Advertisement

Large Eddy Simulation of Dispersed Two-Phase Flows and Premixed Combustion in IC-Engines

  • D. DimitrovaEmail author
  • M. Braun
  • J. Janicka
  • A. Sadiki
Chapter
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 1581)

Abstract

An accurate prediction of particle dispersion is an essential issue for reactive two-phase flows as they occur in IC-engines. It is also a challenging application for Large Eddy Simulation (LES) based Eulerian–Lagrangian methods. The main objective of this work is to assess the state-of-the-art model capabilities of the LES based Eulerian–Lagrangian method as implemented into the commercial CFD code, FLUENT/ANSYS. This is achieved by carrying out various parameter studies that may enable a deeper understanding of the interactions between the numerics and modeling involved, and thus an increasing of the predictive ability and the reliability of transfer of findings from one configuration to others. In this report, special attention is paid to the prediction of the particle preferential accumulation, because of its importance for simulations of mixing and combustion in turbulent reacting two-phase flows. The combustion itself is not considered. The conclusions are based on a systematic variation of relevant flow parameters, such as the Reynolds number and the particle Stokes number, so that a wide range of applications is covered. Therefore, several particle–laden flow configurations, such as two plane channel flows, a free jet and an evaporating spray at low temperature, have been investigated. The results presented in this report are especially for the two plane channel flows characterized by low and high Reynolds numbers, respectively. It was observed that the maximum preferential accumulation occurs at a constant Stokes number and that this number does not depend on the Reynolds number. The magnitude of the accumulation, however, depends on the Reynolds number of the flow. The effect of a sub-grid dispersion model on the particle accumulation was found to be less pronounced for particles with characteristic time scales in the order of the Kolmogorov scale.

Keywords

Two-phase flow Preferential accumulation Particle dispersion modeling Eulerian–Lagrangian method LES 

Notes

Acknowledgment

The authors are grateful to the financial support by the German Research Council (DFG).

