def enthalpy(tau,delta,ni,ti,vi,ui,R,ho,so,rho_c,Tc,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A,M_amu,ideal_n,ideal_gamma,ideal_eqn_type): from helmholtz_functions.ideal_helmholtz_energy_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_from_Cp_o_over_R from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta from helmholtz_functions.ideal_helmholtz_from_coef_dtau import ideal_helmholtz_from_coef_dtau from pylab import zeros dalpha_tau=zeros(len(tau)) dalpha_delta=zeros(len(tau)) dalpha_o=zeros(len(tau)) #M_H2=2.01594 T=Tc/tau if(ideal_eqn_type=='Cp'): for i in range(0,len(tau)): dalpha_o[i]=ideal_helmholtz_energy_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/M_amu,Tc,tau[i],delta[i],n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) if(ideal_eqn_type=='Coef'): for i in range(0,len(tau)): dalpha_o[i]=ideal_helmholtz_from_coef_dtau(delta[i],tau[i],ideal_n,ideal_gamma) if(ideal_eqn_type=='none'): dalpha_o[1]==0.0 for i in range(0,len(tau)): dalpha_tau[i]=d_alpha_d_tau(tau[i],delta[i],N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta[i]=d_alpha_d_delta(tau[i],delta[i],N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) R_specific=R/M_amu h1=R_specific*T*1.0 h2=R_specific*T*tau*(dalpha_o+dalpha_tau) h3=R_specific*T*delta*dalpha_delta h=h1+h2+h3 return h
def cp_h2_mod(T,Pin): from helmholtz_functions.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta from helmholtz_functions.d_alpha_d_tau_d_tau import d_alpha_d_tau_d_tau from helmholtz_functions.d_alpha_d_delta_d_delta import d_alpha_d_delta_d_delta from helmholtz_functions.d_alpha_d_delta_d_tau import d_alpha_d_delta_d_tau from numpy import asarray,zeros from scipy.optimize import fsolve from residual_pressure import residual_pressure bars_to_kPa=100 P=Pin*bars_to_kPa R=8.314472 R_hydrogen=R/2.01594 M_amu=2.01594 density_guess=P/(R_hydrogen*T) rho_c=15.508*2.01594 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel delta_guess=density_guess/rho_c ######################################## #Hydrogen parameters from Leachman,2007 ######################################## Tc=33.145 tau=Tc/T R=8.314472 R_hydrogen=R/2.01594 N_i=[-6.93643,0.01,2.1101,4.52059,0.732564,-1.34086,0.130985,-0.777414,0.351944,-0.0211716,0.0226312,0.032187,-0.0231752,0.0557346]; t_i=[0.6844,1,0.989,0.489,0.803,1.1444,1.409,1.754,1.311,4.187,5.646,0.791,7.249,2.986] d_i=[1,4,1,1,2,2,3,1,3,2,1,3,1,1] p_i=[0,0,0,0,0,0,0,1,1,0/1,0/1,0/1,0/1,0/1] phi_i=[0,0,0,0,0,0,0,0,0,1.685,0.489,0.103,2.506,1.607]# Not, we need to use -sign here Beta_i=[0,0,0,0,0,0,0,0,0, 0.171,0.2245,0.1304,0.2785,0.3967] #Note, we need to use - sign here gamma_i=[0,0,0,0,0,0,0,0,0,0.7164,1.3444,1.4517,0.7204,1.5445] D_i=[0,0,0,0,0,0,0,0,0,1.506,0.156,1.736,0.67,1.6620] Tc=33.145 rho_c=15.508*2.01594 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel #delta=density/rho_c tau=Tc/T ni=2.5 ti=0.0 vi=[1.616,-0.4117,-0.792,0.758,1.217] ui=[531,751,1989,2484,6859] R=8.314472 #J/mol/K ho = 7206.9069892047 #J/mol so = 143.4846187346 #J/mol/K n_power_terms=9 n_gaussian_terms=5 n_critical_terms=0 n_power_terms_w_exp=0 n_ideal_gas_terms_pow=0 n_ideal_gas_terms_exp=5 RES_a = zeros(len(ui)) RES_b = zeros(len(ui)) RES_B = zeros(len(ui)) RES_C = zeros(len(ui)) RES_D = zeros(len(ui)) RES_A = zeros(len(ui)) To=273.15 rho_o=((0.001/(R*To))*1000) ############################################# ## End parameters -> should be data structure ############################################# delta=fsolve(residual_pressure,delta_guess,args=(P,tau,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A,R,Tc,rho_c,M_amu)) dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) dalpha_tau=d_alpha_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta=d_alpha_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau_tau=d_alpha_d_tau_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_delta=d_alpha_d_delta_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_tau=d_alpha_d_delta_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) #Isochoric heat capacity cv=-1.0*R_hydrogen*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau)) #Isobaric heat capacity cp=cv+R_hydrogen*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta) #default is in kJ/kg-K convert to erg/K/mol for DeBoer's TCM # kJ 1000J 1e7 ergs 1 kg M_amu g erg #----- * ----- * --------- * ------ * -------- = ------- # kg*K kJ 1J 1000 g mol K mol return cp*M_amu*1e7
