A vorticity model for viscous flow past a cylinder

Abstract

A~tract--A mathematical model is proposed for the steady two-dimensional flow of a viscous incompressible fluid past a cylinder which incorporates the details of the structure of the vorticity in this case where its behaviour is known. The model is constructed to be consistent both with boundary-layer theory for sutficiently large Reynolds numbers and with the asymptotic solution at large distances from the cylinder. The governing Navier-Stokes equations are transformed to a set of equations which we refer to as the modified Navier-Stokes equations and are then solved numerically. Solutions have been obtained for the cases of flow past a stationary and a rotating circular cylinder and flow past an inclined elliptic cylinder. Good agreement is found with existing results.

Steady flow of power-law fluids across an unconfined elliptical cylinder

“…Since the governing equations in the Cartesian coordinates have been solved using FLUENT, hence all the above-noted expressions are written in Cartesian coordinates only. Corresponding expressions, especially for the individual drag coefficients, in other coordinate systems are available in the literature, e.g., see Dennis and Young (2003), D'Alessio and Dennis (1994), Khan et al (2005), Kiya and Arie (1975), Sugihara-Seki (1993), etc.…”

“…Subsequently, Patel (1981) presented a semianalytical solution of the Navier-Stokes equations to investigate the viscous, incompressible flow around an impulsively started elliptic cylinder at various angles of incidence (0, 30, 45 and 90 • ) at Re = 200. D'Alessio and Dennis (1994) employed the vorticity-stream function form of the Navier-Stokes equations in terms of transformed coordinates to enforce the correct decay of vorticity at large distances from the elliptic cylinder. They presented the values of drag and lift coefficients for Re=5 and 20 for different inclinations of the elliptic cylinder ranging from 0 • to 90 • .…”

Effect of boundary vorticity discretization on explicit stream-function vorticity calculations

“…We consider two schemes for discretizing a Poisson equation, one the usual second-order central di erence scheme and one a fourth-order scheme (see Reference [17]). We also set out a number of well-known schemes for discretizing the boundary vorticity, that of References [2,[18][19][20][21]. We note in passing some consequences for stability from the discretization of the advection-di usion equation.…”

“…Since the velocity ÿeld on that boundary, u(x; 0), is not zero, the formulae assume that y = u implicitly on the boundary. The formulae below are due to Thom [2], Woods [18], Jensen [19], d'Alessio and Dennis [20] and Briley [21].…”

Heat Transfer Characteristics of Nanofuid Flow around an Elliptical Cylinder

“…For (ε<1), the steady regime was reported to end at Re ≈ (35-40) which is comparable to the commonly used value of ∼(40-45) for circular and square cylinders. D' Alessio and Dennis [15] tested the vorticity-stream function form of the Navier-Stokes equations in terms of transformed coordinates to enforce the correct decay of vorticity at large distances from the elliptic cylinder. They presented the values of drag and lift coefficients for Re = (5-20) for different inclinations of the elliptic cylinder ranging from 0• to 90•.…”