Transported Joint Probability Density Function Modeling of Turbulent Dilute Spray Flows

Abstract

A transported joint probability density function (PDF) model for turbulent spray flows is presented, where a one-point one-time statistical description of the gas-phase mixture fraction and the gas velocity is used. This approach requires the closure of the molecular mixing, which is achieved through use of the extended interaction-by-exchange-with-the-mean (IEM) model and a simplified Langevin model for the closure of the gas velocity both of which are extended through additional terms accounting for spray evaporation. These equations require the solution of the turbulent time scales and the mean pressure field through a Eulerian description. The numerical approach includes a Lagrangian Monte Carlo method for the solution of modeled joint PDF equation with a Eulerian finite-volume algorithm to determine the turbulent time scale and the mean pressure field. For the dispersed liquid phase, Lagrangian equations are used to describe the droplet heating, evaporation, and motion in the framework of a discrete droplet model. The convective droplet evaporation model is employed, and the infinite conductivity model with consideration of non-equilibrium effects based on the Langmuir-Knudsen law is used. The droplet turbulent dispersion is modeled with two different Lagrangian stochastic models. The resulting spray evolution equations are solved by a Lagrangian discrete droplet method using the point source approximation for a dilute spray. The numerical results are compared with experimental data of Gounder et al. [1], where the experimental set B of the acetone spray flows SP2 and SP6 are simulated. Comparison of numerical and experimental results includes droplet size, liquid volume flux as well as the mean and fluctuating velocities. Generally, good agreement is achieved, although the radial droplet dispersion is somewhat under-predicted by the computations. The droplet fluctuating velocities show sensitivity to the different dispersion models.