第三章 風洞實驗
第五節 縮尺模型試驗結果
為了解不同縮尺效應可能造成之試驗誤差，本案製作 3 組不同縮尺之風 壓模型，建築物體參考文獻資料，取美國德州科技大學之實場量測建築尺寸 設計製作，其外觀、幾何尺寸與量測點位如圖 3.52 與 3.53 所示，其建築尺寸 經計算後發現 1/250 縮尺模型尺寸僅剩 3.7×5.5×1.6 cm，無法製作與進行量測，
因此選定為 1/100 縮尺、1/50 縮尺與 1/25 縮尺，藉由三種尺寸之壓力量測試 驗探討模型縮尺之影響(尺寸如表 3.11)。
圖 3.52 TTU 量測建築外觀 圖 3.53 TTU 量測建築尺寸與點位 (資料來源：文獻 Lin 等人(1995)、Mehta 等人(1992)) 表 3.11 實際建物與縮尺模型尺寸
寬 ( cm ) 長 ( cm ) 高 ( cm ) 實際建築物尺寸 922.02 1379.22 398.68 1/100 縮尺 9.22 13.79 3.99
1/50 縮尺 18.44 27.58 7.97 1/25 縮尺 36.88 55.17 15.95
(資料來源：本研究整理)
1. 風壓模型試驗條件
由於 TTU 建物之位置地況較接近於 C 地況，研究中將試驗來流條件設 為 1/250 與 1/50 之 C 地況來流擺設，並取文獻資料壓力點 50101 與 50501 兩 處典型位置之平均、擾動與極值壓力值進行比對。資料比對參考文獻 Tieleman
48
等人(1996)之內容，其分析了現場 860 筆資料並製圖，且所選之壓力資料量 測之風速於現場建築高處皆大於 8 m/s 以上，單一筆資料擷取時間為 15 分鐘。
由於在風洞內之試驗時間有限，本案無法取相同數量之試驗資料分析，經時 間縮尺後取 10 段等長 15 分鐘之擷取時間並進行量測，模型之壓力管連接於 scanivalve 電子式壓力掃描系統進行量測，試驗風速於模型高處設定為 8 m/s，
使風速縮尺為 1，時間縮尺即可由幾何縮尺計算而得，模型連接架設狀況如 圖 3.54 所示。
圖 3.54 模型架設示意圖
(資料來源：本研究整理) 試驗分別將縮尺 1/25、縮尺 1/50 與縮尺 1/100 之模型放置於 C 地況 1/250 與 1/50 流場內(圖 3.55 至圖 3.60)，風向角以 15 度為間隔，由 90 度轉至 270 度進行量測，量測資料經下式計算分別得出平均、擾動壓力係數：
平均壓力係數 2
n
1 i
i
p U
2 1 n
p C =
= (3-1)
擾動壓力係數 2
n
1 i
2 i
p
U
2 1 n
) p p ( '
C
−
=
= (3-1)
另取各分段量測時序內最大壓力值之前 5 數值平均代表極值壓力係數。
第三章 風洞實驗
49
圖 3.55 1/250 C 地況 1/100 模型 圖 3.56 1/50 C 地況 1/100 模型
圖 3.57 1/250 C 地況 1/50 模型 圖 3.58 1/50 C 地況 1/50 模型
圖 3.59 1/250 C 地況 1/25 模型 圖 3.60 1/50 C 地況 1/25 模型 (資料來源：本研究整理)
50
Azimuth angle (deg) -Cp
TTU 50101 (Tieleman et al.) TTU 50101 average C1/50-1/25 scale model C1/50-1/50 scale model C1/50-1/100 scale model C1/250-1/25 scale model C1/250-1/50 scale model C1/250-1/100 scale model
Azimuth angle (deg) -Cp
TTU 50501 (Tieleman et al.) TTU 50101 average C1/50-1/25 scale model C1/50-1/50 scale model C1/50-1/100 scale model C1/250-1/25 scale model C1/250-1/50 scale model C1/250-1/100 scale model
第三章 風洞實驗 在 50501 之擾動與極值壓力差異問題，在文獻 Lin 等人(1995)、Tieleman 等人(1996)亦得到類似結果並指出可能原因眾多，包含壓力管尺寸、建築邊 角幾何失真、紊流尺度、角渦流雷諾數效應以及實場之非定常效應皆可能影
Azimuth angle (deg) Cp'
TTU 50101 (Tieleman et al.) TTU 50101 average C1/50-1/25 scale model C1/50-1/50 scale model C1/50-1/100 scale model C1/250-1/25 scale model C1/250-1/50 scale model C1/250-1/100 scale model
Azimuth angle (deg) Cp'
TTU 50501 (Tieleman et al.) TTU 50101 average C1/50-1/25 scale model C1/50-1/50 scale model C1/50-1/100 scale model C1/250-1/25 scale model C1/250-1/50 scale model C1/250-1/100 scale model
Azimuth angle (deg) Cp(peak)
TTU 50101 (Tieleman et al.) TTU 50101 average C1/50-1/25 scale model C1/50-1/50 scale model C1/50-1/100 scale model C1/250-1/25 scale model C1/250-1/50 scale model C1/250-1/100 scale model
