基于RSM的带有热障涂层气膜孔参数优化的数值研究

闫浩楠; 张丽; 朱惠人; 刘存良; 何爱杰; 刘松

doi:10.13224/j.cnki.jasp.20210295

基于RSM的带有热障涂层气膜孔参数优化的数值研究

doi: 10.13224/j.cnki.jasp.20210295

闫浩楠¹,
张丽¹,
朱惠人^{1, 2},
刘存良^{1, 2},
何爱杰³,
刘松³

1.
西北工业大学动力与能源学院，西安 710129
2.
西北工业大学陕西省航空动力系统热科学重点实验室，西安 710129
3.
中国航发四川燃气涡轮研究院，成都 610500

基金项目: 国家科技重大专项（2017-Ⅲ-0001-0025）；国家科技专项重点基础研究项目（2017-JCJQ-ZD-031-00）

详细信息

作者简介:
闫浩楠（1997-），男，硕士生，研究方向为航空发动机高温部件冷却和换热技术

中图分类号: V232.4
计量
- 文章访问数: 552
- HTML浏览量: 496
- PDF量: 65
- 被引次数: 0
出版历程
- 收稿日期: 2020-06-10
- 网络出版日期: 2023-03-29

Numerical study on parameter optimization of the film hole with thermal barrier coating based on RSM

1.
School of Power and Energy，Northwestern Polytechnical University，Xi’an 710129，China
2.
Shaanxi Key Laboratory of Thermal Sciences in Aero-engine System， Northwestern Polytechnical University，Xi’an 710129，China
3.
Sichuan Gas Turbine Establishment，Aero Engine Corporation of China，Chengdu 610500，China

摘要

摘要:
为解决有涂层时多种因素导致气膜冷效优化计算成本增大的问题，通过Box-Behnken方法合理设计3个吹风比(0.5、1.0和1.5)下，气膜孔流向倾角、长径比和涂层厚度3种参数的耦合模型，利用Realizable k-ε湍流模型进行数值模拟，将模拟结果通过响应面分析法(RSM)得到响应方程，最终通过响应方程预测最优参数。结果表明：孔倾角和涂层厚度为影响有涂层（TBC）气膜孔冷效的主要因素，长径比为影响冷效的次要因素。通过响应方程预测能达到最优气膜冷效时的模型，结果显示优化模型在所研究吹风比范围内气膜冷效相对于参考提升了55.45%～90.95%，响应方程的预测误差范围为2.71%～13.42%，具有较高的准确性。
- 气膜冷却 /
- 热障涂层 /
- 长径比 /
- 响应面分析 /
- 几何参数
Abstract:
In order to solve the problem that many factors may lead to the increase of calculation cost of optimizing air film cooling efficiency, a coupling model of flow angle, length-diameter ratio and coating thickness at three blowing ratios (0.5, 1.0 and 1.5) was reasonably designed by Box-Behnken design method. Realizable k-ε turbulence model was used for numerical simulation. Response Surface Methodology (RSM) was used to analyze the simulation results to obtain the response equation, finally the optimal parameters were predicted by the regression equation. Researches showed that flow angle and coating thickness are the main factors affecting the cooling efficiency of film holes with thermal barrier coating (TBC), and the length-diameter is the secondary factor affecting the cooling efficiency. The response equation was used to predict the optimization model with best film cooling efficiency. Within the studied blowing ratio range, the results showed that the film cooling efficiency of the optimized model was 55.45%−90.95% higher than that of the reference, and the prediction error range of the response equation was 2.71%−13.42% with higher accuracy.
- film cooling /
- thermal barrier coating /
- length-diameter radio /
- response surface analysis /
- geometric parameter

HTML

图 1 3阶2² BBD因子设计矩阵

Figure 1. Third-order 2² matrix designed by BBD

下载: 全尺寸图片幻灯片

图 2 计算模型及孔内几何参数

Figure 2. Calculation model and geometric parameters in hole

下载: 全尺寸图片幻灯片

图 3 TBC堵塞圆柱型气膜孔的剖视图^[11]

Figure 3. Section view of TBC blocked cylindrical film hole^[11]

下载: 全尺寸图片幻灯片

图 4 网格无关性验证

Figure 4. Grid independence validation

下载: 全尺寸图片幻灯片

图 5 流体域计算网格

Figure 5. Fluid domain computing grid

下载: 全尺寸图片幻灯片

图 6 计算结果与实验结果对比

Figure 6. Comparison of calculation results and experimental results

下载: 全尺寸图片幻灯片

图 7 设计结构在3种吹风比下的气膜冷效分布云图

Figure 7. Distribution contour of film cooling efficiency under three blow ratios was designed

