本文架設一小尺度的室內空腔與機架伺服器模型模擬伺服器運作時之發熱情形，以熱電偶量測溫度，並以CFD分析軟體ANSYS Fluent進行數值求解，先藉由網格獨立性分析劃分出合適的網格後，以最小平方法求出熱源之發熱功率，以方均根誤差分析後選擇適合的流動模型，並探討不同變因對空腔內之溫度分布與流場的影響。
由結果可得知，當空腔頂部與底部皆有開孔時，使用零方程式模型具有最佳的精確度；而當空腔僅有頂部開孔時則以RNG k-ε模型具有最佳的精確度。增加兩層架間距對層架表面、壁面的溫度與熱對流係數影響均不明顯，熱對流係數的變化幅度小於10 %，但會使空腔頂部產生小規模渦流而降低通風效率。在空腔頂部與底部設置通風口可在室內形成二進二出的風道，避免形成大範圍迴流泡而降低對流效益，對溫度、熱對流係數皆有明顯的改善，其中 (h_p1 ) ̅的變化幅度最高更可達42 %。降低層架高度間距對整體溫度與對流係數影響不顯著，但可提高整體空間利用率。

SUMMARY
In this research, a small scale model of cavity with rack servers within is investigated. 12 T-type thermocouples are used to measure temperature data. After generating an appropriate mesh by grid independence analysis, CFD software Ansys Fluent is applied to obtain numerical results. The unknown heat source can be solved by least square method. Finally, the appropriate turbulence model can be determined by the comparison of root mean square error (RMSE) between the numerical and experimental results. The effect on temperature contour and streamline resulted from 3 different parameters are discussed.
It is found that Zero-eq model is suitable for cases with 4 ventilation openings while RNG k-ε model is suitable for cases with 2. Increasing the distance between two racks have limited effect on rack surface temperature and convection coefficients. Nevertheless, it will result in small eddies at the top of cavity, which could reduce the ventilation performance. In comparison with cases without openings at the bottom of cavity, the convection coefficients could be 42% better. Openings at the bottom of cavity allow cool air filling in and develop displacement ventilation which can avoid large circulation in the room. Lastly, Decreasing the height interval of rack leads to a temperature rise of about 2 K on rack surface. However, it is acceptable for a better space usage

