Velocity Reconstruction in Pool Fires using Physics-Informed Machine Learning

Abstract

In many flow experiments it is complex to measure all flow states of interest, leading to the need for a method to retrieve unmeasured flow states from measured ones. This work focuses on Hidden Fluid Mechanics (HFM), which refers to a Physics-Informed Neural Network (PINN) able to incorporate the Navier-Stokes (NS) equations into the loss function of the Neural Network (NN) for the purpose of reconstructing flow fields.

As HFM is a recent framework which has not been applied to many flows yet, it is unknown if HFM is capable of reconstructing flow fields in chemically reacting flows where strong gradients are present. For this reason, the performance of HFM is investigated here using data sets from Direct Numerical Simulations (DNS) of an axisymmetric pool fire in cylindrical coordinates, for which the velocity fields are purposely removed and attempted to be recovered from the density, pressure and temperature fields. The implementation has been performed making use of TensorFlow in Python, where both steady and unsteady pool fires are considered.

Pool fires are simplified representations of real-life accidental and forest fires, illustrating the importance of their research. If the critical pool diameter is not exceeded, a steady flow occurs. However, if surpassed, the flow exhibits an unsteady flickering behaviour known as puffing.

The main finding is that both in the steady and unsteady pool fires, the PINN is capable of reconstructing the most prominent features of the velocity fields when density, pressure and temperature are provided, even though strong gradients are usually underestimated by the PINN, causing wrongly predicted extreme values. This implies that the method can be used mainly for qualitative purposes, as the exact values are not always captured. It is found that the accuracy is lower in the unsteady flow compared to the steady flow. Furthermore, the axial velocity field is generally reconstructed to a higher accuracy than the radial velocity field.

It is found that the accuracy decreases when increasing the spacing between provided data points, from which implications on possible applications to real-life measured data can be drawn, as not all measurement equipment might reach the required spatial resolution. Investigating the effect of adding artificial white noise to mimic measurement noise, it has been found that the method is robust to noise, but less so for the steady case than for the unsteady flow case. Lastly, the effect of removing the density and/or pressure from the provided flow states is investigated, where it is found to have a detrimental effect on the accuracy except if physical assumptions are given to the PINN (i.e. the ideal gas law). Using the right assumptions, it is found that for the steady case providing only the temperature field is deemed enough to reach a relatively similar accuracy compared to not removing any flow states, whereas for the unsteady case at least the temperature and pressure fields need to be provided. The current research shows the capabilities but also the limitations of the HFM framework in case of steady and unsteady flow with chemical reactions and strong gradients, creating opportunities for further research of HFM in other flow cases and for potentially applying the framework to real experimental data of fires or other flows.