Experimental Determination of the Turbulent Prandtl Number

Abstract

The description of heat transfer processes in physical and chemical gas dynamics within the framework of RANS (Reynolds-averaged Navier–Stokes) turbulence models involves determination of the turbulent thermal conductivity coefficient. Historically, the turbulence models make it possible to find the turbulent viscosity distribution, from which the turbulent thermal conductivity is determined using the turbulent Prandtl number (TPN). However, the TPN can depend on the problem parameters and vary within the flow domain. The applicability of the models proposed for calculating spatial variations in the TPN is restricted to specific flows. For example, the Kays–Crawford model describes the growth of the TPN in the boundary layer near a rigid wall. To validate and improve these models, it is necessary to use experimental verification. In the present study, an experiment carried out for the impact jet of heated gas is considered. The average temperature field, measured using the background oriented schlieren (BOS), contains information on the turbulent thermal conductivity coefficient. The experiment also includes velocity measurements at individual points using a hot-wire anemometer. The physics-informed neural network (PINN) combines the experimental data with equations for reconstructing the fields of hydrodynamic quantities, including the turbulent viscosity and the turbulent thermal conductivity. It is shown that the standard condition of constant turbulent Prandtl number can be used at the center of the jet, but the TPN decreases toward the periphery. The obtained TPN distributions are compared with available studies, both experimental and numerical, using the large eddy simulation (LES) method. The proposed method expands the capabilities for studying various flows in which the temperature field or the concentration field (to determine the turbulent Schmidt number) can be measured, including flows of chemically reacting media.