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Title:Modeling and Control of High-Velocity Oxygen-Fuel (HVOF) Thermal Spray: A Tutorial Review

Author:Li, Mingheng; Christofides, Panagiotis D.

Publication Date:2009

Series:UCLA Previously Published Works

Also Available:

Permalink:https://escholarship.org/uc/item/9cw1965d

DOI:http://dx.doi.org/10.1007/s11666-009-9309-2

Abstract:This work provides a tutorial overview of recent research efforts in modeling and control of the high-velocity oxygen-fuel (HVOF) thermal spray process. Initially, the modeling of the HVOF thermalspray, including combustion, gas dynamics, particle in-flight behavior, and coating microstructureevolution is reviewed. The influence of the process operating conditions as predicted by thefundamental models on particle characteristics and coating microstructure is then discussed andcompared with experimental observations. Finally, the issues of measurement and automaticcontrol are discussed and comments on potential future research efforts are made.

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Modeling and Control of High-VelocityOxygen-Fuel (HVOF) Thermal Spray:

A Tutorial ReviewMingheng Li and Panagiotis D. Christofides

(Submitted January 6, 2009; in revised form February 17, 2009)

This work provides a tutorial overview of recent research efforts in modeling and control of thehigh-velocity oxygen-fuel (HVOF) thermal spray process. Initially, the modeling of the HVOF thermalspray, including combustion, gas dynamics, particle in-flight behavior, and coating microstructure evo-lution is reviewed. The influence of the process operating conditions as predicted by the fundamentalmodels on particle characteristics and coating microstructure is then discussed and compared withexperimental observations. Finally, the issues of measurement and automatic control are discussed andcomments on potential future research efforts are made.

Keywords control, HVOF, modeling

1. Introduction

High-velocity oxygen fuel (HVOF) is a thermal spraytechnique that was introduced in 1980s (Ref 1). It is aparticulate deposition process in which microsized parti-cles of metals, alloys, or cermets are propelled andheated in a sonic/supersonic combusting gas stream andare deposited on a substrate at high speeds to form alayer of coating. Compared with plasma spray, coatingssprayed by the HVOF process have outstanding charac-teristics including higher density, bond strength, andtoughness, as a result of the significantly higher particlevelocity at impact and relatively lower particle temper-ature. High-velocity oxygen fuel sprayed functionalcoatings are now widely used in various industries toenhance performance, extend product life, and reducemaintenance cost. Representative examples include WC/Co-based wear-resistant coatings for drilling tools, YSZ-based thermal barrier coatings for turbine blades, andnickel-base corrosion-resistant coatings for chemicalreactors. More recently, the HVOF process has beenused for processing nanostructured coatings usingmicrosized nanocrystalline powder particles (Ref 2-4),which exhibit superior properties over conventional

counterparts in terms of microhardness, elastic modulus,wear resistance, and thermal conductivity.

Modeling and control play an important role in thedesign and operation of the HVOF thermal spray process,partly because of its inherent complexity. Generally, therelationship among processing conditions, particle char-acteristics, and the resulting coating properties is highlynonlinear and might not be thoroughly revealed byexperimental studies. As a result, the optimization ofHVOF thermal spray based on the conventional design ofexperiments (DOE) methodology could be limited, espe-cially when the HVOF system is significantly modified(Ref 5). Mathematical modeling is an excellent comple-ment to the experimental approach. It provides a funda-mental understanding of the underlying momentum andheat-transfer mechanisms, which in turn, might be used toguide system design and operation (Ref 6, 7). Moreover,the compensation of feed disturbances and process vari-ability during real-time process operation becomesessential in order to fabricate coatings of a consistentquality. This motivates the development and implemen-tation of real-time control systems in HVOF thermalspray to suppress variations in the particle temperatureand velocity at the point of impact on the substrate. Suchefforts have been facilitated by recent advances in the gasand particle velocity and temperature measurements viareal-time diagnostic techniques (Ref 8).

2. Modeling of HVOF Thermal Spray

2.1 Multiscale Character of HVOF Thermal Spray

Figure 1 shows a schematic of a representative HVOFthermal spray system (Sulzer Metco Diamond Jet Hybrid2700, Sulzer Metco, Westbury, NY). In this process, thepremixed fuel gas (typically propylene or hydrogen) andoxygen are fed to the air cap, where they react to produce

Mingheng Li, Department of Chemical and Materials Engineer-ing, California State Polytechnic University, Pomona, CA 91768;Panagiotis D. Christofides, Department of Chemical and Biomo-lecular Engineering, University of California, Los Angeles, CA90025; and Department of Electrical Engineering, University ofCalifornia, Los Angeles, CA 90025. Contact e-mails: [email protected]. edu and [email protected]

JTTEE5 18:753768

DOI: 10.1007/s11666-009-9309-2

1059-9630/$19.00 The Author(s). This article is published with open access at Springerlink.com

Journal of Thermal Spray Technology Volume 18(5-6) Mid-December 2009753

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high-temperature combustion gases. The exhaust gases,together with the air injected from the annular inlet orifice,expand through the nozzle to reach supersonic velocity.The air cap is cooled by both water and air to prevent itfrom melting. The powder particles are injected at thecentral inlet nozzle using nitrogen as the carrier gas.Consequently, rapid momentum and heat transfer betweenthe gas and the powder particles lead to acceleration andheating of the particles. The molten or semimolten parti-cles are carried toward the substrate by the expanding gasjet. The particles hit the substrate, cool, and solidify,forming a thin layer of coating material with low porosity.

The multiscale character of a typical HVOF thermalspray process is shown in Fig. 2 (Ref 9). The microstruc-ture of HVOF sprayed coatings results from the defor-mation, solidification, and sintering of the depositedparticles, which are dependent on the substrate properties(e.g., substrate temperature) as well as the physical andchemical state (e.g., temperature, velocity, melting ratio,and oxidant content) of the particles at the point of impacton the substrate. The particle in-flight behavior, however,is coupled with the gas dynamics, which are directlyrelated to various processing conditions such as gas flowrate, fuel/oxygen ratio, spray distance, and so forth. Whilethe macroscopic thermal/flow field can be readilydescribed by continuum-type differential equations gov-erning the compressible two-phase flow, the process ofparticle deposition is stochastic and discrete in nature andis best described by stochastic simulation methods (Ref 9).

