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

Abstract

SUMMARYThe e ect of location of the lateral boundaries, of the computational domain, on the critical parameters for the instability of the ow past a circular cylinder is investigated. Linear stability analysis of the governing equations for incompressible ows is carried out via a stabilized ÿnite element method to predict the primary instability of the wake. The generalized eigenvalue problem resulting from the ÿnite 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 6 D=H 6 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 ÿrst 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.

Global linear stability analysis of time‐averaged flows

“…Details of the formulation for the LSA can be found in our earlier articles [7,9,12]. The non-linear equation system resulting from the finite element discretization of the flow equations is solved using the generalized minimal residual technique [13] in conjunction with diagonal preconditioners.…”

“…Various investigations, in the past, have shown that the LSA of the steady-state flow can provide a reasonably accurate estimate of the critical Reynolds number (Re c ) and the non-dimensional vortex shedding frequency (St c ) at the onset of the instability [3,[5][6][7]9]. In a recent study [9], it has been shown, via the LSA analysis, that to a large extent the blockage can explain the scatter in the data for the critical parameters at the onset of the instability, from various researchers in the past. The extrapolated values for a computational domain with an infinite lateral width are Re c = 47.380 and St c = 0.1163.…”

Numerical evaluation of passive control of VIV by small control rods

“…A large number of numerical and experimental investigations have been conducted on the wake flows behind circular cylinders, as shown in the reviews by King [1], Sarpkaya [2,3], Bearman [4,5], Sumer and Fredsoe [6], Gabbai and Benaroya [7], Williamson and Govardhan [8,9], and Wu et al [10], Wu et al [11]. Alternating vortex shedding presents in the wake over a wide range of Reynolds numbers, resulting in structural vibration, acoustic noise, and significant increases in the drag and lift fluctuations [12][13][14][15]. This kind of fluctuations may cause fatigue in the structures and then sometimes lead to failure.…”

The influence of advection schemes and turbulence closure models on drag coefficient calculation around a circular cylinder at high Reynolds number

“…This specific Reynolds number is chosen because it is applicable to coastal marine structures, and this is also the upper bound that could be achieved in some laboratory measurements, thus the data are available to validate the numerical results. Besides the advection schemes and turbulence closure models, other factors such as the surface roughness of the cylinder (Szechenyi, 1975;Achenbach and Heinecke, 1981;Nakamura and Tomonari, 1982), the background turbulence intensity (Cheung and Melbourne, 1983;Kwok, 1986;Norberg and Sunden, 1987), and the distance between the cylinder and lateral boundary (Kumar and Mittal, 2006), could also influence the final results, which is not discussed in the present paper.…”