def enthalpy_normal_h2(T,density): from helmholtz_functions.ideal_helmholtz_energy_from_Cp_o_over_R import ideal_helmholtz_energy_from_Cp_o_over_R from helmholtz_functions.ideal_helmholtz_energy_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_from_Cp_o_over_R from helmholtz_functions.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta from helmholtz_functions.helmholtz_energy_residual import helmholtz_energy_residual from helmholtz_functions.d_alpha_d_tau_d_tau import d_alpha_d_tau_d_tau from helmholtz_functions.d_alpha_d_delta_d_delta import d_alpha_d_delta_d_delta from helmholtz_functions.d_alpha_d_delta_d_tau import d_alpha_d_delta_d_tau from helmholtz_functions.ideal_helmholtz_energy_from_Cp_o_over_R_vector import ideal_helmholtz_energy_from_Cp_o_over_R_vector from helmholtz_functions.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector from thermodynamic_functions.Virial_B_vector import Virial_B_vector from math import sqrt from pylab import zeros from numpy import asarray N_i=[-6.93643,0.01,2.1101,4.52059,0.732564,-1.34086,0.130985,-0.777414,0.351944,-0.0211716,0.0226312,0.032187,-0.0231752,0.0557346]; t_i=[0.6844,1,0.989,0.489,0.803,1.1444,1.409,1.754,1.311,4.187,5.646,0.791,7.249,2.986] d_i=[1,4,1,1,2,2,3,1,3,2,1,3,1,1] p_i=[0,0,0,0,0,0,0,1,1,0/1,0/1,0/1,0/1,0/1] phi_i=[0,0,0,0,0,0,0,0,0,1.685,0.489,0.103,2.506,1.607]# Not, we need to use -sign here Beta_i=[0,0,0,0,0,0,0,0,0, 0.171,0.2245,0.1304,0.2785,0.3967] #Note, we need to use - sign here gamma_i=[0,0,0,0,0,0,0,0,0,0.7164,1.3444,1.4517,0.7204,1.5445] D_i=[0,0,0,0,0,0,0,0,0,1.506,0.156,1.736,0.67,1.6620] Tc=33.145 rho_c=15.508*2.01594 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel delta=density/rho_c tau=Tc/T R=8.314472 R_hydrogen=R/2.01594 ni=2.5 ti=0.0 vi=[1.616,-0.4117,-0.792,0.758,1.217] ui=[531,751,1989,2484,6859] R=8.314472 #J/mol/K ho = 7206.9069892047 #J/mol so = 143.4846187346 #J/mol/K n_power_terms=9 n_gaussian_terms=5 n_critical_terms=0 n_ideal_gas_terms_pow=0 n_ideal_gas_terms_exp=5 RES_a = zeros(len(ui)) RES_b = zeros(len(ui)) RES_B = zeros(len(ui)) RES_C = zeros(len(ui)) RES_D = zeros(len(ui)) RES_A = zeros(len(ui)) To=273.15 rho_o=((0.001/(R*To))*1000) h2_component_params={'N_i':asarray([-6.93643,0.01,2.1101,4.52059,0.732564,-1.34086,0.130985,-0.777414,0.351944,-0.0211716,0.0226312,0.032187,-0.0231752,0.0557346]), 't_i':asarray([0.6844,1,0.989,0.489,0.803,1.1444,1.409,1.754,1.311,4.187,5.646,0.791,7.249,2.986]), 'd_i':asarray([1,4,1,1,2,2,3,1,3,2,1,3,1,1]), 'p_i':asarray([0,0,0,0,0,0,0,1,1,0/1,0/1,0/1,0/1,0/1]), 'phi_i':asarray([0,0,0,0,0,0,0,0,0,1.685,0.489,0.103,2.506,1.607]), 'Beta_i':asarray([0,0,0,0,0,0,0,0,0, 0.171,0.2245,0.1304,0.2785,0.3967]), 'gamma_i':asarray([0,0,0,0,0,0,0,0,0,0.7164,1.3444,1.4517,0.7204,1.5445]), 'D_i':asarray([0,0,0,0,0,0,0,0,0,1.506,0.156,1.736,0.67,1.6620]), 'Tc':float(33.145), 'rho_c':float(15.508*2.01594), # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel 'R':float(8.314472), 'ni':float(2.5), 'ti':float(0.0), 'vi':asarray([1.616,-0.4117,-0.792,0.758,1.217]), 'ui':asarray([531,751,1989,2484,6859]), #'R':float(8.314472) #J/mol/K 'ho':float(7206.9069892047), #J/mol 'so':float(143.4846187346), #J/mol/K 'n_power_terms':int(9), 'n_power_terms_wo_exp':int(7), 'n_power_terms_w_exp':int(2), 'n_gaussian_terms':int(5), 'n_critical_terms':int(0), 'n_ideal_gas_terms_pow':int(0), 'n_ideal_gas_terms_exp':int(5), 'RES_a':zeros(5), 'RES_b':zeros(5), 'RES_B':zeros(5), 'RES_C':zeros(5), 'RES_D':zeros(5), 'RES_A':zeros(5), 'To':float(273.15), 'rho_o':float((0.001/(8.314472*273.15))*1000), 'M_amu':float(2.01594), 'ideal_eqn_type':'Cp'} tau_v=asarray([tau,tau]) delta_v=asarray([delta,delta]) Virial_b=Virial_B_vector(tau_v,h2_component_params,h2_component_params,h2_component_params,1.0,1.0,rho_c/2.01594,Tc,'pure') #Calculate Ideal Terms ideal=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) ideal_v=ideal_helmholtz_energy_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) #print ideal-ideal_v dalpha_o=ideal_helmholtz_energy_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) dalpha_o_tau_tau_vector=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/2.01594,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) #print