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.

Wind energy is among the fastest-growing sources of renewable energy worldwide. Understanding and mitigating the deleterious effects of interactions between wakes of multiple turbines is critical for the efficient utilization of the wind resource. In large wind farms, the wake interactions can limit the power density, or the power extracted per unit land area. The turbulent wake interactions also determine fatigue loads on downstream turbines, which has a direct bearing on the levelized cost of energy. Previous work has shown that wake losses are closely tied to wind farm layout parameters such as inter-turbine spacing

The idea of mounting multiple rotors per tower has been explored in recent years (

Analysis of the wake of a four-rotor turbine was carried out in our previous work

The results for the wake of an isolated turbine were confirmed recently in

Interactions between several multi-rotor wind turbines arranged in a four by four grid were studied using several Reynolds-averaged Navier–Stokes (RANS) simulations and one LES in

Schematic of

In this paper, we extend our previous work

The primary aim of this paper is to quantify the benefits associated with the wakes of multi-rotor turbines for a wide range of tip spacings, thrust coefficients and inter-turbine spacings using LES. A second aim is to develop an analytical modeling framework, combining elements from previously published studies, and to evaluate its ability to predict the mean velocity profiles in the wakes of multi-rotor wind farms. This study differs from that of

This paper is organized as follows. The LES methodology, details of the simulations and the analytical framework are described in Sect.

The LES-filtered incompressible Navier–Stokes equations are solved on a structured uniform Cartesian mesh using Fourier collocation in

Half-channel (HC) simulations are carried out using the concurrent precursor-simulation methodology

Precursor simulations (without turbines and with streamwise periodicity) are carried out first for 50 time units (1 time unit

Suite of isolated turbine (sets IT

The suite of simulations carried out is listed in Table

Field measurements and simulations reported in

An analytical modeling framework based on the model by

The combined effect of multiple turbine rotors has been modeled in the past using several empirical techniques. Primary among these are addition of the velocity deficits (implying linear addition of the momentum deficit), square root of the sum of the squares of the velocity deficits (implying addition of the kinetic energy deficit; also termed quadratic merging) and considering the largest deficit to be dominant. In this study, a hybrid between the first two approaches is found to give the best results. Appendix

This modeling framework involves two empirical parameters:

Precursor ABL simulation results are shown first in Fig.

Profiles of time- and horizontally averaged

Profiles of mean velocity deficit at the centerline and downstream of an isolated

Results of an isolated one-rotor turbine and an isolated four-rotor turbine with

Figure

Simulations with varying grid sizes (the IT

The added TKE profiles in Fig.

A change of

Isolated four-rotor turbines with varying tip spacings,

Contours of

Velocity profiles downstream of an isolated one-rotor turbine and isolated four-rotor turbines with different tip spacings:

An intuitive explanation for the increasing rate of wake recovery with increasing tip spacing is as follows. The characteristic length scale of the wake of the one-rotor turbine is diameter

The wakes of the individual rotors of a four-rotor turbine expand with downstream distance and eventually merge to form a single wake. The axial distance where individual wakes of the four rotors may be considered to have merged increases with increasing

The contour plot of TKE shown in Fig.

Effect of tip spacing on disk-averaged

A succinct representation of the effect of tip spacing on the wake of an isolated four-rotor turbine with respect to that of an isolated one-rotor turbine is shown in Fig.

Figure

The disk-averaged added turbulence intensity can be compared to that reported in Fig. 18b, d and f of

The IT2-

Effect of thrust coefficient on disk-averaged

The analytical modeling framework predicts the mean velocity deficits of the one-rotor and four-rotor turbines accurately. Empirical parameters values

Wind farms comprised of a line of five turbines aligned with each other and with the mean wind direction are studied here. These cases are labeled WF

The effect of tip spacing on the contours of velocity deficit and TKE is seen in Fig.

Contours of

Disk-averaged

The effect of tip spacing on four-rotor wind farms is quantified in Fig.

The velocity deficits of the four-rotor turbines are seen in Fig.

The relative powers of the turbines are shown in Fig.

The effect of axial spacing on the performance of four-rotor wind farms can be studied by comparing Fig.

Interaction between the effects of tip spacing and axial spacing is also seen when comparing Fig.

Disk-averaged

Figure

Effect of tip spacing, thrust coefficient and axial spacing on

The effect of all governing parameters (

Each data point in Fig.

