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Sep 2010

Volume 22, Issue 9, Articles (09xxxx)

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Phys. Fluids 22, 091106 (2010); http://dx.doi.org/10.1063/1.3483215 (1 page)

D. M. Harris, V. A. Miller, and C. H. K. Williamson
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back to top Instability and Transition

Vortex dynamics in a wire-disturbed cylinder wake

I. Yildirim, C. C. M. Rindt, and A. A. Steenhoven

Phys. Fluids 22, 094101 (2010); http://dx.doi.org/10.1063/1.3466659 (15 pages) | Cited 2 times

Online Publication Date: 1 September 2010

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The effect of a thin control wire on the wake properties of the flow around a circular cylinder has been investigated numerically. The governing equations are solved using a spectral element method for a Reynolds number of ReD = 100. The diameter ratio of the main cylinder and the wire equals D/d = 50 so no vortex shedding is expected to occur for the wire. However, the vorticity introduced by the wire in the vicinity of the upper shear layer of the cylinder still affects the vortex dynamics in the wake of the main cylinder. The primary effect of the wire is the reduction of the velocity fluctuations in the vortex formation region of the main cylinder. The maximum decrement occurs at a wire position of yw/D = 0.875. The secondary effect of the wire is observed in the kinematics of the vortices, leading to a modified vortex arrangement and strength difference between the upper and lower vortices. Due to these effects, for yw/D ≤ 0.875, a downward wake deflection is observed, while for larger values of yw/D>0.875, an upward deflection is found. The maximum downward deflection occurs at wire position yw/D = 0.75 where the maximum positive mean lift coefficient, minimum drag coefficient, and minimum fluctuating lift coefficient are seen. Based on the observations, it is concluded that the deflection of the wake is primarily caused by a modification of the vortex arrangement in the wake. This modified vortex arrangement is caused by different formation times of the upper and lower vortices, by different vortex strengths, or by both.
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47.15.Tr Laminar wakes
47.15.ki Inviscid flows with vorticity
47.32.-y Vortex dynamics; rotating fluids

Feedback control of the vortex-shedding instability based on sensitivity analysis

Simone Camarri and Angelo Iollo

Phys. Fluids 22, 094102 (2010); http://dx.doi.org/10.1063/1.3481148 (14 pages) | Cited 1 time

Online Publication Date: 14 September 2010

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In the present work, a simple proportional feedback control is designed to suppress the vortex-shedding instability in the wake of a prototype bluff-body flow, i.e., the flow around a square cylinder confined in a channel with an incoming Poiseuille flow. Actuation is provided by two jets localized on the cylinder surface and velocity sensors are used for feedback control. This particular configuration is a pretext to propose a more general strategy for designing a controller, which is independent of the type of actuation and sensors. The method is based on the linear stability analysis of the flow, carried out on the unstable steady solution of the equations, which is also the target flow of the control. The idea is to use sensitivity analysis to predict the displacement in the complex plane of some selected eigenvalues, found by the linear stability analysis of the flow, as a function of the control design parameters. In this paper, it is shown that the information provided by only sensitivity analysis carried out on the uncontrolled system is not sufficient to design a controller which stabilizes the flow. Therefore, the control is designed iteratively by successive linearizations. Apart from possible constraints, the position of the sensors, the direction along which velocity is measured, and the feedback coefficients are outputs of the design procedure. The proposed strategy leads to a successful control up to a Reynolds number which is at least twice as large as the critical one for the primary instability, using only one velocity sensor.
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47.32.cd Vortex stability and breakdown
47.15.Fe Stability of laminar flows
47.80.Cb Velocity measurements
47.85.L- Flow control
47.60.Dx Flows in ducts and channels
47.15.Tr Laminar wakes

Role of wall deformability on interfacial instabilities in gravity-driven two-layer flow with a free surface

Gaurav and V. Shankar

Phys. Fluids 22, 094103 (2010); http://dx.doi.org/10.1063/1.3480633 (12 pages) | Cited 2 times

