Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T13:48:25.791Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct simulations of low-Reynolds-number turbulent flow in a rotating channel

Published online by Cambridge University Press:  26 April 2006

Reidar Kristoffersen  and
Helge I. Andersson
Reidar Kristoffersen
Affiliation:
Department of Applied Mechanics, Faculty of Mechanical Engineering, The Norwegian Institute of Technology, N-7034 Trondheim, Norway Also: ERCOFTAC Pilot Centre, EPFL-Ecublens, CH-1015 Lausanne, Switzerland.
Helge I. Andersson
Affiliation:
Department of Applied Mechanics, Faculty of Mechanical Engineering, The Norwegian Institute of Technology, N-7034 Trondheim, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations of fully developed pressure-driven turbulent flow in a rotating channel have been performed. The unsteady Navier–Stokes equations were written for flow in a constantly rotating frame of reference and solved numerically by means of a finite-difference technique on a 128 × 128 × 128 computational mesh. The Reynolds number, based on the bulk mean velocity Um and the channel half-width h, was about 2900, while the rotation number Ro = 2|Ω|h/Um varied from 0 to 0.5. Without system rotation, results of the simulation were in good agreement with the accurate reference simulation of Kim, Moin & Moser (1987) and available experimental data. The simulated flow fields subject to rotation revealed fascinating effects exerted by the Coriolis force on channel flow turbulence. With weak rotation (Ro = 0.01) the turbulence statistics across the channel varied only slightly compared with the nonrotating case, and opposite effects were observed near the pressure and suction sides of the channel. With increasing rotation the augmentation and damping of the turbulence along the pressure and suction sides, respectively, became more significant, resulting in highly asymmetric profiles of mean velocity and turbulent Reynolds stresses. In accordance with the experimental observations of Johnston, Halleen & Lezius (1972), the mean velocity profile exhibited an appreciable region with slope 2Ω. At Ro = 0.50 the Reynolds stresses vanished in the vicinity of the stabilized side, and the nearly complete suppression of the turbulent agitation was confirmed by marker particle trackings and two-point velocity correlations. Rotational-induced Taylor-Görtler-like counter-rotating streamwise vortices have been identified, and the simulations suggest that the vortices are shifted slightly towards the pressure side with increasing rotation rates, and the number of vortex pairs therefore tend to increase with Ro.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 163 - 197
Copyright
© 1993 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

Alfrfdsson, P. H. &Johansson, A. V. 1984 On the detection of turbulence-generating events. J. Fluid Mech. 139, 325–345.Google Scholar
Alfredsson, P. H., Johansson, A. V., Haritonidis, J. H. &Eckelmann, H. 1988 The fluctuating wall-shear stress and the velocity field in the viscous sublayer. Phys. Fluids 31, 1026–1033.Google Scholar
Alfredsson, P. H. &Persson, H. 1989 Instabilities in channel flow with system rotation. J. Fluid Mech. 202, 543–557.Google Scholar
Andersson, H. I. &Kristoffersen, R. 1992 Statistics of numerically generated turbulence. Acta Appl. Math. 26, 293–314.Google Scholar
Andersson, H. I. &Mazumdar, H. P. 1993 Rapid distortion of homogeneous low Reynolds number turbulence by uniform shear and weak rotation. Eur. J. Mech. B. Fluids 12, 31–42.Google Scholar
Bertoglio, J.-P. 1982 Homogeneous turbulent field within a rotating frame. AIAA J. 20, 1175–1181.Google Scholar
Bidokhti, A. A. &Tritton, D. J. 1992 The structure of a turbulent free shear layer in a rotating fluid. J. Fluid Mech. 241, 469–502.Google Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177–191.Google Scholar
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGARDograph 169.
Cambon, C., Benoit, J. P., Shao, L. &Jacquin, L. 1993 Stability analysis and direct simulation of rotating turbulence with organized eddies. In Some Applied Problems in Fluid Mechanics (ed. H. P. Mazumdar), pp. 125–153. Indian Statistical Institute.
Cambon, C. &Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.Google Scholar
Cambon, C., Teissedre, C. &Jeandel, D. 1985 Etude d’effets couplés de déformation et de rotation sur une turbulence homogène. J. Méc. Théor. Appl. 4, 629–657.Google Scholar
Cousteix, J. &Aupoix, B. 1981 Modélisation des équations aux tensions de Reynolds dans un repere en rotation. La Recherche Aérospatiale No. 1981–4, pp. 275–285.
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME I: J. Fluids Engng 100, 215–223.Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–480.Google Scholar
Eckelmann, H. 1974 The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech. 65, 439–459.Google Scholar
Galperin, B. &Mellor, G. L. 1991 The effects of streamline curvature and spanwise rotation on near-surface, turbulent boundary layers. Z. Angew. Math. Phys. 42, 565–583.Google Scholar
Gavrilakis, S., Tsai, H. M., Voke, P. R. &Leslie, D. C. 1986 Large-eddy simulation of low Reynolds number channel flow by spectral and finite difference methods. In Direct and Large Eddy Simulation of Turbulence (ed. U. Schumann &R. Friedrich). Notes on Numerical Fluid Mechanics, vol. 15, pp. 105–118. Vieweg.
