Reynolds-Averaged Turbulence Modeling Using Type I and Type II Machine Learning Frameworks with Deep Learning

TL;DR

This paper explores the use of deep learning within Type I and Type II machine learning frameworks to improve turbulence modeling in RANS equations, introducing a flow features coverage mapping method to assess data sufficiency.

Contribution

It introduces a flow features coverage mapping method and compares Type I and Type II ML frameworks for turbulence modeling, highlighting their capabilities and limitations.

Findings

Type I ML errors accumulate without sufficient transient data.

DL can identify flow transients from sampled data.

Type II ML requires close initial conditions for effective unsteady flow simulation.

Abstract

Deep learning (DL)-based Reynolds stress with its capability to leverage values of large data can be used to close Reynolds-averaged Navier-Stoke (RANS) equations. Type I and Type II machine learning (ML) frameworks are studied to investigate data and flow feature requirements while training DL-based Reynolds stress. The paper presents a method, flow features coverage mapping (FFCM), to quantify the physics coverage of DL-based closures that can be used to examine the sufficiency of training data points as well as input flow features for data-driven turbulence models. Three case studies are formulated to demonstrate the properties of Type I and Type II ML. The first case indicates that errors of RANS equations with DL-based Reynolds stress by Type I ML are accumulated along with the simulation time when training data do not sufficiently cover transient details. The second case uses Type I ML to show that DL can figure out time history of flow transients from data sampled at various times. The case study also shows that the necessary and sufficient flow features of DL-based closures are first-order spatial derivatives of velocity fields. The last case demonstrates the limitation of Type II ML for unsteady flow simulation. Type II ML requires initial conditions to be sufficiently close to reference data. Then reference data can be used to improve RANS simulation.