dalpha_o_tau_tau-dalpha_o_tau_tau_vector #Calculate Residual Terms residual=helmholtz_energy_residual(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau=d_alpha_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta=d_alpha_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) print T, Virial_b,dalpha_delta dalpha_tau_tau=d_alpha_d_tau_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_delta=d_alpha_d_delta_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_tau=d_alpha_d_delta_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) #compressibility Density<-->Pressure Z=delta*dalpha_delta+float(1.0) #Enthalpy h1=R_hydrogen*T*1.0 h2=R_hydrogen*T*tau*(dalpha_o+dalpha_tau) h3=R_hydrogen*T*delta*dalpha_delta h=h1+h2+h3 #Entropy s=R_hydrogen*(tau*dalpha_o+tau*dalpha_tau-ideal-residual) #Absolute Helmholtz Energy absolute_helmholtz_energy=R_hydrogen*T*(ideal+residual) #Isochoric heat capacity cv=-1.0*R_hydrogen*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau)) #Isobaric heat capacity cp=cv+R_hydrogen*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta) # Speed of Sound? a1 = 1 + delta*dalpha_delta - delta*tau*dalpha_delta_tau; b1 = tau*tau*(dalpha_o_tau_tau + dalpha_tau_tau); w = 1 + 2*delta*dalpha_delta + delta*delta*dalpha_delta_delta - a1*a1/b1; speed_o_sound=sqrt(R_hydrogen*T*w*1000) return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound,R_hydrogen*T*ideal,residual*R_hydrogen*T
def enthalpy_methane(T,density): from helmholtz_functions.ideal_helmholtz_energy_from_Cp_o_over_R import ideal_helmholtz_energy_from_Cp_o_over_R from helmholtz_functions.ideal_helmholtz_energy_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_from_Cp_o_over_R from helmholtz_functions.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta from helmholtz_functions.helmholtz_energy_residual import helmholtz_energy_residual from helmholtz_functions.d_alpha_d_tau_d_tau import d_alpha_d_tau_d_tau from helmholtz_functions.d_alpha_d_delta_d_delta import d_alpha_d_delta_d_delta from helmholtz_functions.d_alpha_d_delta_d_tau import d_alpha_d_delta_d_tau from helmholtz_functions.ideal_helmholtz_energy_from_Cp_o_over_R_vector import ideal_helmholtz_energy_from_Cp_o_over_R_vector from helmholtz_functions.ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector import ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector from helmholtz_functions.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector from thermodynamic_functions.Virial_B_vector import Virial_B_vector from math import sqrt from pylab import zeros from numpy import asarray N_i=[0.43679010280e-01, 0.67092361990, -0.17655778590e01, 0.85823302410, -0.12065130520e01, 0.51204672200, -0.40000107910e-03 , -0.12478424230e-01, 0.31002697010e-01, 0.17547485220e-02, -0.31719216050e-05, -0.22403468400e-05, 0.29470561560e-06, 0.18304879090, 0.15118836790, -0.42893638770, 0.68940024460e-01, -0.14083139960e-01, -0.30630548300e-01, -0.29699067080e-01, -0.19320408310e-01, -0.11057399590, 0.99525489950e-01, 0.85484378250e-02, -0.61505556620e-01, -0.42917924230e-01, -0.18132072900e-01, 0.34459047600e-01, -0.23859194500e-02, -0.11590949390e-01, 0.66416936020e-01, -0.23715495900e-01, -0.39616249050e-01, -0.13872920440e-01, 0.33894895990e-01, -0.29273787530e-02, 0.93247999460e-04, -0.62871715180e01, 0.12710694670e02, -0.64239534660e01] t_i= [-0.5, 0.5, 1.0, 0.5, 1.0, 1.5, 4.5, 0.0, 1.0, 3.0, 1.0, 3.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 2.0, 2.0, 5.0, 5.0, 5.0, 2.0, 4.0, 12.0, 8.0, 10.0, 10.0, 10.0, 14.0, 12.0, 18.0, 22.0, 18.0, 14.0, 2.0, 0.0, 1.0, 2.0] d_i=[1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 4.0, 4.0, 8.0, 9.0, 10.0, 1.0, 1.0, 1.0, 2.0, 4.0, 5.0, 6.0, 1.0, 2.0, 3.0, 4.0, 4.0, 3.0, 5.0, 5.0, 8.0, 2.