Skip to main content
Log in

Nonlinear algebraic model of the Reynolds stresses for a disperse turbulent flow with low-inertia particles

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The purpose of the study is to present an explicit self-consistent algebraic model of the Reynolds stresses (nonlinear turbulent viscosity) for calculating two-phase flows laden with small heavy particles. The model is tested by means of comparing with the results of the solution of a system of differential equations for all components of the Reynolds stresses and the data of direct numerical calculations in a homogeneous shear flow with particles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R.A. Gore and C.T. Crowe, “Effect of Particle Size on Modulating Turbulent Intensity,” Int. J. Multiphase Flow 15, 279 (1989).

    Article  Google Scholar 

  2. G. Hetsroni, “Particle-Turbulence Interaction,” Int. J. Multiphase Flow 15, 735 (1989).

    Article  Google Scholar 

  3. O.A. Druzhinin and S. Elghobashi, “On the Decay Rate of Isotropic Turbulence Laden with Microparticles,” Phys. Fluids 11, 602 (1999).

    Article  MATH  ADS  Google Scholar 

  4. O.A. Druzhinin, “The Influence of Particle Inertia on the Two-Way Coupling and Modification of Isotropic Turbulence by Microparticles,” Phys. Fluids 13, 3738 (2001).

    Article  ADS  Google Scholar 

  5. A. Ferrante and S. Elghobashi, “On the Physical Mechanisms of Two-Way Coupling in Particle-Laden Isotropic Turbulence,” Phys. Fluids 15, 315 (2003).

    Article  ADS  Google Scholar 

  6. F. Mashayek, “Droplet-Turbulence Interactions in Low-Mach-Number Homogeneous Shear Two-Phase Flows,” J. Fluid Mech. 367, 163 (1998).

    Article  MATH  ADS  Google Scholar 

  7. A.M. Ahmed and S. Elghobashi, “On the Mechanisms of Modifying the Structure of Turbulent Homogeneous Shear Flows by Dispersed Particles,” Phys. Fluids 12, 2906 (2000).

    Article  ADS  Google Scholar 

  8. M. Tanaka, Y. Maeda, and Y. Hagiwara, “Turbulence Modification in a Homogeneous Turbulent Shear Flow Laden with Small Heavy Particles,” Int. J. Heat Fluid Flow 23, 615 (2002).

    Article  Google Scholar 

  9. S.E. Elghobashi and T.W. Abou-Arab, “A Two-Equation Turbulence Model for Two-Phase Flows,” Phys. Fluids 26, 931 (1983).

    Article  MATH  ADS  Google Scholar 

  10. M.A. Rizk and S.E. Elghobashi, “A Two-Equation Turbulence Model for Dispersed Dilute Confined Two-Phase Flows,” Int. J. Multiphase Flow 15, 119 (1989).

    Article  Google Scholar 

  11. O. Simonin, “Second-Moment Prediction of Dispersed-Phase Turbulence in Particle-Laden Flows,” in: Proc. 8th Symp. on Turbulent Shear Flows. Munich, Germany, 1991. Vol. 1 (1991), p. 7-4–1.

  12. A.A. Vinberg, L.I. Zaichik, and V.A. Pershukov, “Calculation of the Momentum and Heat Transfer in Turbulent Gas-Particle Jet Flows,” Fluid Dynamics 27(3), 353 (1992).

    Article  MATH  ADS  Google Scholar 

  13. K.D. Squires and J.K. Eaton, “Effect of Selective Modification of Turbulence on Two-Equation Models for Particle-Laden Turbulent Flows,” Trans. ASME. J. Fluids Eng. 116, 778 (1994).

    Article  Google Scholar 

  14. M. Mandø, M.F. Lightstone, L. Rosendahl, C. Yin, and H. Sørensen, “Turbulence Modulation in Dilute Particle-Laden Flows,” Int. J. Heat Fluid Flow 30, 331 (2009).

    Article  Google Scholar 

  15. A. Benavides and B. van Wachem, “Eulerian-Eulerian Prediction of Dilute Turbulent Gas-Particle Flow in a Backward-Facing Step,” Int. J. Heat Fluid Flow 30, 452 (2009).

    Article  Google Scholar 

  16. M.A. Pakhomov and V.I. Terekhov, “Effect of Vaporizing Droplets on the Structure of a Submergent Spray,” Fluid Dynamics 44(3), 419 (2009).

    Article  ADS  Google Scholar 

  17. D.B. Taulbee, E. Mashayek, and C. Barré, “Simulation and Reynolds Stress Modeling of Particle-Laden Turbulent Shear Flows, ” Int. J. Heat Fluid Flow 20, 368 (1999).

    Article  Google Scholar 

  18. L.X. Zhou, Y. Xu, L.S. Fan, and Y. Li, “Simulation of Swirling Gas-Particle Flows Using an Improved Second-Order Moment Two-Phase Model,” Powder Technol. 116, 178 (2001).

    Article  Google Scholar 

  19. S. Lain and M. Sommerfeld, “Turbulence Modulation in Dispersed Two-Phase Flow Laden with Solids from a Lagrangian Perspective,” Int. J. Heat Fluid Flow 24, 616 (2003).

