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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