Cylinders with square cross-section: wake instabilities with incidence angle variation

• Published in: Journal of fluid mechanics Vol. 630; pp. 43 - 69
• Main Authors: SHEARD, GREGORY J., FITZGERALD, MATTHEW J., RYAN, KRIS
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.07.2009
• Subjects: Cross-sections; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Nonlinearity (including bifurcation theory); Physics; Reynolds number; Stability analysis; Transition to turbulence; Turbulent flows, convection, and heat transfer; Wakes; Three dimensional flow; Bluff body; Reynolds number; Digital simulation; Hydrodynamic instability; Bifurcation; Wakes; Modelling; Incidence angle; Transition flow; Square section; Mesh generation
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112009006879

The wakes behind square cylinders with variation in incidence angle are computed over a range of Reynolds numbers to elucidate the three-dimensional stability and dynamics up to a Reynolds number of Re = 300, based on the projected height of the inclined square cylinder. Three-dimensional instability modes are predicted and computed using a linear stability analysis technique and three-dimensional simulations, respectively. Depending on the incidence angle, the flow is found to transition to three-dimensional flow through either a mode A instability, or a subharmonic mode C instability. The mode A instability is predicted as the first-occurring instability at incidence angles smaller than 12° and greater than 26°, with the mode C instability predicted between these incidence angles. At a zero-degree angle of incidence, the wake instabilities closely match modes A, B and a quasi-periodic mode predicted in earlier studies behind square and circular cylinders. With increasing angle of incidence, the three-dimensional wake transition Reynolds number first increases from Re = 164 as the mode A instability weakens, before decreasing again beyond an incidence angle of 12° as the wake becomes increasingly unstable to the mode C instability, and then again to the mode A instability as the incidence angle approaches 45°. A spanwise autocorrelation analysis from computations over a cylinder span 20 times the square cross-section side length reveals that beyond the onset of three-dimensional instabilities, the vortex street breaks down with patterns consistent with spatio-temporal chaos. This effect was more pronounced at higher incidence angles.