Stochastic-probabilistic efficiency enhanced dispersion modeling of turbulent polydispersed sprays

Abstract

A stochastic-probabilistic, efficiency enhanced dispersion (SPEED) model is developed for the prediction of turbulent two-phase flows. The SPEED model computes both the mean and variance of droplet positions at each Lagrangian integral time step. The mean position is determined with an improved conventional stochastic model, whereas the variance is determined by a newly derived Lagrangian equation with a Lagrangian autocorrelation function. A memoryless Markovian chain is used to determine the autocorrelation function. The distribution of a physical droplet in space is determined with a prescribed probability density function. The efficiency of the SPEED model is that a minimal number of droplet trajectories are required for Lagrangian trajectory computations during which a large amount of smooth noise-free solution can be attained. The developed SPEED model is first validated against a benchmark test where the measured mean-squared dispersion width is available. Then the results include the prediction of a polydispersed turbulent spray with detailed experunental measurements. Numerical results of the SPEED model, using only a total number of 6 x 10 2 droplet trajectories, are compared with those of a conventional stochastic discrete delta-function model using a total number of 2.1 x 10 4 trajectories, and with a previous stochastic dispersion-width transport model. It is found that the SPEED model is numerically more efficient than the dispersion-width transport model and needs much fewer number of droplet trajectories than the standard model.