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Feb 2013

Volume 25, Issue 2, Articles (02xxxx)

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Phys. Fluids 25, 025102 (2013); http://dx.doi.org/10.1063/1.4790640 (31 pages)

T. A. Casey, J. Sakakibara, and S. T. Thoroddsen
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back to top Instability and Transition

Dielectrophoretic force-driven thermal convection in annular geometry

Harunori N. Yoshikawa, Olivier Crumeyrolle, and Innocent Mutabazi

Phys. Fluids 25, 024106 (2013); http://dx.doi.org/10.1063/1.4792833 (14 pages)

Online Publication Date: 27 February 2013

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The thermal convection driven by the dielectrophoretic force is investigated in annular geometry under microgravity conditions. A radial temperature gradient and a radial alternating electric field are imposed on a dielectric fluid that fills the gap of two concentric infinite-length cylinders. The resulting dielectric force is regarded as thermal buoyancy with a radial effective gravity. This electric gravity varies in space and may change its sign depending on the temperature gradient and the cylinder radius ratio. The linear stability problem is solved by a spectral-collocation method. The critical mode is stationary and non-axisymmetric. The critical Rayleigh number and wavenumbers depend sensitively on the electric gravity and the radius ratio. The mechanism behind the instability is examined from an energetic viewpoint. The instability in wide gap annuli is an exact analogue to the gravity-driven thermal instability.
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47.55.pb Thermal convection
82.45.-h Electrochemistry and electrophoresis
47.60.Dx Flows in ducts and channels
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
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Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes

J. Carballido-Landeira, P. M. J. Trevelyan, C. Almarcha, and A. De Wit

Phys. Fluids 25, 024107 (2013); http://dx.doi.org/10.1063/1.4790192 (10 pages)

Online Publication Date: 28 February 2013

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In a gravitational field, a horizontal interface between two miscible fluids can be buoyantly unstable because of double diffusive effects or because of a Rayleigh-Taylor instability arising when a denser fluid lies on top of a less dense one. We show here both experimentally and theoretically that, besides such classical buoyancy-driven instabilities, a new mixed mode dynamics exists when these two instabilities act cooperatively. This is the case when the upper denser solution contains a solute A, which diffuses sufficiently faster than a solute B initially in the lower layer to yield non-monotonic density profiles after contact of the two solutions. We derive analytically the conditions for existence of this mixed mode in the (R, δ) parameter plane, where R is the buoyancy ratio between the two solutions and δ is the ratio of diffusion coefficient of the solutes. We find an excellent agreement of these theoretical predictions with experiments performed in Hele-Shaw cells and with numerical simulations.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.pd Multidiffusive convection
02.60.Cb Numerical simulation; solution of equations
47.11.-j Computational methods in fluid dynamics
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
back to top Turbulent Flows

Implicit large-eddy simulation of passive scalar mixing in statistically stationary isotropic turbulence

A. J. Wachtor, F. F. Grinstein, C. R. DeVore, J. R. Ristorcelli, and L. G. Margolin

Phys. Fluids 25, 025101 (2013); http://dx.doi.org/10.1063/1.4783924 (19 pages) | Cited 3 times

Online Publication Date: 4 February 2013

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Turbulent mixing of a passive scalar by forced isotropic turbulence with a prescribed mean scalar gradient is studied in the context of implicit large-eddy simulation. The simulation strategy uses a multi-dimensional compressible flux-corrected transport algorithm, with low wavenumber momentum forcing imposed separately for the solenoidal and dilatational velocity components. Effects of grid resolution on the flow and scalar mixing are investigated at turbulent Mach numbers 0.13 and 0.27. Turbulence metrics are used to show that an implicit large-eddy simulation can accurately capture the mixing transition and asymptotic self-similar behaviors predicted by previous theoretical, laboratory, and direct numerical simulation studies, including asymptotically constant scalar variance and increasing velocity-to-scalar Taylor micro-scales ratio as function of effective Reynolds number determined by grid resolution. The results demonstrate the feasibility of predictive under-resolved simulations of high Reynolds number turbulent scalar mixing using implicit large-eddy simulation.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.wj Turbulent mixing layers
47.40.Dc General subsonic flows
47.11.-j Computational methods in fluid dynamics
47.27.ep Large-eddy simulations
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Scanning tomographic particle image velocimetry applied to a turbulent jet

