未來工作

第五章結論及未來工作

5.2 未來工作

本論文完成初步混合對流之探討，未來發展建議如下：

（1）高雷諾數與高葛拉斯赫夫數下可以嘗試以人工黏滯方式處理。

（2）配合紊流模式進行混合對流之分析。

（3）其他幾何造型之參數對熱傳之影響。

參考文獻

[1] Mohamad, A. A. and Viskanta, R., “Flow and heat transfer in a lid-driven cavity filled with a stably stratified fluid,” Heat Transfer Laboratory, School of Mechanical Engineering,, Vol.19, 1995.

[2] Prasas, A. K. and Koseff, J. R., “Combined forced and natural convection heat transfer in a deep lid-driven cavity flow,” International Journal of Heat and Fluid Flow, Vol.17, No. 5, 1996, pp. 460-467.

[3] Wang, C. C. and Chen, C. K., “Forced convection in a wavy-wall channel,”

International Journal of Heat and Mass Transfer, Vol.45, 2002, pp. 2587-2595.

[4] Manca, O., Nardini, S., Khanafer, K. and Vafai, K., “Effect of Heated Wall Position on Mixed Convection in a Channel with an Open Cavity,” Numer. Heat Transfer A, Vol.43, 2003, pp. 259-282.

[5] Zhang, J., “Numerical simulation of 2D square driven cavity using fourth-order compact finite difference schemes,” Comput. Math. Appl., Vol.45, 2003, pp. 43-52.

[6] Oztop, H. F. and Dagtekin, I., “Mixed convection in two-sided lid-driven differentially heated square cavity,” International Journal of Heat and Mass Transfer, Vol.47, 2004, pp. 1761-1769.

[7] Al-Amiri, A. and Khanafer, K. M., “Numerical simulation of double-diffusive mixed convection within a rotating horizontal annulus,” International Journal of Thermal Sciences, Vol.45, 2006, pp. 567-578.

[8] Shah, P., Rovagnati, B., Mashayek, F., and Jacobs, G. B., “Subsonic compressible flow in two-sided lid-driven cavity. Part II: Unequal walls temperatures,” International Journal of Heat and Mass Transfer, Vol.50, 2007, pp. 4219-4228.

[9] Al-Amir, A., Khanafer, K. M., Bull, J., and Pop, I., “Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity,” International Journal

of Heat and Mass Transfer, Vol.50, 2007, pp. 1771-1780.

[10] Chiu, H. C. and Yan, W. M., “Mixed convection heat transfer in inclined rectangular ducts with radiation effects,” International Journal of Heat and Mass Transfer, Vol.51, 2008, pp. 1085-1094.

[11] Basak, T.,., Roy, S., Sharma, P. K. and Pop, I., “Analysis of mixed convection flows within a square cavity with linearly heated side wall(s),” International Journal of Heat and Mass Transfer, Vol.52, 2009, pp. 2224-2242.

[12] Ouertatani, N., Cheikh, N., B., Beya, B. B., Lili, T. and Campo, A., “Mixed convection in a double lid-driven cubic cavity,” International Journal of Thermal Sciences, Vol.48, 2009, pp. 1265-1272.

[13] Oztop, H. F., Zhao, Z., and Yu, B., “Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition,” International Communications in Heat and Mass Transfer, Vol.36, 2009, pp. 661-668.

[14] Castelloes, F. V., Quaresma, J. N. N. and Cotta, R. M., “Convective heat transfer enhancement in low Reynolds number flows with wavy walls,” International Journal of Heat and Mass Transfer, Vol.53, 2010, pp. 2022-2034.

[15] Sivasankaran, S., Sivakumar, V. and Prakash, P., “Numerical study on mixed convection in a lid-driven cavity with non-uniform heating on both sidewalls,”

International Journal of Heat and Mass Transfer, Vol.53, 2010, pp. 4304-4315.