To account for the differences in the front turbine power, the average power of turbines 2 through 5 is replotted in Fig.

Appendix

Predictions of the analytical modeling framework for wind farms comprised of a line of five turbines are examined in this section. The parameter

Wake widths extracted from three one-rotor LES with fixed

The wake growth rate parameter values for all turbines in the one-rotor wind farm simulations are compiled in Fig.

LES results and model predictions of

Model predictions are compared to LES results for two cases in Fig.

LES results and model predictions of relative power using spatially constant

The influence of using spatially constant values for the wake growth rate parameter on the model predictions is shown in Fig.

Relative power for one-rotor and four-rotor wind farms with fixed

Relative power for one-rotor and four-rotor wind farms with fixed

Relative power predictions for all the wind farm cases are compared to LES results in Figs.

The errors are seen to be smallest for the one-rotor cases. For one-rotor wind farms, typically, the power of the second turbine is smallest, and there is a slight recovery for turbines 3, 4 and 5. This behavior is reproduced well by the analytical model. In the four-rotor cases, the relative power saturates farther into the wind farm, typically at the third row for

In conclusion, the analytical modeling framework is capable of reproducing LES results of one-rotor and four-rotor wind farms with reasonable accuracy, comparable to previous results for one-rotor turbines

This paper is devoted to studying the turbulent wake of a multi-rotor wind turbine configuration and to comparing it with a conventional single-rotor wind turbine wake. The potential benefits offered by this configuration, with four rotors (with diameters

The LES results outlined in Sect.

In Sect.

The effect of smaller velocity deficits is reflected in the relative powers, or equivalently, the wake losses experienced by wind farms. Wind farms comprised of multi-rotor turbines always show benefits over similar wind farms comprised of one-rotor turbines. The benefits are due to smaller wake losses only for the first downstream turbine (i.e., the second turbine in the array) for a realistic tip spacing of

The analytical model predictions are sensitive to the tunable parameters. The results in Sects.

The actuator drag-disk model provides a crude representation of the processes occurring very near the turbine disks. While this crude representation is sufficient for the purposes of capturing the interactions between the turbines and the atmospheric boundary layer, future studies should focus on using the actuator-disk/line models with rotation of the blades included. Potential benefits associated with co-rotation and counter-rotation of the rotors in the multi-rotor configuration can be studied. Recent work by

A brief justification for following the hybrid linear-quadratic methodology of wake merging is provided in this Appendix.

Evaluation of linear and quadratic wake merging methods for

Figure

Figure

Thus, a hybrid linear-quadratic merging strategy is seen to give best results. It should be noted that this is an empirical choice, and a physics-based/first-principles approach for wake superposition is a topic of active research.

Finding an appropriate single-rotor turbine which can be considered as a reference against which a multi-rotor turbine can be compared is not straightforward. This is because the lower and upper pair of rotors in the four-rotor configuration are subjected to different wind speeds and turbulence levels as compared to each other and to the single rotor in the one-rotor configuration. In this work, we consider a single-rotor turbine with the same total frontal area, same thrust coefficient and same mean hub height as a multi-rotor turbine to be a reference. To test the appropriateness of this assumption, the potential power, computed as

Potential power and potential power normalized by one-rotor potential power for isolated turbines with varying tip spacings.

Single-rotor and multi-rotor turbines with the same rotor area, same mean hub height and same thrust coefficient have been considered to be equivalent in the main body of this paper. This equivalence was based on the “local” thrust coefficient,

In this Appendix, three additional one-rotor wind farm simulations are reported, with

Figure

Figure

In summary, this Appendix ensures that the qualitative conclusions regarding the benefits of the four-rotor wind farms remain unchanged, regardless of whether “1-Rot” (

Adding results of

Adding results of

The LES code used for these simulations is available on GitHub at

All authors jointly designed the numerical experiments and interpreted the results. NSG and ASG wrote the code and performed the simulations. NSG prepared the paper with contributions from all authors.

The authors declare that they have no conflict of interest.

Computational resources on TACC's Stampede2 cluster via NSF XSEDE Research Allocation TG-ATM170028 and on Stanford HPCC's Certainty cluster are gratefully acknowledged.

This paper was edited by Johan Meyers and reviewed by Søren Juhl Andersen and Paul van der Laan.