796 lines
39 KiB
Plaintext
796 lines
39 KiB
Plaintext
Helium !Short name
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7440-59-7 !CAS number
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Helium-4 !Full name
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He !Chemical formula {He}
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R-704 !Synonym
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4.002602 !Molar mass [g/mol]
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2.1768 !Triple point temperature [K]
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4.2238 !Normal boiling point [K]
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5.1953 !Critical temperature [K]
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228.32 !Critical pressure [kPa]
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17.3837 !Critical density [mol/L]
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-0.3836 !Acentric factor
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0.0 !Dipole moment [Debye]; (exactly zero for monatomic molecules)
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NBP !Default reference state
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10.0 !Version number
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1046 !UN Number :UN:
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cryogen !Family :Family:
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0.0 !Heating value (upper) [kJ/mol] :Heat:
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A1 !Safety Group (ASHRAE Standard 34, 2010) :Safety:
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1S/He !Standard InChI String :InChi:
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SWQJXJOGLNCZEY-UHFFFAOYSA-N !Standard InChI Key :InChiKey:
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???? !Alternative fluid for mixing rules :AltID:
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3b8eed30 !Hash number from InChI Key :Hash:
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!The fluid files contain general information about the fluid in the first 15 to 20 lines, followed by sections for the
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! equations of state, transport equations, and auxiliary equations. Equations of state are listed first. The NIST recommended
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! equations begin with a hash mark (#). The secondary equations begin with the @ symbol. These symbols can be swapped to
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! select a secondary equation as primary and the primary as secondary. The equation of state section also contains auxiliary
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! equations for the ideal gas heat capacity or ideal gas Helmholtz energy. Below the equations of state (both primary and
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! secondary) are the transport equations, first viscosity and then thermal conductivity. These are then followed by the
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! secondary equations if available. The transport section also contains auxiliary equations required to calculate either the
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! dilute gas state or the critical enhancement. At the end of the file are additional but not necessary auxiliary equations,
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! including simple equations for the vapor pressure, saturated liquid and vapor densities, melting line (for some fluids), and
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! sublimation line (for even fewer fluids). This section also contains the equations for dielectric constant and surface
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! tension if available. The sections are divided by different symbols (these being _-+=^*~) to aid the eye in locating a
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! particular section. Secondary equations are indented 10 spaces to avoid confusion with the NIST recommended equations. The
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! end of the fluid file is marked with @END. Anything below that is ignored.
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! compiled by E.W. Lemmon, NIST Physical and Chemical Properties Division, Boulder, Colorado
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! 01-23-97 EWL, Original version.
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! 11-06-00 EWL, Switch transport equations to hardcoded models.
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! 08-05-04 EWL, Add Harvey and Lemmon dielectric correlation.
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! 11-18-04 MLH, Add tPr coeff.
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! 12-11-09 EWL, Add 40 term EOS derived from the McCarty and Arp BWR equation.
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! 09-08-10 EWL, Add equation of state of Ortiz-Vega.
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! 12-06-12 EWL, Add surface tension coefficients of Mulero et al. (2012).
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! 04-08-13 EWL, Add second equation of state of Ortiz-Vega.
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! 06-04-14 EWL, Add final equation of state of Ortiz-Vega.
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! 02-10-17 EWL, Update ancillary equations.
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! 05-15-17 EWL, Change the hard coded VS0 model to the VS7 reverse Polish notation.
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________________________________________________________________________________
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#EOS !---Equation of state---
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FEQ !Helmholtz equation of state for helium of Ortiz-Vega et al. (2015).
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:TRUECRITICALPOINT: 5.1953 17.3837 !True EOS critical point [K, mol/L] (where dP/dD=0 and d^2P/dD^2=0 at constant T)
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:DOI:
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?
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?```````````````````````````````````````````````````````````````````````````````
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?Ortiz-Vega, D.O., Hall, K.R., Holste, J.C., Arp, V.D., Harvey, A.H., and Lemmon, E.W.,
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? final equation of state, to be submitted to J. Phys. Chem. Ref. Data, 2018.
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?
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?The uncertainties below 50 K in density are 0.25% at pressures up to 10 MPa.
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? From 50 K to 200 K, the uncertainties decrease linearly from 0.2% at 50 K to
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? 0.05% at 200 K for all pressures up to 50 MPa. Between 200 K and 500 K, the
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? uncertainty is 0.03% up to pressures of 40 MPa and 0.1% between 40 MPa and 100
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? MPa. For all other states not listed here, the uncertainties increase to 0.5%
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? in density. The uncertainties in the speed of sound are 0.01% for the vapor
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? phase and 0.2% for the liquid phase. The uncertainty in vapor pressure is
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? less than 0.02%, and that for heat capacities is about 2%. Uncertainties in
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? the critical region are higher for all properties except vapor pressure.
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?
