ecuatii hvof

Modeling and Control of an Industrial High Velocity

Oxygen-Fuel (HVOF) Thermal Spray Process

Mingheng Li, Dan Shi and Panagiotis D. Christofides

Department of Chemical Engineering

University of California, Los Angeles

7th Southern CaliforniaNonlinear Control Workshop

Oct. 31 - Nov. 1, 2003

OUTLINE OF THE PRESENTATION

Introduction. High Velocity Oxygen-Fuel (HVOF) thermal spray process. Motivation for process control. Background on the modeling and control of the HVOF thermal sprayprocess.

Current work. Modeling of gas and particle behavior in the Metco Diamond JetHybrid HVOF thermal spray process.

Stochastic modeling of coating microstructure. Effect of operating conditions on particle velocity and temperature. Feedback control of the Metco Diamond Jet hybrid HVOF thermalspray process.

DIAMOND JET HYBRID HVOF THERMAL SPRAY PROCESS

CHARACTERISTICS OF THE DIAMOND JET HYBRID HVOFTHERMAL SPRAY PROCESS

Schematic diagram of the Metco Diamond Jet (DJ) hybrid HVOF gun.

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Typical operating conditions. Gas flow rate 18 g/s (12 l/s). Powder feed rate 20-80 g/min. Powder size 5-45 m. Coating thickness 100-300 m. Spray distance 150-300 mm.

Process characteristics. Flame temperature 2800 oC. Exit Mach number 2. Exit gas velocity 2000 m/s. Deposition efficiency 70%. Coating porosity 1-2%.

MODELING AND CONTROL: MOTIVATION ANDBACKGROUND

Motivation for process control. To suppress the influence of external disturbances and to reduce coatingvariability.

To produce coatings with desired microstructure and resulting thermaland mechanical properties.

Fundamental modeling of the HVOF process. Modeling of thermal/fluid field in HVOF process using CFD technology(e.g. Power et al., 1991, Dolatabadi et al., 2002) or semi-empiricalmethod (e.g. Tawfik and Zimmerman, 1997).

Modeling of coating microstructure evolution and porosity (e.g. Cai andLavernia, 1997, Ghafouri-Azar et al., 2003).

Control of thermal spray process. Advances in on-line particle temperature and velocity measurement. PID control in plasma thermal spray process (Fincke et al., 2002).

CONTROL PROBLEM FOR THE HVOF PROCESS

Multiscale feature of the HVOF process.

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Main control objectives. Velocity, temperature and molten state of particles at impact.

Manipulated inputs: On-line measurements:Total gas flow rate Particle velocity

Fuel/oxygen ratio Particle temperature

MODELING OF THE DJH HVOF PROCESS - CFD(Li, Shi and Christofides, CES, 2004)

Contours of pressure, mach number, temperature and velocity.

Flow/thermal field characteristics. Overexpanded flow at the exit of the torch (Pe < Pb). Compression and Expansion waves (shock diamonds) alternatively occuralong the centerline in the external flow field.

MODELING OF THE HVOF PROCESS - SIMPLIFIED MODEL(Li, Shi and Christofides, IECR, 2003)

Main assumptions. One way coupling of the two-phase flow due to small particle loading. Steady gas fluid/thermal field. Chemical equilibrium at the entrance of the combustion chamber. Isentropic frozen flow during passage of the Laval nozzle.

Modeling procedure.Chamber pressure

momentum heat transfertransfer

isentropic flowchemical equilibriumInternal flow field

Sphericity

Power size

Chamber entrance External flow fieldsupersonic free jet

Particle velocityParticle temperature

and molten state

Fuel/oxy ratio

Mass flow rate

Simulated pressure under four different operating conditions are all within6% of the experimentally measured values provided by the manufacturer.

MODEL OF GAS PHASE BEHAVIOR

Chemical equilibrium is solved by minimization of Gibbs energy ( Gordonand McBride, 1994).

Internal flow field is solved by laws governing isentropic compressible flow(Roberson and Crowe, 1997)

T2T1

=1 + [( 1)/2]M211 + [( 1)/2]M22

,P2P1

={1 + [( 1)/2]M211 + [( 1)/2]M22

} (1)

,

21

={1 + [( 1)/2]M211 + [( 1)/2]M22

} 1(1)

,A2A1

=M1M2

{1 + [( 1)/2]M221 + [( 1)/2]M21

} (+1)2(1)

,

mg = tvtAt =P0T0At

[MprR

(2

+ 1

)(+1)/(1)]1/2 External flow field is correlated by empirical formulas (Tawfik andZimmerman, 1997).

v/ve

(T Ta)/(Te Ta)

= 1 exp(

1 x/)

MODEL OF PARTICLE INFLIGHT BEHAVIOR

Model for particle velocity, temperature and degree of melting in the gasflow field.

mpdvpdt

=12CDgAp(vg vp)|vg vp|, vp(0) = vp0

dxpdt

= vp, xp(0) = 0

mpcppdTpdt

=

hAp(Tg Tp) + Sh, (Tp 6= Tm)

0, (Tp = Tm), Tp(0) = Tp0

Hmmpdfpdt

=

hAp(Tg Tp) + Sh, (Tp(0) = Tm)

0, (Tp 6= Tm), fp(0) = 0

4th Runge-Kutta method is used to solve the above differential equationstogether with the gas dynamics.