2.2 Gas Dynamics

The gas and particle dynamics in the HVOF thermalspray are coupled with each other. To simplify the anal-ysis, the assumption of one-way coupling is usually madewhen the particle loading, which is defined as the ratio ofmass flow rate of particles to that of gases, is low (about4-5%). Under such an assumption, the existence of par-ticles has a minimal influence on the gas thermal and flowdynamics, while the particle in-flight behavior is derivedfrom the particle momentum and heat-transfer equations(Ref 10, 11). The modeling of the two-way coupling of thegas and particulate phases is also possible at the expenseof a higher computational cost (Ref 12).

The gas flow in HVOF thermal spray is essentially acompressible reacting flow process featured with turbu-lence and subsonic/sonic/supersonic transitions (Ref 13).A comprehensive description of this process requirestime-consuming direct numerical simulations. To simplifythe simulation, the Reynolds-Averaged Navier-Stokes(RANS) equations are usually used so that the small-scaleturbulent fluctuations might not be directly solved. Toconvert the Navier-Stokes equations into the ensemble-averaged form, the Boussinesq hypothesis (Ref 14) isemployed to represent the Reynolds stresses (with fluc-tuation terms) with the mean velocity gradients (withoutfluctuation terms). Specifically, the governing equationsinclude the conservations of mass, momentum, energy,species transport, turbulent kinetic energy, dissipationrate, and so forth (Ref 11). The equations written inCartesian tensor notation are:

Continuity:

@q@t

@@xj

qvj 0 Eq 1

where q is the density, t is the time, and vj are the velocitycomponents in each of the xj directions.

Momentum balance:

@

@tqvi @

@xjqvivj @p

@xi

@@xj

l@vi@xj

@vj@xi

23dij

@vl@xl

@@xj

qv0iv0j; i 1; 2; 3 (Eq 2)

where p is the pressure, l is the molecular viscosity, dij isthe Kronecker delta, and qv0iv0j is the Reynolds stressterm representing the effect of turbulence. Based on theBoussinesq approximation,

qv0iv0j lt@vi@xj

@vj@xi

2

3qk lt

@vl@xl

dij

where lt is the turbulent viscosity [lt qcl k2=

] and k is

the turbulence kinetic energy (k = v02i ).

7.95 mm 54.0 mm

10.94

mm

7.16

mm

15.6 mm

Cooling Water Inlet Cooling Water Outlet

Air

Powderand N2

Oxygenand Fuel

Extended Air Cap

12o 2o

Fig. 1 Diamond Jet Hybrid thermal spray gun

754Volume 18(5-6) Mid-December 2009 Journal of Thermal Spray Technology

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Turbulence model (using the k- model as an example):

@

@tqk @

@xiqvik @

@xjl lt

rk

@k

@xj

Gk Gb q YM (Eq 3)and

@

@tq @

@xiqvi @

@xjl lt

r

@

@xj

C1 kGk C3Gb C2q

2

k(Eq 4)

where is the turbulence dissipation rate, Gk and Gb arethe generations of turbulence kinetic energy caused by themean velocity gradients and buoyancy, respectively, andYM is the contribution of the fluctuating dilatation incompressible turbulence to the overall dissipation rate.C1 = 1.44, C2 = 1.92, Cl = 0.09, rk = 1.0, and r = 1.3.

Species transport:

@

@tqyi @

@xjqvjyi @

@xjJi Ri; i 1; . . . ; N 1

Eq 5where yi is the mass fraction of each species, Ji is thediffusion flux of species i calculated by Maxwell-Stefanequations, Ri is net rate of production of species i bychemical reaction, and N is total number of speciesinvolved in the reaction.

Energy balance:

@

@tqH @

@xiqviH @

@xjC

@H

@xj

SH Eq 6

where C is the ratio of the effective viscosity and thePrandtl number, H is the total enthalpy defined byH PNi1 Hiyi and SH is the source term (e.g., heat gen-erated by the exothermic reaction).

Ideal gas law:

p qRT Eq 7where R is the specific gas constant, or the molecular gasconstant divided by the molecular weight of the gas.

In the modeling of HVOF thermal spray, it is veryimportant to note that because of the high operatingtemperature, combustion products will dissociate into anumber of species with low molecular weight, for example,OH and H and so forth (Ref 5, 13). The predicted tem-perature could be significantly higher if such a dissociationis not taken into account. Depending on the computa-tional time, single or multistep reduced reaction chemistrymodels may be used. In the literature, differentapproaches have been used to model the reaction rate,including: (a) infinitely fast reaction rate (e.g., Ref 10, 13,15, 16) or instantaneous chemical equilibrium at theentrance of the combustion chamber, (b) finite reactionrate in Arrhenius form (e.g., Ref 17-20), (c) finite reactionrate limited by turbulent mixing (e.g., Ref 11, 12, 21-25) orthe reaction is faster than the mixing rate so that theoverall combustion process is limited by the latter.

In many practical situations such as the HVOF thermalspray, the eddy-dissipation model describes the limitingrate, and thus knowledge of accurate Arrhenius rate datais not needed (Ref 12). Based on the fact that the gasresidence time in the combustion chamber (convergentsection of the nozzle) is much longer than the one in thesubsequent sections, it is reasonable to assume that thereaction occurs primarily in the combustion chamber fol-lowing a global one-step equilibrium chemistry model,which can be determined by minimizing the Gibbs freeenergy under constant enthalpy and constant pressureusing existing equilibrium codes (Ref 26). The pressurecan be measured at the operating conditions. Alterna-tively, if the mass flow rates of oxygen and fuel areavailable, a previously developed approach (Ref 11) can

Gas dynamicsTemperatureMelting

Oxidation

VelocityCompositionPressureDensityVelocity

Temperature

behavior

Particleinflight

Particle mass flow rateParticle size and shape

Injection velocity and angleSpray distance and angle

Gas mass flow rateFuel/oxygen ratio

Nozzle design

OperatingconditionsSubstrate properties

Processdynamics

CoatingmicrostructureCoating porosity, hardness, deposition efficiency

mic

rosc

ale

mac

rosc

ale

Fig. 2 Multiscale character of the HVOF thermal spray process (Ref 9, 27)


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be used to determine the chamber pressure. Specifically,with the given oxygen and fuel flow rates, a combustionpressure is assumed, based on which a quasi-one-dimensional model is used to calculate the equilibriumcomposition and temperature at the combustion chamber.The total mass flow rate at the throat of the nozzle is thencalculated, based on which the pressure is adjusted untilthe discrepancy between the calculated and the specifiedtotal mass flow rates falls below a user-specified tolerance(Ref 27).

