Multi-objective optimization design of strut-type lattice cooling thin channel
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摘要:
基于子结构法建立超燃冲压发动机燃烧室主动冷却通道体胞的流-固-热多场耦合有限元模型，在相同体积分数和载荷工况条件下，仿真研究了支杆数量对支杆式点阵冷却细通道传热特性的影响，开展了支杆截面形状的多目标优化。研究表明：与槽道式矩形通道相比，支杆式点阵通道的平均努塞尔数提高了至少64.2%，显著提高了冷却通道传热性能，但流动阻力增大5.8倍以上；支杆式点阵通道的传热性能随支杆数量的增加先提高后降低，其中以两杆式点阵通道的传热性能最好。最大化平均努塞尔数、最小化压降和最高温度的点阵通道多目标优化结果显示：相同体积分数下，支杆数量越多，支杆截面形状对点阵通道的流动和传热性能的影响越小，圆截面杆是两杆及以上支杆式点阵通道兼顾传热和压降要求的1种合适方案；与圆截面杆方案相比，单杆式点阵通道各优化方案的目标性能提升最大，其中折中解的平均努塞尔数增大20.2%、最高温度下降4.4%，压降增大55.1%，展现出较好的综合性能。研究结果为点阵通道设计提供参考。
Abstract:The coupled fluid-solid-thermal finite element model of the active cooling channels in a scramjet combustion chamber was established using the substructure method. The effects of the number of struts on the heat transfer characteristics of strut-type lattice cooling channels under identical volume fractions and loading conditions were investigated, and a multi-objective optimization of the strut cross-sectional shape was conducted. The results showed that, compared with the rectangular smooth channel, the average Nusselt number of the strut-type lattice channel increased by at least 64.2%, significantly enhancing the heat transfer performance of the cooling channel, but the flow resistance increased by more than 5.8 times; the heat transfer performance of the strut-type lattice channel first increased and then decreased with the increase in the number of struts, with the two-strut lattice channel exhibiting the best heat transfer performance. The multi-objective optimization results of the lattice channel, which aimed to maximize the average Nusselt number, and minimize the pressure drop with the highest temperature, showed that under the same volume fraction, the more number of struts meant the lesser impact of the cross-sectional shape on the flow and heat transfer performance of the lattice channel. The circular cross-section strut served as a suitable solution for balancing heat transfer and pressure drop requirements for two or more struts-type lattice channels. The optimal solutions of the single-strut lattice channel exhibited the largest improvement in the target performance, of which the average Nussle number of the compromise solution increased by 20.2%, the maximum temperature decreased by 4.4%, and the pressure drop increased by 55.1%, demonstrating better overall performance. The results could provide a reference for the design of lattice channels.
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Key words:
- active cooling /
- lattice channel /
- shape optimization /
- convective heat transfer /
- scramjet
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图 1 燃烧室及单根冷却通道模型示意图
Figure 1. Schematic of the combustion chamber and the unit cell of cooling channel model
图 4 7 MPa压力下正十二烷的热物性曲线
Figure 4. Thermal physical performance curves of n-dodecane at 7 MPa pressure
图 5 单杆直排式点阵通道示意图
Figure 5. Schematic diagram of single-strut straight row lattice channel
图 8 传热实验结构气壁面温度云图
