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van der Bos F.,TU Munich | Geurts B.J.,University of Twente | Geurts B.J.,TU Eindhoven | Geurts B.J.,International Collaboration for Turbulence Research
Computer Methods in Applied Mechanics and Engineering | Year: 2010

A computational error-assessment of large-eddy simulation (LES) in combination with a discontinuous Galerkin finite element method is presented for homogeneous, isotropic, decaying turbulence. The error-landscape database approach is used to quantify the total simulation error that arises from the use of the Smagorinsky eddy-viscosity model in combination with the Galerkin discretization. We adopt a modified HLLC flux, allowing an explicit control over the dissipative component of the numerical flux. The optimal dependence of the Smagorinsky parameter on the spatial resolution is determined for second and third order accurate Galerkin methods. In particular, the role of the numerical dissipation relative to the contribution from the Smagorinsky dissipation is investigated. We observed an 'exchange of dissipation' principle in the sense that an increased numerical dissipation implied a reduction in the optimal Smagorinsky parameter. The predictions based on Galerkin discretization with fully stabilized HLLC flux were found to be less accurate than when a central discretization with (mainly) Smagorinsky dissipation was used. This was observed for both the second and third order Galerkin discretization, suggesting to emphasize central discretization of the convective nonlinearity and stabilization that mimics eddy-viscosity as sub-filter dissipation. © 2009 Elsevier B.V. All rights reserved.

Liberzon A.,Tel Aviv University | Liberzon A.,International Collaboration for Turbulence Research
International Journal of Heat and Fluid Flow | Year: 2011

Effects of dilute polymer solutions on a lid-driven cubical cavity turbulent flow are studied via particle image velocimetry (PIV). This canonical flow is a combination of a bounded shear flow, driven at constant velocity and vortices that change their spatial distribution as a function of the lid velocity. From the two-dimensional PIV data we estimate the time averaged spatial fields of key turbulent quantities. We evaluate a component of the vorticity-velocity correlation, namely 〈ω 3v〉, which shows much weaker correlation, along with the reduced correlation of the fluctuating velocity components, u and v. There are two contributions to the reduced turbulent kinetic energy production -〈u v〉S uv, namely the reduced Reynolds stresses, -〈u v〉, and strongly modified pointwise correlation of the Reynolds stress and the mean rate-of-strain field, S uv. The Reynolds stresses are shown to be affected because of the derivatives of the Reynolds stresses, ∂〈u v〉/∂y that are strongly reduced in the same regions as the vorticity-velocity correlation. The results, combined with the existing evidence, support the phenomenological model of polymer effects propagating from the polymer scale to the velocity derivatives and through the mixed-type correlations and Reynolds stress derivatives up to the turbulent velocity fields. The effects are shown to be qualitatively similar in different flows regardless of forcing type, homogeneity or presence of liquid-solid boundaries. © 2011 Elsevier Inc.

Ahlers G.,University of California at Santa Barbara | Ahlers G.,International Collaboration for Turbulence Research | He X.,Max Planck Institute for Dynamics and Self-Organization | He X.,International Collaboration for Turbulence Research | And 6 more authors.
New Journal of Physics | Year: 2012

