# zbMATH — the first resource for mathematics

Effect of blockage on critical parameters for flow past a circular cylinder. (English) Zbl 1330.76072
Summary: 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
Full Text:
##### References:
 [1] Kovasznay, Proceedings of the Royal Society, Series A 198 pp 174– (1949) [2] On the development of turbulent wakes from vortex streets. Technical Report 1191, NACA, 1954. [3] Berger, Annual Review of Fluid Mechanics 4 pp 313– (1972) [4] Coutanceau, Journal of Fluid Mechanics 79 pp 231– (1977) [5] Williamson, Journal of Fluid Mechanics 206 pp 579– (1989) [6] Norberg, Journal of Fluid Mechanics 258 pp 287– (1994) [7] Norberg, Journal of Fluids and Structures 15 pp 459– (2001) [8] Gresho, International Journal for Numerical Methods in Fluids 4 pp 619– (1984) [9] Jackson, Journal of Fluid Mechanics 182 pp 23– (1987) [10] Zebib, Journal of Engineering Mathematics 21 pp 155– (1987) · Zbl 0632.76063 [11] Ding, International Journal for Numerical Methods in Fluids 31 pp 451– (1999) [12] Morzynski, Zeitschrift fur Angewandte Mathematik und Mechanik 71 pp t424– (1991) [13] Chen, Journal of Fluid Mechanics 284 pp 23– (1995) [14] Morzynski, Computer Methods in Applied Mechanics and Engineering 169 pp 161– (1999) [15] Shair, Journal of Fluid Mechanics 17 pp 546– (1963) [16] Sahin, Physics of Fluids 16 pp 1305– (2004) [17] Tezduyar, Computer Methods in Applied Mechanics and Engineering 95 pp 221– (1992) [18] Mittal, Journal of Fluid Mechanics 476 pp 303– (2003) [19] . A multi-dimensional upwind scheme with no crosswind diffusion. In Finite Element Methods for Convection Dominated Flows, (ed.). AMD-vol. 34. ASME: New York, 1979; 19–35. [20] Brooks, Computer Methods in Applied Mechanics and Engineering 32 pp 199– (1982) [21] Hughes, Computer Methods in Applied Mechanics and Engineering 59 pp 85– (1986) [22] Mittal, Computer Methods in Applied Mechanics and Engineering 188 pp 269– (2000) [23] Tezduyar, International Journal for Numerical Methods in Fluids 43 pp 555– (2003) [24] The Algebraic Eigenvalue Problem. Clarendon Press: Oxford, 1965. · Zbl 0258.65037 [25] Stewart, Numerische Mathematik 25 pp 123– (1976) [26] Modern Algorithms for Large Sparse Eigenvalue Problems. Akademie-Verlag: Berlin, 1987. · Zbl 0613.65032 [27] Methods of simultaneous iteration for calculating eigenvectors of matrices. In Topics in Numerical Analysis II, (ed.). Academic Press: New York, 1975; 169–185. [28] Behr, Computer Methods in Applied Mechanics and Engineering 123 pp 309– (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.