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Numerical Modeling of Wind Turbine Wakes
Abstract
An aerodynamical model for studying three-dimensional flow fields about wind turbine rotors is presented. The developed algorithm combines a three-dimensional Navier-Stokes solver with a so-called actuator line technique in which the loading is distributed along lines representing the blade forces. The loading is determined iteratively using a bladeelement approach and tabulated airfoil data. Computations are carried out for a 500 kW Nordtank wind turbine equipped with three LM19.1 blades. The computations give detailed information about basic features of wind turbine wakes, including distributions of interference factors and vortex structures. The model serves in particular to analyze and verify the validity of the basic assumptions employed in the simple engineering models
... Note that the MRSL in Fig. 4 degenerates from Fig. 1, where the sub-rotors are represented with a single actuator disk (blue surface), and the lifting devices/wings are represented with four actuator lines (red surfaces). This simplification enables more efficient numerical modeling (Sorensen and Shen, 2002;Mikkelsen, 2004), and a detailed parameterization is provided in Sect. 3.4. ...
... A2). This allows avoiding the exceptionally high computational cost required to resolve the boundary layer around the complex geometry (Sorensen and Shen, 2002;Mikkelsen, 2004). These actuator methods are realized in OpenFOAM using a customized library building upon actuationDiskSource (a built-in library of OpenFOAM v2106) and turbinesFoam (Bachant et al., 2019), and we call it flyingActuationDiskSource (Li et al., 2024b). ...
... ξ ele denotes the position vector of the actuator element. The projection is done by the Gaussian normalization kernel, and it is introduced to improve the robustness of the numerical modeling (Sorensen and Shen, 2002;Mikkelsen, 2004), where ε is called the smearing factor. For the actuator elements of the MRSL's rotors, f ele = −T eleê x is assigned, and its smearing factor, denoted as ε R , is set to 1.0 , as it is commonly used for actuator disks (Mikkelsen, 2004;Wu and Porté-Agel, 2011). ...
Numerical simulations of wind farms consisting of innovative wind energy harvesting systems are conducted. The novel wind harvesting system is designed to generate strong lift (vertical force) with lifting devices. It is demonstrated that the trailing vortices generated by these lifting devices can substantially enhance wake recovery rates by altering the vertical entrainment process. Specifically, the wake recovery of the novel systems is based on vertical advection processes instead of turbulent mixing. Additionally, the novel wind energy harvesting systems are hypothesized to be feasible without requiring significant technological advancements, as they could be implemented as multi-rotor systems with lifting devices (MRSLs), where the lifting devices consist of large airfoil structures. Wind farms with these novel wind harvesting systems, namely MRSLs, are termed regenerative wind farms, inspired by the concept that the upstream MRSLs actively entrain energy for the downstream ones. With the concept of regenerative wind farming, much higher wind farm capacity factors are anticipated. Specifically, the simulation results indicate that wind farm efficiencies can be nearly doubled by replacing traditional wind turbines with MRSLs under the tested conditions, and this disruptive advancement can potentially lead to a profound reduction in the cost of future renewable energy.
... Such problems may include background shear [2], turbulence [3], multirotor interactions [4][5][6], blockage [7] and others. Secondly, aligned with its original introduction for wind turbine applications [1], the ALM enables simulation of the spatial and temporal structure of turbine wakes. Even when using high performance supercomputers, adequately resolving the wake region may be prohibitively expensive when a BR mesh is used to model the rotor. ...
... This kernel is characterised by its shape and size. The majority of implementations use a spherical Gaussian kernel proposed in the original ALM paper [1], but other shapes such as elliptical kernels have been proposed [12]. The size of the force smearing kernel that is represented by the standard deviation of the Gaussian function, , is a matter of ongoing discussion. ...
... Most methods attempt to eliminate the circulation-induced velocity that results from the lift force applied by the blade to yield the incident velocity that the blade experiences in the absence of the local blade-induced flow. Velocity sampling at the collocation point has been adopted by many authors [1,6,[15][16][17]. This is supported by the assumption that the perturbation velocity due to the foil's circulation vanishes at the collocation point [18]. ...
The actuator line method (ALM) is a widely used tool for the modelling of horizontal axis turbines and wind and tidal farm flows. The method uses a virtual blade representation to simulate the dynamics of wind turbines without the computational expense associated with resolving the blade geometry. Within the ALM, the flow is first sampled at each blade section, allowing for the calculation of the sectional lift and drag forces that are in turn imposed on the flow domain using a smearing kernel. In this work, the effect of the flow sampling method on the robustness of the ALM is discussed. Implementations of two widely used types of methods for horizontal axis wind turbines are tested: point sampling, where the flow is sampled at or near the collocation point, and volume average sampling where flow field information from multiple points centred at the collocation point is averaged into a representative blade‐local velocity vector. A third method, line average sampling, that was initially proposed for sampling flows from blade‐resolved simulations is adapted for the ALM framework. This method samples the flow symmetrically around a control element in order to eliminate the interference of the bound circulation, thus allowing the inflow velocity at the aerofoil to be determined. When evaluating power and thrust coefficients and the flow field at the rotor plane predicted by the ALM, the line average sampling approach is demonstrated to be more robust and converges faster with time step for two different rotors: a small wind rotor and a high‐solidity tidal rotor. This suggests that carefully selecting the sampling method could be key in alleviating the very strict time‐step restriction imposed by the ALM, a widely acknowledged limitation of the method. Such an advancement could contribute towards improving the computational efficiency and tractability of the method.
... These assumptions necessitate empirical corrections for phenomena such as dynamic inflow, yaw misalignment, and tip loss, classifying BEM-based methods as "low-fidelity." 5 On the other hand, fully resolved computational fluid dynamics (CFD) methods achieve the highest fidelity by capturing unsteady, three-dimensional flows around turbines. These methods accurately predict system responses under complex conditions, but their high computational cost makes them impractical for optimization tasks or large-scale wind farm analyses. ...
... [6][7][8][9] To bridge the gap between low-fidelity BEM methods and computationally expensive CFD, Sørensen and Shen introduced the actuator line model (ALM). 5 ALM uses radially distributed body forces along actuator lines representing the rotor blades. Unlike BEM, the angles of attack for blade elements are dynamically calculated within the CFD framework, avoiding overly simplified assumptions. ...
This paper presents an improved actuator line model (ALM) for wind turbine modeling. A multi-rigid body system and multiple control systems are incorporated to overcome limitations observed in conventional ALM, which are one-way coupling and the need for artificial parameters such as rotational speed, blade pitch angle, and yaw direction, which could introduce inaccuracies when applied to large-scale simulations. Furthermore, an entropic lattice Boltzmann method (ELBM) solver is used for flow field simulation. This model's efficacy is verified with conditions that match those of another study, using the widely studied NREL (National Renewable Energy Laboratory) 5 MW wind turbine. Additional comparison is also made with particle imaging velocimetry (PIV) measurements using a scaled NREL UAE Phase IV turbine. The utility of this model is demonstrated in the context of a single turbine under various wind speeds and two turbines in tandem with different spacings and wind speeds, showcasing its efficiency and accuracy.
... Although using CFD methods for calculation yields accurate results, substantial computational resources are necessitated, and a relatively prolonged calculation time is entailed. Sørensen and Shen [10], leveraging principles of fluid dynamics, introduced the actuator line model (ALM), which replaces wind turbine blades with virtual rotating lines subjected to volumetric forces. By solving the Navier-Stokes (N-S) equations, the forces on each blade element are calculated and then synthesized to efficiently and accurately compute the loads on the wind turbines under yawed conditions. ...
... Flowchart for the new modified model.One of the pivotal elements in applying this model lies in accurately determining the variable parameters m in Equation(10). This paper introduces two distinct methodologies for establishing the value of m. ...
The yaw state constitutes a typical operating condition for wind turbines. However, the widely used Blade Element Moment (BEM) theory, due to its adoption of planar disc assumptions, introduces certain computational inaccuracies in yaw conditions. This research aims to develop a new modified BEM method by replacing the momentum theory in traditional BEM with the Madsen analytical linear two-dimensional actuator disc model in order to enhance the accuracy in calculating the aerodynamic performance of yawed wind turbines. Two approaches are introduced to determine the variable parameters in the new modified model: one based on traditional BEM predictions in non-yaw conditions and the other using empirical values determined using experimental data. The new modified model is evaluated against experimental data, CENER FAST, and HAWC2 for the MEXICO rotor. From the comparisons, the new modified method demonstrates closer agreements with experimental values, particularly in the mid and outer parts of the blades. At a wind speed of 15 m/s and a yaw angle of 30°, the discrepancies between computation and measurement are reduced by at least 2.33, 1.22, and 3.25 times at spanwise locations of 60%Radius (R), 82%R, and 92%R, respectively, compared to CENER FAST or HAWC2, demonstrating the feasibility of the proposed methodology.
... Although useful, these methods often fall short in capturing intricate aspects of blade loading and wake effects, particularly in tightly clustered turbines within wind farms. Recent advances in rotor blade modeling, particularly through the Actuator Line Model (ALM) and Computational Fluid Dynamics (CFD), as introduced by Sorensen et al. [1] and others [2][3][4][5], have improved our understanding of wind turbine aerodynamics. ALM simplifies the representation of rotor blades by modeling them as lines with distributed forces along their radial direction, allowing detailed and physically ...
... In this study, the turbine blades are represented using the actuator line model (ALM) as shown in Figure 1, which effectively simulates the aerodynamic forces on the blades without explicitly resolving the blade geometry [1]. The ALM is a computational technique that enhances the traditional actuator disk model (ADM) by representing the blades as individual lines rather than simplifying the entire rotor into a single disk representation. ...
