An Embedding Method for Bluff Body Flows: Interactions of Two Side-by-Side Cylinder Wakes

Abstract

We introduce a simple method for the numerical simulation of bluff body flows where the solid object is represented by a distributed body force in the Navier–Stokes equations. The body force density is found at every time step to reduce the velocity within the computational cells occupied by the rigid body to a prescribed value. The method combines certain ideas from the immersed boundary method which was developed to treat biofluid mechanical flows and the volume-of-fluid method for simulating flows with fluid–fluid interfaces. The main advantage of this embedding method is that the computations can be effected on a regular Cartesian grid, without the need to fit the grid to the bluff body surfaces. Thus, flow past several complex bodies can be treated as easily as flow past a single body. The method is validated by reproducing well-established results for vortex shedding from a stationary cylinder. The flow past two side-by-side cylinders is then investigated. When the distance between the cylinders is small, they are seen to shed vortices in-phase, whereas for larger distances, the shedding occurs in anti-phase. For intermediate distances, various shedding patterns are observed, including quasi-periodic, asymmetric and chaotic regimes. Mean values and phase portraits associated with the cylinder lift and drag coefficients, as well as spectral analysis of the same data, are used to describe the flow. A transition diagram that can be compared with experiments or models outlines the various dynamical regimes as a function of the distance between the cylinders and the Reynolds number.