Multi-objective Optimization of Horizontal Axis Wind Turbine Arrays: Impact of Spacing Distance on Noise Generation and Power Efficiency

Document Type : Regular Article

Authors

1 Laboratory of Green and Mechanical Development (LGMD), Ecole Nationale Polytechnique -ENP. P.B. 182 EL Harrach, Algiers, 16200, Algeria

2 Arts et Métiers Institute of Technology, CNAM, LIFSE, F-75013, Paris, France

10.47176/jafm.19.1.3680

Abstract

This work explores the effect of spacing between co-axially positioned Horizontal Axis Wind Turbines (HAWTs) on their aerodynamic behavior and acoustic emissions under uniform inflow conditions. The aerodynamic simulations employ the Actuator Disk Method (ADM) integrated within an Unsteady Reynolds-Averaged Navier-Stokes (URANS) framework, utilizing the standard k-ε turbulence model to resolve near-wake turbulent structures. For noise prediction, the Ffowcs Williams-Hawkings (FW-H) acoustic analogy is applied using the Farassat-1A formulation on a permeable spherical surface surrounding the rotor to estimate the generated acoustic pressures. These pressure signals served as input sources for far-field noise computations based on the Linearized Euler Equations (LEE). The findings demonstrate that wake interactions significantly influence the downstream turbine's performance and acoustic output in multiple-turbine arrangements. A multi-objective optimization process was carried out to achieve a trade-off between energy production and acoustic emissions, identifying an inter-turbine spacing of 6D as an optimal configuration. The study also emphasizes the limitations of relying solely on single-turbine aeroacoustic models for wind farm analysis, underscoring the necessity of full-scale aeroacoustic evaluation when considering wake effects and acoustic interference among turbines. 

