A Method for Constructing Empirical Correlation Equations for Film Cooling Based on Symbolic Regression and Undetermined Coefficient Optimisation

YAN Xiao; MA Can; SU Xinrong; YUAN Xin

doi:10.19805/j.cnki.jcspe.2026.240812

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A Method for Constructing Empirical Correlation Equations for Film Cooling Based on Symbolic Regression and Undetermined Coefficient Optimisation

更新时间：2026-10-10

- A Method for Constructing Empirical Correlation Equations for Film Cooling Based on Symbolic Regression and Undetermined Coefficient Optimisation
- Chinese Journal of Power Engineering Vol. 46, Issue 4, Pages: 30-38(2026)
- 作者机构：
  
  1. 清华大学热科学与动力工程教育部重点实验室,北京,100084
  2. 中国船舶重工集团公司第七一九研究所船舶热能动力全国重点实验室,湖北,武汉,430205
- 作者简介：
- 基金信息：
- DOI：10.19805/j.cnki.jcspe.2026.240812
  CLC： TK474.8
- Published：2026
- 稿件说明：
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严晓, 马灿, 苏欣荣, 袁新. 基于符号回归与待定系数优化的气膜冷却经验关联式构造方法[J]. 动力工程学报, 2026, 46(4): 30-38.
严晓, 马灿, 苏欣荣, 袁新. 基于符号回归与待定系数优化的气膜冷却经验关联式构造方法[J]. 动力工程学报, 2026, 46(4): 30-38. DOI： 10.19805/j.cnki.jcspe.2026.240812.

DOI： 10.19805/j.cnki.jcspe.2026.240812

摘要

针对透平设计中经验关联式构造依赖学者经验

半经验半拟合方法不确定性大

且传统多项式拟合泛化性差、物理意义不足的问题

提出一种基于符号回归与待定系数优化的气膜冷却经验关联式构造方法。以气膜冷却横向平均有效度和表面有效传热系数为研究对象

针对工业设计场景

改进符号回归方法

通过选取关键特征量

添加待定系数并结合最小二乘法优化

构造适用于不同孔型、湍流度等工况的关联式。结果表明:根据改进后的方法所构造的关联式拟合效果优异

Abstract

To address the problems in turbine design where the construction of empirical correlations relies heavily on expert experience

the semi-empirical and semi-fitting method exhibits significant uncertainties

and traditional polynomial fitting suffers from poor generalization and insufficient physical interpretability

a method for constructing film cooling empirical correlations based on symbolic regression and optimization of undetermined coefficients was proposed. Taking the laterally averaged effectiveness and surface effective heat transfer coefficient of film cooling as the research objects

the symbolic regression method was improved for industrial design scenarios. By selecting key feature variables

incorporating undetermined coefficients

and optimizing with the least square method

correlations applicable to various working conditions such as different hole types and turbulence intensities were constructed. Results show that the correlations established by the improved method demonstrate excellent fitting performance

with a maximum correlation coefficient of 0.997 2 and a maximum relative error of 8.47% for the surface heat transfer coefficient. The correlations comply with the physical laws of film cooling and can effectively extrapolate to predict parameter values under other working conditions.

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references

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刘鹏敏, 崔晓峰, 林翅翔, 等. 进气条件对扇形孔气膜冷却特性的影响[J]. 动力工程学报, 2023, 43(3): 319-325.LIU Pengmin, CUI Xiaofeng, LIN Chixiang, et al. Effect of inlet condition on film cooling performance of a fan-shaped hole[J]. Journal of Chinese Society of Power Engineering, 2023, 43(3): 319-325.

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