T. A. Casey, J. Sakakibara, and S. T. Thoroddsen

Phys. Fluids 25, 025102 (2013); http://dx.doi.org/10.1063/1.4790640 (31 pages)

Online Publication Date: 21 February 2013

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We introduce a modified tomographic PIV technique using four high-speed video cameras and a scanning pulsed laser-volume. By rapidly illuminating adjacent subvolumes onto separate video frames, we can resolve a larger total volume of velocity vectors, while retaining good spatial resolution. We demonstrate this technique by performing time-resolved measurements of the turbulent structure of a round jet, using up to 9 adjacent volume slices. In essence this technique resolves more velocity planes in the depth direction by maintaining optimal particle image density and limiting the number of ghost particles. The total measurement volumes contain between 1 ×106 and 3 ×106 velocity vectors calculated from up to 1500 reconstructed depthwise image planes, showing time-resolved evolution of the large-scale vortical structures for a turbulent jet of Re up to 10 000.
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47.80.Jk Flow visualization and imaging
42.62.Eh Metrological applications; optical frequency synthesizers for precision spectroscopy
47.27.wg Turbulent jets
47.32.C- Vortex dynamics
47.80.Cb Velocity measurements

Experimental study of skin friction drag reduction on superhydrophobic flat plates in high Reynolds number boundary layer flow

Elias Aljallis, Mohammad Amin Sarshar, Raju Datla, Vinod Sikka, Andrew Jones, and Chang-Hwan Choi

Phys. Fluids 25, 025103 (2013); http://dx.doi.org/10.1063/1.4791602 (14 pages)

Online Publication Date: 21 February 2013

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In this paper, we report the measurement of skin friction drag on superhydrophobic-coated flat plates in high Reynolds (Re) number boundary layer flows, using a high-speed towing tank system. Aluminum flat plates with a large area (4 feet × 2 feet, 3/8 in. thick) and sharpened leading/trailing edges (1 in. long) were prepared as a boundary layer flow model. Spray coating of hydrophobic nanoparticles was applied to make two different types of superhydrophobic coatings: one with low contact angle and high contact angle hysteresis, and the other with high contact angle and low contact angle hysteresis. Skin friction drag of the superhydrophobic plates was measured in the flow speed up to 30 ft/s to cover transition and turbulent flow regimes (105 < ReL < 107), and was compared to that of an uncoated bare aluminum plate. A significant drag reduction was observed on the superhydrophobic plate with high contact angle and low contact angle hysteresis up to ∼30% in transition regime (105 < ReL < 106), which is attributed to the shear-reducing air layer entrapped on the superhydrophobic surface. However, in fully turbulence regime (106 < ReL < 107), an increase of drag was observed, which is ascribed to the morphology of the surface air layer and its depletion by high shear flow. The texture of superhydrophobic coatings led to form a rugged morphology of the entrapped air layer, which would behave like microscale roughness to the liquid flow and offset the drag-reducing effects in the turbulent flow. Moreover, when the superhydrophobic coating became wet due to the removal of air by high shear at the boundary, it would amplify the surface roughness of solid wall and increase the drag in the turbulent flow. The results illustrate that drag reduction is not solely dependent on the superhydrophobicity of a surface (e.g., contact angle and air fraction), but the morphology and stability of the surface air layer are also critical for the effective drag reduction using superhydrophobic surfaces, especially in high Re number turbulent flow regimes.
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47.27.nb Boundary layer turbulence
47.55.dr Interactions with surfaces
47.80.Jk Flow visualization and imaging
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
47.27.Cn Transition to turbulence
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Reynolds-number scaling of turbulent channel flow

M. P. Schultz and K. A. Flack

Phys. Fluids 25, 025104 (2013); http://dx.doi.org/10.1063/1.4791606 (13 pages)

