Thermal fluids field reconstruction with Bayesian inference for forced convection system

Abstract

In many nuclear applications, there is a need to extract as much information as possible within the constraints of instrumenting a process, structure, component, or system. We applied Bayesian inference to reconstruct variables of interest in thermal-fluid problems: distribution of heat flux boundary condition from the limited number of point-wise temperature measurements at the wall in a forced convection problem. We show that it is possible to efficiently reconstruct a steady-state heat flux boundary using a physics-based mapping with an appropriate prior distribution of the boundary condition. The inferencing problem includes the source of uncertainty: noisy temperature measurement and inadequately characterized physics model (wall function and turbulent diffusivity) while using the Reynolds-averaged Navier-Stokes (RANS) turbulence model. We compared the result against flow experiments on single-phase turbulent flow in a rectangular channel visualized with infrared thermometry. The advanced high-resolution diagnostic provides temperature distribution and heat flux profile at the heat transfer interface. The measurements are used to validate the proposed reconstruction methodology. When put in suitable locations, the reconstruction gives reasonable accuracy with a small number of sensors. The established Bayesian inference method will be applied to more extensive flow conditions in the near future to understand its usefulness and applicability. The method presented here can potentially support the advancement of nuclear digital twin technology, where we expect new modes of operation and decision-making processes with less human intervention, remote monitoring, and, ultimately, autonomous operation.