Vortex shedding induced by polygonal cylinders

Polygonal cylinders are widely used in many engineering fields. However, the identification of the flow pattern induced by the vortex shedding is always limited to the case of a single or multiple circular cylinders. In the present study, numerical simulations were conducted using the PHOENICS code to characterize the wake dynamics behind a single and two polygonal cylinders at Reynolds number Re=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{e}=100$$\end{document}: circular and face-oriented octagonal (8F) and hexagonal (6F). The simulations were conducted for two side-by-side and tandem polygonal cylinders. For each flow configuration, two gaps between the cylinders are considered: 1.5D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.5 D$$\end{document} and 3D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3 D$$\end{document} where D is the cylinder diameter. Numerical results show that the drag and lift forces are well reproduced for a single and two circular cylinders in side-by-side and tandem arrangements. The single cylinder (8F) leads to 9.3% drag force reduction compared to the circular one. For a transverse gap T=1.5D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=1.5 D$$\end{document}, the variations of drag forces are irregular for the different cylinder shapes (circular, 8F or 6F). In all cylinder shapes, the lower cylinder leads to a negative lift and for the upper one, the lift is positive. For the same longitudinal gap L=1.5D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L=1.5 D$$\end{document}, a constant drag force is obtained as obtained by previous numerical studies of two circular cylinders in tandem arrangement. By increasing the gap distance between the two inline cylinders to L=3D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L=3 D$$\end{document}, the drag coefficient of the downstream cylinder is negative except for the (8F) shape. For the same gap distance and two side-by-side circular cylinders, the drag coefficient is almost the same for the upper and lower cylinders due to the small interaction between the two cylinders. The (8F) tandem cylinders lead to a drag force of about 14.3% compared to the circular cylinder.