References

  1. 1.
    AGARD: A selection of test cases for the validation of large-Eddy simulations of turbulent flows. Agard Advisory Report 345, Neuilly-Sur-Seine, France (1998)Google Scholar
  2. 2.
    ANSYS Fluent 12.0 Documentation. ANSYS Inc. (2009)Google Scholar
  3. 3.
    Apte, S.V., Mahesh, K., Moin, P., Oefelein, J.C.: Large-eddy simulation of swirling particle-laden flows in a coaxial-jet combustor. Int. J. Multiphase Flow 29, 1311–1331 (2003)zbMATHCrossRefGoogle Scholar
  4. 4.
    Apte, S.V., Mahesh, K., Moin, P.: Large-eddy simulation of evaporating spray in a coaxial combustor. Proc. Combust. Inst. 32, 2247–2256 (2009)CrossRefGoogle Scholar
  5. 5.
    Armenio, V., Piomelli, U., Fiorotto, V.: Effect of the subgrid scales on particle motion. Phys. Fluids 11, 3030–3042 (1999)zbMATHCrossRefGoogle Scholar
  6. 6.
    Armsfield, S., Street, R.: The fractional step method for the Navier–Stokes equations on staggered grids: accuracy of three variations. J. Comput. Phys. 153, 660–665 (1999)CrossRefGoogle Scholar
  7. 7.
    Axerio, J., Iaccarino, G.: Flow asymmetry and vortical structures behind a rotating tire. Bull. Am. Phys. Soc. 54(2009)Google Scholar
  8. 8.
    Barth, T.J., Jespersen, D.: The design and application of upwind schemes on unstructured meshes. Technical Report AIAA-89-0366, AIAA 27th Aerospace Science Meeting, Reno, Nevada (1989)Google Scholar
  9. 9.
    Benson, M.J., Eaton, J.K.: The effects of wall roughness on the particle velocity field in fully developed channel flow. Report No. TSD-150. Thermosciences Division, Stanford University (2003)Google Scholar
  10. 10.
    Boileau, M., Pascaud, S., Riber, E., Cuenot, B., Gicquel, L.Y.M., Poinsot, T.J., Cazalens, M.: Investigation of two-fluid method for large eddy simulation of spray combustion in gas turbines. Flow Turb. Combust. 80, 291–321 (2008)CrossRefGoogle Scholar
  11. 11.
    Burton, T.M., Eaton, J.K.: Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67–111 (2005)zbMATHCrossRefGoogle Scholar
  12. 12.
    Caraman, N., Boree, J., Simonin, O.: Effect of collisions on the dispersed phase fluctuations in a dilute tube flow: experimental and theoretical analysis. Phys. Fluids 15, 3602–3612 (2003)CrossRefGoogle Scholar
  13. 13.
    Celik, I., Klein, M., Freitag, M., Janicka, J.: Assessment measures for urans/des/les: an overview with applications. J. Turbul. 7(48), 48 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Chrigui, M., Gounder, J., Sadiki, A., Masri, A.R., Janicka, J.: Partially premixed reacting acetone spray using LES and FGM tabulated chemistry. Combust. Flame 159(8), 2718–2741 (2012)CrossRefGoogle Scholar
  15. 15.
    Clamen, A., Gauvin, W.H.: Effects of turbulence on the drag coefficients of spheres in a supercritical flow regime. AIChE J. 15, 184 (1961)CrossRefGoogle Scholar
  16. 16.
    Crowe, C., Sommerfeld, M., Tsuji, Y.: Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton (1998)Google Scholar
  17. 17.
    Crowe, T.: Modeling turbulence in multiphase flows. Eng. Turbul. Model. Exp. 2, 899–913 (1993)Google Scholar
  18. 18.
    Daubert, T.E., Danner, R.D.: Data compilation tables of properties of pure compounds. Technical report, Design Institute for Physical Property Data. AIChE, New York (1987)Google Scholar
  19. 19.
    Dennis, S.C.R., Singh, S.N., Ingham, D.B.: The steady flow due to a rotating sphere at low and moderate Reynolds numbers. J. Fluid Mech. 101, 257–279 (1980)zbMATHCrossRefGoogle Scholar
  20. 20.
    Deutsch, E., Simonin, O.: Large eddy simulation applied to the motion of particles in stationary homogeneous fluid turbulence. In: Turbulence Modification in Multiphase Flows, vol. 110, pp. 35–42. ASME, Portland (1991)Google Scholar
  21. 21.
    Dimitrova, D.: On the reliability of large-eddy simulation for dispersed two-phase flows. PhD thesis, TU-Darmstadt, Germany (2010)Google Scholar
