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


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


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

6171135 nozzle design influence on the supersonic particle deposition process

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