GAS AND PARTICLE INFLIGHT BEHAVIOR

Axial velocity & temperature profiles of gas and particles of different sizes.

Axial distance along the centerline (m)

Axia

lve

loci

ty(m

/s)

0 0.1 0.2 0.3 0.4 0.50

500

1000

1500

5 m10 m20 m30 m40 mgas

Axial distance along the centerline (m)

Axia

lte

mpe

ratu

re(K

)

0 0.1 0.2 0.3 0.4 0.50

500

1000

1500

2000

2500 5 m10 m20 m30 m40 mgas

Gas velocity & temperature decay in the free jet due to entrainment of air. Particles are accelerated and heated first, and then decelerated and cooledbecause of the velocity and temperature decay of the supersonic free jet.

Small particles change velocity and temperature easier than bigger onesbecause of their smaller momentum and thermal inertias.

PARTICLE VELOCITY AND TEMPERATURE AT IMPACT

Particle diameter (m)

Axia

lpa

rticl

eve

loci

tya

t8in

chst

an

doff

(m/s

)

0 20 40 60 800

200

400

600

800

1000

1200


Axia

lpa

rticl

ete

mpe

ratu

rea

t8in

chst

an

doff

(K)

0 20 40 60 801000

1200

1400

1600

1800


Axia

lpa

rticl

em

elti

ng

ratio

at8

inch

sta

ndo

ff

0 20 40 60 800

0.2

0.4

0.6

0.8

1 Particle velocity, temperature anddegree of melting are strong functions

of particle size.

Particles of moderate sizes have thelarger velocity and temperature than

other ones.

Particles of different sizes may havedifferent molten states.

MODELING OF POWDER SIZE DISTRIBUTION(Li and Christofides, CES, 2003; JTST, 2003)

Lognormal size distribution.

f(dp) =1

2pidpexp

[ (ln dp )

2

22

]

Cumulative weight function.

F =

dp0

16pix3f(x)dx

0

16pix3f(x)dx

= ln dp(+32)

12pi

ex22 dx

Volume-based average of particle properties (PP).

PP =

0

16pid3pPP (dp)f(dp)d(dp) 0

16pid3pf(dp)d(dp)

=

0

d3pPP (dp)f(dp)d(dp)

exp(3+922)

STOCHASTIC MODELING OF COATING MICROSTRUCTURE(Shi, Li and Christofides, IECR, 2003)

Modeling procedure.

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Particle size and hitting point are determined by random numbersfollowing lognormal distribution and uniform distribution, respectively.

Particle velocity, temperature and melting ratio at impact are solved by thepreviously described thermal spray process model.

Coating growth is described by several rules. Particle deformation obeys Madejski model (1991). Melted part of a particle fits the coating surface as much as possible. Unmelted part of a particle bounces off the coating surface if it hits asolid surface and attaches to it otherwise.

COMPUTER SIMULATION OF COATING MICROSTRUCTURE

Ideal lamellar microstructure of acoating formed by fully melted par-

ticles (top).

Microstructure of a coating formedby particles of nonuniform molten

states (bottom left).

Pores distribution in a coatingformed by particles of nonuniform

molten states (right bottom).

INFLUENCE OF OPERATING CONDITIONS ON COATINGMICROSTRUCTURE - FUEL FLOW RATE

80 100 120 140 160 180 200 220 240 260 2800.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Flow rate of fuel (SCFH)

Parti

cle

mel

ting

ratio

d50 = 20md50 = 30md50 = 40md50 = 50m

80 100 120 140 160 180 200 220 240 260 2800.4

0.6

0.8

1

1.2

1.4

1.6

1.8


Poro

sity

(%)

d50 = 20md50 = 30md50 = 40md50 = 50m

80 100 120 140 160 180 200 220 240 260 2805

10

15

20

25

30

35

40


Rou

ghne

ss (

m)

d50 = 20md50 = 30md50 = 40md50 = 50m

80 100 120 140 160 180 200 220 240 260 28020

30

40

50

60

70

80


Dep

ositio

n Ef

ficie

ncy

(%)

d50 = 20md50 = 30md50 = 40md50 = 50m

PARAMETRIC ANALYSIS OF GAS DYNAMICS

Gas properties at gun exit for different pressures and equivalence ratios.

