6171135 nozzle design influence on the supersonic particle deposition process
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Nozzle Design I nf luence onNozzle Design I nf luence on
the Supersonic Part iclethe Supersonic Part icle
Deposit ion ProcessDeposit ion Process
by
Victor Champagne, Dennis Helfritch, Phillip Leyman,
Robert Lempicki and Scott Grendahl
U.S. Army Research Laboratory
Aberdeen Proving Ground, MD
presented at the
Cold Spray 2004 Conference
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PurposePurpose
• Nozzle geometry
• Accelerating gas characteristics
• Particle characteristics
To improve cold spray deposition
through the investigation of:
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OutlineOutline
1. Calculate the gas flow and temperature in
the nozzle2. Calculate particle velocity and
temperature through the nozzle
3. Calculate penetration depth and
particle/substrate mixing
4. Calculate the deposition efficiency
5. Compare with experiment
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ApplyApply GasdynamicGasdynamic Analysis t oAnalysis t o
Simple Nozzle GeometrySimple Nozzle Geometry
r tr e
L
• The gas obeys the perfect gas law
• There is no friction impeding the gas flow
• The gas flow is adiabatic• No shocks or discontinuities
• Flow is one-dimensional
• Particles do not influence gas conditions
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Part icle Mot ion/ Deposit ionPart icle Mot ion/ Deposit ion
• Using the gas flow already calculated, employ
solid rocket nozzle particle drag and heat transfer relationships* to calculate particle conditions.
• Particles are assumed to be spherical.
• Particle initial temperature = 293 degree K.
• Use empirical relationships between particle
velocity and particle/substrate materialcharacteristics to calculate deposition effects.
*D. Carlson and R. Hoglund: “Particle Drag and Heat Transfer inRocket Nozzles,” AIAA Journal, 1964, 2 (11), pp. 1980 -1984.
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Condit ions of Calculat ionsCondit ions of Calculat ions
Unless otherwise stated, all calculations are carried
out for the following conditions:
• Area ratio = 4, Length = 0.1m
• Nitrogen accelerating gas
• 2.76 MPa, 673 degree K stagnation conditions
• Copper particles
• Mass mean diameter 20 microns
• Log-normal distribution, SD = 1.5
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Typical Calculat ionTypical Calculat ion
0
200
400
600
800
1000
0.00 0.02 0.04 0.06 0.08 0.10
Nozzle Axis, meters
V e l o c i t y & T e m p e
r a t u r e ,
m / s & d e g r e e K
particle velocity particle temp nozzle throat
gas velocity gas temp
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Part icle Exit Condit ions as a Funct ionPart icle Exit Condit ions as a Funct ion
of Diamet er and Accelerat ing Gasof Diamet er and Accelerat ing Gas
0
500
1000
1500
2000
2500
0 20 40 60 80 100
Particle Diameter, microns
P a r t i c l e V
e l o c i t y , m
/ s
0
100
200
300
400
500
P a r t i c l e T
e m p ,
d e g .
K
Velocity, He Velocity, N2 Temperature, He Temperature, N2
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400
450
500
550
600
650
700
5 10 15 20 25 30
Nozzle Length, cm
P
a r t i c l e E x i t
V e l o c i t y , m / s
A/A* = 12.25, calculated
A/A* = 4.0, calculated
A/A* = 12.25, measured
A/A* = 4.0, measured
Effect of Nozzle Lengt hEffect of Nozzle Lengt h
on Part icle Velocit yon Part icle Velocit y
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Deposit ion Calculat ionsDeposit ion Calculat ions
Part icle/ Subst ratePart icle/ Subst rate
( )B
E10x4Volume
5−
=
Empirical micrometeorite penetration into spacecraft*
Substituting 1/2mV2 for energy, with volume = 2r πr 2
( )
5.0
4 B10x5.7V ⎥⎦⎤⎢
⎣⎡ ⎟⎟
⎠ ⎞⎜⎜
⎝ ⎛ ρ=
*R.J. Eichelberger and J.W. Gehring: “Effects of Meteoroid Impacts on
Space Vehicles,” ARS J., 1963, 32 (10), p. 1583.
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Copper Deposit ed on AluminumCopper Deposit ed on Aluminum
Particle/substrate equation predicts a velocity of 500
m/s needed for full penetration. Photograph below
shows this condition.