下载: 全尺寸图片幻灯片

图 8 不同孔倾角的面平均气膜冷效

Figure 8. Surface average film cooling efficiency with different hole dip angles

下载: 全尺寸图片幻灯片

图 9 不同长径比下的面平均冷效

Figure 9. Surface average cooling efficiency with different aspect ratios

下载: 全尺寸图片幻灯片

图 10 不同热障涂层厚度下的面平均冷效

Figure 10. Surface average cooling efficiency with different thermal barrier coating thicknesses

下载: 全尺寸图片幻灯片

图 11 M=0.5时双因素交互曲面

Figure 11. Two-factor interactive surface when M=0.5

下载: 全尺寸图片幻灯片

图 12 M=1.0时双因素交互曲面

Figure 12. Two-factor interactive surface when M=1.0

下载: 全尺寸图片幻灯片

图 13 M=1.5时双因素交互曲面

Figure 13. Two-factor interactive surface when M=1.5

下载: 全尺寸图片幻灯片

图 14 优化模型与参考模型不同吹风比下的冷效云图

Figure 14. Distribution contour of film cooling efficiency of the optimization model and the reference model with different blowing ratios

下载: 全尺寸图片幻灯片

表 1 BBD方法设计的实验工况

Table 1. BBD method design of experimental conditions

工况	孔倾角/（°）	长径比	涂层厚度/mm
参考	45	1.75	0.325
Case 1	60	4.375	0.5
Case 2	45	7	0.15
Case 3	45	4.375	0.325
Case 4	30	4.375	0.15
Case 5	45	1.75	0.15
Case 6	60	1.75	0.325
Case 7	45	4.375	0.325
Case 8	45	1.75	0.5
Case 9	60	7	0.325
Case 10	30	1.75	0.325
Case 11	60	4.375	0.15
Case 12	30	4.375	0.5
Case 13	45	7	0.5
Case 14	30	7	0.325
Case 15	45	4.375	0.325

下载: 导出CSV

表 2 各实验工况下游面平均气膜冷效

Table 2. Surface average film cooling efficiency of each experimental condition

工况	响应值η_ave
工况	M=0.5	M=1.0	M=1.5
参考	0.0384	0.0268	0.0258
Case 1	0.0161	0.0056	0.0044
Case 2	0.0591	0.0337	0.0299
Case 3	0.0324	0.0274	0.0248
Case 4	0.0700	0.0429	0.0371
Case 5	0.0617	0.0335	0.0303
Case 6	0.0273	0.0219	0.0184
Case 7	0.0324	0.0273	0.0248
Case 8	0.0265	0.0218	0.0180
Case 9	0.0234	0.0223	0.0164
Case 10	0.0669	0.0410	0.0355
Case 11	0.0498	0.0286	0.0255
Case 12	0.0529	0.0384	0.0329
Case 13	0.0288	0.0297	0.0209
Case 14	0.0506	0.0344	0.0359
Case 15	0.0324	0.0273	0.0248

下载: 导出CSV

表 3 M=0.5时孔出口下游面平均气膜冷效方差分析

Table 3. Variance analysis of surface average film cooling efficiency at the downstream of hole outlet when M=0.5

方差来源	平方和	自由度	均方	P值
模型	4174.74	9	463.86	0.0011
A（角度）	1914.47	1	1914.47	0.0001
B（长径比）	52.43	1	52.43	0.147
C（厚度）	1691.3	1	1691.3	0.0002
AB	38.35	1	38.35	0.2024
AC	69.1	1	69.1	0.1061
BC	5.88	1	5.88	0.5908
A²	152.62	1	152.62	0.0328
B²	39.05	1	39.05	0.1989
C²	261.08	1	261.08	0.0123
残差	89.15	5	17.83
失拟项	89.15	3	29.72	< 0.0001
纯误差	1.67$ \times $10⁻⁷	2	8.33$ \times $10⁻⁸
总和	4263.88	14

下载: 导出CSV

表 4 M=1.0时孔出口下游面平均气膜冷效方差分析

Table 4. Variance analysis of surface average film cooling efficiency at the downstream of hole outlet when M=1.0

