湍流管流的数量级分析与数据驱动的物理信息符号回归
流体动力学
2026-02-20 v1 计算物理
摘要
粗糙管道的摩擦损失常通过半经验公式预测，如科尔布鲁克-白方程 (Colebrook,1939)，但无法完全再现尼库拉兹的粗糙管实验 (1950)。本研究对鲁棒南特-纳维-斯塔克方程进行数量级分析，推导黏性和湍流贡献于管道沿程压降的比例关系。这些关系通过幂律包络约束局部压降对平均速度、粗糙度、粘度和密度的灵敏度，作为符号回归的物理先验。我们结合尼库拉兹的粗管和光滑管数据 (Zagarola 和 Smits,1998)，旨在推导能贴合实验数据且满足上述约束的紧凑摩擦因子公式。我们采用修改版遗传编程引擎 (GPTIPS2) 优化模型结构，并基于适应度、复杂度和约束违规进行评估。该方法产生可解释且准确再现 various 粗糙度水平下和 Re ~ 10^7 范围内摩擦因子的表达式。
引用
@article{arxiv.2602.17082,
title = {Order of Magnitude Analysis and Data-Based Physics-Informed Symbolic Regression for Turbulent Pipe Flow},
author = {Yunus Emre Ünal and Özgür Ertunç and Ismail Ari and Ivan Otić},
journal= {arXiv preprint arXiv:2602.17082},
year = {2026}
}
备注
The derived relations accurately represent the transition from smooth-wall to fully rough limits up to Reynolds numbers of about 30 million and beyond. This method can also apply to other physical problems where only order-of-magnitude estimates are possible from constitutive laws