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Sep 2010

Volume 22, Issue 9, Articles (09xxxx)

Issue Cover Spotlight Figure

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 Laminar Flows

Oscillatory instability of a three-dimensional lid-driven flow in a cube

Yuri Feldman and Alexander Yu. Gelfgat

Phys. Fluids 22, 093602 (2010); http://dx.doi.org/10.1063/1.3487476 (9 pages) | Cited 4 times

Online Publication Date: 30 September 2010

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A series of time-dependent three-dimensional (3D) computations of a lid-driven flow in a cube with no-slip boundaries is performed to find the critical Reynolds number corresponding to the steady-oscillatory transition. The computations are done in a fully coupled pressure-velocity formulation on 1043, 1523, and 2003 stretched grids. Grid-independence of the results is established. It is found that the oscillatory instability of the flow sets in via a subcritical symmetry-breaking Hopf bifurcation at Recr ≈ 1914 with the nondimensional frequency ω = 0.575. Three-dimensional patterns in the steady and oscillatory flow regimes are compared with the previously studied two-dimensional configuration and a three-dimensional model with periodic boundary conditions imposed in the spanwise direction.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.54.-r Pattern selection; pattern formation
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.10.A- Mathematical formulations
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
back to top Turbulent Flows

Turbulent oscillating channel flow subjected to a free-surface stress

W. Kramer, H. J. H. Clercx, and V. Armenio

Phys. Fluids 22, 095101 (2010); http://dx.doi.org/10.1063/1.3481149 (13 pages) | Cited 1 time

Online Publication Date: 1 September 2010

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The channel flow subjected to a wind stress at the free surface and an oscillating pressure gradient is investigated using large-eddy simulations. The orientation of the surface stress is parallel with the oscillating pressure gradient and a purely pulsating mean flow develops. The Reynolds number is typically Reω = 106 and the Keulegan–Carpenter number—the ratio between the oscillation period and advection time scale—is KC = 80. Results compare favorably to the data from direct numerical simulations obtained over a single period. A slowly pulsating mean flow occurs with the turbulent flow essentially being statistically steady. Logarithmic boundary layers are present at both the bottom wall and the free surface. Turbulent streaks are observed in the bottom and free-surface layer. The viscous sublayer below the free surface is, however, much thinner. This observation is verified by simulations we performed for a purely wind-driven channel flow. For the oscillating flow, additional low-speed splats (localized regions of upwelling) occur at the free surface when the mean velocity and stress are in the same direction.
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47.27.nd Channel flow
47.60.Dx Flows in ducts and channels
47.27.nb Boundary layer turbulence
47.27.ep Large-eddy simulations

Effect of the Prandtl number on a stratified turbulent wake

Matthew B. de Stadler, Sutanu Sarkar, and Kyle A. Brucker

Phys. Fluids 22, 095102 (2010); http://dx.doi.org/10.1063/1.3478841 (15 pages) | Cited 3 times

Online Publication Date: 15 September 2010

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Direct numerical simulation is employed to study the effect of the Prandtl number, Pr = ν/α with ν the molecular viscosity and α the molecular diffusivity, on a turbulent wake in a stratified fluid. Simulations were conducted at a Reynolds number of 10 000, Re = UD/ν with U the velocity of the body and D the diameter of the body, for a range of Prandtl numbers: 0.2, 1, and 7. The simulations were run from x/D = 6 to x/D = 1200, a range that encompasses the near, intermediate, and far wake. Mean quantities such as wake dimensions and defect velocity were found to be weakly affected by Prandtl number, the same result was observed for vorticity as well. The Prandtl number has a strong effect on the density perturbation field and this results in a number of differences in quantities such as the total energy of the wake, wave flux, scalar and turbulent dissipation, mixing efficiency, spectral distribution of energy in the density and velocity fields, and the transfer of energy between kinetic and potential modes. The approximation Pr = 1 for the ocean is often used in practice. As the qualitative behavior of the large-scale features was the same for the three cases, we conclude that Pr = 1 is a reasonable approximation for the Pr = 7 case in stratified wake simulations, given the significantly higher computational cost required at large Prandtl number.
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47.27.wb Turbulent wakes
47.55.Hd Stratified flows
47.27.ek Direct numerical simulations
02.60.Cb Numerical simulation; solution of equations
47.32.-y Vortex dynamics; rotating fluids

Asymmetries in an obstructed turbulent channel flow

George K. El Khoury, Bjørnar Pettersen, Helge I. Andersson, and Mustafa Barri

Phys. Fluids 22, 095103 (2010); http://dx.doi.org/10.1063/1.3478974 (13 pages) | Cited 2 times

