  This paper presents a novel CFD-driven machine learning framework to develop
Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an
extension of the gene expression programming method (Weatheritt and Sandberg,
2016), but crucially the fitness of candidate models is now evaluated by
running RANS calculations in an integrated way, rather than using an algebraic
function. Unlike other data-driven methods that fit the Reynolds stresses of
trained models to high-fidelity data, the cost function for the CFD-driven
training can be defined based on any flow feature from the CFD results. This
extends the applicability of the method especially when the training data is
limited. Furthermore, the resulting model, which is the one providing the most
accurate CFD results at the end of the training, inherently shows good
performance in RANS calculations. To demonstrate the potential of this new
method, the CFD-driven machine learning approach is applied to model
development for wake mixing in turbomachines. A new model is trained based on a
high-pressure turbine case and then tested for three additional cases, all
representative of modern turbine nozzles. Despite the geometric configurations
and operating conditions being different among the cases, the predicted wake
mixing profiles are significantly improved in all of these a posteriori tests.
Moreover, the model equation is explicitly given and available for analysis,
thus it could be deduced that the enhanced wake prediction is predominantly due
to the extra diffusion introduced by the CFD-driven model.