方差来源	平方和	自由度	均方	P值
模型	1132.22	6	188.7	0.0005
A（角度）	787.11	1	787.11	<0.0001
B（长径比）	0.4217	1	0.4217	0.8558
C（厚度）	242.45	1	242.45	0.002
AB	11.86	1	11.86	0.3485
AC	75.6	1	75.6	0.0361
BC	14.77	1	14.77	0.2988
残差	95.71	8	11.96
失拟项	95.71	6	15.95	< 0.0001
纯误差	6.67$ \times $10⁻⁹	2	3.33$ \times $10⁻⁹
总和	1227.93	14

下载: 导出CSV

表 5 M=1.5时孔出口下游面平均气膜冷效方差分析

Table 5. Variance analysis of surface average film cooling efficiency at the downstream of hole outlet when M=1.5

方差来源	平方和	自由度	均方	P值
模型	1133.18	6	188.86	< 0.0001
A（角度）	777.51	1	777.51	< 0.0001
A （长径比）	0.1162	1	0.1162	0.8265
A （厚度）	295.14	1	295.14	< 0.0001
A	1.47	1	1.47	0.4439
AC	56.19	1	56.19	0.0011
BC	2.76	1	2.76	0.3018
残差	18.13	8	2.27
失拟项	18.13	6	3.02	< 0.0001
纯误差	1.87$ \times $10⁻⁷	2	9.33$ \times $10⁻⁸
总和	1151.31	14

下载: 导出CSV

表 6 RSM方法的优化参数与预测值

Table 6. Optimized parameters and predicted values with RSM method

吹风比	孔倾角/（°）	长径比	涂层厚度/mm	预测响应值η_ave
M=0.5	30	1.75	0.15	0.0832
M=1.0	30	1.75	0.15	0.0436
M=1.5	30	1.753	0.15	0.0377

下载: 导出CSV

表 7 优化结果分析

Table 7. Analysis of optimization results

吹风比	参考模型冷效值	优化模型响应方程预测值	优化模型计算结果值	相对于参考值的提升/%	预测误差/%
M=0.5	0.0377	0.0832	0.0720	90.95	13.42
M=1.0	0.0261	0.0436	0.0435	66.64	2.71
M=1.5	0.0251	0.0377	0.0387	54.45	2.73

下载: 导出CSV

参考文献(21)

