Robust optimisation of the pressure-gradient distribution in turbulent boundary layers

Abstract: In order to better characterise pressure-gradient turbulent boundary layers (TBLs), and to advance the theory of these flows, typically canonical conditions are required. This is achieved by keeping the Clauser pressure-gradient parameter, β, constant along the streamwise direction, see for instance Mellor and Gibson [9] and Bobke et al. [1] It is, however, very challenging to obtain the correct boundary conditions when performing numerical simulations or wind-tunnel experiments so that a give mean pressure gradient is kept constant along the edge of a turbulent boundary layer. This study tackles this issue through numerically optimising the shape of the upper boundary of a 2D channel flow to obtain a target constant-β distribution at the TBL over the bottom wall. The shape of the upper boundary of the channel is parameterised and the parameters are optimised through Bayesian optimisation based on Gaussian process regressiong (GPR). To simulate the turbulent flow within the channel at a low computational cost, steady RANS (Reynolds-Averaged Navier-Stokes) simulations are conducted, which show a good agreement with DNS (Direct Numerical Simulation) and LES (Large-Eddy Simulation) benchmark data. The simulations are performed using the open-source finite-volume-based software OpenFoam. Through the optimisation process, constant-β distributions are achieved after few iterations for several target values of β, corrensponding to ZPG (zero-pressure-gradient) and APG (adverse-pressure-gradient) TBLs. The results of constant-β distributions show very good agreement with reference data. The impact of parameterisation of the upper wall on the performance of the optimisation and the accuracy of the results is also studied. This study can be a very powerful tool to set constant-β distributions in experiments.