The computational fluid dynamic (CFD) simulation isable to provide the detailed temperature and velocityinformation of the gas field. For example, Fig. 3 shows thetemperature contour in the combustion chamber of theDiamond Jet 2700 gun (Ref 11). The function of air isclearly demonstrated; the hot flame is surrounded bythe cooling air around the torch wall, thus protectingthe hardware from being overheated. Figure 4 shows thecontour and centerline profile of static pressure in theinternal and external gas fields. The pressure graduallydecreases from 6.2 bar in the combustion chamber to 0.6bar (or a gage pressure of 0.4 bar) at the exit of thenozzle, which is close to a 0.3 bar gage pressure mea-sured by the manufacturer (Ref 11). Because this pressureis less than the ambient pressure, the flow is underex-panded and a mach disk is formed downstream of thenozzle exit. The flow adjusts to the ambient pressure bya series of shock waves, which are usually observedexperimentally.

For a quasi-one-dimensional analysis, the assumptionsof instantaneous equilibrium at the entrance of the com-bustion chamber and frozen flow along the nozzle can beused (Ref 28). The mathematical model accounting forwall friction and water cooling is described by (Ref 29):

dM2

M2 1 c 1=2M

2

1 M2

2 dAA

kcM2 dxD 1 cM

2

1 c 1=2M2dq

cpT

Eq 8

dT

T c 1M

2

1 M2dA

A k cM

2

2

dx

D 1 cM

2

c 1M2dq

cpT

Eq 9where A is the cross-sectional area perpendicular to the flowdirection, D is the diameter of the nozzle, c is the heatcapacity ratio, and M is the mach number (note thatv/M = a =

cRT

pis the sonic velocity. At the throat of the

nozzle, where the flow area reaches the minimum, the machnumber is 1). k is the Darcy friction coefficient correlated asa function of the Reynolds number of the equivalentroughness of the wall by the Colebrook equation (Ref 30):

1k

p 2 log10e=D3:72

2:51Re

k

p

Eq 10

The term (dq/dx) is the heat-removal rate per unit lengthof the nozzle, which might be estimated by fitting exper-imental data and model prediction (Ref 31). Equations 8and 9 are integrated simultaneously using the Runge-Kutta method.

For an even simpler analysis neglecting friction or cooling(this is reasonable from the combustion chamber to thenozzle throat in HVOF guns such as the Sulzer MetcoDiamond Jet Hybrid 2700 (Sulzer Metco, Westbury, NY)and the Praxair-Tafa JP-5000 (Praxair Surface Technolo-gies, Indianapolis, IN)), the following isentropic equationsmay also be used to relate the temperature, pressure, anddensity at two points along the nozzle (Ref 32):

T2T1

1 c 1=2M21

1 c 1=2M22Eq 11

p2p1

1 c 1=2M21

1 c 1=2M22

c=c1Eq 12

q2q1

1 c 1=2M21

1 c 1=2M22

1=c1Eq 13

Static Temperature (K)3.3E+032.7E+032.1E+031.5E+039.0E+023.0E+02

Fig. 3 Contour of static temperature in the combustion cham-ber (Ref 11)

Axial distance along the centerline (m)Sta

ticpr

ess

ure

(105

Pa)

0 0.1 0.2 0.30

2

4

6

Static pressure (105Pa): 4.4E-01 1.6E+00 2.8E+00 4.0E+00 5.1E+00 6.3E+00

Fig. 4 Contours of the static pressure in the Diamond JetHVOF thermal spray gun (Ref 11)


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A2A1

M1M2

1 c 1=2M221 c 1=2M21

c1=2c1Eq 14

Based on the aforementioned relationships, it can bederived that the total mass flow rate is:

_m p0T0

p Athc Mpr

Rg

2

c 1 c1=c1s

Eq 15

where Ath is the cross-sectional area at the throat (wherethe area is the minimum), Rg is the molecular gas constant,Mpr is the average molecular weight of the combustionproducts, and T0 and p0 are, respectively, the stagnationtemperature and stagnation pressure in the combustionchamber. This equation clearly reveals that the mass flowrate and the combustion pressure are not independent,which explains why the combustion pressure should besolved using an iterative procedure when the flow rates ofoxygen and fuel are provided. Table 1 shows a comparisonbetween predicted and experimentally measured chamberpressures under various operating conditions of a Dia-mond Jet thermal spray gun using the approach developedin Ref 27. The discrepancy is generally less than 6%,which validates the assumption of chemical equilibrium inthe chamber.

Equations 8 and 9 or 11 to 14 are only applicable in theinternal flow field. For a one-dimensional analysis of theexternal field, empirical formulas might be correlatedfrom experimental measurement (Ref 28, 33-36). Tawfikand Zimmerman provided the following correlation for-mulas for typical HVOF processing conditions (Ref 29):

v

ve

1; x xc1 exp 0:851x=xc

; x>xc

(Eq 16

T TaTe Ta

1; x xc1 exp 1:251x=xc

; x > xc

(Eq 17

where the subscripts a and e stand for ambient con-dition and nozzle exit condition, respectively, and xc is thepotential core length (xc/De = 4.2 + 1.1 M

2e , Ref 29).

Figure 5 shows the axial profiles of gas velocity and statictemperature along the centerline in a Metco Diamond Jetthermal spray process based on a simplified quasi-one-dimensional model (Ref 27, 37) and a CFD model(Ref 11). It can be seen that the general trends are similar,while the centerline temperature derived from the one-dimensional model is higher than the one from the CFDmodel. This is because the former is not able to handle the

mixing of cold carrier gas and the hot combustion flame inthe combustion chamber, which is multidimensional innature.

