Abstract. The high computational demand of large-eddy simulations (LESs) remains the biggest obstacle for a wider applicability of the method in the field of wind energy. Recent progress of GPU-based (graphics processing unit) lattice Boltzmann frameworks provides significant performance gains alleviating such constraints. The presented work investigates the potential of LES of wind turbine wakes using the cumulant lattice Boltzmann method (CLBM). The wind turbine is represented by the actuator line model (ALM). The implementation is validated and discussed by means of a code-to-code comparison to an established finite-volume Navier–Stokes solver. To this end, the ALM is subjected to both laminar and turbulent inflow while a standard Smagorinsky sub-grid-scale model is employed in the two numerical approaches. The resulting wake characteristics are discussed in terms of the first- and second-order statistics as well the spectra of the turbulence kinetic energy. The near-wake characteristics in laminar inflow are shown to match closely with differences of less than 3 % in the wake deficit. Larger discrepancies are found in the far wake and relate to differences in the point of the laminar-turbulent transition of the wake. In line with other studies, these differences can be attributed to the different orders of accuracy of the two methods. Consistently better agreement is found in turbulent inflow due to the lower impact of the numerical scheme on the wake transition. In summary, the study outlines the feasibility of wind turbine simulations using the CLBM and further validates the presented set-up. Furthermore, it highlights the computational potential of GPU-based LBM implementations for wind energy applications. For the presented cases, near-real-time performance was achieved using a single, off-the-shelf GPU on a local workstation.
An analytical model for representing body forces in numerical actuator disc models of wind turbines is developed and validated. The model is based on the assumption that the rotor disc is subject to a constant circulation modified for tip and root effects. The model comprises expressions for both the axial and the azimuthal force distributions, and is generalized to be utilized for all kinds of inflow, including wind shear, turbulence, and shadow effects in wind farms. The advantage of the model is that it does not depend on any detailed knowledge concerning the wind turbine being analysed, but only requires knowledge regarding the rated wind speed and nameplate capacity. To validate the analytical model, results are compared to numerically generated results using detailed information regarding geometry and airfoil data for the 2 MW Tjaereborg wind turbine and the 10MW DTU reference turbine. The comparisons show very good agreement between the loadings using the new analytical model and the airfoil data based method for the two tested wind turbines, demonstrating that the analytical model represents a simple and reliable way of introducing body forces in actuator disc simulations without any prior knowledge of the wind turbine being analysed.
The growing use of large-eddy simulations for the modelling of wind farms makes the need for efficient numerical frameworks more essential than ever. GPU-accelerated implementations of the Lattice Boltzmann Method (LBM) have shown to provide significant performance gains over classical Navier-Stokes-based computational fluid dynamics. Yet, their use in the field of wind energy remains limited to date. In this fundamental study the cumulant LBM is scrutinised for actuator line simulations of wind turbines. The numerical sensitivity of the method in a simple uniform inflow is investigated with respect to spatial and temporal resolution as well as the width of the actuator line’s regularisation kernel. Comparable accuracy and slightly better stability properties are shown in relation to a standard Navier-Stokes implementation. The results indicate the overall suitability of the cumulant LBM for wind turbine wake simulations. The potential of the LBM for future wind energy applications is clarified by means of a brief comparison of computational performance.
The lattice Boltzmann method (LBM) sees a growing popularity in the field of atmospheric sciences and wind energy, largely due to its excellent computational performance. Still, LBM large-eddy simulation (LES) studies of canonical atmospheric boundary layer flows remain limited. One reason for this is the early stage of development of LBM-specific wall models. In this work, we discuss LBM–LES of isothermal pressure-driven rough-wall boundary layers using a cumulant collision model. To that end, we also present a novel wall modeling approach, referred to as inverse momentum exchange method (iMEM). The iMEM enforces a wall shear stress at the off-wall grid points by adjusting the slip velocity in bounce-back boundary schemes. In contrast to other methods, the approach does not rely on the eddy viscosity, nor does it require the reconstruction of distribution functions. Initially, we investigate different aspects of the modeling of the wall shear stress, i.e., an averaging of the input velocity as well as the wall-normal distance of its sampling location. Particularly, sampling locations above the first off-wall node are found to be an effective measure to reduce the occurring log-layer mismatch. Furthermore, we analyze the turbulence statistics at different grid resolutions. The results are compared to phenomenological scaling laws, experimental, and numerical references. The analysis demonstrates a satisfactory performance of the numerical model, specifically when compared to a well-established mixed pseudo-spectral finite difference (PSFD) solver. Generally, the study underlines the suitability of the LBM and particularly the cumulant LBM for computationally efficient LES of wall-modeled boundary layer flows.
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