  22. 22.
    Drew, D.A., Passman, S.L.: Theory of Multicomponent Fluids. Springer, New York (1999)Google Scholar
  23. 23.
    Elghobashi, S., Truesdell, G.C.: Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655–700 (1992)CrossRefGoogle Scholar
  24. 24.
    Faeth, G.M.: Evaporation and combustion of sprays. Prog. Energy Combust. Sci. 9, 1–76 (1998)CrossRefGoogle Scholar
  25. 25.
    Fede, P., Simonin, O.: Numerical study of the subgrid turbulence effects on the statistics of heavy colliding particles. Phys. Fluids 18, 045103 (2006)CrossRefGoogle Scholar
  26. 26.
    Ferziger, J.H., Peric, M.: Computational Methods for Fluid Mechanics, 3rd edn. Springer, Berlin/New York (2002)Google Scholar
  27. 27.
    Fessler, J.R., Eaton, J.K.: Turbulence modification by particles in a backward-facing step flow. J. Fluid Mech. 394, 97–117 (1999)zbMATHCrossRefGoogle Scholar
  28. 28.
    Fessler, J.R., Kulick, J.D., Eaton, J.K.: Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 3742–3749 (1994)CrossRefGoogle Scholar
  29. 29.
    Fevrier, P., Simonin, O., Squires, K.D.: Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study. J. Fluid Mech. 533, 1–46 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Vittoria, M.S., Geurts, B.J., Meyers, J., Sagaut, P.: Quality and reliability of large-eddy simulations. ERCOFTAC Series; vol. 16, ISBN/EAN: 978-94-007-0230-1, Springer (2010)Google Scholar
  31. 31.
    Fröhlich, J.: Large Eddy Simulation Turbulenter Strömungen. B. G. Teubner Verlag, Wiesbaden (2006)Google Scholar
  32. 32.
    Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: Dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3(7), 1760–1765 (1991)zbMATHCrossRefGoogle Scholar
  33. 33.
    Goryntsev, D., Sadiki, A., Klein, M., Janicka, J.: Analysis of cycle variation of liquid fuel-air mixing processes in a realistic DISI IC-engine using large eddy simulation. Int. J. Heat Fluid Flow 31, 845–849 (2010)CrossRefGoogle Scholar
  34. 34.
    Hahn, F., Olbricht, C., Janicka, J.: Large eddy simulation of an evaporating spray based on an Eulerian–Lagrangian approach. In: Proceedings of ILASS, Como Lake, Italy, pp. ILASS08-2-9, 8–10 Sept 2008Google Scholar
  35. 35.
    Hardalupas, Y., Taylor, A.M.K.P., Whitelaw, J.H.: Velocity and particle flux characteristics of turbulent particle-laden jets. Proc. R. Soc. Lond. A 426, 31–78 (1989)CrossRefGoogle Scholar
  36. 36.
    Hinze, J.O.: Turbulence, 2nd edn. McGraw-Hill, New York (1975)Google Scholar
  37. 37.
    Hjelmfelt Jr., T., Mockros, L.F.: Motion of discrete particles in a turbulent fluid. Appl. Sci. Res. 16, 149–161 (1966)CrossRefGoogle Scholar
  38. 38.
    Holmes, D.G., Conell, S.D.: Solution of the 2d Navier–Stokes equations on unstructured adaptive grids. In: AIAA 9th Computational Fluid Dynamics Conference, Buffalo (1989)Google Scholar
  39. 39.
    James, S., Zhu, J., Anand, M.S.: Large eddy simulations as a design tool for gas turbine combustion systems. AIAA J. 44, 674–686 (2006)CrossRefGoogle Scholar
  40. 40.
    Janicka, J., Sadiki, A.: Large eddy simulation for turbulent combustion systems. Proc. Combust. Inst. 30, 573–574 (2005)CrossRefGoogle Scholar
  41. 41.
    Kim, S.-E., Makarov, B.: In: 17th AIAA Computational Fluid Dynamics Conference, Toronto Ontario, AIAA Paper 2005–5253, 6–9 June 2005Google Scholar
  42. 42.
    Kolmogorov, N.: Local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 299–303 (1941)Google Scholar
  43. 43.
    Kuerten, H., Vreman, A.W.: Can turbophoresis be predicted by large-eddy simulation? Phys. Fluids 17, 011701 (2005)CrossRefGoogle Scholar
  44. 44.
    Kuerten, J.G.M.: Subgrid modeling in particle-laden channel flow. Phys. Fluids 18, 025108 (2006)CrossRefGoogle Scholar
  45. 45.