Hill, P. G. &Moon, I. M. 1962 Effects of Coriolis on the turbulent boundary layer in rotating fluid machines. MIT Gas Turbine Lab. Rep. 69.
Hopfinger, E. J. 1989 Turbulence and vortices in rotating fluids. In Theoretical and Applied Mechanics (ed. P. Germain, M. Piau &D. Caillerie), pp. 117–138. Elsevier.
Hopfinger, E. J. &Linden, P. F. 1990 The effect of background rotation on fluid motions: a report on Euromech 245. J. Fluid Mech. 211, 417–435.Google Scholar
Howard, J. H. G., Patankar, S. V. &Bordynuik, R. M. 1980 Flow prediction in rotating ducts using Coriolis-modified turbulence models. Trans. ASME I: J. Fluids Engng 102, 456–461.Google Scholar
Ibal, G. 1990 Adverse pressure gradient and separating turbulent boundary layer flows with system rotation. PhD thesis, University of Melbourne.
Johnston, J. P. 1973 The suppression of shear layer turbulence in rotating systems. Trans. ASME I: J. Fluids Engng 95, 229–236.Google Scholar
Johnston, J. P. &Eide, S. A. 1976 Turbulent boundary layers on centrifugal compressor blades: prediction of the effects of surface curvature and rotation. Trans. ASME I: J. Fluids Engng 98, 374–381.Google Scholar
Johnston, J. P., Halleen, R. M. &Lezius, D. K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbullent channel flow. J. Fluid Mech. 56, 533–557.Google Scholar
Karlsson, R. I. 1993 Near-wall measurements of turbulence structure in boundary layers and wall jets. In Near-Wall Turbulent Flows (ed. R. M. C. So, C. G. Speziale &B. E. Launder), pp. 423–432. Elsevier.
Karlsson, R. I. &Johansson, T. G. 1988 LDV measurements of higher order moments of velocity fluctuations in a turbulent boundary layer. In Laser Anemometry in Fluid Mechanics III (ed. R. J. Adrian, T. Asanuma, D. F. G. Durao, F. Durst J. H. Whitelaw), pp. 273–289. Ladoan-Instituto Superior Tecnico.
Kasagi, N. &Hirata, M. 1975 Transport phenomena in near-wall region of turbulent boundary layer around a rotating cylinder. ASME Winter Annual Meeting, Houston, Paper 75-WA/HT-58.
Kasagi, N. &Nishino, K. 1991 Probing turbulence with three-dimensional particle-tracking velocimetry. Exp. Thermal Fluid Sci. 4, 601–612.Google Scholar
Kikuyama, K., Nishibori, K., Murakami, M. &Hara, S. 1987 Effects of system rotation upon turbulent boundary layer on a concave surface. In Proc. 6th Symp. on Turbulent Shear Flows, Toulouse, pp. 1.4.1–6.
Kim, J. 1983 The effect of rotation on turbulence structure. In Proc. 4th Symp. on Turbulent Shear Flows, Karlsruhe, pp. 6.14–6.19.
Kim, J., Moin, P. &Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Koyama, H., Masuda, S., Ariga, I. &Watanabe, I. 1979 Stabilizing and destabilizing effects of Coriolis force on two-dimensional laminar and turbulent boundary layers. Trans. ASME A: J. Engng Power 101, 25–31.Google Scholar
Koyama, H. S. &Ohuchi, M. 1985 Effects of Coriolis force on boundary layer development. In Proc. 5th Symp. on Turbulent Shear Flows, Ithaca, pp. 21.19–21.24.
Kreplin, H.-P. &Eckelmann, M. 1979 Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids 22, 1233–1239.Google Scholar
Kristoffersen, R. &Andersson, H. I. 1991 Numerical transition to turbulence in plane Poiseuille flow. In Numerical Methods in Laminar and Turbulent Flow (ed. C. Taylor, J. H. Chin &G. M. Homsy), vol. 7, pp. 222–232. Pineridge.
Kristoffersen, R., Nilsen, P. J. &Andersson, H. I. 1990 Validation of Reynolds stress closures for rotating channel flows by means of direct numerical simulations. In Engineering Turbulence Modelling and Experiments (ed. W. Rodi &E. N. Ganic), pp. 55–64. Elsevier.
Launder, B. E. 1889a Second-moment closure: present⃛and future? Intl J. Heat Fluid Flow 10, 282–300.Google Scholar
Launder, B. E. 1989b Second-moment closure and its use in modelling turbulent industrial flows. Intl J. Num. Meth. Fluids 9, 963–985.Google Scholar
Launder, B. E. &Tselepidakis, D. P. 1993 Application of a new second-moment closure to turbulent channel flow rotating in orthogonal mode. Intl. J. Heat Fluid Flow (to appear.)Google Scholar
Launder, B. E., Tselepidakis, D. P. &Younis, B. A. 1987 A second-moment closure study of rotating channel flow. J. Fluid Mech. 183, 63–75.Google Scholar
Masuda, S., Okamae, K. &Ariga, I. 1985 Transition of boundary layer on rotating flat plate. In Laminar–Turbulent Transition (ed. V. V. Kozlov), pp. 699–704. Springer.
