Bayesian optimization of traveling wave-like wall deformation for friction drag reduction in turbulent channel flow

We attempt to optimize the control parameters of traveling wave-like wall deformation for turbulent friction drag reduction using the Bayesian optimization. The Bayesian optimization is an optimization method based on stochastic processes, and it is good at finding the parameter values to minimize (or maximize) an expensive cost function or a blackbox function. The parameter value to be tested in the next iteration step is chosen based on the acquisition function that accounts for both the exploration term searching in high uncertainty regions and the exploitation term searching in the regions of high possibility over the current best observations. First, we investigate the effectiveness of the Bayesian optimization using a two-parameter test function with known optimum value. As a result, the Bayesian optimization is shown to successfully work. Next, we apply the Bayesian optimization to the control parameters of traveling wave-like wall deformation for friction drag reduction in a turbulent channel flow at the friction Reynolds number of Re_τ = 180. While the wavenumber (k⁺) is fixed, the velocity amplitude (v⁺) and the phasespeed (c⁺) are chosen as the variable to optimize. As a result of the Bayesian optimization, although the bulk-mean velocity in the optimized case varies periodically, we achieved the maximum drag reduction rate of 60.5% when (v⁺, c⁺) = (10.0, 42), which is higher than that in the previous study (Nabae et al., 2020), i.e., 36.1%. In the optimized case, by repeating laminarization of flow field and re-transition to turbulent flow due to the inflection instability, the bulk-mean velocity increases and decreases periodically.