﻿ 猫耳形气膜孔的参数化设计与组合实验优化
 上海理工大学学报  2023, Vol. 45 Issue (5): 460-467, 476 PDF

1. 上海理工大学 能源与动力工程学院，上海 200093;
2. 杭州中能汽轮动力有限公司，杭州 310018

Parametric design and combined experiment optimization of Nekomimi film hole
QIAN Xiaodong1,2, BAO Amei1, WEI Shuang2, LU Yufeng1, CHEN Liu1
1. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. Hangzhou Chinen Steam Turbine Power Co., Ltd., Hangzhou 310018, China
Abstract: The hole type is the key way to improve the film cooling effectiveness. Nekomimi film hole has good cooling performance but complicated configuration. The Isight software was used to optimize Nekomimi film hole through parametric modeling. Variable sensitivity was conducted to reduce variable dimensions and potential value ranges. The Latin hypercubic and the uniform design methods were both used to construct design sample space to improve the prediction accuracy of the surrogate model. Results show that the deviation of cooling efficiency between the surrogate model and the simulated computation is within 1.0%. An optimal hole obtained via the multi-island genetic algorithm has significant 85.7% improvement of surface averaged film cooling efficiency over the reference hole. The surface averaged cooling efficiency of the optima hole is increased by 76% compared to the reference hole, and the laterally and the centerline cooling efficiency are consistant with numerical results.
Key words: film cooling     surrogate model     parametric modeling     sensitivity analysis     combined experimental design

1 物理模型及验证 1.1 物理模型和边界条件

 图 1 计算域及边界条件 Fig. 1 Calculation domain and boundary conditions
 $M = \frac{{{\rho _{\rm c}}{u_{\rm c}}}}{{{\rho _\infty }{u_\infty }}} = \frac{{{{{m_{\rm c}}} \mathord{\left/ {\vphantom {{{m_{\rm c}}} {{A_{\rm c}}}}} \right. } {{A_{\rm c}}}}}}{{{\rho _{\rm c}}{u_\infty }}}$ (1)

 ${\overline \eta _{\rm s}} = \frac{1}{{10D}}\int_0^{10D} {\int_{ - 6.5D}^{6.5D} {\frac{\eta }{{13D}}{\rm d}y} {\rm d}x}$ (2)

 $\eta = \frac{{{T_\infty } - {T_{\rm w}}}}{{{T_\infty } - {T_{\rm c}}}}$ (3)

1.2 网格划分

 图 2 模型网格拓扑结构 Fig. 2 Model grid topology
1.3 湍流模型验证

 图 3 基于Realizable k- $\varepsilon$ 湍流模型验证 Fig. 3 Turbulence model verification based on Realizable k- $\varepsilon$
2 优化平台 2.1 优化流程

 图 4 优化流程图 Fig. 4 Optimized flow diagram
2.2 参数化建模

 图 5 猫耳孔几何图 Fig. 5 Nekomimi geometry

 $L_{\rm m} = mD$ (4)
 $tt = 360t$
 $x_{\rm t} = r_1\cos (tt)$
 $y_{\rm t} = r_2\sin (tt)$ (5)
 $Q = qD$ (6)

2.3 参数敏感性

 $N = \frac{{{N_i} - {N_{\min }}}}{{{N_{\max }} - {N_{\min }}}}$ (7)

 图 6 变量对面平均冷却效率的影响 Fig. 6 Effect of variables on surface averaged cooling efficiency

 图 7 气膜孔各参数的全局敏感度 Fig. 7 Global sensitivity of parameters of flim cooling hole
2.4 实验设计

 图 8 CED样本空间分布 Fig. 8 Spatial distribution of samples based on CED
2.5 代理模型

3 结果及分析 3.1 实验设计的影响

3.2 优化孔与基准孔的数值比较

 图 9 气膜冷却效率分布云图（M=1.5） Fig. 9 Distribution of film cooling efficiency （M=1.5）

 图 10 不同截面处的涡量和流线图 (M=1.5) Fig. 10 Vorticity and streamlines at different corss-sections (M=1.5)

 图 11 基准孔与优化孔的横向冷却效率和中心线冷却效率对比 Fig. 11 Comparison of lateral and centerline cooling efficiency between reference and optimized hole
3.3 试验验证

 图 12 优化孔气膜冷却效率数值模拟结果与实验结果对比 Fig. 12 Comparison of film cooling effectivness of the optimized hole between numerical and experimental results