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 2.0, 0.0, 0.0, 0.0] p_i=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 0/1, 0/1, 0/1, 0/1] phi_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20.0,40.0,40.0,40.0]# Not, we need to use -sign here Beta_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,200,250,250,250] #Note, we need to use - sign here gamma_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.07,1.11,1.11,1.11] D_i=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.0,1.0,1.0,1.0] Tc=190.564 rho_c=10.139128*16.0428 # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel delta=density/rho_c tau=Tc/T R=8.31451 R_methane=R/16.0428 ni=4.0016 ti=0 vi=[0.84490000e-02,4.6942000,3.4865000,1.6572000,1.4115000] ui=[648.0,1957.0,3895.0,5705.0,15080.0] R=8.31451 #J/mol/K ho = 8295.6883966242294 #J/mol - - so = 28.384819963016852 #J/mol/K rho_o=26.326811491312679 #mol/L To=111.66720547358069 n_power_terms=36 n_gaussian_terms=4 n_critical_terms=0 n_ideal_gas_terms_pow=0 n_ideal_gas_terms_exp=5 RES_a = zeros(len(ui)) RES_b = zeros(len(ui)) RES_B = zeros(len(ui)) RES_C = zeros(len(ui)) RES_D = zeros(len(ui)) RES_A = zeros(len(ui)) ch4_component_params={'N_i':asarray([0.43679010280e-01,0.67092361990, -0.17655778590e01, 0.85823302410, -0.12065130520e01,0.51204672200, -0.40000107910e-03 ,-0.12478424230e-01,0.31002697010e-01,0.17547485220e-02,-0.31719216050e-05,-0.22403468400e-05,0.29470561560e-06,0.18304879090, 0.15118836790,-0.42893638770,0.68940024460e-01,-0.14083139960e-01,-0.30630548300e-01,-0.29699067080e-01,-0.19320408310e-01,-0.11057399590,0.99525489950e-01,0.85484378250e-02, -0.61505556620e-01,-0.42917924230e-01,-0.18132072900e-01,0.34459047600e-01,-0.23859194500e-02,-0.11590949390e-01,0.66416936020e-01,-0.23715495900e-01, -0.39616249050e-01, -0.13872920440e-01,0.33894895990e-01,-0.29273787530e-02,0.93247999460e-04,-0.62871715180e+01,0.12710694670e+02,-0.64239534660e+01]), 't_i':asarray([-0.5, 0.5,1.0,0.5,1.0,1.5,4.5,0.0,1.0,3.0,1.0,3.0,3.0,0.0,1.0,2.0,0.0,0.0,2.0,2.0,5.0,5.0,5.0,2.0,4.0,12.0,8.0,10.0,10.0,10.0,14.0,12.0,18.0,22.0,18.0,14.0,2.0,0.0,1.0,2.0]), 'd_i':asarray([1.0,1.0,1.0,2.0,2.0,2.0,2.0,3.0,4.0,4.0,8.0,9.0,10.0,1.0,1.0,1.0,2.0,4.0,5.0,6.0,1.0,2.0,3.0,4.0,4.0,3.0,5.0,5.0,8.0,2.0,3.0,4.0,4.0,4.0,5.0,6.0,2.0,0.0,0.0,0.0]), 'p_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,2,2,2,2]), 'phi_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20.0,40.0,40.0,40.0]), 'Beta_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,200,250,250,250]), 'gamma_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.07,1.11,1.11,1.11]), 'D_i':asarray([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1]), 'Tc':float(190.564), 'rho_c':float(10.139128*16.0428), # mol/l -> kg/m^3 factors of 1000 liter converstion, and gram conversion cancel 'R':float(8.31451), 'ni':float(4.0016), 'ti':float(0.0), 'vi':asarray([0.84490000e-02,4.6942000,3.4865000,1.6572000,1.4115000]), 'ui':asarray([648.0,1957.0,3895.0,5705.0,15080.0]), #'R':float(8.314472) #J/mol/K 'ho':float(8295.6883966242294), #J/mol 'so':float(28.384819963016852), #J/mol/K 'n_power_terms':int(36), 'n_power_terms_wo_exp':int(13), 'n_power_terms_w_exp':int(36-13), 'n_gaussian_terms':int(4), 'n_critical_terms':int(0), 'n_ideal_gas_terms_pow':int(0), 'n_ideal_gas_terms_exp':int(5), 'RES_a':zeros(4), 'RES_b':zeros(4), 'RES_B':zeros(4), 'RES_C':zeros(4), 'RES_D':zeros(4), 'RES_A':zeros(4), 'To':float(111.66720547358069), 'rho_o':float(26.326811491312679), 'M_amu':float(16.0428), 'ideal_eqn_type':'Cp'} tau_v=asarray([tau,tau]) delta_v=asarray([delta,delta]) Virial_b=Virial_B_vector(tau_v,ch4_component_params,ch4_component_params,ch4_component_params,1.0,1.0,rho_c/16.0428,Tc,'pure') #Calculate Ideal Terms ideal=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) ideal_v=ideal_helmholtz_energy_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) #print ideal-ideal_v dalpha_o=ideal_helmholtz_energy_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) dalpha_o_v=ideal_helmholtz_energy_dtau_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) print dalpha_o-dalpha_o_v dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau,delta,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) dalpha_o_tau_tau_vector=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R_vector(ni,ti,vi,ui,R,ho,so,rho_c/16.0428,Tc,tau_v,delta_v,n_ideal_gas_terms_pow,n_ideal_gas_terms_exp,To,rho_o) #print dalpha_o_tau_tau-dalpha_o_tau_tau_vector #Calculate Residual Terms