Numerical simulation of turbulent flow through a straight square duct using a near wall linear k – ε model.
DOI:
https://doi.org/10.1260/175095407782219256Abstract
The aim of this work is to predict numerically the turbulent flow through a straight square duct using Reynolds Average Navier-Stokes equations (RANS) by the widely used k – ε and a near wall turbulence k – ε − fμ models. To handle wall proximity and no-equilibrium effects, the first model is modified by incorporating damping functions fμ via the eddy viscosity relation. The predicted results for the streamwise, spanwise velocities and the Reynolds stress components are compared to those given by the k – ε model and by the direct numerical simulation (DNS) data of Gavrilakis (J. Fluid Mech., 1992). In light of these results, the proposed k – ε − fμ model is found to be generally satisfactory for predicting the considered flow.
References
Pope S.B., A more general effective-viscosity hypothesis, J. Fluid Mech., 1975, 72, 331–340. https://doi.org/10.1017/s0022112075003382
Speziale C.S., Sarkar S. and Gatski T.B., Modelling the presses-strain correlation of turbulence: An invariant dynamical systems approach, J. Fluid Mech., 1991, 227, 245–272.
Joung Y., Choi S.V. and Choi J.II, Direct numerical simulation of turbulent flow in a square duct : Analysis of secondary flows, Journal of Engineering mechanics, 2007, 133 (2), 213–221.
Xu H., and Pollard A., Large-eddy simulation of turbulent flow in square annular duct, Physics of Fluids, 13(11), 3321–3337. https://doi.org/10.1063/1.1410386
Vasquez M.S. and Métais O., Large-eddy simulation of the turbulent flow through a heated square duct, J. Fluid Mech., 2002, 453, 201–238.
Belhoucine L., Deville M., Elazehari A.R. and Bensalah M.O., Explicit algebraic Reynolds stress model of incompressible turbulent flow in rotating square duct, Computers & Fluids, 2004, 33, 179–199. https://doi.org/10.1016/s0045-7930(03)00055-0
Nishino K., Kasagi N., Turbulence statistics measurement in a two-dimensional channel flow using a three-dimensional particle tracking velocimeter, Seventh Symposium on Turbulent Shear Flows, Stanford University, August 21–23, 1989.
Mompean G., Numerical simulation of a turbulent flow near a right-angled corner using the Speziale non- linear model with RNG k – ε equations, Computers & Fluids, 1998, 27, 847–859. https://doi.org/10.1016/s0045-7930(98)00004-8
Huser A. Biringen S. and Hatay F.F., Direct numerical simulation of turbulent flow in a square duct: Reynolds stress budgets, Physics of Fluids, 1994, 6 (9), 3144–3152. https://doi.org/10.1063/1.868138
Gavrilakis S., Numerical simulation of turbulent low-Reynolds-Number flow through a straight square duct, J. Fluid Mech., 1992, 244, 101–129. https://doi.org/10.1017/s0022112092002982
Huser A. and Biringen S., Direct numerical simulation of turbulent flow in a square duct, J. Fluid Mech., 1993, 257, 65–95. https://doi.org/10.1017/s002211209300299x
Yoshizawa A. and Nisizima S.A., A non equilibrium representation of the turbulent viscosity based on a two- scale turbulent theory, Physics of Fluids A, 1993, 5:3302–305. https://doi.org/10.1063/1.858690
Shih T.H., Zhu J. and Lumley J.L., A new Reynolds stress algebraic equation model, Comput. Methods Appl. Mech. Eng., 1995, 125, 287–302. https://doi.org/10.1016/0045-7825(95)00796-4
Wallin S. and Johansson A.V., An explicit algebraic Reynolds model for incompressible and compressible turbulent flows, J. Fluid Mech., 2000, 403, 89–132. https://doi.org/10.1017/s0022112099007004
Gatski T.B., Rumsey C.L., Linear and non-linear eddy viscosity models, Closure Strategies for Turbulent and transitional flows, Launder B.E. and Sandham N.D. eds., Cambridge University Press, 2001, 9–46. https://doi.org/10.1017/cbo9780511755385.003
Yang X.D., Ma H.Y. and Huang Y.N., Prediction of homogeneous flow and a backward facing step slow with some linear and non-linear k – ε turbulence models., Nonlinear Science and Numerical simulation, 2005, 10, 315–328. https://doi.org/10.1016/j.cnsns.2003.07.001
Speziale C.G. and Abid R., Near wall integration of Reynolds stress turbulence closures with no wall damping, AIAA Journal, 1995, 33 (10), 1947–7. https://doi.org/10.2514/3.12754
Nisizima S., Numerical study of turbulent square-duct flow using an anisotropic k – ε model, Theo. Comput. of Fluid Dynamics, 1990, 2, 183. https://doi.org/10.1007/bf00271429
Patel C.V., Rodi W. and Scheuerer G., Turbulence models for near-wall and low Reynolds number flow: a review, AIAA Journal, 1984, 23, 1308–1319. https://doi.org/10.2514/3.9086
El Yahyaoui O., Mompean G. and Naji H., Evaluation a priori d'un modèle non-linéaire de turbulence, C.R. Mécanique, 2002, 330, 27–34, Paris. https://doi.org/10.1016/s1631-0721(02)01423-7
Naji H., Mompean G. and El Yahyaoui O., Evaluation of explicit algebraic stress models using direct numerical simulations, Journal of Turbulence 5, 2004, 38. https://doi.org/10.1088/1468-5248/5/1/038
Leonard B.P., A stable accurate convective modelling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering, 1979, 19, 59–88. https://doi.org/10.1016/0045-7825(79)90034-3
Mompean G., Gavrilakis S., Machiels L. and Deville M.O., On predicting the turbulence-induced secondary flows using non-linear k – ε models, Physics of Fluids, 1996, 8, 1856–1868. https://doi.org/10.1063/1.868968
Harlow F.H. and Welch J.E., Numerical calculation of time-dependent viscous incompressible flow or fluid with free surface, Physics of Fluids, 1965, 8, 2182–2189. https://doi.org/10.1063/1.1761178
Wilcox D.C., Turbulence modelling for CFD. DCW Indsutries, Inc., 2nd edition, La cañada, California, 2004.
Gavrilakis S., Conditional sampling of the turbulent vorticity field near a smooth corner, Physics of Fluids., 1998, 10 (6), 1537–1539. https://doi.org/10.1063/1.869673
Cheesewright R., McGrath G., and Petty D.G., LDA measurements of turbulent flow in a duct of square cross section at low Reynolds number, Aeronautical Engineering Department, University of London, Report No. ER 101, 1990.
Published
How to Cite
Issue
Section
Copyright (c) 2007 A Rechia, H Naji, G Mompean, A Marjani
This work is licensed under a Creative Commons Attribution 4.0 International License.