Numerical solution of the Navier–Stokes equations for the flow in a cylinder cascade

Gajjar, Jitesh S. B.; Azzam, Nabila A.

doi:10.1017/s0022112004001594

Cited by 25 publications

(34 citation statements)

References 24 publications

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“…This imposes a further parameter, defined here as H , the ratio of the channel width to the body width. Numerical solutions for circular cylinder cascades have been presented by Fornberg (1991) (with Re 6 400 in the present terms and 5 6 H 6 100) and, very recently and to much higher Reynolds numbers, by Gajjar & Azzam (2004). Similar computations for flat-plate cascades have been by presented by Natarajan, Fornberg & Acrivos (1993) (with Re 6 400 and 5 6 H 6 25) and Ingham, Tang & Morton (1990) (with Re 6 500 and H = 2).…”

Section: Introductionsupporting

confidence: 55%

The stability of laminar symmetric separated wakes

Castro

2005

J. Fluid Mech.

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Time-dependent computations of the two-dimensional incompressible uniformvelocity laminar flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the well-known anti-symmetric (von Kármán-type) vortex shedding is suppressed by the imposition of a symmetry plane on the downstream plate centreline. With a further symmetry plane at the channel's upper boundary, the only two governing parameters in the problem are the channel half-width, H , and the Reynolds number, Re (based on the body half-width and the upstream velocity, U ). The former is restricted to the range 3 6 H 6 30 and the interest lies in determining the nature of the initial instability which occurs in the separated wake as Re is gradually increased. It is found that for sufficiently large H and at a critical Re, a long-time-scale global (supercritical) instability is initiated, which in its saturated (limit) state takes the form of 'lumps' of vorticity being periodically shed from the tail end of the separated bubble. Stability calculations of corresponding mean flow profiles (typical of those found in the separated wake) are undertaken by examining the impulse response of particular profiles via appropriate solution of the Orr-Sommerfeld equation. The results of this analysis extend those available from related published work and are consistent with the behaviour found from the numerical computations. Taken together, all the results suggest that this type of global instability may be generic to many kinds of separated wakes and, indeed, may provide the fundamental explanation for the very low-frequency oscillations often noticed in fully turbulent wake bubbles.

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Section: Introductionsupporting

confidence: 55%

The stability of laminar symmetric separated wakes

Castro

2005

J. Fluid Mech.

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“…They have also presented a detailed review of the work done on steady flow past bluff bodies. The results from the present computations are in good agreement with published results [18][19][20][21]. For example, the steady-state drag coefficient from the present computations for Re = 100 flow is 1.065 and the length of the wake bubble, measured from the cylinder centre, is 6.67D.…”

Section: Steady Flowsupporting

confidence: 91%

“…Fornberg [18][19][20] has presented results for steady flow past a cylinder for Re upto 800 in a series of papers. Recently, Gajjar and Azzam [21] have been able to obtain steady flow solutions for Re as large as 3500. They have also presented a detailed review of the work done on steady flow past bluff bodies.…”

Section: Steady Flowmentioning

confidence: 99%

Instability of the separated shear layer in flow past a cylinder: Forced excitation

Mittal

2007

Numerical Methods in Fluids

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SUMMARYThe receptivity of the separated shear layer for Re = 300 flow past a cylinder is investigated by forced excitation via an unsteady inflow. In order to isolate the shear layer instability, a numerical experiment is set up that suppresses the primary wake instability. Computations are carried out for one half of the cylinder, in two dimensions. The flow past half a cylinder with steady inflow is found to be stable for Re = 300. However, an inlet flow with pulsatile perturbations, of amplitude 1% of the mean, results in the excitation of the shear layer mode. The frequency of the perturbation of the inlet flow determines the frequency associated with the shear layer vortices. For a certain range of forced frequencies the recirculation region undergoes a low-frequency longitudinal contraction and expansion. An attempt is made to relate this instability to a global mode of the wake determined from a linear stability analysis. Interestingly, this phenomenon disappears when the outflow boundary of the computational domain is shifted sufficiently downstream. This study demonstrates the need of carefully investigating the effect of the location of outflow boundaries if the computational results indicate the presence of low-frequency fluctuations. The effect of Re and amplitude of unsteadiness at the inlet are also presented. All computations have been carried out using a stabilized finite element formulation of the incompressible flow equations.

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“…We note that under the action of the control, the recirculation bubble downstream of the cylinder extends to x < 2. This bubble is much smaller than the bubble in the uncontrolled steady flow, which reaches x = 6.6, obtained by numerically suppressing unsteadiness (Fornberg 1991;Gajjar & Azzam 2004). The reduction of the length of the bubble significantly attenuates the inflection point instabilities associated with the recirculation zone and therefore this stabilized flow is expected to be more stable than the uncontrolled steady flow, as will be verified later.…”

Section: Control Effects Of the Optimal Controlmentioning

confidence: 68%

Nonlinear optimal suppression of vortex shedding from a circular cylinder

2015

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This study is focused on two-and three-dimensional incompressible flow past a circular cylinder for Re ≤ 1000. To gain insight into the mechanisms underlying the suppression of unsteadiness for this flow we determine the nonlinear optimal open-loop control driven by surface-normal wall transpiration. The spanwise-constant wall transpiration is allowed to oscillate in time although steady forcing is determined to be most effective. At low levels of control cost, defined as the square integration of the control, the sensitivity of unsteadiness with respect to wall transpiration is a good approximation of the optimal control. The distribution of this sensitivity suggests that the optimal control at small magnitude is achieved by applying suction upstream of the upper and lower separation points and blowing at the trailing edge. At high levels of wall transpiration the assumptions underlying the linearised sensitivity calculation become invalid since the base flow is eventually altered by the size of the control forcing. The large magnitude optimal control is observed to spread downstream of the separation point, draw the shear layer separation towards the rear of the cylinder through suction while blowing along the centreline eliminates the recirculation bubble in the wake. We further demonstrate that it is possible to completely suppress vortex shedding in two-and three-dimensional flow past a circular cylinder up to Re = 1000, accompanied by 70% drag reduction when a nonlinear optimal control of moderate magnitude (with root mean square value 8% of the free stream velocity) is applied. This is confirmed through linearised stability analysis about the steady state solution when the nonlinear optimal wall transpiration is applied. While continuously distributed wall transpiration is not physically realisable, the study highlights localised regions where discrete control strategies could be further developed. It also highlights the appropriate range of application for linear and nonlinear optimal control to this type of flow problem.

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Numerical solution of the Navier–Stokes equations for the flow in a cylinder cascade

Cited by 25 publications

References 24 publications

The stability of laminar symmetric separated wakes

The stability of laminar symmetric separated wakes

Instability of the separated shear layer in flow past a cylinder: Forced excitation

Nonlinear optimal suppression of vortex shedding from a circular cylinder

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