Statistical analysis and accuracy of PIV data

Abstract

In an assessment of PIV measurement accuracy under practical experimental circumstances, grid-generated turbulence in its early decay (xiM =13.6-15.2, ReA z 25) has been studied. Since a realtime processor was used, it was practical to acquire a statistically significant sample size of 3000 vector maps so that accurate turbulence statistics could be calculated. Results include moments of velocity components and spatial structures in terms of auto-correlations, turbulence scales and spectra. Data fall within limits of standard error estimates. This study demonstrates the need for large sample sizes, particularly for higher order statistics. Displacement vector [L] dpiXe! Pitch of pixels on CCD chip [L] d,truct Diameter of smallest resolved velocity-structure [L] f Longitudinal correlation function g Lateral correlation function g' Theoretical correlation function G k ID power density spectrum [VIP] k Turbulent kinetic energy [VIP] k' Harmonic number M Mesh spacing [mm] N Number of samples N, Number of vector maps N« Side of interrogation area [pixels] N, Number of vectors in x-direction N, Number of vectors in y-direction ReM Reynolds number based on mesh spacing, MUiv ReA Reynolds number based on the Taylor microscale, A,<J Iv s(U) Standard error on U [LIT] s(uu) Standard error on uu [VIP] S Object.image scale factor Time between pulses [T] u Turbulent component of velocity in x [LIT] U Mean velocity inx [LIT] V Velocity vector [LIT] v Turbulent component of velocity in y [LIT] 206 v Y E T) tc A Statistical Analysis and Accuracy ofPN DataMean velocityin y [LIT] Windowfunction Coordinatein directionof flow [L] Coordinate, lateral [L] Disspationof turbulentkinetic energy [VIP] Kolmogorov scale [L] Wave number [V], /(= 2nklb: Taylor microscale [L] Integral length scale of componentu, in Xl direction [L] Kinematic viscosity [VII] Rms velocitycomponentin X [LIT]

Particle image velocimetry measurement of indoor airflow field: A review of the technologies and applications

“…The uncertainty in the ensemble average PIV data describing turbulent flows is mainly dependent on the sample size and the order of statistics. Ullum et al [98] investigated the effect of sample size on the accuracy of time-averaged PIV data for a single point in a grid-generated turbulence in its early decay. It was concluded that 100 vector maps for a component of mean velocity were required for an uncertainties of averages at a given point to be within 1% for a flow of 10% turbulence intensity.…”

Active flow control over a backward-facing step using plasma actuation

“…Uzol and Camci 46 and Ullum et al 47 Six random locations in the field of view, indicated in Figure 7, were selected as samples and their stream-wise velocity component compared.…”

Dual-plane PIV investigation of acoustically excited jets in a swirl nozzle

“…Originally used to obtain two-dimensional velocity fields, developments over the last decade have led to the successful realization of three-dimensional velocity fields (Lynch and Thurow, 2011). Statistical properties of the mean and turbulent components can be estimated from ensemble averaging (Ullum et al, 1998). However, accuracy of the statistical analysis depends on the sample size over which the ensemble averages are formed (Uzol and Camci, 2001).…”