0.5 1 1.50.8

0.9

1

1.1

1.2

1.3

Gas

pro

perti

es

Equivalence ratio

temperaturevelocitydensitymomentum fluxmass flow rate

5 10 150.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Combustion pressure (bar)G

as p

rope

rties

temperaturevelocitydensitymomentum fluxmass flow rate

Equivalence ratio () is the fuel/oxygen ratio divided by its stoichiometricvalue.

Tg is a function of but changes little with P .v2g is a linear function of P but does not change with .

CONTROL PROBLEM FORMULATION(Li, Shi and Christofides, IECR, 2003)

Differential equation for particle flow and thermal field.

mpidvpidt

=12ApiCDig(vg vpi)|vg vpi |, vpi(0) = vpi0 , i = 1, ..., N

dxpidt

= vpi , xpi(0) = 0, i = 1, ..., N

hAp(Tg Tpi) =

mpicpp

dTpidt

, (Tpi 6= Tm), Tpi(0) = Tpi0

Hmmpidfpidt

, (Tpi = Tm), fpi(0) = 0, i = 1, ..., N

t = tf , vp = vpsp , fp = fpsp

100 particles of different sizes are traced to calculate volume-based averageof velocity, temperature and melting ratio.

Two PI controllers are used.

CLOSED-LOOP SIMULATION RESULTS

Step response in the presence of change in set-points (5% increase inparticle velocity and 5% increase in particle melting ratio).

Time (s)

Parti

cle

me

ltin

gra

tio

0 5 10 15 20 25 300.46

0.48

0.5

0.52

melting ratioParti

cle

velo

city

(m/s

)

0 5 10 15 20 25 30440

450

460

470

480

velocity

Time (s)

Oxy

gen

flow

rate

(scfh

)

0 10 20 30550

600

650

700

750

800

850

oxygen

Pro

pyle

ne

flow

rate

(scfh

)

0 10 20 30170

180

190

200

210

220

230

propylene

Equ

iva

len

cera

tio

0 10 20 300.88

0.92

0.96

1

1.04

1.08

equivalence ratio

Time (s)

Pre

ssu

re(b

ar)

0 10 20 306

7

8

9

10

pressure

The feedback controller drives thecontrolled outputs into the new set-

point values in a short time.

The system switches from a fuel-richcondition to a fuel-lean condition.

CLOSED-LOOP SIMULATION RESULTS

Controlled output and manipulated input profiles in the presence ofvariation in powder size distribution.

Parti

cle

velo

city

(m/s

)

0 100 200 300 400 500 600 700440

445

450

455

velocity (without control)velocity (with control)

Time (s)

Parti

cle

me

ltin

gra

tio

0 100 200 300 400 500 600 7000.44

0.45

0.46

0.47

melting ratio (without control)melting ratio (with control)

Pro

pyle

ne

flow

rate

(scfh

)

0 100 200 300 400 500 600 700175

180

185

190

195

200

propylene (without control)propylene (with control)

Time (s)

Oxy

gen

flow

rate

(scfh

)

0 100 200 300 400 500 600 700560

580

600

620

640

660

oxygen (without control)oxygen (with control)

Time (s)

Equ

iva

len

cera

tio

0 100 200 300 400 500 600 7001.01

1.02

1.03

1.04

1.05

equivalence ratio (without control)equivalence ratio (with control)

Pro

pyle

ne

flow

rate

(scfh

)

0 100 200 300 400 500 600 7006.6

6.8

7

7.2

7.4

7.6

pressure (without control)pressure (with control)

Particle velocity and melting ratiodrop as the powder size increases.

The controller compensates for thevariation in powder size distribution

and maintains velocity & melting ra-

tio of particles at impact.

SUMMARY

Modeling and analysis of gas dynamics and particle inflight behavior in theDiamond Jet Hybrid HVOF thermal spray process.

Particle velocity is a strong function of combustion pressure. Particle temperature is highly dependent on equivalence ratio. Particle velocity and temperature are highly dependent on particle size.

Modeling of coating microstructure using stochastic simulation. Ideal lamellar coating microstructure may be disturbed due tononuniform melting behavior of particles.

A good melting condition helps to decrease coating porosity and toimprove deposition efficiency.

Formulation and solution of control problem for the Diamond Jet HybridHVOF thermal spray process.

Control of particle velocity and melting ratio at impact. Robustness test of the proposed controller in the presence of externaldisturbances.

ACKNOWLEDGEMENT

Financial support from a 2001 ONR Young Investigator Award, isgratefully acknowledged.

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