A Historical Review of Turbulence Flow Modeling and Simulation in Hydraulics

آب و توسعه پایدار

Article 6, Volume 5, Issue 2 - Serial Number 11, March 2019, Pages 49-60   

Document Type: review paper

DOI: 10.22067/jwsd.v5i2.68927

Authors

Maedeh Oskouhi; Kazem Esmaili^*

Ferdowsi University of Mashhad

Abstract

This paper reviews from a historical perspective the various methods for treating and simulating turbulence. After highlighting the main characteristic features of turbulence and its role in hydraulics, a necessary brief overview is given of the main methods used in hydraulic flow calculations for dealing with turbulence and its effects. These are 1) empirical relations, 2) solution methods for the Reynolds-Averaged Navier-Stokes (RANS), 3) Direct Numerical Simulations (DNS), and 4) Large-Eddy Simulations (LES). Brief comments are made on the historical development of different methods. Moreover, some application examples are presented for RANS, DNS, and LES methods.

Keywords

Keywords: Turbulent flow; Modeling; Empirical relations; RANS model; Direct Numerical Simulation; Large-Eddy Simulations

References

ASCE. 1988. Turbulence modeling of surface water flow and transport. Parts I–V, J. Hydraul. Eng.

Boussinesq J. 1877. Essai sur la theorie des eaux courantes. Memoires presentes par divers savants à l’Academie des Sciences, Paris.

Burchard H. 2002. Applied turbulence modelling in marine waters. lecture notes in earth sciences 100, Springer, Berlin.

Casey M. and Wintergerste. T. 2000. Best practice guidelines. ERCOFTAC Publication.

Chen C.J. and Rodi W. 1980. Vertical turbulent buoyant jets: A review of experimental data. Pergamon Press, Oxford, U.K.

Doneker R.L. and Jirka G.H. 1991. Expert system for mixing-zone analysis and design of pollutant discharges. J. Water Res. Plann. Manage, 117(6): 679–697.

Doneker R.L. and Jirka G.H. 2001. CORMIX-GT system for mixing zone analysis of brine water disposal. Desalination, 139(1–3): 263–274.

Durbin P. and Pettersson-Reif B.A. 2001. Statistical theory and modelling for turbulent flows. Wiley, Hoboken, NJ.

Elder J.W. 1959. The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech, 5(4): 544–560.

Fang H.W. 2000. Three-dimensional calculations of flow and bed-load transport in the Elbe River. Institut für Hydromechanik, Universität Karlsruhe, Karlsruhe, Germany. 763.

Fröhlich J. 2006. Large Eddy Simulation turbulenter Strömungen. Teubner, Wiesbaden.

Gauckler P. 1868. On the movement of water in pipes. Ann. Ponts Chaussees, 38(1): 229–281.

Hanjalic K. and Launder B.E. 2012. Modelling turbulence in engineering and the environment. Cambridge University Press, Cambridge, U.K.

Herlina H. and Wissink J.G. 2014. Direct numerical simulations of turbulent scalar transport across a flat surface. J. Fluid Mech, 744: 217–249.

Imberger J. and Patterson C. 1981. A dynamic reservoir simulation model: DYRESM: 5. Transport models for inland and coastal waters, H.B. Fischer, ed, Academic Press, Cambridge, MA.

Kline S.J., Morkovin M.V., Sovran G. and Cockrell D.D. 1969. Proc. Computation of Turbulent Boundary Layers–1968 AFOSR-IFPStanford Conf, Thermosciences Div, Dept. of Mechanical Engineering, Stanford Univ, Stanford, CA.

Kline S.J., Cantwell B.J. and Lilley G.M. 1981. Proc. 1980-81 AFOSR-HTTM-Stanford Conf. on Complex Turbulent Flows: Comparison of Computations and Experiment, Thermosciences Div, Dept. of Mechanical Engineering, Stanford Univ, Stanford, CA.

Lakehal D., Krebs P., Krijgsman J. and Rodi W. 1999. Computing shear flow and sludge blanket in secondary clarifiers. J. Hydraul. Eng, 125(3): 253–262.

Launder B.E. and Spalding D.B. 1974. The numerical computation of turbulent flow. Comput. Methods. Appl. Mech. Eng, 3(2): 269–289.

Launder B.E. and Rodi W. 1983. The turbulent wall jet: Measurements and modelling. Annu. Rev. Fluid Mech, 15(1): 429–459.

Launder B.E. and Sandham N.D. eds. 2004. Closure strategies for turbulent and transitional flows. Cambridge University Press, Cambridge, U.K.

Leschziner M. 2016. Statistical turbulence modelling for fluid mechanics: Demystified. Imperial College Press, London.

