Abstract
This work was aimed at gaining understanding of the physical behaviours of the flow and temperature separation process in a vortex tube. To investigate the cold mass fraction’s effect on the temperature separation, the numerical calculation was carried out using an algebraic Reynolds stress model (ASM) and the standard k-ɛ model. The modelling of turbulence of compressible, complex flows used in the simulation is discussed. Emphasis is given to the derivation of the ASM for 2D axisymmetrical flows, particularly to the model constants in the algebraic Reynolds stress equations. The TEFESS code, based on a staggered Finite Volume approach with the standard k-ɛ model and first-order numerical schemes, was used to carry out all the computations. The predicted results for strongly swirling turbulent compressible flow in a vortex tube suggested that the use of the ASM leads to better agreement between the numerical results and experimental data, while the k-ɛ model cannot capture the stabilizing effect of the swirl.
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References
Ahlborn, B., Keller, J.U., Staudt, R., Treitz, G., Rebhan, E., 1994. Limits of temperature separation in a vortex tube. J. Physics D: Applied Physics, 27(3):480–488. [doi:10.1088/0022-3727/27/3/009]
Aljuwayhel, N.F., Nellis, G.F., Klein, S.A., 2005. Parametric and internal study of the vortex tube using a CFD model. International Journal of Refrigeration, 28(3):442–450. [doi:10.1016/j.ijrefrig.2004.04.004]
Amitani, T., Adachi, T., Kato, T., 1983. A study on temperature separation in a large vortex tube. Trans. JSME, 49:877–884.
Behera, U., Paul, P.J., Kasthurirengan, S., Karunanithi, R., Ram, S.N., Dinesh, K., Jacob, S., 2005. CFD analysis and experimental investigations towards optimizing the parameters of Ranque-Hilsch vortex tube. Int. J. Heat and Mass Transfer, 48(10):1961–1973. [doi:10.1016/j.ijheatmasstransfer.2004.12.046]
Frohlingsdorf, W., Unger, H., 1999. Numerical investigations of the compressible flow and the energy separation in the Ranque-Hilsch vortex tube. Int. J. Heat and Mass Transfer, 42(3):415–422. [doi:10.1016/S0017-9310(98)00191-4]
Gatski, T.B., 1996. Turbulent Flows: Model Equations and Solution Methodology. In: Peyret, R. (Ed.), Handbook of Computational Fluid Mechanics. Academic Press Ltd., London.
Hilsch, R., 1947. The use of expansion of gases in a centrifugal field as a cooling process. Review of Scientific Instruments, 18(2):108–113. [doi:10.1063/1.1740893]
Nash, J.M., 1991. Vortex Expansion Devices for High Temperature Cryogenics. Proceedings of the Intersociety Energy Conversion Engineering Conference, 4:521–525.
Negm, M.I.M., Serag, A.Z., Abdel Ghany, S.M., 1988. Performance characteristics of energy separation in double stage vortex tubes. Modelling, Simulation & Control B: Mechanical & Thermal Engineering, Materials & Resources, Chemistry, 14:21–32.
Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Incorp., Washington DC.
Promvonge, P., 1999. Numerical Simulation of Turbulent Compressible Vortex-Tubes Flow. Proceedings of the 3rd ASME/JSME Joint Fluids Engineering Conference. San Francisco, California.
Promvonge, P., Eiamsa-ard, S., 2004. Experimental investigation of temperature separation in a vortex tube refrigerator with snail entrance. ASEAN Journal on Science & Technology for Development, 21:297–308.
Pun, W.M., 1992. An Introduction to the TEFESS Code. Internal Report, Mechanical Engineering Department, Imperial College of Science, Technology & Medicine.
Ranque, G.J., 1933. Experiments on expansion in a vortex with simultaneous exhaust of hot air and cold air. Le Journal de Physique et le Radium (Paris), 4:112–114, S-115. Also translated as General Electric Co., Schenectady Works Library, T.F. 3294 (1947).
Ranque, G.J., 1934. Method and Apparatus for Obtaining from a Fluid under Pressure Two Outputs of Fluid at Different Temperatures. US Patent No. 1,952,281.
Rodi, W.A., 1976. New algebraic relations for calculating the Reynolds stresses. Z. Angew. Math. Mech., 56:T219–T221.
Scheper, G.W., 1951. The vortex tube; internal flow data and a heat transfer theory. J. ASRE, Refrigerating Engineering, 59:985–989.
Sloan, D.G., Smith, P.J., Smoot, L.D., 1986. Modeling of swirl in turbulent flow system. Progr. Energy Combust. Sci., 12(3):163–250. [doi:10.1016/0360-1285(86)90016-X]
Stephan, K., Lin, S., Durst, M., Huang, F., Seher, D., 1983. An investigation of energy separation in a vortex tube. Int. J. Heat Mass Transfer, 26(3):341–348. [doi:10.1016/0017-9310(83)90038-8]
Stephan, K., Lin, S., Durst, M., Huang, F., Seher, D., 1984. A similarity relation for energy separation in a vortex tube. Int. J. Heat Mass Transfer, 27(6):911–920. [doi:10.1016/0017-9310(84)90012-7]
Wilcox, C.D., 1993. Turbulent Modelling for CFD. DCW Industries Inc., California.
Zhang, J., Nieh, S., Zhou, L., 1992. A new version of algebraic stress model for simulating strongly swirling turbulent flows. J. Numerical Heat Transfer, 22:49–62.
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Smith, Ea., Pongjet, P. Numerical prediction of vortex flow and thermal separation in a subsonic vortex tube. J. Zhejiang Univ. - Sci. A 7, 1406–1415 (2006). https://doi.org/10.1631/jzus.2006.A1406
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DOI: https://doi.org/10.1631/jzus.2006.A1406