Estimation of time-resolved velocity fields with modal analysis

Abstract

Turbulence constitutes one of the still unsolved and most challenging phenomena ever covered by Fluid Mechanics. However, the state of the art methods do not provide the necessary commitment between spatial and temporal resolutions that are required for a complete comprehension of turbulent ows. This fact has boosted the development of methods relying in statistics and that are able to combine the benefits from several approaches in order to overcome such spatiotemporal limitations. Among the multiple proposals, the dynamic estimation of fluid properties based on Extended Proper Orthogonal Decomposition modes postulates as one of the most promising approaches. This method is able to estimate time-resolved turbulent velocity fields by extending the temporal correlation between time-resolved singlepoint velocity measurements and non-time-resolved field measurements obtained at synchronized times to the \out-of-sample" time instants. This study is based on the work performed by Discetti et al. who proposed a standard truncation criterion for the filtration of the measurement signals based on the aforementioned random distribution of noise. For this purpose a parametric study is performed in order to evaluate the already proposed standard truncation threshold and two possible variants under the effects of di erent factors. Channel ow data generated using a DNS is used for the validation of the approach due to its large wealth of motion scales. The average estimation error is used as the figure of merit in the assessment of the filtration procedure performance and estimation quality.