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Rigorous assessment of the uncertainty is crucial to the utility of numericalsimulation of Turbulent flow. The Turbulent flows are often stationary andergodic, after some initial transient time. Therefore, the time averaged of aquantity (velocity, TKE (turbulence kinetic energy), total drag, etc) convergesto a constant as the averaging interval increases. This infinite-time-averagestatistic is of particular interest in many problems, such as aerodynamic shapeoptimization. Since taking an average over the infinite time horizon is notpossible, some finite-time approximation of the infinite-time-average statisticof interest is used in practice. However, because of the initial transientbehavior of the turbulence simulations, this estimate is biased. This issue issolved by deleting the initial transient part of the simulation. The otherimportant issue is the error of this approximation decreases slowly, like thereciprocal of the square roots of the averaging time. In this paper, we developa framework to first automatically deleted the transient part of a turbulencesimulation, then, quantify precisely the uncertainty of such afinite-time-average approximation of an infinite-time-average statistic of astationary and ergodic process.

Uncertainty Quantification of the time averaging of a Statistics Computed from Numerical Simulation of Turbulent Flow