Flow temporal reconstruction from non time-resolved data part II: practical implementation, methodology validation, and applications

This paper proposes a method to sort experimental snapshots of a periodic flow using information from the first three POD coefficients. Even in presence of turbulence, phase-average flow fields are reconstructed with this novel technique. The main objective is to identify and track traveling coherent structures in these pseudo periodic flows. This provides a tool for shedding light on flow dynamics and allows for dynamical contents comparison, instead of using mean statistics or traditional point-based correlation techniques. To evaluate the performance of the technique, apart from a laminar test on the relative strength of the POD modes, four additional tests have been performed. In the first of these tests, time-resolved PIV measurements of a turbulent flow with an externally forced main frequency allows to compare real phase-locked average data with reconstructed phase obtained using the technique proposed in the paper. The reconstruction technique is then applied to a set of non-forced, non time-resolved Stereo PIV measurements in an atmospheric burner, under combustion conditions. Besides checking that the reconstruction on different planes matches, there is no indication of the magnitude of the error for the proposed technique. In order to obtain some data regarding this aspect, two additional tests are performed on simulated non-externally forced laminar flows with the addition of a digital filter resembling turbulence (Klein et al. in J Comput Phys 186:652–665, 2003). With this information, the limitation of the technique applicability to periodic flows including turbulence or secondary frequency features is further discussed on the basis of the relative strength of the Proper Orthogonal Decomposition (POD) modes. The discussion offered indicates coherence between the reconstructed results and those obtained in the simulations. In addition, it allows defining a threshold parameter that indicates when the proposed technique is suitable or not. For those researchers interested on the background and possible generalizations of the technique, part I of this work (Legrand et al. in Exp Fluid (submitted in 2010) 2011) offers the mathematic fundamentals of the general space–time reconstruction technique using POD coefficients. Noteworthy, the involved computational time is relatively small: all the reconstructions have been performed in the order of minutes.