PTW_2007

UNIVERSITY OF KENTUCKY
PTW 2007
Dr. Alexander Jittu, PEng,
Technical Consultant
Lexington, October 15th and 16th, 2007

- 2 -PTW2007-University of Kentucky, October 15 &16 2007
Title
UNDERSTANDING THE PHYSICS BEHIND THE MECHANISMS OF:
ATOMIZATION,ELECTROSTATIC CHARGING AND PAINT PARTICLES
TRANSPORT WITH FOCUS ON THE INDIRECT CHARGED BELL

Electrostatic Bell-Atomization, Charge, Transport
1- HV Power Supply
2- Bell
3- HV Ring
4- Bell Cup
5- Grounded Part
6- Electrostatic Field
1
2
43 5
6

Atomization
1- Fluid Tip
2- Bell Cup
3- Bell Type (serrated or NON serrated)
4- Bell Disk ( distributor disk)
5- Fluid Flow
6- Shaping Air
7- Bell Cup Angle
8- Bell Angular Velocity

Atomization
Mechanics- Dynamics defines:
V = (π * D * n) / 60 - (Bell Cup Edge Speed)
Where:
π = 3.14
D = Cup Diameter (mm)
n = Rotational Speed (Rev./Min or RPM)
V = Cup Edge Speed (mm/sec)
F= (m * v²)/r - (Centrifugal Force )
Where:
m = Mass (kg)
V = Cup Edge Speed (m/sec)
r = Radius (r) = ½(D)
F = Force in (N) Newton

Atomization
The characteristics of the liquid feed or pumping system and the flow
characteristics in the lines whether steady laminar, or turbulent need to be
known
Flow characteristics in the atomizer also need to be known over the full range
of flow conditions since the level of flow turbulence, possible flow separation,
cavitation, for example, could change as the atomization conditions change
The liquid sheet at the exit of the atomizer needs to be characterized in terms
of the sheet angle, thickness, stability, and relative velocity between the sheet
and the surrounding flow
Breakup length and the nature of the breakup, whether random or periodic
will have a significant impact on the spray quality
At the exit, higher liquid velocities will increase induced airflow and induced
airflow will assist in sheet breakup
Airflow will also serve to redistribute the drops by size class due to the flow of
air inward toward the core of the spray cone, and as the region of recirculating
flow increases

Electrostatic Charging
Poisson equation :
0
2
ε
ρ
−=∇ V (1.1) VE −∇= (1.2) )( EpEeqFe += (1.3)
pk
pk
u
dt
dx = qEuuuDgm
dt
d
m pkggk
upk
k k +−+= ))((
pkgpDgkkgk uuCrrD −+= )(Re6 2
2
1
ρππµ (1.7)
)Re
6
11(
Re
24 3
2
d
d
DC += for Red <1000
CD = 0.424 for Red >1000 (1.8)
(1.10)
2
2/31
AT
TAg
+
=µ
µg = gas viscosity
A1&A2 = ct.
T = gas temperature
q/m is the charge to mass ratio
E
m
q
m
uuuDg
dt
du
k
k
pkggkpk
++= − ))((
(1.4)
(1.5)
kkk rm ρπ 3
3
4= (1.6)

Mechanism of Paint Particles Transport
Spray drops will deform from spherical due to the spray formation process, the
drop collisions, and to the interaction with the aerodynamic forces
Increased velocity in the liquid sheet will result in large drops with higher
velocity
These drops can lead to more severe collisions and breakup, secondary
breakup, and a general redistribution of the spray size distribution due to
relative relaxation rates in drop momentum
The rate of drop coalescence may also be related to the relative velocities of
the drops and the density number
Spray interaction with the induced and ambient flow field is also known to
affect drop size distributions

Based on author’s experience, correlation of drop size with pressure at one plane in
the spray pattern may be useful, but does not provide much insight to the mechanisms
that lead to that outcome
Clearly, measuring only the drop size distribution in a plane will not provide sufficient
information to describe the spray process
Drop size, velocity, air mean velocity and turbulence, drop number density, drop flux,
and angles of trajectory are the basic information needed for a reasonable description
of the spray
Typically, there are a high population of small drops, and a very low population of large
drops in the distribution
This characteristic affects the sampling statistics, since a very large number of small
drops must be measured if a statistically representative sample of the large drops in
the distribution is to be obtained

For the reliable determination of the linear mean diameter D10 and the droplet
density number, accurate measurements and counting of the small drops,
which have the largest population, are required.
To obtain reliable measurements of the Sauter mean diameter or volumes
mean diameter, it is necessary to obtain a good statistical representation of
the largest drops in the distribution and to measure their size accurately.
Because the large drops have a much lower rate of occurrence than the small
drops, the large drops are often measured without adequate statistical
representation.
For proper characterization of the spray, it is important to make detailed
measurements over the volume occupied by the spray. These measurements
must be made at sufficient spatial and temporal resolution in order to fully
describe the dynamics and the development of the spray as it enters into the
flow field of interest.

