Helium !Short name 7440-59-7 !CAS number Helium-4 !Full name He !Chemical formula {He} R-704 !Synonym 4.002602 !Molar mass [g/mol] 2.1768 !Triple point temperature [K] 4.2238 !Normal boiling point [K] 5.1953 !Critical temperature [K] 228.32 !Critical pressure [kPa] 17.3837 !Critical density [mol/L] -0.3836 !Acentric factor 0.0 !Dipole moment [Debye]; (exactly zero for monatomic molecules) NBP !Default reference state 10.0 !Version number 1046 !UN Number :UN: cryogen !Family :Family: 0.0 !Heating value (upper) [kJ/mol] :Heat: A1 !Safety Group (ASHRAE Standard 34, 2010) :Safety: 1S/He !Standard InChI String :InChi: SWQJXJOGLNCZEY-UHFFFAOYSA-N !Standard InChI Key :InChiKey: ???? !Alternative fluid for mixing rules :AltID: 3b8eed30 !Hash number from InChI Key :Hash: !The fluid files contain general information about the fluid in the first 15 to 20 lines, followed by sections for the ! equations of state, transport equations, and auxiliary equations. Equations of state are listed first. The NIST recommended ! equations begin with a hash mark (#). The secondary equations begin with the @ symbol. These symbols can be swapped to ! select a secondary equation as primary and the primary as secondary. The equation of state section also contains auxiliary ! equations for the ideal gas heat capacity or ideal gas Helmholtz energy. Below the equations of state (both primary and ! secondary) are the transport equations, first viscosity and then thermal conductivity. These are then followed by the ! secondary equations if available. The transport section also contains auxiliary equations required to calculate either the ! dilute gas state or the critical enhancement. At the end of the file are additional but not necessary auxiliary equations, ! including simple equations for the vapor pressure, saturated liquid and vapor densities, melting line (for some fluids), and ! sublimation line (for even fewer fluids). This section also contains the equations for dielectric constant and surface ! tension if available. The sections are divided by different symbols (these being _-+=^*~) to aid the eye in locating a ! particular section. Secondary equations are indented 10 spaces to avoid confusion with the NIST recommended equations. The ! end of the fluid file is marked with @END. Anything below that is ignored. ! compiled by E.W. Lemmon, NIST Physical and Chemical Properties Division, Boulder, Colorado ! 01-23-97 EWL, Original version. ! 11-06-00 EWL, Switch transport equations to hardcoded models. ! 08-05-04 EWL, Add Harvey and Lemmon dielectric correlation. ! 11-18-04 MLH, Add tPr coeff. ! 12-11-09 EWL, Add 40 term EOS derived from the McCarty and Arp BWR equation. ! 09-08-10 EWL, Add equation of state of Ortiz-Vega. ! 12-06-12 EWL, Add surface tension coefficients of Mulero et al. (2012). ! 04-08-13 EWL, Add second equation of state of Ortiz-Vega. ! 06-04-14 EWL, Add final equation of state of Ortiz-Vega. ! 02-10-17 EWL, Update ancillary equations. ! 05-15-17 EWL, Change the hard coded VS0 model to the VS7 reverse Polish notation. ________________________________________________________________________________ #EOS !---Equation of state--- FEQ !Helmholtz equation of state for helium of Ortiz-Vega et al. (2015). :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) :DOI: ? ?``````````````````````````````````````````````````````````````````````````````` ?Ortiz-Vega, D.O., Hall, K.R., Holste, J.C., Arp, V.D., Harvey, A.H., and Lemmon, E.W., ? final equation of state, to be submitted to J. Phys. Chem. Ref. Data, 2018. ? ?The uncertainties below 50 K in density are 0.25% at pressures up to 10 MPa. ? From 50 K to 200 K, the uncertainties decrease linearly from 0.2% at 50 K to ? 