Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Wind-blown particulate transport: A review of computational fluid dynamics models

1 Optiflow Company, 160 Chemin de la Madrague-Ville, Marseille, 13015, France
2 Department of Mathematical Sciences Giuseppe Luigi Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129, Italy

The transport of particulate by wind constitutes a relevant phenomenon in environmental sciences and civil engineering, because erosion, transport and deposition of particulate can cause serious problems to human infrastructures. From a mathematical point of view, modeling procedure for this phenomenon requires handling the interaction between different constituents, the transfer of a constituent from the air to the ground and viceversa, and consequently the ground-surface interaction and evolution. Several approaches have been proposed in the literature, according to the specific particulate or application. We here review these contributions focusing in particular on the behavior of sand and snow, which almost share the same mathematical modeling issues, and point out existing links and analogies with wind driven rain. The final aim is then to classify and analyze the different mathematical and computational models in order to facilitate a comparison among them. A first classification of the proposed models can be done distinguishing whether the dispersed phase is treated using a continuous or a particle-based approach, a second one on the basis of the type of equations solved to obtain particulate density and velocity, a third one on the basis of the interaction model between the suspended particles and the transporting fluid.
  Article Metrics


1. Abadie MO, Mendes N (2008) Numerical assessment of turbulence effect on the evaluation of wind-driven rain specific catch ratio. Int Commun Heat Mass Transfer 35: 1253–1261.    

2. Al-Hajraf S, Rubini P (2001) Three-dimensional homogeneous two-phase flow modelling of drifting sand around an open gate. WIT Trans Eng Sci 30: 309–325.

3. Alhajraf S (2000) Numerical simulation of drifting sand, PhD thesis, Cranfield University.

4. Anderson RS, Haff PK (1988) Simulation of eolian saltation. Science 241: 820–823.    

5. Anderson RS, Hallet B (1986) Sediment transport by wind: Toward a general model. Geol Soc Am Bull 97: 523–535.    

6. Andreotti B, Claudin P, Douady S (2002a) Selection of dune shapes and velocities part 1: Dynamics of sand, wind and barchans. Eur Phys J B 28: 321–339.

7. Andreotti B, Claudin P, Douady S (2002b) Selection of dune shapes and velocities part 2: A two-dimensional modelling. Eur Phys J B 28: 341–352.

8. Andrews M, O'rourke P (1996) The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. Int J Multiphase Flow 22: 379–402.    

9. Arastoopour H, Pakdel P, Adewumi M (1990) Hydrodynamic analysis of dilute gas-solids flow in a vertical pipe. Powder Technol 62: 163–170.    

10. Balachandar S, Eaton J (2010) Turbulent dispersed multiphase flow. Annu Rev Fluid Mech 42: 111–133.    

11. Bang B, Nielsen A, Sundsbø P, et al. (1994) Computer simulation of wind speed, wind pressure and snow accumulation around buildings (SNOW-SIM). Energy Build 21: 235–243.    

12. Barnea E, Mizrahi J (1973) A generalized approach to the fluid dynamics of particulate systems: Part 1. General correlation for fluidization and sedimentation in solid multiparticle systems. Chem Eng J 5: 171–189.

13. Benyahia S, Syamlal M, O'Brien TJ (2006) Extension of Hill-Koch-Ladd drag correlation over all ranges of Reynolds number and solids volume fraction. Powder Technol 162: 166–174.    

14. Beyers J, Sundsbø P (2004) Numerical simulation of three-dimensional, transient snow drifting around a cube. J Wind Eng Ind Aerod 92: 725–747.    

15. Beyers M, Waechter B (2008) Modeling transient snowdrift development around complex three-dimensional structures. J Wind Eng Ind Aerod 96: 1603–1615.    

16. Blocken B (2014) 50 years of computational wind engineering: past, present and future. J Wind Eng Ind Aerod 129: 69–102.    

17. Blocken B, Carmeliet J (2010) Overview of three state-of-the-art wind-driven rain assessment models and comparison based on model theory. Build Environ 45: 691–703.    

18. Blocken B, Stathopoulos T, Carmeliet J (2007) CFD simulation of the atmospheric boundary layer: Wall function problems. Atmos Environ 41: 238–252.    

19. Boutanios Z, Jasak H (2017) Two-way coupled Eulerian-Eulerian simulations of drifting snow with viscous treatment of the snow phase. J Wind Eng Ind Aerod 169: 67–76.    

