Phys. Fluids (1994-Present) - Physics of Fluids

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Numerical simulation of the three-dimensional screech phenomenon from a circular jet

X. D. Li and J. H. Gao

Phys. Fluids 20, 035101 (2008); http://dx.doi.org/10.1063/1.2844474 (12 pages) | Cited 3 times

Online Publication Date: 3 March 2008

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Despite great advances on jet screech research during the past few decades, the prediction of jet screech amplitudes still remains a challenging task. The main objective of this paper is to develop an accurate three-dimensional computational aeroacoustic procedure for the simulation of screech phenomenon from an underexpanded supersonic circular jet. The three-dimensional Navier–Stokes equations and a modified two-equation standard k-ϵ turbulence model are solved in the generalized curvilinear coordinate system. A dispersion-relation-preserving scheme is utilized for space discretization. The 2N storage low-dissipation and low-dispersion Runge–Kutta scheme is applied for time marching. Numerical results are presented and compared with available experimental data over Mach number range from 1.17 to 1.60. The predicted shock cell structure and radial density profiles agree very well with the measured results by Panda and Seasholtz [“Measurement of shock structure and shock-vortex interaction in underexpanded jets using Rayleigh scattering,” Phys. Fluids 11, 3761 (1999)] . In particular, it is shown that not only the predicted wavelengths, but also the amplitudes of the flapping and helical modes are in good agreement with experimental data by Ponton et al. [“Near field pressure fluctuations in the exit plane of a choked axisymmetric nozzle,” NASA Tech. Memo TM-113137, 1997] . It is found that although the instantaneous flow fields accompanying the flapping and helical jet screech tones are not axisymmetric yet, the long time average mean flow field is still almost axisymmetric. This is because of the slow rotation of the flapping plane around the jet axis. The real time pressure signal of a Ma_j = 1.30 screeching jet at r/D = 2 in the nozzle exit plane is analyzed. The results indicate that the acoustic field of the simulated flapping and rotating motions of the screeching jet agree well with Ponton and Seiner’s experimental measurements [ “Acoustic study of B helical mode for choked axisymmetric nozzle,” AIAA J. 33, 413 (1995) ].

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47.60.Kz	Flows and jets through nozzles
47.11.-j	Computational methods in fluid dynamics
47.40.Ki	Supersonic and hypersonic flows
47.27.Sd	Turbulence generated noise
47.10.ad	Navier-Stokes equations
47.40.Nm	Shock wave interactions and shock effects

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Evolution of isolated turbulent trailing vortices

Karthik Duraisamy and Sanjiva K. Lele

Phys. Fluids 20, 035102 (2008); http://dx.doi.org/10.1063/1.2840200 (11 pages) | Cited 1 time

Online Publication Date: 3 March 2008

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In this work, the temporal evolution of a low swirl-number turbulent Batchelor vortex is studied using pseudospectral direct numerical simulations. The solution of the governing equations in the vorticity-velocity form allows for accurate application of boundary conditions. The physics of the evolution is investigated with an emphasis on the mechanisms that influence the transport of axial and angular momentum. Excitation of normal mode instabilities gives rise to coherent large scale helical structures inside the vortical core. The radial growth of these helical structures and the action of axial shear and differential rotation results in the creation of a polarized vortex layer. This vortex layer evolves into a series of hairpin-shaped structures that subsequently breakdown into elongated fine scale vortices. Ultimately, the radially outward propagation of these structures results in the relaxation of the flow towards a stable high-swirl configuration. Two conserved quantities, based on the deviation from the laminar solution, are derived and these prove to be useful in characterizing the polarized vortex layer and enhancing the understanding of the transport process. The generation and evolution of the Reynolds stresses is also addressed.

