Temperature assimilation for convective flows by convolutional neural networks

Abstract

The transport of heat in convective flows plays an important role in nature and in many technical applications. Precise predictions of such convective flows can be made in Direct Numerical Simulations (DNS), which require a substantial amount computing time and storage space. Thus, DNSs can only be used for predictions over comparatively short time periods and for flow problems, which can usually also be investigated in the laboratory due to their dimensions. A canonical laboratory experiment that is well suited for basic investigations of turbulent, thermal convection flows and the development of models is the so-called turbulent Rayleigh-B ́enard convection, which occurs as a result of buoyancy forces in cells heated from below and cooled from above with adiabatic side walls. Compared to the DNS, measurements can capture the velocity field over long periods of time. However, in order to be able to determine the heat transport in convective flows, additional spatial temperature measurements are typically carried out. Respective combined measurements are also very laborious and therefore only applied scarcely. In order to provide an estimated temperature distribution based on precise velocity field measurements, the assimilation of the temperature field from the velocity vector field is pursued. So far, the approach of extracting temperature fields based on the conservation laws has been explored [1]. At the same time, machine learning provides promising tools for regression tasks such as theone at hand [2]