Uncertainty quantification for time varying quantities in turbulent flows

Sammanfattning: Quantification of uncertainty in results is crucial in both experiments and simulations of turbulence, yet this practice is notably underutilized. This thesis project delves into statistical tools within the framework of uncertainty quantification to systematically quantify uncertainties that occur in the time varying quantities of turbulence. Two main categories of variance estimators for quantifying time averaging uncertainties in turbulent flow time series are examined in detail – the batch-means based methods and autoregressive model-based methods. The batch size is critical to estimation of uncertainty by the batch methods. We discuss reasons for biased estimates and provide guidance on the selection of batch sizes for the non-overlapping, overlapping and batch means-batch correlations estimators, to obtain consistent estimates of uncertainty when dealing with turbulence time samples. The autoregressive model (ARM)-based estimator was found to be more efficient than the batch methods, in terms of computational efficiency and sample requirements. A novel insight into the operating principle of the ARM, enabled fast quantification of uncertainty with few samples and with batch means series. The extension of univariate autoregressive processes to model entire 2D space-time fields of turbulence, through vector autoregression has been discussed and its potential as a turbulent inflow boundary condition has been illustrated. A crucial flow case that questioned the reliability of Computational Fluid Dynamics (CFD), namely flow through Food and Drug Administration benchmark nozzle device was also simulated in this doctoral thesis project, with a well-defined turbulent inflow boundary condition. Novel insights on the flow physics due to geometrical effects were obtained through statistical analysis, anisotropy invariant maps and proper orthogonal decomposition. These insights provide answers to many open questions in this domain. This work provides analyses and methods to increase the reliability of simulations, expanding the scope of CFD to applications where safety and precision are paramount.