CoolProp
Static Public Member Functions | List of all members
CoolProp::TransportRoutines Class Reference

Static Public Member Functions

static CoolPropDbl viscosity_dilute_kinetic_theory (HelmholtzEOSMixtureBackend &HEOS)
 The general dilute gas viscosity from used for ECS. More...
 
static CoolPropDbl viscosity_dilute_collision_integral (HelmholtzEOSMixtureBackend &HEOS)
 The dilute gas viscosity term that is based on collision integral or effective cross section. More...
 
static CoolPropDbl viscosity_dilute_powers_of_T (HelmholtzEOSMixtureBackend &HEOS)
 A dilute gas viscosity term formed of summation of power terms. More...
 
static CoolPropDbl viscosity_dilute_powers_of_Tr (HelmholtzEOSMixtureBackend &HEOS)
 A dilute gas viscosity term formed of summation of power terms of the reduced temperature. More...
 
static CoolPropDbl viscosity_dilute_collision_integral_powers_of_T (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_initial_density_dependence_Rainwater_Friend (HelmholtzEOSMixtureBackend &HEOS)
 The initial density dependence term \(B_{\eta}\) from Rainwater-Friend theory. More...
 
static CoolPropDbl viscosity_initial_density_dependence_empirical (HelmholtzEOSMixtureBackend &HEOS)
 An empirical form for the initial density dependence. More...
 
static CoolPropDbl viscosity_higher_order_modified_Batschinski_Hildebrand (HelmholtzEOSMixtureBackend &HEOS)
 The modified Batschinski-Hildebrand contribution to the viscosity. More...
 
static CoolPropDbl viscosity_dilute_ethane (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_dilute_cyclohexane (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_methanol_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 Viscosity hardcoded for Methanol. More...
 
static CoolPropDbl viscosity_heavywater_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_water_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_helium_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_R23_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_m_xylene_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_o_xylene_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_p_xylene_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_toluene_higher_order_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_ethane_higher_order_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_hydrogen_higher_order_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_benzene_higher_order_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_hexane_higher_order_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_heptane_higher_order_hardcoded (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_higher_order_friction_theory (HelmholtzEOSMixtureBackend &HEOS)
 Higher-order viscosity term from friction theory of Sergio Quinones-Cisneros. More...
 
static CoolPropDbl viscosity_Chung (HelmholtzEOSMixtureBackend &HEOS)
 Implement the method of: More...
 
static CoolPropDbl conductivity_dilute_ratio_polynomials (HelmholtzEOSMixtureBackend &HEOS)
 The general dilute gas conductivity term formed of a ratio of polynomial like terms. More...
 
static CoolPropDbl conductivity_residual_polynomial (HelmholtzEOSMixtureBackend &HEOS)
 This term is given by

\[ \Delta\lambda(\rho,T) = \displaystyle\sum_iA_i\tau^{t,i}\delta^{d_i} \]

. More...

 
static CoolPropDbl conductivity_critical_simplified_Olchowy_Sengers (HelmholtzEOSMixtureBackend &HEOS)
 The simplified critical conductivity term of Olchowy and Sengers. More...
 
static CoolPropDbl conductivity_critical_hardcoded_CO2_ScalabrinJPCRD2006 (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_critical_hardcoded_R123 (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_dilute_hardcoded_CO2 (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_dilute_hardcoded_ethane (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_dilute_eta0_and_poly (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_residual_polynomial_and_exponential (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_hardcoded_heavywater (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_hardcoded_water (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_hardcoded_R23 (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_hardcoded_helium (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_hardcoded_methane (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_critical_hardcoded_ammonia (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl viscosity_ECS (HelmholtzEOSMixtureBackend &HEOS, HelmholtzEOSMixtureBackend &HEOS_Reference)
 Calculate the viscosity using the extended corresponding states method. More...
 
static CoolPropDbl viscosity_rhosr (HelmholtzEOSMixtureBackend &HEOS)
 
static CoolPropDbl conductivity_ECS (HelmholtzEOSMixtureBackend &HEOS, HelmholtzEOSMixtureBackend &HEOS_Reference)
 
static void conformal_state_solver (HelmholtzEOSMixtureBackend &HEOS, HelmholtzEOSMixtureBackend &HEOS_Reference, CoolPropDbl &T0, CoolPropDbl &rhomolar0)
 

Member Function Documentation

§ conductivity_critical_simplified_Olchowy_Sengers()

CoolPropDbl CoolProp::TransportRoutines::conductivity_critical_simplified_Olchowy_Sengers ( HelmholtzEOSMixtureBackend HEOS)
static

The simplified critical conductivity term of Olchowy and Sengers.