residual=helmholtz_energy_residual(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau=d_alpha_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta=d_alpha_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau_tau=d_alpha_d_tau_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_delta=d_alpha_d_delta_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_tau=d_alpha_d_delta_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) #compressibility Density<-->Pressure Z=delta*dalpha_delta+float(1.0) #Enthalpy h1=R_methane*T*1.0 h2=R_methane*T*tau*(dalpha_o+dalpha_tau) h3=R_methane*T*delta*dalpha_delta h=h1+h2+h3 #Entropy s=R_methane*(tau*dalpha_o+tau*dalpha_tau-ideal-residual) #Absolute Helmholtz Energy absolute_helmholtz_energy=R_methane*T*(ideal+residual) #Isochoric heat capacity cv=-1.0*R_methane*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau)) #Isobaric heat capacity cp=cv+R_methane*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta) # Speed of Sound? a1 = 1 + delta*dalpha_delta - delta*tau*dalpha_delta_tau; b1 = tau*tau*(dalpha_o_tau_tau + dalpha_tau_tau); w = 1 + 2*delta*dalpha_delta + delta*delta*dalpha_delta_delta - a1*a1/b1; speed_o_sound=sqrt(R_methane*T*w*1000) return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound,R_methane*T*ideal,residual*R_methane*T
def enthalpy_helium(T,density): from math import sqrt,exp from numpy import sort,asarray,shape,concatenate,power from helmholtz_functions.ideal_helmholtz_energy_from_Cp_o_over_R import ideal_helmholtz_energy_from_Cp_o_over_R from helmholtz_functions.ideal_helmholtz_energy_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_from_Cp_o_over_R from helmholtz_functions.ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R import ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R from helmholtz_functions.mBWR_to_Helmholtz import mBWR_to_Helmholtz from helmholtz_functions.helmholtz_energy_residual import helmholtz_energy_residual from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau from helmholtz_functions.d_alpha_d_tau_d_tau import d_alpha_d_tau_d_tau from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta from helmholtz_functions.d_alpha_d_delta_d_delta import d_alpha_d_delta_d_delta from helmholtz_functions.d_alpha_d_delta_d_tau import d_alpha_d_delta_d_tau M_He=4.0026#02 g/mol R=8.314310 # R_He=R/M_He To=4.230359714841141 #Kelvin rho_o=31.163394763964778 # mol/L ho=108.78863197310453 # J/mol so=3.6929233790579463 # J/mol/K Tc=5.19530# Kelvin rho_c=17.3990 #(mol/L) mBWR_Coef=[0.4558980227431e-4,#1 0.1260692007853e-2,#2 -0.7139657549318e-2,#3 0.9728903861441e-2,#4 -0.1589302471562e-1,#5 0.1454229259623e-5,#6 -0.4708238429298e-4,#7 0.1132915232587e-2,#8 0.2410763742104e-2,#9 -0.5093547838381e-8,#10 0.2699726927900e-5,#11 -0.3954146691114e-4,#12` 0.1551961438127e-8,#13 0.1050712335785e-7,#14 -0.5501158366750e-7,#15 -0.1037673478521e-9,#16 0.6446881346448e-12,#17 0.3298960057071e-10,#18 -0.3555585738784e-12,#19 -0.6885401367690e-2,#20 0.9166109232806e-2,#21 -0.6544314242937e-5,#22 -0.3315398880031e-4,#23 -0.2067693644676e-7,#24 0.3850153114958e-7,#25 -0.1399040626999e-10,#26 -0.1888462892389e-11,#27 -0.4595138561035e-14,#28 0.6872567403738e-14,#29 -0.6097223119177e-18,#30 -0.7636186157005e-17,#31 0.3848665703556e-17]#32 rho=density/M_He #mol/L # delta=rho/rho_c # tau=Tc/T # tau_o=Tc/To # delta_o=rho_o/rho_c ni=2.5 ti=0.0 vi=[0.0] ui=[0.0] npower=1 n_exp=0 tau=Tc/T delta=rho/rho_c n_power=1 #phi_o=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o) #N=mBWR_Coef #abwr=ABWR(N,T,rho,rho_c) #residual=abwr/(R*T) [N_i,d_i,t_i,p_i]=mBWR_to_Helmholtz(mBWR_Coef,T,rho,rho_c,Tc,R) #print shape(sorted_array) #print d_i #print t_i #N_i=sorted_array[3,:] #d_i=sorted_array[2,:] #t_i=sorted_array[1,:] #p_i=sorted_array[0,:] #print 'heres p_i',p_i,p_ii Beta_i=0 gamma_i=0 D_i=0 n_power_terms=len(N_i) n_gaussian_terms=0 n_critical_terms=0 RES_a=0 RES_b=0 RES_B=0 RES_C=0 RES_D=0 RES_A=0 phi_i=0 #residual2=helmholtz_energy_residual(tau,delta,ni,ti,di,pi,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) #helmholtz=residual2#-residual#residual2#(ideal+residual)/M_He#(ideal+residual)/M_He #print residual,residual2 #Calculate Ideal Terms ideal=ideal_helmholtz_energy_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o) dalpha_o=ideal_helmholtz_energy_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o) dalpha_o_tau_tau=ideal_helmholtz_energy_dtau_dtau_from_Cp_o_over_R(ni,ti,vi,ui,R,ho,so,rho_c,Tc,tau,delta,n_power,n_exp,To,rho_o) #Calculate