Multi-objective optimization of rectangular channel with miniature slit ribs
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摘要:
开展了矩形通道内微小狭缝肋的换热和流阻性能的多目标优化研究。选取缝宽、相邻缝间距、狭缝的前端面和后端面与壁面距离四个参数作为优化变量，采用非支配排序遗传算法（NSGA-Ⅱ）获得了Pareto 最优解。分析了Pareto最优前沿面上四种优化方案下微小狭缝肋的流动和传热热特性。结果表明：优化后的微小狭缝肋的换热能力与实心肋相当，而流动阻力有所降低，肋壁的换热均匀性得到显著提高。
Abstract:A multi-objective optimization study of the heat transfer and flow resistance characteristics of the miniature slit ribs in a rectangular channel was carried out. Four parameters were selected as the optimization variables: the slit width, the distance between adjacent slits, and the distance between the front and rear ends of the slit and the wall surface, and the Pareto optimal solution was obtained by using the non-dominated sorting genetic algorithm (NSGA-Ⅱ). The flow and heat transfer characteristics of the miniature slit ribs under the four optimization schemes on the Pareto optimal front surface were analyzed. The results showed that the optimized miniature slit ribs provided nearly the same heat transfer as the solid ribs, while the flow resistance was reduced, and the uniform heat transfer of the ribbed wall was significantly improved.
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图 1 计算区域和边界条件示意图（单位：mm）
Figure 1. Schematic view of the computational domain and boundary conditions (unit: mm)
图 2 狭缝肋的布置和它的截面形状示意图
Figure 2. Schematic diagram of slit rib configuration and its cross-section shape
图 3 狭缝肋结构全局和局部的六边形网格结构示意图
Figure 3. Schematic of structured hexagonal global and local mesh structures of the slit rib
图 4 不同雷诺数下预测的可穿透微小肋通道相对平均努塞尔数和相对摩擦因子对比
Figure 4. Comparisons of the predicted relative average value of the Nusselt numbers and the friction factor for channel with miniature slit ribs at different Re
图 6
$\overline{Nu}/\overline{Nu}_0 $ 和f0/f 随运行次数的变化Figure 6.
$\overline{Nu}/\overline{Nu}_0 $ and f0/f versus the run counter
图 8 狭缝中心流向截面上的流线和流向速度分布（Re=40 000）
Figure 8. Streamlines and streamwise velocity contours on the central streamwise plane of the slit （Re=40 000）
图 9 狭缝中心流向截面上的湍动能分布
Figure 9. Contours of turbulence kinetic energy on the central streamwise plane of the slit
图 10 不同展向截面上的流线和湍动能分布
Figure 10. Streamlines and contours of turbulence kinetic energy on various spanwise cross-sections
图 11 狭缝中心流向截面上的展向涡量分布
Figure 11. Contours of span vorticity on the streamwise center plane of the slit
图 12 展向截面X=0.5h上的流向涡量分布
Figure 12. Contours of streamwise vorticity on cross-section X = 0.5h
图 13 X、Z中心截面上第三排肋片附近的温度分布
Figure 13. Temperature contours on the X、Z central plane of the third rib
图 15 相对平均努塞尔数、相对摩擦因子和综合热性能随雷诺数的变化
Figure 15. Variations of relative averaged Nusselt number, relative friction factor and thermal-hydraulic performance with Re
表 1 微小扩张型狭缝肋的网格收敛性结果
Table 1. Grid convergence results for miniaturediffuser slit rib
参数 $\Delta p $/Pa Nu $\varphi_{1} $ 1.192 100.64 $\varphi_{2} $ 1.171 101.34 ${\boldsymbol{}}\varphi_{3} $ 1.172 100.94 $\varphi_{{\rm{e x t}}}^{21} $ 1.193 100.00 $e_{ {\rm{e x t} } }^{21}$/% 0.038 0.64 $I_{{\rm{gc,fine}}}^{21}$/% 0.048 0.80 
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表 2 设计变量和设计空间
Table 2. Design variables and design space
变量 基准值/mm 最小值/mm 最大值/mm $L_{0} $ 20 1 50 $B_{0} $ 20 1 50 $ h_{1}$ 2.2 0.1 3.2 $h_{2} $ 0.6 0.1 3.2
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表 3 Pareto优化设计结果
Table 3. Results of Pareto optimal designs
方案 设计变量 目标函数值（Kriging model） 目标函数值（RANS） 预测精度误差/% L0/mm B0/mm h1/mm h2/mm $\overline{Nu}/\overline{Nu}_{0} $ f0/f $\overline{Nu}/\overline{Nu}_{0} $ f0/f $\overline{Nu}/\overline{Nu}_{0} $ f0/f Baseline 0 0 0 0 1.4514 0.2853 Opt 1 12.33 5.78 0.17 0.51 1.4508 0.2552 1.4095 0.2914 2.93 12.42 Opt 2 12.50 49.54 0.50 0.39 1.3465 0.3060 1.4265 0.2942 5.61 4.01 Opt 3 13.72 1.50 0.71 0.28 1.3961 0.2673 1.3912 0.2994 0.35 10.72 Opt 4 12.33 44.89 0.16 0.51 1.3799 0.2942 1.4132 0.2936 2.36 0.204
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