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!```````````````````````````````````````````````````````````````````````````````
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2.1768 !Lower temperature limit [K]
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2000.0 !Upper temperature limit [K]
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1000000.0 !Upper pressure limit [kPa]
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141.22 !Maximum density [mol/L]
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CPP !Pointer to Cp0 model
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4.002602 !Molar mass [g/mol]
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2.1768 !Triple point temperature [K]
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5.0393 !Pressure at triple point [kPa]
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36.48 !Density at triple point [mol/L]
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4.2238 !Normal boiling point temperature [K]
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-0.3836 !Acentric factor
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5.1953 228.32 17.3837 !Tc [K], pc [kPa], rhoc [mol/L]
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5.1953 17.3837 !Reducing parameters [K, mol/L]
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8.3144598 !Gas constant [J/mol-K]
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12 4 11 12 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms
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0.015559018 1.0 4. 0. !a(i),t(i),d(i),l(i)
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3.0638932 0.425 1. 0.
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-4.2420844 0.63 1. 0.
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0.054418088 0.69 2. 0.
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-0.18971904 1.83 2. 0.
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0.087856262 0.575 3. 0.
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2.2833566 0.925 1. 1.
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-0.53331595 1.585 1. 2.
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-0.53296502 1.69 3. 2.
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0.99444915 1.51 2. 1.
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-0.30078896 2.9 2. 2.
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-1.6432563 0.8 1. 1.
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0.8029102 1.26 2. 2. 2. -1.5497 -0.2471 3.15 0.596 0. 0. 0.
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0.026838669 3.51 1. 2. 2. -9.245 -0.0983 2.54505 0.3423 0. 0. 0.
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0.04687678 2.785 2. 2. 2. -4.76323 -0.1556 1.2513 0.761 0. 0. 0.
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-0.14832766 1. 1. 2. 2. -6.3826 -2.6782 1.9416 0.9747 0. 0. 0.
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0.03016211 4.22 1. 2. 2. -8.7023 -2.7077 0.5984 0.5868 0. 0. 0.
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-0.019986041 0.83 3. 2. 2. -0.255 -0.6621 2.2282 0.5627 0. 0. 0.
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0.14283514 1.575 2. 2. 2. -0.3523 -0.1775 1.606 2.5346 0. 0. 0.
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0.007418269 3.447 2. 2. 2. -0.1492 -0.4821 3.815 3.6763 0. 0. 0.
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-0.22989793 0.73 3. 2. 2. -0.05 -0.3069 1.61958 4.5245 0. 0. 0.
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0.79224829 1.634 2. 2. 2. -0.1668 -0.1758 0.6407 5.039 0. 0. 0.
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-0.049386338 6.13 2. 2. 2. -42.2358 -1357.6577 1.076 0.959 0. 0. 0.
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eta beta gamma epsilon
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EXP[eta*(delta-epsilon)^2+beta*(tau-gamma)^2]
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#AUX !---Auxiliary function for Cp0
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CPP !Ideal gas heat capacity function for helium of Ortiz-Vega et al. (2015).
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?
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?```````````````````````````````````````````````````````````````````````````````
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?Ortiz-Vega, D.O., Hall, K.R., Holste, J.C., Arp, V.D., Harvey, A.H., and Lemmon, E.W., 2018.
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?
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!```````````````````````````````````````````````````````````````````````````````
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0. !
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10000. !
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0. !
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0. !
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1.0 8.3144598 !Reducing parameters for T, Cp0
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1 0 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh
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2.5 0.0
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#AUX !---Auxiliary function for PX0
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PX0 !Helmholtz energy ideal-gas function for helium of Ortiz-Vega et al. (2015).
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?
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?```````````````````````````````````````````````````````````````````````````````
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?Ortiz-Vega, D.O., Hall, K.R., Holste, J.C., Arp, V.D., Harvey, A.H., and Lemmon, E.W., 2018.
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?
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!```````````````````````````````````````````````````````````````````````````````
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1 2 0 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau))
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1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms
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0.1733487932835764 0.0 !aj, ti for [ai*tau**ti] terms
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0.4674522201550815 1.0 !aj, ti for [ai*tau**ti] terms
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--------------------------------------------------------------------------------
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@EOS !---Equation of state---
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FEK !Helmholtz equation of state for helium of Kunz and Wagner (2004).
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?
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?```````````````````````````````````````````````````````````````````````````````
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?Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M.
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? "The GERG-2004 Wide-Range Equation of State for Natural Gases
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? and Other Mixtures," GERG Technical Monograph 15,
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? Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 2007.
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?
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!```````````````````````````````````````````````````````````````````````````````
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2.1768 !Lower temperature limit [K]
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1500.0 !Upper temperature limit [K]
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100000.0 !Upper pressure limit [kPa]
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88.73 !Maximum density [mol/L]
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PHK !Pointer to Cp0 model
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4.002602 !Molar mass [g/mol]
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2.1768 !Triple point temperature [K]
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4.8565 !Pressure at triple point [kPa]
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36.537 !Density at triple point [mol/L]
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4.22 !Normal boiling point temperature [K]
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-0.3859 !Acentric factor
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5.1953 227.46 17.399 !Tc [K], pc [kPa], rhoc [mol/L]
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5.1953 17.399 !Reducing parameters [K, mol/L]
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8.314472 !Gas constant [J/mol-K]
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12 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms
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-0.45579024006737 0.0 1. 0.
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1.2516390754925 0.125 1. 0.
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-1.5438231650621 0.75 1. 0.
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0.020467489707221 1.0 4. 0.