Wind power plays an increasingly vital role in sustainable energy development. However, accurately simulating wind turbine aerodynamics, particularly in offshore wind farms, remains challenging due to complex environmental factors such as the marine atmospheric boundary layer. This study investigates the integration and assessment of the Actuator Line Model (ALM) within the high-order spectral/hp element framework, Nektar++, for wind turbine aerodynamic simulations. The primary objective is to evaluate the implementation and effectiveness of the ALM by analyzing aerodynamic loads, wake behavior, and computational demands. A three-bladed NREL-5MW turbine is modeled using the ALM in Nektar++, with results compared against established computational fluid dynamics (CFD) tools, including SOWFA and AMR-Wind. The findings demonstrate that Nektar++ effectively captures velocity and vorticity fields in the turbine wake while providing aerodynamic load predictions that closely align with finite-volume CFD models. Furthermore, the spectral/hp element framework exhibits favorable scalability and computational efficiency, indicating that Nektar++ is a promising tool for high-fidelity wind turbine and wind farm aerodynamic research.
... The ADM has the lowest requirement of computing resources, so it is widely adopted in the flow field simulation of wind farms [98,99]. Compared with the ADM, the ALM can provide more detailed wake characteristics and the blade tip vortex can be clearly simulated [100,101]. In the ASM, the blade surface pressure source term is distributed on the actuator surface, which further improves the simulation precision; meanwhile, the computation cost increases accordingly [102]. ...
... According to the simplification of wind turbines (shown in Figure 11), actuator methods are classified into an actuator dis method (ADM), actuator line method (ALM) and actuator surface method (ASM) [97 The ADM has the lowest requirement of computing resources, so it is widely adopted i the flow field simulation of wind farms [98,99]. Compared with the ADM, the ALM ca provide more detailed wake characteristics and the blade tip vortex can be clearly simu lated [100,101]. In the ASM, the blade surface pressure source term is distributed on th actuator surface, which further improves the simulation precision; meanwhile, the com putation cost increases accordingly [102]. ...
With the urgent demand for net-zero emissions, renewable energy is taking the lead and wind power is becoming increasingly important. Among the most promising sources, offshore wind energy located in deep water has gained significant attention. This review focuses on the experimental methods, simulation approaches, and wake characteristics of floating offshore wind turbines (FOWTs). The hydrodynamics and aerodynamics of FOWTs are not isolated and they interact with each other. Under the environmental load and mooring force, the floating platform has six degrees of freedom motions, which bring the changes in the relative wind speed to the turbine rotor, and furthermore, to the turbine aerodynamics. Then, the platform’s movements lead to a complex FOWT wake evolution, including wake recovery acceleration, velocity deficit fluctuations, wake deformation and wake meandering. In scale FOWT tests, it is challenging to simultaneously satisfy Reynolds number and Froude number similarity, resulting in gaps between scale model experiments and field measurements. Recently, progress has been made in scale model experiments; furthermore, a “Hardware in the loop” technique has been developed as an effective solution to the above contradiction. In numerical simulations, the coupling of hydrodynamics and aerodynamics is the concern and a typical numerical simulation of multi-body and multi-physical coupling is reviewed in this paper. Furthermore, recent advancements have been made in the analysis of wake characteristics, such as the application of instability theory and modal decomposition techniques in the study of FOWT wake evolution. These studies have revealed the formation of vortex rings and leapfrogging behavior in adjacent helical vortices, which deepens the understanding of the FOWT wake. Overall, this paper provides a comprehensive review of recent research on FOWT wake dynamics.
... However, simulating large-scale rotors with diameters on the order of 100 m still requires significant computational resources and time costs. Therefore, the Actuator Line Model (ALM) [18], which combines the advantages of CFD and BEMT, has been proposed. The ALM models the blade using virtual actuator lines, without directly solving the actual flow around the blades, thus effectively modeling the three-dimensional wake dynamics. ...
... The wind turbine blades are modeled using the Actuator Line Method (ALM), which was first proposed by [18], due to its effective balance between fidelity and computational resources, it has been widely applied in wind turbine simulations. The ALM replaces the blades with virtual forces, representing the blades as force actuator points based on the momentum of the blade elements. ...
As wind turbines increase in size, blades become longer, thinner, and more flexible, making them more susceptible to large geometric nonlinear deformations, which pose challenges for aeroelastic simulations. This study presents a nonlinear aeroelastic model that accounts for large deformations of slender, flexible blades, coupled through the Actuator Line Method (ALM) and Geometrically Exact Beam Theory (GEBT). The accuracy of the model is validated by comparing it with established numerical methods, demonstrating its ability to capture the bending–torsional coupled nonlinear characteristics of highly flexible blades. A bidirectional fluid–structure coupling simulation of the IEA 15MW wind turbine under uniform flow conditions is conducted. The effect of blade nonlinear deformation on aeroelastic performance is compared with a linear model based on Euler–Bernoulli beam theory. The study finds that nonlinear deformations reduce predicted angle of attack, decrease aerodynamic load distribution, and lead to a noticeable decline in both wind turbine performance and blade deflection. The effects on thrust and edgewise deformation are particularly significant. Additionally, nonlinear deformations weaken the tip vortex strength, slow the momentum exchange in the wake region, reduce turbulence intensity, and delay wake recovery. This study highlights the importance of considering blade nonlinear deformations in large-scale wind turbines.
... The above CFD method requires significant computational resources. Sørensen and Shen 47 proposed the actuator line (AL) method in the field of wind energy in order to find a workable compromise between low-order models and three-dimensional simulations of the real geometry, but it has then been used in the field of tidal energy. [48][49][50] The proposed methodology incorporates a body-force scheme into a CFD solver. ...
... The AL model, initially introduced by Sørensen and Shen, 47 represents a highly effective methodology that integrates conventional blade element momentum theory with the Navier-Stokes equations to accurately analyze the primary dynamics of the wake surrounding the TST. This AL approach incorporates several actuator lines rotating around the axis of each blade, tailored to the specific count of TST blades. ...
The misalignment between flow and rotor can significantly alter the efficiency of the tidal stream turbine (TST), and therefore, it is vital to predict the flow in the tidal field and the performance of the TST under yaw-offset conditions. First, this paper implements a high-precision Lagrangian dynamic sub-grid-scale model based on the large-eddy simulation (LES) method. A classical computational fluid dynamics benchmark case is selected to validate the accuracy of the dynamic LES (DLES) method. The results indicate that the newly implemented dynamic LES method exhibits reduced dissipation and effectively captures the local effects of non-uniform flow fields, including vortex structures. Second, an efficient high-fidelity numerical method (AL-DLES) for forecasting the TST wake is presented by integrating an actuator line (AL) code with the aforementioned DLES method based on the Lagrangian framework. After comparing the experimental results, it was discovered that the newly developed AL-DLES coupling approach, which addresses the issues of challenging turbine meshing, rapid wake dissipation, and insufficient flow field fidelity in previous methods, can accurately simulate the forces acting on the TST while also capturing detailed characteristics of the flow field. Furthermore, the study will be extended to investigate the TST wake dynamics under various yaw-offset conditions, exploring the mechanisms of instability evolution in wake meandering. Meanwhile, the latest third-generation (Ωnew) vortex identification program is implemented and successfully applied to the wake vortex visualization of the TST under yaw-offset conditions. Through a comparative analysis of three distinct vortex identification approaches, it was demonstrated that the Ωnew method exhibits superior accuracy in capturing the vortex system located behind the rotor, eliminating the need for manual threshold selection. In addition, it is capable of simultaneously capturing both strong and weak vortices, which is a vital aspect for future wake research.
... The actuator line method (ALM) implementation, first proposed by Sørensen and Shen, 38 is a blade element formulation that represents wind turbine blades as discretized blade line elements that each, in turn, represent a 2D airfoil profile. The static airfoil lift and drag data are input through airfoil polars or lookup tables. ...
... 40 In ALM models, the thrust T and the blade loading are preserved through the parameter e=D grid , where D grid is the local grid length. 38 turbinesFoam follows the suggestion of Troldborg 41 to choose e=D grid ¼ 2. However, later works of Martínez et al. 42 and Jha et al. 43,44 show that varying this parameter shows a significant change in blade loads and power estimations of the rotor. Therefore, we tuned e=D grid by performing a sensitivity study of the normal load profile as a function of e=D grid . ...
Vertical-axis wind turbines (VAWTs), particularly in offshore wind farms, are gaining attention for their capacity to potentially enhance wake recovery and increase the power density of wind farms. Previous research on VAWT wake control strategies have demonstrated that the pitch offset is favorable for VAWT wake recovery. In the present study, an investigation on the wake recovery and its mechanisms for an H-Rotor and a novel X-Rotor VAWTs with fixed blade pitch offsets is conducted through qualitative and quantitative methods. The actuator line method is utilized in this study. Results indicate that the two rotors produce distinct vortex systems that drive the wake recovery process—which is augmented with pitch offsets. Through quantitative studies, the contribution of wake recovery due to advection increases dramatically with pitch offsets in the near wake. With pitch offsets, the inline available power increases up to 2.3 times for the rotors when compared to when there is no pitch offset. The mean kinetic energy flux occurs mostly above and below the rotors as well as the windward side, suggesting the mechanism of power replenishment for these rotors with pitch offsets. These results encourage further research into the effectiveness of wake recovery in the wind-farm level with the ground and atmospheric boundary layer influences.
... Further information on the mesh optimization process, including its parallelisation, may be found in (30,17,18,33,19) and the references therein. TURBINE PARAMETRISATION Our actuator line model (ALM) follows the approach of (34,35) in which the turbine blades are represented by rotating virtual lines -the actuator lines (AL). Point forces are computed along each AL, (at each blade element's midpoint) using the relative velocity U extracted from the fluid solver by evaluating the globally-defined finite element solution at these points, the solid body velocity U b of each point, and the lift and drag coefficients obtained from look-up tables using airfoil data for the blade element's respective profile. ...
... In this work, we presented the implementation and validation of a uRANS-based, mesh-adaptive ALM which is able to optimize the number of elements/cells that are required to resolve the wake field within a full-size wind farm. Our ALM implementation is based on the original model of (34) with additional models being used to account for blade end effects and the impact of the tower shadow on the near wake field. The fluid flow is resolved using a uRANS formulation of the governing equations and the k-ω SST turbulence closure model. ...