2.3 Particle Dynamics

The modeling of particulate phase in the HVOF ther-mal spray is typically based on the Lagrangian approach.First, the average distance between individual particles inthe HVOF thermal spray process can be estimated basedon the analysis of Crowe et al. (Ref 38). Specifically,

Lddp

p6

1 jj

1=3Eq 18

where Ld is the distance between two particles and j is theratio of particle loading to particle/gas density ratio. Basedon a particle loading of 4% and a density ratio of 103 to104, Ld/dp is about 20-50, which implies that the individualpowder particles are isolated from each other (Ref 37).Therefore, it is reasonable to assume that particle coagu-lation is negligible (Ref 11, 27), and thus the powder sizedistribution does not change during flight (Ref 22). In themodeling of particle dynamics, it is usually assumed thatthe major force acting on a particle in the HVOF thermalspray process is the drag force, and other forces, such asthe Basset history term, gravitational force, forces causedby pressure gradients, and so forth, can be neglected(Ref 21, 39). With these assumptions, the particle motionalong the axial direction in the Cartesian coordinates isdescribed by:

mpdvpdt

12

CDqgAp vg vp

vg vp ; dxp

dt vp

Eq 19where mp, vp, dp, and xp are the mass, velocity, diameter,and position of the particle, respectively. Ap is the pro-jected area of the particle on the plane perpendicular tothe flow direction. vg and qg are the velocity and density ofthe gas. CD is the drag coefficient, which is a functionof the local Reynolds number (Re) defined by Re =(dp|vg vp|qg)/lg, where lg is the gas viscosity (Ref 30). Inthe processing of nanostructured coatings, the particles aretypically not spherical (Ref 16) and the correspondingshape factor can be taken into account in the CD calcu-lation in this case (Ref 40, 41). Note that the particlesexperience forces from all three spatial directions andequations similar to Eq 19 should also be solved in theother two Cartesian coordinates.

Table 1 Comparison of computational and experimental results (Ref 21) for a Diamond Jet thermal spray gun using aquasi-one-dimensional model (Ref 27)

Case O2, scfh C3H6, scfh Air, scfh N2, scfh Pexpchamber, psia P

calcchamber, psia Error, %

1 635 185 790 29.4 69.7 68.7 1.42 635 185 395 29.4 59.7 56.1 6.03 879 185 795 29.4 76.7 77.6 1.24 347 110 632 29.4 44.7 44.8 0.2


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Assuming spherical particles, the particle heating canbe described by a partial different equation (Ref 42):

qpcpp@Tpr; t

@t 1

r2@

@rr2kp

@Tpr; t@r

; 0 r rp

B:C:

@Tp0; t@r

0 (Eq 20)

kp@Tprp; t

@r hTg Tprp; t

where rp is the radius of the particle, k is the thermalconductivity of the gas, and h is the heat-transfer coeffi-cient correlated by the Ranz-Marshall empirical equation(Ref 30):

h kgdp

2 0:6Re1=2Pr1=3h i

Eq 21

where the Prandtl number (Pr) is calculated by Pr cpglg=kg where cpg , lg, and kg are the heat capacity, vis-cosity, and thermal conductivity of the gas, respectively.

In general, particles in the HVOF thermal spray pro-cess experience melting and solidification (Ref 42). In sucha case, Eq 20 should be modified to account for thepropagation of the melting/solidification front toward/from the particle center. This is a Stefan problem withmoving boundaries (Ref 25, 43). Further work on thebreakup, cooling, and solidification of metal particles isalso available in the literature (Ref 44, 45). For good heat-conducting particles, if the Biot number (Bi = hdp/6kp) isless than 0.1, the internal particle temperature gradientscan be ignored. In such a case, Eq 20 can be simplified tothe following form (Ref 27):

hA0pTg Tp mpcpp

dTpdt ; TpTm; f 1

8>: Eq 22

where A0p is the surface area of the particle, Tm is themelting point of the particle, DHm is the enthalpy of

melting, and fp is the melting ratio, or the ratio of themelted mass to the total mass of the particle (0 fp 1).A numerical integration method is provided in Ref 27for the particle heating/cooling with phase transitions. Asmentioned previously, because of the high turbulence inthe fluid flow, the particles are likely to be affected by theinstantaneous fluctuation in the fluid phase. However,either the RANS equations or the quasi-one-dimensionalmodel solves only for the mean fluid velocity. In order toaccount for the turbulent dispersion of particles, the sto-chastic tracking approach can be used in which a randomvelocity fluctuation term is added to the mean gas phasevelocity (Ref 22). The fluctuation velocity component ineach spatial direction is kept constant over the charac-teristic lifetime of the eddies and is updated in each timeinterval. Each run of the above discrete random walkmodel provides a snapshot profile of particle motion in thegas field. A statistical effect of the turbulence on particledispersion may be obtained by computing the particletrajectories in this manner for a sufficiently large numberof independent simulations.

Key conclusions from the modeling of particledynamics (Ref 11, 22, 27, 46, 47) are summarized in thefollowing paragraphs.

Particles are affected by the gas field to differentextents depending on their size. Small particles may beaccelerated and heated up to very high velocities andtemperatures. However, because of the entrainment of theambient air in the external field, the gas velocity andtemperature decay downstream of the potential core(Fig. 5). As a result, the velocities and temperatures ofsmall particles drop more sharply than those of largerparticles because of their smaller momentum and thermalinertias. In some cases, small particles may reach themelting point in a short period of time and become fullymelted during flight. However, they may eventually be in aliquid/solid or even solid state as they reach the substrate.For particles of large sizes, the periods for acceleration andheating are both longer, and the velocity (or temperature)profiles become nearly flat after their velocity and tem-perature are higher than those of the gas. A typical profile

Distance along the centerline (m)(a) (b)

Gas

axi

al v

elci

ty in

the

cent

erlin

e (m

/s)

250

500

750

1000

1250

1500

1750

20001-D model2-D CFD model

Distance along the centerline (m)

Gas

tem

pera

ture

in th

e ce

nter

line

(K)

0 0.1 0.2 0.30

0 0.1 0.2 0.30

500

1000

1500

2000

2500

30001-D model2-D CFD model

Fig. 5 Comparison of (a) axial gas velocity and (b) static temperature along the centerline solved using a simplified quasi-one-dimensional model (Ref 27, 37) and a CFD model (Ref 11)


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of particle velocity, temperature, and melting degree isshown in Fig. 6 (Ref 37).

The effect of particle turbulence dispersion is shown inFig. 7 (Ref 22). This snapshot profile of the particle tra-jectories in the flow field is obtained by feeding 100 par-ticles to the HVOF thermal spray system from 5 uniformlydistributed radial locations in the carrier nitrogen streamand 20 uniformly distributed sizes between 1 and 20 lm. Itis seen that although most particles are highly concen-trated in the centerline inside of the HVOF torch, theparticles tend to expand toward the radial direction whenthey approach the substrate, due to substantial radial gasvelocities (Ref 22). Small particles are significantly influ-enced by the gas flow pattern close to the substrate. Theyare also sensitive to the fluctuations in the gas phase andhave more random trajectories. Some of them might evenfollow the gas stream and will not be deposited on thesubstrate. Note that submicron particles might be depos-ited on the substrate by thermophoretic force; however,this force is not as strong as the turbulent dispersion.