Online Publication Date: 21 February 2013

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Results of an experimental study of smooth-wall, fully developed, turbulent channel flow are presented. The Reynolds number (Rem) based on the channel height and the bulk mean velocity ranged from 10 000 to 300 000. The present results indicate that the skin-friction coefficient (Cf) closely follows a power law for Rem < 62 000. At higher Reynolds numbers, Cf is best described by a log law. Detailed two-component velocity measurements taken at friction Reynolds numbers of Reτ = 1000–6000 indicate that the mean flow and Reynolds shear stress display little or no Reynolds-number dependence. The streamwise Reynolds normal stress (math+), on the other hand, varies significantly with Reynolds number. The inner peak in math+ is observed to grow with Reynolds number. Growth in math+ farther from the wall is documented over the entire range of Reynolds number giving rise to a plateau in the streamwise Reynolds normal stress in the overlap region of the profile for Reτ = 6000. The wall-normal Reynolds normal stress (math+) displays no Reynolds-number dependence near the wall. Some increase in math+ in the outer layer is noted for Reτ ≤ 4000. The trends in the present Reynolds stress results agree qualitatively with recent experimental results from pipe and boundary layer flows.
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47.27.nd Channel flow
47.60.Dx Flows in ducts and channels
47.27.nb Boundary layer turbulence

Three-dimensional simulation of natural convection in a reservoir sidearm

Karl A. Dittko, Michael P. Kirkpatrick, and Steven W. Armfield

Phys. Fluids 25, 025105 (2013); http://dx.doi.org/10.1063/1.4792709 (26 pages)

Online Publication Date: 27 February 2013

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Numerical simulations were conducted of turbulent natural convection in a shallow tetrahedron domain representing the sidearm of a lake or water reservoir. The tetrahedron cavity is a more realistic, three-dimensional approximation of a lake or reservoir sidearm than the two-dimensional triangle cavity often seen in the literature. Lateral temperature gradients exist due to the varying depth of the cavity, resulting in lateral circulation. These flows are important in a reservoir as they can carry with them particles and various pollutants, transporting and mixing them with the central section. Therefore, study in this area is important in water quality management. The simulations use a Cartesian grid with an Immersed Boundary Method for the sloped bottom surfaces. Heat input is through a solar radiation model consisting of a heat flux from the sloped bottom boundaries and an internal heating source term in the body of the water. Also studied is the night time model where cooling is through a heat flux at the top boundary. Scaling analysis from the literature is extended to suit the new geometry and numerical simulations are used to validate the results. The numerical simulations include calculating horizontal heat transfer profiles, volumetric flow rates, and analysis of complex flow features. The extension to three dimensions results in significant changes to the flow and introduces some complex features, such as helical flow both towards and away from the tip. Some general parameterisations are proposed for the tetrahedron cavity based on the numerical simulations.
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47.27.te Turbulent convective heat transfer
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics
47.27.E- Turbulence simulation and modeling
47.27.wj Turbulent mixing layers
back to top Compressible Flows

On the interaction of shock waves and sound waves in transonic buffet flow

A. Hartmann, A. Feldhusen, and W. Schröder

Phys. Fluids 25, 026101 (2013); http://dx.doi.org/10.1063/1.4791603 (17 pages) | Cited 1 time

Online Publication Date: 15 February 2013

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To support Lee's buffet mechanism model [B. H. K. Lee, “Self-sustained shock oscillations on airfoils at transonic speeds,” Prog. Aerosp. Sci. 37, 147–196 (2001)10.1016/S0376-0421(01)00003-3], the sound wave propagation in the flow field outside the separation of a transonic buffet flow at a Mach number M = 0.73 and an angle of attack α = 3.5° over a DRA 2303 supercritical airfoil is determined using high-speed particle-image velocimetry. Furthermore, the shock wave is influenced by an artificial sound source which evidently changes the shock oscillation properties. The dominant buffet mechanism is shown to be a feedback loop between the shock position and the noise generation at the trailing edge of the airfoil. The sound wave propagation speed is detected by correlating the surface pressure signals and the velocity fluctuations in the flow field. The quantitative results for the natural and the artificial sound source convincingly coincide and are in good agreement with a reformulated version of Lee's buffet model.
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47.85.Gj Aerodynamics
47.32.Ff Separated flows
47.40.Dc General subsonic flows
47.40.Nm Shock wave interactions and shock effects
47.80.Jk Flow visualization and imaging
back to top Geophysical Flows