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-0.34476212380781 0.75 1. 1.
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-0.020858459512787 2.625 3. 1.
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0.016227414711778 0.125 5. 1.
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-0.057471818200892 1.25 5. 1.
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0.019462416430715 2.0 5. 1.
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-0.03329568012302 1.0 2. 2.
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-0.010863577372367 4.5 1. 3.
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-0.022173365245954 5.0 2. 3.
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@AUX !---Auxiliary function for PH0
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PHK !Ideal gas Helmholtz form for helium of Kunz and Wagner (2004).
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?
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?```````````````````````````````````````````````````````````````````````````````
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?Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M.
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? "The GERG-2004 Wide-Range Equation of State for Natural Gases
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? and Other Mixtures," GERG Technical Monograph 15,
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? Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 2007.
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?
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!```````````````````````````````````````````````````````````````````````````````
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0. !
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10000. !
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0. !
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0. !
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1 2 0 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)); cosh; sinh
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1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms
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13.628409737 0.0 !aj, ti for [ai*tau**ti] terms
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-143.470759602 1.0
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@EOS !---Equation of state---
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FE1 !Helmholtz equation of state for helium of Ortiz-Vega et al. (2010).
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?
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?```````````````````````````````````````````````````````````````````````````````
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?Ortiz-Vega, D.O., Hall, K.R., Arp, V.D., and Lemmon, E.W.,
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? Interim equation, 2010.
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?
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?Below 50 K, the uncertainties in density are 0.5% at pressures up to 10 MPa.
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? From 50 K to 200 K the uncertainties decrease to 0.2 % at pressures up to 50
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? MPa. At higher temperatures the uncertainties in density are 0.1 % up to
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? pressures of 20 MPa. At all temperatures and at pressures higher than listed
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? here, the uncertainties increase to 1% in density. The uncertainties in the
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? speed of sound are 0.04% for the vapor phase and 0.25% for the liquid phase.
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? The uncertainties in vapor pressure are less than 0.05% and for the heat
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? capacities are about 5%. Uncertainties in the critical region are higher for
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? all properties except vapor pressure.
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?
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!```````````````````````````````````````````````````````````````````````````````
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2.1768 !Lower temperature limit [K]
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2000.0 !Upper temperature limit [K]
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1000000.0 !Upper pressure limit [kPa]
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141.22 !Maximum density [mol/L]
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CPP !Pointer to Cp0 model
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4.002602 !Molar mass [g/mol]
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2.1768 !Triple point temperature [K]
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5.043 !Pressure at triple point [kPa]
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36.46 !Density at triple point [mol/L]
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4.222 !Normal boiling point temperature [K]
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-0.385 !Acentric factor
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5.1953 227.6 18.13 !Tc [K], pc [kPa], rhoc [mol/L]
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5.1953 18.13 !Reducing parameters [K, mol/L]
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8.314472 !Gas constant [J/mol-K]
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12 4 9 12 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms
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0.009288766 1.0 4. 0. !a(i),t(i),d(i),l(i)
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0.9258069 0.28 1. 0.
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-1.718156 0.735 1. 0.
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0.7606137 0.64 2. 0.
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-1.024864 0.82 2. 0.
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0.1052455 1.16 3. 0.
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-0.1875722 1.28 1. 1.
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-0.1287812 2.0 1. 2.
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-0.002227619 0.41 3. 2.
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0.1823465 1.33 2. 1.
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-0.04450014 4.2 2. 2.
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-0.00008729033 0.6 8. 1.
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0.0385432 3.0 1. 2. 2. -1.0833 -0.0385 1.9776 0.6914 0. 0. 0.
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-0.9585106 1.0 1. 2. 2. -18.3824 -19.8246 1.6178 0.8590 0. 0. 0.
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-0.0545401 8.2 1. 2. 2. -5.0573 -9.3799 0.4371 0.8787 0. 0. 0.
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-0.0368726 1.0 2. 2. 2. -0.2832 -0.8073 0.5355 2.7182 0. 0. 0.
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-0.001021851 2.71 2. 2. 2. -6.0582 -0.031 0.7777 2.0301 0. 0. 0.
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0.06166348 1.0 2. 2. 2. -0.2444 -0.0061 0.4832 0.89 0. 0. 0.
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0.02493437 1.0 3. 2. 2. -0.0539 -0.3581 0.8162 1.179 0. 0. 0.
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-0.008127424 2.0 3. 2. 2. -0.185 -0.7518 1.2896 0.568 0. 0. 0.
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-0.008233032 1.0 2. 2. 2. -0.5941 -7.4629 0.3577 1.6412 0. 0. 0.
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@EOS !---Equation of state---
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BWR !MBWR equation of state for helium of McCarty and Arp (1990).
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?
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?```````````````````````````````````````````````````````````````````````````````
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?McCarty, R.D. and Arp, V.D.,
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? "A New Wide Range Equation of State for Helium,"
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? Adv. Cryo. Eng., 35:1465-1475, 1990.
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?
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?The uncertainties of the equation of state range from 1% at low
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? temperatures (<20 K) to 0.1% at temperatures between 200 and 400 K, and
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? from 3% in the speed of sound in the liquid phase to 0.1% in the speed
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? of sound between 100 and 500 K. The uncertainty of heat capacities is
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? about 5%.