Online Publication Date: 15 September 2010

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The linear stability of gravity-driven flow of two superposed Newtonian liquid layers down a deformable, inclined, wall is analyzed in order to examine the effect of wall deformability on the interfacial instabilities in the system. There are three distinct interfacial modes in this composite system, viz., gas-liquid (GL), liquid-liquid (LL), and liquid-solid (LS) modes. For a rigid-wall, the GL interface becomes unstable above a critical Reynolds number, while the stability of the LL interface depends on the relative placement of the liquid layers. When the more viscous liquid is adjacent to rigid surface, the LL mode becomes unstable beyond a critical Reynolds number (Re), while it becomes unstable even at Re = 0 when the less viscous liquid is next to rigid-wall. Our asymptotic results show that solid deformability has a stabilizing effect on both GL and LL modes in the low-wavenumber limit when the more viscous liquid layer is near the deformable wall. Numerical results reveal that both the GL and LL interfacial instabilities can be suppressed for all wavenumbers when the solid layer becomes sufficiently deformable. With further increase in solid deformability, all three interfacial modes become unstable. However, the parameters characterizing the solid (shear modulus, thickness, and solid viscosity) can be chosen such that the GL and LL interfaces remain stable (which are otherwise unstable in flow down a rigid incline) at all wavenumbers without the destabilization of LS interface. When the thickness of the top (less viscous) liquid layer is greater, it is more difficult to obtain stable flow configuration by manipulating the solid parameters. When the less viscous liquid is adjacent to the deformable surface, solid deformability always has a destabilizing effect on LL interfacial mode, and it is not possible to simultaneously stabilize both GL and LL interfaces for this configuration.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.Ca Gas/liquid flows
47.35.Bb Gravity waves
68.03.Kn Dynamics (capillary waves)
02.60.-x Numerical approximation and analysis
47.55.Hd Stratified flows

Laboratory experiments on multipolar vortices in a rotating fluid

R. R. Trieling, G. J. F. van Heijst, and Z. Kizner

Phys. Fluids 22, 094104 (2010); http://dx.doi.org/10.1063/1.3481797 (12 pages) | Cited 1 time

Online Publication Date: 16 September 2010

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The instability properties of isolated monopolar vortices have been investigated experimentally and the corresponding multipolar quasisteady states have been compared with semianalytical vorticity-distributed solutions to the Euler equations in two dimensions. A novel experimental technique was introduced to generate unstable monopolar vortices whose nonlinear evolution resulted in the formation of multipolar vortices. Dye-visualization and particle imaging techniques revealed the existence of tripolar, quadrupolar, and pentapolar vortices. Also evidence was found of the onset of hexapolar and heptapolar vortices. The observed multipolar vortices were found to be unstable and generally broke up into multipolar vortices of lesser complexity. The characteristic flow properties of the quadrupolar vortex were in close agreement with the semianalytical model solutions. Higher-order multipolar vortices were observed to be susceptible to strong inertial oscillations.
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47.32.Ef Rotating and swirling flows
47.80.Jk Flow visualization and imaging
47.32.cd Vortex stability and breakdown

Direct numerical simulation of breakdown to turbulence in a Mach 6 boundary layer over a porous surface

Nicola De Tullio and Neil D. Sandham

Phys. Fluids 22, 094105 (2010); http://dx.doi.org/10.1063/1.3481147 (15 pages) | Cited 3 times

Online Publication Date: 21 September 2010

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Transition to turbulence of a Mach 6 flat plate boundary layer over a porous surface is investigated by direct numerical simulation considering two Reynolds numbers based on the laminar boundary layer displacement thickness, namely, Reδ∗ = 6000 and Reδ∗ = 20 000. The transition was initiated by perturbing the laminar boundary layer with small random disturbances and was followed all the way to the turbulent state. The porous geometry was modeled by directly resolving the flow within the pores and the damping of the primary Mack mode of instability was verified. The presence of a porous surface was found to reduce the secondary instability growth rate by reducing the amplitude of the second mode saturation. In particular, the pores suppress the growth of the secondary wave in the near wall region, so that the secondary instability mainly happens near the critical layer. Besides the secondary instabilities Fourier analysis shows additional modes growing at the same rate as the primary instability, consistent with a model for sound waves scattering from the porous surface. The transient growth of u′, ρ′, and T′ fluctuations, in the form of streamwise streaks, appears to favor the fundamental type of secondary instability. Additional calculations revealed that an oblique first mode wave is the most amplified mode in this porous surface configuration. This wave is slightly destabilized by the pores. With the oblique first mode excited, the flow becomes turbulent due to the nonlinear interactions without the need for secondary instabilities.
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47.27.nb Boundary layer turbulence
47.40.Ki Supersonic and hypersonic flows
47.27.ek Direct numerical simulations
47.27.Cn Transition to turbulence
47.56.+r Flows through porous media
47.20.Lz Secondary instabilities
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