Residual Terms residual=helmholtz_energy_residual(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau=d_alpha_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta=d_alpha_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau_tau=d_alpha_d_tau_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_delta=d_alpha_d_delta_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_tau=d_alpha_d_delta_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) #compressibility Density<-->Pressure Z=delta*dalpha_delta+float(1.0) #Enthalpy h1=R_He*T*1.0 h2=R_He*T*tau*(dalpha_o+dalpha_tau) h3=R_He*T*delta*dalpha_delta h=h1+h2+h3 #Entropy s=R_He*(tau*dalpha_o+tau*dalpha_tau-ideal-residual) #Absolute Helmholtz Energy absolute_helmholtz_energy=R_He*T*(ideal+residual) #Isochoric heat capacity cv=-1.0*R_He*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau)) #Isobaric heat capacity cp=cv+R_He*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta) # Speed of Sound? a1 = 1 + delta*dalpha_delta - delta*tau*dalpha_delta_tau; b1 = tau*tau*(dalpha_o_tau_tau + dalpha_tau_tau); w = 1 + 2*delta*dalpha_delta + delta*delta*dalpha_delta_delta - a1*a1/b1; speed_o_sound=power(R_He*T*w*1000,0.5) return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound,ideal,residual
def enthalpy_h2o(T,density): from helmholtz_functions.ideal_helmholtz_from_coef import ideal_helmholtz_from_coef from helmholtz_functions.ideal_helmholtz_from_coef_dtau import ideal_helmholtz_from_coef_dtau from helmholtz_functions.ideal_helmholtz_from_coef_dtau_dtau import ideal_helmholtz_from_coef_dtau_dtau from helmholtz_functions.d_alpha_d_tau import d_alpha_d_tau from helmholtz_functions.d_alpha_d_delta import d_alpha_d_delta from helmholtz_functions.helmholtz_energy_residual import helmholtz_energy_residual from helmholtz_functions.d_alpha_d_tau_d_tau import d_alpha_d_tau_d_tau from helmholtz_functions.d_alpha_d_delta_d_delta import d_alpha_d_delta_d_delta from helmholtz_functions.d_alpha_d_delta_d_tau import d_alpha_d_delta_d_tau from helmholtz_functions.d_alpha_d_tau_vector import d_alpha_d_tau_vector from helmholtz_functions.d_alpha_d_delta_vector import d_alpha_d_delta_vector from helmholtz_functions.ideal_helmholtz_from_coef_dtau_vector import ideal_helmholtz_from_coef_dtau_vector from thermodynamic_functions.enthalpy_vector import enthalpy_vector from helmholtz_functions.d_alpha_d_delta_d_delta_vector import d_alpha_d_delta_d_delta_vector from helmholtz_functions.d_alpha_d_delta_vector import d_alpha_d_delta_vector from helmholtz_functions.d_alpha_d_tau_d_tau_vector import d_alpha_d_tau_d_tau_vector from helmholtz_functions.d_alpha_d_delta_d_tau_vector import d_alpha_d_delta_d_tau_vector from helmholtz_functions.ideal_helmholtz_from_coef_vector import ideal_helmholtz_from_coef_vector from helmholtz_functions.ideal_helmholtz_from_coef_dtau_dtau_vector import ideal_helmholtz_from_coef_dtau_dtau_vector from helmholtz_functions.helmholtz_energy_residual_vector import helmholtz_energy_residual_vector from pylab import zeros from math import sqrt from numpy import asarray N_i=[0.12533547935523E-1,0.78957634722828E1, -0.87803203303561E1, 0.31802509345418, -0.26145533859358, -0.78199751687981E-2, 0.88089493102134E-2, -0.66856572307965, 0.20433810950965, -0.66212605039687E-4, -0.19232721156002, -0.25709043003438, 0.16074868486251, -0.40092828925807E-1, 0.39343422603254E-6, -0.75941377088144E-5, 0.56250979351888E-3, -0.15608652257135E-4, 0.11537996422951E-8, 0.36582165144204E-6, -0.13251180074668E-11, -0.62639586912454E-9, -0.10793600908932, 0.17611491008752E-1, 0.22132295167546, -0.40247669763528, 0.58083399985759, 0.49969146990806E-2, -0.31358700712549E-1, -0.74315929710341, 0.47807329915480, 0.20527940895948E-1, -0.13636435110343, 0.14180634400617E-1, 0.83326504880713E-2, -0.29052336009585E-1, 0.38615085574206E-1, -0.20393486513704E-1, -0.16554050063734E-2, 0.19955571979541E-2, 0.15870308324157E-3, -0.16388568342530E-4, 0.43613615723811E-1, 0.34994005463765E-1, -0.76788197844621E-1, 0.22446277332006E-1, -0.62689710414685E-4, -0.55711118565645E-9, -0.19905718354408, 0.31777497330738, -0.11841182425981, -0.31306260323435e2, 0.31546140237781e2, -0.25213154341695e4, -0.14874640856724, 0.31806110878444] t_i=[-0.5, 0.875, 1.0, 0.5, 0.75, 0.375, 1.0, 4.0, 6.0, 12.0, 1.0, 5.0, 4.0 , 2.0, 13.0, 9.0 , 3.0 , 4.0, 11.0, 4.0, 13.0, 1.0, 7.0, 1.0 , 9.0, 10.0, 10.0 , 3.0 , 7.0, 10.0, 10.0, 6.0, 10.0, 10.0, 1.0 , 2.0, 3.0, 4.0 , 8.0 , 6.0, 9.0, 8.0, 16.0, 22.0, 23.0,23.0 , 10.0, 50.0, 44.0, 46.0 , 50.0, 0.0, 1.0, 4.0] d_i=[1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0, 1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0, 4.0, 5.0, 7.0, 9.0, 10.0, 11.0, 13.0, 15.0, 1.0, 2.0, 2.0, 2.