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?
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!```````````````````````````````````````````````````````````````````````````````
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2.1768 !Lower temperature limit [K]
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1500.0 !Upper temperature limit [K]
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100000.0 !Upper pressure limit [kPa]
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88.73 !Maximum density [mol/L]
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CPP !Pointer to Cp0 model
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4.0026 !Molar mass [g/mol]
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2.1768 !Triple point temperature [K]
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4.8565 !Pressure at triple point [kPa]
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36.537 !Density at triple point [mol/L]
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4.230 !Normal boiling point temperature [K]
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-0.382 !Acentric factor
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5.1953 227.46 17.399 !Tc [K], pc [kPa], rhoc [mol/L]
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5.1953 17.399 !Reducing parameters [K, mol/L]
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17.399 !gamma
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0.0831431 !Gas constant [L-bar/mol-K]
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32 1 !Nterm, Ncoeff per term
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0.0004558980227431 0.01260692007853 -0.07139657549318
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0.09728903861441 -0.1589302471562 0.1454229259623e-4
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-0.0004708238429298 0.01132915223587 0.02410763742104
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-0.5093547838381e-7 0.26997269279e-4 -0.0003954146691114
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0.1551961438127e-7 0.1050712335785e-6 -0.550115836675e-6
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-0.1037673478521e-8 0.6446881346448e-11 0.3298960057071e-9
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-0.3555585738784e-11 -0.0688540136769 0.09166109232806
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-0.6544314242937e-4 -0.0003315398880031 -0.2067693644676e-6
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0.3850153114958e-6 -0.1399040626999e-9 -0.1888462892389e-10
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-0.4595138561035e-13 0.6872567403738e-13 -0.6097223119177e-17
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-0.7636186157005e-16 0.3848665703556e-16
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@EOS !---Equation of state---
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FE2 !Helmholtz equation of state of McCarty and Arp (1990).
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?
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?```````````````````````````````````````````````````````````````````````````````
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?McCarty, R.D. and Arp, V.D.,
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? "A New Wide Range Equation of State for Helium,"
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? Adv. Cryo. Eng., 35:1465-1475, 1990.
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?
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?The coefficients used in this equation are derived from the BWR coefficients
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? given in the original manuscript. The uncertainties are thus the same
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? as those given for the BWR EOS.
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?
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!```````````````````````````````````````````````````````````````````````````````
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2.1768 !Lower temperature limit [K]
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1500.0 !Upper temperature limit [K]
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100000.0 !Upper pressure limit [kPa]
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88.73 !Maximum density [mol/L]
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CPP !Pointer to Cp0 model
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4.0026 !Molar mass [g/mol]
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2.1768 !Triple point temperature [K]
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4.8565 !Pressure at triple point [kPa]
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36.537 !Density at triple point [mol/L]
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4.230 !Normal boiling point temperature [K]
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-0.382 !Acentric factor
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5.1953 227.46 17.399 !Tc [K], pc [kPa], rhoc [mol/L]
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5.1953 17.399 !Reducing parameters [K, mol/L]
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8.31431 !Gas constant [J/mol-K]
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40 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms
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-2.08984171567 3.0 0. 0. !a(i),t(i),d(i),l(i)
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0.381792817549 4.0 0. 0.
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-0.0441393943069 5.0 0. 0.
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0.0954038242224 0.0 1. 0.
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1.15744872054 0.5 1. 0.
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-2.87584069992 1.0 1. 0.
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0.754294125268 2.0 1. 0.
|
|
-0.237177092854 3.0 1. 0.
|
|
0.026474346333 0.0 2. 0.
|
|
-0.164983375328 1.0 2. 0.
|
|
0.764132237117 2.0 2. 0.
|
|
0.312978947837 3.0 2. 0.
|
|
-0.00107558759761 0.0 3. 0.
|
|
0.109732330796 1.0 3. 0.
|
|
-0.309354837550 2.0 3. 0.
|
|
0.000823154284944 1.0 4. 0.
|
|
0.0149309620852 2.0 5. 0.
|
|
-0.0150469153718 3.0 5. 0.
|
|
-0.00213800009686 2.0 6. 0.
|
|
0.000198095303505 2.0 7. 0.
|
|
0.00195115121471 3.0 7. 0.
|
|
-0.000320152846941 3.0 8. 0.
|
|
2.08984171567 3.0 0. 2.
|
|
-0.381792817549 4.0 0. 2.
|
|
0.0441393943069 5.0 0. 2.
|
|
1.19594006419 3.0 2. 2.
|
|
-0.152740402594 4.0 2. 2.
|
|
0.0441393941765 5.0 2. 2.
|
|
0.469369369369 3.0 4. 2.
|
|
-0.0763702010715 4.0 4. 2.
|
|
-0.00206787489008 5.0 4. 2.
|
|
0.0744548107827 3.0 6. 2.
|
|
0.00393354771579 4.0 6. 2.
|
|
-0.000689291627989 5.0 6. 2.
|
|
0.00601642971226 3.0 8. 2.
|
|
0.000983386926042 4.0 8. 2.
|
|
-0.000235321870328 5.0 8. 2.
|
|
0.000201249794359 3.0 10. 2.
|
|
0.000485142401906 4.0 10. 2.
|
|
-0.470643739266e-4 5.0 10. 2.
|
|
|
|
|
|
@EOS !---Cubic equation of state---
|
|
PRT !Translated Peng-Robinson equation for helium.
