Order of Magnitude Analysis and Data-Based Physics-Informed Symbolic Regression for Turbulent Pipe Flow

TL;DR

This paper develops a physics-informed symbolic regression approach, combining order-of-magnitude analysis with genetic programming, to derive accurate, interpretable correlations for turbulent pipe flow friction factors that align with experimental data.

Contribution

It introduces a novel physics-informed symbolic regression method that integrates scaling laws as constraints to produce interpretable models for turbulent pipe flow friction.

Findings

Accurately predicts friction factors across various roughness levels and Reynolds numbers.

Provides physically consistent and interpretable correlations for turbulent pipe flow.

Validated up to Reynolds number of approximately 10^7.

Abstract

Friction losses in rough pipes are often predicted using semi-empirical correlations, such as the Colebrook-White equation (Colebrook,1939), which do not fully replicate Nikuradse's rough-pipe experiments (1950). This study derives scaling relations for the viscous and turbulent contributions to the streamwise pressure drop through an order-of-magnitude analysis of the Reynolds-averaged Navier-Stokes equations and the kinetic-energy transport equations. These relations impose constraints on the local sensitivity of the pressure drop to factors such as mean velocity, roughness, viscosity, and density through exponent envelopes and serve as a physical prior for symbolic regression. By combining Nikuradse's rough-pipe and smooth-pipe data of Zagarola and Smits (1998), we aim to derive compact correlations for the friction factor that fit experimental data while adhering to the derived constraints. A modified genetic programming engine (GPTIPS2) optimizes model structure and evaluates it based on fitness, complexity, and constraint violation. This method yields interpretable expressions that accurately reproduce friction factors across various roughness levels and Reynolds numbers, validated up to $Re \sim 10^7$.