Johan Meyers

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...

Database analysis of errors in large-eddy simulation

A database of decaying homogeneous, isotropic turbulence is constructed including reference direct numerical simulations at two different Reynolds numbers and a large number of corresponding large-eddy simulations at various subgrid resolutions. Errors in large-eddy simulation as a function of physical and numerical parameters are investigated. In particular, employing the Smagorinsky subgrid parametrization, the dependence of modeling and numerical errors on simulation parameters is quantified. The interaction between these two basic sources of error is shown to lead to their partial cancellation for several flow properties. This leads to a central paradox in large-eddy simulation related to possible strategies that can be followed to improve the accuracy of predictions. Moreover, a framework is presented in which the global parameter dependence of the errors can be classified in terms of the “subgrid activity” which measures the ratio of the turbulent to the total dissipation rate. Such an analysis allows one to quantify refinement strategies and associated model parameters which provide optimal total simulation error at given computational cost.

On the model coefficients for the standard and the variational multi-scale Smagorinsky model

A theoretical analysis is presented on the behaviour of the model coefficients for the well-known Smagorinsky model and two variational multi-scale (VMS) variants of the Smagorinsky model. The dependency on two important parameters is addressed, i.e. the ratio of the LES-filter width ∆ and the Kolmogorov scale η on the one hand, and the ratio of the integral length scale L and the LES-filter width ∆ on the other hand. First of all, it is demonstrated that the model coefficients vary strongly with ∆/η. By evaluating the model coefficients as functions of the subgrid activity s (which expresses the relative contribution of the subgrid-scale model in the total dissipation, and corresponds to a nonlinear transformation of ∆/η), we show that a classical Lilly–Smagorinsky model overestimates the dissipation, even in cases where the dissipation of the subgrid-scale model is dominant. Therefore, generic and easy-to-use modifications to the different models are proposed, which provide close approximations to the models employing ‘exact’ coefficients. For the standard Smagorinsky model, this modified model corresponds to approximating the eddy viscosity νt as νt =( ν 2 Lilly + ν 2 ) 1/2 − ν, with νLilly the turbulent viscosity obtained by employing Lilly’s classical Smagorinsky constant and ν the laminar viscosity. Similar easy-to-use relations are presented for the variational multi-scale Smagorinsky models. Next to the ∆/η dependence of the model coefficients, the L/∆ behaviour is also elaborated. Although a strong dependence on L/∆ is observed for low values of the ratio, we do not advocate the use of L/∆-dependent model coefficients. Rather, the asymptotic L/∆ independence and the speed of asymptotic convergence are used as a tool to compare the quality of subgrid-scale models (e.g. L/∆ > 10 is a minimum order of magnitude for the small–small VMS model), and differences are observed between the standard Smagorinsky model and its two VMS variants. Finally, for the VMS models, the influence of the shape of the high-pass filter, used in the variational multi-scale formulation, is investigated. We observed that smooth high-pass filters result in more robust VMS Smagorinsky models.

Large Eddy Simulations of large wind-turbine arrays in the atmospheric boundary layer

Large Eddy Simulations (LES) of arrays of wind turbines in the atmospheric turbulent boundary layer with many turbines often require simplifled models for the efiects of individual turbines, in order to avoid having to use very flne grid spacings near the individual (moving) turbine blades. This goal can be accomplished using the actuator disk model. This approach, however, raises several issues when implemented in the context of LES. In particular, the question is raised of which reference velocity should be used when parameterizing the induced forces: instantaneous versus time averaged, undisturbed velocity or the local one. Also, one may consider including tangential forces to represent the angular momentum in the wakes. In this paper we present several arguments to make the appropriate choices, and illustrate the efiects of these choices in LES of two wind turbine arrays, one with an aligned and one with a staggered arrangement. Predicted power outputs, as well as features of the predicted ∞ow flelds are analyzed.