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47.11.-j	Computational methods in fluid dynamics
47.20.-k	Flow instabilities
47.27.E-	Turbulence simulation and modeling
47.32.-y	Vortex dynamics; rotating fluids

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The nonlinear large-eddy simulation method applied to Sc ≈ 1 and Sc⪢1 passive-scalar mixing

Gregory C. Burton

Phys. Fluids 20, 035103 (2008); http://dx.doi.org/10.1063/1.2840199 (14 pages) | Cited 7 times

Online Publication Date: 7 March 2008

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The nonlinear large-eddy simulation (nLES) method is extended here to simulations of Sc ≈ 1 and Sc⪢1 turbulent mixing of passive-scalar fields. These are the first LES studies to reproduce the instantaneous structure of the scalar-energy field ?start math

²end?(x,t) at viscous-convective scales in the high Schmidt-number regime. The simulations employ a refinement of the nLES method with multifractal modeling first proposed by G. C. Burton and W. J. A. Dahm [Phys. Fluids 17, 075111 (2005)] . In this approach, the nonlinear inertial stresses math

in the filtered Navier–Stokes equation and the nonlinear scalar fluxes math

in the filtered advection-diffusion equation are calculated directly, using multifractal models for the subgrid velocity and scalar fields, ujsgs and ϕ^sgs. Resolved energy levels are controlled by a new adaptive backscatter limiter that adjusts locally to changing flow conditions consistent with the mechanism governing energy transfer in actual hydrodynamic turbulence. No artificial viscosity or diffusivity closures are applied and no explicit de-aliasing is performed. The nLES approach is shown to simulate accurately Sc ≈ 1 mixing for flows between Re_λ ≈ 35 and 4100, the highest Re_λ tested. Characteristics of the resulting scalar field are examined, including the turbulence-to-scalar time-scale ratio and total scalar variance 〈ϕ^′2〉, indicating good agreement with prior studies. Simulations between Sc = 8 and 8192 produce the first scalar-energy spectra from an LES that exhibit k⁻¹ scaling in the viscous-convective range, consistent with the analytical prediction of G. K. Batchelor [J. Fluid Mech. 5, 113 (1959)] . The simulations indicate decreasing scalar anisotropy and increasing intermittency with increasing Schmidt number, also consistent with prior studies.

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47.51.+a	Mixing
47.85.Dh	Hydrodynamics, hydraulics, hydrostatics
47.11.-j	Computational methods in fluid dynamics

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Inertial consistent subgrid model for large-eddy simulation based on the lattice Boltzmann method

Yu-Hong Dong, Pierre Sagaut, and Simon Marie

Phys. Fluids 20, 035104 (2008); http://dx.doi.org/10.1063/1.2842379 (12 pages) | Cited 4 times

Online Publication Date: 10 March 2008

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The recently introduced inertial-range (IR) consistent Smagorinsky model and the classical Smagorinsky model are applied to the large-eddy simulation (LES) of decaying homogeneous isotropic turbulence based on the lattice Boltzmann method (LBM), which is implemented using the 19-velocity D3Q19 lattice model. The objectives of this study are to examine the effectiveness of the LES-LBM technique for study of turbulence and to extend and validate the efficiency of the inertial-range consistent Smagorinsky model for lattice Boltzmann fluid dynamics. The LES-LBM results are compared with the direct numerical simulation data as well as experimental data. The time evolution of the kinetic energy and the decay exponents of the dissipation rate, the velocity derivative skewness, and instantaneous energy spectra are analyzed. The dependency of behavior of the model coefficients on the ratio of grid width Δ and the Kolmogorov scale η is examined numerically. The results demonstrate that the LES-LBM in conjunction with the IR consistent Smagorinsky model can be used to simulate turbulence more satisfactorily than the standard Smagorinsky model.

