NUMERICAL STUDIES ON THE EARLY STAGES OF IMPULSIVELY STARTED UNSTEADY FLOW PAST SHARP-EDGED CYLINDERS

Abstract

The early stages of an impulsively started flow over bluff bodies, such as square and trapezoidal cylinders, have been numerically investigated for a range of Reynolds number from 25 to 1000. In the present study, the two-dimensional Navier-Stokes equations are expressed in the generalized curvilinear co-ordinate. A modified SIMPLE method based on a non-staggered grid system is introduced. Implementation of boundary conditions and programming are much easier with the non-staggered grid system. For the solution domain over the trapezoidal cylinders, a multi-domain iterative process was introduced to carry out the iteration at different sub-domains at the same time instant. Singularities at sharp corners have been avoided by this method. For trapezoidal cylinders, both tapered and expanded cross-section were considered. Computational results were obtained for a series of side ratio to study the effects of different cross-sections. Intermediate cases between a square cylinder and the more tapered and expanded trapezoidal cylinders have also been numerically evaluated. Early stages of an impulsively started flow around square and trapezoidal cylinders were simulated and studied. The computational results show that the characteristics of the flow depend on Reynolds number. Drag coefficient increases with decreasing Reynolds number. The surface pressure coefficients tend toward a stationary value as time advances. Secondary eddy occurred only if the Reynolds number is above a critical value for a given geometric parameter. The wake length increases as time advances before reaching steady state. At the same instant, the wake length is also longer for a higher Reynolds number. Other characteristics of the early stages of an impulsively started flow field such as the development of the twin vortices behind the cylinders can also be observed from the series of development contour plots of the flow field streamlines and pressure distributions. The surface pressure coefficients and the drug coefficients for various square and trapezoidal cylinders are also presented.