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Volume translation of Peng Robinson EOS.
|
|
? Translation computed so that sat. liquid density at Tr=0.7 matches MBWR equation
|
|
? of state for He of McCarty and Arp (1990).
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
2.1768 !Lower temperature limit [K]
|
|
1500.0 !Upper temperature limit [K]
|
|
100000.0 !Upper pressure limit [kPa]
|
|
88.73 !Maximum density [mol/L]
|
|
CPP !Pointer to Cp0 model
|
|
4.0026 !Molar mass [g/mol]
|
|
-0.382 !Acentric factor
|
|
5.1953 !Critical temperature [K]
|
|
227.46 !Critical pressure [kPa]
|
|
17.399 !Critical density [mol/L]
|
|
8.314472 !Gas constant [J/mol-K]
|
|
1 !Number of parameters
|
|
-0.005886
|
|
|
|
|
|
|
|
|
|
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
|
|
|
#ETA !---Viscosity---
|
|
VS7 !Pure fluid viscosity model for helium of Arp et al. (1998).
|
|
:DOI:
|
|
:WEB: https://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1334.pdf
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Arp, V.D., McCarty, R.D., and Friend, D.G.,
|
|
? "Thermophysical Properties of Helium-4 from 0.8 to 1500 K with
|
|
? Pressures to 2000 MPa,"
|
|
? NIST Technical Note 1334 (revised), 1998.
|
|
?
|
|
?The uncertainty in viscosity is 10%.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
2.1768 !Lower temperature limit [K]
|
|
1500.0 !Upper temperature limit [K]
|
|
100000.0 !Upper pressure limit [kPa]
|
|
88.73 !Maximum density [mol/L]
|
|
NUL !Omega model
|
|
!
|
|
!Variables
|
|
$VR RED CNST TEMP LOG 300 TEMP POP> =TAU !Reducing function for T for next line, equal to the first coefficient below or LOG(T) depending on T>300.
|
|
$VR SUMTAU:5 EXP DUP =V1 =V5 100 TEMP EXIT< !eta0a
|
|
$VR SUMEX:3 SUM:1 * DUP =V5 110 TEMP EXIT>= V1 - TEMP 100 - 10 / * V1 + =V5 !eta0, with value depending on whether or not T<110
|
|
!
|
|
!Dilute gas
|
|
$DG V5
|
|
!
|
|
!Residual function
|
|
$RF SUMTAU:15 EXP V1 * V5 - 100 TEMP EXIT<= V5 + V1 - !Viscosity, which depends on T>100
|
|
!
|
|
!Coefficients
|
|
$CF
|
|
0.1 1. 249.837480718 0. 0 !Reducing parameters for eta, T, rho
|
|
5.7037825 0. 0. 0. 0
|
|
-0.135311743 -1. 0. 0. 0 ! eta0a
|
|
1.00347841 0. 0. 0. 0
|
|
1.20654649 1. 0. 0. 0
|
|
-0.149564551 2. 0. 0. 0
|
|
0.0125208416 3. 0. 0. 0
|
|
!
|
|
-4.1249 0. 0. 0. 0 ! V3
|
|
12.451 -1. 0. 0. 0
|
|
-295.67 -2. 0. 0. 0
|
|
196.0 0.71938 0. 0. 0
|
|
!
|
|
-47.5295259 -1. 1. 0. 0 ! eta0e
|
|
87.6799309 0. 1. 0. 0
|
|
-42.0741589 1. 1. 0. 0
|
|
8.33128289 2. 1. 0. 0
|
|
-0.589252385 3. 1. 0. 0
|
|
547.309267 -1. 2. 0. 0
|
|
-904.870586 0. 2. 0. 0
|
|
431.404928 1. 2. 0. 0
|
|
-81.4504854 2. 2. 0. 0
|
|
5.37008433 3. 2. 0. 0
|
|
-1684.39324 -1. 3. 0. 0
|
|
3331.08630 0. 3. 0. 0
|
|
-1632.19172 1. 3. 0. 0
|
|
308.804413 2. 3. 0. 0
|
|
-20.2936367 3. 3. 0. 0
|
|
NUL !Pointer to the viscosity critical enhancement auxiliary function (none used)
|
|
|
|
|
|
|
|
|
|
================================================================================
|
|
|
|
#TCX !---Thermal conductivity---
|
|
TC7 !Pure fluid thermal conductivity model for helium of Hands and Arp (1981).
|
|
:DOI: 10.1016/0011-2275(81)90211-3
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Hands, B.A. and Arp, V.D.,
|
|
? "A Correlation of Thermal Conductivity Data for Helium,"
|
|
? Cryogenics, 21(12):697-703, 1981.
|
|
?
