Design of the wavy wall in a partially heated channel using CFD simulations and human-assisted Bayesian optimization

2025/09/04 by Kamiński, Piotr, Wawrzak, Karol, Li, Yiqing +2
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.2509.04030

Abstract

This study explores heated wavy wall shape design in channel flow using machine learning, aiming to minimize temperature variation (σ_T) while limiting pressure loss (Δp). A cost function J defined as a product of σ_T and Δp balances these competing objectives. Optimization is performed via Bayesian optimization (BO) coupled with Reynolds-Averaged Navier-Stokes (RANS) computations in an active learning loop involving up to 1000 subsequent iterations. Two shaping strategies are considered: a sinusoidal-type function defined by four parameters (two waviness amplitudes, wave count, and tilt), and a higher-dimensional approach employing a Piecewise Cubic Hermite Interpolation Polynomial (PCHIP) with 19 control points. Results show the sinusoidal design reduces σ_T over 60-fold but increases Δp fourfold, while the PCHIP shape offers only a 15-fold σ_T reduction but with a twofold Δp increase. Flow characteristics such as turbulent kinetic energy, pressure, temperature, and Nusselt number are examined for both optimal and suboptimal shapes along the Pareto front. The insights gained motivated a human-aided refinement of the BO result, leading to a further 17.7% reduction in J. This was achieved by replacing small-amplitude waviness periods with flat segments, which additionally significantly facilitates manufacturability.

Citations

• Deep reinforcement learning for turbulent drag reduction in channel flows
• Machine Learning for Fluid Mechanics
• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• Two-equation eddy-viscosity turbulence models for engineering applications

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