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47.11.-j	Computational methods in fluid dynamics
47.27.E-	Turbulence simulation and modeling
47.27.eb	Statistical theories and models

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A study of time correlations in lattice Boltzmann-based large-eddy simulation of isotropic turbulence

Yu-Hong Dong and Pierre Sagaut

Phys. Fluids 20, 035105 (2008); http://dx.doi.org/10.1063/1.2842381 (11 pages) | Cited 7 times

Online Publication Date: 10 March 2008

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As one of statistical characteristics of turbulent flow, space-time correlation is important when studies contribute to understanding of the mechanism of sound radiation and wave scattering by turbulence. This paper combines large-eddy simulations (LES) with the lattice Boltzmann method (LBM) to study the effects of subgrid models on time correlations in decaying isotropic turbulence. The performance of the inertial-range (IR) consistent model and the classical Smagorinsky model is evaluated in terms of two-time Eulerian velocity correlations at the LBM framework. The present study compares the correlations evaluated by LES and the direct numerical simulations based on the lattice Boltzmann equation and Navier–Stokes (NS) equations, respectively. It shows that the lattice Boltzmann subgrid models yield an underestimation of the magnitude of the time correlation on different time intervals and on a variety of wavenumber modes, similar to NS subgrid models. It is also observed that the calculated decorrelation time scale is in good agreement with the theoretical analysis for the Eulerian time microscale and scales nearly as τ(k)∝(Vk)⁻¹. It appears that τ(k) may be either underestimated or overestimated depending on the shape of initial energy spectrum to some extent. Furthermore, compared to the classical Smagorinsky model with different initial spectra, the IR consistent subgrid model shows promising performance on the prediction of the time-space correlations in turbulent flows.

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47.11.Qr	Lattice gas
47.27.eb	Statistical theories and models
47.27.ep	Large-eddy simulations
47.27.Gs	Isotropic turbulence; homogeneous turbulence

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The mean and turbulent flow structure of a weak hydraulic jump

S. K. Misra, J. T. Kirby, M. Brocchini, F. Veron, M. Thomas, and C. Kambhamettu

Phys. Fluids 20, 035106 (2008); http://dx.doi.org/10.1063/1.2856269 (21 pages) | Cited 5 times

Online Publication Date: 12 March 2008

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The turbulent air–water interface and flow structure of a weak, turbulent hydraulic jump are analyzed in detail using particle image velocimetry measurements. The study is motivated by the need to understand the detailed dynamics of turbulence generated in steady spilling breakers and the relative importance of the reverse-flow and breaker shear layer regions with attention to their topology, mean flow, and turbulence structure. The intermittency factor derived from turbulent fluctuations of the air–water interface in the breaker region is found to fit theoretical distributions of turbulent interfaces well. A conditional averaging technique is used to calculate ensemble-averaged properties of the flow. The computed mean velocity field accurately satisfies mass conservation. A thin, curved shear layer oriented parallel to the surface is responsible for most of the turbulence production with the turbulence intensity decaying rapidly away from the toe of the breaker (location of largest surface curvature) with both increasing depth and downstream distance. The reverse-flow region, localized about the ensemble-averaged free surface, is characterized by a weak downslope mean flow and entrainment of water from below. The Reynolds shear stress is negative in the breaker shear layer, which shows that momentum diffuses upward into the shear layer from the flow underneath, and it is positive just below the mean surface indicating a downward flux of momentum from the reverse-flow region into the shear layer. The turbulence structure of the breaker shear layer resembles that of a mixing layer originating from the toe of the breaker, and the streamwise variations of the length scale and growth rate are found to be in good agreement with observed values in typical mixing layers. All evidence suggests that breaking is driven by a surface-parallel adverse pressure gradient and a streamwise flow deceleration at the toe of the breaker. Both effects force the shear layer to thicken rapidly, thereby inducing a sharp free surface curvature change at the toe.

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47.27.W-	Boundary-free shear flow turbulence
47.80.Cb	Velocity measurements
47.35.Jk	Wave breaking
92.10.Sx	Coastal, estuarine, and near shore processes

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Three regularization models of the Navier–Stokes equations

Jonathan Pietarila Graham, Darryl D. Holm, Pablo D. Mininni, and Annick Pouquet

Phys. Fluids 20, 035107 (2008); http://dx.doi.org/10.1063/1.2880275 (15 pages) | Cited 12 times

