Annual Research Briefs, 1992

This report contains the 1992 annual progress reports of the Research Fellows and students of the Center for Turbulence Research. Considerable effort was focused on the large eddy simulation technique for computing turbulent flows. This increased activity has been inspired by the recent predictive successes of the dynamic subgrid scale modeling procedure which was introduced during the 1990 Summer Program. Several Research Fellows and students are presently engaged in both the development of subgrid scale models and their applications to complex flows. The first group of papers in this report contain the findings of these studies. They are followed by reports grouped in the general areas of modeling, turbulence physics, and turbulent reacting flows. The last contribution in this report outlines the progress made on the development of the CTR post-processing facility

Meshless Direct Numerical Simulation of Turbulent Incompressible Flows

A meshless direct pressure-velocity coupling procedure is presented to perform Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent incompressible flows in regular and irregular geometries. The proposed method is a combination of several efficient techniques found in different Computational Fluid Dynamic (CFD) procedures and it is a major improvement of the algorithm published in 2007 by this author. This new procedure has very low numerical diffusion and some preliminary calculations with 2D steady state flows show that viscous effects become negligible faster that ever predicted numerically. The fundamental idea of this proposal lays on several important inconsistencies found in three of the most popular techniques used in CFD, segregated procedures, streamline-vorticity formulation for 2D viscous flows and the fractional-step method, very popular in DNS/LES. The inconsistencies found become important in elliptic flows and they might lead to some wrong solutions if coarse grids are used. In all methods studied, the mathematical basement was found to be correct in most cases, but inconsistencies were found when writing the boundary conditions. In all methods analyzed, it was found that it is basically impossible to satisfy the exact set of boundary conditions and all formulations use a reduced set, valid for parabolic flows only. For example, for segregated methods, boundary condition of normal derivative for pressure zero is valid only in parabolic flows. Additionally, the complete proposal for mass balance correction is right exclusively for parabolic flows. In the streamline-vorticity formulation, the boundary conditions normally used for the streamline function, violates the no-slip condition for viscous flow. Finally, in the fractional-step method, the boundary condition for pseudo-velocity implies a zero normal derivative for pressure in the wall (correct in parabolic flows only) and, when the flows reaches steady state, the procedure does not guarantee mass balance. The proposed procedure is validated in two cases of 2D flow in steady state, backward-facing step and lid-driven cavity. Comparisons are performed with experiments and excellent agreement was obtained in the solutions that were free from numerical instabilities. A study on grid usage is done. It was found that if the discretized equations are written in terms of a local Reynolds number, a strong criterion can be developed to determine, in advance, the grid requirements for any fluid flow calculation. The 2D-DNS on parallel plates is presented to study the basic features present in the simulation of any turbulent flow. Calculations were performed on a short geometry, using a uniform and very fine grid to avoid any numerical instability. Inflow conditions were white noise and high frequency oscillations. Results suggest that, if no numerical instability is present, inflow conditions alone are not enough to sustain permanently the turbulent regime. Finally, the 2D-DNS on a backward-facing step is studied. Expansion ratios of 1.14 and 1.40 are used and calculations are performed in the transitional regime. Inflow conditions were white noise and high frequency oscillations. In general, good agreement is found on most variables when comparing with experimental data

Turbulence: Numerical Analysis, Modelling and Simulation

The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is available for calibration, the importance of a sound mathematical foundation that addresses the needs of practical computing increases. This Special Issue is directed at this crossroads of rigorous numerical analysis, the physics of turbulence and the practical needs of turbulent flow simulations. It seeks papers providing a broad understanding of the status of the problem considered and open problems that comprise further steps

Transport et production dans les écoulements turbulents de paroi à des nombres de Reynolds modérés

The direct numerical simulations of a fully turbulent channel flow are investigated to study the large scales effects on the flow quantities such as the Reynolds stresses and vorticity transport processes. Large computational domains are used so as to cover the largest scales of the flow. The simulations are performed in a wide range of Reynolds numbers (Reτ=180, 395, 590 and 1100) going from weakly to moderately high Reynolds number turbulent flows. The invariance of the wall-normal vorticity fluctuations scaled in wall variables in the inner layer versus the Reynolds number is analyzed using a spectral analysis. The vorticity transport equations are investigated in detail, presumably for the first time. The transport mechanism of the Reynolds shear stresses are subsequently analyzed in the inner layer and the overlapping zone. In the wall layer, different terms of the Reynolds stresses transport expressed in inner scales depend on the Reynolds number. This scaling failure lead us to focus on the statistics of the production when the streamwise or normal velocity fluctuations cross a given level, through the conditional Palm statistics. The main aim is to identify those amplitudes of the fluctuations that contribute more to the production and those which are responsible for the production Reynolds dependence.L'approche de simulation numérique directe est utilisée pour la simulation d'un écoulement en canal pleinement turbulent afin d'étudier l'influence des grandes échelles de l'écoulement ainsi que la dynamique du transport des contraintes de Reynolds et de la vorticité. Les simulations sont réalisées sur un domaine de calcul de grande taille afin de pouvoir capturer l'intégralité des grandes structures de l'écoulement, et portent sur une gamme relativement étendue de nombres de Reynolds (Reτ =180, 395, 590 et 1100) allant des écoulements faiblement turbulents à des écoulements modérément turbulents. L'invariance remarquable des fluctuations de vorticité normale est expliquée à travers une analyse spectrale de la vorticité. L'étude des différents termes du transport de l'intensité turbulente de la vorticité révèle par ailleurs que le pic de production de la vorticité transverse est situé à proximité immédiate de la paroi et pourrait ouvrir la voie à des stratégies de réduction de la traînée basées sur la réduction de la vorticité transverse. Le transport des contraintes de Reynolds dans la couche interne et dans la couche de recouvrement est également étudié. A proximité des parois, la dépendance des termes de transport avec le nombre de Reynolds dans les échelles internes montre que ces dernières ne suffisent pas à caractériser la dynamique des contraintes de Reynolds dans cette zone. Cette insuffisance des échelles internes nous a amenés à nous intéresser plus particulièrement au processus de production à travers les statistiques de la production conditionnées par le passage par niveau des fluctuations de la vitesse normale ou longitudinale. Cette étude nous a permis d'identifier les fluctuations qui contribuent le plus à la production et celles qui sont à l'origine de la dépendance avec le nombre de Reynolds