Azimuth angle (deg) Cp(peak)
18 TTU 50501 (Tieleman et al.) TTU 50101 average C1/50-1/25 scale model C1/50-1/50 scale model C1/50-1/100 scale model C1/250-1/25 scale model C1/250-1/50 scale model C1/250-1/100 scale model
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響。而另 Cochran 等人(1992)提及實場量測之壓力管在更大尺寸之狀況下量 測之擾動值與極值下降約達 25%，較接近於實驗量測之值，即實場量測之壓 力管尺寸對量測資料影響不可忽視。
表 3.12 50101 平均風壓係數誤差表
地況縮尺 1/50 1/250
模型縮尺 1/25 1/50 1/100 1/25 1/50 1/100
平均誤差 10.10% 10.77% 12.77% 15.84% 14.64% 16.02%
90 23.49% 4.11% 27.14% -0.57% -9.71% -16.40%
105 6.00% -3.06% 15.80% -13.02% -25.14% -24.16%
120 -2.14% -7.02% 10.66% -9.74% -14.08% -15.12%
135 0.99% -7.09% 8.20% -5.69% 3.45% 0.98%
150 5.21% -2.60% 11.11% -0.05% 4.57% 7.64%
165 -5.63% -20.23% -6.07% -3.30% -3.42% -7.59%
180 -14.38% -26.21% -19.60% -24.58% -21.41% -25.27%
195 4.98% -1.02% 6.33% 32.47% 37.80% 27.43%
210 -23.14% -20.32% 5.29% -28.51% -6.38% 8.09%
225 -17.03% -18.50% 7.42% -15.80% 0.87% 5.54%
240 -9.58% -5.38% 26.08% -28.69% -15.16% 15.14%
255 6.37% -3.39% 7.31% 29.73% 34.63% 32.89%
270 -12.32% -21.07% -15.01% -13.81% -13.72% -22.06%
(資料來源：本研究整理)
第三章 風洞實驗
53
表 3.13 50501 平均風壓係數誤差表
地況縮尺 1/50 1/250
模型縮尺 1/25 1/50 1/100 1/25 1/50 1/100
平均誤差 11.41% 15.89% 22.06% 13.28% 23.59% 23.52%
90 9.77% -6.59% 24.36% -14.50% -18.45% -22.50%
105 11.14% -1.97% 15.78% -3.35% -12.74% -10.83%
120 2.52% -7.42% 7.95% 0.15% -2.77% -9.42%
135 5.74% -5.70% 9.94% 3.22% 11.25% 6.42%
150 5.64% -2.78% 9.19% 1.44% 8.17% 8.67%
165 1.09% -12.05% 1.77% 1.35% 2.75% 0.00%
180 -14.28% -23.75% -14.06% -23.07% -18.76% -20.27%
195 -12.54% -19.90% -16.16% -18.69% -14.32% -17.19%
210 -0.20% -11.65% -12.84% 2.07% 12.31% -3.34%
225 0.55% -4.79% 4.17% 23.46% 43.74% 31.57%
240 18.16% 21.48% 45.27% 19.14% 52.58% 58.09%
255 27.04% 45.09% 69.29% 6.04% 39.96% 57.89%
270 39.67% 43.46% 55.96% 56.14% 68.93% 57.90%
表 3.14 50101 擾動風壓係數誤差表
地況縮尺 1/50 1/250
模型縮尺 1/25 1/50 1/100 1/25 1/50 1/100
平均誤差 14.49% 17.44% 24.02% 28.07% 23.94% 21.27%
90 53.10% 57.30% 103.30% 15.20% 57.80% 59.50%
105 4.27% 9.20% 42.00% -29.67% -16.00% -10.60%
120 -12.55% -1.95% 26.45% -32.73% -18.14% -11.64%
135 -13.65% -7.50% 17.38% -35.46% -19.31% -12.38%
150 18.58% 19.04% 40.62% -7.73% 8.08% 22.27%
165 8.54% -6.67% 6.90% -9.62% -0.44% -0.85%
180 3.78% -5.48% 12.06% -36.46% -23.72% -22.48%
195 3.04% -14.47% -14.23% -19.41% -21.73% -19.55%
210 -6.52% -10.63% 4.48% -15.80% 1.18% 12.06%
225 -31.55% -31.14% -1.18% -70.94% -53.67% -45.96%