As the spray develops with downstream distance from the atomizer, the spray
size distribution will evolve due to the relative velocities of the difference size
drops and interaction with the turbulent flow field.
Preferential deceleration of different drop size classes will cause local
changes in the predicted mean size distribution, depending on the
measurement technique used, and on the local droplet number density.
The drop sizes may change due to secondary breakup resulting from Weber
number affects, droplet stripping due to aerodynamic shear forces and drop
collisions and coalescence.

Probability of Drop CollisionProbability of Drop Collision
ΦΦΦΦi iw = 2d + D10
Target Drop
i i iL = v t
di

There are five distinct collision regimes:
- Bouncing
- Coalescence with minor deformation
- Coalescence with substantial deformation
- Coalescence followed by separation for near head-on collisions and
- Coalescence followed by separation for off-center collisions

The probability for drop collisions can be estimated from knowing the drop’s
speed relative to other target drops and the drop number density. For example,
the swept volume, Vi, for a drop of diameter di to collide with a drop of mean
diameter D10, moving at a mean relative velocity, vi, is:
Where D10 is the linear or length mean diameter. This approximation indicates
the dependence of the swept volume on the relative velocity and the possible
interaction time, ti. Assuming a spatial Poisson distribution of particles of number
density, N particles per cc, then:
Where Pci is the probability of a collision of the particle of diameter di with
another particle of mean diameter D10 within time ti, based on the Poisson
probability of another particle existing in the swept volume, Vi.
ikV
ici ekVP −
=
),,( ,10 iii tvDdfVi =

The figure shows the process schematically. One drop is assumed to be
moving with an average relative velocity, vi compared to the surrounding
drops. This drop sweeps out a volume equal to its cross sectional area, plus
the average cross sectional area of another drop, which it might encounter.
The linear mean drop size, D10, was used for the target drop. The probability
of collision is equal to the probability of another drop being present in the
swept volume
This is a somewhat imperfect approximation and should be refined however, it
does provide an estimate to determine whether collisions and coalescence
could be responsible for the changes in the drop size distribution
These values are characteristic of spray densities denoted as being between
dense and dilute (mean drop separation of 10 drop diameters)
Particle collisions may lead to coalescence, breakup, or a rebound depending
on several parameters, including the Weber and Ohnesorge numbers

If a prediction model is done for the particle size and distribution on an axial
cross section of the spray pattern, the axial cross-sectional mass fraction will
be :
Mfi (x) is the mass fraction corresponding to droplet diameters in the range of
“i” along the laser beam of infinitesimally small cross section positioned at x,
m (x) and “x+ “and “x-“ are the upper and lower limits of the spray boundary
along the major axis
The m fi (x) values are determined directly from the Malvern measurements
The m (x) terms are given by:
m (x) = ρ V (x)
∑ ∫
=
=
+
−
+
−
∫
= kj
j
x
x
j
x
x
i
i
xdxmxmf
dxxmxmf
Mf
1
)()()(
)()(

Mechanism of Atomization & Paint Particles Transport
Due to the fact that the particle size plays a very important role in achieving
the paint quality requirements and color matching I developed a mathematical
function for a general bell (vortex or soft pattern):
F (y (i)) = k+y1 +y2 +y3 +y4+y5 +y6 +y7 +y8+y9 +y10 +y11 +y12+y13 +y14
+y15
Where:
F (y (i)) = particle size
k = constant
y i,I = 1 to15 are functions of :
- Atomization Energy
- Fluid Flow
- HV
- Measurement Location

Mechanism of Atomization/Paint Particles Transport
.

The drop size distributions at different locations in the flow will change due to
the response of the difference size classes to the aerodynamics
Φ = ρN (di)[π (di) ³/6]V(di) /t where:
Φ - Paint Particles Flux
ρ - density of fluid (paint)
N (di) - number of drops of diameter di per unit volume
V (di) - velocity of drops of diameter di
If evaporation = 0 than FLUX = constant
If changes in V (di), than we will have changes in N (di)

Conclusions
Film built, film built uniformity, coefficient of variance, transfer efficiency, color
match, DOI, gloss and spray pattern profile are very important tasks for all the
suppliers and customers
Due to the increasing demands for greater coating efficiency and finish quality,
liquid and powder equipment suppliers continue advancing the technology by
offering to the market new equipment features
Unfortunately, a single solution to all challenges that would work in every type
of application has yet to be found
The knowledge of the basics of electrostatic technology and fluid dynamics
(including atomization and paint particles transport) will help finishers to take
the correct decisions about which features of equipment will bring them closer
to meeting their optimization goals

End
Thank you for your kind attention and please ask questions

PTW_2007

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