結論 - 中華大學

本研究透過數值程式之分析進行了非正交網格之驗證得以進行稜形夾角改變對孔穴內自然對流之影響，接著以同心圓柱熱傳問題觀察瑞利數增加下內部流場結構之變化與熱傳增益之情形，進而處理內部圓柱於上下週期運動下之動態熱傳分析，最後進行開放圓柱之熱傳分析。由前面之結果可得下述結論：

1. 當稜形夾角在 30^o下自然熱傳問題中，本研究之結果與文獻所提供之紐塞數、

溫度分布與流線分布皆相當一致。

2. 在相同瑞利數下改變稜形之夾角，其最大熱傳量發生在 90^o，不受左右壁面擠壓之造型下，若相同夾角則瑞利數越大平均紐塞數越高，另外流場內部之漩渦數目會隨對流效應之增強而變多，因此當夾角縮小至 30^o或是放大至 165^o時其左右壁面之摩擦增強，其內部只剩一個迴旋。

3. 針對同心圓之自然熱傳問題也利用文獻之數據進行紐塞數、溫度分布與流線分布之比對，並進行不同瑞利數之探討，當瑞利數小於10 其流場結構左右各一大迴旋，當瑞利數於5 × 10 則左右各一大迴旋內部開始分裂成為兩個漩渦，

若瑞利數增至1 × 10 則同心圓下方產生另一迴流且內部有兩個漩渦，並將原先一個大迴旋內部兩個漩渦之結構向上擠壓，形成更複雜之流場現象，此一渦流與迴旋數目增多之現象可以說明層流開始轉換至不穩定流動之發展歷程。

4. 當內部圓柱處於上下週期運動時，目前分析程式以雙時間步階方式進行非穩態之計算，透過文獻之結果與目前分析結果在瞬間流線與溫度分布很相近，但在瞬間最大與最小之熱傳發展上有較延後之差異。

5. 最後在開放圓柱之熱傳分析上，針對上下游之邊界設定上至少需有 10 直徑對局部紐塞數之影響將不會超過 2%。

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表一、壁面傾角 90^o下之平均紐塞爾數 Reference Average Nusselt number, Nu

Ra = 10 Ra = 10 Ra = 10 Ra = 10 Davish[5] 2.234 4.51 8.789 - Hortmann[21] 2.4468 5.5231 8.8359 -

Nag[22] 2.24 4.51 8.82 -

Shi[23] 2.247 4.532 8.839 16.935 Bilgen[24] 2.245 4.521 8.8 16.629

Present 2.25 4.52 8.83 16.58

表二、不同壁面傾角下之平均紐塞爾數 Angle(α) Average Nusselt number,

Ra=10⁴ Ra=10⁵ Ra=10⁶ Ra=10⁷

15⁰ 1.13 1.31 2.87 7.48

30⁰ 1.18 2.43 5.75 12.16

45⁰ 1.53 3.45 7.32 14.44

60⁰ 1.90 4.06 8.21 15.71

75⁰ 2.14 4.40 8.67 16.38

90⁰ 2.25 4.52 8.83 16.58

105⁰ 2.23 4.47 8.72 16.39

120⁰ 2.09 4.23 8.34 15.77

135⁰ 1.78 3.78 7.63 14.61

150⁰ 1.31 2.99 6.41 12.71

165⁰ 1.19 1.69 4.10 9.10

表三、不同瑞利數下內外圓柱之平均紐塞爾數

Ra = 10 Ra = 5 × 10 Ra = 10 Ra = 5 × 10 Ra = 10 Inner 3.31 4.88 5.81 8.44 9.88

Outer 1.27 1.88 2.23 3.23 3.79

表四、在Re = 20、不同上下游距離之阻力係數與文獻比較圖

Present Liao and Lin[28] Triton [26] Ye et al. [27] Wang et al. [25]

5D 2.35

2.21 2.22 2.03 2.18

10D 2.12 20D 2.07 30D 2.05

(a)流線圖(Anandalakshmi and Basak)

(b)流線圖(Present)

(c)溫度圖(Anandalakshmi and Basak) (d)溫度圖(Present)

圖 4-1 傾斜角度30 、Ra = 10 、Pr = 1000與文獻[16]流線溫度之比較圖

(a)Left Wall (b)Right Wall

(c)Bottom wall

圖 4-2 在傾斜角度30 、Ra = 10 、Pr = 1000與文獻[16]局部紐塞數比較圖

Distance

LocalNusseltNumber

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14 16 18 20 22 24

Present

Anandalakshmi and Basak

Distance

LocalNusseltNumber

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14 16 18 20 22 24

Present

Anandalakshmi and Basak

Distance

LocalNusseltNumber

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14 16 18 20 22 24

Present

Anandalakshmi and Basak

(A)15⁰ (B)30⁰ (C)45⁰

(D)60⁰ (E)75⁰

(F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-3 在Ra = 10 下流線分布圖

(A)15⁰ (B)30⁰ (C)45⁰

(D)60⁰ (E)75⁰ (F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-4 在Ra = 10 下流線分布圖