[16] Sivakumar, V., Sivasankaran, S., Prakash, P. and Lee, J., “Effect of heating location and size on mixed convection in lid-driven cavities,” Computers and Mathematics with Applications, Vol.59, 2010, pp. 3053-3065.

[17] Yang, Y. L., Lin, Y. C., “A Numerical Study of Natural Convective Heat Transfer in a Cavity Using a High-order Differential Scheme,” Journal of Aeronautics, Astronautics

[18] Yang, Y. L., Lin, Y. C., “Numerical Investigation of Natural Convection in an Inclined Wavy Cavity Using a High-order Differential Scheme,” 2010航太學會學術研討會，

論文編號C2-2, 2010, 開南大學。

[19] Choi, Y. H. and Merkle, C. L., “The Application of Preconditioning in Viscous Flows,”

Journal of Computational Physics, Vol. 105, No. 2, 1993, pp. 207-223.

[20] Weiss, J. M. and Smith, W. A., “Preconditioning Applied to Variable and Constant Density Time-Accurate Flows on Unstructured Meshes,” AIAA Paper 94-2209, June 1994.

[21] Edwards, J. R. and Liou, M. S., “Low-Diffusion Flux-Splitting Methods for Flows at All Speeds,” AIAA Journal, Vol. 36, No. 9, 1998, pp. 1610-1617.

[22] Irons, B. M., “Engineering Applications of Numerical Integration in Stiffness Methods,” AIAA Journal, Vol. 4, No. 11, 1966, pp. 2035-2037.

[23] Ghia, U., Ghia, K. N., and Shin, C. T., “High-Re Solution for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method,” J. of Computational Physics, Vol. 48, No. 3, 1982, pp. 387-411.

[24] de Vahl Davis, G., “Natural Convection of Air in a Square Cavity a Bench Mark Numerical Solution,” International Journal for Numerical Methods in Fluids, Vol. 3, 1983, pp. 249-164.

表一、中央最大速度、半腰最大垂直速度、左側壁最大與最小局部紐塞數與文獻[24]

比較表。

Ref. [24] present solution Difference (%)

Ra=10⁶ 61×61

u_max 64.63 64.848 0.34

y@Umax 0.850 0.8495 -0.059

vmax 219.36 220.199 0.38

x@Vmax 0.0379 0.04141 9.3

Numax 17.925 17.5961 -1.8

y@NUmax 0.0378 0.03824 1.2

Numin 0.989 0.9855 -0.35

y_@NUmin 1.000 1.0000 0

表二、平均紐塞數與文獻[7]及二階有限體積法比較表(波數 N=0，1，2，3)。

Nu

^N=0 ^N=1 ^N=2 ^N=3

Al-Amiri[7] 7.353 7.353 8.080 7.219 2^nd order FV 6.6308 6.7905 7.4604 6.6725 Present results 6.6563 6.7962 7.4449 6.5770

表三、平均紐塞數比較表。

M=0.001 M=0.005 M=0.008

Nu

^7.4449 ^7.5326 ^7.6400

表四、不同振輻與葛拉斯赫夫數下平均紐塞數比較。

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25 Gr=10³ 6.5808 7.3720 7.6299 7.6652 6.8316 6.2956 Gr=10⁴ 6.6563 7.4449 7.6963 7.7390 6.9290 6.3271 Gr=10⁵ 6.9091 7.7896. 7.9887 8.0649 7.6427 6.6186

表五、不同振輻與雷諾數下平均紐塞數比較。

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25 Re=250 3.5646 3.8667 4.1164 4.2772 4.3675 4.1250 Re=500 4.7491 5.2619 5.5762 5.7443 5.6952 5.1851

圖 2-1 正方形孔穴式意圖。

=v=0 adiabatic x-mon.

u=v=0 adiabatic x-mon. u=U

top,v=0,T=T

top,y-mom.

u=v=0, T=T

bot,y-mom.

