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Direct numerical simulation of a turbulent flow in a rotating channel with a sudden expansion

  • Eric Lamballais (a1)
Abstract

The effects of spanwise rotation on the channel flow across a symmetric sudden expansion are investigated using direct numerical simulation. Four rotation regimes are considered with the same Reynolds number $\mathit{Re}=5000$ and expansion ratio $\mathit{Er}=3/2$ . Upstream from the expansion, inflow turbulent conditions are generated realistically for each rotation rate through a very simple and efficient technique of recycling without the need for any precursor calculation. As the rotation is increased, the flow becomes progressively asymmetric with stabilization (destabilization) effects on the cyclonic (anticyclonic) side, respectively. These rotation effects, already present in the upstream channel, lead further downstream to an increase (reduction) of the separation size behind the cyclonic (anticyclonic) step. In the cyclonic separation, the free-shear layer created behind the step corner leads to the formation of large-scale spanwise vortices that become increasingly two-dimensional as the rotation is increased. Conversely, in the anticyclonic region, the turbulent structures in the separated layer are more elongated in the streamwise direction and also more active in promoting reattachment. For the highest rotation rate, a secondary separation is observed further downstream in the anticyclonic region, leading to the establishment of an elongated recirculation bubble that deflects the main flow towards the cyclonic wall. The highest level of turbulent kinetic energy is obtained at high rotation near the cyclonic reattachment in a region where stabilization effects are expected. The phenomenological model of absolute vortex stretching is found to be useful in understanding how the rotation influences the dynamics in the various regions of the flow.

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Corresponding author
Email address for correspondence: eric.lamballais@univ-poitiers.fr
References
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Abbott, D. E. & Kline, S. J. 1962 Experimental investigation of subsonic turbulent flow over single and double backward facing steps. Trans. ASME: J. Basic Engng 84 (3), 317325.
del Alamo, J. C. & Jimenez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
Alfredsson, P. H. & Persson, H. 1989 Instabilities in channel flow with system rotation. J. Fluid Mech. 202, 543557.
Barri, M. & Andersson, H. I. 2010a Computer experiments on rapidly rotating plane Couette flow. Commun. Comput. Phys. 7 (4), 683717.
Barri, M. & Andersson, H. I. 2010b Turbulent flow over a backward-facing step. Part 1. Effects of anti-cyclonic system rotation. J. Fluid Mech. 665, 382417.
Barri, M., El Khoury, G. K., Andersson, H. I. & Pettersen, B. 2009a DNS of backward-facing step flow with fully turbulent inflow. Intl J. Numer. Meth. Fluids 64, 777792.
Barri, M., El Khoury, G. K., Andersson, H. I. & Pettersen, B. 2009b Inflow conditions for inhomogeneous turbulent flows. Intl J. Numer. Meth. Fluids 60, 227235.
Bech, K. H. & Andersson, H. I. 1997 Turbulent plane Couette flow subject to strong system rotation. J. Fluid Mech. 347, 289314.
Biau, D. & Bottaro, A. 2004 Transient growth and minimal defects: two possible initial paths of transition to turbulence in plane shear flows. Phys. Fluids 16 (10), 35153529.
Bidokhti, A. A. & Tritton, D. J. 1992 The structure of a turbulent free shear layer in a rotating fluid. J. Fluid Mech. 241, 469502.
Bradshaw, B. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177191.
Brethouwer, G. 2005 The effect of rotation on rapidly sheared homogeneous turbulence and passive scalar transport. Linear theory and direct numerical simulation. J. Fluid Mech. 542, 305342.
Brethouwer, G., Schlatter, P. & Johansson, A. V. 2011 Turbulence, instabilities and passive scalars in rotating channel flow. J. Phys.: Conf. Ser. 318, 032025.
Buell, J. C. & Huerre, P. 1988 Inflow/outflow boundary conditions and global dynamics of spatial mixing layers. In Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program, Stanford University (SEE N89-24538 18-34) pp. 1927.