Olchowy, G. A. & Sengers, J. V. (1989), "A Simplified Representation for the Thermal Conductivity of Fluids in the Critical Region", International Journal of Thermophysics, 10, (2), 417-426

\[ \lambda^{(c)} = \frac{\rho c_p R_DkT}{6\pi\eta\zeta}(\Omega-\Omega_0) \]

\[ \Omega = \frac{2}{\pi}\left[ \left( \frac{c_p-c_v}{c_p}\right)\arctan(q_d\zeta)+\frac{c_v}{c_p}q_d\zeta \right] \]

\[ \Omega_0 = \frac{2}{\pi}\left[1-\exp\left(-\frac{1}{(q_d\zeta)^{-1}+(q_d\zeta\rho_c/\rho)^2/3} \right) \right] \]

\[ \zeta = \zeta_0\left(\frac{p_c\rho}{\Gamma\rho_c^2}\right)^{\nu/\gamma}\left[\left.\frac{\partial \rho(T,\rho)}{\partial p} \right|_{T}- \frac{T_R}{T}\left.\frac{\partial \rho(T_R,\rho)}{\partial p} \right|_{T} \right]^{\nu/\gamma}, \]

where \(\lambda^{(c)}\) is in W \(\cdot\)m \(^{-1}\) \(\cdot\)K \(^{-1}\), \(\zeta\) is in m, \(c_p\) and \(c_v\) are in J \(\cdot\)kg \(^{-1}\cdot\)K \(^{-1}\), \(p\) and \(p_c\) are in Pa, \(\rho\) and \(\rho_c\) are in mol \(\cdot\)m \(^{-3}\), \(\eta\) is the viscosity in Pa \(\cdot\)s, and the remaining parameters are defined in the following tables.

It should be noted that some authors use slightly different values for the "universal" constants

Coefficients for use in the simplified Olchowy-Sengers critical term

Parameter Variable Value
Boltzmann constant \(k\) \(1.3806488\times 10^{-23}\) J \(\cdot\)K \(^{-1}\)
Universal amplitude \(R_D\) 1.03
Critical exponent \(\nu\) 0.63
Critical exponent \(\gamma\) 1.239
Reference temperature \(T_R\) 1.5 \(T_c\)

Recommended default constants (see Huber (I&ECR, 2003))

Parameter Variable Value
Amplitude \(\Gamma\) 0.0496
Amplitude \(\zeta_0\) 1.94 \(\times\) 10 \(^{-10}\) m
Effective cutoff \(q_d\) 2 \(\times\) 10 \(^{9}\) m

§ conductivity_dilute_ratio_polynomials()

CoolPropDbl CoolProp::TransportRoutines::conductivity_dilute_ratio_polynomials ( HelmholtzEOSMixtureBackend HEOS)
static

The general dilute gas conductivity term formed of a ratio of polynomial like terms.

\[ \lambda^0 = \frac{A_i\displaystyle\sum_iT_r^{n_i}}{B_i\displaystyle\sum_iT_r^{m_i}} \]

with \(\lambda^0\) in W/m/K, T_r is the reduced temperature \(T_{r} = T/T_{red}\)

§ conductivity_hardcoded_helium()

CoolPropDbl CoolProp::TransportRoutines::conductivity_hardcoded_helium ( HelmholtzEOSMixtureBackend HEOS)
static

dh/dx derived using sympy:

E1,x,x0,E2,beta,gamma = symbols('E1,x,x0,E2,beta,gamma')
h = E1*(1 + x/x0)*pow(1 + E2*pow(1 + x/x0, 2/beta), (gamma-1)/(2*beta))
ccode(simplify(diff(h,x)))

§ conductivity_residual_polynomial()

CoolPropDbl CoolProp::TransportRoutines::conductivity_residual_polynomial ( HelmholtzEOSMixtureBackend HEOS)
static

This term is given by

\[ \Delta\lambda(\rho,T) = \displaystyle\sum_iA_i\tau^{t,i}\delta^{d_i} \]

.

