Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder

TLDR

The study numerically investigates and physically analyzes the pressure and velocity fields in the unsteady laminar wake behind a circular cylinder. The authors solve the velocity–pressure form of the incompressible Navier–Stokes equations using a predictor–corrector pressure method, a second‑order finite‑volume scheme, and an ADI procedure, and they trigger vortex shedding with a short numerical perturbation to study unsteady body forces at Re = 100, 200, 1000. After a transient, the wake becomes periodic, with drag and lift oscillation frequencies matching experiments, and the study reveals phase relations between pressure and velocity, the influence of viscous rotation, eddy convection, and near‑wake scale interactions, including the evolution of secondary eddies relative to primary ones.

Abstract

The dynamic characteristics of the pressure and velocity fields of the unsteady incompressible laminar wake behind a circular cylinder are investigated numerically and analysed physically. The governing equations, written in a velocity—pressure formulation and in conservative form, are solved by a predictor—corrector pressure method, a finite-volume second-order-accurate scheme and an alternating-direction-implicit (ADI) procedure. The initiation mechanism for vortex shedding and the evaluation of the unsteady body forces are presented for Reynolds-number values of 100, 200 and 1000.The vortex shedding is generated by a physical perturbation imposed numerically for a short time. The flow transition becomes periodic after a transient time interval. The frequency of the drag and lift oscillations agree well with the experimental data.The study of the interactions of the unsteady pressure and velocity fields shows the phase relations between the pressure and velocity, and the influence of different factors: the strongly rotational viscous region, the convection of the eddies and the almost inviscid flow.The interactions among the different scales of structures in the near wake are also studied, and in particular the time-dependent evolution of the secondary eddies in relation to the fully developed primary ones is analysed.