本文使用數值模擬探討具有多個V型擋板渠道之紊流流場與熱傳特性。採用控制體積法和SIMPLE法求解紊流強制對流橢圓、耦合、穩態之三維統御偏微分方程式。本文研究參數分別為: 雷諾數(8000 ≤ Re ≤ 20000)，無因次化V型擋板高度 (0.1 ≤ e/H ≤ 0.3)，無因次化V型擋板間距 (2 ≤ Pr ≤ 4)和V型擋板角度 (45ﾟ≤ α ≤ 75ﾟ)，並詳細討論上述參數對於紐賽數(Nu)與摩擦因子( f )的影響。
比較數值結果與參考文獻之實驗數據後，驗證結果顯示相較於其他紊流模型(RNG , Realizable and SST )，standard 模型數值結果較接近參考文獻之數據，故往後數值計算皆採用standard 模型。由不同研究參數組合之數值模擬結果可知，相同雷諾數時，V型擋板角度α = 45ﾟ有著較佳的熱傳表現和最小的摩擦因子。數值結果顯示最大紐賽數發生於Pr = 2，α = 45ﾟ及e/H = 0.3，而最大摩擦因子則發生於Pr = 2，α = 60ﾟ及e/H = 0.3。
此外，經過數值結果驗證後，利用反應曲面法(RSM)規劃實驗組數，再以熱性能係數( )為目標函數，並使用迴歸分析得到熱性能係數與無因次擋板高度 (e/H)、無因次擋板間距 (Pr)及擋板角度 (α)的關係式，並使用基因演算法求得熱性能係數及其對應之最佳設計參數組合。最佳化結果顯示，最佳解為Pr = 2，α = 45ﾟ及e/H = 0.1，其基因演算法與CFD之熱性能係數結果誤差小於2%，對於此具有多個V型擋板渠道，最佳化結果顯示熱性能係數( )之增益約為12%。

Numerical simulations are used to investigate the fluid flow and heat transfer characteristics of turbulent flow in a channel with multi V-shaped baffles in this study. The elliptical, coupled, steady-state and three-dimensional governing partial differential equations for turbulent forced convection are solved numerically using the finite volume approach with SIMPLE algorithm. The parameter of this study are Reynolds number (8000 ≤ Re ≤ 20000), dimensionless V-shaped baffle height (0.1 ≤ e/H ≤ 0.3), dimensionless V-shaped baffle pitch (2 ≤ Pr ≤ 4), and V-shaped baffle angle (45ﾟ≤ α ≤ 75ﾟ). Furthermore, the effects of the above-mentioned parameters on the Nusselt number and the friction factor are discussed in detail as well.
The validations show that the numerical results of the standard model are much closer to the experimental data of the reference than the other turbulence models (RNG , Realizable and SST ) in the studied ranges. Therefore, subsequent numerical computations are performed with standard model. From the numerical results of the combination of different design parameters, it can be found that the better heat transfer performance and minimum friction factor occur at α = 45ﾟwhen Reynolds number is the same. The maximum Nusselt number appears at Pr = 2, α = 45ﾟand e/H = 0.3, and maximum friction factor is found at Pr = 2，α = 60ﾟand e/H = 0.3.
In addition, after the validation of the numerical results, response surface methodology (RSM) is employed to set up the test groups. The objective function is defined as thermal performance factor with three design parameters, dimensionless V-shaped baffle height (e/H), dimensionless V-shaped baffle pitch (Pr), V-shaped baffle angle (α), and is obtained by regression analysis. Moreover, Genetic algorithm (GA) is applied to obtain the maximum thermal performance factor and the optimal set of design parameters. The predicted optimal thermal performance factor of Genetic algorithm closely agreed with those from the CFD computational results within 2% difference at the optimal set The numerical optimization indicates the enhancement of the thermal performance factor can achieve 12% in this channel with multi V-shaped baffles.

[1] P. K. Agarwal and W. W. Bower, Navier-Stokes computations of turbulent compressible two-dimensional impinging jet flow fields, AIAA Journal, vol. 20, 1982, 577 - 584.
[2] J. C. Han, L. R. Glicksman, and W. M. Rohsenow, An investigation of heat transfer and friction for rib-roughened surfaces, International Journal of Heat and Mass Transfer, vol. 21, 1978, 1143 - 1156.