    Kulick, J.D., Fessler, J.R., Eaton, J.K.: On the interactions between particles and turbulence in a fully-developed channel flow in air. Mechanical Engineering Report MD-66, Stanford University (1993)Google Scholar
  46. 46.
    Kulick, J.D., Fessler, J.R., Eaton, J.K.: Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109–134 (1994)CrossRefGoogle Scholar
  47. 47.
    Lam, K., Banerjee, S.: On the condition of streak formation in bounded flows. Phys. Fluids A 4, 306–320 (1992)zbMATHCrossRefGoogle Scholar
  48. 48.
    Leonard, B.P.: The ultimate conservative difference scheme applied to unsteady one dimensional advection. Comput. Methods Appl. Mech. Eng. 88, 17–74 (1991)zbMATHCrossRefGoogle Scholar
  49. 49.
    Lilly, D.K.: A proposed modification of the germano subgrid-scale closure model. Phys. Fluids 4, 633–635 (1992)CrossRefGoogle Scholar
  50. 50.
    Longmire, E.K., Eaton, J.K.: Structure of a particle-laden round jet. J. Fluid Mech. 236, 217–257 (1992)CrossRefGoogle Scholar
  51. 51.
    Marchioli, C., Soldati, A.: Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283–315 (2002)zbMATHCrossRefGoogle Scholar
  52. 52.
    Marchioli, C., Soldati, A.: Dns of particle-laden turbulent channel flow. In: Proceedings of 11th Workshop on Two-Phase Flow Predictions, Merseburg, Germany (2005)Google Scholar
  53. 53.
    Marchioli, C., Soldati, A., Kuerten, J.G.M., Arcen, B., Tanière, A., Goldensoph, G., Squires, K.D., Cargnelutti, M.F., Portela, L.M.: Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: results of an international collaborative benchmark test. Int. J. Multiphase Flow 34, 879–893 (2008)CrossRefGoogle Scholar
  54. 54.
    Masoudi, M., Sirignano, W.A.: Nonlinear capillary waves on swirling, axisymmetric free liquid films. Int. J. Multiphase Flow 27, 1707–1734 (2001)CrossRefGoogle Scholar
  55. 55.
    Mathey, F., Cokljat, D.: Assessment of the vortex method for large-eddy simulation inlet conditions. Prog. Comput. Fluid Dyn. 6, 58–67 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  56. 56.
    Mathur, S.R., Murthy, J.Y.: A pressure-based method for unstructured meshes. Num. Heat Trans. 31, 195–215 (1997)CrossRefGoogle Scholar
  57. 57.
    Mei, R.: An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Int. J. Multiphase Flow 18, 145–147 (1992)zbMATHCrossRefGoogle Scholar
  58. 58.
    Meyers, J., Geurts, B., Sagaut, P.: Quality Reliability of Large Eddy Simulations. Ercoftac Series, vol. 13. Springer, Berlin (2008)zbMATHCrossRefGoogle Scholar
  59. 59.
    Moin, P., Apte, S.V.: Large eddy simulation of realistic gas turbine combustor. AIAA J. 44, 698–708 (2006)CrossRefGoogle Scholar
  60. 60.
    Morsi, S.A., Alexander, A.J.: An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech. 55, 193–208 (1972)zbMATHCrossRefGoogle Scholar
  61. 61.
    Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to re_ = 590. Phys. Fluids 11, 943–945 (1999)zbMATHCrossRefGoogle Scholar
  62. 62.
    Odar, F., Hamilton, W.S.: Forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 18, 302–314 (1964)zbMATHCrossRefGoogle Scholar
  63. 63.
    Oefelein, J.C.: Simulation and analysis of turbulent multiphase combustion at high pressures. PhD thesis, The Pennsylvania State University (1997)Google Scholar
  64. 64.
    Olbricht, C.: Numerische Verbrennung technischer Verbrennungssysteme. PhD thesis, TU Darmstadt (2009)Google Scholar
  65. 65.
    Paris, D.: Turbulence attenuation in a particle-laden channel flow. PhD thesis, Stanford University (2001)Google Scholar
  66. 66.
    Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere, Washington, DC (1980)zbMATHGoogle Scholar
  67. 67.
    Picciotto, M., Marchioli, C., Reeks, M.W., Soldati, A.: Statistics of velocity and preferential accumulation of micro-particles in boundary layer turbulence. Nucl. Eng. Des. 235, 1239–1249 (2005)CrossRefGoogle Scholar
  68. 68.