We report on the experimental results for heat-transport measurements, in the form of the Nusselt number Nu, by turbulent Rayleigh-Bénard convection (RBC) in a cylindrical sample of aspect ratio F = D/L = 0.50 (D = 1.12 m is the diameter and L = 2.24 m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bar as the fluid. They are for the Rayleigh-number range 3 × 10 12 ≲ Ra ≲ 10 15 and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra 1 * ≃ 1.4 × 10 13 we find Nu = N 0 Ra γeff with γeff = 0.312 ± 0.002, which is consistent with classical turbulent RBC in a system with laminar boundary layers below the top and above the bottom plate. For Ra 1 * < Ra < Ra 2 * (with Ra 2 * ≃ 5× 10 14) γeff gradually increases up to 0.37 ±0.01. We argue that above Ra 2 * the system is in the ultimate state of convection where the boundary layers, both thermal and kinetic, are also turbulent. Several previous measurements for Y = 0.50 are re-examined and compared with our results. Some of them show a transition to a state with γeff in the range from 0.37 to 0.40, albeit at values of Ra in the range from 9 × 10 10 to 7 × 10 11 which is much lower than the present Ra 1 * or Ra 2 *. The nature of the transition found by them is relatively sharp and does not reveal the wide transition range observed in this work. In addition to the results for the genuine Rayleigh-Bénard system, we present measurements for a sample which was not completely sealed; the small openings permitted external currents, imposed by density differences and gravity, to pass through the sample. That system should no longer be regarded as genuine RBC because the externally imposed currents modified the heat transport in a major way. It showed a sudden decrease of γeff from 0.308 for Ra < Ra t ≃ 4× 10 13 to 0.25 for larger Ra. A number of possible experimental effects are examined in a sequence of appendices; none of these effects is found to have a significant influence on the measurements. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Pumir A.,International Collaboration for Turbulence Research | Pumir A.,Ecole Normale Superieure de Lyon | Pumir A.,Max Planck Institute for Dynamics and Self-Organization | Xu H.,International Collaboration for Turbulence Research | And 10 more authors.
Physical Review X | Year: 2014

In statistically homogeneous turbulent flows, pressure forces provide the main mechanism to redistribute kinetic energy among fluid elements, without net contribution to the overall energy budget. This holds true in both two-dimensional (2D) and three-dimensional (3D) flows, which show fundamentally different physics. As we demonstrate here, pressure forces act on fluid elements very differently in these two cases. We find in numerical simulations that in 3D pressure forces strongly accelerate the fastest fluid elements, and that in 2D this effect is absent. In 3D turbulence, our findings put forward a mechanism for a possibly singular buildup of energy, and thus may shed new light on the smoothness problem of the solution of the Navier-Stokes equation in 3D.

Salazar J.P.L.C.,Cornell University | Salazar J.P.L.C.,International Collaboration for Turbulence Research | Salazar J.P.L.C.,Federal University of Santa Catarina | Collins L.R.,Cornell University | Collins L.R.,International Collaboration for Turbulence Research
Journal of Fluid Mechanics | Year: 2012

In the present study, we investigate the scaling of relative velocity structure functions, of order two and higher, for inertial particles, both in the dissipation range and the inertial subrange using direct numerical simulations (DNS). Within the inertial subrange our findings show that contrary to the well-known attenuation in the tails of the one-point acceleration probability density function (p.d.f.) with increasing inertia (Bec et al., J. Fluid Mech., vol. 550, 2006, pp. 349-358), the opposite occurs with the velocity structure function at sufficiently large Stokes numbers. We observe reduced scaling exponents for the structure function when compared to those of the fluid, and correspondingly broader p.d.f.s, similar to what occurs with a passive scalar. DNS allows us to isolate the two effects of inertia, namely biased sampling of the velocity field, a result of preferential concentration, and filtering, i.e. the tendency for the inertial particle velocity to attenuate the velocity fluctuations in the fluid. By isolating these effects, we show that sampling is playing the dominant role for low-order moments of the structure function, whereas filtering accounts for most of the scaling behaviour observed with the higher-order structure functions in the inertial subrange. In the dissipation range, we see evidence of so-called "crossing trajectoriesa", the "sling effect" or "caustics", and find good agreement with the theory put forth by Wilkinson et al. (Phys. Rev. Lett., vol. 97, 2006, 048501) and Falkovich & Pumir (J. Atmos. Sci., vol. 64, 2007, 4497) for Stokes numbers greater than 0.5. We also look at the scaling exponents within the context of the model proposed by Bec et al. (J. Fluid Mech., vol. 646, 2010, pp. 527-536). Another interesting finding is that inertial particles at low Stokes numbers sample regions of higher kinetic energy than the fluid particle field, the converse occurring at high Stokes numbers. The trend at low Stokes numbers is predicted by the theory of Chun et al. (J. Fluid Mech., vol. 536, 2005, 219-251). This work is relevant to modelling the particle collision rate (Sundaram & Collins, J. Fluid Mech., vol. 335, 1997, pp. 75-109), and highlights the interesting array of phenomena induced by inertia. © 2012 Cambridge University Press.

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