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

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.