二維反正切函數風力機尾流模型之分析

An Analysis of Two-Dimensional Arctangent Function Wind Turbine Wake Model

王名暉(MING-HUI WANG)

指導教授 ： 許政行

中原大學/工學院/機械工程學系/碩士(2022年)

https://doi.org/10.6840/cycu202201420

摘要

本研究主旨為開發一數學理論分析模型，透過模型預測風力機後方各下游位置的尾流速度。此模型使用基於風力機圓盤理論的質量及動量守恆進行推導，並且假設尾流速度缺陷形狀為反正切函數分布，另外在此模型中的尾流擴增率並非常數，而是考慮環境周圍紊流以及轉子產生的紊流所造成的影響。
本研究將反正切函數尾流模型針對實地雷達測量、兩種不同推力大小設定的風洞實驗以及本研究根據台灣離岸風速塔測量資料所建立的不同入流風速大小的數值模擬以上三種數據進行驗證及預測，並且加入其他三個現今較為主流的尾流模型(高帽、高斯、餘弦模型)進行比較。
經由驗證及預測結果可以發現本研究提出的模型所預測的正規化尾流速度，與實驗和數值模擬數據皆有很好的一致性。反正切函數尾流模型於實地雷達測量數據的預測，在不同下游位置的平均相對誤差皆小於6%，而在兩種不同推力條件的風洞實驗數據的預測上，三個由近到遠不同下游距離平均相對誤差也皆小於3%，此外在下游距離由近到遠及三種不同入流風速下的CFD數值模擬數據預測，其平均相對誤差也皆低於8.5%。由以上預測結果表明，該模型適用於各種風力機數據的流向速度場預測，可為日後風力機間距排列的選擇提供一定的參考。

關鍵字

數學理論分析模型 ； 尾流速度預測 ； 反正切函數分布

並列摘要

The main purpose of this study is to develop a mathematical theoretical analysis model to predict the wake velocity at various downstream locations behind the wind turbine. This model is derived using the conservation of mass and momentum based on the wind turbine actuator disc theory, and assuming an arctangent function distribution for the wake velocity deficit shape. The wake growth rate in this model is not constant, but consider the effects of the ambient turbulence and the turbulent flow generated by the rotor.
In this study, the arctangent function wake model is verified by on-site radar measurements, wind tunnel experiments with two different thrust settings, and numerical simulations of different inflow wind speeds established in this study based on Taiwan's offshore wind tower measurement data ,and add the other three more mainstream wake models (top hat, Gaussian, cosine model) for comparison.
Through the verification and prediction results, it can be found that the normalized wake velocity predicted by the model proposed in this study is in good agreement with the experimental and numerical simulation data. The mean relative errors (MRE) of the arctangent function wake model in the prediction of the field radar measurement data is less than 6% at different downstream positions, and in the prediction of the wind tunnel experimental data under two different thrust conditions, the mean relative errors of three different downstream distances from near to far are all less than 3%. In addition, the mean relative errors of CFD numerical simulation data predictions from near to far downstream distances and under three different inflow wind speeds are also less than 8.5%. The above prediction results show that the model is suitable for the prediction of the flow direction velocity field of various wind turbine data, and can provide a certain reference for the selection of wind turbine spacing in the future.

並列關鍵字

Mathematical theoretical analysis model ； Wake velocity prediction ； Arctangent function distribution

參考文獻

[1] 台灣電力公司官方網站, https://www.taipower.com.tw/tc/index.aspx

[2] 經濟部能源局官方網站,風力發電4年推動計畫, https://www.moeaboe.gov.tw/ECW/populace/content/ContentDesc.aspx?menu_id=5493

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[5] Frandsen, Sten. "On the wind speed reduction in the center of large clusters of wind turbines." Journal of Wind Engineering and Industrial Aerodynamics 39.1-3 (1992): 251-265.