Key word: CFD, Inverse method, Natural convection, Indoor ventilation

1. 台灣電力公司企劃處, 110年電業年報. 2022.
2. J. Choi, Y. Kim, A. Sivasubramaniam, J. Srebric, Q. Wang, and J. Lee, A CFD-Based Tool for Studying Temperature in Rack-Mounted Servers. IEEE Transactions on Computers, 2008. 57(8): p. 1129-1142.
3. Y. Wang, X. Meng, X. Yang, and J. Liu, Influence of convection and radiation on the thermal environment in an industrial building with buoyancy-driven natural ventilation. Energy and Buildings, 2014. 75: p. 394-401.
4. H. Mlaouah, T. Tsuji, and Y. Nagano, A study of non-Boussinesq effect on transition of thermally induced flow in a square cavity. International Journal of Heat and Fluid Flow, 1997. 18(1): p. 100-106.
5. H.B. Awbi and A. Hatton, Natural convection from heated room surfaces. Energy and Buildings, 1999. 30(3): p. 233-244.
6. I.V. Miroshnichenko, M.A. Sheremet, and A.A. Mohamad, Numerical simulation of a conjugate turbulent natural convection combined with surface thermal radiation in an enclosure with a heat source. International Journal of Thermal Sciences, 2016. 109: p. 172-181.
7. J. Salat, S. Xin, P. Joubert, A. Sergent, F. Penot, and P. Le Quéré, Experimental and numerical investigation of turbulent natural convection in a large air-filled cavity. International Journal of Heat and Fluid Flow, 2004. 25(5): p. 824-832.
8. A.K.A. Shati, S.G. Blakey, and S.B.M. Beck, An empirical solution to turbulent natural convection and radiation heat transfer in square and rectangular enclosures. Applied Thermal Engineering, 2013. 51(1-2): p. 364-370.
9. L. El Moutaouakil, Z. Zrikem, and A. Abdelbaki, Interaction of Surface Radiation With Laminar and Turbulent Natural Convection in Tall Vertical Cavities: Analysis and Heat Transfer Correlations. Heat Transfer Engineering, 2015. 36(17): p. 1472-1484.
10. S.G. Martyushev and M.A. Sheremet, Conjugate natural convection combined with surface thermal radiation in a three-dimensional enclosure with a heat source. International Journal of Heat and Mass Transfer, 2014. 73: p. 340-353.
11. E. Yu and Y. Joshi, A numerical study of three-dimensional laminar natural convection in a vented enclosure. International Journal of Heat and Fluid Flow, 1997. 18(6): p. 600-612.
12. S.N. Singh and S.P. Venkateshan, Numerical study of natural convection with surface radiation in side-vented open cavities. International Journal of Thermal Sciences, 2004. 43(9): p. 865-876.
13. V. Dubovsky, G. Ziskind, S. Druckman, E. Moshka, Y. Weiss, and R. Letan, Natural convection inside ventilated enclosure heated by downward-facing plate: experiments and numerical simulations. International Journal of Heat and Mass Transfer, 2001. 44(16): p. 3155-3168.
14. M. Ishizuka and Y. Kitamura, Studies on natural convection-induced flow and thermal behaviour inside electronic equipment cabinet model. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2003. 217(3): p. 323-328.
15. E. Bilgen and A. Muftuoglu, Cooling strategy by mixed convection of a discrete heater at its optimum position in a square cavity with ventilation ports. International Communications in Heat and Mass Transfer, 2008. 35(5): p. 545-550.
16. R. Abhinav, P.B.S. Sunder, A. Gowrishankar, S. Vignesh, M. Vivek, and V.R. Kishore, Numerical study on effect of vent locations on natural convection in an enclosure with an internal heat source. International Communications in Heat and Mass Transfer, 2013. 49: p. 69-77.
17. N.K. Bansal, R. Mathur, and M.S. Bhandari, Solar chimney for enhanced stack ventilation. Building and Environment, 1993. 28(3): p. 373-377.
18. G. Ziskind, V. Dubovsky, and R. Letan, Ventilation by natural convection of a one-story building. Energy and Buildings, 2002. 34(1): p. 91-101.
19. J. Hirunlabh, W. Kongduang, P. Namprakai, and J. Khedari, Study of natural ventilation of houses by a metallic solar wall under tropical climate. Renewable Energy, 1999. 18(1): p. 109-119.
20. Q. Chen and W. Xu, A zero-equation turbulence model for indoor airflow simulation. Energy and buildings, 1998. 28(2): p. 137-144.
21. E.M. Sparrow, J.C.K. Tong, and J.P. Abraham, Fluid Flow in a System with Separate Laminar and Turbulent Zones. Numerical Heat Transfer, Part A: Applications, 2008. 53(4): p. 341-353.
22. D. Zhou, M. Zhang, and C. Du. Enhancing rack servers air cooling capability with extra system inlet airflow through air ducts between racks. in 2017 16th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm). 2017.
23. R. Ghosh, V. Sundaralingam, and Y. Joshi. Effect of rack server population on temperatures in data centers. in 13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems. 2012.
24. ASHRAE, 2021 Equipment Thermal Guidelines for Data Processing Environments, fifth edition, in ASHRAE. 2021.
25. J. Smagorinsky, General circulation experiments with the primitive equations: I. The basic experiment. Monthly weather review, 1963. 91(3): p. 99-164.
26. L. Prandtl, 7. Bericht über Untersuchungen zur ausgebildeten Turbulenz. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 1925. 5(2): p. 136-139.
27. B.E. Launder and D.B. Spalding, PAPER 8 - THE NUMERICAL COMPUTATION OF TURBULENT FLOWS, in Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion, S.V. Patankar, et al., Editors. 1983, Pergamon. p. 96-116.
28. S.A. Orszag, Renormalisation group modelling and turbulence simulations. Near-wall turbulent flows, 1993.
29. D.C. Wilcox, Turbulence modeling for CFD. Vol. 2. 1998: DCW industries La Canada, CA.
30. F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 1994. 32(8): p. 1598-1605.
31. H.-T. Chen, S.-C. Chang, M.-H. Hsu, and C.-H. You, Experimental and numerical study of innovative plate heat exchanger design in simplified hot box of SOFC. International Journal of Heat and Mass Transfer, 2021. 181.
32. H.-T. Chen, M.-C. Lin, and J.-R. Chang, Numerical and experimental studies of natural convection in a heated cavity with a horizontal fin on a hot sidewall. International Journal of Heat and Mass Transfer, 2018. 124: p. 1217-1229.
33. H.-T. Chen, W.-Y. Su, Y.-J. Zheng, T.-S. Yang, and K.-X. Chen, Prediction of 3D natural convection heat transfer characteristics in a shallow enclosure with experimental data. Progress in Nuclear Energy, 2022. 153.
34. V.S. Arpaci, S.-H. Kao, and A. Selamet, Introduction to heat transfer. 1999: Prentice Hall.
35. A.Ç. Yunus, Heat and mass transfer: fundamentals and applications. 2019: McGraw-Hill Education.
36. 余宗樺, 具有各種隔板之封閉倉儲的三維自然對流熱傳特性研究. 2021.
37. 許名勛, 四管於封閉空腔內之三維自然對流的熱傳特性研究. 2021.
38. J.H. Ferziger, M. Perić, and R.L. Street, Computational methods for fluid dynamics. Vol. 3. 2002: Springer.
39. I. ANSYS, ANSYS Fluent Theory Guide. 2013.
40. S.V. Patankar, Numerical heat transfer and fluid flow. Series in computational methods in mechanics and thermal sciences. 1980, Washington ;: Hemisphere.
41. H.-T. Chen, M.-H. Hsu, Y.-C. Huang, and K.-H. Chang, Experimental and numerical study of inverse natural convection-conduction heat transfer in a cavity with a fin. Numerical Heat Transfer, Part A: Applications, 2023: p. 1-18.
42. H.-T. Chen, M.-H. Hsu, K.-C. Yang, K.-H. Chang, and K.-C. Liu, Study of inverse natural convection-conduction heat transfer for in-line tube heat exchanger in a hot box with experimental data. Journal of the Taiwan Institute of Chemical Engineers, 2022. 141: p. 104600.
43. L.F.A. Azevedo and E.M. Sparrow, Natural Convection in Open-Ended Inclined Channels. Journal of Heat Transfer, 1985. 107(4): p. 893-901.
44. J. Lloyd and W.R. Moran, Natural Convection Adjacent to Horizontal Surface of Various Planforms. Journal of Heat Transfer-transactions of The Asme, 1974. 96: p. 443-447.
45. 林. 黃榮芳, 許清閔, 工業通風-原理與實務：通風系統設計與改良方法. 2020.
46. T. Panitz and D.T. Wasan, Flow attachment to solid surfaces: The Coanda effect. AIChE Journal, 1972. 18(1): p. 51-57.