Online Publication Date: 15 September 2010

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The asymmetric flow pattern caused by a single thin-plate obstruction in a plane channel has been explored by means of direct numerical simulations. The blockage ratio was 1:2 and the bulk Reynolds number about 5700. In order to mimic an infinitely long channel section upstream of the obstruction, realistic dynamic inflow conditions were provided by a promising technique proposed by Barri et al. [“Inflow conditions for inhomogeneous turbulent flows,” Int. J. Numer. Methods Fluids 60, 227 (2009)] . The fluid downstream of the symmetric obstruction was sucked toward one side where a modestly long region of rather strong recirculating flow was observed. The weaker recirculation bubble formed at the opposite side was 17 times longer than the obstruction height and almost four times the size of the shorter bubble. The overall flow pattern turned out to be rather different from that observed in a similar study of channel flow subjected to periodically repeating obstructions by Makino et al. [“Turbulent structures and statistics in turbulent channel flow with two-dimensional slits,” Int. J. Heat Fluid Flow 29, 602 (2008)] . An anomalous variation of the pressure coefficient was observed with an excessively low pressure below the shorter of the bubbles. A locally high pressure occurred where the deflected jet flow impinges on the wall, whereas another pressure minimum could be associated with the flow acceleration caused by the severe blockage due to the major recirculation bubble. The turbulent fluctuations were suppressed due to the acceleration through the obstruction and high levels of streamwise velocity persisted far downstream. Exceptionally high turbulence levels were observed in the mixing-layers emanating from the two sides of the obstruction. The turbulence in these mixing-layers turned out to be qualitatively and quantitatively different on the two sides and exhibited distinctly different anisotropies.
Show PACS
47.27.nd Channel flow
47.60.Dx Flows in ducts and channels
47.54.-r Pattern selection; pattern formation
47.27.ek Direct numerical simulations
47.55.db Drop and bubble formation
47.27.wg Turbulent jets
back to top Geophysical Flows

Steady interaction of a vortex street with a shear flow

Darren Crowdy and Rhodri Nelson

Phys. Fluids 22, 096601 (2010); http://dx.doi.org/10.1063/1.3480398 (10 pages)

Online Publication Date: 7 September 2010

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A one parameter family of explicit solutions of the Euler equations is presented comprising a steadily propagating point vortex street situated in a region of uniform vorticity below a periodically deformed vortex jump separating a region of irrotational flow from a uniform shear flow. Various features of the new solutions are described. The limiting solutions are such that the vortex jump develops a periodic sequence of cusps. The stability of the equilibria is investigated numerically using a cylindrical contour dynamics algorithm. The equilibria not too close to the limiting case are found to be structurally robust for a large range of parameter values.
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47.32.cb Vortex interactions
47.32.ck Vortex streets
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
02.60.-x Numerical approximation and analysis
back to top Others

Vortex ring with swirl: A numerical study

M. Cheng, J. Lou, and T. T. Lim

Phys. Fluids 22, 097101 (2010); http://dx.doi.org/10.1063/1.3478976 (9 pages) | Cited 2 times

Online Publication Date: 2 September 2010

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In this paper, we use a lattice Boltzmann method to study the effect of swirl on the dynamics of an isolated three-dimensional vortex ring in a viscous incompressible fluid. We focus on a fixed Reynolds number of 800 and vary swirl magnitude and vortex core size. Results show that increasing swirl for a fixed core size or increasing core size for a fixed swirl causes vortex ring to slow down or even travel backward initially. A simplified physical explanation for this dynamic behavior is proposed. Our results further show that while a weak swirl causes vortex filaments to undergo helical winding, a sufficiently strong swirl transforms these windings into convoluted three-dimensional vortex structure with vortex loops trailing behind it. Each of these vortex loops may reconnect with itself, through the process of vortex reconnection, to form a ringlet.
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47.32.cf Vortex reconnection and rings
47.32.Ef Rotating and swirling flows
47.11.Qr Lattice gas
02.60.-x Numerical approximation and analysis
47.15.-x Laminar flows
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Publisher's Note: “Jet propulsion without inertia” [ Phys. Fluids 22, 081902 (2010) ]

Saverio E. Spagnolie and Eric Lauga

Phys. Fluids 22, 099901 (2010); http://dx.doi.org/10.1063/1.3489020 (1 page)

Online Publication Date: 2 September 2010

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Abstract Unavailable
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47.60.Kz Flows and jets through nozzles
47.11.-j Computational methods in fluid dynamics
47.56.+r Flows through porous media
99.10.Fg Publisher's note
FREE

Erratum: “Oscillation of cylinders of rectangular cross section immersed in fluid” [ Phys. Fluids 22, 052001 (2010) ]

Douglas R. Brumley, Michelle Willcox, and John E. Sader

Phys. Fluids 22, 099902 (2010); http://dx.doi.org/10.1063/1.3487694 (1 page)

Online Publication Date: 13 September 2010

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Abstract Unavailable
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99.10.Cd Errata
02.60.-x Numerical approximation and analysis
FREE

Erratum: “A new particle interaction mixing model for turbulent dispersion and turbulent reactive flows” [ Phys. Fluids 22, 035103 (2010) ]

Daniel W. Meyer

Phys. Fluids 22, 099903 (2010); http://dx.doi.org/10.1063/1.3489130 (1 page)

Online Publication Date: 15 September 2010

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Abstract Unavailable
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99.10.Cd Errata
47.27.wj Turbulent mixing layers
47.70.Fw Chemically reactive flows
47.51.+a Mixing
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