Numerical models of the flow and wakes due to turbines operating within a real-scale offshore wind farm can lead to a prohibitively large computational cost, particularly when considering blade-resolved simulations. With the introduction of turbine parametrizations such as the actuator disk (AD) or the actuator line (AL) models, this problem has been partially addressed, yet the computational cost associated with these simulations remains high. In this work, we present an implementation and validation of an AL model within the mesh-adaptive three-dimensional fluid dynamics solver, Fluidity, under a unsteady Reynolds-averaged Navier-Stokes based turbulence modelling approach. A key feature of this implementation is the use of mesh optimization techniques, which allow for the automatic refinement or coarsening of the mesh locally according to the resolution needed by the fluid flow solver. The model is first validated against experimental data from wind tunnel tests. Finally, we demonstrate the benefits of mesh-adaptivity by considering flow past the Lillgrund offshore wind farm.
... It is because a better understanding of the corresponding flow field assists the optimization of wind turbine layout and helps to assess the environmental footprint of energy harvesting projects [11,[26][27][28][29][30][31]. A number of investigators have performed large eddy simulations to advance the understanding of the wake structure [12,[32][33][34][35][36]. ...
... where t and x i are time and space coordinates, respectively; ρ and ν are the density and viscosity of water, respectively; U i and p represent Reynolds-averaged velocity and pressure, respectively. The body force term f i is a momentum sink used to account for the hydrodynamic effects of the turbines, which is often computed from actuation disk models [26] and is active only in the regions of the computational domain that are occupied by the turbines. ...
The growth of computational resources in the past decades has expanded the application of Computational Fluid Dynamics (CFD) from the traditional fields of aerodynamics and hydrodynamics to a number of new areas. Examples range from the heat and fluid flows in nuclear reactor vessels and in data centers to the turbulence flows through wind turbine farms and coastal vegetation plants. However, in these new applications complex structures are often exist (e.g., rod bundles in reactor vessels and turbines in wind farms), which makes fully resolved, first-principle based CFD modeling prohibitively expensive. This obstacle seriously impairs the predictive capability of CFD models in these applications. On the other hand, a limited amount of measurement data is often available in the systems in the above-mentioned applications. In this work we propose a data-driven, physics-based approach to perform full field inversion on the effects of the complex structures on the flow. This is achieved by assimilating observation data and numerical model prediction in an iterative Ensemble Kalman method. Based on the inversion results, the velocity and turbulence of the flow field can be obtained. A major novelty of the present contribution is the non-parametric, full field inversion approach adopted, which is in contrast to the inference of coefficient in the ad hoc models often practiced in previous works. The merits of the proposed approach are demonstrated on the flow past a porous disk by using both synthetic data and real experimental measurements. The spatially varying drag forces of the porous disk on the flow are inferred. The proposed approach has the potential to be used in the monitoring of complex system in the above mentioned applications.
... 1,2 The Actuator Line Model (ALM) is known to depend on a high grid resolution (on the order of 50 grid points per rotor) when using Large-Eddy Simulations (LES) to provide grid-converged results. 3,2 However, in order to study large wind farms and the associated large-scale properties of coupling with the atmospheric boundary layer, wind farms consisting of many turbines must be considered. 4,5,6 When many turbines must be included in the computational domain, fine spatial resolution on each rotor is often not affordable, especially if one wishes to repeat the LES varying flow conditions, rotor designs, etc. ...
... The ALM implementation in LESGO 7 incorporates a wind turbine into the Navier-Stokes Equation, see Eq. 1, as a body force term. 3 This body force is calculated dynamically depending on the local velocity at the location of each actuator point. The actuator points are used to calculate the blade forces with a high accuracy before they are projected on the computational grid used to calculate the flow field. ...
In this work the accuracy of the Actuator Line Model (ALM) in Large Eddy Simulations of wind turbine flow is studied under the specific conditions of very coarse spatial resolutions. For finely-resolved conditions, it is known that ALM provides better accuracy compared to the standard Actuator Disk Model (ADM) without rotation. However, we show here that on very coarse resolutions, flow induction occurring at rotor scales can affect the predicted inflow angle and can adversely affect the ALM predictions. We first provide an illustration of coarse LES to reproduce wind tunnel measurements. The resulting flow predictions are good, but the challenges in predicting power outputs from the detailed ALM motivate more detailed analysis on a case with uniform inflow. We present a theoretical framework to compare the filtered quantities that enter the Large-Eddy Simulation equations as body forces with a scaling relation between the filtered and unfiltered quantities. The study aims to apply the theoretical derivation to the simulation framework and improve the current results for an ALM, especially in the near wake where the largest differences are observed.
... Whether purely analytical or numerical and whether predicting wind speed deficit or added turbulence intensity or both, wake models are useful to understand the behavior of a wind turbine wake, but they cannot provide any information on the effects of the wake on the surrounding environment, such as changes in vertical mixing or surface temperature or heat and momentum fluxes at the surface. Large-eddy simulation (LES) has been a successful numerical approach to study wind turbine wakes (Breton et al., 2017) and their effects on the surrounding environment (Wu et al., 2023) because of their high spatial and temporal resolutions (order of a few meters and tens of seconds, respectively), as well as the accuracy of the actuator disk (Sørensen and Myken, 1992;Madsen, 1996;Mikkelsen, 2003) and actuator line (Sorensen and Shen, 2002) models used to incorporate the effects of the rotating blades. Many LES studies have been conducted to capture wind speed and TKE properties in wind turbine wakes (Eriksson et al., 2015;Vanderwende et al., 2016;Lee and Lundquist, 2017;Deskos et al., 2019;Siedersleben et al., 2020;Feng et al., 2022). ...
Wind turbine wakes are plume-like regions characterized by reduced wind speed and enhanced turbulence kinetic energy (TKE) that form downstream of wind turbines. Numerical mesoscale models, like the Weather Research and Forecasting (WRF) model, are generally effective at reproducing the wind speed deficit but lack skills at simulating the TKE added by wind turbines. Here we propose an analytical formulation for added TKE by a wind turbine that reproduces, via least-squares error parameter fitting, the main features of the three-dimensional structure of added TKE as simulated in previous large-eddy simulation (LES) studies, including a streamwise peak at x=4D–6D (where D is the turbine diameter), a vertical peak near the upper-rotor region, and an annular Gaussian-like distribution along the rotor edge. Validation of the proposed formulation against independent LES results and wind tunnel observations from the literature indicates a promising performance in the case of a single wind turbine wake. The ultimate goal is to insert the proposed formulation, after further improvements, in the WRF model for use within existing or new wind farm parameterizations.
... In the LES-coupled simulation environment, the turbine blades are represented via the Actuator Line Method (ALM), where each blade segment exerts dynamic forces on the surrounding air, thereby influencing local flow properties such as velocity and turbulence (Sørensen and Shen, 2002). The interaction between OpenFAST's fine temporal resolution and the coarser LES 355 grid in AMR-Wind necessitates sophisticated interpolation techniques and phase adjustments to ensure accurate and timely controller responses. ...
Wind farm control optimizes wind turbines collectively, implying that some turbines operate suboptimally to benefit others, resulting in a farm-level performance increase. This study presents a novel control strategy to optimize wind farm performance by synchronizing the wake dynamics of multiple turbines using an Extended Kalman Filter (EKF)-based phase estimator in a Helix control framework. The proposed method influences downstream turbine wake dynamics by accurately estimating the phase shift of the upstream periodic Helix wake and applying it to its downstream control actions with additional phase offsets. The estimator integrates a dynamic Blade Element Momentum model to improve wind speed estimation accuracy under dynamic conditions. The results, validated through turbulent large-eddy simulations in a three-turbine array, demonstrate that the EKF-based estimator reliably tracks the phase of the incoming Helix wake, with slight offsets attributed to model discrepancies. When integrated with the closed-loop synchronization controller, significant power enhancement with respect to the single-turbine Helix can be attained (up to +10 % on the third turbine), depending on the chosen phase offset. Flow analysis reveals that the optimal phase offset sustains the natural Helix oscillation throughout the array, whereas the worst phase offset creates destructive interference with the incoming wake, which appears to negatively impact wake recovery.
... 24 This method discretizes the turbine blades and tower into multiple elements. 25 For each element, lift and drag forces are calculated using the Blade Element Momentum (BEM) theory. 5 These forces are then distributed across the surrounding grid cells using a Gaussian distribution and incorporated as external forces in the Navier-Stokes equations. ...
Prediction of wake and output power for an offshore wind turbine under various wind conditions is essential to maximize energy generation and minimize wake effects. In previous studies, deep learning (DL) models developed using high-fidelity computational fluid dynamics (CFD) simulation results have demonstrated high accuracy and efficiency in predicting the wake characteristics and output power of offshore wind turbines. However, these existing DL models were typically developed for specific types of wind turbines, which cannot be directly used for a new turbine type. Development of a new DL model relying solely on simulation data from a new wind turbine would waste the valuable information contained in previous datasets and existing DL models, leading to increased computational costs for data collection. To address this issue, this paper aims to leverage a previously established simulation dataset and a pre-trained DL model for a wind turbine to develop a new model for another type of wind turbine. The proposed method requires only a small number of new simulations for model development using transfer learning with fine-tuning and model-agnostic meta-learning (MAML), thereby enhancing computational efficiency. The results demonstrate that the models developed using fine-tuning and MAML achieve lower prediction errors and less model training time compared to those trained directly on new wind turbine data. Furthermore, the model trained using MAML outperforms the fine-tuning model when the dataset size is extremely small, while the fine-tuning model has lower prediction errors with relatively larger datasets.
... The ALM is used to represent wings and individual wind turbine blades as body forces in the momentum equation [75,79,80], dividing the forces along a blade or wing into forces at actuator points along a line. In this approach, aerodynamic forces such as lift and drag are computed at each actuator point using a sampled velocity from the fluid solver and lookup tables for lift and drag coefficients, C l and C d : ...
