Charles Meneveau

A Lagrangian dynamic subgrid- scale model of turbulence

The dynamic model for large-eddy simulation of turbulence samples information from the resolved velocity field in order to optimize subgrid-scale model coefficients. When the method is used in conjunction with the Smagorinsky eddy-viscosity model, and the sampling process is formulated in a spatially local fashion, the resulting coefficient field is highly variable and contains a significant fraction of negative values. Negative eddy viscosity leads to computational instability and as a result the model is always augmented with a stabilization mechanism. In most applications the model is stabilized by averaging the relevant equations over directions of statistical homogeneity. While this approach is effective, and is consistent with the statistical basis underlying the eddy-viscosity model, it is not applicable to complex-geometry inhomogeneous flows. Existing local formulations, intended for inhomogeneous flows, are most commonly stabilized by artificially constraining the coefficient to be positive. In this paper we introduce a new dynamic model formulation, that combines advantages of the statistical and local approaches. We propose to accumulate the required averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to in-homogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model be purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are slightly superior to those of the spatially (planar) averaged dynamic model. The relationship between the model and vortical structures in isotropic turbulence, as well as ejection events in channel flow, is investigated. Computational overhead is kept small (about 10% above the CPU requirements of the spatially averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet

The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of R λ ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Using a priori testing, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensor L ij , which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During the a priori test, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardina et al. (1980). A relationship between L ij and a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, an ad hoc weighting function that depends on the alignment between L ij and the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.

The multifractal nature of turbulent energy dissipation

The intermittency of the rate of turbulent energy dissipation e is investigated experimentally, with special emphasis on its scale-similar facets. This is done using a general formulation in terms of multifractals, and by interpreting measurements in that light. The concept of multiplicative processes in turbulence is (heuristically) shown to lead to multifractal distributions, whose formalism is described in some detail. To prepare proper ground for the interpretation of experimental results, a variety of cascade models is reviewed and their physical contents are analysed qualitatively. Point-probe measurements of e are made in several laboratory flows and in the atmospheric surface layer, using Taylors frozen-flow hypothesis. The multifractal spectrum f (α) of e is measured using different averaging techniques, and the results are shown to be in essential agreement among themselves and with our earlier ones. Also, long data sets obtained in two laboratory flows are used to obtain the latent part of the f (α) curve, confirming Mandelbrots idea that it can in principle be obtained from linear cuts through a three-dimensional distribution. The tails of distributions of box-averaged dissipation are found to be of the square-root exponential type, and the implications of this finding for the f (α) distribution are discussed. A comparison of the results to a variety of cascade models shows that binomial models give the simplest possible mechanism that reproduces most of the observations. Generalizations to multinomial models are discussed.

A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer

A scale-dependent dynamic subgrid-scale model for large-eddy simulation of turbulent flows is proposed. Unlike the traditional dynamic model, it does not rely on the assumption that the model coefficient is scale invariant. The model is based on a second test-filtering operation which allows us to determine from the simulation how the coefficient varies with scale. The scale-dependent model is tested in simulations of a neutral atmospheric boundary layer. In this application, near the ground the grid scale is by necessity comparable to the local integral scale (of the order of the distance to the wall). With the grid scale and/or the test-filter scale being outside the inertial range, scale invariance is broken. The results are compared with those from (a) the traditional Smagorinsky model that requires specification of the coefficient and of a wall damping function, and (b) the standard dynamic model that assumes scale invariance of the coefficient. In the near-surface region the traditional Smagorinsky and standard dynamic models are too dissipative and not dissipative enough, respectively. Simulations with the scale-dependent dynamic model yield the expected trends of the coefficient as a function of scale and give improved predictions of velocity spectra at different heights from the ground. Consistent with the improved dissipation characteristics, the scale-dependent model also yields improved mean velocity profiles.

Large eddy simulation study of fully developed wind-turbine array boundary layers

It is well known that when wind turbines are deployed in large arrays, their efficiency decreases due to complex interactions among themselves and with the atmospheric boundary layer (ABL). For wind farms whose length exceeds the height of the ABL by over an order of magnitude, a “fully developed” flow regime can be established. In this asymptotic regime, changes in the streamwise direction can be neglected and the relevant exchanges occur in the vertical direction. Such a fully developed wind-turbine array boundary layer (WTABL) has not been studied systematically before. A suite of large eddy simulations (LES), in which wind turbines are modeled using the classical “drag disk” concept, is performed for various wind-turbine arrangements, turbine loading factors, and surface roughness values. The results are used to quantify the vertical transport of momentum and kinetic energy across the boundary layer. It is shown that the vertical fluxes of kinetic energy are of the same order of magnitude as the power...