Online Publication Date: 17 March 2008

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We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier–Stokes. The consequences on the applicability of the regularizations as subgrid-scale (SGS) models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-α model are compared to two previously employed regularizations, the Lagrangian-averaged Navier–Stokes α-model (LANS-α) and Leray-α, albeit at significantly higher Reynolds number than previous studies, namely, Re ≈ 3300, Taylor Reynolds number of Re_λ ≈ 790, and to a direct numerical simulation (DNS) of the Navier–Stokes equations. We derive the de Kármán–Howarth equation for both the Clark-α and Leray-α models. We confirm one of two possible scalings resulting from this equation for Clark-α as well as its associated k⁻¹ energy spectrum. At subfilter scales, Clark-α possesses similar total dissipation and characteristic time to reach a statistical turbulent steady state as Navier–Stokes, but exhibits greater intermittency. As a SGS model, Clark-α reproduces the large-scale energy spectrum and intermittency properties of the DNS. For the Leray-α model, increasing the filter width α decreases the nonlinearity and, hence, the effective Reynolds number is substantially decreased. Therefore, even for the smallest value of α studied Leray-α was inadequate as a SGS model. The LANS-α energy spectrum ∼ k¹, consistent with its so-called “rigid bodies,” precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in numerical resolution. We find, however, that this same feature reduces its intermittency compared to Clark-α (which shares a similar de Kármán–Howarth equation). Clark-α is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than α, whereas high-order intermittency properties for larger values of α are best reproduced by LANS-α.

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47.10.A-

Mathematical formulations

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Fluctuations of statistics among subregions of a turbulence velocity field

Hideaki Mouri, Akihiro Hori, and Masanori Takaoka

Phys. Fluids 20, 035108 (2008); http://dx.doi.org/10.1063/1.2890499 (6 pages) | Cited 1 time

Online Publication Date: 18 March 2008

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To study subregions of a turbulence velocity field, a long record of velocity data of grid turbulence is divided into smaller segments. For each segment, we calculate statistics such as the mean rate of energy dissipation and the mean energy at each scale. Their values significantly fluctuate, in lognormal distributions at least as a good approximation. Each segment is not under equilibrium between the mean rate of energy dissipation and the mean rate of energy transfer that determines the mean energy. These two rates still correlate among segments when their length exceeds the correlation length. Also between the mean rate of energy dissipation and the mean total energy, there is a correlation characterized by the Reynolds number for the whole record, implying that the large-scale flow affects each of the segments.

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47.27.eb	Statistical theories and models
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion

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Planar laser imaging of differential molecular diffusion in gas-phase turbulent jets

C. J. Brownell and L. K. Su

Phys. Fluids 20, 035109 (2008); http://dx.doi.org/10.1063/1.2884465 (20 pages) | Cited 3 times

Online Publication Date: 18 March 2008

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Planar laser Rayleigh scattering yields quantitative, two-dimensional measurements of differential diffusion in a turbulent propane-helium jet issuing into air. The jet exit Reynolds number ranges from 1000 to 3000, corresponding to estimated outer-scale Reynolds numbers from 4300 to 13 000. Using a technique originally proposed by Bilger and Dibble [Combust. Sci. Technol. 28, 161 (1982) ], the imaging measurements allow direct determination of a normalized scalar difference quantity ξ. For the lower Re, significant differential diffusion develops in the pretransitional portion of the flow. Downstream of the turbulent transition, radial profiles of mean ξ take on a characteristic form, with an excess of the less-diffusive propane on the jet boundary. This characteristic form is independent of Reynolds number, and is thus apparently independent of the degree of differential diffusion in the pretransition range. Evolution of the ξ fields in the turbulent part of the flow is surprisingly consistent with the mixing of conventional scalar quantities. Fluctuation profiles of ξ have a self-similar, bimodal shape for each Re, and power spectra of ξ are monotonically decreasing, with a distinct k^−5/3 inertial range. This spectral form is at odds with prior analytical and computational results in isotropic turbulence, which predicted that the spectrum would show a peak intermediate between the diffusive cutoffs of the individual scalars. The discrepancy appears to be due to the forcing applied in the simulations; the differential diffusion in the experiments preferentially develops in the jet near field, so the resulting evolution is more akin to a decay process. This is further emphasized by the observation that the thickness of ξ structures in the jet decreases with downstream distance. The present results indicate that consideration of differential diffusion must account for the details of the flow configuration, particularly the uniformity of turbulence levels. This has important implications for reacting flows, where local laminarization by heat release can be significant.