Gravity currents in non-rectangular cross-section channels: Analytical and numerical solutions of the one-layer shallow-water model for high-Reynolds-number propagation

T. Zemach and M. Ungarish

Phys. Fluids 25, 026601 (2013); http://dx.doi.org/10.1063/1.4790796 (24 pages)

Online Publication Date: 22 February 2013

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We consider the propagation of a high-Reynolds-number gravity current at the bottom of a horizontal channel along the horizontal coordinate x. The bottom and top of the channel are at z = 0, H, and the cross-section is given by the general −f1(z) ⩽ yf2(z) for 0 ⩽ zH. We use a one-layer, Boussinesq, shallow-water formulation to solve the time-dependent motion produced by release from rest of a fixed volume of fluid from a lock. The dependent variables are the position of the horizontal interface, h(x, t), and the speed (averaged over the area of the current), u(x, t). The non-rectangular cross-section geometry enters the formulation via f(h) and integrals of f(z) and zf(z), where f(z) = f1(z) + f2(z) is the width of the channel. For a given geometry f(z), the only input parameter in the lock-release problem is the height ratio H/h0 of ambient to lock. In general, the solution is obtained by a finite-difference numerical code. Analytical results are derived for the initial dam-break slumping motion, and for the long-time self-similar phase. The model is illustrated for various cross-section shapes: power-law (f(z) = bzα, where b, α are positive constants), trapezoidal, V-shaped valley, and circle-segment. In addition to the quantitative results, the qualitative similarities and differences between the classical rectangular and the general non-rectangular channel have been elucidated: in the first case there is always an initial “slumping” stage of propagation with speed uN = const., followed by a stage of decreasing speed, then a phase of self-similar behavior during which uN decreases like time to some power. In the non-rectangular cross-section channel, the first two stages appear, but the self-similar phase is attained only when the cross-section shape is given by a power-law. When the cross-section of the channel expands upwards, the speed of propagation is larger, and the decay of speed after the slumping stage is weaker, than in the classical rectangular counterpart. The theoretical results are in good agreement with previously published experimental data, but a sharp comparison is not feasible because the experiments were performed in full-depth-lock configurations where the one-layer model is not expected to be accurate.
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47.60.Dx Flows in ducts and channels
02.70.Bf Finite-difference methods
47.10.A- Mathematical formulations
47.11.Bc Finite difference methods
47.53.+n Fractals in fluid dynamics
back to top Others

Benchmark problems for mixtures of rarefied gases. I. Couette flow

Felix Sharipov and José L. Strapasson

Phys. Fluids 25, 027101 (2013); http://dx.doi.org/10.1063/1.4791604 (13 pages)

Online Publication Date: 15 February 2013

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The planar Couette flow for gaseous mixture He–Ar is calculated by the direct simulation Monte Carlo method based on ab initio potential over the whole range of the gas rarefaction for several values of the mole fraction and for two values of the wall speed. The smaller value of the speed corresponds to the limit when the nonlinear terms are negligible, while the larger value describes a nonlinear flow. The shear stress, velocity gradient, temperature, and mole fraction profiles are presented. The reported results can be used as benchmark data to test model kinetic equations for gaseous mixtures. To study the influence of the intermolecular potential, the same simulations are carried out for the hard sphere molecular model. A relative deviation of the results based on this model from those based on the ab initio potential are analyzed. It is pointed out that the difference between the shear stresses of the two potentials for the linearized solution is within 1%, while it reaches 6% for the nonlinear cases.
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47.45.Ab Kinetic theory of gases
61.20.Ja Computer simulation of liquid structure
64.75.Cd Phase equilibria of fluid mixtures, including gases, hydrates, etc.
47.11.-j Computational methods in fluid dynamics
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