[1]	朱惠人, 张丽, 郭涛, 等. 高温透平叶片的传热与冷却[M]. 西安: 西安交通大学出版社, 2018.
[2]	SCHULZ U,LEYENS C,FRITSCHER K,et al. Some recent trends in research and technology of advanced thermal barrier coatings[J]. Aerospace Science and Technology,2003,7(1): 73-80. doi: 10.1016/S1270-9638(02)00003-2
[3]	BUNKER R S. Effect of partial coating blockage on film cooling effectiveness[R]. ASME Paper 2000-GT-0244, 2000.
[4]	LUTUM E,JOHNSON B V. Influence of the hole length-to-diameter ratio on film cooling with cylindrical holes[J]. Journal of Turbomachinery,1999,121(2): 209-216. doi: 10.1115/1.2841303
[5]	蒋兴文. 平板气膜冷却的传热特性研究[D]. 北京: 清华大学, 2015. JIANG Xingwen. Research on heat transfer characteristics of flat air film cooling[D]. Beijing: Tsinghua University, 2015. (in Chinese)
[6]	蒋兴文, 高诚, 彭威, 等. 气膜冷却中流量系数的实验研究[R]. 西安: 工程热物理学会, 2014.
[7]	彭宁建. 壁厚对平板气膜冷却特性影响研究[D]. 沈阳: 沈阳航空航天大学, 2017. PENG Ningjian. Research on the effect of wall thickness on cooling characteristics of flat air film[D]. Shenyang: Shenyang Aerospace University, 2017. (in Chinese)
[8]	YUEN C H,MARTINEZ-BOTAS R F. Film cooling characteristics of a single round hole at various streamwise angles in a crossflow: Part Ⅰ effectiveness[J]. International Journal of Heat and Mass Transfer,2003,46(2): 221-235. doi: 10.1016/S0017-9310(02)00274-0
[9]	刘捷,韩振兴,刘建军,等. 射流注入角对平板气膜冷却特性影响的实验研究[J]. 工程热物理学报,2007,28(3): 409-411. doi: 10.3321/j.issn:0253-231X.2007.03.015 LIU Jie,HAN Zhenxing,LIU Jianjun,et al. Experimental study on the effect of jet injection angle on the cooling characteristics of flat air film[J]. Journal of engineering thermophysics,2007,28(3): 409-411. (in Chinese) doi: 10.3321/j.issn:0253-231X.2007.03.015
[10]	郭洪波,彭立全,宫声凯,等. 电子束物理气相沉积热障涂层技术研究进展[J]. 热喷涂技术,2009,1(2): 7-14. doi: 10.3969/j.issn.1674-7127.2009.02.002 GUO Hongbo,PENG Liquan,GONG Shengkai,et al. Advances in thermal barrier coatings by electron beam physical vapor deposition[J]. Thermal Spraying Technology,2009,1(2): 7-14. (in Chinese) doi: 10.3969/j.issn.1674-7127.2009.02.002
[11]	PU Jian,WANG Fuqiang,WANG Jianhua,et al. Numerical investigation of effects of blockage, inclination angle, and hole-size on film cooling effectiveness at concave surface[J]. Journal of Turbomachinery,2021,143(2): 1-59.
[12]	刘飞,毛杰,邓子谦,等. 等离子喷涂-物理气相沉积制备热障涂层对气膜冷却孔的影响[J]. 表面技术,2017,46(8): 21-26. doi: 10.16490/j.cnki.issn.1001-3660.2017.08.004 LIU Fei,MAO Jie,DENG Ziqian,et al. Effect of thermal barrier coating prepared by plasma spray and physical vapor deposition on gas film cooling hole[J]. Surface Technology,2017,46(8): 21-26. (in Chinese) doi: 10.16490/j.cnki.issn.1001-3660.2017.08.004
[13]	张鹏飞,白林超,张超. 叶栅环境下凹坑气膜孔的冷却特性研究[J]. 天津理工大学学报,2019,35(6): 13-17. ZHANG Pengfei,BAI Linchao,ZHANG Chao. Research on cooling characteristics of cavitation film under cascade environment[J]. Journal of Tianjin University of Technology,2019,35(6): 13-17. (in Chinese)
[14]	WANG Jin,CUI Pei,BENGT S,et al. Effects of deposition height and width on film cooling[J]. Numerical Heat Transfer: Part A Applications,2016,70(6): 673-687. doi: 10.1080/10407782.2016.1193351
[15]	FU Jianfeng,ZHAO Yaqian,WU Qiuli. Optimising photoelectrocatalytic oxidation of fulvic acid using response surface methodology[J]. Journal of Hazardous Materials,2007,144(1/2): 499-505.
[16]	MADARIA P R, MOHAN N, RAJAGOPAL C, et al. Application of carbon aerogel for electrolytic removal of mercury from aqueous solutions[J]. Journal of Scientific and Industrial Research, 2004, 63(11): 938-943.
[17]	MIRZA T,TAN H S. Determination of captopril in pharmaceutical tablets by anion-exchange HPLC using indirect photometric detection; a study in systematic method development[J]. Journal of Pharmaceutical and Biomedical Analysis,2001,25(1): 39-52. doi: 10.1016/S0731-7085(00)00462-3
[18]	ZAMIRI A,YOU S J,JIN T C,et al. Large eddy simulation in the optimization of laidback fan-shaped hole geometry to enhance film-cooling performance[J]. International Journal of Heat and Mass Transfer,2020,158: 120014.1-120014.17.
[19]	FERREIRA S L C,BRUNS R E,FERREIRA H S,et al. Box-Behnken design: an alternative for the optimization of analytical methods[J]. Analytica Chimica Acta,2007,597(2): 179-186. doi: 10.1016/j.aca.2007.07.011
[20]	BEZERRA M A,SANTELLI R E,OLIVEIRA E P,et al. Response surface methodology (RSM) as a tool for optimization in analytical chemistry[J]. Talanta,2008,76(5): 965-977. doi: 10.1016/j.talanta.2008.05.019
[21]	李佳,卢义,袁新,等. 基于压力敏感漆的气膜冷却孔形实验研究[J]. 清华大学学报(自然科学版),2010,50(8): 1267-1270. LI Jia,LU Yi,YUAN Xin,et al. Based on the gas pressure sensitive paint film cooling hole shape experimental study[J]. Journal of Tsinghua University (Natural Science Edition),2010,50(8): 1267-1270. (in Chinese)