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Direct numerical simulation of turbulent flow in a square duct

Published online by Cambridge University Press:  26 April 2006

Asmund Huser  and
Sedat Biringen
Asmund Huser
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA Current address: DNV Technica, N-1322 Høvik, Norway.
Sedat Biringen
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA
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Abstract

A direct numerical simulation of a fully developed, low-Reynolds-number turbulent flow in a square duct is presented. The numerical scheme employs a time-splitting method to integrate the three-dimensional, incompressible Navier-Stokes equations using spectral/high-order finite-difference discretization on a staggered mesh; the nonlinear terms are represented by fifth-order upwind-biased finite differences. The unsteady flow field was simulated at a Reynolds number of 600 based on the mean friction velocity and the duct width, using 96 × 101 × 101 grid points. Turbulence statistics from the fully developed turbulent field are compared with existing experimental and numerical square duct data, providing good qualitative agreement. Results from the present study furnish the details of the corner effects and near-wall effects in this complex turbulent flow field; also included is a detailed description of the terms in the Reynolds-averaged streamwise momentum and vorticity equations. Mechanisms responsible for the generation of the stress-driven secondary flow are studied by quadrant analysis and by analysing the instantaneous turbulence structures. It is demonstrated that the mean secondary flow pattern, the distorted isotachs and the anisotropic Reynolds stress distribution can be explained by the preferred location of an ejection structure near the corner and the interaction between bursts from the two intersecting walls. Corner effects are also manifested in the behaviour of the pressure-strain and velocity-pressure gradient correlations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 65 - 95
Copyright
© 1993 Cambridge University Press

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References

Anderson, D. A., Tennehill, J. C. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer. McGraw-Hill.
Balint, J.-L., Wallace, J. M. & Vukoslavcević, P. 1991 The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties. J. Fluid Mech. 228, 53.Google Scholar
Brundrett, E. & Baines, W. D. 1964 The production and diffusion of vorticity in a square duct. J. Fluid Mech. 19, 375.Google Scholar
Demuren, A. O. 1990 Calculation of turbulence-driven secondary motion in ducts with arbitrary cross-section. AIAA Paper 90-0245.
Demuren, A. O. & Rodi, W. 1984 Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189.Google Scholar
Gavrilakis, S. 1992 Numerical simulation of low Reynolds number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101.Google Scholar
Gessner, F. B. 1973 The origin of secondary flow in turbulent flow along a corner. J. Fluid Mech. 58, 1.Google Scholar
Gessner, F. B. & Emery, A. F. 1981 The numerical prediction of developing flow in rectangular ducts. Trans. ASME I: J. Fluids Engng 103, 445.Google Scholar
Gessner, B. F. & 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. & Emery, A. F. 1979 Measurement of developing turbulent flow in a square duct. In Turbulent Shear Flows I, p. 119. Springer.
Gresho, P. M. 1990 On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces an early consistent mass matrix. Part 1: Theory. Intl J. Numer. Meth. Fluids 11, 587.Google Scholar
Hartnett, J. P., Koh, J. C. Y. & McComas, S. T. 1962 A comparison of predicted and measured friction factors for turbulent flow through rectangular ducts. Trans. ASME C: J. Heat Transfer 84, 82.Google Scholar
Huser, A. 1992 Direct numerical simulation of turbulent flow in a square duct. Doctoral thesis, University of Colorado, Boulder.
Huser, A. & Biringen, S. 1992 Calculation of shear-driven cavity flows at high Reynolds numbers. Intl J. Numer. Meth. Fluids 14, 1087. Also in AIAA paper 90-1531.Google Scholar
Kim, J. & Moin, P. 1984 Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59, 308.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.Google Scholar
Launder, B. E. 1990 Phenomenological modelling: present⃛and future? Whither Turbulence? Turbulence at the Crossroads (ed. J. L. Lumley). Lecture Notes in Physics, vol. 357, p. 439. Springer.
Launder, B. E. & Ying, W. M. 1972 Secondary flows in ducts of square cross-section. J. Fluid Mech. 54, 289.Google Scholar
Le, H. & Moin, P. 1991 An improvement of fractional step methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 92, 369.Google Scholar
Lumley, J. L. 1991 Order and disorder in turbulent flows. In New Perspectives in Turbulence, p. 105. Springer.
Madabhushi, R. K. & Vanka, S. P. 1991 Large eddy simulation of turbulence-driven secondary flow in a square duct. Phys. Fluids A 3, 2734.Google Scholar
Mansour, N. N., Kim, J. & Moin, P. 1988 Reynolds-stress and dissipation rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341.Google Scholar
Moin, P. & Moser, R. D. 1989 Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200, 471.Google Scholar
Moser, R. D. & Moin, P. 1987 The effects of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479.Google Scholar
Nikuradse, J. 1930 Turbulente Strömung in nicht kreisförmigen Rohren. Ing. Arch. 1, 306.Google Scholar
Perkins, H. J. 1970 The formation of streamwise vorticity in turbulent flow. J. Fluid Mech. 44, 721.Google Scholar
Prandtl, L. 1926 Uber die ausgebildete Turbulenz. Verh. 2nd Intl Kong. fur Tech. Mech., Zurich. [English transl. NACA Tech. Memo. 435, 62].
Prandtl, L. 1952 Essentials of Fluid Dynamics, p. 145. Glasgow: Blackie.
Rai, M. M. & Moin, P. 1991 Direct simulation of turbulent flow using finite difference schemes. J. Comput. Phys. 96, 15. Also in AIAA paper 89-369.Google Scholar
Spalart, P. R. 1985 Numerical simulation of boundary layers. NASA TM 88220-88222.
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Ann. Rev. Fluid Mech. 5, 13.Google Scholar