Cambon, C., Benoit, J. P., Shao, L. & Jacquin, L. 1994 Stability analysis and large-eddy simulation of rotating turbulence with organized eddies. J. Fluid Mech. 278, 175200.
Comte-Bellot, G. 1965 Ecoulement turbulent entre deux paroi parallèles. Documentation Scientifique et Technique de l’Armement 419. Publications Scientifiques et Techniques du Ministère de l’Air.
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453480.
Grundestam, O., Wallin, S. & Johansson, A. V. 2008 Direct numerical simulations of rotating turbulent channel flow. J. Fluid Mech. 598, 177199.
Hamba, F. 2006 The mechanism of zero mean absolute vorticity state in rotating channel flow. Phys. Fluids 18, 125104.
Hart, J. E. 1971 Instability and secondary motion in a rotating channel flow. J. Fluid Mech. 45, 341351.
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.
Iwamoto, K., Suzuki, Y. & Kasagi, N. 2002 Reynolds number effect on wall turbulence: toward effective feedback control. Intl J. Heat Fluid Flow 23 (5), 678689.
Jiménez, J. 1990 Transition to turbulence in two-dimensional Poiseuille flow. J. Fluid Mech. 218, 265297.
Johnson, J. A. 1963 The stability of shearing motion in a rotating fluid. J. Fluid Mech. 17 (3), 337352.
Johnston, J. P., Halleen, R. M. & Lezius, D. K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533557.
Khaledi, H. A., Barri, M. & Andersson, H. I. 2009 On the stabilizing effect of the Coriolis force on the turbulent wake of a normal plate. Phys. Fluids 21, 095104.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Kravchenko, A. G. & Moin, P. 1997 On the effect of numerical errors in large eddy simulation of turbulent flows. J. Comput. Phys. 131, 310322.
Kristoffersen, R. & Andersson, H. I. 1993 Direct simulations of low-Reynolds-number turbulent flow in rotating channel. J. Fluid Mech. 256, 163197.
Laizet, S. & Lamballais, E. 2009 High-order compact schemes for incompressible flows: a simple and efficient method with quasi-spectral accuracy. J. Comput. Phys. 228, 59896015.
Laizet, S., Lamballais, E. & Vassilicos, J. C. 2010 A numerical strategy to combine high-order schemes, complex geometry and parallel computing for high resolution DNS of fractal generated turbulence. Comput. Fluids 39 (3), 471484.
Laizet, S. & Li, N. 2011 Incompact3d: a powerful tool to tackle turbulence problems with up to computational cores. Intl J. Numer. Meth. Fluids 67 (11), 17351757.
Lamballais, E., Fortuné, V. & Laizet, S. 2011 Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation. J. Comput. Phys. 230, 32703275.
Lamballais, E., Lesieur, M. & Métais, O. 1996a Effects of spanwise rotation on the vorticity stretching in transitional and turbulent channel flow. Intl J. Heat Fluid Flow 17 (3), 324332.
Lamballais, E., Lesieur, M. & Métais, O. 1996b Influence of a solid-body rotation upon coherent vortices in a channel. C. R. Acad. Sci. Paris II B 323, 95101.
Lamballais, E., Métais, O. & Lesieur, M. 1998 Spectral-dynamic model for large-eddy simulations of turbulent rotating channel flow. Theor. Comput. Fluid Dyn. 12, 149177.
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349374.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.
Lesieur, M. 2008 Turbulence in Fluids. 4th edn. Springer.
Lesieur, M., Yanase, S. & Métais, O. 1991 Stabilizing and destabilizing effects of a solid-body rotation on quasi-two-dimensional shear layers. Phys. Fluids 3, 403407.
Lezius, D. K. & Johnston, J. P. 1976 Roll-cell instabilities in rotating laminar and turbulent channel flows. J. Fluid Mech. 77, 153175.
