Results of numerical simulation of the mixing of a turbulent jet with a cocurrent incompressible-fluid flow (Schmidt number Sc ≈ 1000) in a cylindrical channel of circular cross section (axisymmetric mixer) with the use of the standard k-ε turbulence model and different models for the averaged value of the mixture fraction and its variance have been given. For the problem of mixing of an inert passive impurity, two regimes of flow — the regime with the formation of a recirculation zone and that without its formation — have been considered. The formulated statistical model has been verified with the use of experimental data and results of calculation by large-eddy simulation.
Similar content being viewed by others
References
G. N. Abramovich, Theory of Turbulent Jets [in Russian], Izd. Fiz.-Mat. Lit., Moscow (1960).
B. A. Kolovandin, Simulation of Inhomogeneous Turbulence Heat Transfer [in Russian], Nauka i Tekhnika, Minsk (1980).
P. Moin and K. Mahesh, Direct numerical simulation: A tool in turbulence research, Ann. Rev. Fluid Mech., 30, 539–578 (1998).
J. H. Ferziger, Large eddy simulation: its role in turbulence research, in: D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt (Eds.), Theoretical Approaches in Turbulence, Springer-Verlag, New York (1987), pp. 51–72.
V. L. Zhdanov, N. V. Kornev, E. Hassel, and A. D. Chorny, Mixing of confined coaxial flows, Int. J. Heat Mass Transfer, 49, 3942–3956 (2006).
I. Tkatchenko, N. Kornev, S. Jahnke, G. Steffen, and E. Hassel, Performances of LES and RANS models for simulation of complex flows in a coaxial jet mixer, Flow, Turbulence and Combustion, 78, No. 2, 111–127 (2007).
V. L. Zhdanov, N. V. Kornev, and E. Hassel, The influence of the mixer geometry on the scalar field formation, Lasermethoden in der Strömungsmesstechnik, 13 Fachtagung, 6–8 September, 2005, Cottbus, Germany (2005), pp. 37-1–37-8.
H. J. Henzler, Investigations on Mixing Fluids, Doctoral Dissertation, Aachen (1978).
H. A. Becker, H. C. Hottel, and G. C. Williams, Mixing and flow in ducted turbulent jets, Proc. IX Symp. (Int.) on Combustion, Academic Press, London (1963), pp. 7–20.
M. Barchilon and R. Curtet, Some details of the structure of an axis-symmetrical confined jet with backflow, J. Basic Eng., No. 12, 777–787 (1964).
A. D. Chornyi and V. L. Zhdanov, Turbulent mixing of a passive admixture in an axisymmetric jet mixer, in: Proc. 6th Russian National Heat Transfer Conf., 19–23 November 2006 [in Russian], Vol. 2, Izd. MÉI, Moscow (2006), pp. 266–269.
Yu. V. Lapin and M. Kh. Strelets, Internal Flows of Gas Mixtures [in Russian], Nauka, Moscow (1989).
S. B. Pope, An explanation of the turbulent round-jet/plane-jet anomaly, AIAA J., 16, 279–281 (1978).
A. Rubel, On the vortex stretching modification of the k-ε-model in radial jets, AIAA J., 23, 1129–1130 (1985).
C. G. Speciale, On nonlinear k-l-and k-ε-models of turbulence, J. Fluid Mech., 178, 459–475 (1987).
B. B. Dally, D. F. Fletcher, and A. R. Masri, Flow and mixing fields of turbulent bluff-body jets and flames, Combust. Theory Model., 2, 193–219 (1998).
F. C. Lockwood and P. Stokalis, Assessment of two turbulence models for turbulent round diffusion jets with combustion, in: Turbulent Shear Flows, Vol. 4, Springer-Verlag, Berlin (1983), pp. 328–344.
J. J. Mc Guirk and W. Rodi, The calculation of the three-dimensional turbulent free jets, in: F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw (Eds.), Proc. 1st Symp. on Turbulent Shear Flows, New York (1979), pp. 71–83.
J. P. Sanders, B. Sarh, and I. Gokalp, Variable density effects in axisymmetric isothermal turbulent jets: A comparison between a first-and a second-order turbulence model, Int. J. Heat Mass Transfer, 40, No. 4, 823–842 (1997).
R. Borghi and D. Escudie, Assessment of a theoretical model of turbulent combustion by comparison with a simple experiment, Combust. Flame, 56, 149–164 (1984).
E. J. Smith, G. J. Nathan, and B. B. Dally, Range of validity of a modified k-ε model of the non-reacting flow from a precessing jet nozzle, Proc. III Int. Conf. on CFD in the Minerals and Process Industries (CSIRO), 10–12 December 2003, Melbourne, Australia (2003), pp. 499–504.
R. Luppes, The Numerical Simulation of Turbulent Jets and Diffusion Flames, PhD Thesis, Eindhoven (2000).
J. Baldyga and J. R. Bourne, Turbulent Mixing and Chemical Reactions, Wiley & Sons, New York (1999).
F. E. Kruis and L. Falk, Mixing and reaction in a tubular jet reactor: A comparison of experiments with a model based on a prescribed PDF, Chem. Eng. Sci., 51, No. 10, 2439–2448 (1996).
A. D. Chornyi, Numerical simulation of the interaction of turbulent jets with a co-current flow in a cylindrical channel, Dokl. Nats. Akad. Nauk Belarusi, 51, No. 1, 104–110 (2007).
V. L. Zhdanov, A. D. Chornyi, and É. Hassel, Analysis of the process of mixing a passive admixture in a jet mixer, Inzh.-Fiz. Zh., 80, No. 2, 46–59 (2007).
P. J. Guiraud, J. Bertrand, and J. Costes, Laser measurements of local velocity and concentration in a turbulent jet-stirred tubular reactor, Chem. Eng. Sci., 46, 1289–1297 (1991).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 4, pp. 666–681, July–August, 2008.
Rights and permissions
About this article
Cite this article
Chornyi, A.D., Kornev, N.V. & Hassel, E. Simulation of the turbulent mixing of a passive impurity in a jet mixer. J Eng Phys Thermophy 81, 692–707 (2008). https://doi.org/10.1007/s10891-008-0097-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-008-0097-1