20. Businger J, Wyngaard J, Izumi Y, et al. (1971) Flux profile relationships in the atmospheric surface layer. J Atmos Sci 28: 181–189.    

21. Canuto C, Lo Giudice A (2018) A multi-timestep robin-robin domain decomposition method for time dependent advection-diffusion problems. App Math Comput (In press).

22. Chapman S, Cowling T (1970) The Mathematical Theory of Non-uniform Gases, Cambridge Mathematical Library.

23. Chen C, Wood P (1985) A urbulence closure model for dilute gas particle flows. Can J Chem Eng 63: 349–360. Available from: https://doi.org/10.1002/cjce.5450630301.

24. Choi E (1992) Simulation of wind-driven-rain around a building. J Wind Eng 52: 60–65.

25. Choi E (1997) Numerical modelling of gust effect on wind-driven rain. J Wind Eng Ind Aerod 72: 107–116.    

26. Creyssels M, Dupont P, Moctar AOE, et al. (2009) Saltating particles in a turbulent boundary layer: Experiment and theory. J Fluid Mech 625: 47–74.    

27. Deen N, Annaland MVS, der Hoef MV, et al. (2007) Review of discrete particle modeling of fluidized beds. Chem Eng Sci 62: 28–44.    

28. Di Felice R (1994) The voidage function for fluid-particle interaction systems. Int J Multiphase Flow 20: 153–159.    

29. Durán O, Parteli EJ, Herrmann HJ (2010) A continuous model for sand dunes: Review, new developments and application to barchan dunes and barchan dune fields. Earth Surf Processes Landforms 35: 1591–1600.    

30. Dyer J (1974) A review of flux profile relationships. Boundary-Lay Meteorol 7: 363–372.    

31. Elghobashi S (1991) Particle-laden turbulent flows: Direct simulation and closure models, In: Oliemans, R.V.A. Editor, Computational Fluid Dynamics for the Petrochemical Process Industry, Dordrecht: Springer, 91–104.

32. Elghobashi S (1994) On predicting particle-laden turbulent flows. Appl Sci Res 52: 309–329.    

33. Ergun S (1952) Fluid flow through packed columns. J Chem Eng Prog 48: 89–94.

34. Faber TE (1995) Fluid Dynamics for Physicists, Cambridge University Press.

35. Farimani AB, Ferreira AD, Sousa AC (2011) Computational modeling of the wind erosion on a sinusoidal pile using a moving boundary method. Geomorphology 130: 299–311.    

36. Gauer P (1999) Blowing and drifting snow in alpine terrain: a physically-based numerical model and related field measurements. PhD thesis, ETH Zurich, Switzerland.

37. Germano M, Piomelli U, Moin P, et al. (1991) A dynamic subgrid-scale eddy viscosity model. Phys Fluids A 3: 1760–1765.    

38. Gidaspow D (1994) Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions, Academic press.

39. Gosman A, Lekakou C, Politis S, et al. (1992) Multidimensional modeling of turbulent two-phase flows in stirred vessels. AIChE J 38: 1946–1956.    

40. Hangan H (1999) Wind-driven rain studies. A C-FD-E approach. J Wind Eng Ind Aerod 81: 323–331.    

41. Ho TD, Dupont P, Ould El Moctar A, et al. (2012) Particle velocity distribution in saltation transport. Phys Rev E 85: 052301. Available from: https://doi.org/10.1103/PhysRevE. 85.052301.

42. Ho TD, Valance A, Dupont P, et al. (2011) Scaling laws in aeolian sand transport. Phys Rev Lett 106: 094501. Available from: https://doi.org/10.1103/PhysRevLett.106.094501.    

43. Ho TD, Valance A, Dupont P, et al. (2014) Aeolian sand transport: Length and height distributions of saltation trajectories. Aeolian Res 12: 65–74.    

44. Hrenya CM, Sinclair JL (1997) Effects of particle-phase turbulence in gas-solid flows. AlChE J 43: 853–869. Available from: https://aiche.onlinelibrary.wiley.com/doi/abs/10. 1002/aic.690430402.    

45. Hsu TJ, Jenkins JT, Liu PL (2004) On two-phase sediment transport: Sheet flow of massive particles. Proc R Soc A 460: 2223–2250. Available from: https://doi.org/10.1098/rspa. 2003.1273.    