0.05% at 200 K for all pressures up to 50 MPa. Between 200 K and 500 K, the ? uncertainty is 0.03% up to pressures of 40 MPa and 0.1% between 40 MPa and 100 ? MPa. For all other states not listed here, the uncertainties increase to 0.5% ? in density. The uncertainties in the speed of sound are 0.01% for the vapor ? phase and 0.2% for the liquid phase. The uncertainty in vapor pressure is ? less than 0.02%, and that for heat capacities is about 2%. Uncertainties in ? the critical region are higher for all properties except vapor pressure. ? !``````````````````````````````````````````````````````````````````````````````` 2.1768 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 141.22 !Maximum density [mol/L] CPP !Pointer to Cp0 model 4.002602 !Molar mass [g/mol] 2.1768 !Triple point temperature [K] 5.0393 !Pressure at triple point [kPa] 36.48 !Density at triple point [mol/L] 4.2238 !Normal boiling point temperature [K] -0.3836 !Acentric factor 5.1953 228.32 17.3837 !Tc [K], pc [kPa], rhoc [mol/L] 5.1953 17.3837 !Reducing parameters [K, mol/L] 8.3144598 !Gas constant [J/mol-K] 12 4 11 12 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.015559018 1.0 4. 0. !a(i),t(i),d(i),l(i) 3.0638932 0.425 1. 0. -4.2420844 0.63 1. 0. 0.054418088 0.69 2. 0. -0.18971904 1.83 2. 0. 0.087856262 0.575 3. 0. 2.2833566 0.925 1. 1. -0.53331595 1.585 1. 2. -0.53296502 1.69 3. 2. 0.99444915 1.51 2. 1. -0.30078896 2.9 2. 2. -1.6432563 0.8 1. 1. 0.8029102 1.26 2. 2. 2. -1.5497 -0.2471 3.15 0.596 0. 0. 0. 0.026838669 3.51 1. 2. 2. -9.245 -0.0983 2.54505 0.3423 0. 0. 0. 0.04687678 2.785 2. 2. 2. -4.76323 -0.1556 1.2513 0.761 0. 0. 0. -0.14832766 1. 1. 2. 2. -6.3826 -2.6782 1.9416 0.9747 0. 0. 0. 0.03016211 4.22 1. 2. 2. -8.7023 -2.7077 0.5984 0.5868 0. 0. 0. -0.019986041 0.83 3. 2. 2. -0.255 -0.6621 2.2282 0.5627 0. 0. 0. 0.14283514 1.575 2. 2. 2. -0.3523 -0.1775 1.606 2.5346 0. 0. 0. 0.007418269 3.447 2. 2. 2. -0.1492 -0.4821 3.815 3.6763 0. 0. 0. -0.22989793 0.73 3. 2. 2. -0.05 -0.3069 1.61958 4.5245 0. 0. 0. 0.79224829 1.634 2. 2. 2. -0.1668 -0.1758 0.6407 5.039 0. 0. 0. -0.049386338 6.13 2. 2. 2. -42.2358 -1357.6577 1.076 0.959 0. 0. 0. eta beta gamma epsilon EXP[eta*(delta-epsilon)^2+beta*(tau-gamma)^2] #AUX !---Auxiliary function for Cp0 CPP !Ideal gas heat capacity function for helium of Ortiz-Vega et al. (2015). ? ?``````````````````````````````````````````````````````````````````````````````` ?Ortiz-Vega, D.O., Hall, K.R., Holste, J.C., Arp, V.D., Harvey, A.H., and Lemmon, E.W., 2018. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.3144598 !Reducing parameters for T, Cp0 1 0 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.5 0.0 #AUX !---Auxiliary function for PX0 PX0 !Helmholtz energy ideal-gas function for helium of Ortiz-Vega et al. (2015). ? ?``````````````````````````````````````````````````````````````````````````````` ?Ortiz-Vega, D.O., Hall, K.R., Holste, J.C., Arp, V.D., Harvey, A.H., and Lemmon, E.W., 2018. ? !``````````````````````````````````````````````````````````````````````````````` 1 2 0 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)) 1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms 0.1733487932835764 0.0 !aj, ti for [ai*tau**ti] terms 0.4674522201550815 1.0 !aj, ti for [ai*tau**ti] terms -------------------------------------------------------------------------------- @EOS !---Equation of state--- FEK !Helmholtz equation of state for helium of Kunz and Wagner (2004). ? ?``````````````````````````````````````````````````````````````````````````````` ?Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M. ? "The GERG-2004 Wide-Range Equation of State for Natural Gases ? and Other Mixtures," GERG Technical Monograph 15, ? Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 2007. ? !``````````````````````````````````````````````````````````````````````````````` 2.1768 !Lower temperature limit [K] 1500.0 !Upper temperature limit [K] 100000.0 !Upper pressure limit [kPa] 88.73 !Maximum density [mol/L] PHK !Pointer to Cp0 model 4.002602 !Molar mass [g/mol] 2.1768 !Triple point temperature [K] 4.8565 !Pressure at triple point [kPa] 36.537 !Density at triple point [mol/L] 4.22 !Normal boiling point temperature [K] -0.3859 !Acentric factor 5.1953 227.46 17.399 !Tc [K], pc [kPa], rhoc [mol/L] 5.1953 17.399 !Reducing parameters [K, mol/L] 8.314472 !Gas constant [J/mol-K] 12 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms -0.45579024006737 0.0 1. 0. 1.2516390754925 0.125 1. 0. -1.5438231650621 0.75 1. 0. 0.020467489707221 1.0 4. 0. -0.34476212380781 0.75 1. 1. -0.020858459512787 2.625 3. 1. 0.016227414711778 0.125 5. 1. -0.057471818200892 1.25 5. 1. 0.019462416430715 2.0 5. 1. -0.03329568012302 1.0 2. 2. -0.010863577372367 4.5 1. 3. -0.022173365245954 5.0 2. 3. @AUX !---Auxiliary function for PH0 PHK !Ideal gas Helmholtz form for helium of Kunz and Wagner (2004). ? ?``````````````````````````````````````````````````````````````````````````````` ?Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M. ? "The GERG-2004 Wide-Range Equation of State for Natural Gases ? and Other Mixtures," GERG Technical Monograph 15, ? Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 2007. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1 2 0 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)); cosh; sinh 1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms 13.628409737 0.0 !aj, ti for [ai*tau**ti] terms -143.470759602 1.0 @EOS !---Equation of state--- FE1 !Helmholtz equation of state for helium of Ortiz-Vega et al. (2010). ? ?``````````````````````````````````````````````````````````````````````````````` ?Ortiz-Vega, D.O., Hall, K.R., Arp, V.D., and Lemmon, E.W., ? Interim equation, 2010. ? ?Below 50 K, the uncertainties in density are 0.5% at pressures up to 10 MPa. ? From 50 K to 200 K the uncertainties decrease to 0.2 % at pressures up to 50 ? MPa. At higher temperatures the uncertainties in density are 0.1 % up to ? pressures of 20 MPa. At all temperatures and at pressures higher than listed ? here, the uncertainties increase to 1% in density. The uncertainties in the ? speed of sound are 0.04% for the vapor phase and 0.25% for the liquid phase. ? The uncertainties in vapor pressure are less than 0.05% and for the heat ? capacities are about 5%. Uncertainties in the critical region are higher for ? all properties except vapor pressure. ? !``````````````````````````````````````````````````````````````````````````````` 2.1768 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 141.22 !Maximum density [mol/L] CPP !Pointer to Cp0 model 4.002602 !Molar mass [g/mol] 2.1768 !Triple point temperature [K] 5.043 !Pressure at triple point [kPa] 36.46 !Density at triple point [mol/L] 4.222 !Normal boiling point temperature [K] -0.385 !Acentric factor 5.1953 227.6 18.13 !Tc [K], pc [kPa], rhoc [mol/L] 5.1953 18.13 !Reducing parameters [K, mol/L] 8.314472 !Gas constant [J/mol-K] 12 4 9 12 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.009288766 1.0 4. 0. !a(i),t(i),d(i),l(i) 0.9258069 0.28 1. 0. -1.718156 0.735 1. 0. 0.7606137 0.64 2. 0. -1.024864 0.82 2. 0. 0.1052455 1.16 3. 0. -0.1875722 1.28 1. 