Distribution of probability of the vapor phase occurrence in a cavitating flow based on the concentration of PIV tracers in liquid

Abstract

We present a new method of extracting information on average vapor distribution in a cavitating flow based on statistical processing of PIV data for a liquid phase. For this, vectors on instantaneous velocity fields are analyzed over the entire statistical ensemble of instantaneous realizations considering their status: valid-vectors that passed validation procedures, outliers-the ones with incorrect values, out-of-flow-those calculated on insufficient number of seeding particles (tracers), masked-they correspond to unilluminated flow regions. The suggested approach is based on the two basic principles: absence of the tracers in the vapor phase and statistical independence of the successive measurements. The case study is performed for a cavitating 2D symmetric hydrofoil under unsteady cloud cavitation conditions with regular shedding of large-scale cloud cavities. Comparing statistical distribution laws in different flow regions makes it possible to recognize the stable sheet cavity and its pulsating part and determine the location of cloud cavity detachments. This approach for PIV data analysis is shown to be an effective tool to characterize time-averaged distribution of the dispersed phase in cavitating flow based merely on velocity measurements for the liquid phase. Using it allows one to substantially reduce consumption of computational resources and save time when investigating the structure of cavitating flows, limiting to standard PIV measurements in liquid. This method can be also applied to analyze the structure of other types of dispersed two-phase flows.

Cavitation suppression and transformation of turbulence structure in the cross flow around a circular cylinder: Surface morphology and wettability effects

“…5 a and 5b), which leads us to the conclusion that the ensemble volume of 1000 realizations is sufficient to calculate the first four moments of turbulent fluctuations, provided that the procedure of statistical filtration [28] is employed. The representativeness of the sample volume to evaluate the time-averaged vapor content using the method of quantification of the probability of dispersed phase occurrence [52] was verified in a similar fashion (see Fig. 6 ).…”

“…As visible in Fig. 7 , each of the distributions obeys an exponential law, which implies all events in the ensembles are statistically independent [52] .

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Fig. 6 Spatial distributions of the time-averaged vapor fraction over and in the wake of the smooth (reference) cylinder in R-II ( Table 2 ) obtained by the evaluation method of vapor phase occurrence developed by Pervunin et al [52] for different sample volumes N = (a) 1000 and (b) 5000 realizations. The black diagonal crosses in image (a) display the sampling points where distributions of velocity fluctuations are further analyzed.

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“…In this article, we experimentally investigate the effect of different types of surface roughness (regular large-scale and irregular small-scale) on the development of cavitation and the structure of turbulence in the wake of a round cylinder in two characteristic regimes through high-speed visualization of vapor cavities and Particle Image Velocimetry (PIV) measurements of velocity fields. Using the procedure of statistical filtration of velocity vectors [28] and the method of vapor phase detection [52] , we obtain spatial distributions of the first four statistical moments of the flow velocity and the time-averaged vapor concentration. The layout of this paper is as follows.…”