Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-18T21:27:05.574Z Has data issue: false hasContentIssue false
  • English
  • Français

On nonlinear K-l and K-ε models of turbulence

Published online by Cambridge University Press:  21 April 2006

Charles G. Speziale
Charles G. Speziale
Affiliation:
The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The commonly used linear K-l and K-ε models of turbulence are shown to be incapable of accurately predicting turbulent flows where the normal Reynolds stresses play an important role. By means of an asymptotic expansion, nonlinear K-l and K-ε models are obtained which, unlike all such previous nonlinear models, satisfy both realizability and the necessary invariance requirements. Calculations are presented which demonstrate that this nonlinear model is able to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model. Furthermore, the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts - a phenomenon which the linear models are fundamentally unable to describe. An additional application of this model to the improved prediction of separated flows is discussed briefly along with other possible avenues of future research.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 459 - 475
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chapman, S. & Cowling, T. G. 1953 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
Chen, C. P. 1985 Multiple-scale turbulence closure modelling of confined recirculating flows. NASA CR 178536. NASA-Marshall Space Flight Center.
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453.Google Scholar
Gessner, F. B. & Emery, A. F. 1976 A Reynolds stress model for turbulent corner flows - Part I: Development of the model. Trans. ASMS I: J. Fluids Engng 98, 261.Google Scholar
Gessner, F. B. & Jones, J. B. 1965 On some aspects of fully-developed turbulent flow in rectangular channels. J. Fluid Mech. 23, 689.Google Scholar
Gessner, F. B. & Po, J. K. 1977 A Reynolds stress model for turbulent corner flows - Part II: Comparisons between theory and experiment. Trans. ASME I: J. Fluids Engng 99, 269Google Scholar
Hanjalic, K. & Launder, B. E. 1972 A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52, 609.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Hussain, A. K. M. F. & Reynolds, W. C. 1975 Measurements in fully-developed turbulent channel flow. Trans. ASME I: J. Fluids Engng 97, 568.Google Scholar
Laufer, J. 1951 Investigation of turbulent flow in a two-dimensional channel. NACA TN 1053.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537.Google Scholar
Launder, B. E. & Ying, W. M. 1971 Fully developed turbulent flow in ducts of square cross section. Rep. TM/TN/A/11. Imperial College of Science and Technology.Google Scholar
Lumley, J. L. 1970 Toward a turbulent constitutive relation. J. Fluid Mech. 41, 413.Google Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123.Google Scholar
Mellor, G. L. & Herring, H. J. 1973 A survey of the mean turbulent field closure models. AIAA J. 11, 590.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341.Google Scholar
Rivlin, R. S. 1957 The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids. Q. Appl. Maths 15, 212.Google Scholar
Rodi, W. 1982 Example of turbulence models for incompressible flows. AIAA J. 20, 872.Google Scholar
Saffman, P. G. 1977 Results of a two-equation model for turbulent flows and development of a relaxation stress model for application to straining and rotating flows. In Project SQUID Workshop on Turbulence in Internal Flows (ed. S. Murthy), p. 191. Hemisphere.
Schowalter, W. R. 1978 Mechanics of Non-Newtonian Fluids. Pergamon.
Speziale, C. G. 1981 Some interesting properties of two-dimensional turbulence. Phys. Fluids 24, 1425.Google Scholar
Speziale, C. G. 1982 On turbulent secondary flows in pipes of non-circular cross-section. Intl J. Engng Sci. 20, 863.Google Scholar
Speziale, C. G. 1983 Closure models for rotating two-dimensional turbulence. Geophys. Astrophys. Fluid Dyn. 23, 69.Google Scholar
Speziale, C. G. 1984 On the origin of turbulent secondary flows in non-circular ducts. In Computation of Internal Flows: Methods and Applications, ASME FED 14, p. 101. ASME.
Speziale, C. G. 1985 Modeling the pressure gradient-velocity correlation of turbulence. Phys. Fluids 28, 69.Google Scholar
Thangam, S. & Speziale, C. G. 1985 Numerical study of non-Newtonian secondary flows in rectangular ducts. Tech. Rep. ME-RT-85035. Stevens Institute of Technology.Google Scholar
Truesdell, C. & Noll, W. 1965 The nonlinear field theories of mechanics. In Handbuch der Physik, vol. III/3. Springer.
Yoshizawa, A. 1984 Statistical analysis of the deviation of the Reynolds stress from its eddy viscosity representation. Phys. Fluids 27, 1377.Google Scholar