Miyake, Y. &Kajishima, T. 1986a Numerical simulation of the effects of Coriolis force on the structure of turbulence. Global effects. Bull. JSME 29, 3341–3346.Google Scholar
Miyake, Y. &Kajishima, T. 1986b Numerical simulation of the effects of Coriolis force on the structure of turbulence. Structure of turbulence. Bull. JSME 29, 3347–3351.Google Scholar
Moin, P. &Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.Google Scholar
Moon, I. M. 1964 Effects of Coriolis forces on the turbulent boundary layer in rotating fluid machines. MIT Gas Turbine Lab. Rep. 74.
Moore, J. 1967 Effect of Coriolis on turbulent flow in rotating rectangular channels. MIT Gas Turbine Lab. Rep. 89.
Moser, R. D. &Moin, P. 1987 The effect of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479–510.Google Scholar
Nilsen, P. J. &Andersson, H. I. 1990a Reynolds stress modelling of developing flow in a rotating channel. In Proc. 4th Intl Symp. on Refined Flow Modelling and Turbulence Measurements, Wuhan (ed. Z. Liang, C. J. Chen &S. Cai), pp. 54–61. IAHR.
Nilsen, P. J. &Andersson, H. I. 1990b Rotational effects on sudden expansion flows. In Engineering Turbulence Modelling and Experiments (ed. W. Rodi &E. N. Ganic), pp. 65–72. Elsevier.
Nilsen, P. J. &Andersson, H. I. 1993 Modelling the effects of solid-body rotation on turbulent mixing-layers. In Engineering Turbulence Modelling and Experiments 2 (ed. W. Rodi &F. Martelli), pp. 83–92. Elsevier.
Nishino, K. &Kasagi, N. 1989 Turbulence statistics measurements in a two-dimensional channel flow using a three-dimensional particle tracking velocimeter. In Proc. 7th Symp. on Turbulent Shear Flows, Stanford, pp. 22.1.1–6.
Rothe, P. H. &Johnston, J. P. 1979 Free shear layer behavior in rotating systems. Trans. ASME I: J. Fluids Engng 101, 117–120.Google Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys,. 18, 376–404.Google Scholar
Shima, N. 1993 Prediction of turbulent boundary layers with a second-moment closure: Part II – Effects of streamline curvature and spanwise rotation. Trans. ASME I: J. Fluids Engng 115, 64–69.Google Scholar
Smith, C. R. &Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.Google Scholar
Speziale, C. G. 1982 Numerical study of viscous flow in rotating rectangular ducts. J. Fluid Mech. 122, 251–271.Google Scholar
Speziale, C. G. 1986 The effect of the Earth's rotation on channel flow. Trans. ASME E: J. Appl. Mech. 53, 198–202.Google Scholar
Speziale, C. G. &Thangham, S. 1983 Numerical study of secondary flows and roll-cell instabilities in rotating channel flow. J. Fluid Mech. 130, 377–395.Google Scholar
Taylor, G. I. 1935 Distribution of velocity and temperature between concentric rotating cylinders. Proc. R. Soc. Lond. A 151, 494–512.Google Scholar
Thomas, T. G. &Takhar, H. S. 1988 Frame-invariance of turbulence constitutive relations. Astrophys. Space Sci. 141, 159–168.Google Scholar
Tritton, D. J. 1978 Turbulence in rotating fluids. In Rotating Fluids in Geophysics (ed. P. H. Roberts &A. M. Soward), pp. 105–138. Academic.
Tritton, D. J. 1985 Experiments on turbulence in geophysical fluid dynamics. In Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics (ed. M. Ghil), pp. 172–192. North-Holland.
Tritton, D. J. 1992 Stabilization and destabilization of turbulent shear flow in a rotating fluid. J. Fluid Mech. 241, 503–523.Google Scholar
Tritton, D. J. &Davies, P. A. 1981 Instabilities in geophysical fluid dynamics. In Hydrodynamic Instabilities and the Transition to Turbulence. Topics in Applied Physics (ed. H. L. Swinney &J. P. Gollub), vol. 45, pp. 229–269. Springer.
Watmuff, J. H., Witt, H. T. &Joubert, P. N. 1985 Developing turbulent boundary layers with system rotation. J. Fluid Mech. 157, 405–448.Google Scholar
Wattendorf, F. L. 1935 A study of the effect of curvature on fully developed turbulent flow. Proc. R. Soc. Lond. A 148, 565–598.Google Scholar
Witt, H. T. &Joubert, P. N. 1985 Effects of rotation on turbulent wakes. In Proc. 5th Symposium on Turbulent Shear Flows, Ithaca, pp. 21.25–21.30.