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47.80.Jk	Flow visualization and imaging
51.20.+d	Viscosity, diffusion, and thermal conductivity
47.27.wg	Turbulent jets
47.27.wj	Turbulent mixing layers

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Effect of heat release on turbulence and scalar-turbulence interaction in premixed combustion

G. Hartung, J. Hult, C. F. Kaminski, J. W. Rogerson, and N. Swaminathan

Phys. Fluids 20, 035110 (2008); http://dx.doi.org/10.1063/1.2896285 (16 pages) | Cited 16 times

Online Publication Date: 25 March 2008

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Stereoscopic particle image velocimetry and planar laser induced fluorescence measurements of hydroxyl radical are simultaneously applied to measure, respectively, local turbulence intensities and flame front position in premixed ethylene-air flames stabilized on a bluff body. Three different equivalence ratios, 0.55, 0.63, and 0.7, and three different Reynolds numbers, 14 000, 17 000, and 21 000, are considered. Laser measurements were made for five different flame configurations within the ranges above and in the corresponding cold flows. By comparing the measurements of the cold and the corresponding hot flows, the effect of heat release on the turbulence and its interaction with the flame front is studied. All the flames are in the thin reaction zone regime. Typical flow features forming behind the bluff body are observed in the cold flows, whereas in the reacting flows the mean velocities and thus the shape, size, and characteristics of the recirculating eddy behind the bluff body are strongly influenced by the heat release. The strong acceleration across the mean flame and the radial outward shift of the stagnation plane of the recirculating eddy yield negative radial velocities which are absent in the corresponding cold flow cases. The spatial intermittency of the flame front leads to an increase in the turbulent kinetic energy. Although a decrease in the mean and rms values of the strain rate tensor e_ij components is observed for the reacting case as one would expect, the local flow acceleration across the flame front leads to a substantial increase in the skewness and the kurtosis of the probability density functions (PDFs) of e_ij components. The turbulence-scalar interaction is studied by analyzing the orientation of the flame front normal with the eigenvectors of e_ij. The PDFs of this orientation clearly show that the normals have an increased tendency to align with the extensive strain rate, which implies that the scalar gradients are destroyed by the turbulence as the scalar isosurfaces are pulled apart. This result questions the validity of passive scalar turbulence physics commonly used for premixed flame modeling. However, the influence of Lewis number on this alignment behavior is not clear at this time.

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47.27.-i	Turbulent flows
47.70.Pq	Flames; combustion

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Computational coarse graining of a randomly forced one-dimensional Burgers equation

Sunil Ahuja, Victor Yakhot, and Ioannis G. Kevrekidis

Phys. Fluids 20, 035111 (2008); http://dx.doi.org/10.1063/1.2856212 (10 pages)

Online Publication Date: 26 March 2008

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We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in time. We demonstrate coarse projective integration and coarse dynamic renormalization as tools that accelerate the extraction of macroscopic information (integration in time, self-similar shapes, nontrivial dynamic exponents) from short bursts of appropriately initialized direct simulation. These procedures solve numerically an effective evolution equation for the energy spectrum without ever deriving this equation in closed form.

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47.11.St	Multi-scale methods
47.27.ef	Field-theoretic formulations and renormalization

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Aerodynamic loads on cactus-shaped cylinders at low Reynolds numbers

Pradeep Babu and Krishnan Mahesh

Phys. Fluids 20, 035112 (2008); http://dx.doi.org/10.1063/1.2887982 (9 pages) | Cited 5 times

Online Publication Date: 31 March 2008

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Direct numerical simulations of flow past cactus-shaped cylinders are performed at Reynolds numbers of 20, 100, and 300. The results are contrasted to those from smooth cylinders at the same Reynolds numbers. The cavities in the cactus-shaped cylinders are seen to reduce the forces acting on them. At Reynolds number of 20, the drag is reduced by 22% due to reduction in the viscous forces. At Reynolds number of 100, the unsteady pressure forces increase, while the unsteady viscous forces acting on the cactus-shaped cylinder decrease. The overall reduction in drag force is about 18%. At Reynolds number of 300, onset of three dimensionality is observed together with significant decrease in pressure and viscous forces. Both the mean and fluctuating forces are found to decrease considerably. The Strouhal number is also found to decrease by about 10%. These reductions in force magnitudes and observed wake instabilities are attributed to the presence of large-scale, quiescent, recirculating flow within the cactus cavities.