Quality and Reliability of Large-Eddy Simulations

Part I Numerical and mathematical analysis of subgrid-scale-model and discretization errors. Architecture of approximate deconvolution models of turbulence, by A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz, I. Stanculescu, C. Trenchea Adaptive turbulence computation based on weak solutions and weak uniqueness, by Johan Hoffman On the application of wavelets to LES sub-grid modelling, by Marta de la Llave Plata, Stewart Cant Analysis of truncation errors and design of physically optimized discretizations, by Stefan Hickel, Nikolaus A. Adams Spectral behavior of various subgrid-scale models in LES at very high Reynolds number, by R. Cocle, L. Bricteux, G. Winckelmans Performance assessment of a new advective subgrid model through two classic benchmark test cases, by Luiz E.B. Sampaio, Angela O. Nieckele, Margot Gerritsen Assessment of dissipation in LES based on explicit filtering from the computation of kinetic energy budget, by Christophe Bogey, Christophe Bailly Optimal unstructured meshing for large eddy simulations, by Yacine Addad, Ulka Gaitonde, Dominique Laurence, Stefano Rolfo Analysis of uniform and adaptive LES in natural convection flow, by Andreas Hauser, Gabriel Wittum Part II Computational error-assessment Influence of time step size and convergence criteria on large eddy simulations with implicit time discretization, by Michael Kornhaas, Dorte C. Sternel, Michael Schafer Assessment of LES quality measures using the error landscape approach, by Markus Klein, Johan Meyers, Bernard J. Geurts Analysis of numerical error reduction in explicitly filtered LES using two-point turbulence closure, by Julien Berland, Christophe Bogey, Christophe Bailly Sensitivity of SGS models and of quality of LES to grid irregularity, by Ghader Ghorbaniasl, Chris Lacor Anisotropic grid refinement study for LES, by Peter Toth, Mate Marton Lohasz Part III Modelling and error-assessment of near-wallflows Expectations in the wall region of a large-eddy simulation, by Philippe R. Spalart, Mikhail Kh. Strelets, and Andrey Travin Large eddy simulation of atmospheric convective boundary layer with realistic environmental forcings, by Aaron M. Botnick, Evgeni Fedorovich Accuracy close to the wall for large-eddy simulations of flow around obstacles using immersed boundary methods, by Mathieu J. B. M. Pourquie On the control of the mass errors in finite volume-based approximate projection methods for large eddy simulations, by Andrea Aprovitola, Filippo Maria Denaro Part IV Error assessment in complex applications Reliability of large-eddy simulation of nonpremixed turbulent flames: scalar dissipation rate modeling and 3D-boundary conditions, by L. Vervisch, G. Lodato, P. Domingo LES at work: quality management in practical large-eddy simulations, by Christer Fureby, Rickard E. Bensow Quality of LES predictions of isothermal and hot round jet, by Artur Tyliszczak, Andrzej Boguslawski, Stanislaw Drobniak LES for street-scale environments and its prospects, by Zheng-Tong Xie, Ian P. Castro Large eddy simulations of the Richtmyer-Meshkov instability in a converging geometry, by Manuel Lombardini, Ralf Deiterding, D.I. Pullin Quality assessment in LES of a compressible swirling mixing layer, by Sebastian R. Muller, Leonhard Kleiser Accuracy of large-eddy simulation of premixed turbulent combustion, by A.W. Vreman, R.J.M. Bastiaans, B.J. Geurts Mesh dependency of turbulent reacting large-eddy simulations of a gas turbine combustion chamber, by Guillaume Boudier, Gabriel Staffelbach, Laurent Y.M. Gicquel, Thierry J. Poinsot Analysis of SGS particle dispersion model in LES of channel flow, by Jacek Potorski, Miroslaw Luniewski Numerical Data for Reliability of LES for Non-isothermal Multiphase Turbulent Channel Flow, by Marek Jaszczur, Luis M. Portela Lagrangian tracking of heavy particles in large-eddy simulation of turbulent channel fl

Is plane-channel flow a friendly case for the testing of large-eddy simulation subgrid-scale models?