We present AMR‐Wind, a verified and validated high‐fidelity computational‐fluid‐dynamics code for wind farm flows. AMR‐Wind is a block‐structured, adaptive‐mesh, incompressible‐flow solver that enables predictive simulations of the atmospheric boundary layer and wind plants. It is a highly scalable code designed for parallel high‐performance computing with a specific focus on performance portability for current and future computing architectures, including graphical processing units (GPUs). In this paper, we detail the governing equations, the numerical methods, and the turbine models. Establishing a foundation for the correctness of the code, we present the results of formal verification and validation. The verification studies, which include a novel actuator line test case, indicate that AMR‐Wind is spatially and temporally second‐order accurate. The validation studies demonstrate that the key physics capabilities implemented in the code, including actuator disk models, actuator line models, turbulence models, and large eddy simulation (LES) models for atmospheric boundary layers, perform well in comparison to reference data from established computational tools and theory. We conclude with a demonstration simulation of a 12‐turbine wind farm operating in a turbulent atmospheric boundary layer, detailing computational performance and realistic wake interactions.
... Subsequently, an additional 100 s is allowed for the wake to fully develop and stabilize. The wind turbine rotor is simulated using an actuator line model, 51 while wind turbine generator characteristics and yaw control system parameters are referenced from Ref. 52. In the simulation process, the wind speed is decomposed into three directions: x, y, and z, representing stream-wise, span-wise, and wall-normal, respectively. ...
This paper explores innovative approaches for reconstructing the wake flow field of yawed wind turbines from sparse data using data-driven and physics-informed machine learning techniques. The physics-informed machine learning wake flow estimation (WFE) integrates neural networks with fundamental fluid dynamics equations, providing robust and interpretable predictions. This method ensures adherence to essential fluid dynamics principles, making it suitable for reliable wake flow estimation in wind energy applications. In contrast, the data-driven machine learning wake flow estimation (DDML-WFE) leverages techniques such as proper orthogonal decomposition to extract significant flow features, offering computational efficiency and reduced reconstruction costs. Both methods demonstrate satisfactory performance in reconstructing the instantaneous wake flow field under yawed conditions. DDML-WFE maintains comparable performance even with reduced measurement resolution and increased noise, highlighting its potential for real-time wind turbine control. The study employs a limited number of measurement points to balance data collection challenges while capturing essential flow field characteristics. Future research will focus on optimizing turbine control strategies in wind farms by incorporating multi-scale modules and advanced data-driven techniques for temporal prediction of wake flow fields.
... If a mid-fidelity model can capture the primary aerodynamic effects of curved blades with significantly lower computational demands than CFD, it becomes a favorable alternative. Examples include the blade element vortex cylinder (BEVC) method for prebend effects (Li 45 et al., 2022b), a vortex-based coupled near-and far-wake model for sweep effects (Li et al., 2022d), corrections to Prandtl's tip-loss factor for sweep effects (Fritz et al., 2022), higher-fidelity lifting-line (LL) approaches (Phillips and Snyder, 2000;Ramos-García et al., 2016;Boorsma et al., 2020;Branlard et al., 2022) and the actuator line (AL) method (Sørensen and Shen, 2002;Meyer Forsting et al., 2019;Martínez-Tossas and Meneveau, 2019). Before confidently applying these models for load calculations and design optimization, consistent aerodynamic benchmarks Horcas et al., 2023) or even 50 aeroelastic benchmarks (Behrens de Luna et al., 2022;Zahle et al., 2024) are essential. ...
Advancements in wind turbine technology have led to larger, more flexible blades and an increasing interest in aerodynamic load calculations and design optimization of blades featuring significant sweep, prebend or coning. High-fidelity blade-resolved computational fluid dynamics (CFD) simulations provide precise rotor performance predictions but are computationally expensive. In contrast, the low-fidelity blade element momentum (BEM) method is computationally efficient but unable to model wake-induced effects of non-straight blades and coned rotors. To bridge this gap, mid-fidelity aerodynamic models, which balance accuracy and computational efficiency, are essential for design optimization tasks. Consistent aerodynamic benchmarks are crucial to effectively evaluate these models, particularly for modeling wake-induced effects across different blade geometries. Previous studies typically used the same chord and twist distributions across different curved blade geometries. However, this approach introduces inconsistencies, as it does not guarantee the same local aerodynamic conditions (e.g., angle of attack and local thrust coefficient) along the blade span due to projection effects of velocities and forces between the 2-D airfoil section and the 3-D flow. Consequently, wake-induced effects on loading and induction become entangled with unwanted projection effects, hindering the clear evaluation of how blade curvature alone influences the loads and induction. This study introduces a framework to disentangle wake-induced and projection effects in aerodynamic comparisons of curved blades. Within the BEM framework, we derive the necessary modifications to the chord and twist distributions of curved blades, ensuring the same spanwise circulation distribution as a baseline straight blade. These adjustments remove projection-driven discrepancies, enabling a consistent evaluation of wake-induced effects on loading and induction. Numerical validations using BEM and CFD confirm the effectiveness of these modifications. Additionally, projection effects in existing CFD results can be effectively isolated and removed. Using this framework, we discovered a novel insight from analysis of the CFD results: the wake-induced effects of moderate blade sweep and prebend can be modeled independently and then superimposed. This previously inaccessible insight significantly simplifies the modeling process and provides valuable guidance for developing mid-fidelity engineering aerodynamic models. Overall, this study advances the understanding of blade sweep and prebend effects on normal and tangential aerodynamic loads, supporting future blade design optimization.
... By including boundary layer effects, turbulence, and dynamic stall, blade-resolved models provide an in-depth understanding of the flow surrounding individual blades [Liu et al., 2017]; however, they demand highly refined grids in the vicinity of the blades, leading to prohibitively high computational costs [de Oliveira et al., 2022]. To mitigate computational expense, the actuator line method (ALM) employs a discretization of rotor blades into lines of actuator points [Sorensen and Shen, 2002]. These points project lift and drag forces, derived from pre-tabulated airfoil performance data. ...
This paper presents a wind farm layout optimization framework that integrates polynomial chaos expansion, a Kriging model, and the expected improvement algorithm. The proposed framework addresses the computational challenges associated with high-fidelity wind farm simulations by significantly reducing the number of function evaluations required for accurate annual energy production predictions. The polynomial chaos expansion-based prediction method achieves exceptional accuracy with reduced computational cost for over 96%, significantly lowering the expense of training the ensuing surrogate model. The Kriging model, combined with a genetic algorithm, is used for surrogate-based optimization, achieving comparable performance to direct optimization at a much-reduced computational cost. The integration of the expected improvement algorithm enhances the global optimization capability of the framework, allowing it to escape local optima and achieve results that are either nearly identical to or even outperform those obtained through direct optimization. The feasibility of the polynomial chaos expansion-Kriging framework is demonstrated through four case studies, including the optimization of wind farms with 8, 16, and 32 turbines using low-fidelity wake models, and a high-fidelity case using computational fluid dynamics simulations. The results show that the proposed framework is highly effective in optimizing wind farm layouts, significantly reducing computational costs while maintaining or improving the accuracy of annual energy production predictions.
... To represent the dynamic response of the turbine, Nalu-Wind is coupled to the National Renewable Energy Lab's OpenFAST software suite (National Renewable Energy Laboratory, 2024b). An actuator line model (ALM) with an isotropic Gaussian spreading function is used to represent the 115 turbine aerodynamic forces computed in OpenFAST as body forces in the LES (Sorensen and Shen, 2002). The filtered lifting line correction is applied with ε/∆x = 2 and ϵ opt /c = 0.25, where c is the chord length, to improve the ALM's representation of the force distribution along the blade (Martínez-Tossas and Meneveau, 2019;Martínez-Tossas et al., 2024). ...
Recent advancements in the use of active wake mixing (AWM) to reduce wake effects on downstream turbines open new avenues for increasing power generation in wind farms. However, a better understanding of the fluid dynamics underlying AWM is still needed to make wake mixing a reliable strategy for wind farm flow control. In this work, a spectral proper orthogonal decomposition (SPOD) is used to analyze the dynamics of coherent flow structures that are induced in the wake through blade pitch actuation. The data are generated using the Exawind software suite to perform a large eddy simulation of an AWAKEN 2.8 MW turbine operating in a stable atmospheric boundary layer. SPOD tracks the modal behavior of flow structures from their generation in the turbine induction field, through their growth in the near wake region, and to their subsequent evolution and energy transfers in the far wake. SPOD is shown to be a useful tool in the context of AWM because it translates the wavenumber and frequency inputs to the turbine controller to structures in the wake. A decomposition of the radial shear stress flux in the wake is also developed using SPOD to measure the contribution of coherent flow structures to mean flow turbulent entrainment and wake recovery. The effectiveness of AWM is connected to its ability to excite inherent structures in the wake of the turbine that arise using baseline controls. The effects of AWM on blade loading are also analyzed by connecting the axial force along the blade to the SPOD analysis of the turbine induction field. Lastly, the performance of different AWM strategies is demonstrated in a two-turbine array.
... First, a desired ABL condition was established using precursor simulations. The boundary layer was initialized with small velocity and temperature perturbations near the surface to accelerate turbulence development, and the precursors were run for tens of thousands of seconds to establish Second, the turbine was introduced into AMR-Wind through coupling with the OpenFAST software suite (National Renewable Energy Laboratory, 2024b), which has been the subject of validation work for the case of turbines without coupling to LES and with coupling to LES (Hsieh et al., 2024 computed in OpenFAST to body forces in the LES that are distributed to the surrounding fluid (Sorensen and Shen, 2002). ...