    Article  Google Scholar 

  20. N.A. Beishuizen, B. Naud, and D. Roekaertes, “Evaluation of a Modified Reynolds Stress Model for Turbulent Dispersed Two-Phase Flows Including Two-Way Coupling,” Flow, Turbulence, Combustion 79, 321 (2007).

    Article  Google Scholar 

  21. P. Boulet and S. Moisette, “Influence of the Particle-Turbulence Modulation Modeling in the Simulation of a Non-Isothermal Gas-Solid Flow,” Int. J. Heat Mass Transfer 45, 4201 (2002).

    Article  MATH  Google Scholar 

  22. C.G. Speziale, “On Non-Linear K-I and K-ɛ Models of Turbulence,” J. Fluid Mech. 178, 459 (1987).

    Article  MATH  ADS  Google Scholar 

  23. F. Mashayek and D.B. Taulbee, “Turbulent Gas-Solid Flows. Part II. Explicit Algebraic Models,” Numer. Heat Transfer. Pt. B 41, 31 (2002).

    Article  ADS  Google Scholar 

  24. S.S. Girimaji, “Fully Explicit and Self-Consistent Algebraic Reynolds Stress Model,” Theoret. Comput. Fluid Dynamics 8, 387 (1996).

    MATH  ADS  Google Scholar 

  25. S.S. Girimaji, “A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Turbulent Curved Flows,” Phys. Fluids 9, 1067 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. S. Wallin and A.V. Johansson, “An Explicit Algebraic Reynolds Stress Model for Incompressible and Compressible Turbulent Flows,” J. Fluid Mech. 403, 89 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. T.B. Gatski and C.L. Rumsey, “Linear and Nonlinear Eddy Viscosity Models,” in: Closure Strategies for Turbulent and Transitional Flows, Cambridge Univ. Press, Cambridge (2002), p. 9.

    Google Scholar 

  28. C.T. Crowe, “On Models for Turbulence Modulation in Fluid-Particle Flows,” Int. J. Multiphase Flow 26, 719 (2000).

    Article  MATH  Google Scholar 

  29. I.V. Derevich, “Two-ParameterModel of a Turbulent Flow with a Dispersed-Particle Admixture,” Fluid Dynamics 33(4), 497 (1998).

    Article  MATH  ADS  Google Scholar 

  30. L.I. Zaichik and V.M. Alipchenkov, Statistical Models of Particle Motion within Turbulent Fluids [in Russian], Fizmatlit, Moscow (2007).

    Google Scholar 

  31. L.I. Zaichik, V.M. Alipchenkov, and A.R. Avetissian, “Transport and Deposition of Colliding Particles in Turbulent Channel Flows,” Int. J. Heat Fluid Flow 30, 443 (2009).

    Article  Google Scholar 

  32. J. Choi, K. Yeo, and C. Lee, “Lagrangian Statistics in Turbulent Channel Flows,” Phys. Fluids 16, 779 (2004).

    Article  ADS  Google Scholar 

  33. S.B. Pope, “Stochastic Lagrangian Models of Velocity in Homogeneous Turbulent Shear Flow,” Phys. Fluids 14, 1696 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  34. G.T. Csanady, “Turbulent Diffusion od Heavy Particles in the Atmosphere,” J. Atmos. Sci. 20, 201 (1963).

    Article  ADS  Google Scholar 

  35. W. Rodi, “A New Algebraic Relation for Calculating the Reynolds Stresses,” Zeitschr. Appl. Math. Mech. 56, T219 (1976).

    Google Scholar 

  36. C.G. Speziale, S. Sarkar, and T.B. Gatski, “Modeling the Pressure-Strain Correlation of Turbulence: an Invariant Dynamical Systems Approach,” J. Fluid Mech. 227, 245 (1991).

    Article  MATH  ADS  Google Scholar 

  37. T. Jongen and T.B. Gatski, “A Unified Analysis of Planar Homogeneous Turbulence Using Single-Point Closure Equations,” J. Fluid Mech. 399, 117 (1999).

    Article  MATH  ADS  Google Scholar 

  38. T.B. Gatski and C.G. Speziale, “On Explicit Algebraic Stress Models for Complex Turbulent Flows,” J. Fluid Mech. 254, 59 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  39. B. Oesterlé and L.I. Zaichik, “Time Scales for Predicting Dispersion of Arbitrary-Density Particles in Isotropic Turbulence,” Int. J. Multiphase Flow 32, 838 (2006).

    Article  MATH  Google Scholar 

  40. L.I. Zaichik, O. Simonin, and V.M. Alipchenkov, “Two Statistical Models for Predicting Collision Rates of Inertial Particles in Homogeneous Isotropic Turbulence,” Phys. Fluids 15, 2995 (2003).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Authors

Additional information

Original Russian Text © V. M. Alipchenkov, L. I. Zaichik, 2010, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2010, Vol. 45, No. 6, pp. 86–101.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alipchenkov, V.M., Zaichik, L.I. Nonlinear algebraic model of the Reynolds stresses for a disperse turbulent flow with low-inertia particles. Fluid Dyn 45, 909–923 (2010). https://doi.org/10.1134/S0015462810060098

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462810060098

Keywords

Navigation