How to estimate the transport properties: dynamic viscosity, thermal conductivity and diffusivity of a gas, if measurements are not available?
Tagged: 16, cfx, fluiddynamics, General, General  CFX, materialproperties


January 25, 2023 at 7:16 amFAQParticipant
Some gases are rare or have low vapour pressure and so measurements of transport properties may not be available from the literature. Dynamic Viscosity ============== Transport properties can still be estimated based on the kinetic theory of gases. For example, Poling. Prausnitz and O’Connell, “The Properties of Gases and Liquids” lists critical constants for many substances. Then from Bird, Stewart and Lightfoot, “Transport Phenomena”, Wiley NY 1960, p2223, for spherical nonpolar molecules, we can estimate the LennardJones parameters: epsilon/k = 0.77*Tc where the critical temperature, Tc is in K, the characteristic diameter, sigma in Angstroms, = 0.841*Vc^(1/3) with the critical volume, Vc in cm3/mol (or sigma = 2.44(Tc/pc)^(1/3) with the critical pressure, pc, in atm). The dynamic viscosity for a gas at low density is then given by: Mu = 2.6693×10^6*(MT)^(1/2)/sigma^2*Omega in kg/m/s, where M is the molecular weight in kg/kmol and Omega can be found as a function of epsilon /k in Table B2, p746. Specific Heat Capacity ================= The specific heat at constant pressure, Cp, is usually easily found in the literature, for example, Alexander Burcat and Branko Ruscic, Ideal Gas Thermochemical Database with updates from Active Thermochemical Tables in ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics mirrored at http://garfield.chem.elte.hu/Burcat/burcat.html has NASA polynomials for many materials in the form of tworange NASA polynomials (S. Gordon and B.J. McBride, “Computer Program for Calculation of Complex Chemical Equilibrium Composition, Rocket Performance, Incident and Reflected Shocks and ChapmanJouguet Detonations”, NASA SP273 (1971)),. So for example, THERMO 200.0 1000.0 6000.0 Br J6/82BR 1 0 0 0G 200.000 6000.000 1 2.08851053E+00 7.12118611E042.70003073E07 4.14986299E112.31188294E15 2 1.28568767E+04 9.07351144E+00 2.48571711E+00 1.50647525E045.37267333E07 3 7.20921065E102.50205558E13 1.27092168E+04 6.86030804E+00 1.34535890E+04 4 END The lower polynomial is valid for 200K < T < 1000K: Cp = R/M*(a1+a2*T+a3*T^2+a4*T^3+a5*T^4), where a1 = 2.48571711E+00 a2 = 1.50647525E04 a3 = 5.37267333E07 a4 = 7.20921065E10 a5 = 2.50205558E13 and the upper for 1000K < T < 6000K a1 = 2.08851053E+00 a2 = 7.12118611E04 a3 = 2.70003073E07 a4 = 4.14986299E11 a5 = 2.31188294E15 and R is the universal gas constant (8314.41 J/kmol/K) and M is the molecular weight. Thermal Conductivity ================ You can estimate k from Bird, Stewart and Lightfoot, p257. the Eucken formula gives k = (Cp + 5/4*R/M)*Mu, which for monotonic gases can be simplified to k = 15/4*(R/M)*Mu.

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