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

Oliveira, T. F.; Miserda, R. B.; Cunha, F. R.

doi:https://doi.org/10.1155/2007/24627

Mathematical Problems in Engineering

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Dynamics and Control in Sciences and Engineering

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Research Article | Open Access

Volume 2007 | Article ID 024627 | https://doi.org/10.1155/2007/24627

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

T. F. Oliveira,¹R. B. Miserda,¹and F. R. Cunha¹

Academic Editor: José Manoel Balthazar

Received12 Sept 2006

Revised18 Jan 2007

Accepted06 Mar 2007

Published21 May 2007

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.

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Copyright

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.

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