Abstract
The lattice Boltzmann method (LBM) has recently been used to simulate wave propagation, one of the challenging aspects of wind turbine modeling and simulation. However, standard LB methods suffer from the instability that occurs at low viscosities and from its characteristic lattice uniformity, which results in issues of accuracy and computational efficiency following mesh refinement. The local radial point interpolation cumulant lattice Boltzmann method (LRPIC-LBM) is proposed in this paper to overcome these shortcomings. The LB equation is divided into collision and streaming steps. The collision step is modeled by the cumulant method, one of the stable LB methods at low viscosities. In addition, the streaming step, which is naturally a pure advection equation, is discretized in time and space using the Lax–Wendroff scheme and the local radial point interpolation method (RPIM), a mesh free method. We describe the propagation of planar acoustic waves, including the temporal decay of a standing plane wave and the spatial decay of a planar acoustic pulse. The analysis of these specific benchmark problems has yielded qualitative and quantitative data on acoustic dispersion and dissipation, and their deviation from analytical results demonstrates the accuracy of the method. We found that the LRPIC-LBM replicates the analytical results for different viscosities, and the errors of the fundamental acoustic properties are negligible, even for quite low resolutions. Thus, this method may constitute a useful platform for effectively predicting complex engineering problems such as wind turbine simulations, without parameter dependencies such as the number of points per wavelength Nppw and resolution σ or the detrimental effect caused by the use of coarse grids found in other accurate and stable LB models.
Highlights
Evidence of early sailing boats on the Nile and of Persian pumps and mills from the first century B.C. shows humans have been interested in Wind Energy since ancient times [1]
The aim of this paper is to study the capability of the local radial point interpolation cumulant lattice Boltzmann method (LBM) (LRPIC-LBM) to simulate the propagation of planar acoustic waves, including the temporal decay of a standing plane wave and the spatial decay of a planar acoustic pulse of Gaussian shape and calculate the deviation from theoretical results, and to determine whether this method might be useful for wind turbine problems
Numerical studies are conducted for the propagation of planar acoustic waves, concentrating on numerical dissipation and dispersion
Summary
Evidence of early sailing boats on the Nile and of Persian pumps and mills from the first century B.C. shows humans have been interested in Wind Energy since ancient times [1]. A wind turbine is defined as a device which converts the wind’s kinetic energy into electrical energy [2,3] It plays a key role on producing intermittent renewable energy and implementing a strategy to lower costs and reducing the reliance on fossil fuels [4,5]. Wind turbines have unique aerodynamic and aeroacoustic behavior that makes their prediction most challenging [6,7], their simulation needs an enormous number of grid points or cells, and long enough time samples [8]. Researchers and centers such as the National Renewable Energy Laboratory (NREL) and the National.
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