A Meta-Model to Predict the Drag Coefficient of a Particle Translating in Viscoelastic Fluids: A Machine Learning Approach.

Célio Fernandes,Ana I. Roriz,Salah A. Faroughi

doi:10.3390/polym14030430

Célio Fernandes, Ana I. Roriz + Show 1 more

Open Access

https://doi.org/10.3390/polym14030430

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Journal: Polymers	Publication Date: Jan 21, 2022
Citations: 13	License type: CC BY 4.0

Affiliation: Texas State University, University of Minho

Abstract

This study presents a framework based on Machine Learning (ML) models to predict the drag coefficient of a spherical particle translating in viscoelastic fluids. For the purpose of training and testing the ML models, two datasets were generated using direct numerical simulations (DNSs) for the viscoelastic unbounded flow of Oldroyd-B (OB-set containing 12,120 data points) and Giesekus (GI-set containing 4950 data points) fluids past a spherical particle. The kinematic input features were selected to be Reynolds number, , Weissenberg number, , polymeric retardation ratio, , and shear thinning mobility parameter, . The ML models, specifically Random Forest (RF), Deep Neural Network (DNN) and Extreme Gradient Boosting (XGBoost), were all trained, validated, and tested, and their best architecture was obtained using a 10-Fold cross-validation method. All the ML models presented remarkable accuracy on these datasets; however the XGBoost model resulted in the highest and the lowest root mean square error (RMSE) and mean absolute percentage error (MAPE) measures. Additionally, a blind dataset was generated using DNSs, where the input feature coverage was outside the scope of the training set or interpolated within the training sets. The ML models were tested against this blind dataset, to further assess their generalization capability. The DNN model achieved the highest and the lowest RMSE and MAPE measures when inferred on this blind dataset. Finally, we developed a meta-model using stacking technique to ensemble RF, XGBoost and DNN models and output a prediction based on the individual learner’s predictions and a DNN meta-regressor. The meta-model consistently outperformed the individual models on all datasets.

Highlights

The flow of particle-laden complex fluids has been the centerpiece of many welldocumented experimental, theoretical, and numerical approaches [1,2,3,4]
Direct numerical simulations (DNSs), following the methodology implemented by Faroughi et al [6] on the physical system elaborated in Section 2, were employed to generate the training dataset for the viscoelastic drag coefficient correction of a sphere translating in Oldroyd-B fluids (α = 0)
We showed that different Machine Learning (ML) models perform better on different sections of the data when inferred against blind datasets

Summary

Introduction

The flow of particle-laden complex fluids has been the centerpiece of many welldocumented experimental, theoretical, and numerical approaches [1,2,3,4]. The ML or DL algorithms can be trained and integrated with traditional physics-based forward modeling to predict the flow dynamics under different conditions at a reduced computational cost The latter is done by learning the solutions for ordinary and partial differential equations governing the system [13] or learning the closure laws for the pertinent physics, e.g., lift and drag forces, turbulence models, etc. We propose to take the first step and complement the Eulerian-Lagrangian multi-phase approach with a data-driven drag model for the translation of a spherical particle in constant viscosity and shear thinning matrix-based viscoelastic fluids.

Underlying Physics

Machine Learning Regression Algorithms

Results and Discussion

Data Collection and Analysis for Oldroyd-B Fluids

Data Collection and Analysis for Giesekus Fluids

ML Models Development

Hyperparameter Tuning

Training and Testing

Models Performance on Blind Datasets

Model Ensembling

Conclusions