Optimal model parameters for multi-objective large-eddy simulations

A methodology is proposed for the assessment of error dynamics in large-eddy simulations. It is demonstrated that the optimization of model parameters with respect to one flow property can be obtained at the expense of the accuracy with which other flow properties are predicted. Therefore, an approach is introduced which allows to assess the total errors based on various flow properties simultaneously. We show that parameter settings exist, for which all monitored errors are "near optimal," and refer to such regions as "multi-objective optimal parameter regions." We focus on multi-objective errors that are obtained from weighted spectra, emphasizing both large- as well small-scale errors. These multi-objective optimal parameter regions depend strongly on the simulation Reynolds number and the resolution. At too coarse resolutions, no multi-objective optimal regions might exist as not all error-components might simultaneously be sufficiently small. The identification of multi-objective optimal parameter regions can be adopted to effectively compare different subgrid models. A comparison between large-eddy simulations using the Lilly-Smagorinsky model, the dynamic Smagorinsky model and a new Re-consistent eddy-viscosity model is made, which illustrates this. Based on the new methodology for error assessment the latter model is found to be the most accurate and robust among the selected subgrid models, in combination with the finite volume discretization used in the present study

Large-eddy simulation of the flow in a lid-driven cubical cavity

Large-eddy simulations of the turbulent flow in a lid-driven cubical cavity have been carried out at a Reynolds number of 12000 using spectral element methods. Two distinct subgrid-scales models, namely a dynamic Smagorinsky model and a dynamic mixed model, have been both implemented and used to perform long-lasting simulations required by the relevant time scales of the flow. All filtering levels make use of explicit filters applied in the physical space (on an element-by-element approach) and spectral (modal) spaces. The two subgrid-scales models are validated and compared to available experimental and numerical reference results, showing very good agreement. Specific features of lid-driven cavity flow in the turbulent regime, such as inhomogeneity of turbulence, turbulence production near the downstream corner eddy, small-scales localization and helical properties are investigated and discussed in the large-eddy simulation framework. Time histories of quantities such as the total energy, total turbulent kinetic energy or helicity exhibit different evolutions but only after a relatively long transient period. However, the average values remain extremely close

A framework to assess the quality and robustness of LES codes

We present a framework which can be used to rigourously assess and compare large-eddy simulation methods. We apply this to LES of homogeneous isotropic turbulence using three different discretizations and a Smagorinsky model. By systematically varying the simulation resolution and the Smagorinsky coefficient, one can determine parameter regions for which one, two or multiple flow predictions are simultaneously predicted with minimal error. To this end errors on the predicted longitudinal integral length scale, the resolved kinetic energy and the resolved enstrophy are considered. Parameter regions where all considered errors are simultaneously (nearly) minimal are entitled ‘multi-objective optimal’ parameter regions. Surprisingly, we find that a standard second-order method has a larger ‘multiobjective optimal’ parameter region than two considered fourth order methods. Moreover, the errors in the respective ‘multi-objective optimal’ regions are also lowest for the second-order scheme

Direct measurements of anisotropic energy transfers in a rotating turbulence experiment

We investigate experimentally the influence of a background rotation on the energy transfers in decaying grid turbulence. The anisotropic energy flux density, ${\bf F} ({\bf r}) =$, where $\delta {\bf u}$ is the vector velocity increment over separation ${\bf r}$, is determined for the first time using Particle Image Velocimetry. We show that rotation induces an anisotropy of the energy flux $\nabla \cdot {\bf F}$, which leads to an anisotropy growth of the energy distribution $E({\bf r}) = < (\delta {\bf u})^2 >$, in agreement with the K\'arm\'an-Howarth-Monin equation. Surprisingly, our results prove that this anisotropy growth is essentially driven by a nearly radial, but orientation-dependent, energy flux density ${\bf F} ({\bf r})$.Comment: to appear in Physical Review Letters (July 8, 2011 issue

Large-eddy simulations of stratified plane Couette flow using the anisotropic minimum-dissipation model

