8/18/2019 Behaviour of Particle in PIV

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Behaviour of particle in PIVEquation of unsteady motion of a particle suspended in a turbulent

ow without interactions from other particles at time t is given by Basset,

1888 as

Relative motion of a suspended particle

Where,

p is particle velocity,

f is uid velocity,

dp is particle diameter,

!p is density of particle," is #inematic viscosity of uid,

$ is relative velocity of particle wrt uid,

%f  is density of uid&

  'he (rst term in the equation represent viscous force, given by

sto#es law& )econd term is acceleration force, third term represents the

force due to pressure gradient and (nal term is the *Basset history

integral+ which represents the resistance caused by the unsteadiness in

the ow (eld&

  n this equation e-ternal forces on particle such asgravitational, centrifugal, electrostatic forces are neglected but in

practical cases such as swirler the centrifugal and gravitational forces

should be considered for better results& )ome e-ceptions can be made by

aligning the .$ setup parallel to gravitational (eld to directly include

gravitational e/ects without comple-ing the computations&

  When the uid velocity f  is constant 0laminar ow and if the

density of particle is much greater than the density of uid, then velocity

of particle, p generally follows e-ponential law2

p 3 f 41 5 e-p05t6ts7

Rela-ation time, ts 3 !p  dp9618"

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References:

• :elling ;, 'racer particles and seeding for particle image

velocimetry, :eas& )ci& 'echnol& 8 011@& .rinted in the

&• Crant , .article image velocimetry2 a review&

• :ar#us Ra/el, et al&, .article image velocimetry2 a practical guide,

)pringer, 1