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47.10.-g	General theory in fluid dynamics
47.15.-x	Laminar flows

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Experiments on three-dimensional wall-layer scale Lorentz actuators in high-Reynolds-number axisymmetric turbulent boundary layers

P. R. Bandyopadhyay, J. M. Castano, and D. P. Thivierge

Phys. Fluids 20, 035113 (2008); http://dx.doi.org/10.1063/1.2887983 (14 pages)

Online Publication Date: 31 March 2008

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Drag reduction of high-Reynolds-number axisymmetric bodies in saltwater flow using numerous small Lorentz actuators is considered. The actuators are three-dimensional and each of them encompasses the footprint of approximately one turbulence production domain at a Reynolds number Re_τ of 10³, based on friction velocity and boundary layer thickness. The actuators seed the turbulent boundary layer locally with pulsing toroids of vorticity that straddle the periphery of the actuators. The central downward jet of the toroid counters the upward flow between naturally occurring near-wall vortex pairs. Owing to the presence of the wall, the downward central jet is deflected into wall-jets that lie underneath the toroid. The agglomerated effects of the pulsing of the power applied to the three-dimensional actuators are modeled as Stokes oscillators. An axisymmetric body containing 2¹⁰ numbers of subcentimeter-scale electromagnetic surface actuators was built. Measurements over this body show that drag reduction efficiency is higher compared to that expected in two-dimensional actuators at similar Reynolds numbers. Drag reduction depends on the parameter St T⁺/(2π Reτn), where St is Stuart number and T⁺ is pulsing time scale in wall-layer variables, approximately in the same manner as two-dimensional actuators do. However, the exponent n is zero—not 1.0 like that in two-dimensional actuators. At Re_τ≫10³, the same three-dimensional actuators would no longer match the footprints of the unit turbulence production domains and the same applied power would be a weaker perturbation on the streak vorticity. A denser clustering of three-dimensional actuators for the same input power is a likely solution for higher Reynolds numbers.

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47.27.nb	Boundary layer turbulence
47.85.ld	Boundary layer control
47.85.lb	Drag reduction
47.32.-y	Vortex dynamics; rotating fluids
47.27.wg	Turbulent jets

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Development of a dynamic model for the subfilter scalar variance using the concept of optimal estimators

G. Balarac, H. Pitsch, and V. Raman

Phys. Fluids 20, 035114 (2008); http://dx.doi.org/10.1063/1.2896287 (9 pages) | Cited 11 times

Online Publication Date: 31 March 2008

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The concept of optimal estimators, recently introduced by Moreau et al. [Phys. Fluids 18, 1 (2006)] is used as an a priori tool to discuss the accuracy of subfilter models. Placed in the framework of large-eddy simulation of combustion problems, this work focuses on the subfilter models used to evaluate the subfilter variance of a conserved scalar, the mixture fraction. The a priori tests are performed using 512³ direct numerical simulation data of forced homogeneous isotropic turbulence. First, the performance of the most commonly used models for the subfilter variance is studied. Using optimal estimators, the Smagorinsky-type model [ Pierce and Moin, Phys. Fluids 10, 3041 (1998) ] is shown to have the best set of parameters. However, the conventional dynamic formulation of the model leads to large errors in the variance prediction. It was found that assumptions used in the model formulation are not verified. A new dynamic procedure based on a Taylor series expansion is then proposed to improve the predictive accuracy. The a priori tests show that the new model substantially improves predictive accuracy.

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