  Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the
dominant tool for engineering design and analysis applications involving
turbulent flows, standard RANS models are known to be unreliable in many flows
of engineering relevance, including flows with separation, strong pressure
gradients or mean flow curvature. With increasing amounts of 3-dimensional
experimental data and high fidelity simulation data from Large Eddy Simulation
(LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling
has become a promising approach to increase the predictive capability of RANS
simulations. Recently, a data-driven turbulence modeling approach via machine
learning has been proposed to predict the Reynolds stress anisotropy of a given
flow based on high fidelity data from closely related flows. In this work, the
closeness of different flows is investigated to assess the prediction
confidence a priori. Specifically, the Mahalanobis distance and the kernel
density estimation (KDE) technique are used as metrics to quantify the distance
between flow data sets in feature space. The flow over periodic hills at
Re=10595 is used as the test set and seven flows with different configurations
are individually used as training set. The results show that the prediction
error of the Reynolds stress anisotropy is positively correlated with
Mahalanobis distance and KDE distance, demonstrating that both extrapolation
metrics can be used to estimate the prediction confidence a priori. A
quantitative comparison using correlation coefficients shows that the
Mahalanobis distance is less accurate in estimating the prediction confidence
than KDE distance. The extrapolation metrics introduced in this work and the
corresponding analysis provide an approach to aid in the choice of the data
source and to assess the prediction confidence for data-driven turbulence
modeling.
