Study of the thermal field of turbulent channel flows via Direct Numerical Simulations

Abstract

The main goal of this thesis is the study of heat transfer in turbulent channels to obtain a better knowledge about the phenomenon of turbulence. For this, a study has been carried out from the point of view of computational fluid mechanics, specifically, the technique of direct numerical simulations (DNS) has been used. This type of simulation is very computationally expensive, but the results they provide are highly accurate and faithful to reality, as long as the discretization schemes are correct. The main idea of the simulations conducted has been to expand the current state of the art, regarding the two main parameters that characterize the flow: the friction Reynolds number, Re τ and the Prandtl number, P r . Two flow configurations have been used: Poiseuille flow and Couette flow, the former being the main focus of the study. Regarding the temperature field, a mixed boundary condition has been used and it has been considered as a passive scalar.Thus, the simulated friction Reynolds numbers for a Poisuille flow have been Re τ = 500, 1000 and 2000, for Prandtl numbers ranging from 0.007 (molten metals) up to 10 (water) , passing through 0.71 which is the most used value since this is the Prandtl number of the air. Also, a simulation has been performed with Re τ = 5000 and P r = 0.71, which is the thermal DNS with the highest friction Reynolds number up to date. A first distinction of heat flux can be made for Prandtl numbers less or greater than P r = 0.3. When the Prandtl number is less than 0.3, the conductive region extends above the logarithmic layer, and even penetrates to the central region of the channel, forming a practically laminar thermal field, for the lowest Prandtl numbers. For thermal fields where the logarithmic layer begins to emerge, the value of the von Kármán thermal constant, κ t tends to a constant value of approximately κ t = 0.44 as the Reynolds number tends to infinity, and that value is independent of the Prandtl number. Regarding the variance of the temperature, θ + and the turbulent heat flow in the direction of the current, u + θ + , the collapse in the outer region is determined by the friction Péclet number, P e τ = Re τ P r, instead of the Reynolds or Prandtl number. Furthermore, it has been observed that for the highest Prandtl numbers, the maximum value of the variance of the temperature is constant. This has a significant impact on the scaling of the θ + budget terms. Specifically, the dissipation and viscous diffusion, which scale with much greater precision near the wall for high Prandtl numbers. This is an important result, since many models of the energy equation are based on these budget equations, so obtaining good scaling for different parameters means greater reliability of the models. Finally, it should be noted that new correlations have been presented for the Nusselt number, N u, valid for the ranges of Re τ and P r studied.Finally, with regard to Poiseuille flow simulations, the isothermal case has been studied with Re τ = 10000, which is also the largest DNS o...

Optimization of the Creation of a Training Set for the Calibration of a Model Reproducing the Vibration Behavior of an Overhead Line Conductor

“…But before going into detail, let's quickly come back to this concept called neural networks [21][22][23] A neural network extracts nonlinear patterns from data. it is therefore a set of interconnected formal neurons allowing the resolution of complex problems such as pattern recognition or natural language processing, thanks to the adjustment of the weighting coefficients in a learning phase [24][25][26][27][28].A neural network is inspired by the functioning of biological neurons and takes shape in a computer in the form of an algorithm. The neural network can modify itself according to the results of its actions, which allows learning and problem solving without an algorithm, therefore without classical programming [29][30][31].…”