Drag and lift coefficients of inclined finite circular cylinders at moderate Reynolds numbers

The flow around two-dimensional cylinders at moderate Reynolds numbers has been much studied, both for cylinders perpendicular to the flow and for cylinders yawed to the flow. In contrast, yawed finite aspect ratio cylinders have received little attention. In this article we describe computer simulations of cylinders with aspect ratios 2  L/D  20 yawed at angles 0°  α  90° relative to a free stream. The simulations were carried out for Reynolds numbers in the range 1  Re  40. The simulations show that the Independence Principle [Zdravkovich MM. Flow around circular cylinders, vol. 2: applications. New York: Oxford University Press; 2003[1]] is not accurate for α  45°. We have also found that for all aspect ratios, the ratio of the lift to drag force reaches a maximum for 40° < α < 50°. Finally, we present C_L and C_D relationships as best curve fits to computational data.     

Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method

In this paper, two versions of a second-order characteristic-based split scheme are developed in the framework of incremental projection method for the solution of incompressible flow problem. After the demonstration of the good accuracy and effectiveness of the developed schemes, a flow over three equal circular cylinders arranged in equilateral-triangle arrangement is numerically investigated on unstructured mesh systems. The examined Reynolds number is 100 and the flow is supposed to be laminar. Computations by the developed algorithm are then performed for six gap spacings, s, ranging from 0.5 to 4.0, and for three incidence angles, α = 0°, 30° and 60°. Numerical results show that, at sufficiently small and large s, the range of which is different for different α, the flow interference is dominated by proximity and wake effect, respectively. And in the intermediate range of the spacing, the flow pattern is influenced by both of them. The mean force results are compared with the existing experimental measurements and that shows a similar trend in the variation of mean force with the spacing for different Reynolds number. It is also observed that the interference effect transitions plays an important role in the variation of the fluctuating forces and Strouhal number.     

Flow patterns past two circular cylinders in proximity

Flow patterns past two nearby circular cylinders of equal diameter immersed in the cross-flow at low Reynolds numbers (Re ? 160), were numerically studied using an immersed boundary method. We considered all possible arrangements of the two cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. Ten distinct flow patterns were identified in total based on vorticity contours and streamlines, which are Steady, Near-Steady, Base-Bleed, Biased-Base-Bleed, Shear-Layer-Reattachment, Induced-Separation, Vortex-Impingement, Flip-Flopping, Modulated Periodic, and Synchronized-Vortex-Shedding. Collecting all the numerical results obtained, we propose a general flow-pattern diagram for each Re, and a contour diagram on vortex-shedding frequency for each cylinder at Re = 100. The perfect symmetry implied in the geometrical configuration allows one to use these diagrams to identify flow pattern and vortex-shedding frequencies in the presence of two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main-flow direction.     

Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers

Transient wake flow patterns and dynamic forces acting on a rotating spherical particle with non-uniform surface blowing are studied numerically for Reynolds numbers up to 300 and dimensionless angular velocities up to Ω=1. This range of Reynolds numbers includes the three distinct wake regimes i.e., the steady axisymmetric, the steady non-symmetrical and the unsteady with vortex shedding. The Navier–Stokes equations for an incompressible viscous flow are solved by a finite volume method in a three-dimensional, time accurate manner. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that unsteady three-dimensional wake flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects and thus, vortex shedding occurs even at Re=200. Global properties, such as the lift and drag coefficients, and the Strouhal number are also significantly affected. It is shown that the present data for the average lift and drag coefficients correlate well with:

C_L/(1+Ω)^3.6=0.11

C_D(1+20V_S)^0.2/(1+Ω)^Re/1000=24(1+Re^2/3/6)/Re

where V_S is the average surface blowing velocity normalized by the free stream velocity.