Fernando Porté-Agel

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.

ON MONIN-OBUKHOV SIMILARITY IN THE STABLE ATMOSPHERIC BOUNDARY LAYER

Atmospheric measurements from several field experiments have been combined to develop a better understanding of the turbulence structure of the stable atmospheric boundary layer. Fast response wind velocity and temperature data have been recorded using 3-dimensional sonic anemometers, placed at severalheights (≈1 m to 4.3 m) above the ground. The measurements wereused to calculate the standard deviations of the three components of the windvelocity, temperature, turbulent kinetic energy (TKE) dissipation andtemperature variance dissipation. These data were normalized and plottedaccording to Monin–Obukhov similarity theory. The non-dimensional turbulencestatistics have been computed, in part, to investigate the generalapplicability of the concept of z-less stratification for stable conditions. From the analysis of a data set covering almost five orders ofmagnitude in the stability parameter ζ = z/L (from near-neutral tovery stable atmospheric stability), it was found that this concept does nothold in general. It was only for the non-dimensional standard deviation oftemperature and the average dissipation rate of turbulent kinetic energythat z-less behaviour has been found. The other variables studied here(non-dimensional standard deviations of u, v, and w velocity components and dissipation of temperature variance) did not follow the concept of z-less stratification for the very stable atmospheric boundary layer. An imbalance between production and dissipation of TKE was found for the near-neutral limit approached from the stable regime, which matches with previous results for near-neutral stability approached from the unstable regime.

Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer

When deployed as large arrays, wind turbines significantly interact among themselves and with the atmospheric boundary layer. In this study, we integrate a three-dimensional large-eddy simulation with an actuator line technique to examine the characteristics of wind-turbine wakes in an idealized wind farm inside a stable boundary layer (SBL). The wind turbines, with a rotor diameter of 112m and a tower height of 119m, were “immersed” in a well-known SBL case that bears a boundary layer height of approximately 175m. Two typical spacing setups were adopted in this investigation. The super-geostrophic low-level jet near the top of the boundary layer was eliminated owing to the energy extraction and the enhanced mixing of momentum. Non-axisymmetric wind-turbine wakes were observed in response to the non-uniform incoming turbulence, the Coriolis effect, and the rotational effects induced by blade motion. The Coriolis force caused a skewed spatial structure and drove a part of the turbulence energy away from th...

Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain

The accuracy of large-eddy simulations (LESs) of the atmospheric boundary layer (ABL) over complex terrain relies on the ability of the subgrid-scale (SGS) models to capture the effect of subgrid turbulent fluxes on the resolved fields of velocity and scalars (e.g., heat, water vapor, and pollutants). A common approach consists of parameterizing the SGS stresses and fluxes using eddy viscosity and eddy diffusivity models, respectively. These models require the specification of two parameters: the Smagorinsky coefficient in the eddy viscosity model and, in addition, the SGS Schmidt/Prandtl number in the eddy diffusivity model. This is complicated by the dependence of the coefficients on local conditions such as distance to the ground, mean shear, and atmospheric stability. In this study, scale-dependent dynamic SGS models are used in conjunction with Lagrangian averaging to compute both the Smagorinsky coefficient and the SGS Schmidt (or Prandtl) number dynamically as the flow evolves in both space and time based on the local dynamics of the resolved scales. These tuning-free models are implemented in LES of both homogeneous and heterogeneous neutral atmospheric boundary layers with surface fluxes of a passive scalar. In the homogeneous simulations the models are shown to accurately predict the resolved flow statistics (mean profiles and spectra of velocity and scalar concentration) and spatial distributions of the SGS model coefficients and parameters. In simulations over heterogeneous surfaces both coefficients adjust in a self-consistent way to horizontal flow inhomogeneities associated with changes in surface conditions. For smooth-to-rough (rough-to-smooth) abrupt changes in surface roughness the Smagorinsky coefficient decreases (increases) in response to increased (decreased) mean shear and flow anisotropy associated with these transitions. The SGS Schmidt number also adjusts to inhomogeneities in the scalar field associated with changes in surface scalar flux. This illustrates the need for local calculation of model coefficients and brings into question the common practice of using a constant SGS Schmidt/Prandtl number in LES of the ABL.

Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: A scale-dependent dynamic modeling approach

Abstract A new tuning-free subgrid-scale model, termed locally averaged scale-dependent dynamic (LASDD) model, is developed and implemented in large-eddy simulations (LES) of stable boundary layers. The new model dynamically computes the Smagorinsky coefficient and the subgrid-scale Prandtl number based on the local dynamics of the resolved velocity and temperature fields. Overall, the agreement between the statistics of the LES-generated turbulence and some well-established empirical formulations and theoretical predictions (e.g., the local scaling hypothesis) is remarkable. Moreover, the simulated statistics obtained with the LASDD model show relatively little resolution dependence for the range of grid sizes considered here. In essence, it is shown here that the new LASDD model is a robust subgrid-scale parameterization for reliable, tuning-free simulations of stable boundary layers, even with relatively coarse resolutions.

Simulation of Turbulent Flow Inside and Above Wind Farms: Model Validation and Layout Effects

A recently-developed large-eddy simulation framework is validated and used to investigate turbulent flow within and above wind farms under neutral conditions. Two different layouts are considered, consisting of thirty wind turbines occupying the same total area and arranged in aligned and staggered configurations, respectively. The subgrid-scale (SGS) turbulent stress is parametrized using a tuning-free Lagrangian scale-dependent dynamic SGS model. The turbine-induced forces are modelled using two types of actuator-disk models: (a) the ‘standard’ actuator-disk model (ADM-NR), which calculates only the thrust force based on one-dimensional momentum theory and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses blade-element momentum theory to calculate the lift and drag forces (that produce both thrust and rotation), and distributes them over the rotor disk based on the local blade and flow characteristics. Validation is performed by comparing simulation results with turbulence measurements collected with hot-wire anemometry inside and above an aligned model wind farm placed in a boundary-layer wind tunnel. In general, the ADM-R model yields improved predictions compared with the ADM-NR in the wakes of all the wind turbines, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces in the ADM-R appear to be important. Another advantage of the ADM-R model is that, unlike the ADM-NR, it does not require a priori specification of the thrust coefficient (which varies within a wind farm). Finally, comparison of simulations of flow through both aligned and staggered wind farms shows important effects of farm layout on the flow structure and wind-turbine performance. For the limited-size wind farms considered in this study, the lateral interaction between cumulated wakes is stronger in the staggered case, which results in a farm wake that is more homogeneous in the spanwise direction, thus resembling more an internal boundary layer. Inside the staggered farm, the relatively longer separation between consecutive downwind turbines allows the wakes to recover more, exposing the turbines to higher local wind speeds (leading to higher turbine efficiency) and lower turbulence intensity levels (leading to lower fatigue loads), compared with the aligned farm. Above the wind farms, the area-averaged velocity profile is found to be logarithmic, with an effective wind-farm aerodynamic roughness that is larger for the staggered case.

A scale-dependent dynamic model for scalar transport in large-eddy simulations of the atmospheric boundary layer

An important challenge in large-eddy simulationsof the atmospheric boundarylayer is the specification of the subgrid-scale(SGS) model coefficient(s)and, in particular, how to account for factorssuch as position in the flow,grid/filter scale and atmospheric stability.A dynamic SGS model (thatassumes scale invariance of the coefficients)is implemented in simulationsof a neutral boundary layer with a constantand uniform surface flux of apassive scalar. Results from our simulationsshow evidence that the lumpedcoefficient in the eddy-diffusion modelcomputed with the dynamic proceduredepends on scale. This scale dependence isstronger near the surface, and itis more important for the scalar than for thevelocity field (Smagorinskycoefficient) due to the stronger anisotropicbehaviour of scalars. Based onthese results, a new scale-dependent dynamicmodel is developed for theeddy-diffusion lumped coefficient. The newmodel, which is similar to theone proposed earlierfor the Smagorinsky coefficient,is fully dynamic, thus not requiring anyparameter specification or tuning.Simulations with the scale-dependent dynamicmodel yield the expected trendsof the coefficients as functions of positionand filter/grid scale.Furthermore, in the surface layer the newmodel gives improved predictionsof mean profiles and turbulence spectra ascompared with the traditionalscale-invariant dynamic model.