For this reason, particles used in the HVOF thermal spraycoating process cannot be too small. This is true even forthe processing of nanostructured coatings, in which thepowders comprise micron-sized agglomerates with grainsize below 100 nm.

The particle velocity and temperature at impact arestrongly dependent on particle size and also on the tra-jectory that the particle takes. The maximum of particlevelocity and temperature generally occur at median par-ticle sizes. When the same size particles take differenttrajectories (due to differences in the initial injectionlocation and random fluctuations in the gas phase), theymight achieve different velocities and temperatures uponimpact, see Fig. 8. This behavior is consistent withexperimental observations of Zhao et al. (Ref 48).

It is also demonstrated in the modeling study that theparticle temperature can be strongly affected by the axialinjection location and initial injection velocity while theparticle velocity is more robust with respect to these twoparameters. This is also validated by the studies of Hansonet al. (Ref 49, 50). However, the axial injection location isnot a variable to be adjusted in real time, and therefore itsapplication in automatic control might be limited.

While mathematical modeling can provide generaltrends and important insight into the behavior of theHVOF thermal spray process, a perfect match betweenmodel prediction and measurement is very difficult toobtain. For example, the CFD simulations typicallyunderpredict the particle temperature (Ref 6), partlydue to the negligence of exothermic particle oxidation(Ref 12) and the contribution of viscous dissipation to thetwo-phase heat-transfer coefficient (Ref 51). A particleoxidation model has been recently accounted for in theCFD model by Zeoli et al. (Ref 52).

2.4 Powder Size Distribution

It is very important to note that the powder particlesused in the HVOF thermal spray process are typicallypolydisperse, and therefore the powder size distribution isan important parameter that should be accounted for in

Distance along the centerline (m)(a) (b)

Axi

al v

eloc

ity (m

/s)

0

500

1000

1500

20000.5 m1 m5 m10 m20 m30 mgas

Distance along the centerline (m)

Axi

al te

mpe

ratu

re (K

)

0 0.1 0.2 0 0.1 0.20

500

1000

1500

2000

2500

0.5 m1 m5 m10 m20 m30 mgas

Fig. 6 Profiles of (a) particle velocity and (b) temperature along the centerline (Ref 22)

0.05 0 0.05 0.1 0.15 0.2 0.25 0.30.05

0

0.05

thermal spray gun

substrate

Axial position (m)

Rad

ial p

ositio

n (m

)

Fig. 7 Trajectories of different size particles injected at differ-ent radial locations in the flow field (Ref 22)


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the evaluation of the average in-flight particle character-istics. Two commonly used two-parameter powder sizedistribution functions in HVOF thermal spray are lognormal and Rosin-Rammler. A log normal powder sizefunction has following form (Ref 53):

f dp 12p

prdp

exp ln dp l2

2r2

" #Eq 23

where l and r2 are two dimensionless parameters corre-sponding to the mean and the variance of ln dp, whichobeys the normal distribution. For particles that are lognormally distributed, l and r can be determined using(Ref 46, 47):

l lnd10d50d90

3p

1:831 lnd90d10

s !2

r 0:781 lnd90d10

s Eq 24

where d10, d50, and d90 are three characteristic diametersthat can be obtained experimentally (Ref 2).

The Rosin-Rammler powder size distribution functionis:

f dp ndpdpdp

n1exp dpdp

n Eq 25

or

Mdp exp dpdp

n Eq 26

where Mdp is the retained weight fraction (weight fractionof particles with diameter greater than dp), dp is the meanparticle size, and n is the spread factor. n and dp in theRosin-Rammler distribution function are the slope andthe inverse of the exponential of the intercept slope ratioof the straight line represented by ln dp versusln(ln Mdp) (Ref 22).

Because of the polydispersity in the size distributionand the strong effect of particle size on particle velocityand temperature, it is more appropriate to relate the

coating properties with volume-averaged powder proper-ties PP

instead of a single particle size because larger

particles have a stronger influence on coating propertiesthan smaller ones. The volume-averaged powder proper-ties are defined as:

PP R dub

dlb16 pd

3pPPdpf dpddpR dub

dlb16 pd

3pf dpddp

Eq 27

where dlb and dub are the lower and upper bounds in theparticle size such that the denominator is larger than 0.99.

2.5 Particle Impact and Coating Growth

Splat formation and coating growth have been studiedextensively (Ref 6, 54, 55), and a comprehensive reviewhas been provided by Fauchais et al. (Ref 56) to summa-rize the effect of particle properties (temperature, veloc-ity, molten state, oxidization state, etc.) and substrateconditions (roughness, composition, crystallinity, etc.) onparticle flattening, splashing, and solidification. Most ofthe available research work is based on fully melted par-ticles (which is typical of plasma spray processes), whichmight not reflect the fact that particles at impact on thesubstrate in HVOF thermal spray may be in mixed melt-ing states (fully melted, partially melted, or solid) due todifferent sizes and different trajectories in the gas flowfield. This has been substantiated by both experimentalstudies (Ref 57) and numerical simulations (Ref 11, 27).Moreover, in the HVOF thermal spray processing ofcarbides with binding metals, such as the WC-Co powders,only the metals may be in a molten state because the gastemperature in a conventional HVOF thermal spray pro-cess is not high enough for melting carbides, which havehigh melting points (e.g., 3143 K for tungsten carbide)(Ref 58). Ivosevic et al. (Ref 42) studied the deformationof HVOF sprayed polymer particles using the volume offluid (VoF) method and found that when particles arepartially melted, the internal temperature distribution hasa significant effect on the final shape of the splat. Theirmathematical model successfully explained the experi-mentally observed fried-egg shape of the splat, whichfeatures a low-temperature, nearly hemispherical core

0 20 40 60 80 1000

100

200

300

400

500

600

700

Particle size (m) (a) (b)

Parti

cle

axia

l vel

ocity

at i

mpa

ct (m

/s)

0 20 40 60 80 100400

600

800

1000

1200

1400

1600

Particle size (m)

Parti

cle

tem

pera

ture

at i

mpa

ct (K

)

Fig. 8 (a) Axial particle velocity and (b) temperature upon impact as a function of particle size (Ref 22)


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located in the center of a thin disk (Ref 42). Therefore, tosimulate the coating growth in HVOF sprayed coatings, itis necessary to account for partially or unmelted particles.

