Large eddy simulations (LESs) are performed to study the wakes of a multi-rotor wind turbine configuration comprising four identical rotors mounted on a single tower. The multi-rotor turbine wakes are compared to the wake of a conventional turbine comprising a single rotor per tower with the same frontal area, hub height and thrust coefficient. The multi-rotor turbine wakes are found to recover faster, while the turbulence intensity in the wake is smaller, compared to the wake of the conventional turbine. The differences with the wake of a conventional turbine increase as the spacing between the tips of the rotors in the multi-rotor configuration increases. The differences are also sensitive to the thrust coefficients used for all rotors, with more pronounced differences for larger thrust coefficients. The interaction between multiple multi-rotor turbines is contrasted with that between multiple single-rotor turbines by considering wind farms with five turbine units aligned perfectly with each other and with the wind direction. Similar to the isolated turbine results, multi-rotor wind farms show smaller wake losses and smaller turbulence intensity compared to wind farms comprised of conventional single-rotor turbines. The benefits of multi-rotor wind farms over single-rotor wind farms increase with increasing tip spacing, irrespective of the axial spacing and thrust coefficient. The mean velocity profiles and relative powers of turbines obtained from the LES results are predicted reasonably accurately by an analytical model assuming Gaussian radial profiles of the velocity deficits and a hybrid linear-quadratic model for the merging of wakes. These results show that a larger power density can be achieved without significantly increased fatigue loads by using multi-rotor turbines instead of conventional, single-rotor turbines.

Layout studies are critical in designing large wind farms, since wake effects can lead to significant reductions in power generation. Optimizing wind farm layout using computational fluid dynamics is practically unfeasible today because of their enormous computational requirements. Simple statistical models, based on geometric quantities associated with the wind farm layout, are therefore attractive because they are less demanding computationally. Results of large-eddy simulations of the Lillgrund (Sweden) offshore wind farm are used here to calibrate such geometry-based models. Several geometric quantities (e.g., blockage ratio, defined as the fraction of the swept area of a wind turbine that is blocked by upstream turbines) and their linear combinations are found to correlate very well (correlation coefficient of ~0.95) with the power generated by the turbines. Linear models based on these geometric quantities are accurate at predicting the farm-averaged power and are therefore used here to study layout effects in large wind farms. The layout parameters that are considered include angle between rows and columns, angle between incoming wind and columns (orientation), turbine spacings, and staggering of alternate rows. Each can impact wind power production positively or negatively, and their interplay is complex. The orientation angle is the most critical parameter influencing wake losses, as small changes in it can cause sharp variations in power. In general, for a prevailing wind direction, the orientation angle should be small (7.5°–20°) but not zero; staggering and spacing are beneficial; and nonorthogonal layouts may outperform orthogonal ones. This study demonstrates the utility of simple, inexpensive, and reasonably accurate geometry-based models to identify general principles governing optimal wind farm layout.

Large eddy simulations (LESs) of turbulent horizontal buoyant jets are carried out using a high-order numerical method and Sigma subgrid-scale (SGS) eddy-viscosity model, for a number of different Reynolds (Re) and Richardson (Ri) numbers. Simulations at previous experimental flow conditions (Re = 3200, 24, 000 and Ri = 0, 0.01) are carried out first, and the results are found to be qualitatively and quantitatively similar to the experimental results, thus validating the numerical methodology. The effect of varying Ri (values 2×10⁻⁴, 0.001, 0.005, and 0.01) and Re (3200 and 24, 000) is studied next. The presence of stable stratification on one side and unstable stratification on the other side of the jet centreline leads to an asymmetric development of horizontal buoyant jets. It is found that this asymmetry, the total radial spread and the vertical deflection are significantly affected by Ri, while Re affects only the radial asymmetry. The need for developing improved integral models, accounting for this asymmetry, is pointed out. Turbulent production and dissipation rates are investigated, and are found to be symmetric in the horizontal plane, but asymmetric in the mid-vertical plane. A previously proposed model, for correlation between the vertical component of the fluctuating scalar flux vector and the vertical cross-correlation component of the Reynolds tensor, is modified based on the current LES results. Instantaneous scalar and velocity fields are analysed to reveal the structure of horizontal buoyant jets. Similar to the developed turbulent jet, the flow close to the nozzle too is found to be markedly different in the stable and unstable stratification regions. Persistent coherent vortex rings are found in the stable stratification region, while intermittent breakdown of vortex rings into small-scale structures is observed in the unstable stratification region. Similarities and differences between the flow structures in the horizontal buoyant jet configuration and those in the jet in crossflow configuration are discussed. Finally, a dynamic mode decomposition analysis is carried out, which indicates that the flow in the unstable stratification region is more energetic and prone to instabilities, as compared to the flow in the stable stratification region.