Numerical Study of the Early Stages of Impulsively Started Unsteady Laminar Flow Past a Square Cylinder

Abstract

The time development of the symmetrical standing zones of recirculation, which is formed in the early stages of the impulsively started laminar flow over the square cylinder, have been studied numerically. The Reynolds number considered ranges from 25 to 1,000. Main flow characteristics of the developing recirculation region aft of the square cylinder and its interaction with the separating shear layer from the leading edges are studied through the developing streamlines. Other flow characteristics are analysed in terms of pressure contours, surface pressure coefficient, wake length and drag coefficient. Four main‐flow types and three subflow types of regimes are identified through a detailed analysis of the evolution of the flow characteristics. Typically, for a given Reynolds number, it is noted that flow starts with no separation (type I main‐flow). As time advances, symmetrical standing zone of recirculation develops aft of the square cylinder (type II main‐flow). The rate of growth in width, length and structure of the aft end eddies (sub‐flow (a)) depends on the Reynolds number. In time, separated flow from the leading edges of the square cylinder also develops (type III main‐flow) and forms growing separation bubbles (sub‐flow (b)) on the upper and lower surfaces of the square cylinder. As time advances, the separation bubbles on the upper and lower surfaces of the cylinder grow towards downstream regions and eventually merge with the swelling symmetrical eddies aft of the cylinder. This merging of the type II and type III flows created a complex type IV main‐flow regime with a disturbed tertiary flow zone (sub‐flow (c)) near the merging junction. Eventually, depending on the Reynolds number, the flow develops into a particular category of symmetrical standing recirculatory flow of specific characteristics.

Flow around impulsively started square prisms

“…Also, from the flow visualization images of Finaish (1991) for an impulsively started square prism (one of the few experimental studies in the literature), asymmetry is evident at t n = 4.7. In contrast, the numerical simulations of Lee et al (1996) for the impulsively started square prism did not show any asymmetry up to the end of the simulation time, at t n =8. As the cylinder and the prisms move through the fluid following the impulsive start, the velocity fields (Fig.…”

“…The results were qualitative in nature and no measurements were made of the recirculation zone and its primary eddies. Lee et al (1996) performed numerical simulations of impulsively started flow around a square prism for Re= 25-1000. Similar numerical studies by Lee (1998a,b) examined the early stages of an impulsively started flow past non-rectangular, sharp-edged prisms.…”

Early stages of an impulsively started unsteady laminar flow past tapered trapezoidal cylinders

“…A hybrid difference scheme [16] implemented for the convection related terms is outlined as follows:…”