A Priori Field Study of the Subgrid-Scale Heat Fluxes and Dissipation in the Atmospheric Surface Layer

Field measurements are carried out to study statistical properties of the subgrid-scale (SGS) heat fluxes and SGS dissipation of temperature variance in the atmospheric surface layer, and to evaluate the ability of several SGS models to reproduce these properties. The models considered are the traditional eddy-diffusion model, the nonlinear (gradient) model, and a mixed model that is a linear combination of the other two. High-resolution wind velocity and temperature fields are obtained from arrays of 3D sonic anemometers placed in the surface layer. The basic setup consists of two horizontal parallel arrays (seven sensors in the lower array and five sensors in the upper array) at different heights (2.4 and 2.9 m, respectively). Data from this setup are used to compute the SGS heat flux and dissipation of temperature variance by means of 2D filtering in horizontal planes, invoking Taylor’s hypothesis. Model coefficients are measured from the data by requiring the real and modeled timeaveraged dissipation rates to match. Various other experimental setups that differ mainly in the separation between the sensors are utilized to show that filter size has a considerable effect on the various model coefficients near the ground. For the basic setup, conditional averaging is used to study the relation between large-scale coherent structures (sweeps and ejections) and the SGS quantities. It is found that under unstable conditions, negative SGS dissipation, indicative of backscatter of temperature variance from the subgrid scales to the resolved field, is most important during the onset of ejections transporting relatively warm air upward. Large positive SGS dissipation of temperature variance is associated with the end of ejections (and/or the onset of sweeps) characterized by strong drops in temperature and vertical velocity under unstable conditions. These results are also supported by conditionally sampled 2D (streamwise and vertical) velocity and temperature distributions, obtained using an additional setup consisting of the 12 anemometers placed in a vertical array. The nonlinear and mixed model reproduce the observations better than the eddy-diffusion model.

Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary-Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-Eddy Simulations

The ‘local scaling’ hypothesis, first introduced by Nieuwstadt two decades ago, describes the turbulence structure of the stable boundary layer in a very succinct way and is an integral part of numerous local closure-based numerical weather prediction models. However, the validity of this hypothesis under very stable conditions is a subject of ongoing debate. Here, we attempt to address this controversial issue by performing extensive analyses of turbulence data from several field campaigns, wind-tunnel experiments and large-eddy simulations. A wide range of stabilities, diverse field conditions and a comprehensive set of turbulence statistics make this study distinct

Wind-tunnel study of surface boundary conditions for large-eddy simulation of turbulent flow past a rough-to-smooth surface transition

A wind-tunnel experiment was performed to test surface boundary condition formulations for large-eddy simulation downwind of a rough-to-smooth surface transition in a turbulent boundary layer for (Reτ ≈ 1.5 × 104). Single and x-wire anemometers were used to obtain simultaneous high-resolution measurements of surface shear stress and wind velocity at different heights and positions downwind of the transition. One-dimensional filtering, using Taylors hypothesis, was used to obtain filtered signals of both velocity and surface shear stress. Experimental results show substantial differences between measured and modelled shear stress using standard boundary conditions based on the direct application of the similarity theory (the log law under neutral conditions) with local fluctuating filtered velocities. Those errors affect both the average value as well as higher order statistics of the predicted surface shear stress. The best performance is obtained with a model that calculates the average surface shear st...