Simulation of Average Turbulent Pipe Flow: A Three-Equation Model

Khalid  Alammar

doi:10.4236/ojfd.2014.41005

Khalid Alammar^*

Abstract: The aim of this study is to evaluate a three-equation turbulence model applied to pipe flow. Uncertainty is approximated by comparing with published direct numerical simulation results for fully-developed average pipe flow. The model is based on the Reynolds averaged Navier-Stokes equations. Boussinesq hypothesis is invoked for determining the Reynolds stresses. Three local length scales are solved, based on which the eddy viscosity is calculated. There are two parameters in the model; one accounts for surface roughness and the other is possibly attributed to the fluid. Error in the mean axial velocity and Reynolds stress is found to be negligible.

Keywords: Pipe Flow; Reynolds Stress; Turbulence Modeling

Cite this paper: Alammar, K. (2014) Simulation of Average Turbulent Pipe Flow: A Three-Equation Model. Open Journal of Fluid Dynamics, 4, 69-73. doi: 10.4236/ojfd.2014.41005.

References

[1] Hinze, J.O. (1975) Turbulence. McGraw-Hill Publishing Co., New York.

[2] Eggels, J.G., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. and Nieuwstadt, F.T.M. (1993) Fully-Developed Turbulent Pipe Flow: A Comparison between Direct Numerical Simulation and Experiment. Journal of Fluid Mechanics, 268, 175-209. http://dx.doi.org/10.1017/S002211209400131X

[3] Loulou, P., Moser, R., Mansour, N. and Cantwell, B. (1997) Direct Simulation of Incompressible Pipe Flow Using a b-Spline Spectral Method. Technical Report TM 110436, NASA-Ames Research Center, Mountain View.

[4] Wu, X. and Moin, P. (2008) A Direct Numerical Simulation Study on the Mean Velocity Characteristics in Pipe Flow. Journal of Fluid Mechanics, 608, 81-112. http://dx.doi.org/10.1017/S0022112008002085

[5] Lawn, C.J. (1971) The Determination of the Rate of Dissipation in Turbulent Pipe Flow. Journal of Fluid Mechanics, 48, 477-505. http://dx.doi.org/10.1017/S002211207100171X

[6] Rudman, M. and Blackburn, H. (1999) Large Eddy Simulation of Turbulent Pipe Flow. 2nd International Conference on CFD in the Minerals and Process Industry, CSIRO, Melbourne, 6-8 December 1999, 503-508.

[7] Yamamoto, Y., Kunugi, T., Satake, S. and Smolentsev, S. (2008) DNS and k-ε Model Simulation of MHD Turbulent Channel Flows with Heat Transfer. Fusion Engineering and Design, 83, 1309-1312. http://dx.doi.org/10.1016/j.fusengdes.2008.10.001

[8] Launder, B. and Spalding, D. (1972) Mathematical Models of Turbulence. Academic Press, Waltham.

[9] Alammar, K. (2008) Turbulence: A New Zero-Equation Model. 7th International Conference on Advancements in Fluid Mechanics, Wessex Institute of Technology, New Forest, 21-23 May 2008, 365-368.