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The Properties of Helium: Density, Specific Heats, Viscosity, and Thermal Conductivity at Pressures from 1 to 100 Bar and from Room Temperature to About 1800 K

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Downloaded from orbit.dtu.dk on: Oct 04, 2021 The properties of helium: Density, specific heats, viscosity, and thermal conductivity at pressures from 1 to 100 bar and from room temperature to about 1800 K Petersen, H. Publication date: 1970 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Petersen, H. (1970). The properties of helium: Density, specific heats, viscosity, and thermal conductivity at pressures from 1 to 100 bar and from room temperature to about 1800 K. Risø National Laboratory. Denmark. Forskningscenter Risoe. Risoe-R No. 224 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. « Riso Report No. 224 5 o, « Danish Atomic Energy Commission .1 * Research Establishment Ris6 The Properties of Helium: Density, Specific Heats, Viscosity, and Thermal Conductivity at Pressures from 1 to 100 bar and from Room Temperature to about 1800 K by Helge Petersen September, 1970 Sain dUiributort: JUL GjiUtrap, 17, »Wpdt, DK-U07 Capubaftn K, Dnaurk U.D.C m»!:62U34.3t September, 1 970 Rise Report No. 224 The Properties of Helium: Density, Specific Heats. Viscosity, and Thermal Conductivity at Pressures from 1 to 100 bar and from Room Temperature to about 1800 K by Helge Petersen Danish Atomic Energy Commission Research Establishment Rise Engineering Department Section of Experimental Technology Abstract An estimation of the properties of helium is carried out on the basis of a literature survey. The ranges of pressure and temperature chosen are applicable to helium-cooled atomic reactor design. A brief outline of vhe theory for the properties is incorporated, and comparisons of the re­ commended data with the data calculated from intermolecular potential functions are presented. I3BI 87 550 0035 5 - 3 - CONTENTS Page 1. Introduction 5 2. Summary of Recommended Data ,, 5 3. Gas Law 7 4. Specific Heats '2 5. Correlation Formulae for Viscosity and Conductivity '3 6. Viscosity Data ' 2C 7. Thermal Conductivity Data 29 8. Prandtl Number 30 9. Acknowledgements and Notes 32 10. References 33 11.. Tables of Recommended Data 37 - 5 - 1. INTRODUCTION Calculations of the heat transfer and the temperature in the core and the heat exchangers of a helium-cooled reactor require knowledge of some of the thermophysical properties of the helium gas, and the same applies to the treatment of observed data in heat transfer experiments. The properties treated in this report are the density, the specific heats, the thermal conductivity, and the viscosity. The gas properties are only known with a certain accuracy, and it is therefore necessary to survey the existing experimental and theoretical data in the literature to establish a set of recommendable data. The data result­ ing from this survey are presented as equations in order to facilitate the use of computors, and it is shown that very simple equations suffice to ex­ press the data with ample accuracy. Two equations are presented for each property, one in terms of the absolute temperature, T, in Kelvin and the other in terms of the ratio T/T , T being the absolute temperature at zero degrees Celsius, equal to 273.16 K. The ranges of pressure and temperature considered for the data are 1 to 100 bar for pressure and 273 to 1800 K for temperature. The Prandtl number is a combination of the properties which is often used in thermodynamic calculations, and for that reason equations are also presented for this quantity, 2. SUMMARY OF RECOMMENDED DATA FOR HELIUM AT 1 TO 1 00 BAR AND 273 TO 1 800 K kg unit of mass, kilogram m unit of length, metre s unit of time, second N unit of force, newton, kg* m/s J unit of energy, joule, N * m W unit of power, watt, j/s P pressure, bar, 10 N/m • 0.9869 phys. atm T absolute temperature, K T abs. temperature at 0 °C • 273.1 6 K - 6 - Gas Law of Helium P • 10"* 2077.S* p • T * Z • (3-2),(3-3) where p is the density, and Z is the compressibility factor: Z = 1 + 0.4446 -£, = 1 + 0.530 • 10"3 £»-» . (3-18) ,J r-' {T/TO)'- The standard deviation, o, is about 0.03% at a pressure of 1 bar and 0.3% at 100 bar, i. e. a - 0. 