Time-Dependent Viscous Flow over a Circular Cylinder

Abstract

A finite difference method is extended to high Reynolds number flow about circular cylinders with particular emphasis given to the quantitative description of fine flow features. The method is of the explicit type and includes a directional difference scheme for the nonlinear terms which enhances calculational stability at high Reynolds numbers. A cell structure is chosen which provides local cell dimensions consistent with the structure of solutions expected. Solutions are presented for a range of Reynolds numbers from 1 to 3 × 105 in which the flow is started impulsively from rest, and the development is studied up to the approach of the steady-state or the limit cycle condition, whichever is appropriate to the particular Reynolds number.

Numerical Simulation of Viscous Incompressible Flows

“…Much of the early work concerned the two-dimensional flow past an infinite cylinder in a uniform stream (Thorn 1933, Payne 1958). More recent work on the same problem is given by Ingham (1968), Takami & Keller (1969, Thoman & Szewczyk (1969), Underwood (1969), Jordan & Fromm (1972), Collins & Dennis (1973, and others. All these investigations used the vorticity-streamfunction approach.…”

“…When a time-dependent solution is considered, the proper analogue of the biharmonic equation is (22) Two approaches are possible now: explicit (Thoman & Szewczyk 1969, Rimon 1969, or implicit (Pearson 1965a, Israeli 1970). In the explicit scheme, (n+ 1 (the vorticity at the n + 1 time step) is computed first at all the interior grid points from the equation (23) The elliptic equation (n+ 1 = '121/1n+ 1 is solved for I/In+ 1 and then (B is updated.…”

Properties of Nonturbulent Round Liquid Jets in Uniform Crossflows

“…1) a stable wake is present on the downstream side of the cylinder, consisting of a symmetric pair of elongated vortices. Predictions of the temporal development of these stable wakes as well as their finals lengths were compared with measurements of Coutanceau and Bouard 36 and the computations of Kawaguti and Jain 37 and Thoman and Szewczyk, 38 showing good agreement within the uncertainties of the results. At Re=170 (bottom picture of Fig.…”

An Evaluation of the Kuwabara Model

“…Of the three array configurations considered. the Kuwabara flow field was closest to that predicted see equation (11) see equation ( 6 ) see equation (11) = rf . ' F see equation (6) see equation (11) packing density or volume fraction see equation (6) see equation (11) see equation (11) Davies pressure coefficient, see equation (21) height of solution domain …”