|
|
?The uncertainty in thermal conductivity is 5%, except at low temperatures
|
|
? where it increases to 10%.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
2.1768 !Lower temperature limit [K]
|
|
1500.0 !Upper temperature limit [K]
|
|
100000.0 !Upper pressure limit [kPa]
|
|
88.73 !Maximum density [mol/L]
|
|
$DG RED SUM:1 SUMEX:4 *
|
|
$RF RED TR THRD POWR =TR SUMLOGL:15
|
|
$CE TEMP CNST EXIT>= TEMP CNST EXIT<= DENS 0 EXIT>=
|
|
$CE CNST =C1 CNST =C2 CNST =C3 CNST =C4
|
|
$CE DENS CNST / 1 - ABS =V0 !deld
|
|
$CE TEMP CNST / 1 - ABS =V1 !delt
|
|
$CE 1 DPDD / DENS / CNST / =V2 !bkt
|
|
$CE V1 CNST / 2 POWR V0 CNST / SQR + =V3 !r2
|
|
$CE TEMP SQR DENS / WMAS / ETA / DPDT SQR *
|
|
$CE CNST * CNST V1 SQR * CNST V0 4 POWR * - EXP * CNST *
|
|
$CE DUP V2 SQRT * V3 1 EXIT<= POP
|
|
$CE V1 V0 C4 POWR / =V4 !xx
|
|
$CE V4 C1 + C1 / =V5 !x1
|
|
$CE V5 2 C4 / POWR =V6 !x2b
|
|
$CE 1 C3 V6 * + CNST 2 / C4 * POWR =V7 !x2be
|
|
$CE C2 V7 * C1 / C2 C3 * C1 / V6 * V7 * 1 C3 V6 * + / CNST * + =V8 !dhdx
|
|
$CE CNST C2 * V5 * V7 * V4 V8 * C4 * - V0 CNST 1 - POWR * =V9 !d2kt
|
|
$CE V3 V2 * 1 V3 - CNST DENS / SQR * V9 / CNST / + SQRT *
|
|
!
|
|
$CF
|
|
1. 1. 0.2498376 0. 0 !Reducing parameters for T, rho, eta
|
|
0.0027870034 0.7034007057 0. 0. 0 !Pre-exponential term
|
|
3.739232544 -1. 0. 0. 0 !Coefficient, power in T
|
|
-26.20316969 -2. 0. 0. 0
|
|
59.82252246 -3. 0. 0. 0
|
|
-49.26397634 -4. 0. 0. 0
|
|
1. 1. 0.2498376 0. 0 !Reducing parameters for T, rho, eta
|
|
0.000186297053 0. 1. 0. 0 !Coefficient, powers of T, rho, ln(rho)
|
|
-0.7275964435e-6 3. 1. 0. 0
|
|
-0.0001427549651 1. 1. 0. 0
|
|
0.3290833592e-4 2. 1. 0. 0
|
|
-0.5213335363e-7 0. 3. 0. 0
|
|
0.4492659933e-7 1. 3. 0. 0
|
|
-0.5924416513e-8 2. 3. 0. 0
|
|
0.7087321137e-5 0. 2. 0. 1
|
|
-0.6013335678e-5 1. 2. 0. 1
|
|
0.8067145814e-6 2. 2. 0. 1
|
|
0.3995125013e-6 -3. 2. 0. 1
|
|
-2.99050061466e-5 0. 2. 0. 0 !Accounts for the ln(1/Dc) in Eq. (17)
|
|
2.53733162271e-5 1. 2. 0. 0
|
|
-3.40393839209e-6 2. 2. 0. 0
|
|
-1.68574607754e-6 -3. 2. 0. 0
|
|
3.5 0. 0. 0. 0
|
|
12. 0. 0. 0. 0
|
|
0.392 0. 0. 0. 0
|
|
2.8461 0. 0. 0. 0
|
|
0.27156 0. 0. 0. 0
|
|
2.81373100732 0. 0. 0. 0
|
|
17.2782604916 0. 0. 0. 0
|
|
5.18992 0. 0. 0. 0
|
|
1000. 0. 0. 0. 0
|
|
0.2 0. 0. 0. 0
|
|
0.25 0. 0. 0. 0
|
|
3.726229668 0. 0. 0. 0
|
|
-18.66 0. 0. 0. 0
|
|
4.25 0. 0. 0. 0
|
|
0.000034685233 0. 0. 0. 0
|
|
0.1743 0. 0. 0. 0
|
|
0.1743 0. 0. 0. 0
|
|
4.304 0. 0. 0. 0
|
|
4.304 0. 0. 0. 0
|
|
17.2782604916 0. 0. 0. 0
|
|
227460. 0. 0. 0. 0
|
|
NUL !Pointer to critical enhancement auxiliary function
|
|
|
|
|
|
|
|
|
|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
@TRN !---ECS Transport---
|
|
ECS !Extended Corresponding States model (Nitrogen reference); predictive mode for helium.