Keywords

Main Subjects


Amoura, A., Khelladi, S., Smaili, A., & Hamlaoui, M. N. (2022). Toward a Numerical Modeling of Aeroacoustics Noise Induced by Wind Turbine Farm Using Linearized Euler Equations. International Conference on Advanced Renewable Energy Systems, (pp. 95–103). https://doi.org/10.1007/978-981-99-2777-7_11
Amoura, A., Khelladi, S., Smaili, A., & Hamlaoui, M. N. (2025). Validation of a Hybrid Approach for Wind Turbine Noise Prediction Using the Linearized Euler Equations. In Technological and Innovative Progress in Renewable Energy Systems: Proceedings of the 2024 International Renewable Energy Days (IREN Days' 2024). (pp. 97–100). Springer. https://doi.org/10.1007/978-3-031-71926-4_16
Boorsma, K.; Schepers, J. G. (2014). New MEXICO experiment: Preliminary overview with initial validation. ECN.
Boorsma, K., & Schepers, J. G. (2016). Rotor experiments in controlled conditions continued: New Mexico. Journal of Physics: Conference Series, 753, p. 022004. 753, p. 022004. 753, p. 022004. https://doi.org/10.1088/1742-6596/753/2/022004
Brentner, K. S., & Farassat, F. (1998). Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces. AIAA Journal, 36, 1379–1386. https://doi.org/10.2514/2.558.
Broatch, A., Navarro, R., Garcı́a-Tı́scar, J., & Ramı́rez, F. N. (2024). Evaluation of different FW-H surfaces and modal decomposition techniques for the acoustic analysis of UAV propellers through detached eddy simulations. Aerospace Science and Technology, 146, 108956. https://doi.org/10.1016/j.ast.2024.108956
Cao, J. F., Zhu, W. J., Shen, W. Z., Sørensen, J. N., & Sun, Z. Y. (2020). Optimizing wind energy conversion efficiency with respect to noise: A study on multi-criteria wind farm layout design. Renewable Energy, 159, 468–485. https://doi.org/10.1016/j.renene.2020.05.084
Choi, N. J. (2013). Numerical study on the horizontal axis turbines arrangement in a wind farm: Effect of separation distance on the turbine aerodynamic power output. Journal of Wind Engineering and Industrial Aerodynamics, 117, 11-17. https://doi.org/10.1016/j.jweia.2013.04.005
Colas, J., Emmanuelli, A., Dragna, D., Blanc-Benon, P., Cotté, B., & Stevens, R. (2023, June). Exploring the effect of wind farm flow on wind turbine noise propagation through numerical simulations.
Epikhin, A. (2021). Validation of the developed open source library for far-field noise prediction. Proceedings of the 27th International Congress on Sound and Vibration, Denver, Colorado. https://doi.org/10.5281/zenodo.5906668
Epikhin, A., Evdokimov, I., Kraposhin, M., Kalugin, M., & Strijhak, S. (2015). Development of a dynamic library for computational aeroacoustics applications using the OpenFOAM open source package. Procedia Computer Science, 66, 150–157. https://doi.org/10.1016/j.procs.2015.11.018
Farassat, F. (2007). Derivation of Formulations 1 and 1A of Farassat. Tech. rep.
Glauert, H. (1963). Aerodynamic Theory: A General Review of Progress, volume IV, chapter Division L, Airplane Propellers. Aerodynamic Theory: A General Review of Progress, volume IV, chapter Division L, Airplane Propellers. Dover Publications, Inc., New York, NY.
Global Wind Energy Council. (2024). Global Wind Report 2024. Global Wind Report 2024. https://gwec.net/global-wind-report-2024/
Grady, S. A., Hussaini, M. Y., & Abdullah, M. M. (2005). Placement of wind turbines using genetic algorithms. Renewable Energy, 30, 259–270. https://doi.org/10.1016/j.renene.2004.05.007
Hamlaoui, M. N., Bouhelal, A., Smaili, A., & Fellouah, H. (2024a). An Engineering Approach to Improve Performance Predictions for Wind Turbine Applications: Comparison with Full Navier-Stokes Model and Experimental Measurements. Journal of Applied Fluid Mechanics, 17, 1379–1397. https://doi.org/10.47176/jafm.17.7.2404
Hamlaoui, M. N., Bouhelal, A., Smaili, A., Khelladi, S., & Fellouah, H. (2024b). An inverse CFD actuator disk method for aerodynamic design and performance optimization of Horizontal Axis Wind Turbine blades. Energy Conversion and Management, 316, 118818. https://doi.org/https://doi.org/10.1016/j.enconman.2024.118818
Hamlaoui, M. N., Smaili, A., & Fellouah, H. (2021a). Improved stall delay model for hawt performance predictions using 3d navier-stokes solver and actuator disk method. Journal of Applied Fluid Mechanics, 15, 37–50. https://doi.org/10.47176/jafm.15.01.32651
Hamlaoui, M. N., Smaili, A., & Fellouah, H. (2021b). New Stall Delay Approach for HAWT Performance Predictions using a CFD Hybrid Method. In AIAA Scitech 2021 Forum. https://doi.org/10.2514/6.2021-0951
Hamlaoui, M. N., Smaili, A., Dobrev, I., Pereira, M., Fellouah, H., & Khelladi, S. (2022). Numerical and experimental investigations of HAWT near wake predictions using Particle Image Velocimetry and Actuator Disk Method. Energy, 238, 121660. https://doi.org/https://doi.org/10.1016/j.energy.2021.121660
International standard IEC/TC 88.61400-11 Ed.2. (2012). Wind turbines - Part 11: Acoustic noise measurement techniques. Wind turbines - Part 11: Acoustic noise measurement techniques, 2. International Electrotechnical Commission/ Technical Committee.
International Standard ISO 3744. (2010). Acoustics-Determination of sound power levels and sound energy levels of noise sources using sound pressure - Engineering methods for an essentially free field over a reflecting plane. Acoustics-Determination of sound power levels and sound energy levels of noise sources using sound pressure - Engineering methods for an essentially free field over a reflecting plane. International Organization for Standardization.
