Prediction of equivalent sand-grain size and identification of drag-relevant scales of roughness – a data-driven approach

Abstract

Despite decades of research, a universal method for prediction of roughness-induced skin friction in a turbulent flow over an arbitrary rough surface is still elusive. The purpose of the present work is to examine two possibilities; first, predicting equivalent sand-grain roughness size $k_s$ based on the roughness height probability density function and power spectrum (PS) leveraging machine learning as a regression tool; and second, extracting information about relevance of different roughness scales to skin-friction drag by interpreting the output of the trained data-driven model. The model is an ensemble neural network (ENN) consisting of 50 deep neural networks. The data for the training of the model are obtained from direct numerical simulations (DNS) of turbulent flow in plane channels over 85 irregular multi-scale roughness samples at friction Reynolds number $Re_\tau =800$ . The 85 roughness samples are selected from a repository of 4200 samples, covering a wide parameter space, through an active learning (AL) framework. The selection is made in several iterations, based on the informativeness of samples in the repository, quantified by the variance of ENN predictions. This AL framework aims to maximize the generalizability of the predictions with a certain amount of data. This is examined using three different testing data sets with different types of roughness, including 21 surfaces from the literature. The model yields overall mean error 5 %–10 % on different testing data sets. Subsequently, a data interpretation technique, known as layer-wise relevance propagation, is applied to measure the contributions of different roughness wavelengths to the predicted $k_s$ . High-pass filtering is then applied to the roughness PS to exclude the wavenumbers identified as drag-irrelevant. The filtered rough surfaces are investigated using DNS, and it is demonstrated that despite significant impact of filtering on the roughness topographical appearance and statistics, the skin-friction coefficient of the original roughness is preserved successfully.

Asessment of roughness characterization methods for data-driven predictions

“…and power spectrum (PS), respectively. In total, 63 quantities (30+30+3) are transferred to the NN PS model [11].…”

“…The k s values of the roughness samples are obtained through DNS. All the roughness samples in the database yield k + s > 50, which are regarded to be located in the fully rough regime [9,11]. Furthermore, a testing database T inter is constructed, consisting of 20 roughness samples that undergo the identical procedure for generation and evaluation.…”

“…This is particularly useful in scenarios where training samples are scarce. More recently, an MLP model developed by Yang et al [11], employs roughness p.d.f. and PS as model inputs, which can be considered as a higher order statistical representation of roughness.…”

“…This method relies on the random prescription of p.d.f. and PS to emulate a wide range of naturally occurring irregular roughness [11]. To fully realize the potential of each model, Bayesian optimization (BO) is applied to optimize the hyperparameters of each model.…”