46. Huang S, Li Q (2010a) A new dynamic one-equation subgrid-scale model for large eddy simulations. Int J Numer Methods Eng 81: 835–865.

47. Huang S, Li Q (2010b) Numerical simulations of wind-driven rain on building envelopes based on Eulerian multiphase model. J Wind Eng Ind Aerod 98: 843–857.

48. Huang S, Li Q (2011) Large eddy simulations of wind-driven rain on tall building facades. J Struct Eng 138: 967–983.

49. Iversen J, Greeley R, White BR, et al. (1975) Eolian erosion of the martian surface, part 1: Erosion rate similitude. Icarus 26: 321–331.    

50. Iversen J, Rasmussen K (1999) The effect of wind speed and bed slope on sand transport. Sedimentology 46: 723–731. Available from: https://doi.org/10.1046/j.1365-3091. 1999.00245.x.    

51. Jenkins JT, Hanes DM (1998) Collisional sheet flows of sediment driven by a turbulent fluid. J Fluid Mech 370: 29–52. Available from: https://doi.org/10.1017/S0022112098001840.    

52. Ji S, Gerber A, Sousa A (2004) A convection-diffusion CFD model for aeolian particle transport. Int J Numer Methods Fluids 45: 797–817. Available from: https://doi.org/10.1002/fld. 724.    

53. Jiang H, Dun H, Tong D, et al. (2017) Sand transportation and reverse patterns over leeward face of sand dune. Geomorphology 283: 41–47.    

54. Jiang H, Huang N, Zhu Y (2014) Analysis of wind-blown sand movement over transverse dunes. Sci Rep 4: 7114.

55. Jones W, Launder B (1972) The prediction of laminarization with a two-equation model of turbulence. Int J Heat Mass Transfer 15: 301–314.    

56. Kang L (2012) Discrete particle model of aeolian sand transport: Comparison of 2D and 2.5D simulations. Geomorphology 139: 536–544.

57. Kang L, Guo L (2006) Eulerian-Lagrangian simulation of aeolian sand transport. Powder Technol 162: 111–120.    

58. Kang L, Liu D (2010) Numerical investigation of particle velocity distributions in aeolian sand transport. Geomorphology 115: 156–171.    

59. Kang L, Zou X (2011) Vertical distribution of wind-sand interaction forces in aeolian sand transport. Geomorphology 125: 361–373.    

60. Kato M, Launder B (1993) The modeling of turbulent flow around stationary and vibratingsquare cylinders, In: Ninth Symposium on Turbulent Shear Flows, American Society of Mechanical Engineers, 1–6.

61. Kobayashi H (2005) The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys Fluids 17: 045104.    

62. Kobayashi H, Ham F, Wu X (2008) Application of a local sgs model based on coherent structures to complex geometries. Int J Heat Fluid Flow 29: 640–653.    

63. Kok JF, Parteli EJ, Michaels TI, et al. (2012) The physics of wind-blown sand and dust. Rep Prog Phys 75: 106901.    

64. Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl Akad Nauk SSSR 30: 299–303.

65. Kubilay A, Carmeliet J, Derome D (2017) Computational fluid dynamics simulations of wind-driven rain on a mid-rise residential building with various types of facade details. J Build Perform Simul 10: 125–143.    

66. Kubilay A, Derome D, Blocken B, et al. (2013) CFD simulation and validation of wind-driven rain on a building facade with an Eulerian multiphase model. Build Environ 61: 69–81.    

67. Kubilay A, Derome D, Blocken B, et al. (2014) Numerical simulations of wind-driven rain on an array of low-rise cubic buildings and validation by field measurements. Build Environ 81: 283–295.    

68. Kubilay A, Derome D, Blocken B, et al. (2015a) Numerical modeling of turbulent dispersion for wind-driven rain on building facades. Environ Fluid Mech 15: 109–133.

69. Kubilay A, Derome D, Blocken B, et al. (2015b) Wind-driven rain on two parallel wide buildings: field measurements and CFD simulations. J Wind Eng Ind Aerod 146: 11–28.

70. Lakehal D, Mestayer P, Edson J, et al. (1995) Eulero-Lagrangian simulation of raindrop trajectories and impacts within the urban canopy. Atmos Environ 29: 3501–3517.    

71. Li Z, Wang Y, Zhang Y, et al. (2014) A numerical study of particle motion and two-phase interaction in aeolian sand transport using a coupled large eddy simulation-discrete element method. Sedimentology 61: 319–332. Available from: https://doi.org/10.1111/sed. 12057.    

