臺灣博碩士論文加值系統

為了計算風力發電機扇葉對雷達的影響，所以要計算雷達截面積RCS(radar cross section)，因為風力發電機扇葉形狀不規則的原因，所以從入射波以及散射波推導了表面積分計算RCS的方式，以圓柱為例，先將圓柱用二次曲面貼片網格化後，比較以圓柱的解析公式計算以及表面積分計算的正確性，發現結果非常接近，可惜表面積分耗費時間太長。

為了縮短計算時間，在不考慮 時，簡化原本表面積分的計算方式，計算圓柱模型，因網格化的網格沒有扭曲(twist)，結果與利用圓柱計算公式相比也非常接近。

然而因為風力發電機扇葉形狀有扭曲，因此必須要考慮 ，而表面積分的拆解則是使用Boersma多項式，將表面積分變成27個一維積分的計算式，而一維積分計算方式能再用部分積分的方法，先解出通式，再以遞迴的方法計算。此計算結果要與直接使用一維積分的方式比較，是否錯誤。

因遞迴的方法會導致計算結果發散的錯誤，本文提出了五種計算方式，雖然錯誤個數大幅縮小，然而錯誤的數值過大，導致最終的結果差異甚遠，未能因此準確的計算出正確的RCS值，但是理論推導的地方是沒有問題的。所以我們最後再回到原來表面積分的計算方法，而計算結果與使用FEKO所計算的風力發電機扇葉模型RCS相當接近。

關鍵字:風力發電機扇葉、雷達截面積、PATRAN、二次曲面貼片。

For calculating how the wind turbine blades interfere with the radar, we use radar cross section. Because the blades are irregular, we start from incident wave and scatter wave to derive a surface integral to evaluate RCS. In the case of a circular cylinder, we use curvilinear patches to decompose the cylinder surface. The different results between using the surface integral and using cylinder formula are close. Nevertheless, the surface integral method takes a lot of time.

To accelerate the calculation, if is ignored, the surface integral can be simplified. Due to no twisting in the circular cylinder, this approach yields results very close to that by using the analytical formula.

However, the wind turbine blade patches exhibit twisting. So cannot be ignored. We use the Boersma’s polynomial to expand the Fresnel function, and this results in 27 1D integrals. For these 1D integrals, the integration by part method is utilized to derive recurrence relations, which can efficiently evaluate these 1D integrals. Comparisons are made between results by the recurrence method and those by direct numerical integrations.

Unfortunately, the recurrence approach sometimes gives rise to divergently erroneous results. Effort has been made to reduce the errors by setting parameter thresholds to determine what alternative to be used to improve the results. Although the errors are less, the resulting values still does not make any sense comparing with those accurate results. Because of this discrepancy, the proposed accelerating method fails to provide accurate RCS at this time. With recurrence formulae being correct, more tests should be conducted in order to find the real cause of numerical errors. Therefore we resort to the original surface integral in calculating RCS, which has been applied for the wind turbine blade. The obtained result is compared favorably with that by the commercial software, FEKO.

Keywords: blades of wind turbines、RCS、PATRAN、quadratic curvilinear patches.

目次
摘 要 I
Abstract II
目次 III
圖目次 IV
表目錄 V
第一章 序論 1
1.1 研究動機與目的 1
1.2 文獻回顧 1
1.3 章節概要 2
第二章 風力發電機RCS計算 3
2.1 扇葉模型網格化 3
2.2 風力發電機扇葉RCS 11
2.3 Matlab程式驗證 13
2.4考慮 的計算方式 18
2.5 二維積分的計算方式 22
第三章 結論 25
參考文獻 27
附錄1 28
附錄2 30
附錄3 33
附錄4 34

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[7] J. Boersma, “Computation of Fresnel Integrals,” Math. Comp., vol.14, pp.380, 1960.