Wind-farm control strategies aim to increase the efficiency, and therefore lower the levelized cost of energy, of a wind farm. This is done by using turbine settings such as the yaw angle, blade pitch angles, or generator torque to manipulate the wake that negatively affects downstream turbines in the farm. Two inherently different wind-farm control methods have been identified in literature: wake steering (WS) and wake mixing (WM). As one of two companion papers focused on understanding practical aspects of these two wind-farm control strategies using large-eddy simulation (LES), we below analyze the wake quantities of interest for a single wind turbine performing WS and WM, while the companion article (Frederik et al., 2025) focuses on turbine quantities of interest including power and structural loads for the same computational setup and also includes two-turbine arrays with full and partial wake overlap. The simulations, which are based in the LES solver AMR-Wind, are tailored to have inflow conditions representative of measurements from a site off the east coast of the U.S. including with strong veer and low turbulence. The turbine, which is modeled in OpenFAST and coupled to the LES, is the IEA 15 MW, an open-source offshore design. After presenting an overview of the wake recovery for the different wake-control cases, the analysis probes the fluid-dynamic causes for the different performance of the arrays reported in the companion article by examining control volumes around the wakes and the budget of the mean-flow kinetic energy (MKE) within these volumes. In the high veer environment considered, the MKE recovery is dominated by mean convection, and this is shown to especially benefit the WS strategy when a neighboring turbine is directly downstream; there is ≈70 % more available power for a downstream turbine than the baseline case, and this power is gained primarily through mean convection on the left-tip and top-tip faces of the control volume. However, the case with imperfect knowledge of the exact wind direction favors the pulse-type WM strategy, largely because of ≈8 % increased turbulent entrainment from aloft versus the baseline that could be related to an apparent resistance to skewing in the pulsed wake. The general reduced effectiveness of helix-type and other individual-pitch-based WM strategies for inflow with high veer and low turbulence as reported in the companion paper is due, in part, to low magnitudes of phase-averaged turbulent entrainment. Two main findings of this study are thus that veer has a significant impact on the effectiveness of different wake-control strategies and that pulse-type WM may be a useful strategy when the objective is power maximization in realistic, offshore flow environments including imperfect knowledge of the exact wake overlap position on the downstream turbine.
... The ALM combined with CFD is a common approach for studying the wake of wind turbines. It replaces the turbine blades with virtual lines that carry volumetric forces to simulate the aerodynamic interactions between the blades and the surrounding flow field (Sørensen and Shen, 2002), as shown in Fig. 1. Traditional ALM cannot account for the positional changes and additional wind speed corrections caused by floating platform movements. ...
In the marine environment, floating offshore wind turbines (FOWTs) are exposed to perturbations of nonlinear motion response. An in-depth study of the evolution laws of wake vortex and wake deficit under six degrees of freedom conditions in FOWTs can help reduce the blade load and enhance the output for downstream wind turbines. This paper enhances the traditional actuator line model by incorporating velocity corrections that account for platform motion, enabling dynamic simulations of National Renewable Energy Laboratory 5 MW (Megawatt) reference rotor under six degrees of freedom (6-DOF) conditions, including surge, sway, heave, pitch, roll, and yaw. The results indicate except for the surge and pitch, the effect of the motion response of the remaining DOF on the average thrust and power of the FOWT is within 1%. The 6-DOF motion condition drives the evolution of the wake vortex into a vortex ring or long vortex band mode. The wake lengths for surge, sway, and heave are shortened to 0.7, 0.6, and 0.6 times those of the fixed conditions, respectively, while pitch, roll, and yaw slightly increase the wake lengths to 1.1, 1.2, and 1.2 times those of the fixed conditions. All DOF, except for yaw, tend to delay the onset of wake self-similarity, with yaw reducing it by 10% compared to the fixed conditions. The insights garnered from this paper provide guidance for developing engineering wake models and micrositing for floating offshore wind turbines.
... As an alternative to classical fully resolved simulation using RANS solvers, the actuator line method (ALM) provides a reasonable trade-off between computational accuracy and efficiency, and is suited for unsteady simulations to obtain time-accurate flowfield. 37 The sectional lift and drag coefficients are determined using the precomputed lookup airfoil tables of the blade elements after calculating the local Reynolds number and the effective angle of attack. The ALM then distributes the blade loading along a line representing the propeller. ...
Distributed electric propulsion is widely recognized as a disruptive technology in aviation, and the aerodynamic characteristics of a multi-propeller are critical to the design of such configurations. A reformulated vortex particle method is adopted to provide an in-depth analysis of the aerodynamic characteristics between the multiple propellers operating in close proximity. According to the symmetrical distribution features of the particle field, the entire flowfield is divided into a noninterference region and an interference region. The results show that the aerodynamic performance of the middle propeller fluctuates more than the other two adjacent propellers in the hover state, and the flowfield in the noninterference zone exhibits time-independent characteristics. As the advance ratio increases, the performance fluctuations decrease, the radial contraction of the tip vortex is gradually attenuated, and the initial vortex strength decreases. For the interference zone in hover, the aerodynamic load of each blade drops as the propellers approach the interference region and the wake geometry shows asymmetry. The slipstream deformation of the multi-propeller is more pronounced in hover. The downwash from the previous propeller is responsible for the sequential decrease in thrust coefficient for multi-propeller systems operating at different sideslip angles, and the middle propeller experiences the greatest thrust fluctuation.
... The volume field is then used to initialize the wind farm simulation (successor), and data planes are used as inflow boundary conditions. 190 The rotor is modeled with the actuator line model (ALM, Sorensen and Shen, 2002). When considering wind turbines, the large Reynolds numbers and the multiple length scales involved make LES on a fully resolved geometry too computationally demanding to be used extensively. ...
Wind turbine wakes can be treated as a complex system of helical vortices. When this system destabilizes, the wake recovers its velocity deficit through mixing and entertainment of energy from the surrounding flow. How fast and effectively that happens depends on the inflow characteristics and can also be influenced by how the turbines are operated. Dynamic induction control techniques such as the helix affect the onset of instability and the transition from near to far wake, but the exact mechanisms are still unclear. Its potential in a wind farm context has been proved both numerically and experimentally, but a helix wake model does not exist yet. The goal of this study is to derive a data-driven model of the helix wake and characterize it. Dynamic mode decomposition of data generated with large eddy simulations is performed. We simulate the DTU 10 MW model turbine under a range of helix excitation frequencies and different inflows. We show that the helix modes are dominantly present both in laminar and turbulent flow. However, as turbulence intensity increases, they exhibit larger spatial decay and temporal amplitude. Additionally, we identify inflow modes related to the turbulence length scales of the inflow. We show that a very limited number of modes allows us to reconstruct the initial flow field accurately and that the optimum excitation frequency for the control technique depends on the turbulence intensity and on the position of the downstream turbines.
... centered around the blade point, with the distance from the blade point and = 2 g r id the smearing radius, is employed [32][33][34]. For a detailed description of the results obtained with this formulation we refer the reader to Section 6.1 and to the works by [5,6,35]. ...
Wind turbine models integrated into flow solvers often overestimate blade loading in the tip region. This overestimation arises from overestimating the sampled velocity and angle of attack near the blade tip. We use the ratio of tip-corrected to non-tip-corrected axial and tangential velocity components from Blade Element Momentum (BEM) theory to consistently correct the sampled velocity along the blade. This correction accurately captures both the angle of attack and tip loading and it does not require any inter-processor communication, a desirable feature in modern computing systems like GPUs. The method has been validated against a vortex-based smearing correction consistent with lifting line theory and BEM with tip correction, using both NREL-5MW and DTU-10MW turbines and adopting different inflow conditions and grid discretizations. The correction is demonstrated for the Actuator Line Method. It requires only basic turbine data, such as tip speed ratio and airfoil characteristics, making it adaptable to other turbine models, such as the actuator disk with rotation.
... A reference wind turbine developed by the Centre of Renewable Energy Sources and Saving (CRES), INNWIND 10 MW, with a diameter of 178.3 meters and a hub height of 119 meters (Chaviaropoulos et al., 2013), was used in the simulation. The rotor was indirectly modeled by the actuator line model (ALM) (Sørensen & Shen, 2002), from which aerodynamic forces on the rotor are produced synthetically based on airfoil lookup tables, hence ensuring plausible wake aerodynamics behind the rotor. The SOWFA dataset of the 10-minute timeaveraged wake flowfield at the hub height was used for validation. ...
A wake steering has been known to effectively increase wind farm production by deflecting the upstream turbines’ wakes via yaw misalignment, thus minimizing their negative impacts on the downstream turbines' performances. This study presents analytical modeling of horizontal-axis wind turbine (HAWT) wake using low-cost analytical modeling as an alternative to expensive numerical and experimental trials. The existing double-Gaussian (DG) analytical wake model was modified to include the yaw misalignment effect, allowing its usability for the yawed HAWT wake modeling. The benchmark dataset produced by high-fidelity large eddy simulation (LES) of wake flowfields behind the turbine with yaw angles of 0º, 10º, 20º, and 30º were used to validate the accuracy of the DG yaw wake model. Overall, the DG yaw wake model predictions showed good agreement with the benchmark dataset under varying HAWT rotor yaw configurations. The analytical results verified by the LES dataset confirm the effectiveness of yaw misalignment in deflecting the wake trajectory, expediting the wake recovery downstream of the HAWT. In addition, a higher rotor yaw angle improves the wake recovery rate in the prevailing wind direction. Notable deviations against the benchmark dataset were found mainly within the near-wake region owing to flow acceleration arising from turbine-induced turbulence. As a result, the model’s predictions were slightly lower than the benchmark dataset, most likely due to neglecting the acceleration term in the analytical model derivation. Otherwise, the analytical model could accurately predict the mean wake velocity within the far-wake region for all evaluated cases, demonstrating its reliability in estimating wind speed potential within a practical distance for micrositing. These results were also proved quantitatively by statistical evaluations utilizing root mean square error (RMSE) and Pearson correlation coefficient R. The present study points out the importance of the upstream HAWTs’ rotor yaw controls to properly deflect their wakes away from their mainstream trajectories, thus effectively maximizing the wind speed potentials extracted by the downstream HAWTs and improving the overall wind farm production.
... To model the effects of the wind turbines in the flow, a number of different methods are available. Commonly used methods include the actuator surface (Shen and Nørk 2007), actuator line (Sørensen and Shen 2002) or actuator disc (Mikkelsen 2004) models. This work uses the actuator disc model due to its relatively lower computational cost. ...
Improving the power output from wind farms is vital in transitioning to renewable electricity generation. However, in wind farms, wind turbines often operate in the wake of other turbines, leading to a reduction in the wind speed and the resulting power output whilst also increasing fatigue. By using wake steering strategies to control the wake behind each turbine, the total wind farm power output can be increased. To find optimal yaw configurations, typically analytical wake models have been utilised to model the interactions between the wind turbines through the flow field. In this work we show that, for full wind farms, higher-fidelity computational fluid dynamics simulations, in the form of large eddy simulations, are able to find more optimal yaw configurations than analytical wake models. This is because they capture and exploit more of the physics involved in the interactions between the multiple turbine wakes and the atmospheric boundary layer. As large eddy simulations are much more expensive to run than analytical wake models, a multi-fidelity Bayesian optimisation framework is introduced. This implements a multi-fidelity surrogate model, that is able to capture the non-linear relationship between the analytical wake models and the large eddy simulations, and a multi-fidelity acquisition function to determine the configuration and fidelity of each optimisation iteration. This allows for fewer configurations to be evaluated with the more expensive large eddy simulations than a single-fidelity optimisation, whilst producing comparable optimisation results. The same total wind farm power improvements can then be found for a reduced computational cost.
... For the wind-only cases, the turbine blades are modeled using the actuator-line model (ALM) [42]. In this model, each blade is represented by a volumeless line along which aerodynamic body forces are determined. ...
With only a few floating offshore wind turbine (FOWT) farms deployed anywhere in the world, FOWT technology is still in its infancy, building on a modicum of real‐world experience to advance the nascent industry. To support further development, engineers rely heavily on modeling tools to accurately portray the behavior of these complex systems under realistic environmental conditions. This reliance creates a need for verification and validation of such tools to improve reliability of load and dynamic response prediction and analysis capabilities of FOWT systems. The Offshore Code Comparison Collaboration, Continued with Correlation and unCertainty (OC6) project was created under the framework of the International Energy Agency to address this need and considers a three‐sided verification and validation between engineering level models, computational fluid dynamics (CFD), and experimental results. In this paper, a novel floating offshore wind platform, the Stiesdal TetraSpar, is simulated using CFD under the load conditions defined by Phase IV of the OC6 project. The comparison of these CFD results against the experimental results demonstrated the ability to predict the platform response to waves when imposing the measured wave signals as input. Although validation versus experiment was largely successful, the damping behavior was impacted by uncertainties likely originating from the mooring system and sensor umbilical cable. This extensive comparison effort with multiple CFD practitioners offers insight into best practices to achieve reliable results.
... The OpenFAST model of this turbine is used in this work, whose specifications are consistent with those listed in Table III. The OpenFAST simulation is coupled to the LES through the actuator line method (ALM) [26], where the turbine blades are represented as lines composed of discrete segments along their span. Each segment is associated with an "actuator," which is a mathematical representation of the forces applied by that part of the blade on the fluid. ...
Periodic wakes are created on upstream wind turbines by pitching strategies, such as the Helix approach, to enhance wake mixing and thereby increase power production for wind turbines directly in their wake. Consequently, a cyclic load is not only generated on the actuating turbine’s blades but also on the waked wind turbine. While the upstream load is the result of the pitching required for wake mixing, the downstream load originates from interaction with the periodic wake and only causes fatigue damage. This study proposes two novel individual pitch control schemes in which such a periodic load on the downstream turbine can be treated: by attenuation or amplification. The former method improves the fatigue life of the downstream turbine, whereas the latter enhances wake mixing further downstream by exploiting the already-present periodic content in the wake; both were validated on a three-turbine wind farm in high-fidelity large-eddy simulations. Fatigue damage reductions of around 10% were found in the load mitigation case, while an additional power enhancement of 6% was generated on the third turbine when implementing the amplification strategy. Both objectives can easily be toggled depending on a wind farm operator’s demands and the desired loads/energy capture tradeoff.
... The tower diameter d T /D = 1/15 was used to specify the drag force (the same diameter ratio as in the wind tunnel experiments), with a drag coefficient of C D = 1 in low Reynolds number flow [44]. A Gaussian kernel [39,45] was used for both the wind turbine actuator disk and the tower, with a kernel width of ϵ = 2∆x = 0.0391D. Fig. 10 shows the mean streamwise velocity contours in the XY plane. ...
Reducing wake losses in wind farms by deflecting the wakes through turbine yawing has been shown to be a feasible wind farm controls approach. Nonetheless, the effectiveness of yawing depends not only on the degree of wake deflection but also on the resulting shape of the wake. In this work, the deflection and morphology of wakes behind a wind turbine operating in yawed conditions are studied using wind tunnel experiments of a wind turbine modeled as a porous disk in a uniform inflow. First, by measuring velocity distributions at various downstream positions and comparing with prior studies, we confirm that the non-rotating wind turbine model in yaw generates realistic wake deflections. Second, we characterize the wake shape and make first observations of what is termed a curled wake, displaying significant spanwise asymmetry. The wake curling observed in the experiments is also reproduced qualitatively in large eddy simulations using both actuator disk and actuator line models. When a wind turbine is yawed for the benefit of downstream turbines, the asymmetric shape of the wake must be taken into account since it affects how much of it intersects the downstream turbines.
... The method that we use for parameterizing a turbine rotor is the actuator line model proposed by Sørensen and Shen [37]. The basic idea behind the method is to subtract from the flow field an equivalent amount of momentum to that from a turbine rotor without the need to resolve the flow around its actual geometry. ...
We develop a numerical method for simulating coupled interactions of complex floating structures with large-scale ocean waves and atmospheric turbulence. We employ an efficient large-scale model to develop offshore wind and wave environmental conditions, which are then incorporated into a high resolution two-phase flow solver with fluid-structure interaction (FSI). The large-scale wind-wave interaction model is based on the two-fluid dynamically-coupled approach of Yang and Shen (2011), which employs a high-order spectral method for simulating the water motion and a viscous solver with undulatory boundaries for the air motion. The two-phase flow FSI solver, developed by Calderer, Kang, and Sotiropoulos (2014), is based on the level set method and is capable of simulating the coupled dynamic interaction of arbitrarily complex bodies with airflow and waves. The large-scale wave field solver is coupled with the near-field FSI solver by feeding into the latter waves via the pressure-forcing method of Guo and Shen (2009), which has been extended herein for the level set method. We validate the model for both simple wave trains and three-dimensional directional waves and compare the results with experimental and theoretical solutions. Finally, we demonstrate the capabilities of the new computational framework by carrying out large-eddy simulation of a floating offshore wind turbine interacting with realistic ocean wind and waves.
... Contemporary wind turbine models employ various methods to handle the interactions between structural responses and aerodynamic loads. Simplified models can incorporate either the actuator line model (ALM) [6][7][8][9] or actuator disk model (ADM) [10][11][12][13][14] to account for the forces transmitted between the blades and wind field. The displacement of the blades is modeled as a driving source to change the body forces exerted on the flows. ...
Two-way fluid–structure interaction (FSI) simulation of wind turbines has gained significant attention in recent years due to the growth of offshore wind energy development. Strong coupling procedures in these simulations predict realistic behavior with higher accuracy but result in increased computational costs and potential numerical instabilities. This paper proposes a mixed weak and strong coupling approach for the FSI simulation of a 5 MW wind turbine. The deformation of the turbine blade is calculated using a weak coupling approach, ensuring blade deflection meets a convergence criterion before rotating to the next azimuthal position. Fluid and solid solvers are partitioned, utilizing the commercial software packages STAR-CCM+ and Abaqus, respectively. Flexible and rigid blade cases are modeled, and the calculated loads, power, and blade tip displacement for the rotor at a constant rotating speed are compared. The proposed model is validated, showing good agreement with the existing literature and results comparable to those from another validated wind turbine simulator. The effect of rotor–tower interaction is evident in the results. Based on our calculations, the power production of flexible blades is evaluated to be 9.6% lower than that of rigid blades.
... Using the current state-of-the-art supercomputers, it is still impossible to simulate wind farms resolving all the relevant length scales from the thickness of the boundary layer over a wind turbine blade (≈0.016 m at the trailing edge estimated using the equation δ/c = 0.37 (U∞c/ν) −0.2 [1] with ν = 1.5 × 10 −5 m 2 /s, and airfoil chord c = 1 m and U∞ = 100 m/s at the blade tip for a MW scale wind turbine with rotor diameter approximately 100 m, tip speed ratio 10 and incoming wind speed 10 m/s) to the thickness of an atmospheric boundary layer (≈1000 m [2]). Different rotor models including the actuator disk model [3,4,5], the actuator line model [6,7] and the actuator surface model [8] have been developed in the literature to parametrize the interaction between the turbine blades and the incoming flow without directly resolving the boundary layer flow over turbine blades. ...
Actuator line model has been widely employed in wind turbine simulations. However, the standard actuator line model does not include a model for the turbine nacelle which can significantly impact turbine wake characteristics as shown in the literature. Another disadvantage of the standard actuator line model is that more geometrical features of turbine blades cannot be resolved on a finer mesh. To alleviate these disadvantages of the standard model, we develop a new class of actuator surface models for turbine blades and nacelle to take into account more geometrical details of turbine blades and include the effect of turbine nacelle. In the actuator surface model for blade, the aerodynamic forces calculated using the blade element method are distributed from the surface formed by the foil chords at different radial locations. In the actuator surface model for nacelle, the forces are distributed from the actual nacelle surface with the normal force component computed in the same way as in the direct forcing immersed boundary method and the tangential force component computed using a friction coefficient and a reference velocity of the incoming flow. The actuator surface model for nacelle is evaluated by simulating the flow over periodically placed nacelles. Both the actuator surface simulation and the wall-resolved large-eddy simulation are carried out. The comparison shows that the actuator surface model is able to give acceptable results especially at far wake locations on a very coarse mesh. It is noted that although this model is employed for the turbine nacelle in this work, it is also applicable to other bluff bodies. The capability of the actuator surface model in predicting turbine wakes is assessed by simulating the flow over the MEXICO (Model experiments in Controlled Conditions) turbine and a hydrokinetic turbine.
This study develops and validates a machine-learned (ML) actuator line model (ALM) as a promising advancement in turbine/rotor modeling that can be applied for diverse engineering applications. The model alleviates two limitations of the standard ALM, namely, its reliance on the pre-defined lift and drag coefficient tables and its inability to account for flow unsteadiness. The ML-ALM model is trained using a blade-resolved simulation database of forces acting on blade elements for unsteady inflow conditions. The model is validated for solitary turbine performance and wake predictions against experimental data, and is verified for an inline turbine case for the performance and wake predictions of the downstream turbine against blade-resolved simulations. Its engineering applicability is demonstrated for an 8-turbine array farm simulation. The ML-ALM predicts turbine performance and wakes within 10% of blade-resolved results along with credible advection of tip vortical structures including breakdown and turbulent kinetic energy burst, using 92% less computational time than corresponding blade-resolved simulations.
The wind industry sector has emerged as a leading contender in addressing contemporary clean energy demands. This industry is experiencing rapid growth, driven by concerted endeavors to enhance the efficacy of wind farms. A critical aspect in this pursuit revolves around mitigating wake losses, which significantly impact overall power generation. This article delineates the significance of key factors such as inter-turbine distance, yaw misalignment, atmospheric thermal stability, and wind direction in influencing wake dynamics within wind farms. The discourse also highlights the importance of employing high-fidelity computational fluid dynamics (CFD) simulations to understand the intricate physics governing the flow patterns within the wind farms. Furthermore, it includes a brief introduction to the Simulator for Wind Farm Applications (SOWFA) package, a sophisticated tool instrumental in simulating flow dynamics within wind farm environments. Meanwhile, a case study investigating the influence of yaw misalignment on a medium-sized wind farm is also presented. The study unveils a discernible dependency of overall power output and time-averaged turbulence intensity on the angle of yaw misalignment. Notably, the findings underscore the potential benefits of strategic turbine yawing, particularly in scenarios characterized by elevated wake losses.
The actuator line model (ALM), which models the rotor blade as a set of points with an external force term, and the actuator disk model (ADM), which models the rotor as a disk with an external force term, are implemented in the University of Tokyo Cartesian-grid-based automatic flow solver (UTCart) to perform computational simulations of a fixed pitch rotor for multicopters. The objective of this study is to assess the predictive accuracy of rotor wake distributions in the ALM and to clarify the difference in rotor wake flow field between the ADM and ALM. The radial distribution of the blade aerodynamic forces calculated by the blade element theory (BET), an analytical method for estimating the rotor performance, is applied as the prescribed external force term of the ADM and ALM. Additionally, blade-resolved simulations of the rotor are conducted using UTCart with the moving grid method as a reference solution. The results show that the ADM and ALM predict mean velocity distributions in the rotor wake flow field with good agreement to the blade-resolved simulation. The ADM cannot predict the resolved turbulent kinetic energy (TKE). On the other hand, the ALM provides a good distribution of the resolved TKE, although the peak values showed an approximately 55% discrepancy compared to the blade-resolved simulation. The ADM also fails to capture unsteady vortices, while the ALM can predict the root and tip vortex, although it underestimated their magnitude near the rotor. The ALM reduces computational cost by saving the number of cells and the number of steps per revolution compared to the blade-resolved simulations. It is found that the computational cost by the ALM is approximately 2.5% of that by the blade-resolved simulation in this calculation method.
Understanding the aerodynamic behavior of wind turbines is paramount for optimizing their performance and increasing the efficiency of renewable energy generation. This study integrates the Actuator Line Method (ALM), originally developed within the SOWFA wind energy framework by NREL, USA, into OpenFOAM. The integration aims to investigate the aerodynamic performance and near wake evolution surrounding the MEXICO (Model Experiments in Controlled Conditions) wind turbine. Employing incompressible Large Eddy Simulation (LES) alongside the widely-used Smagorinsky model with dynamic coefficients, the methodology provides a comprehensive framework for capturing turbulent flow phenomena. Validation against experimental data from the New MEXICO dataset at a free stream velocity of V0 = 15 m/s ensures the accuracy of the numerical simulations in predicting of both aerodynamic performance and near wake of Horizontal Axis Wind Turbines (HAWT), contributing to advancements in wind turbine aerodynamics crucial for enhancing renewable energy production efficiency.
Wake steering of vertical axis wind turbines (VAWTs) is investigated experimentally and numerically via stereoscopic particle image velocimetry and Reynolds averaged Navier-Stokes simulations. Three different blade pitch angles (-10°, 0°, 10°) of straight H-type VAWTs are adopted to deflect and deform the wake. The experimental results confirm the efficacy of blade pitching on the wake steering, and validate the simulation for both moderate and significant wake deflections. The simulation is then extended to full-scale VAWTs, exploring the wake deflection effects on the power performance of VAWT arrays. The effects of inter-turbine distances and pitching configurations are considered. With the upwind VAWT deflecting the wake, the overall power coefficient is increased by 41%.
This study introduces the actuator farm model (AFM), a novel parameterization for simulating wind turbines within large eddy simulations (LESs) of wind farms. Unlike conventional models like the actuator disk (AD) or actuator line (AL), the AFM utilizes a single actuator point at the rotor center and only requires two to three mesh cells across the rotor diameter. Turbine force is distributed to the surrounding cells using a new projection function characterized by an axisymmetric spatial support in the rotor plane and Gaussian decay in the streamwise direction. The spatial support's size is controlled by three parameters: the half-decay radius r1/2, smoothness s, and streamwise standard deviation σ. Numerical experiments on an isolated National Renewable Energy Laboratory (NREL) 5MW wind turbine demonstrate that selecting r1/2=R (where R is the turbine radius), s between 6 and 10, and σ≈Δx/1.6 (where Δx is the grid size in the streamwise direction) yields wake deficit profiles, turbine thrust, and power predictions similar to those obtained using the actuator disk model (ADM), irrespective of horizontal grid spacing down to the order of the rotor radius.
Using these parameters, LESs of a small cluster of 25 turbines in both staggered and aligned layouts are conducted at different horizontal grid resolutions using the AFM. Results are compared against ADM simulations employing a spatial resolution that places at least 10 grid points across the rotor diameter. The wind farm is placed in a neutral atmospheric boundary layer (ABL) with turbulent inflow conditions interpolated from a previous simulation without turbines. At horizontal resolutions finer than or equal to R/2, the AFM yields similar velocity, shear stress, turbine thrust, and power as the ADM. Coarser resolutions reveal the AFM's ability to accurately capture power at the non-waked wind farm rows, although it underestimates the power of waked turbines. However, the far wake of the cluster can be predicted well even when the cell size is of the order of the turbine radius.
Finally, combining the AFM with a domain nesting method allows us to conduct simulations of two aligned wind farms in a fully neutral ABL and of wind-farm-induced atmospheric gravity waves under a conventionally neutral ABL, obtaining excellent agreement with ADM simulations but with much lower computational cost. The simulations highlight the AFM's ability to investigate the mutual interactions between large turbine arrays and the thermally stratified atmosphere.
Tidal and riverine flows are viable energy sources for consistent energy production. Installing and operating marine hydrokinetic (MHK) turbines requires assessing any potential impact of debris accumulation on turbine performance and sediment transport. More specifically, MHK devices may alter the natural sediment transport processes and cause debris accumulation, disrupting the natural sediment dynamic. In turn, these processes could affect the turbine’s performance. We carried out a series of large-eddy simulations coupled with bed morphodynamics, introducing various debris loads lodged on the upstream face of a utility-scale turbine tower. The objective is to systematically investigate the impact of debris accumulation on the performance and hydro- and morpho-dynamics interactions of the horizontal-axis MHK turbine under rigid and live bed conditions. To that end, we (1) employed the actuator line and surface methods for modeling turbine blades and the nacelle, respectively, (2) directly resolved individual logs, and (3) solved the Exner equation to obtain the instantaneous bed deformation of the live bed. Our analysis revealed that while the spinning rotor amplifies scour around the pile, debris accumulation modifies the sediment dynamics of the system. Also, it found that morphodynamic processes accelerate the wake recovery, slightly enhancing the turbine’s performance.
The flows behind a model wind turbine under two turbine operating regimes are investigated using wind tunnel experiments and large-eddy simulations. Measurements from the model wind turbine experiment reveal that the power coefficient and turbine wake are affected by the operating regime. Simulations employing a new class of actuator surface methods which parameterize both the turbine blades and nacelle with and without a nacelle model are carried out for each operating condition to study the influence of the operating regime and nacelle. For simulations with a nacelle model, the mean flow field is composed of an outer wake, caused by energy extraction from the incoming wind by the turbine blades, and an inner wake directly behind the nacelle, while for the simulations without a nacelle model, the central region of the wake is occupied by a jet. The simulations with the nacelle model reveal an unstable helical hub vortex expanding outwards towards the outer wake; while the simulations without a nacelle model show a stable and columnar hub vortex. The hub vortex for the turbine operating in Region 3 remains in a tight helical spiral and intercepts the outer wake a few diameters further downstream than for the turbine operating in Region 2. Wake meandering commences in a region of high turbulence intensity for all simulations indicating that neither a nacelle model nor an unstable hub vortex is a necessary requirement for wake meandering. However, further analysis of the wake meandering using a filtering technique and dynamic mode decomposition show that the unstable hub vortex energizes the wake meandering. The turbine operating regime affects the shape and expansion of the hub vortex altering the location of the onset of the wake meandering and its oscillating intensity. The unstable hub vortex promotes a energetic meandering which cannot be predicted without a nacelle model.
Three-dimensional and rotational viscous effects on wind turbine blades are investigated by means of a quasi-3D Navier-Stokes model. The governing equations of the model are derived from the 3-D primitive variable Navier-Stokes equations written in cylindrical coordinates in the rotating frame of reference. The latter are integrated along the radial direction and certain assumptions are made for the mean values of the radial derivatives. The validity of these assumptions is cross-checked through fully 3-D Navier-Stokes calculations, The resulting quasi-3D model suggests that three-dimensional and rotational effects be strongly related to the local chord by radii ratio and the twist angle, The equations of the model are numerically integrated by means of a pressure correction algorithm. Both laminar and turbulent flow simulations are performed. The former is used for identifying the physical mechanism associated with the 3-D and rotational effects, while the latter for establishing semiempirical correction laws for the load coefficients, based on 2-D airfoil data. Comparing calculated and measured power curves of a stall controlled wind turbine, it is shown that the suggested correction laws may improve significantly the accuracy of the predictions. [S0098-2202(00)02702-4].
The incompressible flowfield of a two-blade rotor with untapered, untwisted, aspect-ratio-six blades is computed. The artificial compressibility formulation of the incompressible-flow equations is chosen for the numerical solution. Time integration is performed implicitly and space discretization is obtained with an upwind-biased scheme. The numerical method is implemented on a multiblock solver where turbulent flow can be computed by both algebraic and one-equation models. The flowfield is computed on a half-rotor configuration by imposing periodicity conditions in the azimuthal direction. The numerical mesh over the blade consists of three distinct blocks and is wrapped on a cylindrical surface. Turbulence is modeled with a one-equation turbulence model. Comparisons of the computed results with available experimental data are presented.
A non-linear and unsteady actuator disc model for horizontal axis wind turbines is presented. The model consists of a finite-difference solution of the axisymmetric Euler equations in a vorticity-streamfunction formulation. We here show some results, steady as well as unsteady, for an actuator disc with a prescribed elliptic load distribution and for the 20 m radius Nibe turbine. Generally, the results are found to be in good agreement with measurements.
The steady, incompressible laminar Navier-Stokes equations in Cartesian coordinates are solved for the flow field and performance characteristics of a helicopter rotor in forward flight. The rotor is modeled as a distribution of momentum sources, the strengths of which are determined from implicit functional relations involving the flow field properties, the rotor geometry and the aerodynamic characteristics of the blade cross-section. These strengths are calculated along with the rest of the flow field in an iterative manner using a finite-volume based primitive variable algorithm. With no a priori knowledge, the wake is solved for in a time-averaged sense. Blade-loads are obtained for test cases and compared with experimental results. Solutions for the surrounding flow field representing both the near and far wake are also presented.
A multigrid distributive Gauss-Seidel (MG-DGS) method presented in the
paper has been successfully applied to the simulation of unsteady 3D
incompressible flow in the shear-driven cavity. This method has proved
to be efficient and robust when applied to the velocity problem and the
DGS relaxation scheme itself was very efficient for smoothing the
high-frequency errors for the first-order elliptic system. Using
accommodative multigrid procedures, a convergence rate of approximately
0.5 was achieved for uniform grids.
An analytical method somewhat analogous to finite wing theory has been developed which enables the flow induced by a linearized propeller actuator disk with variable radial distribution of load to be solved in closed form for the first time. Analytical solutions are given for various load distributions including the case of an arbitrary polynomial loading. As in finite wing theory, the case of elliptic loading is exceptionally simple and the induced velocities and stream function are simple expressions of elementary functions. Results are also given for a practical propeller load distribution with finite hub. The method can also be used to solve a wide range of analogous electromagnetic problems.
A semi-analytical method has been developed to solve for the inviscid
incompressible
flow induced by a heavily loaded actuator disk with non-uniform loading.
The solution
takes the contraction of the slipstream fully into account. The method
is an extension
of the analytical theory of Conway (1995) for the linearized actuator disk
and is
exact for an incompressible perfect fluid. The solutions for the velocities
and stream
function are given as one-dimensional integrals of expressions containing
complete
elliptic integrals. Any load distribution with bounded radial gradient
can be treated.
Results are presented here for both contra-rotating and normal propellers.
For the
special case of a contra-rotating propeller with a parabolic velocity profile
in the
ultimate wake, the vorticity in the slipstream is shown to be the same
as in the
analytically tractable spherical vortex of Hill (1894) and the related
family of steady
vortices explored by Fraenkel (1970, 1972) and Norbury (1973).
Various wake status have been analysed by a numerical method that combines the actuator disc principle with the Navier–Stokes equations. Results are compared with one-dimensional momentum theory and experiments. The computations are in excellent agreement with one-dimensional momentum theory for rotors working in the windmill brake state as well as in the propeller and hover states. The computations demonstrate that the turbulent wake and vortex ring states are unstable regimes for a rotor with constant loading and that these states, after a complicated transient phase, settle to a steady state. Copyright © 1998 John Wiley & Sons, Ltd.
A finite difference method is presented for solving the 3D Navier–Stokes equations in vorticity–velocity form. The method involves solving the vorticity transport equations in ‘curl-form’ along with a set of Cauchy–Riemann type equations for the velocity. The equations are formulated in cylindrical co-ordinates and discretized using a staggered grid arrangement. The discretized Cauchy–Riemann type equations are overdetermined and their solution is accomplished by employing a conjugate gradient method on the normal equations. The vorticity transport equations are solved in time using a semi-implicit Crank–Nicolson/Adams–Bashforth scheme combined with a second-order accurate spatial discretization scheme. Special emphasis is put on the treatment of the polar singularity. Numerical results of axisymmetric as well as non-axisymmetric flows in a pipe and in a closed cylinder are presented. Comparison with measurements are carried out for the axisymmetric flow cases. Copyright © 2003 John Wiley & Sons, Ltd.
An aerodynamic model for the simulation of unsteady flow past rotors of wind turbines is presented. The model consists of solving the unsteady, axisymmetric Euler or Navier-Stokes equations by a finite-difference method subject to volume forces determined from tabulated airfoil data. Results are compared to the blade-element momentum theory and experiments for the cases of a rotor with a prescribed constant normal load and steady as well as unsteady flows past the 2 MW Tjæreborg wind turbine. The model is found to be in better agreement with measurements than the momentum theory and in particular excellent agreement is obtained with dynamic in-flow phenomena from measured pitching transients.
A finite difference method is presented to solve the 3D Navier-Stokes equations in velocity-vorticity form. Several systems of equations in velocity-vorticity form have been discussed. Applications of the method for flows around both a cube and a sphere are realized. The comparisons between the results of the present formulation and those of the velocity-pressure formulation or the experimental data show that the present method is consistent.
A theoretical model is applied to the rotor aerodynamics of a horizontal axis twin-bladed wind turbine. The model combines a vortex lattice representation of the flow over the blade with a free vortex near wake which is iteratively relaxed into the local flow direction. Beyond this region the near wake is joined to a simplified axisymmetric far wake.Separated flow over the blades is represented by an extension of the source wake model of Parkinson and Jandali in which the separation pressure must be specified. The results are compared with predictions made using standard blade element theory and some experimental blade pressure measurements.
A brief summary of an extended study of horizontal axis wind turbine technology is followed by the results of additional studies of their performance and stability characteristics.
Thesis--Technical University of Denmark, 1986. Includes bibliographical references (p. 129-137).
The paper describes an investigation concerning the question whether Prandtl's classical lifting line theory and Weissinger's extended lifting line theory are really applicable to the aerodynamic analysis of the helicopter rotor in forward flight. The description of the flowfield is based on the acceleration potential instead of the usual velocity potential. By means of the matched asymptotic expansion technique two numerically efficient lifting line theories, fully applicable to the helicopter blade, are derived.
A method has been developed to analyze the wing/rotor interaction of tilt rotor aircraft in hover. The unsteady, thin-layer compressible Navier-Stokes equations are solved using an implicit, finite difference scheme that employs lower upper-alternating direction implicit factorization. The rotor is modeled as an actuator disk that imparts a radial and azimuthal distribution of pressure rise and swirl to the flowfield. The chimera approach of grid point blanking is used to update the rotor boundary conditions. Results are presented for both a rotor alone and for wing/rotor interaction where the thrust coefficient is 0.0164 and wing flap deflection is 67 deg. Many of the complex flow features are captured, including the transition from chordwise to spanwise flow on the wing upper surface, the fountain effect, the wing leading- and trailing-edge separation, and the large region of separated flow beneath the wing. Wing surface pressures compare fairly well with experimental data although the time-averaged download is somewhat higher than the measured value. Discrepancies with experimental results are due to a combination of factors that are discussed.
Results obtained from a recent investigation of the flowfield induced by a heavily loaded actuator disk. First, the governing nonlinear integral equations are formulated from two different points of view, and the iterative solution is briefly outlined. Calculated flow patterns are presented for representative advance ratios and blade circulation distributions. For the static condition, the experimentally observed lingering of the tip vortices in the propeller plane, and the insensitivity of the streamline pattern to thrust coefficient are both accounted for, and a 'dividing streamline' - apparently not previously discussed in the literature, is predicted for the nonstatic case. Finally, the relationship between the actuator disk flow and the zero harmonic of the flowfield induced by a finite-bladed propeller is considered.
Investigation of the Yawed Operation of Wind Turbines by Means of a Vortex Particle Method
- S G Voutsinas
- M A Beleiss
- K G Rados
Sectional Prediction of 3D Effects for Separated Flow on Rotating Blades
- H Snel
- R Houwink
- W J Piers
Polar for NACA 63-415 Airfoil
- M O L Hansen
A Hybrid Wake Model for HAWT
- R Bareiss
- S Wagner