As used by Assael, Perkins, Huber, etc., the residual term is given by

\[ \Delta\lambda(\rho,T) = \displaystyle\sum_i(B_{1,i}+B_{2,i}(T/T_c))(\rho/\rho_c)^i \]

which can be easily converted by noting that \(\tau=Tc/T\) and \(\delta=\rho/\rho_c\)

§ viscosity_Chung()

CoolPropDbl CoolProp::TransportRoutines::viscosity_Chung ( HelmholtzEOSMixtureBackend HEOS)
static

Implement the method of:

Chung, Ting Horng, et al. "Generalized multiparameter correlation for nonpolar and polar fluid transport properties." Industrial & engineering chemistry research 27(4) (1988): 671-679.

§ viscosity_dilute_collision_integral()

CoolPropDbl CoolProp::TransportRoutines::viscosity_dilute_collision_integral ( HelmholtzEOSMixtureBackend HEOS)
static

The dilute gas viscosity term that is based on collision integral or effective cross section.

\[ \eta^0 = \displaystyle\frac{A\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)} \]

\[ \mathfrak{S}(T^*)=\exp\left(\sum_ia_i[\ln T^*]^{t_i}\right) \]

with \(T^* = \frac{T}{\varepsilon/k}\) and \(\sigma\) in nm, M is in kg/kmol. Yields viscosity in Pa-s.

Both the collision integral \(\mathfrak{S}^*\) and effective cross section \(\Omega^{(2,2)}\) have the same form, in general we don't care which is used. The are related through \(\Omega^{(2,2)} = (5/4)\mathfrak{S}^*\) see Vesovic(JPCRD, 1990) for CO \(_2\) for further information

§ viscosity_dilute_kinetic_theory()

CoolPropDbl CoolProp::TransportRoutines::viscosity_dilute_kinetic_theory ( HelmholtzEOSMixtureBackend HEOS)
static

The general dilute gas viscosity from used for ECS.

\[ \eta^0 = \displaystyle\frac{26.692\times 10^{-9}\sqrt{MT}}{\sigma^2\Omega^{(2,2)}(T^*)} \]

\[ \Omega^{(2,2)}(T^*)=1.16145(T^*)^{-0.14874}+0.52487\exp(-0.77320T^*)+2.16178\exp(-2.43787T^*) \]

with \(T^* = \frac{T}{\varepsilon/k}\) and \(\sigma\) in nm, M is in kg/kmol. Yields viscosity in Pa-s.

§ viscosity_dilute_powers_of_T()

CoolPropDbl CoolProp::TransportRoutines::viscosity_dilute_powers_of_T ( HelmholtzEOSMixtureBackend HEOS)
static

A dilute gas viscosity term formed of summation of power terms.

\[ \eta^0 = \displaystyle\sum_ia_iT^{t_i} \]

with T in K, \(\eta^0\) in Pa-s

§ viscosity_dilute_powers_of_Tr()

CoolPropDbl CoolProp::TransportRoutines::viscosity_dilute_powers_of_Tr ( HelmholtzEOSMixtureBackend HEOS)
static

A dilute gas viscosity term formed of summation of power terms of the reduced temperature.

\[ \eta^0 = \displaystyle\sum_ia_i(T/T_c)^{t_i} \]

with T in K, \(\eta^0\) in Pa-s

§ viscosity_ECS()

CoolPropDbl CoolProp::TransportRoutines::viscosity_ECS ( HelmholtzEOSMixtureBackend HEOS,
HelmholtzEOSMixtureBackend HEOS_Reference 
)
static

Calculate the viscosity using the extended corresponding states method.