International Standard ISO 9613-2. (1996). Acoustics-Attenuation of sound during propagation outdoors - Part 2: General method of calculation. Acoustics-Attenuation of sound during propagation outdoors - Part 2: General method of calculation. International Organization for Standardization.
International Standard ISO-1996-1. (2016). Acoustics — Description, measurement and assessment of environmental noise — Part 1: Basic quantities and assessment procedures. Acoustics — Description, measurement and assessment of environmental noise — Part 1: Basic quantities and assessment procedures. International Organization for Standardization.
Khelladi, S. (2024). DGFEM-CAA github repository, https://github.com/skhelladi/DGFEM-CAA/tree/main, accessed: 2025-07-17.
Khelladi, S., Nogueira, X., Bakir, F., & Colominas, I. (2011). Toward a higher order unsteady finite volume solver based on reproducing kernel methods. Computer Methods in Applied Mechanics and Engineering, 200, 2348–2362. https://doi.org/10.1016/j.cma.2011.04.001
Kim, D., Lee, G.-S., & Cheong, C. (2015). Inflow broadband noise from an isolated symmetric airfoil interacting with incident turbulence. Journal of Fluids and Structures, 55, 428–450. https://doi.org/10.1016/j.jfluidstructs.2015.03.015
Kwong, W. Y., Zhang, P. Y., Romero, D., Moran, J., Morgenroth, M., & Amon, C. (2012). Wind farm layout optimization considering energy generation and noise propagation. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 45028, pp. 323–332. https://doi.org/10.1115/DETC2012-71478
Legendre, C., DeBrye, B., Detandt, Y., Talbot, A., Poulos, A., & Raskin, M. (2018). Broadband Noise Prediction of Stochastic Sources Based on the Linearized Euler Equations. INTER-NOISE and NOISE-CON Congress and Conference Proceedings, 258, pp. 3217–3228.
Lin, M., & Porté-Agel, F. (2022). Large-eddy simulation of a wind-turbine array subjected to active yaw control. Wind Energy Science, 7, 2215–2230. https://doi.org/10.5194/wes-7-2215-2022
Luo, K. H., & Lai, H. (2006). A hybrid LES-acoustic analogy method for computational aeroacoustics. In Direct and Large-Eddy Simulation VI (pp. 537–544). Springer.
Masson, C., Smaïli, A., & Leclerc, C. (2001, October). Aerodynamic analysis of HAWTs operating in unsteady conditions. Wind Energy, 4, 1-22. https://doi.org/10.1002/we.43
Mittal, A. (2010). Optimization of the layout of large wind farms using a genetic algorithm. Master's thesis, Case Western Reserve University.
Nyborg, C. M., Fischer, A., Réthoré, P.-E., & Feng, J. (2023). Optimization of wind farm operation with a noise constraint. Wind Energy Science, 8, 255–276. https://doi.org/10.5194/wes-8-255-2023
Rahmani, R., Khairuddin, A., Cherati, S. M., & Pesaran, H. M. (2010). A novel method for optimal placing wind turbines in a wind farm using particle swarm optimization (PSO). 2010 Conference Proceedings IPEC, (pp. 134–139).
Robin, X., & Legendre, C. (2002). Aeroacoustic simulation of multiple wind turbine source interactions. 7th International Conference on Wind Turbine Noise Rotterdam. update, 2002.
Schepers, J. G., Boorsma, K., Cho, T., Gomez-Iradi, S., Schaffarczyk, P., Jeromin, A., Lutz, T., Meister, K., Stoevesandt, B., Schreck, S., & others. (2012). Final report of IEA task 29, Mexnet (phase 1): analysis of Mexico wind tunnel measurements.
Shen, W. Z., Mikkelsen, R., Sørensen, J. N., & Bak, C. (2005). Tip loss corrections for wind turbine computations. Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology, 8, 457–475. https://doi.org/10.1002/we.153
Shen, W. Z., Zhu, W. J., Barlas, E., & Li, Y. (2019). Advanced flow and noise simulation method for wind farm assessment in complex terrain. Renewable Energy, 143, 1812-1825. https://doi.org/https://doi.org/10.1016/j.renene.2019.05.140
Sorkhabi, S. Y., Romero, D. A., Yan, G. K., Gu, M. D., Moran, J., Morgenroth, M., & Amon, C. H. (2016). The impact of land use constraints in multi-objective energy-noise wind farm layout optimization. Renewable Energy, 85, 359–370. https://doi.org/10.1016/j.renene.2015.06.026
Tadamasa, A., & Zangeneh, M. (2011). Numerical prediction of wind turbine noise. Renewable Energy, 36, 1902-1912. https://doi.org/https://doi.org/10.1016/j.renene.2010.11.036
Tingey, E. B., & Ning, A. (2017). Trading off sound pressure level and average power production for wind farm layout optimization. Renewable, 114, 547–555. https://doi.org/10.1016/j.renene.2017.07.057
Wang, Z.-K., Djambazov, G., Lai, C.-H., & Pericleous, K. (2007). Numerical simulation of flow-induced cavity noise in self-sustained oscillations. Computing and Visualization in Science, 10, 123–134. https://doi.org/10.1007/s00791-006-0039-4
Wimshurst, A., & Willden, R. H. (2017). Analysis of a tip correction factor for horizontal axis turbines. Wind Energy, 20, 1515–1528. https://doi.org/10.1002/we.2106
Yang, T., Chen, X., Zhao, Q., & Zhao, G. (2022). Numerical study on the noise propagation characteristics of rotor in non-uniform downwash flowfield Based on Linearized Euler Equations. International Journal of Aeroacoustics, 21, 731–765. https://doi.org/10.1177/1475472X221136883
Zergane, S., Smaili, A., & Masson, C. (2018). Optimization of wind turbine placement in a wind farm using a new pseudo-random number generation method. Renewable Energy, 125, 166–171. https://doi.org/10.1177/1475472X221136883