A rule-based stochastic simulation approach wasdeveloped for the formation of HVOF sprayed coatings inwhich the particles of mixed melting states are accountedfor (Ref 59). The general procedure is shown in Fig. 9.Specifically, it is assumed that the coating formation pro-cess is a sequence of independent discrete events of eachindividual particle landing on the previously formedcoating layer. The powder size and landing location arederived from random number generators, which follow thepowder size distribution function and a uniform distribu-tion function (due to the movement of the HVOF thermalspray gun), respectively. The particle properties uponimpact are then determined based on the gas and particlemodels presented previously. The splat is formed andadded to the previously deposited coating layer followingappropriate rules discussed in the next paragraph. Theparticle deposition is repeated until a desired coatingthickness is reached. The program then calculates thecoating porosity, surface roughness, and depositionefficiency.

The rules governing the particle deformation andcoating growth are summarized (Ref 59):

The deformation of fully melted particles follows thelaw of Madejski (Ref 60):

n Dsdp

nRe; We; Pe Eq 28

where Ds is the diameter of the thin disk formed by theparticle and n is the flattening ratio that depends onseveral dimensionless parameters characterizing theimpact and spreading processes: (a) the Reynoldsnumber, which represents the viscous dissipation of theinertia forces, (b) the Weber number, which quantifiesthe conversion of the kinetic energy into surfaceenergy, and (c) the Peclet number, which expresses thefreezing rate. For partially melted particles, thisassumption is modified such that the unmelted part willform a hemisphere with the equivalent volume and the

melted part will form a ring around this hemisphere,whose flattening ratio can be calculated using the sameformula, see Fig. 10. This rule is based on experimentalobservations (Ref 42).

When a particle hits the substrate, the melted part ofthe particle will fit to the surface as much as possible.The splat will move forward until it is in close contactwith the previously deposited coating surface.

If the unmelted part of a partially melted particle hitsat the point of the previously deposited layer that isformed by an unmelted particle, particle reboundmight occur and consequently a hole is formed in thecenter of the disk. Otherwise, it will attach on thecoating surface as a hemisphere.

If the splat comes to a vertical drop during spreading,the ratio of the splat that has not been settled downwill be calculated. If the step does not continue with agap that can be covered by the splat, the splat willbreak or cover the corner of the step according to theratio and the height of the step. Otherwise, the gapwill be covered by the splat and a pore will be formed.

If the splat encounters a dead end, it will first fill theavailable space, and then flow over the outer surfacedepending on the remaining volume.

Growth rules

Particle size

Coating growth

positionParticle hitting Splat formation

Particle dynamicsGas dynamics Particle temperature

Particle melting degree

Particle velocity

generatorsRandom number

Fig. 9 Multiscale modeling of the HVOF thermal spray process (Ref 9)

Dm

h

Partially melted particle

Splat

Melted partUnmelted part

Dum

dp

Fig. 10 Deformation of partially melted particle upon impacton the substrate (Ref 59)


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The effect of melting state on the coating microstruc-ture is shown in Fig. 11 (Ref 11). When all the particles arefully melted, an ideal lamellar microstructure is formed.However, under normal HVOF processing conditions,many particles might be partially melted or even unmelted.When these particles are embedded in the coating, themicrostructure and resulting physical and mechanicalproperties could be different. The fact that the particles arenot necessarily to be fully melted to achieve excellentcoating microstructure is consistent with practice. This isvery important for the fabrication of nanostructuredcoatings, since the nanostructure in the unmelted particlesis preserved during flight. However, under certain condi-tions where the particle melting ratio is very low, unmeltedparticles may bounce off the substrate, resulting in a high-porosity coating with a low deposition efficiency.

Several results from the stochastic simulations ofcoating growth have been verified by experimental studies(Ref 59). For example, the simulation pointed out that ahigh melting degree (which occurs at an equivalence ratioof about 1.2, or a fuel-rich condition, where the gas andparticle temperatures are the highest) and a high totalmass flow rate would enhance a low coating porosity. Thisis validated by the studies of NiWCrBSi coatings pro-cessing using a Praxair-TAFA JP-5000 HVOF thermalspray system (TAFA Inc., Concord, NH, acquired byPraxair Surface Technologies, Indianapolis, IN) (Ref 61).Similar conclusions have been drawn in NiAl coatingsprocessing using a UTP TopGun HVOF gun (UTP, BadKrozingen, Germany) (Ref 62) and in steel coatingsprocessing using a Praxair-TAFA JP-5000 HVOF gun(Ref 50). The simulation also shows that a better parti-cle melting condition would enhance the depositionefficiency, which is consistent with experimental studies(Ref 50, 62, 63).

A comparison of simulation results (Ref 11) withexperimental studies (Ref 50) shows that the porositypredicted by the model is higher than the experimentallymeasured value under similar operating conditions. Onepossible reason is that the CFD model usually underpre-dicts particle temperature (Ref 12). Further developmentis still necessary to more accurately predict coatingmicrostructure and resulting properties from macroscopicoperating conditions using multiscale models. For

example, residual stress is a key criterion of coatingproperty that may be affected by particle characteristics(Ref 63-66). Finite element analysis of residual stress ofHVOF sprayed coating has been developed (Ref 67, 68).However, the effect of partially molten particles onresidual stress is yet to be explicitly accounted for.

3. Control of HVOF Thermal Spray

As pointed out by Moreau (Ref 69), some automaticcontrol systems have been developed and implemented inthe thermal spray processing to regulate variables such asgas flow and material feed rates, substrate temperature,and robot trajectory. However, the more challenging taskis what and how control actions should be taken to com-pensate for a drift in the particle characteristics observedin the processing. This requires a fundamental under-standing of the relationship between manipulated inputs(i.e., key operating conditions) and controlled outputs(i.e., particle properties at the point of impact on thesubstrate) derived from off-line parametric analysis (e.g.,plasma spray, Ref 70 and HVOF spray, Ref 49, 71) as wellas the integration of real-time diagnostics and controlalgorithms in a feedback loop. Current research anddevelopment of online diagnostic and control systems aremainly focused on plasma spray processes, for example,real-time diagnostics and control of particle velocity andtemperature in plasma spray using PID (Ref 72) and usingartificial neural networks and fuzzy logic (Ref 73, 74). Forthe HVOF thermal spray process, a feedback controlsystem is shown in Fig. 12. In such a closed-loop system,the particle information from the online measurementsystem is compared with the desired set point. The dif-ference is sent to the feedback controller, which adjuststhe processing parameters until the difference becomeszero. The development of such a feedback control systemwould require online measurement and diagnostic tech-niques, control-relevant parametric analysis as well ascontroller design and implementation.

