# Numerical Study of Laminar, Transitional and Turbulent Flow Past Rectangular Cylinders

[Doktorsavhandling]

The subject of flow past slender bluff bodies is of relevance to technical problems associated with energy conservation, structural design and acoustic emissions. The present work is restricted to an important sub-class of slender bluff body flow --- the incompressible flow around a stationary cylinder having a rectangular cross section, the cylinder being exposed to a constant free stream velocity. Time-dependent two- and three-dimensional (2D/3D-) numerical simulations are carried out. Some useful quantities such as the dominant wake frequency (the Strouhal number), mean and RMS values of drag and lift, and various surface pressures etc. were calculated for different Reynolds numbers.

In 2D-simulations, the effects of cylinder side ratio (B/A, where B is the longest side) and flow incidence (.alpha.) were investigated. In these simulations an incompressible non-staggered arrangement SIMPLEC code was used. The QUICK and Van Leer schemes were used for the convective terms. The time discretization was implicit and a second-order Crank-Nicolson scheme was employed. The influence of Reynolds number (Re <= 500), body side ratio (B/A=1-4) and angle of incidence (.alpha.=0°-90°) was investigated. Effect of the various numerical parameters such as time step, domain size, blockage, grid distribution and spatial resolution in both far- and near-body regions was investigated. At outlet of the computational domain, a convective Sommerfeld boundary condition was compared with a traditional Neumann condition. The onset of vortex shedding was investigated using the Stuart-Landau equation at various angles of incidence for a square cylinder.

In 3D-calculations, direct numerical simulation (DNS) of unsteady flow around a square cylinder at zero incidence for moderate Reynolds numbers (Re=150 - 500) and large eddy simulation (LES) at Re=22x10^{3} were performed. %Also the 2D-simulation are carried out for Re=150 - 500 . A non-staggered grid arrangement, incompressible, finite-volume code was used employing an implicit fractional step method with a multi-grid pressure Poisson solver. A second-order central scheme was used for the convective and diffusion terms. The influence of spanwise aspect ratio, finer grid and time step on the results were investigated for DNS. A study of transition from 2D to 3D flow, the wake structure, A- and B-mode of secondary vortices and a comparison of 2D and 3D results with experimental results were carried out in DNS simulations. Some dissimilarities with the flow around a circular cylinder were also investigated.

In LES simulations, three different subgrid scale models, the Smagorinsky, dynamic and dynamic one-equation models for Re=22x10^{3}, were applied and their results were compared with experimental results.

**Nyckelord: **rectangular cylinders, incompressible flow, Reynolds number, numerical simulation, finite volumes, onset of vortex shedding, angle of incidence, blockage, outlet boundary condition, square cylinder, transition, DNS, LES

Denna post skapades 2006-08-25. Senast ändrad 2013-09-25.

CPL Pubid: 1253