An analytical linear two-dimensional actuator disc model and comparisons with computational fluid dynamics (CFD) simulations

IF 3.6 Q3 GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY
H. A. Madsen
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引用次数: 0

Abstract

Abstract. The continuous up-scaling of wind turbines enabled by more lightweight and flexible blades in combination with coning has challenged the assumptions of a plane disc in the commonly used blade element momentum (BEM)-type aerodynamic codes for the design and analysis of wind turbines. The objective with the present work is thus to take a step back relative to the integral 1-dimensional (1-D) momentum theory solution in the BEM model in order to study the actuator disc (AD) flow in more detail. We present an analytical, linear solution for a two-dimensional (2-D) AD flow with one equation for the axial velocity and one for the lateral velocity, respectively. Although it is a 2-D model, we show in the paper that there is a good correlation with axis-symmetric and three-dimensional (3-D) computational fluid dynamics (CFD) simulations on a circular disc. The 2-D model has thus the potential to form the basis for a simple and consistent rotor induction model. For a constant loading, the axial velocity distribution at the disc is uniform as in the case of the classical momentum theory for an AD. However, an important observation of the simulated flow field is that immediately downstream of the disc the axial velocity profiles change rapidly to a shape with increased induction towards the edges of the disc and less induction on the central part. This is typically what is seen at the disc in full non-linear CFD AD simulations, which is what we compare with in the paper. By a simple coordinate rotation the analytical solution is extended to a yawed disc with constant loading. Again, a comparison with CFD, now with a 3-D simulation on a circular disc in yaw, confirms a good performance of the analytical 2-D model for this more complicated flow. Finally, a further extension of the model to simulate a coned disc is obtained using a simple superposition of the solution of two yawed discs with opposite yaw angles and positioned so the two discs just touch each other. Now the validation of the model is performed with results from axis-symmetric CFD simulations of an AD with a coning of both 20 and −20∘. In particular, for the disc coned in the downwind direction there is a very good correlation between the simulated normal velocity to the disc, whereas some deviations are seen for the upwind coning. The promising correlation of the results for the 2-D model in comparison with 3-D simulations of a circular disc with CFD for complicated inflow like what occurs at yaw and coning indicates that the 2-D model could form the basis for a new, consistent rotor induction model. The model should be applied along diagonal lines on a rotor and coupled to an angular momentum model. This application is sketched in the outlook and is a subject for future research.
线性二维致动器圆盘分析模型以及与计算流体动力学 (CFD) 模拟的比较
摘要由于叶片更轻、更灵活,再加上锥形结构,风力涡轮机的规模不断扩大,这对用于设计和分析风力涡轮机的常用叶片动量(BEM)型空气动力学代码中的平面圆盘假设提出了挑战。因此,本研究的目的是相对于 BEM 模型中的一维(1-D)动量理论整体解法后退一步,以便更详细地研究致动器圆盘(AD)流。我们为二维(2-D)AD 流提出了一个分析性线性解决方案,其中一个方程分别表示轴向速度,一个方程表示横向速度。虽然这是一个二维模型,但我们在论文中表明,它与轴对称和三维(CFD)计算流体动力学(CFD)圆盘模拟有很好的相关性。因此,二维模型有可能成为简单一致的转子感应模型的基础。对于恒定负载,圆盘上的轴向速度分布是均匀的,就像经典动量理论中的 AD 一样。然而,对模拟流场的一个重要观察结果是,紧靠圆盘下游的轴向速度剖面迅速变化为圆盘边缘感应增加而中心部分感应减少的形状。这是在全非线性 CFD AD 模拟中在圆盘处看到的典型情况,也是我们在本文中进行比较的情况。通过简单的坐标旋转,分析解决方案扩展到了具有恒定负载的偏航圆盘。通过与 CFD 进行比较(现在是对偏航圆盘进行三维模拟),再次证实了二维分析模型在这种更为复杂的流动中的良好性能。最后,通过对两个偏航角度相反的圆盘进行简单的叠加求解,使两个圆盘刚好相碰,从而进一步扩展了模型,以模拟锥形圆盘。现在,我们利用轴对称 CFD 仿真结果对模型进行验证,仿真结果显示 AD 的锥度分别为 20 和 -20∘。特别是,对于下风方向的圆锥盘,模拟的法向速度与圆锥盘之间的相关性非常好,而对于上风方向的圆锥盘,则出现了一些偏差。二维模型的结果与使用 CFD 对圆盘进行的三维模拟结果相比,具有很好的相关性,这表明二维模型可以作为新的、一致的转子感应模型的基础。该模型应沿对角线应用于转子,并与角动量模型相结合。这种应用在展望中作了概述,是未来研究的一个课题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Wind Energy Science
Wind Energy Science GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY-
CiteScore
6.90
自引率
27.50%
发文量
115
审稿时长
28 weeks
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