基于响应面法的X型桁架阵列通道冷却性能优化

席雷; 高建民; 徐亮; 赵振; 李云龙

doi:10.13224/j.cnki.jasp.20220135

基于响应面法的X型桁架阵列通道冷却性能优化

doi: 10.13224/j.cnki.jasp.20220135

西安交通大学机械制造系统工程国家重点实验室，西安 710049

基金项目: 陕西省自然科学基础研究计划青年项目（2022JQ-545）；中国博士后科学基金（2021M702573）

详细信息

作者简介:
席雷（1990-），男，助理教授，博士，研究方向为涡轮叶片冷却技术。E-mail：xilei100@mail.xjtu.edu.cn

通讯作者:
徐亮（1980-），男，教授，博士，研究方向为涡轮叶片冷却技术。E-mail：xuliang@mail.xjtu.edu.cn

中图分类号: V233.5；TK47
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出版历程
- 收稿日期: 2022-03-15
- 网络出版日期: 2023-09-06

Optimization of cooling performance of X-type truss array channel based on response surface methodology

State Key Laboratory for Manufacturing Systems Engineering， Xi’an Jiaotong University，Xi’an 710049，China

摘要

摘要:
基于数值结果构建了有关X型桁架通道壁面平均努塞尔数、摩擦因数和综合热力系数的2阶响应面模型，分析了桁架杆直径比、桁架杆夹角和桁架杆倾角等对X型桁架通道冷却性能的影响规律，并优化得到了最佳参数。结果表明：增大桁架杆直径比和桁架杆夹角均可以快速地提高平均努塞尔数，但也相应地增大了摩擦因数；增大桁架杆倾角先提高后又降低了平均努塞尔数和摩擦因数；增大桁架杆直径比、桁架杆夹角和桁架杆倾角均会使综合热力系数先增大后减小。当桁架杆直径比为0.0750、桁架杆夹角为60°和桁架杆倾角为33.79°时通道的传热性能最优；当桁架杆直径比为0.067、桁架杆夹角为37.88°和桁架杆倾角为31.36°时通道的综合热力性能最优。
- 桁架阵列 /
- 冷却通道 /
- 流动与传热 /
- 响应面法 /
- 优化设计
Abstract:
Based on the numerical results, the second-order response surface models with high prediction accuracy for the wall average Nusselt number, friction coefficient and comprehensive thermal coefficient of X-type truss channel were built. The influence laws of truss rod diameter ratio, truss rod included angle and truss rod inclination angle on the cooling performance of X-type truss array channel were analyzed, and the optimal parameters were obtained by optimization. The results showed that increasing truss rod diameter ratio and truss rod’s included angle both can greatly improve average Nusselt number, but also increased the friction coefficient accordingly. Enlarging truss rod’s inclination angle first increased and then decreased the average Nusselt number and friction coefficient. Increasing truss rod diameter ratio, truss rod’s included angle and truss rod’s inclination angle made the comprehensive thermal coefficient first increase and then decrease. When truss rod diameter ratio was 0.0750, truss rod’s included angle was 60° and truss rod’s inclination angle was 33.79°, the heat transfer performance of the channel reached the best. When truss rod diameter ratio was 0.067, truss rod’s included angle was 37.88° and truss rod’s inclination angle was 31.36°, the comprehensive thermal performance of the channel was the best.
- truss array /
- cooling channel /
- flow and heat transfer /
- response surface methodology /
- optimization design

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图 1 研究对象

Figure 1. Research object

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图 2 数值模型

Figure 2. Numerical model

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图 3 网格模型

Figure 3. Grid models

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图 4 数值方法验证

Figure 4. Numerical method verification

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图 5 响应面模型的拟合偏差

Figure 5. Fitting deviations of response surface models

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图 6 标准化效应的Pareto图（Re=30 000）

Figure 6. Pareto diagrams of standardization effects （Re=30 000）

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图 7 Nu_a的响应图（Re=30 000）

Figure 7. Response diagrams of Nu_a （Re=30 000）

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图 8 f的响应面图（Re=30 000）

Figure 8. Response diagrams of f （Re=30 000）

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图 9 F的响应面（Re=30 000）

Figure 9. Response diagrams of F （Re=30 000）

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图 10 优化结果（Re=30 000）

Figure 10. Optimization results （Re=30 000）

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表 1 设计变量及其水平

Table 1. Design variables and their levels

变量	水平
变量	低	中	高
d/D	0.0375	0.0563	0.0750
α/（°）	30	45	60
β/（°）	15	30	45

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表 2 CCF试验设计

Table 2. CCF experimental design

序号	输入参数			输出参数			序号	输入参数			输出参数
序号	d/D	α/（°）	β/（°）	Nu_a	f	F	序号	d/D	α/（°）	β/（°）	Nu_a	f	F
1	0.0375	45	30	100.678	0.038	0.619	11	0.0750	30	15	114.529	0.060	0.606
2	0.0563	45	30	120.464	0.054	0.660	12	0.0750	60	45	134.040	0.103	0.592
3	0.0375	30	45	94.262	0.038	0.582	13	0.0750	60	15	129.925	0.084	0.615
4	0.0563	45	15	111.956	0.048	0.637	14	0.0750	45	30	138.637	0.075	0.680
5	0.0563	45	30	120.464	0.054	0.660	15	0.0563	30	30	114.142	0.047	0.653
6	0.0563	60	30	124.294	0.061	0.655	16	0.0563	45	30	120.464	0.054	0.660
7	0.0750	30	45	129.400	0.070	0.651	17	0.0375	60	45	97.120	0.048	0.554
8	0.0563	45	30	120.464	0.054	0.660	18	0.0563	45	30	120.464	0.054	0.660
9	0.0563	45	45	114.864	0.053	0.633	19	0.0375	30	15	98.238	0.035	0.620
10	0.0375	60	15	103.233	0.042	0.616	20	0.0563	45	30	120.464	0.054	0.660

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表 3 Nu_a、f和F模型的回归系数

Table 3. Regression coefficients for models of Nu_a，f and F

回归系数	Nu_a	f	F
b₀	49.7	0.0956	−0.014
b₁	299	−1.706	9.68
b₂	0.483	−0.001613	0.02546
b₃	1.435	−0.000278	0.00577
b₁₁	−1016	14.54	−83.7
b₂₂	−0.00354	0.000011	−0.00025
b₃₃	−0.02935	−0.000005	0.000015
b₁₂	5.41	0.01809	−0.0169
b₁₃	12.92	0.00925	−0.0577
b₂₃	− 0.00716	0.000007	0.000008

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