x y

圖 4-1 剪切流計算網格圖(41×41)。

圖 4-2 剪切流場流線分佈圖。

X U

V Y

0 0.2 0.4 0.6 0.8 1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1

圖 4-3 剪切流場速度斷面分佈圖。

2.0 1.0 0.0 -1.0 -1.0

-2.0

-3.0

3.0 4.0

-2.0

-3.0 -2.0

-1.0 0.0 0.0

-4.0

圖 4-4 剪切流場渦度分佈圖。

圖 4-5 自然對流計算網格圖(61×61) 。

圖 4-6 自然對流溫度分佈圖。

圖 4-7 自然對流流線分佈圖。

-0.001

-0.003

0 0.001

0.002

-0.004

圖 4-8 自然對流渦度分佈圖。

X

L o c a l N u s s e lt N u m b e r

0 0.2 0.4 0.6 0.8 1

0 5 10 15 20 25 30

mesh 41x41 mesh 81x81 mesh 161x161 Al-Amiri et al.

圖 4-10 不同網格數之頂面局部紐塞數與文獻[7]比較圖。

X

L o c a l N u s s e lt N u m b e r

0 0.2 0.4 0.6 0.8 1

1 2 3 4 5 6 7 8 9

10 mesh 41x41

mesh 81x81 mesh 161x161

圖 4-11 不同網格數之局部紐塞數分佈圖。

圖 4-12 混合對流溫度分佈圖與文獻[7]比較圖。

圖 4-13 混合對流流線分佈圖。

(a) N=0 (b) N=1

圖 4-14 波數影響之溫度分佈圖。

(a) N=0 (b) N=1

4-15 波數影響之流線分佈圖。

X

L o c a l N u s s e lt N u m b e r

0 0.2 0.4 0.6 0.8 1 1.2

0 4 8 12 16 20 24

present results Al-Amiri et al.

n=2

n=3 n=1

n=0

圖 4-16 不同波數之局部紐塞數相較文獻[7]之比較圖。

X

L o c a l N u s s e lt n u m b e r

0 0.2 0.4 0.6 0.8 1 1.2

0 4 8 12 16 20

24 present results

2nd order finite volume scheme

n=3 n=2

n=1 n=0

圖 4-17 不同波數之局部紐塞數相較二階有限體積法之比較圖。

(T-T

_top

)/(T

_bot

-T

_top

)

Y

0 0.2 0.4 0.6 0.8 1

M=0.001 M=0.005 M=0.008

圖 4-18 不同馬赫數中央斷面溫度分佈圖。

X U

V Y

0 0.2 0.4 0.6 0.8 1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1 M=0.001

M=0.005 M=0.008

圖 4-19 不同馬赫數速度斷面分佈圖。

X

L o c a l N u s s e lt N u m b e r

0 0.2 0.4 0.6 0.8 1 1.2

0 4 8 12 16 20 24

M=0.001 M=0.005 M=0.008

圖 4-20 不同馬赫數之局部紐塞數分佈圖。

3 4 5

(T-T

_top

)/(T

_bot

-T

_top

)

Y

0 0.2 0.4 0.6 0.8 1

Gr=10³ Gr=10⁴ Gr=10⁵

圖 4-22 不同葛拉斯赫夫數下中央斷面溫度分佈圖。

圖 4-23 不同葛拉斯赫夫數流線分佈圖(上：Gr=10³，中：Gr=10⁴，下：Gr=10⁵)。

X U

V Y

0 0.2 0.4 0.6 0.8 1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1 Gr=10³

Gr=10⁴ Gr=10⁵

圖 4-24 不同葛拉斯赫夫數速度斷面分佈圖。

Arc Length

L o c a l N u s s e lt N u m b e r

0 0.2 0.4 0.6 0.8 1 1.2

0 5 10 15 20 25

Gr=10³ Gr=10⁴ Gr=10⁵

圖 4-25 不同葛拉斯赫夫數之局部紐塞數分佈圖。

圖 4-26 不同雷諾數之溫度分佈圖(上：Re=250，中：Re=500，下：Re=1000)。

(T-T

_top

)/(T

_bot

-T

_top

)