[3] Denpong Soodphakdee, Masud Behnia, and David Watabe Copeland, A comparison of fin geometries for heat sinks in laminar forced convection: part 1 - round, elliptical, and plate fins in staggered and in-line configurations, The International Journal of Microcircuits and Electronic Packaging, vol. 24, 2001, 68 - 76.
[4] Abdul-Malik Ebrahim Momin, J. S. Saini, and S. C. Solanki, Heat transfer and friction in solar air heater duct with V- shaped rib roughness on absorber plate, International Journal of Heat and Mass Transfer, vol. 45, 2002, 3383 - 3396.
[5] Giovanni Tanda, Heat transfer in rectangular channels with transverse and V-shaped broken ribs, International Journal of Heat and Mass Transfer, vol. 47, 2004, 229 - 243.
[6] X. Yu, J. Feng, Q. Feng, and Q. Wang, Development of a plate-pin fin heat sink and its performance comparisons with a plate fin heat sink, Applied Thermal Engineering, vol. 25, 2005, 173 - 182.
[7] Paisarn Naphon, Heat transfer characteristics and pressure drop in channel with V corrugated upper and lower plates, Energy Conversion and Management, vol. 48, 2007, 1516 - 1524.
[8] Pongjet Promvonge, Heat transfer and pressure drop in a channel with multiple 60° V-baffles, International Communications in Heat and Mass Transfer, vol. 37, 2010, 835 - 840.
[9] Osman Turan, Nilanjan Chakraborty, and Robert J. Poole, Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls, Journal of Non-Newtonian Fluid Mechanics, vol. 165, 2010, 901 - 913.
[10] V. S. Hans, R. P. Saini, and J. S. Saini, Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with multiple v-ribs, Solar Energy, vol.84, 2010, 898 - 911.
[11] Pongjet Promvonge, Withada Jedsadaratanachai, Sutapat Kwankaomeng, and Chinaruk Thianpong, 3D simulation of laminar flow and heat transfer in V-baffled square channel, International Communications in Heat and Mass Transfer, vol. 39, 2012, 85 - 93.
[12] P. Promvonge, S. Sripattanapipat, S. Tamna, S. Kwankaomeng, and C. Thianpong , Numerical investigation of laminar heat transfer in a square channel with 45° inclined baffles, International Communications in Heat and Mass Transfer, vol. 37 , 170 - 177.
[13] Sunil Chamoli, N. S. Thakur, and J. S. Saini, A review of turbulence promoters used in solar thermal systems, Renewable and Sustainable Energy Reviews, vol. 16, 2012, 3154 - 3175.
[14] Anil Kumar, R. P. Saini, and J. S. Saini, Experimental investigation on heat transfer and fluid flow characteristics of air flow in a rectangular duct with Multi V-shaped rib with gap roughness on the heated plate, Solar Energy, vol. 86, 2012, 1733 - 1749.
[15] Parkpoom Sriromreun, Chinaruk Thianpong, and Pongjet Promvonge , Experimental and numerical study on heat transfer enhancement in a channel with Z-shaped baffles, International Communications in Heat and Mass Transfer, vol. 39, 2012, 945 - 952.
[16] Sanjay Yadav, Maneesh Kaushal, Varun, and Siddhartha, Nusselt number and friction factor correlations for solar air heater duct having protrusions as roughness elements on absorber plate, Experimental Thermal and Fluid Science, vol. 44, 2013, 34 - 41.
[17] Lei Tan, Jing-Zhou Zhang, and Hua-Sheng Xu, Jet impingement on a rib-roughened wall inside semi-confined channel, International Journal of Thermal Sciences, vol. 86, 2014, 210 - 218.
[18] Withada Jedsadaratanachai and Amnart Boonloi, Effects of blockage ratio and pitch ratio on thermal performance in a square channel with 30° double V-baffles, Case Studies in Thermal Engineering, vol. 4, 2014, 118 - 128.
[19] Sombat Tamna, Sompol Skullong, Chinaruk Thianpong, and Pongjet Promvonge, Heat transfer behaviors in a solar air heater channel with multiple V-baffle vortex generators, Solar Energy, vol. 110, 2014, 720 - 735.
[20] Dongxu Jin, Manman Zhang, Ping Wang, and Shasha Xu, Numerical investigation of heat transfer and fluid flow in a solar air heater duct with multi V-shaped ribs on the absorber plate, Energy, vol. 89, 2015, 178 - 190.