    Pitsch, H.: Large-eddy simulation of turbulent combustion. Annu. Rev. Fluid Mech. 38, 453–482 (2006)MathSciNetCrossRefGoogle Scholar
  69. 69.
    Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  70. 70.
    Pozorski, J., Apte, S.V.: Filtered particle tracking in isotropic turbulence and stochastic modeling of subgrid–dispersion. Int. J. Multiphase Flow 35, 118–128 (2009)CrossRefGoogle Scholar
  71. 71.
    Prandtl, L.: über die ausgeprägte turbulenz. Z. Angew. Math. Mech. 5, 136–139 (1925)zbMATHGoogle Scholar
  72. 72.
    Qiu, H.-H., Sommerfeld, M.: A reliable method for determinig the measurement volume size and particle mass fluxes using phase-Doppler anemometry. Exp. Fluids 13, 393–404 (1992)CrossRefGoogle Scholar
  73. 73.
    Ranz, W.E., Marshall Jr., W.R.: Evaporation from drops, part i. Chem. Eng. Prog. 48(3), 141–146 (1952)Google Scholar
  74. 74.
    Ranz, W.E., Marshall Jr., W.R.: Evaporation from drops, part ii. Chem. Eng. Prog. 48(4), 173–180 (1952)Google Scholar
  75. 75.
    Rhie, C.M., Chow, W.L.: Numerical study of the turbulent flow part an airfoil with trailing edge separation. AIAA J. 21, 1525–1532 (1983)zbMATHCrossRefGoogle Scholar
  76. 76.
    Riber, E., Moureau, V., Garcia, M., Poinsot, T., Simonin, O.: Evaluation of numerical strategies for large eddy simulation of particulate two-phase recirculating flows. J. Comput. Phys.. doi: 10.1016/j.jcp.2008.10.001, 2008
  77. 77.
    Richardson, L.F.: Weather Prediction by Numerical Process. Cambridge University Press, Cambridge (1922)zbMATHGoogle Scholar
  78. 78.
    Rubinow, S.I., Keller, J.B.: The transverse force on spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459 (1961)MathSciNetzbMATHCrossRefGoogle Scholar
  79. 79.
    Rudoff, R.R., Bachalo, W.D.: Measurements of droplet drag coefficients in polydispersed turbulent flow field. AIAA, pp. 80–0235 (1988)Google Scholar
  80. 80.
    Ruetsch, G.R., Maxey, M.R.: The evolution of small–scale structures in homogeneous turbulence. Phys. Fluids A 4, 2747 (1992)CrossRefGoogle Scholar
  81. 81.
    Rutland, C.J.: Large eddy simulation for internal combustion engine: a review. Int. J. Eng. Resour. 12(5), 421–445 (2011)CrossRefGoogle Scholar
  82. 82.
    Saffman, G.G.: The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400 (1965)zbMATHCrossRefGoogle Scholar
  83. 83.
    Sagaut, P.: Large Eddy Simulation of Incompressible Flows. Springer, Berlin/New York (2001)CrossRefGoogle Scholar
  84. 84.
    Sawatzki, O.: Strömungsfeld um eine rotierende kugel. Acta Mech. 9, 159–214 (1970)zbMATHCrossRefGoogle Scholar
  85. 85.
    Schiller, L., Naumann, Z.: A drag coefficient correlation. VDI Zeitschrift 77, 318 (1935)Google Scholar
  86. 86.
    Schlichting, H., Gersten, K.: Grenzschicht-Theorie, 9th edn. Springer, Berlin/Heidelberg (1997)zbMATHGoogle Scholar
  87. 87.
    Schuman, U.: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404 (1975)CrossRefGoogle Scholar
  88. 88.
    Segura, J.C.: Predictive capabilities of particle-laden large eddy simulation. PhD thesis, Department of Mechanical Engineering, Stanford University (2004)Google Scholar
  89. 89.
    Sirignano, W.A.: Fluid Dynamics and Transport of Droplets and Sprays. Applied Mathematical Sciences 135. Cambridge University Press, New York (2005)Google Scholar
  90. 90.
    Smagorinsky, J.: General circulation experiments with the primitive equations. i. The basic experiment. Mon. Weather Rev. 91, 99–164 (1963)CrossRefGoogle Scholar
  91. 91.
    Snyder, W.H., Lumley, J.L.: Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41–71 (1971)CrossRefGoogle Scholar
  92. 92.
    Sommerfeld, M.: Modellierung und numerische Berechnung von partikelbeladenen turbulenten Strömungen mit Hilfe des Euler/Lagrange-Verfahrens (1998)Google Scholar
  93. 93.
