Hao Lu

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...

A modulated gradient model for large-eddy simulation: Application to a neutral atmospheric boundary layer

The subgrid-scale (SGS) parametrization represents a critical component of a successful large-eddy simulation (LES). It is known that in LES of high-Reynolds-number atmospheric boundary layer turbulence, standard eddy-viscosity models poorly predict mean shear in the near-wall region and yield erroneous velocity profiles. In this paper, a modulated gradient model is proposed. This approach is based on the Taylor expansion of the SGS stress and uses local equilibrium hypothesis to evaluate the SGS kinetic energy. To ensure numerical stability, a clipping procedure is used to avoid local kinetic energy transfer from unresolved to resolved scales. Two approaches are considered to specify the model coefficient: a constant value of 1 and a simple correction to account for the effects of the clipping procedure on the SGS energy production rate. The model is assessed through a systematic comparison with well-established empirical formulations and theoretical predictions of a variety of flow statistics in a neutr...

On the Impact of Wind Farms on a Convective Atmospheric Boundary Layer

With the rapid growth in the number of wind turbines installed worldwide, a demand exists for a clear understanding of how wind farms modify land-atmosphere exchanges. Here, we conduct three-dimensional large-eddy simulations to investigate the impact of wind farms on a convective atmospheric boundary layer. Surface temperature and heat flux are determined using a surface thermal energy balance approach, coupled with the solution of a three-dimensional heat equation in the soil. We study several cases of aligned and staggered wind farms with different streamwise and spanwise spacings. The farms consist of Siemens SWT-2.3-93 wind turbines. Results reveal that, in the presence of wind turbines, the stability of the atmospheric boundary layer is modified, the boundary-layer height is increased, and the magnitude of the surface heat flux is slightly reduced. Results also show an increase in land-surface temperature, a slight reduction in the vertically-integrated temperature, and a heterogeneous spatial distribution of the surface heat flux.

A modulated gradient model for scalar transport in large-eddy simulation of the atmospheric boundary layer

As a simple alternative to the standard eddy-diffusivity closure, a nonlinear subgrid-scale (SGS) flux model is introduced and implemented in simulations of a neutral atmospheric boundary layer and a stable atmospheric boundary layer. The new model computes the structure of the SGS flux (relative magnitude of the vector components) based on the normalized gradient vector, which is derived from the Taylor expansion of the exact SGS flux. The SGS magnitude is computed as the product of a SGS velocity scale and a SGS scalar concentration scale, which are estimated based on the local-equilibrium hypothesis. To resolve the instability issue of the original gradient model and ensure numerical stability, we adopt a clipping procedure to avoid local negative SGS dissipation rate of the scalar variance. The model formulation, using constant coefficients, is assessed through a systematic comparison with well-established theoretical predictions and reference results of various flow statistics. Simulation results obtained with the use of this new model show good agreement with the reference results and an evident improvement over results obtained using traditional eddy-diffusivity models. For instance, the new model can deliver the expected surface-layer similarity scalar profile and power-law scaling of the power spectrum of scalar fluctuation.

On the development of a dynamic non-linear closure for large-eddy simulation of the atmospheric boundary layer

A dynamic procedure is developed to compute the model coefficients in the recently introduced modulated gradient models for both momentum and scalar fluxes. The magnitudes of the subgrid-scale (SGS) stress and the SGS flux are estimated using the local equilibrium hypothesis, and their structures (relative magnitude of each of the components) are given by the normalized gradient terms, which are derived from the Taylor expansion of the exact SGS stress/flux. Previously, the two model coefficients have been specified on the basis of theoretical arguments. Here, we develop a dynamic SGS procedure, wherein the model coefficients are computed dynamically according to the statistics of the resolved turbulence, rather than provided a priori or ad hoc. Results show that the two dynamically calculated coefficients have median values that are approximately constant throughout the turbulent atmospheric boundary layer (ABL), and their fluctuations follow a near log-normal distribution. These findings are consistent with the fact that, unlike eddy-viscosity/diffusivity models, modulated gradient models have been found to yield satisfactory results even with constant model coefficients. Results from large-eddy simulations of a neutral ABL and a stable ABL using the new closure show good agreement with reference results, including well-established theoretical predictions. For instance, the closure delivers the expected surface-layer similarity profiles and power-law scaling of the power spectra of velocity and scalar fluctuations. Further, the Lagrangian version of the model is tested in the neutral ABL case, and gives satisfactory results.