This paper presents two- and three-dimensional direct numerical simulations of the flow around a circular cylinder placed symmetrically in a plane channel. Results are presented in the Reynolds number range (based on the cylinder diameter and centerline velocity) of 10 to 390 for a blockage ratio (ratio of the cylinder diameter to the channel height) of 0.2. The aim of this work was to investigate in detail the confinement effect due to the channel’s stationary walls on the force coefficients and the associated Strouhal numbers, as well as on the generated flow regimes. Present results suggest a transition from a 2-D to a 3-D shedding flow regime between Re = 180 and Re = 210. This transition was found to be dominated by mode A and mode B three dimensional instabilities, similar to those observed in the case of an unconfined circular cylinder. This is the first time that the existence of the two modes, and of naturally occurring vortex dislocations, has been confirmed via full 3-D simulations for the case of a confined circular cylinder in a channel. A discontinuity in the variation of the Strouhal number St, and of the base pressure coefficient Cpb, with Re was also observed. This was found to be associated with the onset of mode A instability and the development of vortex dislocations, and parallels what occurs in the unconfined case, but previous studies could not confirm its existence in the confined case. Furthermore, by analyzing the mechanisms affecting the shape and evolution of these instabilities, it is demonstrated that they are significantly affected by the confinement only in the far wake.

[1] The unidirectional, subcritical flow over fixed dunes is studied numerically using large-eddy simulation, while the immersed boundary method is implemented to incorporate the bed geometry. Results are presented for a typical dune shape and two Reynolds numbers, Re = 17,500 and Re = 93,500, on the basis of bulk velocity and water depth. The numerical predictions of velocity statistics at the low Reynolds number are in very good agreement with available experimental data. A primary recirculation region develops downstream of the dune crest at both Reynolds numbers, while a secondary region develops at the toe of the dune crest only for the low Reynolds number. Downstream of the reattachment point, on the dune stoss, the turbulence intensity in the developing boundary layer is weaker than in comparable equilibrium boundary layers. Coherent vortical structures are identified using the fluctuating pressure field and the second invariant of the velocity gradient tensor. Vorticity is primarily generated at the dune crest in the form of spanwise ''roller'' structures. Roller structures dominate the flow dynamics near the crest, and are responsible for perturbing the boundary layer downstream of the reattachment point, which leads to the formation of ''horseshoe'' structures. Horseshoe structures dominate the near-wall dynamics after the reattachment point, do not rise to the free surface, and are distorted by the shear layer of the next crest. The occasional interaction between roller and horseshoe structures generates tube-like ''kolk'' structures, which rise to the free surface and persist for a long time before attenuating.

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This paper presents three-dimensional direct numerical simulations of liquid metal flow around a circular cylinder placed symmetrically in a rectangular duct, under a wide range of magnetic field intensities. Results are presented for values of the Hartmann number (based on the duct width) in the range of 0 ⩽ Ha ⩽ 1120, and the Reynolds number (based on the cylinder diameter and centerline velocity) in the range 0 ⩽ Rec ⩽ 5000. The generated flow regimes and the associated critical values of parameters are investigated in detail through full three-dimensional simulations. The effect of the magnetic field on the wake structure is discussed in relation to the possible mechanisms for the generation or suppression of vortices, and to previous attempts to model magnetohydrodynamic flows using simplified two-dimensional models. Present results reveal a non-monotonic dependance of the critical Reynolds number for the onset of vortex shedding, with respect to the Hartmann number. For certain combinations of Ha and Re values, this work confirms the onset of a new flow regime, the existence of which has been recently suggested based on quasi-two-dimensional simulations. Unexpectedly, the spanwise distribution of the force coefficients along the cylinder is found to become more three-dimensional with increasing Ha. Furthermore, the three-dimensional nature of the present simulations reveals additional counter-intuitive features of the new regime that could not possibly had been captured by quasi-two-dimensional models. One such feature, shown here for the first time, is an increase in the flow unsteadiness with increasing intensity of the magnetic field.