Y

0 0.2 0.4 0.6 0.8 1

Re=250 Re=500 Re=1000

圖 4-27 不同雷諾數中央斷面溫度分佈圖。

圖 4-28 不同雷諾數流線分佈圖(上：Re=250，中：Re=500，下：Re=1000)。

X U

V Y

0 0.2 0.4 0.6 0.8 1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1 Re=250

Re=500 Re=1000

圖 4-29 不同雷諾數速度斷面分佈圖。

Arc Length

L o c a l N u s s e lt N u m b e r

0 0.2 0.4 0.6 0.8 1 1.2

0 5 10 15 20 25

Re=250 Re=500 Re=1000

圖 4-30 不同雷諾數局部紐塞數分佈圖。

A=0 A=0.05 A=0.1

A=0.15 A=0.2 A=0.25

A=0 A=0.05 A=0.1

A=0.15 A=0.2 A=0.25

圖 4-32 不同振幅下流線分佈圖(Gr=10⁴，Re=1000)。

Arc Length

LocalNusseltNumber

0 0.4 0.8 1.2 1.6 2 2.4

0 5 10 15 20 25 30 35 40 45 50

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25

Arc Length

LocalNusseltNumber

0 0.4 0.8 1.2 1.6 2 2.4

0 5 10 15 20 25 30 35 40 45 50

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25

Arc Length

LocalNusseltNumber

0 0.4 0.8 1.2 1.6 2 2.4

0 5 10 15 20 25 30 35 40 45 50

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25

圖 4-33 不同葛拉斯赫夫數(上：Gr=10³，中：Gr=10⁴，下：Gr=10⁵)與不同振輻之局部紐塞數分佈圖。

Amplitude

A v e ra g e N u s s e lt N u m b e r

0 0.05 0.1 0.15 0.2 0.25 0.3

6 6.4 6.8 7.2 7.6 8 8.4

Gr=10³ Gr=10⁴ Gr=10⁵

圖 4-34 不同葛拉斯赫夫數與不同振輻(A=0、0.05、0.1、0.15、0.2、0.25)之平均紐塞數分佈圖。

Arc Length

LocalNusseltNumber

0 0.4 0.8 1.2 1.6 2 2.4

0 5 10 15 20 25

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25

Arc Length

LocalNusseltNumber

0 0.4 0.8 1.2 1.6 2 2.4

0 5 10 15 20 25 30 35

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25

Arc Length

LocalNusseltNumber

0 0.4 0.8 1.2 1.6 2 2.4

0 5 10 15 20 25 30 35 40 45 50

A=0.0 A=0.05 A=0.1 A=0.15 A=0.2 A=0.25

圖 4-35 不同振幅與不同雷諾數(上：Re=250，中：Re=500，下：Re=1000)之局部紐塞數分佈圖。

在文檔中中文摘要 (頁 30-71)

第五章 結論及未來工作

5.2 未來工作

參考文獻

Nu

Nu

X U

V Y

X

L o c a l N u s s e lt N u m b e r

X

L o c a l N u s s e lt N u m b e r

X

L o c a l N u s s e lt N u m b e r

n=2

n=3 n=1

n=0

X

L o c a l N u s s e lt n u m b e r

n=3 n=2

n=1 n=0

(T-T

)/(T

-T

)

Y

X U

V Y

X

L o c a l N u s s e lt N u m b e r

(T-T

)/(T

-T

)

Y

X U

V Y

Arc Length

L o c a l N u s s e lt N u m b e r

(T-T

)/(T

-T

)

Y

X U

V Y

Arc Length

L o c a l N u s s e lt N u m b e r

Amplitude

A v e ra g e N u s s e lt N u m b e r

第五章結論及未來工作