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Klein, S.A., McLinden, M.O., and Laesecke, A., "An Improved Extended Corresponding States Method for Estimation of Viscosity of Pure Refrigerants and Mixtures," Int. J. Refrigeration, 20(3):208-217, 1997. doi: 10.1016/S0140-7007(96)00073-4.
|
|
?McLinden, M.O., Klein, S.A., and Perkins, R.A., "An Extended Corresponding States Model for the Thermal Conductivity of Refrigerants and Refrigerant Mixtures," Int. J. Refrigeration, 23(1):43-63, 2000. doi: 10.1016/S0140-7007(99)00024-9
|
|
?
|
|
?The Lennard-Jones parameters were taken from Reid, R.C., Prausnitz, J.M., and Poling, B.E., "The Properties of Gases and Liquids," 4th edition, New York, McGraw-Hill Book Company, 1987.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
13.957 !Lower temperature limit [K]
|
|
500.0 !Upper temperature limit [K]
|
|
40000.0 !Upper pressure limit [kPa]
|
|
88.73 !Maximum density [mol/L]
|
|
FEQ NITROGEN.FLD
|
|
VS1 !Model for reference fluid viscosity
|
|
TC1 !Model for reference fluid thermal conductivity
|
|
NUL !Large molecule identifier
|
|
1 !Lennard-Jones flag (0 or 1) (0 => use estimates)
|
|
0.2551 !Lennard-Jones coefficient sigma [nm] for ECS method
|
|
10.22 !Lennard-Jones coefficient epsilon/kappa [K] for ECS method
|
|
1 0 0 !Number of terms in f_int term in Eucken correlation, spare1, spare2
|
|
0.00132 0. 0. 0. !Coefficient, power of T, spare1, spare2
|
|
1 0 0 !Number of terms in psi (visc shape factor): poly,spare1,spare2
|
|
1.0 0. 0. 0. !Coefficient, power of Tr, power of Dr, spare
|
|
1 0 0 !Number of terms in chi (t.c. shape factor): poly,spare1,spare2
|
|
1.0 0. 0. 0. !Coefficient, power of Tr, power of Dr, spare
|
|
NUL !Pointer to critical enhancement auxiliary function
|
|
|
|
|
|
|
|
|
|
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|
|
|
#STN !---Surface tension---
|
|
ST1 !Surface tension model for helium of Mulero et al. (2012).
|
|
:DOI: 10.1063/1.4768782
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Mulero, A., Cachadiña, I., and Parra, M.I.,
|
|
? "Recommended Correlations for the Surface Tension of Common Fluids,"
|
|
? J. Phys. Chem. Ref. Data, 41(4), 043105, 2012. doi: 10.1063/1.4768782
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
0. !
|
|
10000. !
|
|
0. !
|
|
0. !
|
|
3 !Number of terms in surface tension model
|
|
5.1953 !Critical temperature used in fit (dummy)
|
|
0.0004656 1.04 !Sigma0 and n
|
|
0.001889 2.468
|
|
-0.002006 2.661
|
|
|
|
|
|
#DE !---Dielectric constant---
|
|
DE3 !Dielectric constant model for helium of Harvey and Lemmon (2005).
|
|
:DOI: 10.1007/s10765-005-2351-5
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Harvey, A.H. and Lemmon, E.W.,
|
|
? "Method for Estimating the Dielectric Constant of Natural Gas Mixtures,"
|
|
? Int. J. Thermophys., 26(1):31-46, 2005. doi: 10.1007/s10765-005-2351-5
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
0. !
|
|
10000. !
|
|
0. !
|
|
0. !
|
|
273.16 1000.0 1.0 !Reducing parameters for T and D
|
|
0 1 3 0 0 0 !Number of terms in dielectric constant model
|
|
0.517254 0. 1. 0. !Coefficient, T exp, D exp
|
|
-0.203 0. 2. 0.
|
|
0.039 1. 2. 0.
|
|
7.47 0. 3. 0.
|
|
|
|
|
|
#MLT !---Melting line---
|
|
ML1 !Melting line model for helium of McCarty and Arp (1990).
|
|
:DOI:
|
|
:WEB: https://link.springer.com/chapter/10.1007/978-1-4613-0639-9_174
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?McCarty, R.D. and Arp, V.D.,
|
|
? "A New Wide Range Equation of State for Helium,"
|
|
? Adv. Cryo. Eng., 35:1465-1475, 1990.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
2.1768 !Lower temperature limit [K]
|
|
1500.0 !Upper temperature limit [K]
|
|
0. !
|
|
0. !
|
|
1. 1000. !Reducing temperature and pressure
|
|
2 0 0 0 0 0 !Number of terms in melting line equation
|
|
-1.7455837 0.0 !Coefficients and exponents
|
|
1.6979793 1.555414
|
|
|
|
|
|
#PS !---Vapor pressure---
|
|
PS5 !Vapor pressure equation for helium of Ortiz-Vega et al. (2010).
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Functional Form: P=Pc*EXP[SUM(Ni*Theta^ti)*Tc/T] where Theta=1-T/Tc, Tc and Pc
|
|
? are the reducing parameters below, which are followed by rows containing Ni and ti.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
0. !
|
|
10000. !
|
|
0. !
|
|
0. !
|
|
5.1953 228.32 !Reducing parameters
|
|
5 0 0 0 0 0 !Number of terms in equation
|
|
-4.0558 1.0
|
|
0.69089 1.5
|
|
1.1982 2.0
|
|
0.79703 5.0
|
|
-9.0432 14.0
|
|
|
|
|
|
#DL !---Saturated liquid density---
|
|
DL1 !Saturated liquid density equation for helium of Ortiz-Vega et al. (2010).
