基于改进型Gappy POD的亚跨声速压气机叶型反设计方法

茅晓晨; 陈飞; 陈璇

doi:10.13224/j.cnki.jasp.20240046

基于改进型Gappy POD的亚跨声速压气机叶型反设计方法

doi: 10.13224/j.cnki.jasp.20240046

西北工业大学动力与能源学院，西安 710072

基金项目: 国家自然科学基金（92152301）；气动院流动显示与测量重点实验室（D5110220177）

详细信息

作者简介:
茅晓晨（1989-），男，副教授，博士，主要从事叶轮机械气动热力学研究。E-mail：maoxiao_chen@nwpu.edu.cn

中图分类号: V231.3
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出版历程
- 收稿日期: 2024-01-20
- 网络出版日期: 2025-07-06

Inverse design method of subsonic and transonic compressor blade based on improved Gappy POD

School of Power and Energy，Northwestern Polytechnical University，Xi’an 710072，China

摘要

摘要:
针对基本Gappy POD（proper orthogonal decomposition）方法的反设计精度较低、可操作性不强，且对跨声速叶型的反设计精度低于亚声速叶型的问题提出改进策略，发展了一套完整的改进型Gappy POD方法。通过验证算例证明了基于改进型Gappy POD方法的压气机叶型反设计更加简单高效，与基本Gappy POD方法相比，两种叶型的反设计精度分别提高了61%和78%，同时反设计耗时分别缩短了77%和63%。进一步研究发现改进型Gappy POD方法对叶型拟合精度提高的收益主要来自压力面重构精度的提高，而在吸力面后半段叶型几何偏差较大，且几何偏差呈现从前缘到尾缘先增大后减小的趋势。
- 压气机叶型 /
- 反设计 /
- 本征正交分解（POD） /
- Gappy POD /
- 重构精度
Abstract:
An improved Gappy POD (proper orthogonal decomposition) method was developed in response to the low inverse design accuracy and limited operability of the method. Furthermore, improvement strategies were proposed to address the issue of lower inverse design accuracy for transonic blade compared with subsonic blade. Through verification examples, the inverse design of compressor blade based on the improved Gappy POD method was proved simpler and more efficient. Compared with the basic method, the inverse design accuracy of the two blades was improved by 61% and 78%, also the inverse design time was shortened by 77% and 63%, respectively. Further research found that the benefits of the improved method in accuracy of blade fitting mainly came from the improvement of pressure surface reconstruction accuracy, while the geometric deviation of the blade in the second half of the suction surface was relatively large, and the geometric deviation showed a trend of increasing first and then decreasing from the leading edge to the trailing edge.
- compressor blade /
- inverse design /
- proper orthogonal decomposition (POD) /
- Gappy POD /
- reconstruction accuracy

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图 1 sub_blade和tran_blade的几何示意图

Figure 1. Geometry schematic of sub_blade and tran_blade

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图 2 不同网格节点数下的叶型表面压力系数分布对比

Figure 2. Comparison of pressure coefficient distribution on blade surface under different grid node numbers

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图 3 sub_blade和tran_blade的网格拓扑结构

Figure 3. Mesh topology structure of sub_blade and tran_blade

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图 4 sub_blade和tran_blade的CFD计算结果与实验结果对比

Figure 4. Comparison between CFD calculation and experimental of sub_blade and tran_blade

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图 5 基本Gappy POD方法下的自适应快照替换过程$ {{E}}_{\text{RSM-pres}} $变化图

Figure 5. $ {{E}}_{\text{RSM-pres}} $ change map in adaptive snapshot replacement process under basic Gappy POD method

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图 6 基本Gappy POD方法的反设计叶型与目标叶型对比

Figure 6. Comparison of inverse design blade and target blade based on basic Gappy POD method

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图 7 基于改进型Gappy POD方法的反设计流程

Figure 7. Inverse design process based on improved Gappy POD method

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图 8 改进型Gappy POD方法下的自适应快照替换过程$ {{E}}_{\text{RSM-pres}} $变化图

Figure 8. $ {{E}}_{\text{RSM-pres}} $ change map in adaptive snapshot replacement process under improved Gappy POD method

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图 9 不同样本数下的$ {{E}}_{\text{RSM-pres}} $变化图

Figure 9. $ {{E}}_{\text{RSM-pres}} $ change map in different sample sizes

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图 10 基本Gappy POD方法与改进型Gappy POD方法反设计叶型的表面压力系数曲线对比

Figure 10. Comparison of surface pressure coefficient curves for inverse design of blades using basic Gappy POD and modified Gappy POD methods

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图 11 不同Gappy POD方法下的反设计叶型几何偏差分布

Figure 11. Geometric deviation distribution of inverse design blades under different Gappy POD methods

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表 1 sub_blade和tran_blade的主要几何参数

Table 1. Main geometric parameters of sub_blade and tran_blade

参数	数值
参数	sub_blade	tran_blade
叶栅稠度$ C/t $	1.82	1.61
进口气流角$ {{\beta }}_{{1}} $/（°）	132	148.5
进口马赫数$ {{Ma}}_{{1}} $	0.67	0.92
叶型安装角$ {{\beta }}_{{{\mathrm{s}}}} $/（°）	112.5	138.51
最大相对厚度$ d/C $	0.055	0.05
叶型弯角$ {\theta } $/（°）	48	14.9

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表 2 sub_blade反设计叶型与目标叶型主要性能对比

Table 2. Comparison of main characteristics between inverse design blade and target blade of sub_blade

项目		静压升$ \pi $	总压损失$ \bar{{ \omega }} $
性能参数	目标叶型	1.176391	0.0245594
	基本Gappy POD方法叶型	1.176456	0.0244121
	改进型Gappy POD方法叶型	1.176413	0.0245182
相对误差/%	基本Gappy POD方法叶型	0.0055	0.600
相对误差/%	改进型Gappy POD方法叶型	0.0187	0.168

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表 3 tran_blade反设计叶型与目标叶型主要性能对比

Table 3. Comparison of main characteristics between inverse design blade and target blade of tran_blade

项目		静压升$\pi$	总压损失$ \bar{{ \omega }} $
性能参数	目标叶型	1.401968	0.0351124
	基本Gappy POD方法叶型	1.401225	0.0352927
	改进型Gappy POD方法叶型	1.403003	0.0351806
相对误差/%	基本Gappy POD方法叶型	0.053	0.513
相对误差/%	改进型Gappy POD方法叶型	0.074	0.194

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