A variety of online sensing and diagnostic toolshave been developed for the thermal spray processes todirectly measure gas enthalpy and particle characteristics.

Fig. 11 Simulated microstructure of coatings formed by fully melted particles and particles with mixed melting states (Ref 11)


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For example, DPV-2000 (Tecnar Automation, Saint-Bruno,QC, Canada) is a commercial optical sensing device thatprovides online measurement of individual particle char-acteristics including temperature (1000-4000 C, precision:3%), velocity (5-1200 m/s, precision: 3%) and size(10-300 lm). The working principle of DPV-2000 is basedon two-wavelength pyrometry and a dual-slit opticaldevice (Ref 75). Due to the presence of a photomaskbetween the two slits, a particle passing the measurementvolume will generate a signal with two-peaks. This signal isthen transmitted through an optical fiber bundle to thedetection module, where the light passes through adichroic mirror and two interference band-pass filters(around 790 and 990 nm, respectively) and is then imagedon two photodetectors. The signals from the photodetec-tors are amplified, filtered, and transmitted to the controlmodule where the particle characteristics are calculated.Specifically, the particle velocity is calculated from thedistance between the image of the two slits in the mea-surement volume and the time-of-flight between the twopeaks of the particle signal. The temperature is deducedfrom the ratio of signals from the two photodetectors (orenergies radiated at the two wavelengths) with theassumption that the particles behave as gray bodies. Thediameter is calculated from the signal at one wavelengthafter a calibration procedure. The analysis rate of DPV-2000 can be up to 4000 particles/s, depending on thespraying conditions. If supplemented with CPS-2000, thesensing system is able to characterize cold particles thatare otherwise not detected. The CPS-2000 is a cold par-ticle sensor that employs a diode laser tuned on one of thepyrometers wavelength to characterize the cold particles.Similar techniques have been developed by IdahoNational Laboratory (Ref 76-79). The particle size andvelocity are measured from a laser-particle sizing systemand a dual crossed-beam laser Doppler velocimeter. Thetemperature measurement is also based on the two-colorpyrometry. Both ensemble and single-particle techniquesare available to provide either time-resolved/spatiallyaveraged or spatially resolved/time-averaged information.Oseir Ltd. (Tampere, Finland) also developed a com-mercial product (SprayWatch) that uses a high-speedcharge-coupled device (CCD) camera to measure theparticle velocity and a two-color pyrometer to measure the

particle temperature (Ref 80). This system is able toanalyze particle characteristics of the entire jet when onlythe averaged particle information is provided.

The online diagnostic techniques supplemented withother measurement tools have significantly facilitated thedevelopment of process maps for HVOF process optimi-zation. These experimental investigations studied theeffect of operating parameters including gun type, fueltype, feedstock type and size, combustion pressure, fuel/oxygen ratio, spray distance on the particle temperature,velocity, melting ratio, oxidant content and the resultingcoating microstructure, porosity, hardness, wear abrasion,and corrosion resistance (e.g., Ref 3, 28, 34, 48-50, 61, 62,65, 71, 81-92). The experimental studies have been sup-plemented by CFD modeling efforts (Ref 10-13, 15-21,23), which provide fundamental understanding of the gasdynamics, particle in-flight, and impact. The studies revealthat particle characteristics upon impact on the substrate(i.e., velocity, temperature, and melting degree) are keyparameters that affect coating porosity, bond strength, andresidual stress. To develop a feedback control system forthe HVOF thermal spray process, it is necessary to choosethe processing parameters that can be manipulated in realtime to suppress the variation in these particle character-istics. It is widely acknowledged that the particle velocityand temperature (or melting degree) can be almost inde-pendently regulated by manipulating pressure in thecombustion chamber and the fuel/oxygen ratio (Ref 27,34), respectively. Both of them are functions of the flowrates of fuel and oxygen (the dependence of chamberpressure on gas flow rates is shown in Eq 15). Therefore,the manipulated input can be chosen to be the gas flowrates. The effect of gas flow rates on particle velocity andtemperature is shown in Fig. 13. The baseline conditionsused in the analysis are the recommended processingconditions for WC-Co coatings (Ref 11). When the totalmass flow increases from 50 to 150% of its baseline value,the velocity does not change much but the density in-creases linearly. As a result, the gas momentum flux qv2g

is tripled, which implies a significant increase in the dragforce for particle motion. This is because the drag force isroughly proportional to qv2g if vp vg. [Strictly speaking,the drag force would not increase by as high as three timesbecause of the change in CD. In fact, based on a dragformula CD = (24/Re) (1 + 0.15Re

0.687) valid for Re < 1000(Ref 30), one can derive that FD = (1/2)CDqgAp(vg vp)|vg vp| = 3pldp (vg vp)(1 + 0.15Re0.687). Therefore, thedrag force might be only doubled at most]. However, thegas temperature, difference of which from the particletemperature provides the driving force for particle heat-ing, increases about only 4%. When the total mass flowrate is fixed, the gas temperature varies with the fuel/oxy-gen ratio with an optimal value slightly larger than thestoichiometric value, and a change in the fuel/oxygen ratiowith a fixed total mass flow rate has little effect on the gaspressure as well as on the gas momentum flux. Similarexperimental studies are shown in Fig. 14 (Ref 71). In thecontrol of HVOF spray, it should be noted that the gastemperature varies only about 12-13% in the equivalenceratio range of interest (0.55-1.8; the peak temperature

HVOFPROCESS

DISTURBANCES

INPUT

CONTROLLERMEASUREMENT

SYSTEM

OUTPUT

FINAL CONTROLELEMENT

SET POINT

INFORMATIONDECISION

Fig. 12 A schematic of feedback control of HVOF thermalspray


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occurs at an equivalence ratio of around 1.2, correspondingto a fuel rich condition), which suggests that the window forparticle temperature control in the HVOF thermal spray israther narrow. This is different from the plasma sprayprocess where the particle temperature can be adjusted in awider range by manipulating the torch current (Ref 72).

