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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 Re1/4180 and Re1/4210. 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. © 2011 American Institute of Physics. 23

Using high resolution numerical simulations, we study the flow of a liquid metal in a pipe subjected to an intense decreasing magnetic field (fringing magnetic field). The chosen flow parameters are such that our study is directly relevant for the design of fusion breeder blankets. Our objectives are to provide a detailed description of the numerical method and of the results for benchmarking purposes but also to assess the efficiency of the so-called ?core flow approximation? that models liquid-metal flows under the influence of intense magnetic fields. Our results are in excellent agreement with available experimental measurements. As far as the pressure drop is concerned, they also match perfectly the predictions of the core flow approximation. On the other hand, the velocity profiles obtained in our numerical simulations show a significant departure from this approximation beyond the inflection point of the magnetic field?s profile. By plotting the momentum budget of the MHD equations, we provide evidence that this discrepancy can be attributed to the role of inertia that is neglected in the core flow approximation. We also consider a case with vanishing outlet magnetic field and we briefly illustrate the transition to turbulence arising in the outlet region of the pipe. Using high resolution numerical simulations, we study the flow of a liquid metal in a pipe subjected to an intense decreasing magnetic field (fringing magnetic field). The chosen flow parameters are such that our study is directly relevant for the design of fusion breeder blankets. Our objectives are to provide a detailed description of the numerical method and of the results for benchmarking purposes but also to assess the efficiency of the so-called ?core flow approximation? that models liquid-metal flows under the influence of intense magnetic fields. Our results are in excellent agreement with available experimental measurements. As far as the pressure drop is concerned, they also match perfectly the predictions of the core flow approximation. On the other hand, the velocity profiles obtained in our numerical simulations show a significant departure from this approximation beyond the inflection point of the magnetic field?s profile. By plotting the momentum budget of the MHD equations, we provide evidence that this discrepancy can be attributed to the role of inertia that is neglected in the core flow approximation. We also consider a case with vanishing outlet magnetic field and we briefly illustrate the transition to turbulence arising in the outlet region of the pipe. 23 47101

Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied, and the ordinary hydrodynamic flow around a solid obstacle. The former problem is of interest both practically and theoretically, and the latter one is a classical problem being well understood in ordinary hydrodynamics. The first analogy is the formation in the MHD flow of an impenetrable region -- core of the magnetic obstacle -- as the interaction parameter $N$, i.e. strength of the applied magnetic field, increases significantly. The core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. In the core, closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. The second analogy is the breaking away of attached vortices from the recirculation pattern produced by the magnetic obstacle when the Reynolds number $Re$, i.e. velocity of the upstream flow, is larger than a critical value. This breaking away of vortices from the magnetic obstacle is similar to that occurring past a real solid obstacle. Depending on the inlet and/or initial conditions, the observed vortex shedding can be either symmetric or asymmetric., minor changes, accepted for PoF, 26 pages, 7 figures

A locally homogeneous representation for the two-point, second-order turbulent velocity fluctuation Rij(x,r) = 〈u′i(x)u′i(x+r)〉 is formulated in terms of three linearly independent structure tensors [Kassinos et al., J. Fluid Mech. 428, 213 (2001)]: Reynolds stress Bij, dimensionality Dij, and stropholysis Q*ijk. These structure tensors are single-point moments of the derivatives of vector stream functions that contain information about the directional and componential anisotropies of the correlation. The representation is a sum of several rotationally invariant component tensors. Each component tensor scales like a power law in r, while its variation in r/r depends linearly on the structure tensors. Continuity and self-consistency constraints reduce the number of degrees of freedom in the model to 17. A finite Re correction is introduced to the representation for separations of the order of Kolmogorov's length scale. To evaluate our representation, we construct a model correlation by fitting the representation to correlations calculated from direct numerical simulation (DNS) of homogeneous turbulence and channel flow. Comparison of the model correlation to the DNS data shows that the representation can capture the character of the anisotropy of two-point second-order velocity correlation tensors. © 2008 American Institute of Physics. 20

