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
Particle diameter (m)
Axia
lpa
rticl
ete
mpe
ratu
rea
t8in
chst
an
doff
(K)
0 20 40 60 801000
1200
1400
1600
1800
Particle diameter (m)
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
Flow rate of fuel (SCFH)
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
Flow rate of fuel (SCFH)
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
Flow rate of fuel (SCFH)
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.