03 • VP%. (3-20) Mass Density of Helium P = 48.14 f [l + 0.4446 -J75J (3-19) 3 1 • 0.17623 ^ [, • 0.53 • lO- -^]" ^m\ The standard deviation is as for Z. Specific Heata cp = 5195. J/kg • K, (4-4) cy = 3117. J/k?- K, (4-5) 1 ' cp/°v = K6667- <4"6> The standard deviation, 9, is at 273 K about 0.05% at a pressure of 1 bar and 0.5% at 100 bar, decreasing to 0.05% at high temperature at all 0,6 pressures, i.e. • « 0.05p' " "-'(T/T^ (4_7) Coefficient of Dynamic Viscosity 7 T 5 0 7 M- 3.674- 10" T°' - 1.865- 10" (T/To) ' kg/m-S. (6-1) The standard deviation, t, ia about 0.4% at 273 K and 2.7% at 1800 K, i.e. e • 0.0015 T%. (6-3) - 7 - Coefficient of Thermal Conductivity k « 2.682 • 10"3(1 + 1.123 - 10"3P) T<0-71 (1 " 2'10 PJ) (7-1) (0 71 2 = 0.144(1 + 2.7 • 10"*P) (T/To) - 0 " " '<>" ?)) w/m. JJ. The standard deviation, o, is about 1 % at 273 K and 6% at 1800 K, i.e. o= 0.0035 T%. (7-4) Prandtl Number Pr = cp { 4 p,. 0.7117 T-(0.01 - 1.42 • 10" P) (8_,} 1 ++ 1.123 • 10"3P 4 , 0.6728 (T.T j-(0.01 - 1.42 • 10~ P) 1 + 2.7 • 10"4P ° The standard deviation is o • 0.004 TV (8-2) 3. GAS LAW The ideal gas law or the ideal equation of state is the p-v-T relation for an ideal gas: p • v = K • T (3-1) 2 p, pressure, N/m Q T, specific molal volume, m /kg-mole R, universal gas constant, 8314.5 J/kg-mole • K T, absolute temperature, K. For a noble gas such as helium the real p-v-T relation deviates little from the real gas law at the pressure and the temperature in a reactor core. The deviation increases numerically with pressure and decreases with temperature. If the ideal gaa law ia applied to helium at a pressure of 60 bar and a temperature of 350 K, the deviation from the real gas law ial.SH. In calculations where »uch d**tttkm» art allowable, tta idW'!•****-' can therefore kV applied; Ttte wtottAdar weight df bettts* t» 4V »w»Y atf« - 8 - this gives the following gas law for helium when considered an ideal gas: „„„ P- '°S ,„ * J (3-2) 2077.3 • p • T l ' P, pressure, bar (1 bar = 105 N/m = 0.9863 phys. atm) p , mass density, kg/m . In some calculations it might, however, be desirable to operate with an expression which gives a greater accuracy. This is normally done by introduction of the compressibility factor, Z, in the gas law: irrr = z • <3-3> The compressibility factor, Z, can be determined by consideration of the virial equation of state. An equation of state for a gas is a relationship between the character­ istic force, the characteristic configuration and the temperature. For an ideal gas the pressure 1B the only characteristic force, the volume being the characteristic configuration, but other forces must be taken into account for a real gas if the pressure is not very low. This can be done by adding force-describing terms to the ideal equation of state. Virial equations are power expansions in terms of volume or pressure respectively p. v = A(l + £- + Sj ...) (3-4) v 2 p- v = A+ B- p+ £i2- p2 + (3-5) The coefficients A, B, C and so on are named virial coefficients, i. e. they are force coefficients. The virial coefficients are obtained experi­ mentally by fitting of the power series to measured isotherms of the gas. This gives a different set of coefficients for each Isotherm, and thus the virial coefficients are temperature-dependent. Equation (3-5) converges less rapidly than eq. (S-4) and thus requires more terms for equal precision. Thia ie of minor importance for density determination, for which only the first correction t(rm, the second virial coefficient, B, U »igniflcant except at extremely high prsasur*. The virial equation of Stat* sufficient for dansity caleulaiioa of Ujht noble |iuu -9- is then: p- v" A+ B • p. (3-6) A system of units often used in this equation is the Amagat units. In this system the pressure pa is in atm, and the volume vQ is expressed in the normal molal volume as a unit, writing pa- vn = A+B-pa = AQ £ + B- pa, (3-7) o A is the ratio of p • v at zero pressure to p • v at the pressure of 1 atm, or A0 - 1 - B0 .
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