Figure 8. Temperature contour plot of the hot-gas side wall in the heat transfer test structure
图 9 传热实验结构气壁面温度对比
Figure 9. Comparison of hot-gas side wall temperature of the test structure
图 10 计算和实验获得的传热系数关联式热
Figure 10. Heat transfer correlations based on numerical and test data
图 11 冷却通道结构单胞及通道截面示意图
Figure 11. Schematic diagram of cooling channel structure unit cell and channel cross-section
图 13 冷却通道气壁面温度分布曲线
Figure 13. Temperature distribution curves of the hot-gas side wall in cooling channels
图 14 冷却通道上壁面Nu分布云图
Figure 14. Nu distributions on the upper wall of the cooling channel
图 15 通道上壁面近壁面流速分布云图
Figure 15. Flow velocity distributions near the upper wall of the channel
图 16 通道上壁面近壁面湍动能分布云图
Figure 16. Turbulent kinetic energy distributions near the upper wall of the channel
图 17 冷却通道流动传热性能对比图
Figure 17. Comprehensive thermal-hydraulic performance of cooling channels
图 21 点阵通道3种优化方案的气壁面温度分布曲线
Figure 21. Temperature distribution curves of the hot-gas side wall for three optimization schemes of lattice channels
图 22 单杆式点阵通道3种方案的通道上表面Nu云图
Figure 22. Nu distribution on the upper wall for the three optimization schemes of single-strut lattice channel
表 1 计算数值与实验数据比较
Table 1. Comparison of numerical and test data
参数 计算值 实验值[31] 相对误差/% 测量点1温度/K 383.6 380 0.96 测量点2温度/K 400.2 398 0.54 测量点3温度/K 405.5 410 1.09 平均壁温/K 396.4 396.1 0.09 出口温度/K 351.2 334.6 4.96 ∆p/MPa 0.02 <0.1 一致 
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表 2 点阵通道几何参数
Table 2. Geometric parameters of lattice channels
点阵通道 d/mm Dh/mm γ 单杆直排式 2.51 2.0 0.8 两杆斜八式 1.55 1.9 0.8 三杆四面体式 1.20 1.8 0.8 四杆金字塔式 1.05 1.7 0.8
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表 3 冷却通道的各种数据对比
Table 3. Comparison of various data of cooling channels
通道类型 Tmax/K Tave/K ∆p/kPa Nu 槽道式 699.8 577.5 7.5 62.9 单杆直排式 652.0 534.9 43.7 103.3 两杆斜八式 626.7 514.7 157.8 138.1 三杆四面体式 632.3 519.3 120.6 121.0 四杆金字塔式 645.4 530.6 125.2 106.2
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表 4 基于Kriging响应面的优选解
Table 4. Optimization schemes based on Kriging response surface
通道类别 方案 优化变量
[a, c, ζ]T响应面预测值 有限元计算值 Tmax/K Δp/kPa Nu Tmax/K Δp/kPa Nu 单杆直排式 圆截面杆 [1.255, 0, 2.0]T 652.0 43.7 103.3 Opt 1（min Δp） [1.2, 0, 5.0]T 656.0 29.8 98.3 660.4 29.7 97.2 Opt 2（max Nu） [0.9, −0.2, 2.0]T 615.4 392.3 163.4 612.9 397.3 165.2 Opt 3（折中解） [1.06, 0.19, 4.15]T 621.4 66.6 125.1 623.4 67.8 124.2 两杆斜八式 圆截面杆 [0.775, 0, 2.0]T 626.7 157.8 138.1 Opt 4（min Δp） [0.5, −0.19, 2.0]T 657.0 48.2 101.8 648.9 48.1 103.9 Opt 5（max Nu） [0.7, 0, 2.05]T 619.5 150.6 137.8 619.9 151.2 138.9 Opt 6（折中解） [0.57, −0.08, 2.0]T 647.0 69.6 112.8 655.9 72.2 108.8 三杆
四面体式圆截面杆 [0.6, 0, 2.0]T 632.3 120.6 121.0 Opt 7（min Δp） [0.46, 0.07, 2.0]T 639.1 91.8 111.5 641.9 94.9 109.5 Opt 8（max Nu） [0.6, 0.2, 2.82]T 628.6 140.9 124.1 625.8 139.9 123.6 Opt 9（折中解） [0.52, 0.20, 2.0]T 635.8 96.8 115.7 641.6 99.0 113.2
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表 5 3种点阵通道的杆截面优化形状
Table 5. Optimization shape of strut cross-section for three types of lattice channels
布局 min Δp max Nu 折中解 单杆式 
两杆式 
三杆式 
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