The generation of large vortices is an inherent nature of bluff-body aerodynamics. The alternate shedding of vortices generates unsteady force which can induce vibration and create damage if its frequency coincides with the natural frequency of the structure. A classic example is the collapse of Tacoma bridge. Flow induced vibration of bluff body can take the form of vortex resonance, galloping or flutter depending on the flow conditions and geometry of the body. It can cause structural damage or render the building uninhabitable if it induces torsional vibration. When buildings are in clusters such as those in an urban city centre, they set up complex flow structures which induce complex wind load on buildings and structures. The interaction between flow and motion of structures causes complex aeroelastic interaction problems. The understanding of such flow structures is important to the economical design of safe buildings.
Bluff-body aerodynamics is much more complex than streamline aerodynamics. However unlike streamline aerodynamics where much is known because of the impetus by the aircraft and defence-related industries, there are still much to be learnt in the bluff-body aerodynamics area. The experimental investigations of bluff-body aerodynamics problems are always tedious and difficult. However, with the recent advances in computer technology both in hardware and software, computational fluid dynamics has become a powerful tool to investigate such problems.
The Navier-Stokes equation is a non-linear partial differential equation because of the presence of non-linear convection terms. Analytical solutions can only be obtained when certain assumptions such as one-dimensionality of flow or neglecting the convection term at low Reynolds number are made. There are many numerical methods to solve the Navier-Stokes equations at high Reynolds number flow. One of them is the direct numerical simulation (DNS) method. It is accurate and does not require turbulence modelling, but the computational effort is large. For flow past bluff bodies where only information about large scale vortical structures is required, DNS method with very fine mesh to resolve small-scale turbulence may not be necessary. We develop a new method of solving the unsteady two-dimensional Navier-Stokes equations in the vorticity-stream function form with a finite-difference method. It uses a body-fit Cartesian coordinate system generated by conformal mapping and a grid with variable mesh size in the computational domain. A mixed difference scheme coupling the 3rd-order upwind scheme with the 4th-order central scheme is used for the discretization of the vorticity transport equation, while a 2nd-order central scheme is used for the discretization of the stream function equation. The results for streamline pattern past an elliptic cylinder with different aspect ratio at a Reynolds number of 1000 and zero angle of attack are as shown below. The proposed method is accurate and computationally efficient.