(A)15⁰ (B)30⁰ (C)45⁰

(D)60⁰ (E)75⁰ (F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-5 在Ra = 10 下流線分布圖

(A)15⁰ (B)30⁰ (C)45⁰

(D)60⁰ (E)75⁰ (F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-6 在Ra = 10 下流線分布圖

(A)15⁰ (B)30⁰

(D)60⁰ (E)75⁰ (F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-7 在Ra = 10 下溫度分布圖

0.9 0.8

0.7 0.6 0.5

0.4 0.3

0.2 0.1

(A)15⁰ (B)30⁰ (C)45⁰

(D)60⁰ (E)75⁰ (F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-8 在Ra = 10 之溫度分布圖

0.9 0.8

0.7 0.6

0.5 0.4 0.3

0.2 0.1

(A)15⁰ (B)30⁰ (C)45⁰

(D)60⁰ (E)75⁰ (F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-9 在Ra = 10 之溫度分布圖

0.9

0.8

0.7 0.6 0.5 0.4 0.3 0.2

0.1

(A)15⁰ (B)30⁰ (C)45⁰

(D)60⁰ (E)75⁰ (F)90⁰

(G)105⁰ (H)120⁰ (I)135⁰

(J)150⁰ (K)165⁰

圖 4-10 在Ra = 10 之溫度分布圖

0.9

0.8

0.7 0.6 0.5 0.4 0.3 0.2

0.1

圖 4-11 不同傾斜角度與瑞利數下平均紐塞數

 N u

avg

0 15 30 45 60 75 90 105 120 135 150 165 180 0

2 4 6 8 10 12 14 16 18 20

Ra=10⁷ Ra=10⁶ Ra=10⁵ Ra=10⁴

圖 4-12 在Ra = 5 × 10 同心圓柱不同角度處溫度與文獻[4]比較圖

圖 4-13 在Ra = 5 × 10 局部紐塞數與文獻[4]比較圖

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1















 keq

0 30 60 90 120 150 180

0 1 2 3 4 5 6 7 8 9 10 11

Kuehn and Goldstein(Outer) Kuehn and Goldstein (Inner) Present(Inner)

Present(outer)

圖 4-14 在Ra = 1 × 10 下流線(左)與溫度(右)分布圖

圖 4-15 在Ra = 5 × 10 下流線(左)與溫度(右)分布圖

圖 4-16 在Ra = 1 × 10 下流線(左)與溫度(右)分布圖

圖 4-17 在Ra = 5 × 10 下流線(左)與溫度(右)分布圖

圖 4-18 在Ra = 1 × 10 下流線(左)與溫度(右)分布圖

(a)Inner

(b)Outer

圖 4-19 在不同瑞利數下外圓局部紐塞數分布圖



LocalNusseltNumber

0 30 60 90 120 150 180

0 2 4 6 8 10 12 14

16 Ra=1X10⁴

Ra=5X10⁴ Ra=1X10⁵ Ra=5X10⁵ Ra=1X10⁶



LocalNusseltNumber

0 30 60 90 120 150 180

0 5 10 15 20 25

Ra=1X10⁴ Ra=5X10⁴ Ra=1X10⁵ Ra=5X10⁵ Ra=1X10⁶

(a)Inner

(b)Outer

圖 4-20 瑞利數Ra = 5 × 10 、 = 0.5、Ω = 1，內外圓柱平均紐塞數發展歷

Dimensionless Time AvreageNusseltNumber(keq)

0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Present Alawadhi.

Dimensionless Time AverageNusseltNumber(keq)

0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Present Alawadhi.

程

圖 4-21 t = 0T時之溫度(上)、流線(下)分布與文獻(左)之比較圖

圖 4-22 t = T時之溫度(上)、流線(下)分布與文獻(左)之比較圖

圖 4-23 t = T時之溫度(上)、流線(下)分布與文獻(左)之比較圖

圖 4-24 t = T時之溫度(上)、流線(下)分布與文獻(左)之比較圖

(a)Inner

(a)Outer

圖 4-25 不同週期時局部紐賽數分布圖

 LocalNusseltNumber(keq)

0 30 60 90 120 150 180

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0T T/4 T/2 3T/4

 LocalNusseltNumber(keq)

0 30 60 90 120 150 180

2 4 6 8 10

0T T/4 T/2 3T/4

(a)

(b)5D (c)10D

(d)15D (e)20D

圖 4-26 在Re = 20、不同上下游大小下，溫度與 vorticity 和文獻[28](a)比較圖

(a)5D

(b)10D

(d)20D

圖 4-27 在Re = 20、不同上下游距離設定下圓柱流線圖

在文檔中中華大學 (頁 33-63)