Onset of global instability in the flow past a circular cylinder cascade

Abstract

The effect of blockage on the onset of instability in the two-dimensional uniform flow past a cascade of cylinders is investigated. The same techniques as those described in Gajjar & Azzam (J. Fluid Mech., vol. 520, 2004, p. 51) are used to tackle the generalized eigenvalue problem arising from a global stability analysis of the linearized disturbance equations. Results have been obtained for the various mode classes, and our results show that for the odd-even modes, which correspond to anti-phase oscillatory motion about the midplane between the cylinders and are the modes most extensively studied in the literature, the effect of blockage has a marginal influence on the critical Reynolds numbers for instability. This is in sharp contrast to results cited in many studies with a fully developed inlet flow past a cylinder placed between confining walls. We are also able to find other unstable modes and in particular for low blockage ratios, the odd-odd modes which correspond to the in-phase oscillatory motion about the midplane between the cylinders are the first to become unstable as compared with the odd-even modes, and with much lower frequencies.

Solving Fluid Dynamics Problems with Matlab

“…In our work, MATLAB was used to first compute the base flows, and then for studies of the onset of instability, by solving the generalised eigenvalue problem. Full details of the numerical methods and results can be found in Boppana and Gajjar (2011). In figures 5, 6 we have shown the results for the streamfunction eigenfunctions.…”

“…In our work we have made extensive use of MATLAB to do 'proof of concept' studies, especially when developing new algorithms and techniques for solving systems of coupled nonlinear partial differential equations, such as those which arise in fluid dynamics. This includes, for instance, codes for investigating instabilities in lid-driven cavities, Boppana and Gajjar (2010), instabilities in flow past circular cylinders, Boppana and Gajjar (2011), and transonic flow past aerofoils Pereira and Gajjar (2010). In some cases MATLAB is used in its own right for solving small problems, but the fact that MATLAB is an interpreted language means that for increasing problem sizes, the MATLAB version of the code can be much slower than equivalent versions in other languages especially when one is dealing with very large sparse matrices.…”

“…Again the same technqiues have been used but for a more complicated geometry. This problem is described in detail in Boppana and Gajjar (2011). The third problem we discuss concerns the inviscid transonic flows past thin airfoils.…”

Modal and non-modal stabilities of flow around a stack of plates

“…effects of stack positioning, blockage ratio, plate aspect ratio and Reynolds number [6][7][8][9]. To reduce the number of independent parameters, the flow past a stack can be simplified as flow past one flat plate confined by periodic (upper and lower) boundaries, as shown in Fig.…”

“…Effects of confinement on flow stabilities have been well investigated, e.g. in confined planar wake flow [10] and flow around arrays of rectangular cylinders [11] or circular cylinders [9], where the critical Reynolds number above which instabilities or vortex …”