A new tensor statistic, the dispersed-phase structure dimensionality Dp, is defined to describe the preferred orientation of clusters of discrete bodies. The evolution of Dp is calculated via direct numerical simulations of passive, Stokesian particles driven by initially isotropic, decaying magnetohydrodynamic turbulence. Results are presented for five magnetic field strengths as characterized by magnetic interaction parameters, N, in the range 0-50. Four field strengths are studied at a grid resolution of 1283. The strongest field strength is also studied at 2563 resolution. In each case, the externally applied magnetic field was spatially uniform and followed a step function in time. Particles with initially uniform distributions were tracked through hydrodynamic turbulence for up to 2800 particle response times before the step change in the magnetic field. In the lower resolution simulation, the particle response time, τp, matched the Kolmogorov time scale at the magnetic field application time t0. The higher-resolution simulation tracked ten sets of particles with τp spanning four decades bracketing the Kolmogorov time scale and the Joule time. The results demonstrate that Dp distinguishes between uniformly distributed particles, those organized into randomly oriented clusters, and those organized into two-dimensional sheets everywhere tangent to the magnetic field lines. Lumley triangles are used to demonstrate that the degree of structural anisotropy depends on τp, N, and the time span over which the magnetic field is applied. © 2008 American Institute of Physics. 20

A series of large-eddy simulations (LES) of turbulent and transitional channel flows of a conductive fluid under the effect of a uniform magnetic field applied in the wall-normal direction, usually referred to as Hartmann flows, are performed using the dynamic Smagorinsky model. The flow is characterized by the hydrodynamic Reynolds number Re and the Hartmann number Ha that is related to the strength of the external magnetic field. Previous measurements and works on stability analysis have shown that a critical modified Reynolds number, based on the Hartmann layer thickness R = Re/Ha, exists at approximately R = 380. Here, the LES are used to investigate the laminarization of flow when decreasing R. Also, similarities of the turbulent flows are explored for different values of Re and Ha but the same values of R or of the interaction parameter N = Ha2/Re. The LES confirm that R is the relevant parameter that describes the transition and a critical Reynolds number for relaminarization is observed at R ≈ 500. However, for turbulent flows at moderate values of the Ha and Re as considered in this study, the similarity with respect to N appears to be better than for R, especially for the first order statistics. Finally, the importance of the dynamic Smagorinsky model as the Hartmann number increases is discussed. © 2007 American Institute of Physics. 19

We consider the transport of a passive scalar under the influence of homogeneous turbulence in a conducting fluid that is exposed to a uniform external magnetic field while being sheared in fixed and rotating frames. The mean scalar gradient is assumed to be uniform and aligned with the transverse direction within the plane of the mean shear, while both the frame-rotation axis and the applied magnetic field are aligned in the direction normal to the plane of the mean shear. For any given frame rotation rate, we find that a key parameter determining the structural morphology of the flow is the ratio of the time scale of the mean shear to the Joule time, τshear/ τm. The most drastic modifications to passive scalar transport are observed when τshear≥τm, and these are shown to be linked to changes in the structure of the velocity and scalar fields. In most cases, the observed evolution of the scalar flux coefficients can be explained in terms of structural information provided by the one-point structure tensors, except for high magnetic Reynolds numbers flows, where the alignment of the velocity fluctuation field with the spatially varying local mean magnetic field can, under certain conditions, lead to loss of coherence and suppression of the correlation between the velocity and scalar fields. © 2007 American Institute of Physics. 19

In this study we apply rapid distortion theory to the case of nonstratified homogeneous turbulence that is sheared in a frame that counter-rotates at a rate that matches in magnitude the rotation associated with the mean shear. In the inviscid case, analytical solutions are worked out for the evolution of the components of the Reynolds stresses and the structure dimensionality tensor, and these are shown to equal each other. The results are compared to direct numerical simulations data with which they proved to be in good agreement, especially in terms of the Reynolds shear stress and of the dimensionless tensor components. Finally, the development of the structure of a passive scalar field with a constant mean gradient is investigated, and remarkable analogies are shown to exist between this case and the case of shear in a fixed frame. © 2006 American Institute of Physics. 18