Preprints
https://doi.org/10.5194/wes-2024-138
https://doi.org/10.5194/wes-2024-138
26 Nov 2024
 | 26 Nov 2024
Status: this preprint is currently under review for the journal WES.

Investigating the Relationship between Simulation Parameters and Flow Variables in Simulating Atmospheric Gravity Waves for Wind Energy Applications

Mehtab Ahmed Khan, Dries Allaerts, Simon J. Watson, and Matthew J. Churchfield

Abstract. Wind farms, particularly offshore clusters, are becoming larger than ever before. Besides influencing the surface wind flow and the inflow for downstream wind farms, large wind farms can trigger atmospheric gravity waves in the inversion layer and the free atmosphere aloft. Wind farm-induced gravity waves can cause adverse pressure gradients upstream of the wind farm, that contribute to the global blockage effect, and can induce favorable pressure gradients above and downstream of the wind farm that enhance wake recovery. Numerical modeling is a powerful means of studying these wind farm-induced atmospheric gravity waves, but it comes with the challenge of handling spurious reflections of these waves from domain boundaries. Typically, approaches which employ radiation boundary conditions and forcing zones are used to avoid these reflections. However, the simulation setup of these approaches heavily relies on ad-hoc processes. For instance, the widely used Rayleigh damping method requires ad-hoc tuning to produce a setup which may be only produce satisfactory results for a particular case. To provide more systematic guidance on setting up realistic simulations of atmospheric gravity waves, we conduct an LES study of flow over a 2D hill and through a wind farm canopy that explores the optimum domain size and damping layer setup depending on the fundamental parameters which determine the flow characteristics.

In this work, we only consider linearly stratified conditions (i.e., no inversion layer), thereby focusing on internal gravity waves in the free atmosphere and their reflections from the domain boundaries. This type of flow is governed by a single Froude number, which dictates most of the internal wave properties, such as wavelength, amplitude, and direction. This in turn will dictate the optimum domain size and Rayleigh damping layer setup. We find the effective horizontal and vertical wavelengths, (the representative wavelengths of the entire wave spectrum), to be the appropriate length scales to size the domain and damping layer thickness, and the optimal Rayleigh damping coefficient scales with the Brunt–Väisälä frequency.

Considering Froude numbers seen in wind farm applications, we propose recommendations to limit the reflections to less than 10 % of the total upwards propagating wave energy. Typically, damping is done at the top boundary, but given the non-periodic lateral boundary conditions of practical wind farm simulation domains, we find that damping the inflow-outflow boundaries is of equal importance to the top boundary. The Brunt–Väisälä frequency-normalized damping coefficient should be between 1 and 10. The damping layer thickness should be at least one effective vertical wavelength; damping layers exceeding 1.5 times the vertical wavelength are found to be unnecessary. The domain length and height should accommodate at least one effective horizontal and vertical wavelength, respectively. Moreover, Rayleigh damping does not damp the waves completely, and the non-damped energy might accumulate over the simulation time.

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Mehtab Ahmed Khan, Dries Allaerts, Simon J. Watson, and Matthew J. Churchfield

Status: open (until 29 Dec 2024)

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Mehtab Ahmed Khan, Dries Allaerts, Simon J. Watson, and Matthew J. Churchfield
Mehtab Ahmed Khan, Dries Allaerts, Simon J. Watson, and Matthew J. Churchfield

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Short summary
To guide realistic atmospheric gravity wave simulations, we conduct an LES study of flow over a 2D hill and through a wind farm canopy, examining optimal domain size and Rayleigh damping layer setup. Wave properties based on a Froude number determine optimal domain and damping parameters. Reasonably accurate solutions require the domain length exceed the effective horizontal wavelength, height and damping thickness equal a vertical wavelength, and normalized-damping coefficient between 1–10.
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