Statistical Vortex-Generator-Jet Model for Turbulent Flow Separation Control

摘要

This contribution describes the development and evaluation of a new statistical modeling approach for active vortex generator jets. Previous experiments from the Technische Universitat Braunschweig and their subsequent evaluation by the present authors showed that the induced flowfield can be reasonably well represented by two-dimensional Lamb-Oseen vortices. Based on that, an analytical expression for the Lamb-Oseen-vortex-model maximum circulation Γ_(max) was derived in terms of the freestream velocity U_∞ the jet-to-freestream velocity ratio λ, and the jet skew angle β, as well as the actuator diameter Φ_(vgj)- Based on the parameterized results, universal values for the Lamb-Oseen-vortex-model parameters at the actuator position were determined for the development of the statistical vortex-generator-jet model. The idea behind the statistical modeling approach is that the vortices are represented by their spanwise-averaged velocity correlations, or vortex stresses, that are added to the turbulence stresses in a Reynolds stress turbulence model. The spanwise-averaged vortex stresses are derived by computing the spanwise-averaged second-order statistics of the vortex flowfield. These vortex-generator-jet model results were compared to the spanwise-averaged vortex stresses from experiments and from fully resolved computational fluid dynamics investigations, and reasonable qualitative as well as quantitative agreement was found.