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233258.
Métais, O., Flores, C., Yanase, S., Riley, J. J. & Lesieur, M. 1995 Rotating free shear flows. Part 2: Numerical simulations. J. Fluid Mech. 293, 4180.
Métais, O., Yanase, S., Flores, C., Bartello, P. & Lesieur, M. 1993 Reorganization of coherent vortices in shear layers under the action of solid-body rotation. In Turbulent Shear Flows VIII, pp. 415430.
Mizushima, J. & Shiotani, Y. 2000 Structural instability of the bifurcation diagram for two-dimensional flow in a channel with a sudden expansion. J. Fluid Mech. 420, 131145.
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341377.
Oberlack, M. 2001 A unified approach for symmetries in plane parallel turbulent shear flows. J. Fluid Mech. 427, 299328.
Ol’shanskii, M. A. & Staroverov, V. M. 2000 On simulation of outflow boundary conditions in finite difference calculations for incompressible fluid. Intl J. Numer. Meth. Fluids 33 (4), 499534.
Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50, 689703.
Parnaudeau, P., Carlier, J., Heitz, D. & Lamballais, E. 2008 Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20, 085101.
Parnaudeau, P., Lamballais, E., Heitz, D. & Silvestrini, J. H. 2004 Combination of the immersed boundary method with compact schemes for DNS of flows in complex geometry. In Direct and Large-Eddy Simulation V (ed. Friedrich, R., Geurts, B. J. & Métais, O.), ERCOFTAC Series, Vol. 9, pp. 581590. Kluwer Academic.
Pedley, T. J. 1969 On the instability of viscous flow in a rapidly rotating pipe. J. Fluid Mech. 35, 97115.
Rothe, P. H. & Johnston, I. P. 1979 Free shear layer behavior in rotating systems. Trans. ASME: J. Fluids Engng 101, 117120.
Salhi, A. & Cambon, C. 1997 An analysis of rotating shear flow using linear theory and DNS and LES results. J. Fluid Mech. 347, 171195.
Schäfer, F., Breuer, M. & Durst, F. 2009 The dynamics of the transitional flow over a backward-facing step. J. Fluid Mech. 623, 85119.
Smyth, R. 1979 Turbulent flow over a plane symmetric sudden expansion. Trans. ASME: J. Fluids Engng 101, 348353.
Tanaka, M., Kida, S., Yanase, S. & Kawahara, G. 2000 Zero-absolute-vorticity state in a rotating turbulent shear flow. Phys. Fluids 12 (8), 19791985.
Tanaka, M., Yanase, S., Kida, S. & Kawahara, G. 1998 Vortical structures in rotating uniformly sheared turbulence. Flow Turbul. Combust. 60, 301332.
Tritton, D. J. 1992 Stabilization and destabilization of turbulent shear flow in a rotating fluid. J. Fluid Mech. 241, 503523.
Tritton, D. J. & Davies, P. A. 1981 Instabilities in geophysical fluid dynamics. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. Swinney, H. L. & Gollub, J. P.), Springer.
Vissher, J. & Andersson, H. I. 2011 Particle image velocimetry measurements of massively separated turbulent flows with rotation. Phys. Fluids 23, 075108.
Witt, H. T. & Joubert, P. N.1985 Effect of rotation on a turbulent wake. In Symposium on Turbulent Shear Flows, 5th, Ithaca, NY, August 7–9.
Yanase, S., Flores, C., Métais, O. & Riley, J. J. 1993 Rotating free-shear flows. I. Linear stability analysis. Phys. Fluids 5 (11), 27252737.
Yanase, S., Tanaka, M., Kida, S. & Kawahara, G. 2004 Generation and sustenance mechanisms of coherent vortical structures in rotating shear turbulence of zero-mean-absolute vorticity. Fluid Dyn. Res. 35 (4), 237254.
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