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Deposit ion Calculat ionsDeposit ion Calculat ions
Part icle/ Part iclePart icle/ Part icle
Critical Velocity = 667 - 14ρ + 0.08Tm + 0.1σµ - 0.4Te
The empirical relationship for the critical velocity
is given by Assadi* as:
*H. Assadi, et al: “Bonding Mechanism in Cold Gas Spraying,”
Acta Materialia, 2003, 51, pp. 4379 – 4394.
ρ = particle density Tm = particle melting point
σµ = particle UTS Te = particle exit temperature
All particles smaller than that exiting with the criticalvelocity will deposit
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Deposit ion Ef f iciencyDeposit ion Ef f iciency
CalculationCalculation
1. Calculate table of particle exit velocities andtemperatures vs. particle diameter.
2. Calculate critical velocities based on the particle
exit temperatures.
3. Find the critical particle size that has an exit
velocity equal to the critical velocity.
4. Integrate the log normal particle size distribution
from the critical diameter to 1/infinity.
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Particle Exit Conditions
0
200
400
600
800
1000
0 20 40 60 80 100
Particle Diameter
E x i t V e l o c i t y
, m / s & T e
m p ,
Cvelocity
temperature
critical velocity
Crit ical Part icle DiameterCrit ical Part icle Diameter
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Effect of Part icle Diameter onEffect of Part icle Diameter on
Deposit ion Ef f iciencyDeposit ion Ef f iciency
1
10
100
0 20 40 60 80
Particle Mass Mean Diameter, microns
D e p o s i t i o
n E f f i c i e n c y
Nitrogen
Helium
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Effect of Nozzle Area Rat io onEffect of Nozzle Area Rat io on
Deposit ion Ef f iciencyDeposit ion Ef f iciency
0
20
40
60
80
100
0 5 10 15 20
Nozzle Area Ratio
D
e p o s i t i o n
E f f i c i e n c y
6 micron MMD
10 micron MMD
30 micron MMD
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Effect of Nozzle Area Rat io onEffect of Nozzle Area Rat io on
Deposit ion Ef f iciencyDeposit ion Ef f iciency -- HeliumHelium
0
20
40
60
80
100
0 5 10 15 20
Nozzle Area Ratio
D e p o s i t i o n
E f f i c i e n c y
10 micron
30 micron
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Effect of Nozzle Lengt hEffect of Nozzle Lengt h
on Deposit ion Ef f iciencyon Deposit ion Ef f iciency
0
10
20
30
40
50
60
70
5 10 15 20 25 30
Nozzle Length, cm
D
e p o s i t i o n E f f i c i e n c y
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ConclusionsConclusions
• Particle exit conditions are principally determined
by nozzle length and particle diameter.
• Particle/surface interaction can be characterized by
particle velocity and surface hardness.
• Particle velocity and deposition efficiency arerelatively insensitive to nozzle area ratio.
• Large improvements to deposition efficiency are
possible through the use of smaller particles and
longer nozzles.
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Parameters for Calculat ionParameters for Calculat ion
0.1 M0 microns Vp, m/s Tp, C Vc, m/s Tp critical critical dia
0.001 delM, M<1 1 890 -11 667
0.05 delM, M>1 3 762 44 645 0 0
673 T0 degK 6 670 153 601 0 0
400 P0 psia 10 602 208 579 0 0
2758000 P0 pascal 30 412 113 617 199 12
28 MW 60 299 58 639 0 0
8314 R 100 230 39 647 0 01.4 gamma
0.9 Vp0/Vg0
0.001 throat radius m
Fn(M0) y0 10 MMD
0.001 y1 67.35 Deposition Efficiency0.002 y2
0 x0
0.03 x10.1 x2
4.00 Ae/A*
1.00E-05 reference diameter m
9 material density g/cc
7.85E-11 particle area m^2
4.71E-12 particle mass kg
2.00E-05 viscosity kg/m-sec same N2-He
293 Tp0 K
390 particle Cp J/kg-K
0.03 gas cond. Kg-m/s^3-K .03N2-.15He
1084 melting Point, C
345 particle UTS, Mpa
12.00 critical diameter
1.5 std dev
1 ERF sign
0.3180 ERF argument
y0
x1
x0
x2
y1
y2
Particle Exit Conditions
0
200
400
600
800
1000
0 20 40 60 80 100
Particle Diameter
E x i t V e l o c i t y , m / s & T
e m p ,
C
velocity
temperature
critical velocity
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Effect of Feeder Gas MixingEffect of Feeder Gas Mixing
0
100
200
300
400
500
600
0 0.1 0.2 0.3 0.4
Hopper Flow/Main Flow
N
o z z l e C h a m b e r G a s
T e m p e r
a t u r e , C
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