[21] Withada Jedsadaratanachai, Nuthvipa Jayranaiwachira, and Pongjet Promvonge, 3D numerical study on flow structure and heat transfer in a circular tube with V-baffles, Chinese Journal of Chemical Engineering, vol. 23, 2015, 342 - 349.
[22] Bharath Viswanath Ravi, Prashant Singh, Srinath V. Ekkad, Numerical investigation of turbulent flow and heat transfer in two-pass ribbed channels, International Journal of Thermal Sciences, vol. 112, 2017, 31 - 43.
[23] J. Wen, H. Yang, X. Tong, K. Li, S. Wang, and Y. Li, Optimization investigation on configuration parameters of serrated fin in plate-fin heat exchanger using genetic algorithm, International Journal of Thermal Sciences, vol.101, 2016, 116 – 125.
[24] S. Mohsin, A. Maqbool, and W. A. Khan, Optimization of cylindrical pin-fin heat sinks using genetic algorithms, IEEE transactions on components and packaging technologies, vol. 32, 2009, 44 - 52.
[25] K.T. Chiang and F. P. Chang, Application of response surface methodology in the parametric optimization of a pin-fin type heat sink, International Communications in Heat and Mass Transfer, vol. 33, 2006, 836 - 845.
[26] K.Y. Kim and D.Y. Shin, Optimization of a staggered dimpled surface in a cooling channel using Kriging model, International Journal of Thermal Sciences, vol. 47, 2008, 1464 - 1472.
[27] Y. Wang, Y. L. He, D. H. Mei, and W. Q. Tao, Optimization design of slotted fin by numerical simulation coupled with genetic algorithm. Applied Energy, vol. 88, 2011, 4441 - 4450.
[28] G. Fabbri, A genetic algorithm for fin profile optimization, International Journal of Heat and Mass Transfer, vol. 40, 2005, 283 - 296.
[29] F. Hajabdollahi, H. H. Rafsanjani, Z. Hajabdollahi, and Y. Hamidi, Multi-objective optimization of pin fin to determine the optimal fin geometry using genetic algorithm, Applied Mathematical Modelling, vol. 36, 2012, 244 - 254.
[30] J. D. Bagley, The behavior of adaptive systems which employ genetic and correlation algorithms, University of Michigan, 1967.
[31] J. H. Holland, Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence: U Michigan Press, 1975.
[32] D. E. Goldberg, Genetic algorithms in search, optimization, and machine learning: Addison-Wesley Reading Menlo Park, 1989.
[33] L. Davis, Handbook of Genetic Algorithms: Van Nostrand Reinhold New York, 1991.
[34] J. R. Koza, Genetic Programming: On the programming of computers by means of natural selection: MIT press, 1992.
[35] B. E. Launder and D. B. Spalding, Lectures in mathematical models of turbulence, Academic press, 1972.
[36] B. E. Launder and D. B. Spalding, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering, vol.3, 1974, 269-289.
[37] V. Yakhot and S. A. Orszag, Renormalization group analysis of turbulence, Journal of Scientific Computing, vol. 1, 1986, 3-51.
[38] T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, A new eddy-viscosity model for high Reynolds number turbulent flows - model development and validation, Computers and Fluids, vol. 24, 1995, 227-238.
[39] M. Serag-Eldin and D. B. Spalding, Computations of three-dimensional gas turbine combustion chamber flows, Journal of Engineering for Power, vol.101, 1979, 326-336.
[40] C. L. V. Jayatilleke, The influence of Prandtl number and surface roughness on the resistance of the laminar sublayer to momentum and heat transfer, University of London, 1969.
[41] S. E. Kim and D. Choudhury, A near-wall treatment using wall functions sensitized to pressure gradient, Separated and Complex Flows, vol. 217, 1995, 273-280.
[42] F. R. Menter, M. Kuntz and R. Langtry, Ten years of industrial experience with the SST turbulence model, Turbulence, Heat and Mass Transfer, vol. 4, 2003, 625 - 632.
[43] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, New York: McGraw-Hill, 1980.
[44] S. V. Patankar and D. B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, International Journal of Heat and Mass Transfer, vol. 15, 1972, 1787-1806.
[45] G. E. Box and K. Wilson, On the experimental attainment of optimum conditions, Journal of the Royal Statistical Society, Series B (Methodological), vol. 13, no. 1, 1951, 1-45.
[46] J. Holland, Genetic algorithms and the optimal allocations of trials, SIAM Journal of Computing, vol. 2, no. 2, 1973, 88-105.