Abstract
A turbulent square-duct flow is studied numerically using an anisotropic k-ɛ model, in which the deviation of the Reynolds stress from its isotropic eddy-viscosity representation plays a central role. The no slip boundary condition on the wall is imposed with the aid of wall damping functions. Various computed turbulent quantitites of a square-duct flow are compared with experimental and numerical results. The comparison shows that the present anisotropic k-ɛ model gives reasonable results to major characteristic properties in a duct flow such as the anisotropy of turbulent intensities and the secondary flow.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baker, A.J., and Orzechowski, J.A. (1983). An Interaction Algorithm for Three-Dimensional Turbulent Subsonic Aerodynamic Juncture Region Flow, AIAA J., 21, 524–533.
Bradshaw, P., Cebeci, T., and Whitelaw, J. H. (1981). Engineering Calculation Methods for Turbulent Flow. Academic Press, New York, pp. 37–76.
Briley, W. R. (1974). Numerical Method for Predicting Three-Dimensional Steady Viscous Flow in Ducts, J. Comput. Phys., 14, 8–28.
Chien, K.-Y. (1982). Prediction of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model, AIAA J., 20, 33–38.
Demuren, A.O., and Rodi, W. (1984). Calculation of Turbulence-Driven Secondary Motion in Non-Circular Ducts, J. Fluid Mech., 140, 189–222.
Gessner, F.B., and Emery, A.F. (1976). A Reynolds Stress Model for Turbulent Corner Flows—Part I: Development of the Model, J. Fluids Engrg., 98, 261–268.
Gessner, F.B., and Emery, A.F. (1981). The Numerical Prediction of Developing Turbulent Flow in Rectangular Ducts, J. Fluids Engrg, 103, 445–455.
Gessner, F.B., and Po. J.K. (1976). A Reynolds Stress Model for Turbulent Corner Flows—Part II: Comparisons Between Theory and Experiment, J. Fluids Engrg, 98, 269–277.
Hamba, F. (1987). Statistical Investigation of the Energy Dissipation Equation in Shear Turbulence, J. Phys. Soc. Japan, 56 (No. 11), 3771–3774.
Hanjalic, K., and Launder, B.E. (1976). Contribution Towards a Reynolds-Stress Closure for Low-Reynolds-Number Turbulence, J. Fluid Mech., 74, 593–610.
Horiuti, K. (1981). Study of Incompressible Turbulent Channel Flow by Large-Eddy Simulation, Theoret. Appl. Mech., 31, 407–427.
Horiuti, K. (1987). Comparison of Conservative and Rotational Forms in Large Eddy Simulation of Turbulent Channel Flow, J. Comput. Phys., 71, 343–370.
Jones, W.P., and Launder, B.E. (1972). The Prediction of Laminarization with a Two-Equation Model of Turbulence, Internat. J. Heat Mass Transfer. 15, 301–314.
Jones, W.P., and Launder, B.E. (1973). The Calculation of Low-Reynolds-Number Phenomena with a Two-Equation Model of Turbulence, Internat. J. Heat Mass Transfer, 16, 1119–1130.
Lam, C.K.G., and Bremhorst, K. (1981). A Modified Form of k-ɛ Model for Predicting Wall Turbulence, J. Fluids Engrg. 103, 456–460.
Launder, B.E., and Sharma, B.I. (1974). Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc, Lett. Heat Mass Transfer, 1, 131–138.
Lumley, J.L. (1980). Second-Order Modeling of Turbulent Flows, in Prediction Methods for Turbulent Flows, edited by W. Kollmann, Hemisphere, Washington, pp. 1–32.
Mansour, N.N., and Kim, J., and Moin, P. (1989). Near-Wall k-ɛ Turbulence Modeling, AIAA J., 27, 1068–1073.
Melling, A., and Whitelaw, J.H. (1976). Turbulent Flow in a Rectangular Duct, J. Fluid Mech., 78, 289–315.
Moin, P., and Kim, J. (1982). Numerical Investigation of Turbulent Channel Flow, J. Fluid Mech., 118, 341–377.
Myong, H.K., and Kasagi, N. (1988). A New Proposal for a k-ɛ Turbulence Model and the Evaluation (1st Report, Development of the Model), Trans. JSME(B), 54 (No. 507), 3003–3009.
Nakao, S. (1984). Contribution to the Reynolds Stress Model as Applied to Near-Wall Region, AIAA J., 22, 303–304.
Nakayama, A., and Chow, W.L. (1986). Turbulent Flows Within Straight Ducts, Encyclopedia of Fluid Mechanics vol. 1, Gulf Publishing Company, Houston, pp. 638–674.
Nakayama, A., Chow, W.L., and Sharma, D. (1983). Calculation of Fully Developed Turbulent Flows in Duct of Arbitrary Cross-Section, J. Fluid Mech., 128, 199–217.
Nakayama, A., Chow, W.L., and Sharma, D. (1984). Three-Dimensional Developing Turbulent Flow in Square Duct, Bull. JSME, 27 (No. 229), 1438–1445.
Nisizima, S. (1987). Numerical Study of Turbulent Channel Flows Using an Improved Anisotropic k-ɛ Model, Trans. JSME(B), 53 (No. 495), 3166–3172.
Nisizima, S., and Yoshizawa, A. (1987). Turbulent Channel and Couette Flows Using an Anisotropic k-ɛ Model, AIAA J., 25, 414–420.
Patel, V.C., Rodi, W., and Scheuerer, G. (1984). Turbulence Models for Near-Wall and Low Reynolds Number Flows, A Review, AIAA J., 23, 1308–1319.
Speziale, C.G. (1987). On Nonlinear k-l and k-ɛ Models of Turbulence. J. Fluid Mech., 178, 459–475.
Speziale, C.G., and Ngo, T. (1988). Numerical Solution of Turbulent Flow Past a Backward Facing Step Using a Nonlinear k-ɛ Model, Internat. J. Engrg. Sci., 26, 1099.
Yoshizawa, A. (1984). Statistical Analysis of the Deviation of the Reynolds Stress from Its Eddy-Viscosity Representation, Phys. Fluids, 27, 1377–1387.
Author information
Authors and Affiliations
Additional information
Communicated by M.Y. Hussaini
Rights and permissions
About this article
Cite this article
Nisizima, S. A numerical study of turbulent square-duct flow using an anisotropic k-ɛ model. Theoret. Comput. Fluid Dynamics 2, 61–71 (1990). https://doi.org/10.1007/BF00271429
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00271429