This method is covered in depth in

Bell, I. H.; Wronski, J.; Quoilin, S. & Lemort, V. (2014), Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp, Industrial & Engineering Chemistry Research, 53, (6), 2498-2508

which is originally based on the methods presented in

Huber, M. L., Laesecke, A. and Perkins, R. A., (2003), Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a, Industrial & Engineering Chemistry Research, v. 42, pp. 3163-3178

and

McLinden, M. O.; Klein, S. A. & Perkins, R. A. (2000), An extended corresponding states model for the thermal conductivity of refrigerants and refrigerant mixtures, Int. J. Refrig., 23, 43-63

§ viscosity_heptane_higher_order_hardcoded()

CoolPropDbl CoolProp::TransportRoutines::viscosity_heptane_higher_order_hardcoded ( HelmholtzEOSMixtureBackend HEOS)
static

From Michailidou-JPCRD-2014-Heptane

§ viscosity_higher_order_friction_theory()

CoolPropDbl CoolProp::TransportRoutines::viscosity_higher_order_friction_theory ( HelmholtzEOSMixtureBackend HEOS)
static

Higher-order viscosity term from friction theory of Sergio Quinones-Cisneros.

Several functional forms have been proposed and this function attempts to handle all of them \( \eta_{HO} = \kappa_ap_a + \kappa_r\Delta p_r + \kappa_i p_{id}+\kappa_{aa}p_a^2 + \kappa_{drdr}\Delta p_r^2 + \kappa_{rr}p_{r}^2 + \kappa_{ii}p_{id}^2 +\kappa_{rrr}p_r^3 + \kappa_{aaa}p_a^3 Watch out that sometimes it is \) p_r \( and other times it is \)p_r

§ viscosity_higher_order_modified_Batschinski_Hildebrand()

CoolPropDbl CoolProp::TransportRoutines::viscosity_higher_order_modified_Batschinski_Hildebrand ( HelmholtzEOSMixtureBackend HEOS)
static

The modified Batschinski-Hildebrand contribution to the viscosity.

\[ \Delta\eta = \displaystyle\sum_{i}a_{i}\delta^{d1_i}\tau^{t1_j}\exp(\gamma_i\delta^{l_i})+\left(\displaystyle\sum_{i}f_i\delta^{d2_i}\tau^{t2_i}\right)\left(\frac{1}{\delta_0(\tau)-\delta}-\frac{1}{\delta_0(\tau)}\right) \]

where \(\tau = T_c/T\) and \(\delta = \rho/\rho_c\)

\[ \delta_0(\tau) = \displaystyle\frac{\displaystyle\sum_{i}g_i\tau^{h_i}}{\displaystyle\sum_{i}p_i\tau^{q_i}} \]

The more general form of \(\delta_0(\tau)\) is selected in order to be able to handle all the forms in the literature

§ viscosity_initial_density_dependence_empirical()

CoolPropDbl CoolProp::TransportRoutines::viscosity_initial_density_dependence_empirical ( HelmholtzEOSMixtureBackend HEOS)
static

An empirical form for the initial density dependence.

Given by the polynomial-like form

\[ \eta^1 = \sum_i n_i\delta^{d_i}\tau^{t_i} \]

where the output is in Pa-s

§ viscosity_initial_density_dependence_Rainwater_Friend()

CoolPropDbl CoolProp::TransportRoutines::viscosity_initial_density_dependence_Rainwater_Friend ( HelmholtzEOSMixtureBackend HEOS)
static

The initial density dependence term \(B_{\eta}\) from Rainwater-Friend theory.

The total contribution from this term is given by

\[ \eta_{RF} = \eta_0B_{\eta}\rho \]

where \(\eta_0\) is the dilute gas viscosity in Pa-s and \(\rho\) is the molar density in mol/m \(^3\) and \(B_{\eta}\) is in m^3/mol.

\[ B_{\eta}(T) = B_{\eta}^*(T^*)N_A\sigma_{\eta}^3 \]

where \(N_A\) is Avogadros number \(6.022\times 10^{23}\) mol \(^{-1}\) and \(\sigma_{\eta}\) is in m.

\[ B_{\eta}^*(T^*) = \displaystyle\sum_ib_i(T^*)^{t_i} \]

IMPORTANT: This function returns \(B_{\eta}\), not \(\eta_{RF}\)

§ viscosity_methanol_hardcoded()

CoolPropDbl CoolProp::TransportRoutines::viscosity_methanol_hardcoded ( HelmholtzEOSMixtureBackend HEOS)
static

Viscosity hardcoded for Methanol.

From Xiang et al., A New Reference Correlation for the Viscosity of Methanol, J. Phys. Chem. Ref. Data, Vol. 35, No. 4, 2006


The documentation for this class was generated from the following files: