# RANS Turbulence Model Development using CFD-Driven Machine Learning

## TL;DR

This paper introduces a CFD-driven machine learning framework for developing RANS turbulence models, enabling more accurate flow predictions by integrating CFD results directly into the training process, especially useful with limited data.

## Contribution

The novel CFD-driven training method evaluates model fitness through integrated RANS calculations, improving turbulence model accuracy and applicability with limited training data.

## Key findings

- Significantly improved wake mixing predictions in turbomachinery cases.
- The trained model introduces extra diffusion, enhancing CFD accuracy.
- Explicit model equations facilitate analysis and understanding.

## Abstract

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.