Numerical study of flow past two counter rotating cylinders using immersed boundary method

Abstract

The adoption of a direct forcing immersed boundary nu- merical method on the uniform flow, at a moderate Reynolds number of 100, past a pair of two rotating circular cylinders placed side-by-side, is the core of the present study. A sim- plified yet novel approach is used to impose a virtual force as a source to the full incompressible two-dimensional Navier- Stokes equations, which are discretized by the finite volume method. The usage of a Cartesian grid that ensures minimal computational cost, is the sali ent feature of the applied im- mersed boundary approach. The gap between the two cylin- ders, and their rotational direction and speed, are the variable parameters used in the analysis of the resulting vortex street. A range of absolute rotational speeds (  (g* 3) 3) for different gap spacings ( g *  3), is considered. Whilst the direction of rotational motion is found to e ither accelerate or decelerate the gap flow, the rotational speed has a bearing on the dominant flow pattern. An observation of the vorticity contours for the decelerating gap flow indicates that when a critical rotational speed (  ≈ 1.4) is reached, the flow becomes steady regardless of the variation of g *. Five  -dependent flow modes emerge; the anti-phase, in-phase, flip-flop, single vortex shedding and suppressed modes. A statistical scrutiny of the validated ransient data for the lift ( L C ) and drag ( D C ) coefficients is ultimately performed. When g * = 0.2, the general trend of decreasing D C with reduction in gap size is broken.