Mathematical Problems in Engineering

Volume 2007 (2007), Article ID 24627, 28 pages

doi:10.1155/2007/24627

## Dynamical Simulation and Statistical Analysis of Velocity Fluctuations of a Turbulent Flow behind a Cube

# T. F. Oliveira, R. B. Miserda, and F. R. Cunha

Fluid Mechanics of Complex Flows Lab, Department of Mechanical Engineering, University of Brasília, Campus Universitário Darcy Ribeiro, Brasília 70910-900, DF, Brazil

Received 12 September 2006; Revised 18 January 2007; Accepted 6 March 2007

Academic Editor: José Manoel Balthazar

Copyright © 2007 T. F. Oliveira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A statistical approach for the treatment of turbulence data generated by computer simulations is presented. A model for compressible flows at large Reynolds numbers and low Mach numbers is used for simulating a backward-facing step airflow. A scaling analysis has justified the commonly used assumption that the internal energy transport due to turbulent velocity fluctuations and the work done by the pressure field are the only relevant mechanisms needed to model subgrid-scale flows. From the numerical simulations, the temporal series of velocities are collected for ten different positions in the flow domain, and are statistically treated. The statistical approach is based on probability averages of the flow quantities evaluated over several realizations of the simulated flow. We look at how long of a time average is necessary to obtain well-converged statistical results. For this end, we evaluate the mean-square difference between the time average and an ensemble average as the measure of convergence. This is an interesting question since the validity of the ergodic hypothesis is implicitly assumed in every turbulent flow simulation and its analysis. The ergodicity deviations from the numerical simulations are compared with theoretical predictions given by scaling arguments. A very good agreement is observed. Results for velocity fluctuations, normalized autocorrelation functions, power spectra, probability density distributions, as well as skewness and flatness coefficients are also presented.