Effect of blockage on critical parameters for flow past a circular cylinder.

*(English)*Zbl 1330.76072Summary: The effect of location of the lateral boundaries, of the computational domain, on the critical parameters for the instability of the flow past a circular cylinder is investigated. Linear stability analysis of the governing equations for incompressible flows is carried out via a stabilized finite element method to predict the primary instability of the wake. The generalized eigenvalue problem resulting from the finite element discretization of the equations is solved using a subspace iteration method to get the most unstable eigenmode. Computations are carried out for a large range of blockage,
\[
0.005\leqslant D/H \geqslant 0.125,
\]
where \(D\) is the diameter of the cylinder and \(H\) is the lateral width of the domain. A non-monotonic variation of the critical \(Re\) with the blockage is observed. It is found that as the blockage increases, the critical \(Re\) for the onset of the instability first decreases and then increases.However, a monotonic increase in the non-dimensional shedding frequency at the onset of instability, with increase in blockage, is observed. The increased blockage damps out the low-frequency modes giving way to higher frequency modes. The blockage is found to play an important role in the scatter in the data for the non-dimensional vortex shedding frequency at the onset of the instability, from various researchers in the past.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76E05 | Parallel shear flows in hydrodynamic stability |

37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |

##### Keywords:

Hopf bifurcation; circular cylinder; linear stability analysis; finite element method; blockage
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\textit{B. Kumar} and \textit{S. Mittal}, Int. J. Numer. Methods Fluids 50, No. 8, 987--1001 (2006; Zbl 1330.76072)

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