d2hdrho2_T_ana) < tol);
CHECK(std::abs((dpdrho_T_num-dpdrho_T_ana)/dpdrho_T_ana) < tol);
CHECK(std::abs((d2pdrho2_T_num-d2pdrho2_T_ana)/d2pdrho2_T_ana) < tol);
CHECK(std::abs((dsdrho_T_num-dsdrho_T_ana)/dsdrho_T_ana) < tol);
CHECK(std::abs((d2sdrho2_T_num-d2sdrho2_T_ana)/d2sdrho2_T_ana) < tol);
CHECK(std::abs((dudrho_T_num-dudrho_T_ana)/dudrho_T_ana) < tol);
CHECK(std::abs((d2udrho2_T_num-d2udrho2_T_ana)/d2udrho2_T_ana) < tol);
}
}
TEST_CASE("Ancillary functions", "[ancillary]")