Advancing Turbulent Flow Modeling with Neural Networks

By Soham NandiReviewed by Susha Cheriyedath, M.Sc.Aug 12 2024

In an article published in the journal Machine Learning and Technology, researchers investigated using physics-informed neural networks (PINNs) to analyze turbulent flow in composite porous-fluid systems. They introduced a novel PINN model that integrated supervised learning with penalization by Reynolds-averaged Navier-Stokes (RANS) equations.

The research evaluated how internal training data impacted PINN prediction accuracy for flow features like leakage and recirculation. Results showed that including internal training data improved accuracy and reduced prediction errors, particularly at porous-fluid interfaces.

Background

Turbulence modeling in composite porous-fluid systems—where a fluid-saturated porous medium interfaces with a clear fluid—presents significant challenges due to sharp velocity and pressure gradients. Traditional methods, such as Reynolds stress models and turbulent eddy viscosity models, struggle to accurately simulate flow at the pore scale, and experimental approaches are limited by inaccuracies and high costs.

Previous work has demonstrated the potential of PINNs in solving laminar flow problems, but their application to turbulent flows with complex physics is underexplored. This study addressed these gaps by employing PINNs to solve RANS equations in composite porous-fluid systems for the first time. It investigated intricate flow phenomena, such as leakage and wake recirculation, and assessed the impact of internal training data on model accuracy. The research advanced the field by demonstrating that PINNs could effectively capture complex flow dynamics, improving predictive accuracy in these challenging systems. 

Computational Approach and Methodology

The researchers detailed the computational methodology employed in utilizing PINNs for modeling turbulent flow in composite porous-fluid systems. Unlike purely data-driven methods, PINNs integrated governing equations directly into their loss functions, enhancing prediction accuracy by leveraging physical laws. The authors used two-dimensional (2D) steady-state incompressible RANS equations to guide the PINN's architecture.

The PINN employed automatic differentiation to compute flow variable derivatives and included residuals of the governing equations as part of its loss function. The architecture involved eight hidden layers with 20 nodes each, using a Tanh activation function and Adam optimizer with a learning rate of 0.0001. The training was conducted with a batch size of 1000 and 20,000 epochs while weighting coefficients balanced the loss terms.

Numerical simulations were configured to generate training datasets for solid and porous blocks, using a pore-scale RANS turbulence model in open field operation and manipulation (OpenFOAM) v2012. The training data covered flow fields for blocks with zero porosity and those with 36.38% porosity. A Reynolds number of 5600 was chosen to capture significant flow features, with the semi-implicit method for pressure-linked equations FOAM (SimpleFoam) solver generating the reference and training datasets. This setup ensures that the PINN model is trained effectively to predict complex turbulent flows in these systems.

Results and Discussion

The researchers evaluated the PINN model's performance on solid and porous block cases. The PINN model, which utilized both boundary and internal data, provided more accurate predictions for flow variables, particularly improving the capture of second-order statistics like Reynolds stress.

In comparing the scenarios where different types of training data were used, it was found that the scenario using only boundary data (scenario 0) had higher error measurements compared to the scenarios that included additional data (scenarios 1 and 2). Among these, scenario 1, which incorporated interface data, demonstrated superior accuracy over scenario 2.

However, the difference in accuracy between scenario 1 and scenario 2 in individual subdomains was minimal. Specifically, scenario 1 was more effective in predicting flow characteristics and channeling effects, which scenario 2 failed to capture. In certain zones, including zones I to III, the presence of interface data had little impact on accuracy, while in zone IV, scenario 1 showed improved performance.

Regarding computational costs, training the PINN model for porous blocks was more time-consuming (7.3 hours) compared to RANS simulations (2.2 hours). Despite the longer training time, PINN predictions were faster (3.2 seconds each). The use of internal training data significantly enhanced the training efficiency by accelerating convergence, though initial training durations were longer than those required for RANS simulations.

In essence, incorporating interface data improved prediction accuracy for specific zones and flow effects, while internal data enhanced the efficiency of PINN training, despite the longer time required compared to traditional RANS simulations.

Conclusion

In conclusion, the researchers demonstrated the effectiveness of PINNs in predicting turbulent flows within composite porous-fluid systems. By integrating internal training data, the PINN model significantly improved accuracy in capturing complex flow features like leakage and recirculation. The authors highlighted that incorporating such data enhanced the model’s predictive performance and reduced errors, particularly for second-order statistics.

Despite longer initial training times compared to traditional methods, PINNs offered faster prediction capabilities and more precise simulations. Future work should focus on refining PINN models to predict turbulent flows with minimal training data and exploring advanced techniques for more accurate flow field reconstruction.