A power-law flame wrinkling model for LES of premixed turbulent combustion Part I: non-dynamic formulation and initial tests

Abstract A model of turbulent sub-grid scale flame speed for premixed combustion is proposed and tested in Large Eddy Simulation (LES). The model is based on writing the unresolved flame surface density in terms of a general power-law expression that involves an inner cutoff scale. This scale is derived from an equilibrium assumption of flame-surface production and destruction. The flame-surface production term is modeled using a parameterization of the effective flame stretch, obtained from a spectral superposition of earlier DNS results of single vortex-flame interactions [8] . The model is implemented in a LES combustion code in the context of Thickened Flame LES (TF-LES) using an empirically chosen (non-dynamic) value for the power-law exponent. Three-dimensional simulations of premixed flame embedded in a time decaying isotropic turbulent flow are performed in several different parameter ranges. Comparisons between direct numerical simulation (DNS) and LES using different resolutions and thickness factors show that the LES reproduces the total reaction rate of the DNS quite well and independently on the thickness factor, resolution, and sub-grid scale model used for the turbulent eddy viscosity. Comparisons between the predicted overall turbulent flame speed sT as function of the r.m.s. velocity and experimental data show good agreement over a significant range of parameters.

A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows

A scale-dependent dynamic subgrid model based on Lagrangian time averaging is proposed and tested in large eddy simulations (LES) of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model is based on the Lagrangian dynamic Smagorinsky model in which required averages are accumulated in time, following fluid trajectories of the resolved velocity field. The model allows for scale dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. The model also uses the empirical observation that when scale dependence occurs (such as when the filter scale approaches the limits of the inertial range), the classic dynamic model yields the coefficient value appropriate for the test-filter scale. Validation tests in LES of high Reynolds number, rough wall, boundary layer flow are performed at various resolutions. Results are compared with other eddy-viscosity subgrid-scale models. Unlike the...

Stretching and quenching of flamelets in premixed turbulent combustion

Abstract The stretch rate of flamelets in premixed turbulent combustion is computed using (1) detailed numerical simulations of vortex-flame interactions and (2) a model for intermittent turbulence taking into account all possible turbulence scales acting on the flame front. Simulations of interactions between isolated vortices and a laminar flame front are used to obtain a relation between the characteristics of a given vortex and the actual flame stretch generated by this structure. Quenching conditions and quenching times are also given by these simulations. A net rate of stretch is then defined in the case of a complete turbulent flow field as the difference between the total rate of flame stretch and the quenching rate due to scales that have a high enough energy and a long enough lifetime to quench locally the flame front. The net rate of stretch is computed for a variety of parameters of interest in practical applications. It is a function of the large-scale turbulence parameters and the laminar flame speed and flame thickness and may be used as an input in most flamelet models for premixed turbulent combustion. Different criteria for total flame quenching in premixed turbulent combustion are derived and compared (1) to the classical Klimov-Williams theory, (2) to a criterion proposed by Poinsot et al. [8, 9], who studied quenching according to the presence near the flame front of a single eddy able to locally quench combustion, and (3) to the experimental results of Abdel-Gayed and Bradley [6, 7].

Analysis of turbulence in the orthonormal wavelet representation

A decomposition of turbulent velocity fields into modes that exhibit both localization in wavenumber and physical space is performed. We review some basic properties of such a decomposition, the wavelet transform. The wavelet-transformed Navier—Stokes equations are derived, and we define new quantities such as e ( r , x ), t ( r , x ) and π( r , x ) which are the kinetic energy, the transfer of kinetic energy and the flux of kinetic energy through scale r at position x . The discrete version of e ( r , x ) is computed from laboratory one-dimensional velocity signals in a boundary layer and in a turbulent wake behind a circular cylinder. We also compute e ( r , x ), t ( r , x ) and π( r , x ) from three-dimensional velocity fields obtained from direct numerical simulations. Our findings are that the localized kinetic energies become very intermittent in x at small scales and exhibit multifractal scaling. The transfer and flux of kinetic energy are found to fluctuate greatly in physical space for scales between the energy containing scale and the dissipative scale. These fluctuations have mean values that agree with their traditional counterparts in Fourier space, but have standard deviations that are much larger than their mean values. In space (at each scale r ), we find exponential tails for the probability density functions of these quantities. We then study the nonlinear advection terms in more detail and define the transfer T ( r | r ′, x ) between scale r and all scales smaller than r ′, at location x . Then we define π sg ( r , x ), the flux of energy caused only by the scales smaller than r , at x , and find negative values for π sg ( r , x ), at almost 50% of the physical space at every scale (backscatter). We propose the inclusion of local backscatter in the phenomenological cascade models of intermittency, by allowing some energy to flow from small to large scales in the context of a multiplicative process in the inertial range.

The fractal facets of turbulence

On montre que plusieurs aspects de la turbulence peuvent etre decrits par des fractales et que leurs dimensions fractales peuvent etre mesurees