List E.J. 1986. Mechanics of turbulent buoyant jets and plumes. Turbulent buoyant jets and plumes, W. Rodi, ed, Pergamon Press, Oxford, U.K.

Lyn D.A. 2008. Turbulence models for sediment transport engineering. Sediment engineering, M. H. Garcia, ed, ASCE, Reston, VA.

Manning R. 1889. On the flow of water in open channels and pipes. Trans. Inst. Civ. Eng, 20: 161–207.

Mellor G.L. and Yamada T. 1982. Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys, 20(4): 851–875.

Menter F.R. 1994. Two-equation eddy viscosity turbulence models for engineering applications. J. AIAA, 32(8): 1598–1605.

Menter F.R. and Egorov Y. 2010. The scale adaptive simulation method for unsteady flow predictions. Part I: Theory and model descriptions. Flow Turbul. Combust, 85(1): 113–138.

Meyer-Peter E. and Müller R. 1948. Formulas for bed-load transport. Association of Hydraulic Research, 2nd Meeting, IAHR, Delft, Netherlands.

Minh Duc B. 1998. Berechnung der Strömung und des Sedimenttransports in Flüssen mit einem tiefengemittelten numerischen Verfahren. Ph.D. thesis, Univ. of Karlsruhe, Karlsruhe, Germany.

Moody L.F. 1944. Friction factors for pipe flow. Trans. ASME, 66(8): 671–684.

Nadaoka K. and Yagi H. 1998. Shallow-water turbulence modeling and horizontal large-eddy computation of river flow. J. Hydraul. Eng, 124(5): 493–500.

Paik J., Ge L. and Sotiropoulos F. 2004. Toward the simulation of complex 3D shear flows using unsteady statistical turbulence models. Int. J. Heat Fluid Flow, 25(3): 513–527.

Pan Y. and Banerjee S. 1995. A numerical study of free-surface turbulence in open channel flow. Phys. Fluids, 7(7): 1649–1664.

Patel V.C., Rodi W. and Scheuerer G. 1985. Turbulence models for near-wall and low Reynolds number flows. AIAA J., 23(9): 1308–1319.

Prandtl L. 1925. Über die ausgebildete Turbulenz. Z. Angew. Math. Mech, 5: 136–139.

Reynolds O. 1895. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. R. Soc, 186: 123–164.

Rodi W. 1980. Turbulence models and their application in hydraulics: A state of the art review, IAHR monograph, 1st Ed, A.A. Balkema, Rotterdam, Netherlands.

Rodi W. 1987. Examples of calculation methods for flow and mixing in stratified fluids. J. Geophys. Res, 92(C5): 5305–5328.

Rodi W. 1993a. Elements of the theory of turbulence.” Coastal, estuarial and harbour engineers’ reference book, M. B. Abbott and W. A. Price, eds, Chapman and Hall, London.

Rodi W. 1993b. Turbulence models and their application in hydraulics: A state of the art review, IAHR monograph, 3rd Ed, A.A. Balkema, Rotterdam, Netherlands.

Rodi W. 1995. Impact of Reynolds-average modelling in hydraulics. Proc. R. Soc. London, Ser. A, 451(1941): 141–164.

Rouse H. 1946. Elementary mechanics of fluids, Wiley, Hoboken, NJ.

Strickler A. 1923. Contributions to the question of velocity formula and the roughness numbers for rivers, channels and pipes. Mitteilung 16, C. Mutzner, ed, Amt für Wasserwirtschaft, Bern, Switzerland (in German).

Van Rijn L. 1993. Principles of sediment transport in rivers, estuaries and coastal seas, Aqua Publications, Blokzijl, Netherlands.

Wallin S. and Johansson A.V. 2000. An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech, 403: 89–132.

Wenka T., Brudy-Zippelius T. and Schmidt A. 2016. 2D and 3D modelling in German inland waterways. Advances in hydroinformatics, P. Goursbesville, et al., eds., Springer, Singapore.

Wilcox D.C. 1993. Turbulence modeling for CFD, 1st Ed., DCW Industries, La Canada, CA.

Wilcox D.C. 2006. Turbulence modeling for CFD, 3rd Ed., DCW Industries, La Canada, CA.

Wu W.M., Rodi W. and Wenka T. 2000. 3D numerical modeling of flow and sediment transport in open channels. J. Hydraul. Eng, 126(1): 4–15.

Wu X. and Moin P. 2009. Forest of hairpins in a low-Reynolds number zero-pressure-gradient flat-plate boundary layer. Phys. Fluids, 21(9).

Yakot V. and Orszag S.A. 1986. Renormalization-group analysis of turbulence. Phys. Rev. Lett, 57(14): 1722–1724.