 图 13 优化孔的横向平均冷却效率和中心线冷却效率数值结果与实验结果对比 Fig. 13 Comparison of laterally averaged and centerline cooling efficiency of the optimized hole between numerical and experimental results
4 结　论

a. 变量的敏感性分析不仅说明入口圆柱段长度和扩散角是控制猫耳形气膜孔冷却效率的主要因素，却而且能够提供各变量的影响规律和缩小变量的最佳取值范围。

b. 组合使用拉丁超立方和均匀设计构建复杂形体的实验样本，提高了样本对设计空间的覆盖度，有效提升了基于样本的代理模型的预测精度，保证了优化方法的“凸”性，也提高了优化效率与精度，降低了气膜孔的优化成本。

c. 通过实验验证，对于气膜孔的面平均冷却效率，实验值与模拟值的差异约为9.3%，但针对气膜孔的横向冷却效率和中心线冷却效率，实验值与模拟值吻合得很好。优化孔削弱了气膜射流的肾型涡，与主流形成明显的分层，使气膜更好地贴附于壁面，从而显著提高了冷却效率。

 [1] 张文武, 郭春海, 张天润, 等. 涡轮叶片先进气膜冷却与相关激光打孔技术进展[J]. 航空制造技术, 2016(22): 26-31. DOI:10.16080/j.issn1671-833x.2016.22.026 [2] 朱志文, 王宏光. 管内振动壁面射流流场的数值模拟[J]. 上海理工大学学报, 2015, 37(2): 110-114. DOI:10.13255/j.cnki.jusst.2015.02.002 [3] GRITSCH M, SCHULZ A, WITTIG S. Film-cooling holes with expanded exits: near-hole heat transfer coefficients[J]. International Journal of Heat and Fluid Flow, 2000, 21(2): 146-155. DOI:10.1016/S0142-727X(99)00076-4 [4] BUNKER R S. A review of shaped hole turbine film-cooling technology[J]. Journal of Heat Transfer, 2005, 127(4): 441-453. DOI:10.1115/1.1860562 [5] HAN C, REN J, JIANG H D. Multi-parameter influence on combined-hole film cooling system[J]. International Journal of Heat and Mass Transfer, 2012, 55(15/16): 4232-4240. [6] KUSTERER K, ELYAS A, BOHN D, et al. The NEKOMIMI cooling technology: cooling holes with ears for high-efficient film cooling[C]//ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. Vancouver: ASME, 2011: 303–313. [7] FORRESTER A I J, KEANE A J. Recent advances in surrogate-based optimization[J]. Progress in Aerospace Sciences, 2009, 45(1/3): 50-79. [8] BHOSEKAR A, IERAPETRITOU M. Advances in surrogate based modeling, feasibility analysis, and optimization: a review[J]. Computers & Chemical Engineering, 2018, 108: 250-267. [9] LIU C, AMEI B, YI Z, et al. Surrogate-based optimization and experiment validation of a fan-shaped film cooling hole with a large lateral space[J]. Applied Thermal Engineering, 2022, 207: 118145. DOI:10.1016/j.applthermaleng.2022.118145 [10] ZHANG H, LI Y F, CHEN Z Y, et al. Multi-fidelity model based optimization of shaped film cooling hole and experimental validation[J]. International Journal of Heat and Mass Transfer, 2019, 132: 118-129. DOI:10.1016/j.ijheatmasstransfer.2018.11.156 [11] SUN Y B, MENG X Y, LONG T, et al. A fast optimal Latin hypercube design method using an improved translational propagation algorithm[J]. Engineering Optimization, 2020, 52(7): 1244-1260. DOI:10.1080/0305215X.2019.1642881 [12] 管俊俊, 张祎, 张也平, 等. 基于代理模型与参数敏感性分析的扇形气膜孔优化[J]. 动力工程学报, 2021, 41(9): 736-742,757. DOI:10.19805/j.cnki.jcspe.2021.09.004 [13] 方开泰. 均匀设计与均匀设计表[M]. 北京: 科学出版社, 1994. [14] 姜同川. 正交试验设计[M]. 济南: 山东科学技术出版社, 1985. [15] BONANNI L, FACCHINI B, TARCHI L, et al. Heat transfer performance of fan-shaped film cooling holes: part I—experimental analysis[C]//ASME Turbo Expo 2010: Power for Land, Sea, and Air. Glasgow: ASME, 2010: 1561–1571. [16] 管俊俊, 陈榴, 戴韧. 离散孔气膜冷却效果的红外热像测量方法[J]. 热能动力工程, 2021, 36(3): 19-25,54. DOI:10.16146/j.cnki.rndlgc.2021.03.003