Based on model predictions and available experimentalobservations, the control problem for the HVOF processis formulated as the one of regulating the volume-basedaverages of velocity and temperature (or melting degree)of particles at impact on the substrate by manipulating theflow rates of fuel and oxygen at the entrance of the HVOFthermal spray gun. The volume-averaged instead ofnumber-averaged particle properties are chosen in thecontrol formulation because large particles contributemore to the coating volume. The information of individualparticle size should be available in order to calculate thevolume-based particle characteristics upon impact. In theabsence of particle size measurements, the control objec-tive could be the number-averaged particle properties,similar to the work of Fincke et al. (Ref 72) in feedbackcontrol of plasma spray. The manipulation of combustionpressure and equivalence ratio is realized by adjusting the

flow rate of fuel, u1 (t), and oxygen, u2 (t). Owing to thealmost decoupled nature of the manipulated input/controlled output pairs, two proportional integral (PI)controllers were proposed in Ref 27 and 47 to regulate theprocess. Specifically, the controllers have the followingform:

_fi yspi yi; fi0 0; i 1;2

u0i Kci yspi yi 1

scifi

u00i ; i 1;2

u1;u2f g f u01;u02

Eq 29

where yspi is the desired set-point value and yi is the valueof the output obtained from the measurement system (y1is the volume-based average of particle velocity, and y2 isthe volume-based average of particle temperature ormelting degree), u01 is the combustion pressure and u

02 is

the equivalence ratio. f is the mapping between the flowrates and the chamber pressure as well as the equivalenceratio. Kci is the proportional gain and sci is the integraltime constant. If the gas phase measurement is available, amodel-based scheme can be used to estimate the particleproperties through the dynamic particle in-flight model

0.5 1 1.50.4

0.6

0.8

1

1.2

1.4

1.6

Total mass flow rate (m/m(a) (b)bl)

Gas

pro

perti

es a

t noz

zle th

roat

(gp/g

p bl)

pressuredensitytemperaturevelocitymolecular weightmomentum flux

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Equivalence ratio /bl

Gas

pro

perti

es a

t noz

zle th

roat

(gp/g

p bl)

pressuredensitytemperaturevelocitymolecular weightmomentum flux

Fig. 13 Influence of (a) total mass flow rate and (b) equivalence ratio on the gas properties at the throat of the nozzle. Normalized basedon a baseline condition (Ref 37)

Fig. 14 (a) Velocity and (b) temperature of aluminum particles as a function of total mass flow rate and fuel/oxygen ratio using PraxairHV-2000 spray gun with propylene as the fuel (Ref 71)


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(Ref 93). Interested readers may also refer to literature forthe design of model-based feedback control systemsemploying nonlinear control techniques for various par-ticulate processes (Ref 94-100).

Closed-loop simulations under the control scheme ofEq 29 have been carried out to demonstrate the effec-tiveness of the proposed control formulation (Ref 37). It isassumed in the computer simulation that the responses ofgas and particle dynamics to the change of gas flow ratesare very fast, which is reasonable for such a supersonicflow. With this simplification, it has been demonstratedthat the feedback controllers are very effective withrespect to set-point changes in both particle velocity andtemperature (i.e., 5% increase in both particle velocityand melting degree). As seen in Fig. 15, both the flowrates of oxygen and fuel increase in order to have a higherparticle velocity. However, the temperature increases andexceeds its desired value because of the increased cham-ber pressure. As a result, the changing rate of oxygen flowbecomes slower than that of fuel after a short time, whichlowers the equivalence ratio and drives the temperaturedown to its set point. Figure 16 demonstrates the responseof the feedback controller in order to maintain the sameparticle velocity and temperature levels in the presence ofa 10% decrease in the spray distance (process distur-bance). The particle velocity does not change much while

the particle temperature increases significantly. Underfeedback control, the manipulated inputs drive the processoutputs to their original steady-state values in 10 s, whichdemonstrates the robustness of the controller.

4. Concluding Remarks

The HVOF thermal spray is an enabling technique forthe processing of functional coatings. Mathematical mod-eling has been an excellent complement to experimentalstudies to provide systematic understanding of the under-lying physics of the process and to enhance coating perfor-mance through optimized system design and operation.However, detailed model development is still needed insome areas, for example, the oxidation, melting, and solid-ification of particles during flight, deformation of partiallymelted and unmelted particles, and its effect on coatingmicrostructure evolution and residual stress, especiallywhen the particles are of irregular shape (which is commonin the processing of nanostructured particles). Furthermodeling efforts should also include the validation andrefining of mathematical models to better match experi-mental measurements (e.g., gas-particle heat transferaccounting for viscous dissipation).

Time (s)(a) (b)

Part

icle

mel

ting

ratio

0.46

0.48

0.5

0.52

melting ratio

Part

icle

vel

ocity

(m/s)

0 5 10 15 20 25 30440

450

460

470

480

velocity

Time (s)

Oxy

gen

flow

rate

(scfh

)

0 10 20 30560

640

720

800

880

oxygen

Prop

ylen

e flo

w ra

te (s

cfh)

165

180

195

210

225

propylene

Fig. 15 Profiles of (a) controlled outputs (average particle velocity and melting ratio) and (b) manipulated inputs (flow rates ofpropylene and oxygen) under the request of 5% increase in particle velocity and 5% increase in melting ratio (Ref 37)

Time (s)(a) (b)

Part

icle

mel

ting

ratio

0 5 10 15 20 25 300.46

0.48

0.5

melting ratio

Part

icle

vel

ocity

(m/s)

449

449.5

450

450.5

velocity

Time (s)

Oxy

gen

flow

rate

(scfh

)

200 10 30560

580

600

620

640

oxygen

Prop

ylen

e flo

w ra

te (s

cfh)

173

174

175

176

177

propylene

Fig. 16 Profiles of (a) controlled outputs (average particle velocity and melting ratio) and (b) manipulated inputs (flow rates ofpropylene and oxygen) in the presence of 10% decrease in spray distance (Ref 37)


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In addition to modeling, feedback control systems havebeen designed in which the particle velocity and temper-ature are controlled by adjusting the flow rates of oxygenand fuel, and their effectiveness and robustness have beentested through computer simulations. Further researchefforts should focus on the development of a demonstra-tion prototype by integrating real-time diagnostics andfeedback control systems in an experimental HVOFthermal spray process.

Acknowledgment

Financial support from NSF and ONR is gratefullyacknowledged.

Open Access

This article is distributed under the terms of the Cre-ative Commons Attribution Noncommercial Licensewhich permits any noncommercial use, distribution, andreproduction in any medium, provided the originalauthor(s) and source are credited.

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97. A. Kalani and P.D. Christofides, Simulation, Estimation andControl of Size Distribution in Aerosol Processes with Simulta-neous Reaction, Nucleation, Condensation and Coagulation,Comput. Chem. Eng., 2002, 26, p 1153-1169

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