The anisotropic minimum-dissipation (AMD) model for large-eddy simulation (LES) has been recently developed, and here the model performance is examined in strat- ified plane Couette flow. To our knowledge this is the first use of the AMD model for resolved LES of stratified wall-bounded flow. A comparison with previously pub- lished direct numerical simulations (DNS) provides insight into model and grid re- quirements. Prandtl numbers of P r = 0.7 − 70 and a range of Richardson numbers show that the AMD LES performs well even with a strong stabilising buoyancy flux. We identify three new requirements for accurate LES of stratified wall-bounded flow. First, the LES must resolve the turbulent structures at the edge of the viscous sublayer in order to satisfy the Obukov length scale condition, L+s > 200. Other- wise the LES solution may laminarise where the DNS solution remains turbulent. Second, the LES must have enough vertical grid resolution within the viscous and diffusive sublayers to resolve the wall fluxes. Third, the grid must be reasonably isotropic (vertical-to-horizontal grid aspect ratio > 0.25) at the edge of the sublayer and through the turbulent interior for the AMD LES to correctly simulate the scalar flux. When these model requirements are fulfilled the AMD LES performs very well, producing vertical mean profiles, friction Reynolds number and Nusselt number con- sistent with DNS solutions at significantly higher grid resolution

Nonlinear global modes in hot jets

International audienceSince the experiments of Monkewitz et al. (J. Fluid Mech. vol. 213, 1990, p. 611), sufficiently hot circular jets have been known to give rise to self-sustained synchronized oscillations induced by a locally absolutely unstable region. In the present investigation, numerical simulations are carried out in order to determine if such synchronized states correspond to a nonlinear global mode of the underlying base flow, as predicted in the framework of Ginzburg - Landau model equations. Two configurations of slowly developing base flows are considered. In the presence of a pocket of absolute instability embedded within a convectively unstable jet, global oscillations are shown to be generated by a steep nonlinear front located at the upstream station of marginal absolute instability. The global frequency is given, within 10% accuracy, by the absolute frequency at the front location and, as expected on theoretical grounds, the front displays the same slope as a k--wave. For jet flows displaying absolutely unstable inlet conditions, global instability is observed to arise if the streamwise extent of the absolutely unstable region is sufficiently large: While local absolute instability sets in for ambient-to-jet temperature ratios S = 0.453, global modes only appear for S = 0.3125. In agreement with theoretical predictions, the selected frequency near the onset of global instability coincides with the absolute frequency at the inlet. For lower S, it gradually departs from this value. © 2006 Cambridge University Press

Numerical studies towards practical large-eddy simulation

Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral characteristics), and adaptability to complex configurations. First, methods are tested on academic test-cases, in order to abridge with fundamental studies. Consistent results are obtained using adaptable finite volume method, with higher order advection fluxes, implicit grid filtering and "low-cost" shear-improved Smagorinsky model. This analysis particularly focuses on mean flow, fluctuations, two-point correlations and spectra. Moreover, it is shown that exponential averaging is a promising tool for LES implementation in complex geometry with deterministic unsteadiness. Finally, adaptability of the method is demonstrated by application to a configuration representative of blade-tip clearance flow in a turbomachine

New subgrid-scale models for large-eddy simulation of Rayleigh-Bénard convection

Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.At the crossroad between flow topology analysis and the theory of turbulence, a new eddy-viscosity model for Large-eddy simulation has been recently proposed by Trias et al.[PoF, 27, 065103 (2015)]. The S3PQR-model has the proper cubic near-wall behaviour and no intrinsic limitations for statistically inhomogeneous flows. In this work, the new model has been tested for an air turbulent Rayleigh-Benard convection in a rectangular cell of aspect ratio unity and n span-wise open-ended distance. To do so, direct numerical simulation has been carried out at two Rayleigh numbers Ra = 108 and 1010, to assess the model performance and investigate a priori the effect of the turbulent Prandtl number. Using an approximate formula based on the Taylor series expansion, the turbulent Prandtl number has been calculated and revealed a constant and Ra-independent value across the bulk region equals to 0.55. It is found that the turbulent components of eddy-viscosity and eddy-diffusivity are positively prevalent to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. On the other hand, the new eddy-viscosity model is preliminary tested for the case of Ra = 108 and showed overestimation of heat flux within the boundary layer but fairly good prediction of turbulent kinetics at this moderate turbulent flow.Peer ReviewedPostprint (published version

Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with {reasonably} large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$} scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$} spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to 2D modes. {The spectrum that} emerges {depends on} the anisotropy of the forcing function{,} the former solution prevailing for forcings in which more energy is injected into 2D modes while the latter prevails for isotropic forcing. {In the case of anisotropic forcing, whence the energy} goes from the 2D to the 3D modes at low wavenumbers, large-scale shear is created resulting in another time scale $\tau_{sh}$, associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the {total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$} scaling