Abstract
The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-ɛ turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.
Similar content being viewed by others
References
G.N. Abramovich, Theory of Turbulent Jets [in Russian], Fizmatgiz, Moscow (1960).
T.-Y. Sun and G.M. Faeth, “Structure of Turbulent Bubbly Jets. I. Method and Centerline Properties,” Int. J. Multiphase Flow 12, 99 (1986).
S. Kumar, D. Nikitopoulos, and E.E. Michaelidis, “Effect of Bubbles on the Turbulence near the Exit of a Liquid Jet,” Experiments Fluids 7, 487 (1989).
G. Hetsroni and M. Sokolov, “Distribution of Mass, Velocity and Intensity of Turbulence in a Two-Phase Turbulent Jet,” Trans. ASME. J. Appl. Mech. 38, 315 (1971).
M.K. Laats and F.A. Frishman, “Assumptions Used in Calculating the Two-Phase Jet,” Fluid Dynamics 5(2), 333 (1970).
F. Prevost, J. Boree, H.J. Nuglish, and G. Charnay, “Measurements of Fluid/Particle Correlated Motion in the Far Field of an Axisymmetric Jet,” Int. J. Multiphase Flow 22, 685 (1996).
R.A. Gore and C.T. Crowe, “Effect of Particle Size on Modulating Turbulent Intensity,” Int. J. Multiphase Flow 15, 279 (1989).
G.N. Abramovich, “Effect of Solid-Particle or Droplet Admixture on the Structure of a Turbulent Gas Jet,” Int. J. Heat Mass Transfer 14, 1039 (1971).
Z. Yuan and E.E. Michaelidis, “Turbulence Modulation in Particulate Flows. A Theoretical Approach,” Int. J. Multiphase Flow 18, 779 (1992).
A.A. Shraiber, L.B. Gavin, V.A. Naumov, and V.P. Yatsenko, Turbulent Flows of Gas Suspensions [in Russian], Naukova Dumka, Kiev (1987).
F. Frishman, M. Hussainov, A. Kartushinky, and A. Mulgi, “Numerical Simulation of Two-Phase Turbulent Pipe-Jet Flow Loaded by Polydispersed Solid Admixture,” Int. J. Multiphase Flow 23, 765 (1997).
I.V. Derevich, “The Hydrodynamics and Heat Transfer and Mass Transfer of Particles under Conditions of Turbulent Flow of Gas Suspension in a Pipe and in an Axisymmetric Jet,” J. High Temp. 40, 78 (2002).
J. Garcia and A.A. Crespo, “Turbulent Model for Gas-Particle Jets,” J. Fluids Eng. 122, 505 (2000).
T.G. Almeida and F.A. Jaberi, “Large-Eddy Simulation of a Dispersed Particle-Laden Turbulent Round Jet,” Int. J. Heat Mass Transfer 51, 683 (2008).
L.I. Zaichik and V.M. Alipchenkov, “Statistical Models for Predicting Particle Dispersion and Preferential Concentration in Turbulent Flows,” Int. J. Heat Fluid Flow 26, 416 (2005).
C.T. Crowe, “On Models for Turbulence Modulation in Fluid-Particle Flows,” Int. J. Multiphase Flow 26, 719 (2000).
L. Schiller and A. Naumann, “Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung,” Z. Verein. Deutsch. Ing. 77, 318 (1933).
J. He and O. Simonini, Non-Equilibrium Prediction of the Particle-Phase Stress Tensor in Vertical Pneumatic Conveying, Ref: HE 44/93.15. Chatou: Laboratoire d’Hydraulique, Electricité de France (1993).
R. Mei, “An Approximate Expression for the Shear Lift Force on a Spherical Particle at Finite Reynolds Number,” Int. J. Multiphase Flow 18, 145 (1992).
A.I. Kartushinsky and E.E. Michaelidis, “An Analytical Approach for the Closure Equations of Gas-Solid Flows with Inter-Particle Collision,” Int. J. Multiphase Flow 30, 159 (2004).
R. Seffal and E.E. Michaelidis, “Similarity Solutions for a Turbulent Round jet,” J. Fluid Eng. 118, 618 (1996).
S.Yu. Krasheninnikov, “Calculation of Axisymmetric Twisted and Nontwisted Turbulent Jets,” Fluid Dynamics 7(3), 426 (1972).
P.J. Roache, Computational Fluid Dynamics, Hermosa Publ., Albuquerque (1976).
I.Yu. Brailovskaya and L.A. Chudov, “Solution of the Boundary Layer Equations Using a Difference Method,” in: Numerical Methods and Programming. No. 1 [in Russian], Moscow Univ. Press, Moscow (1962), p. 167.
G. Hetsroni, “Particle-Turbulence Interaction,” Int. J. Multiphase Flow 15, 735 (1989).
E.E. Michaelidis, Particles, Bubbles and Drops-Their Motion, Heat and Mass Transfer, World. Sci. Publ., Singapore (2006).
Additional information
Original Russian Text © A.I. Kartushinskii, E.E. Michaelides, Yu.A. Rudi, S.V. Tisler, I.N. Shcheglov, 2012, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2012, Vol. 47, No. 6, pp. 99–108.
Rights and permissions
About this article
Cite this article
Kartushinskii, A.I., Michaelides, E.E., Rudi, Y.A. et al. Numerical modeling of a two-dimensional vertical turbulent two-phase jet. Fluid Dyn 47, 769–777 (2012). https://doi.org/10.1134/S0015462812060099
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462812060099