72. Liston G, Brown R, Dent J (1993) A two-dimensional computational model of turbulent atmospheric surface flows with drifting snow. Ann Glaciol 18: 281–286.    

73. Lopes A, Oliveira L, Ferreira AD, et al. (2013) Numerical simulation of sand dune erosion. Environ Fluid Mech 13: 145–168. Available from: https://doi.org/10.1007/s10652-012-9263-2.    

74. Lugo J, Rojas-Solorzano L, Curtis J (2012) Numerical simulation of aeolian saltation within the sediment transport layer using granular kinetic theory. Rev Fac Ing 27: 80–96.

75. Lun CKK, Savage SB, Jeffrey DJ, et al. (1984) Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J Fluid Mech 140: 223–256. Available from: https://doi.org/10.1017/S0022112084000586.    

76. Marval JP, Rojas-Solórzano LR, Curtis JS (2007) Two-dimensional numerical simulation of saltating particles using granular kinetic theory, In: ASME/JSME 2007 5th Joint Fluids Engineering Conference, 929–939.

77. Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32: 1598–1605.    

78. Menter FR, Kuntz M, Langtry R (2003) Ten years of industrial experience with the SST turbulence model. Turbul heat mass transfer 4: 625–632.

79. Mochida A, Lun I (2008) Prediction of wind environment and thermal comfort at pedestrian level in urban area. J Wind Eng Ind Aerod 96: 1498–1527.    

80. Monin A, Obukhov A (1954) Basic laws of turbulent mixing in the surface layer of the atmosphere. Contrib Geophys Inst Acad Sci 151: 163–187.

81. Moore I (1995) Numerical modelling of blowing snow around buildings. PhD thesis, University of Leeds.

82. Naaim M, Florence N, Martinez H (1998) Numerical simulation of drifting snow: Erosion and deposition models. Ann Glaciol 26: 191–196.    

83. Nalpanis P,Hunt J,Barrett C (1993) Saltating particles over flat beds. J Fluid Mech 251: 661–685.    

84. Okaze T, Niiya H, Nishimura K (2018) Development of a large-eddy simulation coupled with Lagrangian snow transport model. J Wind Eng Ind Aerod 183: 35–43.    

85. Okaze T, Takano Y, Mochida A, et al. (2015) Development of a new κ–? model to reproduce the aerodynamic effects of snow particles on a flow field. J Wind Eng Ind Aerod 144: 118–124.

86. Parteli E, Schwämmle V, Herrmann H, et al. (2006) Profile measurement and simulation of a transverse dune field in the lençóis maranhenses. Geomorphology 81: 29–42.    

87. Pasini JM, Jenkins JT (2005) Aeolian transport with collisional suspension. Philos Trans R Soc A 363: 1625–1646. Available from: https://doi.org/10.1098/rsta.2005.1598.    

88. Patankar N, Joseph D (2001) Modeling and numerical simulation of particulate flows by the Eulerian-Lagrangian approach. Int J Multiphase Flow 27: 1659–1684.    

89. Pettersson K, Krajnovic S, Kalagasidis A, et al. (2016) Simulating wind-driven rain on building facades using eulerian multiphase with rain phase turbulence model. Build Environ 106: 1–9.    

90. Pischiutta M, Formaggia L, Nobile F (2011) Mathematical modelling for the evolution of aeolian dunes formed by a mixture of sands: Entrainment-deposition formulation. Commun Appl Ind Math 2: 0003777.

91. Pomeroy J, Gray D (1990) Saltation of snow. Water Resour Res 26: 1583–1594.    

92. Preziosi L, Fransos D, Bruno L (2015) A multiphase first order model for non-equilibrium sand erosion, transport and sedimentation. Appl Math Lett 45: 69–75.    

93. Sagaut P (2006) Large eddy simulation for incompressible flows: An introduction. Springer Science & Business Media.

94. Sato T, Uematsu T, Nakata T, et al. (1993) Three dimensional numerical simulation of snowdrift, In: Murakami, S. Editor, Computational Wind Engineering 1, Elsevier, Oxford, 741–746. Available from: https://doi.org/10.1016/B978-0-444-81688-7.50082-6.

95. Sauermann G, Andrade J, Maia L, et al. (2003) Wind velocity and sand transport on a barchan dune. Geomorphology 54: 245–255.    