240 1.87% -9.86% 7.37% -39.69% -35.75% -0.61%
255 -3.62% -23.74% -16.15% -4.78% -11.49% -16.71%
270 -27.31% -29.76% -20.08% -47.48% -43.88% -41.96%
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表 3.15 50501 擾動風壓係數誤差表
地況縮尺 1/50 1/250
模型縮尺 1/25 1/50 1/100 1/25 1/50 1/100
平均誤差 14.55% 15.46% 18.11% 35.76% 21.41% 20.93%
90 6.41% 9.00% 39.41% -19.76% 11.47% 10.41%
105 2.90% 3.30% 24.90% -32.20% -14.65% -14.40%
120 -25.46% -19.08% 0.17% -44.20% -34.03% -31.97%
135 -25.08% -25.20% -5.08% -41.05% -29.20% -26.86%
150 -3.42% -2.44% 17.75% -28.11% -11.75% -1.60%
165 5.55% -2.32% 14.84% -19.52% -6.52% 0.00%
180 -23.58% -22.85% -4.47% -55.26% -39.79% -34.96%
195 -30.82% -33.00% -22.01% -65.51% -54.43% -48.33%
210 -29.16% -32.37% -28.19% -50.28% -39.34% -41.04%
225 -27.89% -33.98% -35.65% -43.65% -30.05% -40.33%
240 1.36% -5.15% 4.64% -22.83% 3.61% 1.71%
255 -3.19% -0.06% 15.07% -28.61% -0.77% 10.08%
270 4.38% 12.19% 23.22% -13.95% 2.65% 5.05%
表 3.16 50101 極值風壓係數誤差表
地況縮尺 1/50 1/250
模型縮尺 1/25 1/50 1/100 1/25 1/50 1/100
平均誤差 11.37% 11.35% 14.35% 29.10% 22.58% 17.05%
90 52.56% 36.22% 56.01% 22.46% 52.12% 15.64%
105 -9.67% 6.38% 27.60% -33.80% -28.40% -14.55%
120 -10.39% -11.13% 17.52% -35.13% -23.38% -23.72%
135 -14.78% 15.88% 27.60% -34.05% -17.31% -11.94%
150 0.91% 19.32% 3.96% -14.35% -8.53% 0.36%
165 6.97% 2.00% 6.07% -24.02% -1.51% -3.87%
180 -5.89% -14.96% 3.39% -39.39% -30.32% -26.91%
195 10.45% -3.38% -4.60% -27.75% -21.11% -20.63%
210 3.60% -7.41% -10.92% -14.91% 0.65% -12.84%
225 -15.45% -11.79% -19.65% -80.45% -68.40% -44.76%
240 8.13% -0.40% -4.92% -8.02% -10.38% -13.90%
255 3.53% 7.35% -0.23% -7.73% -2.31% 0.51%
270 -5.45% -11.30% -4.09% -36.22% -29.10% -32.05%
第三章 風洞實驗
55
表 3.17 50501 極值風壓係數誤差表
地況縮尺 1/50 1/250
模型縮尺 1/25 1/50 1/100 1/25 1/50 1/100
平均誤差 14.51% 17.11% 16.70% 30.18% 19.26% 21.22%
90 11.60% 20.44% 26.07% -16.97% 18.80% 18.01%
105 -18.64% 3.46% 16.30% -33.22% -26.28% -18.08%
120 -21.13% -18.21% 4.48% -32.45% -16.10% -31.13%
135 -15.70% -12.18% 6.92% -29.43% -15.05% -15.85%
150 7.99% 1.68% 36.23% -14.89% 1.91% 11.45%
165 -6.76% -15.23% -8.11% -17.33% -4.69% 0.00%
180 -21.86% -26.89% -0.03% -45.93% -38.03% -31.81%
195 -6.74% -27.84% -2.89% -49.32% -44.86% -38.00%
210 -27.79% -31.23% -17.49% -39.64% -28.94% -36.41%
225 -35.68% -36.20% -21.31% -42.58% -28.97% -26.21%
240 -7.21% -6.34% 5.34% -34.68% -14.08% -6.36%
255 -2.35% 0.24% 28.60% -30.49% 0.22% 10.94%
270 5.23% 22.51% 43.27% -5.44% 12.49% 12.97%
(資料來源：本研究整理)
56