High Turbulent heat transfert approached with physics enhanced machine learning – THERMAL

Turbulent thermal flows in convection cells are inhomogeneous and very complex to predict and to understand due to the variety and the strong coupling of the physical mechanisms at play. These mechanisms change depending on the regime, the flow location and the scale of interest. Thermal boundary layers form near the surfaces, but being buoyancy-unstable, small scale structures called thermal plumes arise from this instability. Their collective motion produce a large scale circulation (LSC), which may suggest that the kinetic energy distributes from smaller to larger scales. Nevertheless, because the LSC itself shears the boundary layers, it may either contribute to turbulent fluctuations (further destabilizing the boundary layer) or impede the rise of the plumes. Heat is transported in the fluid by the thermal plumes, under both their own buoyancy and the advection by the LSC, but also by the turbulent fluctuations. Finally, turbulence in the bulk is nearly homogeneous and may get the kinetic energy to cascade from the large scale to the smaller dissipative scales (and produce heat locally).
When the turbulence level is increased, either with higher forcing, or by the introduction of perturbations at the cell surfaces, the flow may experience a spectacular change to a regime of higher heat transfer efficiency. However, there exists a lot of discrepancy between experiments, with huge difference in the observed fluxes. Understanding these conflicting results is critical for areas where such high forcings are expected (e.g. cooling of nuclear power plant, geophysical flows), because the lack of understanding of the physical mechanisms impedes the ability to properly predict realistic heat fluxes.
Our goal is to sort among these various mechanisms in order to disentangle the contribution of turbulence and that of the interacting thermal plumes. In order to do so, we wish to use diagnostic tools involving local information such as temperature and velocity correlations, to assess the role of turbulence, and plumes (i.e. statistics about their numbers, their size, their intensity). Such knowledge is key to propose useful physical models because the flow is highly inhomogeneous, and 3D information is pivotal. For example, do the plumes rise evenly over the plate, or only near the edges? How does the spatial distribution of rising plumes change when the forcing is increased?
Despite progress made by careful comparison of experimental and numerical simulations studies, key differences remain in the amount and nature of the information provided by each community, making conjoint understanding very difficult. For instance, experimental data is incomplete, but well converged and can reach high forcings. Numerical simulations are fully resolved in space, but reach lower turbulence level and for shorter durations. The tremendous potential capabilities of recent physics-informed deep learning (DL) techniques will help in seamlessly integrating the benefits of each approach into a new modeling and comprehension of turbulent physics. In this project, we will take advantage of both perceptrons or convolutional neural networks frameworks enhanced with physical constraints, in order to mitigate the risks and to speed up and robustify the training phase of the models. More specifically, thanks to DL, we will be able to infer missing data from experiments, and alleviate the cost of expensive numerical simulations by reducing the storage cost. When trained on either experimental or numerical data, DL models will grant fast access to the local temperature and velocity coupling in time and space, to the local instantaneous heat transfer, and to the local temperature field. This will enable to explore the nature of the scalar in highly turbulent thermal convection.