Otto Laporte Lecture: Fluid Dynamics Prize Talk: Simple Models for Turbulent Flows

We focus on the modeling of two turbulent flows: dispersion from a line source in grid turbulence; and, a lifted non-premixed turbulent jet flame. Stochastic Lagrangian models and PDF methods are described, and are shown to model these flows satisfactorily. For the line source, a Lagrangian approach is taken, with the Langevin equation modeling the velocity following a fluid particle, and with a simple relaxation model for the particle temperature. Comparison with experimental data shows that the resulting model describes accurately the dispersion from single and multiple line sources. These simple stochastic Lagrangian models are then applied to the much more challenging case of a lifted non-premixed jet flame. The stochastic Lagrangian models form the basis for a particle/mesh numerical method for solving a modeled transport equation for the Eulerian joint probability density function (PDF) of velocity and composition. The PDF calculations are in excellent agreement with the experimental data, and exhibit the observed extreme sensitivity of the flame to the temperature of the co-flow. The PDF model calculations presented clearly demonstrate that simple models can be very useful, even though aspects of their behavior may be inaccurate or incomplete. The shortcomings of the Langevin equation are examined, and more advanced models (designed to overcome some of these shortcomings) are described. These include models for fluid-particle acceleration, including the effects of intermittency; models accounting for mean shear, which are correct in the rapid- distortion limit; and models designed for use in conjunction with large-eddy simulations (LES).