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 6.0, 7.0, 9.0, 9.0, 9.0, 9.0, 9.0, 10.0, 10.0, 12.0, 3.0, 4.0, 4.0, 5.0, 14.0, 3.0, 6.0, 6.0, 6.0, 3.0, 3.0, 3.0] p_i=[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 6.0, 6.0, 6.0, 6.0] phi_i=zeros(51+3) phi_i[51]=20.0 # Note, we need to use -sign here phi_i[52]=20.0 # Note, we need to use -sign here phi_i[53]=20.0 # Note, we need to use -sign here Beta_i=zeros(51+5) Beta_i[51]=150.0 #Note, we need to use - sign here Beta_i[52]=150.0 #Note, we need to use - sign here Beta_i[53]=250.0 #Note, we need to use - sign here Beta_i[54]=0.3 #Note, we need to use - sign here Beta_i[55]=0.3 #Note, we need to use - sign here gamma_i=zeros(len(p_i)+3) gamma_i[51]=1.21 gamma_i[52]=1.21 gamma_i[53]=1.25 D_i=zeros(51+3) D_i[51]=1.0 D_i[52]=1.0 D_i[53]=1.0 R=8.314472 Tc = 647.096 #K rho_c =322.0#18.015268*17.8737279956 #322.000214485 #kg m^-3 #mol/liter 17.8737279956 R_h2o = 0.46151805#R/18.015268# #kJ kg^-1 K^-1 delta=density/rho_c tau=Tc/T ideal_n = [-8.32044648201,6.6832105268,3.00632,0.012436,0.97315,1.27950,0.96956,0.24873] ideal_gamma = [0.0,0.0,0.0,1.28728967,3.53734222,7.74073708,9.24437796,27.5075105] n_power_terms=51#len(p_i) n_gaussian_terms=3 n_critical_terms=2 #print delta,tau #critcal terms RES_a=zeros(len(p_i)+5) RES_b=zeros(len(p_i)+5) RES_B=zeros(len(p_i)+5) RES_C=zeros(len(p_i)+5) RES_D=zeros(len(p_i)+5) RES_A=zeros(len(p_i)+5) RES_a[54]=3.5 RES_a[55]=3.5 RES_b[54]=0.85 RES_b[55]=0.95 RES_B[54]=0.2 RES_B[55]=0.2 RES_C[54]=28.0 RES_C[55]=32.0 RES_D[54]=700.0 RES_D[55]=800.0 RES_A[54]=0.32 RES_A[55]=0.32 h2o_component_params={'N_i':asarray([0.12533547935523E-1,0.78957634722828E1, -0.87803203303561E1,0.31802509345418, -0.26145533859358, -0.78199751687981E-2,0.88089493102134E-2, -0.66856572307965,0.20433810950965,-0.66212605039687E-4,-0.19232721156002,-0.25709043003438,0.16074868486251,-0.40092828925807E-1,0.39343422603254E-6, -0.75941377088144E-5,0.56250979351888E-3, -0.15608652257135E-4,0.11537996422951E-8, 0.36582165144204E-6, -0.13251180074668E-11,-0.62639586912454E-9, -0.10793600908932, 0.17611491008752E-1, 0.22132295167546, -0.40247669763528,0.58083399985759, 0.49969146990806E-2, -0.31358700712549E-1,-0.74315929710341,0.47807329915480, 0.20527940895948E-1,-0.13636435110343, 0.14180634400617E-1, 0.83326504880713E-2, -0.29052336009585E-1,0.38615085574206E-1, -0.20393486513704E-1,-0.16554050063734E-2,0.19955571979541E-2, 0.15870308324157E-3, -0.16388568342530E-4, 0.43613615723811E-1, 0.34994005463765E-1, -0.76788197844621E-1,0.22446277332006E-1, -0.62689710414685E-4,-0.55711118565645E-9,-0.19905718354408, 0.31777497330738,-0.11841182425981,-0.31306260323435e2,0.31546140237781e2,-0.25213154341695e4,-0.14874640856724,0.31806110878444]), 't_i':asarray([-0.5, 0.875, 1.0, 0.5, 0.75, 0.375, 1.0, 4.0, 6.0, 12.0, 1.0, 5.0, 4.0 , 2.0, 13.0, 9.0 , 3.0 , 4.0, 11.0, 4.0, 13.0, 1.0, 7.0, 1.0 , 9.0, 10.0, 10.0 , 3.0 , 7.0, 10.0, 10.0, 6.0, 10.0, 10.0, 1.0 , 2.0, 3.0, 4.0 , 8.0 , 6.0, 9.0, 8.0, 16.0, 22.0, 23.0,23.0 , 10.0, 50.0, 44.0, 46.0 , 50.0, 0.0, 1.0, 4.0]), 'd_i':asarray([1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0, 1.0, 1.0, 1.0, 2.0, 2.0, 3.0, 4.0, 4.0, 5.0, 7.0, 9.0, 10.0, 11.0, 13.0, 15.0, 1.0, 2.0, 2.0, 2.