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This article discusses the principles and applications of Particle Image Velocimetry (PIV) as a non-intrusive, whole-field flow measurement technique. PIV offers quantitative velocity data and enables the visualization of instantaneous flow fields, providing insights into fluid dynamics. The text showcases historical developments, optical configurations, interrogation methods, and evaluation criteria associated with PIV. Various concepts, such as image density, spatial correlation, and tracer patterns, are explained in detail to highlight PIV's effectiveness in capturing flow behavior.
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What Is PIV ? J. Westerweel Delft University of Technology The Netherlands
Conventional methods (HWA, LDV) Single-point measurement Traversing of flow domain Time consuming Only turbulence statistics Particle image velocimetry Whole-field method Non-intrusive (seeding) Instantaneous flow field Why use imaging? After: A.K. Prasad, Lect. Notes short-course on PIV, JMBC 1997
Coherent structures in a TBL Kim, H.T., Kline, S.J. & Reynolds, W.C. J. Fluid Mech. 50 (1971) 133-160. Smith, C.R. (1984) “A synthesized model of the near-wall behaviour in turbulent boundary layers.” In: Proc. 8th Symp. on Turbulence (eds. G.K. Patterson & J.L. Zakin) University of Missouri (Rolla).
PIV Interrogation analysis RP RD+ RD- RC+RF Double-exposure image Spatial correlation Interrogation region
PIV result Turbulent pipe flow Re = 5300 100×85 vectors “Hairpin” vortex
Historical development • Quantitative velocity data from particle streak photographs (1930) • Laser speckle velocimetry; Young’s fringes analysis (Dudderar & Simpkins 1977) • Particle image velocimetry • Interrogation by means of spatial correlation • ‘Digital’ PIV • Stereoscopic PIV; holographic PIV
Definitions for PIV • Source density: • Image density: Ctracer concentration [m-3] Dz0light-sheet thickness [m] M0image magnification [-] dtparticle-image diameter [m] DIinterrogation-spot diameter [m]
Particle trajectory Fluid pathline After: Adrian, Adv. Turb. Res. (1995) 1-19 The displacement field • The fluid motion is represented as a displacement field
Velocity from tracer motion Prob(detect) ~ image density (NI) Low image density NI << 1 Particle tracking velocimetry High image density NI >> 1 Particle image velocimetry
Evaluation at high image density Spatial correlation:
Linear system theory Input Output Impulse response Test signals: • Deterministic • Stochastic
The tracer pattern • G(X,t) represents the random ‘pattern’ of tracer particles that moves with the flow Input Output Impulse response:
The tracer ensemble • Consider the ensemble of all realizations of G(X,t) for given u(X,t) Physical space Phase space Liouville’s theorem (continuity): t= PDF oft Homogeneous seeding: Incompressible flow:
Inherent assumptions • Tracer particles follow the fluid motion • Tracer particles are distributed homogeneously • Uniform displacement within interrogation region
“Ingredients” FLOW sampling seeding quantization Pixelization illumination enhancement Acquisition imaging selection registration correlation Interrogation estimation RESULT analysis validation