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Functional Form: D=Dc*[1+SUM(Ni*Theta^ti)] where Theta=1-T/Tc, Tc and Dc are
|
|
? the reducing parameters below, which are followed by rows containing Ni and ti.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
0. !
|
|
10000. !
|
|
0. !
|
|
0. !
|
|
5.1953 17.3837 !Reducing parameters
|
|
6 0 0 0 0 0 !Number of terms in equation
|
|
2.6970 0.44
|
|
-4.0115 0.72
|
|
5.5835 1.0
|
|
-4.7467 1.5
|
|
2.7509 2.5
|
|
-2.4711 5.0
|
|
|
|
|
|
#DV !---Saturated vapor density---
|
|
DV3 !Saturated vapor density equation for helium of Ortiz-Vega et al. (2010).
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Functional Form: D=Dc*EXP[SUM(Ni*Theta^ti)] where Theta=1-T/Tc, Tc and Dc are
|
|
? the reducing parameters below, which are followed by rows containing Ni and ti.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
0. !
|
|
10000. !
|
|
0. !
|
|
0. !
|
|
5.1953 17.3837 !Reducing parameters
|
|
5 0 0 0 0 0 !Number of terms in equation
|
|
-1.8975 0.41
|
|
-6.9133 1.35
|
|
13.711 2.0
|
|
-14.644 2.5
|
|
-23.179 10.0
|
|
|
|
|
|
@END
|
|
c 1 2 3 4 5 6 7 8
|
|
c2345678901234567890123456789012345678901234567890123456789012345678901234567890
|
|
|
|
|
|
@TCX !Thermal conductivity model specification
|
|
TC0 pure fluid thermal conductivity model of Hands and Arp (1981).
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Hands, B.A. and Arp, V.D.,
|
|
? "A Correlation of Thermal Conductivity Data for Helium,"
|
|
? Cryogenics, 21(12):697-703, 1981.
|
|
?
|
|
?The uncertainty in thermal conductivity is 5%, except at low temperatures
|
|
? where it increases to 10%.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
2.1768 !Lower temperature limit [K]
|
|
1500.0 !Upper temperature limit [K]
|
|
100000.0 !Upper pressure limit [kPa]
|
|
88.73 !Maximum density [mol/L]
|
|
HE !Pointer to hardcoded thermal conductivity model
|
|
5 0 15 0 0 0 0 0 !Number of terms for various pieces
|
|
1.0 0.2498376 1. 0. 0 !Reducing parameters for T, rho, eta
|
|
0.0027870034 0.7034007057 0. 0. 0 !Pre-exponential term
|
|
3.739232544 -1. 0. 0. 0 !Coefficient, power in T
|
|
-26.20316969 -2. 0. 0. 0
|
|
59.82252246 -3. 0. 0. 0
|
|
-49.26397634 -4. 0. 0. 0
|
|
0.000186297053 0. 1. 0. 0 !Coefficient, powers of T, rho, ln(rho)
|
|
-0.7275964435e-6 3. 1. 0. 0
|
|
-0.0001427549651 1. 1. 0. 0
|
|
0.3290833592e-4 2. 1. 0. 0
|
|
-0.5213335363e-7 0. 3. 0. 0
|
|
0.4492659933e-7 1. 3. 0. 0
|
|
-0.5924416513e-8 2. 3. 0. 0
|
|
0.7087321137e-5 0. 2. 1. 0
|
|
-0.6013335678e-5 1. 2. 1. 0
|
|
0.8067145814e-6 2. 2. 1. 0
|
|
0.3995125013e-6 -3. 2. 1. 0
|
|
-2.99050061466e-5 0. 2. 0. 0 !Accounts for the ln(1/Dc) in Eq. (17)
|
|
2.53733162271e-5 1. 2. 0. 0
|
|
-3.40393839209e-6 2. 2. 0. 0
|
|
-1.68574607754e-6 -3. 2. 0. 0
|
|
NUL !Pointer to the viscosity critical enhancement auxiliary function (none used)
|
|
|
|
|
|
@ETA !Viscosity model specification
|
|
VS0 pure fluid viscosity model of Arp et al. (1998).
|
|
?
|
|
?```````````````````````````````````````````````````````````````````````````````
|
|
?Arp, V.D., McCarty, R.D., and Friend, D.G.,
|
|
? "Thermophysical Properties of Helium-4 from 0.8 to 1500 K with
|
|
? Pressures to 2000 MPa,"
|
|
? NIST Technical Note 1334 (revised), 1998.
|
|
?
|
|
?The uncertainty in viscosity is 10%.
|
|
?
|
|
!```````````````````````````````````````````````````````````````````````````````
|
|
2.1768 !Lower temperature limit [K]
|
|
1500.0 !Upper temperature limit [K]
|
|
100000.0 !Upper pressure limit [kPa]
|
|
88.73 !Maximum density [mol/L]
|
|
HE !Pointer to hardcoded thermal conductivity model
|
|
0 0 0 0 0 0 0 0 !Number of terms for various pieces
|
|
NUL !Pointer to the viscosity critical enhancement auxiliary function (none used)
|