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 6.0, 7.0, 9.0, 9.0, 9.0, 9.0, 9.0, 10.0, 10.0, 12.0, 3.0, 4.0, 4.0, 5.0, 14.0, 3.0, 6.0, 6.0, 6.0, 3.0, 3.0, 3.0]), 'p_i':asarray([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 6.0, 6.0, 6.0, 6.0]), 'phi_i':phi_i, 'Beta_i':Beta_i, 'gamma_i':gamma_i, 'D_i':D_i, 'R':float(8.314472), 'Tc':float(647.096), #K 'rho_c':float(322.0),#18.015268*17.8737279956 #322.000214485 #kg m^-3 #mol/liter 17.8737279956 'M_amu':float(8.314472/0.46151805), 'ideal_n': asarray([-8.32044648201,6.6832105268,3.00632,0.012436,0.97315,1.27950,0.96956,0.24873]), 'ideal_gamma':asarray([0.0,0.0,0.0,1.28728967,3.53734222,7.74073708,9.24437796,27.5075105]), 'n_power_terms':int(51),#len(p_i) 'n_power_terms_wo_exp':int(7), 'n_power_terms_w_exp':int(51-7), 'n_gaussian_terms':int(3), 'n_critical_terms':int(2), 'RES_a':RES_a, 'RES_b':RES_b, 'RES_B':RES_B, 'RES_C':RES_C, 'RES_D':RES_D, 'RES_A':RES_A, 'ni':int(0), 'ti':int(0), 'vi':int(0), 'ui':int(0), 'ho':int(0), 'so':int(0), 'n_ideal_gas_terms_pow':int(0), 'n_ideal_gas_terms_exp':int(0), 'To':int(0), 'Po':int(0), 'rho_o':int(0), 'ideal_eqn_type':'Coef'} #Calculate Ideal Terms delta_v=asarray([delta,delta,delta]) tau_v=asarray([tau,tau,tau]) ideal=ideal_helmholtz_from_coef(delta,tau,ideal_n,ideal_gamma) ideal_v=ideal_helmholtz_from_coef_vector(delta_v,tau_v,h2o_component_params['ideal_n'],h2o_component_params['ideal_gamma']) #print ideal-ideal_v dalpha_o=ideal_helmholtz_from_coef_dtau(delta,tau,ideal_n,ideal_gamma) dalpha_o_vector=ideal_helmholtz_from_coef_dtau_vector(delta_v,tau_v,h2o_component_params['ideal_n'],h2o_component_params['ideal_gamma']) #print dalpha_o-dalpha_o_vector dalpha_o_tau_tau=ideal_helmholtz_from_coef_dtau_dtau(delta,tau,ideal_n,ideal_gamma) dalpha_o_tau_tau_v=ideal_helmholtz_from_coef_dtau_dtau_vector(delta_v,tau_v,h2o_component_params['ideal_n'],h2o_component_params['ideal_gamma']) #print dalpha_o_tau_tau-dalpha_o_tau_tau_v #Calculate Residual Terms residual=helmholtz_energy_residual(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) residual_v=helmholtz_energy_residual_vector(tau_v,delta_v,h2o_component_params) print residual-residual_v dalpha_tau=d_alpha_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau_vector=d_alpha_d_tau_vector(tau_v,delta_v,h2o_component_params) #print dalpha_tau-dalpha_tau_vector dalpha_delta=d_alpha_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_vector=d_alpha_d_delta_vector(tau_v,delta_v,h2o_component_params) #print dalpha_delta_vector-dalpha_delta dalpha_tau_tau=d_alpha_d_tau_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_tau_tau_vector=d_alpha_d_tau_d_tau_vector(tau_v,delta_v,h2o_component_params) #print dalpha_tau_tau-dalpha_tau_tau_vector dalpha_delta_delta=d_alpha_d_delta_d_delta(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_delta_vector=d_alpha_d_delta_d_delta_vector(tau_v,delta_v,h2o_component_params) #print T, dalpha_delta_delta-dalpha_delta_delta_vector # print dalpha_delta_delta dalpha_delta_tau=d_alpha_d_delta_d_tau(tau,delta,N_i,t_i,d_i,p_i,phi_i,Beta_i,gamma_i,D_i,n_power_terms,n_gaussian_terms,n_critical_terms,RES_a,RES_b,RES_B,RES_C,RES_D,RES_A) dalpha_delta_tau_vector=d_alpha_d_delta_d_tau_vector(tau_v,delta_v,h2o_component_params) #print dalpha_delta_tau_vector-dalpha_delta_tau #compressibility Density<-->Pressure Z=delta*dalpha_delta+float(1.0) #Enthalpy h1=R_h2o*T*1.0 h2=R_h2o*T*tau*(dalpha_o+dalpha_tau) h3=R_h2o*T*delta*dalpha_delta h=h1+h2+h3 h_v=enthalpy_vector(tau_v,delta_v,Tc,rho_c,'pure_substance',h2o_component_params,h2o_component_params,h2o_component_params,0,0) #print dalpha_o,dalpha_o_vector #print h,R_h2o*T*h_v #Entropy s=R_h2o*(tau*dalpha_o+tau*dalpha_tau-ideal-residual) #Absolute Helmholtz Energy absolute_helmholtz_energy=R_h2o*T*(ideal+residual) #Isochoric heat capacity cv=-1.0*R_h2o*(tau*tau*(dalpha_o_tau_tau+dalpha_tau_tau)) #Isobaric heat capacity cp=cv+R_h2o*pow((1.0+delta*dalpha_delta-delta*tau*dalpha_delta_tau),2)/(1.0+2.0*delta*dalpha_delta+delta*delta*dalpha_delta_delta) #print dalpha_delta,dalpha_delta_delta,dalpha_delta_tau,dalpha_tau_tau # Speed of Sound? #print dalpha_delta_delta,dalpha_delta_tau #speed_o_sound_p1 = 1.0 + 2.0*delta*dalpha_delta + delta*delta*dalpha_delta_delta #speed_o_sound_p2 = pow((1.0 + delta*dalpha_delta - delta*tau*dalpha_delta_tau),2) #speed_o_sound_p3 = tau*tau*(dalpha_o_tau_tau + dalpha_tau_tau) #speed_o_sound= sqrt((R_h2o*T)*(speed_o_sound_p1 - speed_o_sound_p2/speed_o_sound_p3)*1000.0) #what it's probably not #d_tau_tau #d_delta #d_o_tau_tau a1 = 1 + delta*dalpha_delta - delta*tau*dalpha_delta_tau; b1 = tau*tau*(dalpha_o_tau_tau + dalpha_tau_tau); w = 1 + 2*delta*dalpha_delta + delta*delta*dalpha_delta_delta - a1*a1/b1; speed_o_sound=sqrt(R_h2o*T*w*1000) return Z,h,s,absolute_helmholtz_energy,cv,cp,speed_o_sound