96. Sauermann G, Kroy K, Herrmann HJ (2001) Continuum saltation model for sand dunes. Phys Rev E 64: 031305.    

97. Schlichting H, Gersten K (2016) Boundary-Layer Theory, Springer.

98. Shi X, Xi P, Wu J (2015) A lattice Boltzmann-Saltation model and its simulation of aeolian saltation at porous fences. Theor Comput Fluid Dyn 29: 1–20.

99. Shih TH, Liou WW, Shabbir A, et al. (1995) A new k-? eddy viscosity model for high Reynolds number turbulent flows. Comput Fluids 24: 227–238.

100. Smagorinsky J (1963) General circulation experiments with the primitive equations: I. the basic experiment. Mon Weather Rev 91: 99–164.    

101. Sun Q, Wang G, Xu Y (2001) DEM applications to aeolian sediment transport and impact process in saltation. Partl Sci Technol 19: 339–353.    

102. Sun X, He R, Wu Y (2018) Numerical simulation of snowdrift on a membrane roof and the mechanical performance under snow loads. Cold Reg Sci Technol 150: 15–24.    

103. Sundsbø P (1998) Numerical simulations of wind deflection fins to control snow accumulation in building steps. J Wind Eng Ind Aerod 74: 543–552.

104. Surry D, Inculet D, Skerlj P, et al. (1994) Wind, rain and the building envelope: A status report of ongoing research at the university of western ontario. J Wind Eng Ind Aerod 53: 19–36.    

105. Syamlal M, O' Brien T (1987) The derivation of a drag coefficient formula from velocity-voidage correlations. Tech Note, US Department of Energy, Office of Fossil Energy, NETL, Morgantown, WV.

106. Thiis TK (2000) A comparison of numerical simulations and full-scale measurements of snowdrifts around buildings. Wind Struct 3: 73–81.    

107. Tominaga Y, Okaze T, Mochida A (2011) CFD modeling of snowdrift around a building: An overview of models and evaluation of a new approach. Build Environ 46: 899–910.    

108. Tong D, Huang N (2012) Numerical simulation of saltating particles in atmospheric boundary layer over flat bed and sand ripples. J Geophys Res Atmos 117. Available from: https://doi. org/10.1029/2011JD017424.

109. Uematsu T, Nakata T, Takeuchi K, et al. (1991) Three-dimensional numerical simulation of snowdrift. Cold Reg Sci Technol 20: 65–73.    

110. Vinkovic I, Aguirre C, Ayrault M, et al. (2006) Large-eddy simulation of the dispersion of solid particles in a turbulent boundary layer. Boundary-layer Meteorol 121: 283–311.    

111. Wang H, Hou X, Deng Y (2015) Numerical simulations of wind-driven rain on building facades under various oblique winds based on Eulerian multiphase model. J Wind Eng Ind Aerod 142: 82–92.    

112. Wen C, Yu Y (1966) A generalized method for predicting the minimum fluidization velocity. AIChE J 12: 610–612.    

113. Werner B (1990) A Steady-State model of Wind-Blown sand transport. J Geol 98: 1–17. Available from: https://doi.org/10.1086/629371.    

114. Wilcox D (2008) Formulation of the k-ω turbulence model revisited. AIAA J 46: 2823–2838. Available from: https://doi.org/10.2514/1.36541.    

115. Wilcox DC (1988) Reassessment of the scale-determining equation for advanced turbulence models. AIAA J 26: 1299–1310.    

116. Wilcox DC (1998) Turbulence Modeling for CFD, 2nd Edition, DCW industries La Canada, California.

117. Xiao F, Guo L, Li D, et al. (2012) Discrete particle simulation of mixed sand transport. Particuology 10: 221–228.    

118. Yakhot V, Orszag S (1986) Renormalization group analysis of turbulence. i. basic theory. J Sci Comput 1: 3–51. Available from: https://doi.org/10.1007/BF01061452.

119. Zhou X,Kang L,Gu M,et al. (2016a) Numerical simulation and wind tunnel test for redistribution of snow on a flat roof. J Wind Eng Ind Aerod 153: 92–105.

120. Zhou X, Zhang Y, Wang Y, et al. (2016b) 3D numerical simulation of the evolutionary process of aeolian downsized crescent-shaped dunes. Aeolian Res 21: 45–52.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved