Figure 3 - uploaded by Pier Francesco Melani
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Schematic representation of the tip vortex structure 3.2. Finite-wing simulations In order to understand the effect of mesh resolution and kernel width β/c on the blade loads and tip vortex structure predicted by the baseline ALM formulation, i.e., without corrections, eight different grids (see Table 1) were tested on the fixed-wing test case, for AR=10 and α=6°. Figure 4 reports the comparison in terms of spanwise lift coefficient and downwash velocity Vy, sampled at 1c distance from the airfoil aerodynamic center, between ALM and blade-resolved CFD. At first glance, it can be observed how the coarser meshes (BX1) are not adequate to resolve the blade 3-D field. This trend is confirmed by Figure 5, for the core radius rC and circulation Γ. Increasing the resolution towards the blade tip, the ALM downwash profile converges towards the CFD one, both in terms of
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Simulation of the complex, unsteady aerodynamics characterizing Darrieus rotors requires computational tools with a fidelity higher than the ubiquitous Blade Element Momentum (BEM) theory. Among them, the Actuator Line Method (ALM) stands out in terms of accuracy and computational cost. This approach, however, still fails to resolve the vortex-like...
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Context 1
... order to quantify the effect of the various modelling strategies on the predicted tip vortex structure, different vortex tracking metrics were selected from the literature. More in detail, the following quantities of interest, as illustrated in Figure 3, were defined: vortex center C: the vortex center defines the axis of rotation of the vortical structure and it is used to track the position of the vortex filament over time. In the present work, this quantity is extracted from the resolved flow field as the minimum of the λ2 scalar field [21]. ...
Context 2
... strategy allows in fact to filter out the contribution of viscous stresses and irrotational straining. vortex core radius rC: the vortex core radius defines the extension of the rotational region, highlighted in Figure 3, in which the fluid particles are characterized by a rigid body motion. This corresponds to an elevated concentration of vorticity. ...
Context 3
... corresponds to an elevated concentration of vorticity. In the present work, this value is exploited to quantify the vortex aging, i.e. viscous decay, in the wake and is computed as the distance between the vortex center C and the point of maximum induced velocity Vind sampled on a plane normal to the vortex line [22], as in Figure 3. vortex circulation ΓV: circulation is a measure of the vortex intensity and is used together with rC to measure its aging in the wake. ...
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... This study builds on these findings to further investigate how the ALM base formulation -in terms of angle of attack (α) sampling and force insertion -can be tuned to effectively describe tip effects. To this end, an in-house ALM tool was employed to simulate a finite wing, for which high-fidelity bladeresolved CFD (BR-CFD) data are available as benchmark [12]. In the first part of the work, different sampling and force insertion strategies are compared for a fixed blade pitch angle of 6°. ...
... The k- Shear Stress Transport (SST) model is used for turbulence closure. Discretization schemes, computational domain, and grid derive from the optimal setup found in a previous work on the same test case [12]. Figure 1a illustrates the adopted computational domain, whose dimensions are selected to minimize blockage effects and allow the blade wake to properly develop. ...
... The standard isotropic Gaussian kernel is used as projection function, using a β constant along the span and equal to 0.1c. This value ensures a correct description of the tip vortex core [12]. As observed in a previous study of the authors [11], this approach leads to two contrasting trends. ...
The Actuator Line Method (ALM) is gaining popularity in wind turbine simulations,
as it can better handle some of the challenging operating conditions experienced by modern machines, such as highly turbulent inflows, severe aero-elastic forcing, and complex rotor-to-rotor interactions. However, it still falls behind other medium-fidelity methods such as the Lifting Line Free Vortex Wake (LLFVW) when it comes to resolving tip vortices and their effect on the blade spanwise load profile. The reason for such behavior is still unclear. A recent study suggested that this issue can be solved by reducing the scale of the angle of attack (α) sampling and force insertion towards the tip, without the need of additional corrections. This study builds on these findings to further investigate how the ALM base formulation - in terms of α sampling and force insertion - can be tuned to properly describe tip effects. An in-house ALM tool was employed to simulate a finite, constant-chord, NACA0018 wing, for which high-fidelity blade-resolved CFD (BR-CFD) data are available as benchmark. In the first part of the work, different strategies are outlined, including a novel approach for the de-coupling of the angle of attack sampling step from the force projection one, here called DE-coupled LineAverage (DELA). Their accuracy and sensitivity to ALM numerical settings are assessed at a fixed wing pitch angle of 6°. The analysis is then extended to a wider range of blade pitch angles, benchmarking the new ALM formulation against BR-CFD, ALM with the Dağ and Sørensen correction, and LLFVW in terms of blade loads, tip vortex structure, and computational effort.
... Mendoza and Goude [20] evaluated the ALM sensitivity to the aerodynamic coefficients by using two different sets of polar data, one measured experimentally [21] that showed underestimated power coefficient values, and the other exported from XFoil [22] that showed an overestimation of the power coefficient at low tip-speed ratios. More recently, Melani et al. [23,24] proposed a number of submodels and corrections to tailor the ALM for use in Darrieus VAWTs, obtaining notable improvements in the overall accuracy, while still seeing some general overestimation of the performance, especially in the dowind region of the rotor. ...
... More specifically, in [1] a novel method to extrapolate the angle of attack on a Darrieus turbine from a CFD-computed flow field. This passage was indeed of capital importance because it represented the only way to get useful benchmarking data from CFD. Thanks also to the information gathered with the new method, in [24] a number of corrections, sub-models and new methods have been presented that allowed tailoring the ALM to Darrieus VAWTs, while leaving some issues open on how to further improve the accuracy of the ALM. ...
... The main features of the ALM code used in this study [24] are: ...
Darrieus vertical-axis turbines are known for their complex aerodynamics connected to the continuous change in the angle of attack experienced by the blades, which often exceeds the static stall limit. Low fidelity tools such as the Blade Element Momentum Theory have been shown lately not to provide sufficient levels of accuracy, while the medium-fidelity Actuator Line Method (ALM) has been increasingly applied to Darrieus rotors. In this method, the blade-flow interaction is modeled as an equivalent momentum loss calculated introducing equivalent aerodynamic forces into the computed Computational Fluid Dynamics (CFD) domain. This strongly reduces the computational cost in comparison to blade-resolved CFD, allowing ALM to be used in three-dimensional problems, e.g., multiple rotors, floating offshore, etc. While several corrections and guidelines have been recently proposed to tailor ALM to Darrieus turbines, issues are still open on how to improve accuracy. The present study aims at assessing to what extent the three main factors of the ALM theory, namely the quality of input polar, the dynamic stall modeling, and the force insertion in the domain, influence the overall accuracy of the method. In particular, this unprecedented understanding is enabled by the novel use of a "frozen ALM", i.e., an ALM method fed by the aerodynamic forces calculated by blade-resolved CFD, which allowed to separate the contributions coming from airfoil performance analysis and force projection in the domain. Based on the results, three main important conclusions are drafted out: i) for high and medium tip-speed ratios, provided that the aerodynamic forces are correct, the ALM method is able to generate extremely accurate solutions of the flow field, almost equivalent to blade-resolved CFD; ii) the relevance of the kernel's shape and smearing function is largely overestimated and current knowledge is adequate for the model to be set; iii) a better dynamic stall model is indeed the real key factor that could lead to an improvement of the ALM accuracy.
... The seminal works of Bachant et al. [39] and Zhao et al. [34] demonstrated that a reduced-order approach consisting of ALM and URANS (with a turbulence model) is both valid and promising for future VAWT investigations. Some recent studies focus on enhancing the fidelity of VAWT ALM (with LES and URANS) by using cubic spline smoothing on the angle of attack combined with a novel inflow velocity sampling procedure [40], evaluating advanced sub-models for tip effects (Glauert correction versus Dag & Sørensen) [41], and developing a cohesive and upgraded framework to account for higher-order aerodynamic effects [42]. ...
The presence of power augmentation effects, or synergy, in vertical-axis wind turbines (VAWTs) offers unique opportunities for enhancing wind-farm performance. This paper uses an open-source actuator-line-method (ALM) code library for OpenFOAM (turbinesFoam) to conduct an investigation into the synergy patterns within two- and three-turbine VAWT arrays. The application of ALM greatly reduces the computational cost of simulating VAWTs by modelling turbines as momentum source terms in the Navier--Stokes equations. In conjunction with an unsteady Reynolds-Averaged Navier--Stokes (URANS) approach using the $k$-$\omega$ shear stress transport (SST) turbulence model, the ALM has proven capable of predicting VAWT synergy. The synergy of multi-turbine cases is characterized using the power ratio which is defined as the power coefficient of the turbine cluster normalized by that for turbines in isolated operation. The variation of the power ratio is characterized with respect to the array layout parameters, and connections are drawn with previous investigations, showing good agreement. The results from 108 two-turbine and 40 three-turbine configurations obtained using ALM are visualized and analyzed to augment the understanding of the VAWT synergy landscape, demonstrating the effectiveness of various layouts. A novel synergy superposition scheme is proposed for approximating three-turbine synergy using pairwise interactions, and it is shown to be remarkably accurate.
The actuator line method (ALM) is increasingly being preferred to the ubiquitous blade element momentum (BEM) approach in several applications related to wind turbine simulation, thanks to the higher level of fidelity required by the design and analysis of modern machines. Its capability to resolve blade tip vortices and their effect on the blade load profile is, however, still unsatisfactory, especially when compared to other medium-fidelity methodologies such as the lifting line theory (LLT). Despite the numerical strategies proposed so far to overcome this limitation, the reason for such behavior is still unclear. To investigate this aspect, the present study uses the ALM tool developed by the authors for the ANSYS® Fluent® solver (v. 20.2) to simulate a NACA0018 finite wing for different pitch angles. Three different test cases were considered: high-fidelity blade-resolved computational fluid dynamics (CFD) simulations (to be used as a benchmark), standard ALM, and ALM with the spanwise force distribution coming from blade-resolved data (frozen ALM). The last option was included to isolate the effect of force projection, using three different smearing functions. For the postprocessing of the results, two different techniques were applied: the LineAverage sampling of the local angle of attack along the blade and state-of-the-art vortex identification methods (VIMs) to outline the blade vortex system. The analysis showed that the ALM can account for tip effects without the need for additional corrections, provided that the correct angle of attack sampling and force projection strategies are adopted.
This study reports the results of the second round of analyses of the Offshore Code Comparison, Collaboration, Continued, with Correlation and unCertainty (OC6) project Phase III. While the first round investigated rotor aerodynamic loading, here, focus is given to the wake behavior of a floating wind turbine under large motion. Wind tunnel experimental data from the UNsteady Aerodynamics for FLOating Wind (UNAFLOW) project are compared with the results of simulations provided by participants with methods and codes of different levels of fidelity. The effect of platform motion on both the near and the far wake is investigated. More specifically, the behavior of tip vortices in the near wake is evaluated through multiple metrics, such as streamwise position, core radius, convection velocity, and circulation. Additionally, the onset of velocity oscillations in the far wake is analyzed because this can have a negative effect on stability and loading of downstream rotors. Results in the near wake for unsteady cases confirm that simulations and experiments tend to diverge from the expected linearized quasi-steady behavior when the rotor reduced frequency increases over 0.5. Additionally, differences across the simulations become significant, suggesting that further efforts are required to tune the currently available methodologies in order to correctly evaluate the aerodynamic response of a floating wind turbine in unsteady conditions. Regarding the far wake, it is seen that, in some conditions, numerical methods overpredict the impact of platform motion on the velocity fluctuations. Moreover, results suggest that the effect of platform motion on the far wake, differently from original expectations about a faster wake recovery in a floating wind turbine, seems to be limited or even oriented to the generation of a wake less prone to dissipation.
The Actuator Line Method (ALM) is being increasingly preferred to the ubiquitous Blade Element Momentum (BEM) approach in several applications related to wind turbine simulation, thanks to the higher level of fidelity required by the design and analysis of modern machines. Its capability to resolve the vortex-like structures shed at the blade tip (i.e., tip vortices) and their effect on the blade load profile is, however, still unsatisfying, especially when compared to other medium-fidelity methodologies such as the Lifting Line Theory (LLT). Despite the numerical strategies proposed so far to overcome this limitation, the reason for such behaviour is still unclear. To investigate this aspect, the present study uses the ALM tool developed by the authors for the ANSYS ® FLUENT ® solver (v. 20.2) to simulate a NACA0018 finite wing for different pitch angles. Three different test cases were considered: high-fidelity blade-resolved CFD simulations, to be used as a benchmark, standard ALM, and ALM with the spanwise force distribution coming from blade-resolved data (frozen ALM). The last option was included to isolate the effect of force projection, using three different smearing functions. For the post-processing of the results, two different techniques were applied: the LineAverage sampling of the local angle of attack along the blade and state-of-the-art Vortex Identification Methods (VIM) to outline the blade vortex system. The analysis showed that the ALM can account for tip effects without the need of additional corrections, provided that the correct angle of attack sampling and force projection strategies are adopted.
This study reports the results of the second round of analyses of the OC6 project Phase III. While the first round investigated rotor aerodynamic loading, here focus is given to the wake behavior of a floating wind turbine under large motion. Wind tunnel experimental data from the UNsteady Aerodynamics for FLOating Wind (UNAFLOW) project are compared with the results of simulations provided by participants with methods and codes of different levels of fidelity. The effect of platform motion both on the near and the far wake is investigated. More specifically, the behavior of tip vortices in the near wake is evaluated through multiple metrics, such as streamwise position, core radius, convection velocity, and circulation. Additionally, the onset of velocity oscillations in the far wake is analyzed because this can have a negative effect on stability and loading of downstream rotors. Results in the near wake for unsteady cases confirm that simulations and experiments tend to diverge from the expected linearized quasi-steady behavior when the rotor reduced frequency increases over 0.5. Additionally, differences across the simulations become significant, suggesting that further efforts are required to tune the currently available methodologies in order to correctly evaluate the aerodynamic response of a floating wind turbine in unsteady conditions. Regarding the far wake, it is seen that, in some conditions, numerical methods over-predict the impact of platform motion on the velocity fluctuations. Moreover, results suggest that, different from original expectations about a faster wake recovery in a floating wind turbine, the effect of platform motion on the far wake seems to be limited or even oriented to the generation of a wake less prone to dissipation.