We present the grid-convergence behavior of channel-flow direct numerical simulations (DNS) at coarse resolutions typically encountered in large-eddy simulation subgrid-model testing. An energy-conservative discretization method is used to systematically vary the streamwise (Nx) and spanwise (Nz) resolution. We observe that the skin friction does not converge monotonously, and at coarse resolutions, a line of Nx–Nz combinations is found where the error on the skinfriction is zero. Along this line, mean profiles are evaluated and found to fit surprisingly well fully resolved DNS results. The location of this line is shown to depend on the Reynolds number and the wall-normal resolution.

Sensitivity analysis of large-eddy simulations to subgrid-scale-model parametric uncertainty using polynomial chaos

We address the sensitivity of large-eddy simulations (LES) to parametric uncertainty in the subgrid-scale model. More specifically, we investigate the sensitivity of the LES statistical moments of decaying homogeneous isotropic turbulence to the uncertainty in the Smagorinsky model free parameter Cs (i.e. the Smagorinsky constant). Our sensitivity methodology relies on the non-intrusive approach of the generalized Polynomial Chaos (gPC) method; the gPC is a spectral non-statistical numerical method well-suited to representing random processes not restricted to Gaussian fields. The analysis is carried out at Reλ = 100 and for different grid resolutions and Cs distributions. Numerical predictions are also compared to direct numerical simulation evidence. We have shown that the different turbulent scales of the LES solution respond differently to the variability in Cs. In particular, the study of the relative turbulent kinetic energy distributions for different Cs distributions indicates that small scales are mainly affected by changes in the subgrid-model parametric uncertainty.

Sensitivity analysis of initial condition parameters on the transitional temporal turbulent mixing layer

This paper aims at determining the most influential inlet turbulence parameters on the downstream transitional mixing region. To this end, a stochastic method is developed to generate a divergence-free random velocity field with a prescribed energy distribution in physical and wave-number space. In addition, predetermined integral length scales can be established. Ten direct numerical simulations of a temporally evolving transitional turbulent mixing layer are examined in detail. Simulation results show a large disparity in mean and instantaneous turbulent quantities, mainly effected by the energy spectrum, the integral length scale and the divergence freeness of the initial field.

Optimality of the dynamic procedure for large-eddy simulations

We present a database analysis to obtain a precise evaluation of the accuracy limitations associated with the popular dynamic eddy-viscosity model in large-eddy simulation. We consider decaying homogeneous isotropic turbulence at two different Reynolds numbers, i.e., Rel = 50 and 100. The large-eddy simulation errors associated with the dynamic model are compared with those arising in the “static” Smagorinsky model. A large number of systematically varied simulations using the Smagorinsky model provides a detailed impression of the dependence of the total simulation error on sid the spatial resolution and siid the resolution of the subgrid dissipation length. This error behavior also induces an “optimal refinement trajectory” which specifies the particular Smagorinsky parameter, in terms of the spatial resolution, for which the total error is minimal. In contrast, the dynamic model gives rise to a self-consistently determined “dynamic trajectory” that represents the dependence of the dynamic coefficient on the spatial resolution. This dynamic trajectory is compared with the optimal refinement trajectory as obtained from the full database analysis of the Smagorinsky fluid. It is shown that the dynamic procedure in which the top-hat test filter is adopted, predicts values for the eddy viscosity as function of resolution and Reynolds number, which quite closely follow the main trends established in the optimal refinement trajectory. Furthermore, a sensitivity analysis, including dependency on test-filter width and filter shape, is discussed. Total simulation errors, due to interacting discretization, and modeling errors associated with the dynamic procedure may be a factor 2 higher compared to the optimum; still the dynamic procedure represents one of the very few self-contained and efficient error-reduction strategies when increasing the spatial resolution.

Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms

As a generalization of the mass–flux based classical stream tube, the concept of momentum and energy transport tubes is discussed as a flow visualization tool. These transport tubes have the property that no fluxes of momentum or energy exist over their respective tube mantles. As an example application using data from large eddy simulation, such tubes are visualized for the mean-flow structure of turbulent flow in large wind farms, in fully developed wind-turbine-array boundary layers. The three-dimensional organization of energy transport tubes changes considerably when turbine spacings are varied, enabling the visualization of the path taken by the kinetic energy flux that is ultimately available at any given turbine within the array.