1. -0.1287812 2.0 1. 2. -0.002227619 0.41 3. 2. 0.1823465 1.33 2. 1. -0.04450014 4.2 2. 2. -0.00008729033 0.6 8. 1. 0.0385432 3.0 1. 2. 2. -1.0833 -0.0385 1.9776 0.6914 0. 0. 0. -0.9585106 1.0 1. 2. 2. -18.3824 -19.8246 1.6178 0.8590 0. 0. 0. -0.0545401 8.2 1. 2. 2. -5.0573 -9.3799 0.4371 0.8787 0. 0. 0. -0.0368726 1.0 2. 2. 2. -0.2832 -0.8073 0.5355 2.7182 0. 0. 0. -0.001021851 2.71 2. 2. 2. -6.0582 -0.031 0.7777 2.0301 0. 0. 0. 0.06166348 1.0 2. 2. 2. -0.2444 -0.0061 0.4832 0.89 0. 0. 0. 0.02493437 1.0 3. 2. 2. -0.0539 -0.3581 0.8162 1.179 0. 0. 0. -0.008127424 2.0 3. 2. 2. -0.185 -0.7518 1.2896 0.568 0. 0. 0. -0.008233032 1.0 2. 2. 2. -0.5941 -7.4629 0.3577 1.6412 0. 0. 0. @EOS !---Equation of state--- BWR !MBWR equation of state for helium of McCarty and Arp (1990). ? ?``````````````````````````````````````````````````````````````````````````````` ?McCarty, R.D. and Arp, V.D., ? "A New Wide Range Equation of State for Helium," ? Adv. Cryo. Eng., 35:1465-1475, 1990. ? ?The uncertainties of the equation of state range from 1% at low ? temperatures (<20 K) to 0.1% at temperatures between 200 and 400 K, and ? from 3% in the speed of sound in the liquid phase to 0.1% in the speed ? of sound between 100 and 500 K. The uncertainty of heat capacities is ? about 5%. ? !``````````````````````````````````````````````````````````````````````````````` 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] 2.1768 !Triple point temperature [K] 4.8565 !Pressure at triple point [kPa] 36.537 !Density at triple point [mol/L] 4.230 !Normal boiling point temperature [K] -0.382 !Acentric factor 5.1953 227.46 17.399 !Tc [K], pc [kPa], rhoc [mol/L] 5.1953 17.399 !Reducing parameters [K, mol/L] 17.399 !gamma 0.0831431 !Gas constant [L-bar/mol-K] 32 1 !Nterm, Ncoeff per term 0.0004558980227431 0.01260692007853 -0.07139657549318 0.09728903861441 -0.1589302471562 0.1454229259623e-4 -0.0004708238429298 0.01132915223587 0.02410763742104 -0.5093547838381e-7 0.26997269279e-4 -0.0003954146691114 0.1551961438127e-7 0.1050712335785e-6 -0.550115836675e-6 -0.1037673478521e-8 0.6446881346448e-11 0.3298960057071e-9 -0.3555585738784e-11 -0.0688540136769 0.09166109232806 -0.6544314242937e-4 -0.0003315398880031 -0.2067693644676e-6 0.3850153114958e-6 -0.1399040626999e-9 -0.1888462892389e-10 -0.4595138561035e-13 0.6872567403738e-13 -0.6097223119177e-17 -0.7636186157005e-16 0.3848665703556e-16 @EOS !---Equation of state--- FE2 !Helmholtz equation of state of McCarty and Arp (1990). ? ?``````````````````````````````````````````````````````````````````````````````` ?McCarty, R.D. and Arp, V.D., ? "A New Wide Range Equation of State for Helium," ? Adv. Cryo. Eng., 35:1465-1475, 1990. ? ?The coefficients used in this equation are derived from the BWR coefficients ? given in the original manuscript. The uncertainties are thus the same ? as those given for the BWR EOS. ? !``````````````````````````````````````````````````````````````````````````````` 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] 2.1768 !Triple point temperature [K] 4.8565 !Pressure at triple point [kPa] 36.537 !Density at triple point [mol/L] 4.230 !Normal boiling point temperature [K] -0.382 !Acentric factor 5.1953 227.46 17.399 !Tc [K], pc [kPa], rhoc [mol/L] 5.1953 17.399 !Reducing parameters [K, mol/L] 8.31431 !Gas constant [J/mol-K] 40 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms -2.08984171567 3.0 0. 0. !a(i),t(i),d(i),l(i) 0.381792817549 4.0 0. 0. -0.0441393943069 5.0 0. 0. 0.0954038242224 0.0 1. 0. 1.15744872054 0.5 1. 0. -2.87584069992 1.0 1. 0. 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)