Study of the thermal field of turbulent channel flows via direct numerical simulations

Resumen

The main objective of this thesis is the study of thermal turbulent channel flows to obtain a greater 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. The main idea of the simulations conducted has been to expand the current state of the art, in relation to the two main parameters that characterize the flow: the friction Reynolds number, Re¿, and the Prandtl number, Pr. 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¿ = 500, 1000 and 2000, for Prandtl numbers that vary from 0.007 (molten metals) to 10 (water), passing through 0.71 which is the value more used because this is the Prandtl number of the air. In addition, a simulation has been carried out with Re¿ = 5000 and Pr = 0.71, which is the thermal DNS with the highest friction Reynolds number to date. It should be noted that for the highest Prandtl numbers, it has been observed that the maximum value of the variance of the temperature is constant. This has an important benefit in scaling near the wall of the dissipation and viscous diffusion budget terms of the ¿'+. Finally, with regard to Poiseuille flow simulations, the isothermal case has been studied with Re¿ = 10000, which is the highest DNS of a turbulent channel flow, obtaining for the first time in a DNS a perfectly developed logarithmic layer in the velocity field. A theoretical study, based on Lie symmetries, has been carried out in parallel to the simulations. The main objective has been the generation of scald laws, based on first principles, of the field of velocity, temperature and high order moments of both fields. The result is that for sufficiently high Reynolds and Péclet numbers, these fields scale as defect laws of power functions of the distance to the wall in the center of the channel. In the same way, a scaling of the speed in the logarithmic layer has been obtained for the case of Re¿ = 10000, obtaining the classic logarithmic function for the average velocity and a potential function for the moments of higher orders. The scaling laws have been validated with the data obtained in the DNS, obtaining excellent precision. Finally, a set of Couette flow simulations have been carried out with the Prandtl number of air, Pr = 0.71, and Reynolds friction numbers of Re¿ = 180, 250 and 500. The main objective was the study of coherent structures that are formed in these Couette flows. Specifically, it has been seen that turbulent intensities depend on the number and size of the structures. For this reason, a minimum width of the computational domain of 6¿h is required for the statistics to be independent. A last series of simulations has been carried out considering stratified flow. The objective was to study whether Couette structures persist in this type of flow. Thus, for a Re¿ = 500 and the Prandtl number of air, Pr = 0.71, the values of the friction Richardson number have been varied according to, Ri¿ = 0.5, 1.65 and 2.90, for each simulation. For the two cases with the highest friction Richardson number, the Couette flow structures weaken to the point of being almost non-existent. The main statistics of the simulations are available in the research group's database, which is open to the scientific community and can be accessed from the following link http://personales.upv.es/serhocal/