    Sommerfeld, M.: Theoretical and experimental modelling of particulate flows. Technical Report Lecture Series 2000–06, von Karman Institute for Fluid Dynamics (2000)Google Scholar
  94. 94.
    Sommerfeld, M., Qiu, H.H.: Particle concentration measurements by phase-Doppler anemometry in complex dispersed two-phase flows. Exp. Fluids 18, 187–198 (1995)CrossRefGoogle Scholar
  95. 95.
    Sommerfeld, M., Qiu, H.H.: Spray evaporation in turbulent flow URL http://www-mvt.iw.uni-halle.de/index.php?spray_evaporation. Data base (1998)
  96. 96.
    Sommerfeld, M., Qiu, H.H.: Experimental studies of spray evaporation in turbulent flow. Int. J. Heat Fluid Flow 19, 10–22 (1998)CrossRefGoogle Scholar
  97. 97.
    Squires, K.D., Eaton, J.K.: Preferential concentration of particles by turbulence. Phys. Fluids A 3, 1169–1178 (1991)CrossRefGoogle Scholar
  98. 98.
    Stokes, G.G.: On the effect of the inertial friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8–106 (1851)Google Scholar
  99. 99.
    Tang, L., Wen, F., Yang, Y., Crowe, C.T., Chung, J.N., Troutt, T.R.: Self-organizing particle dispersion mechanism in a plane wake. Phys. Fluids A 4, 2244–2251 (1992)CrossRefGoogle Scholar
  100. 100.
    Torobin, L.B., Gauvin, W.H.: The drag coefficient of single sphere moving in steady and accelerated motion in a turbulent fluid. AIChE J. 7, 615–619 (1961)CrossRefGoogle Scholar
  101. 101.
    Truesdell, C., Toupin, R.: The Classical Field Theories, volume III of Handbuch der Physik, chapter 1 Part. Springer, Berlin (1960)Google Scholar
  102. 102.
    Uhlherr, P.H.T., Sinclair, C.G.: The effect of free stream turbulence on the drag coefficient of spheres. In: Proceedings of Chemca ’70, 1:1 (1970)Google Scholar
  103. 103.
  104. 104.
    Vance, M., Squires, K.W., Simonin, O.: Properties of the particle velocity field in gas-solid turbulent channel flow. Phys. Fluids 18, 063302 (2006)CrossRefGoogle Scholar
  105. 105.
    Vargaftik, N.B.: Handbook of Physical Properties of Liquids and Gases, 2nd edn. Taylor & Francis Inc, Washington, DC (1983)Google Scholar
  106. 106.
    VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen (Hrsg.): VDI-Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer, Berlin (2002)Google Scholar
  107. 107.
    Vreman, W.: Turbulence characteristics of particle-laden pipe flow. J. Fluid Mech. 584, 235–279 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  108. 108.
    Vreman, A.W., Geurts, B.J., Deen, N.G., Kuipers, J.A.M.: Large-eddy simulation of a particle-laden turbulent channel flow. In: Friedrich, R., et al. (eds.) Direct and Large-Eddy Simulation, vol. 5, pp. 271–278, Kluwer Academic Publishers (2004)Google Scholar
  109. 109.
    Wang, L.P., Maxey, M.R.: Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68 (1993)CrossRefGoogle Scholar
  110. 110.
    Wang, Q., Squires, K.D.: Large-eddy simulation of particle-laden turbulent channel flow. Phys. Fluids 8, 1207–1223 (1996)zbMATHCrossRefGoogle Scholar
  111. 111.
    Wilcox, D.C.: Turbulence Modeling for CFD. D C W Industries (2000)Google Scholar
  112. 112.
    Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T., Tsuji, Y.: Large-eddy simulation of turbulent gas-particle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech. 442, 303–334 (2001)zbMATHCrossRefGoogle Scholar
  113. 113.
    Young, J., Leeming, A.: A theory of particle deposition in turbulent pipe flow. J. Fluid Mech. 340, 129–159 (1997)zbMATHCrossRefGoogle Scholar
  114. 114.
    Zarin, N.A., Nicholls, J.A.: Sphere drag in solid rockets – non continuum and turbulence effects. Combust. Sci. Technol. 3, 273 (1971)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Fluent/ANSYS Deutschland GmbHDarmstadtGermany
  2. 2.Department of Mechanical and Processing Engineering, Institute for Energy and Powerplant TechnologyTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations