review of modeling of liquid precursor peer reviewed ... · liquid precursors and particles into...

Review of Modeling of Liquid PrecursorDroplets and Particles Injected into Plasmas

and High-Velocity Oxy-Fuel (HVOF) FlameJets for Thermal Spray Deposition

ApplicationsBaki M. Cetegen and Saptarshi Basu

(Submitted May 14, 2009; in revised form June 16, 2009)

This article presents a review of the current state-of-the-art in modeling of liquid chemical precursordroplets and particles injected into high-temperature jets in the form of DC-arc plasmas and high-velocity oxy-fuel flames to form coatings. Conventional thermal spray processes have typically utilizedpowders that are melted and deposited as a coating on hardware surfaces. However, production ofcoatings utilizing liquid precursors has emerged in the last decade as a viable alternative to powderdeposition. Use of liquid precursors has advantages over powder in terms of their relative ease of feedingand tailoring of chemical compositions. In this article, we review the modeling approaches to injection ofliquid precursors and particles into plasmas and high-velocity oxy-fuel flames. Modeling approaches forthe high-temperature DC-arc plasma and oxy-fuel flame jets are first reviewed. This is followed by theliquid spray and droplet level models of the liquid precursors injected into these high-temperature jets.The various knowledge gaps in detailed modeling are identified and possible research directions aresuggested in certain areas.

Keywords HVOF coatings, HVOF process, plasma sprayforming, spray deposition, TS coating process

1. Introduction

Production of high-value materials in the form ofpowders and thin coatings is a large multibillion dollarsmanufacturing enterprise around the world. Specificfunctional materials have been synthesized by differentprocesses including spray drying and pyrolysis (Ref 1) aswell as combustion and plasma processing (Ref 2). Amongthe different processing techniques, plasma and high-velocity oxy-fuel (HVOF) flame jet techniques (Ref 2)have been successfully employed for generation of high-value protective coatings on hardware components such asthermal barrier coatings on gas turbine blades and corro-sion and wear resistant coatings in other applications. Inall these, a powder of the coating material is typicallyheated in a plasma or HVOF flame jet to deposit partiallyor fully molten particles onto a substrate forming a thincoating (Ref 2). The velocity and temperatures generated

by DC-arc plasma and HVOF flame systems span differ-ent ranges and therefore each system is appropriate fordifferent applications. DC-arc systems create plasma jetsthat have nozzle exit velocities of several hundred metersper second and gas temperatures exceeding 10000 K. Onthe other hand, HVOF systems produce supersonic gasspeeds at the nozzle exit of several kilometers per secondand temperatures between 4000 and 6000 K depending onthe fuel and oxidizer used.

An alternate route to the typically employed powderinjection process into a plasma or HVOF jet is the injectionof a liquid spray composed of droplets containing the dis-solved salts of the materials to be deposited (Ref 3-6). Inthis case, droplets injected into a high-temperature plasmaor HVOF environment vaporize and concentrate the saltsolutes followed by heterogeneous and/or homogeneousnucleation of solid intermediates, their chemical transfor-mations and melting before deposition on a substrate sur-face. This in situ processing of liquid precursor containingdroplets in a high-temperature environment criticallydetermines not only the chemical make-up of the generatedcoatings but also its microstructural characteristicsdepending on the thermal, chemical and physical processesthat occur at the droplet scale. For example, depending onthe heating rate of droplets and the nature of precipitationduring heat-up and vaporization phases, different particlemorphologies can be obtained including solid particles,hollow shells, and fragmented shells as schematicallyshown in Fig. 1. When droplets are small and the solutediffusivity is high, increase of solute concentration occurs

Baki M. Cetegen, Mechanical Engineering Department, Univer-sity of Connecticut, Storrs, CT 06269-3139; and SaptarshiBasu, Mechanical, Materials and Aerospace Engineering,University of Central Florida, Orlando, FL 32816. Contacte-mail: [email protected].

JTTEE5 18:769–793

DOI: 10.1007/s11666-009-9365-7

1059-9630/$19.00 � ASM International

Journal of Thermal Spray Technology Volume 18(5-6) Mid-December 2009—769

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uniformly throughout the droplet, leading to volumetricprecipitation and consequently forming solid particles asshown as path (A) in Fig. 1. When rapid vaporizationoccurs on the droplet surface and the solute diffusivity islow such that a high solute concentration builds up aroundthe droplet periphery, as shown in path B in Fig. 1, therecould be different outcomes including fragmented shells(B-I) as a result of internal pressurization for low vaporpermeability through the formed shell, hollow sphericalshells (B-II) for the case of high permeability through theshell, or rapid disintegration of the shell containing some ofthe liquid leading to secondary atomization (B-III) as aresult of rapid internal pressurization and shell rupture.Another path is that of formation of a plastic shell thatinflates due to internal liquid vaporization and eventualrupture and collapse of the deformed shell (path C in

Fig. 1). The morphology of the formed deposits and coatingmicrostructure is naturally affected by the produced par-ticle morphologies and their impact conditions that formthe coating. In this review article, we first survey themodeling studies on DC-arc plasmas and HVOF jets. Thisis followed by presentation of particle and droplet levelmodels, precursor chemistries and precipitation kinetics aswell as some results from previous modeling studies.

2. Thermo-Fluid Modeling of DC-ArcPlasmas

DC-arc plasmas employed in thermal spray applica-tions (Ref 2) utilize a continuous arc break-down in a gasmixture flowing between the anode and cathode of a

Nomenclature

Apore total area of the pores

a,b stoichiometric coefficients in Eq 5

Bi Biot number

CD drag coefficient

Cp,d specific heat

d diameter of the droplets

D12 mass diffusivity of the vapor phase into plasma

Ds mass diffusivity of zirconium acetate into water

e internal energy

Gk turbulence kinetic energy generation due to mean

velocity gradient

h heat transfer coefficient

hlv latent heat of vaporization for liquid

H total enthalpy

Ji species mass flux vector

JT heat flux vector

k thermal vector conductivity

Kn Knudsen number, k/d

Le Lewis number, Le = a/D

_m mass flow rate at the droplet surface due to

vaporization

P pressure

Pe Peclet number

pv vapor pressure inside the solid shell

p1 pressure outside the droplet

Pr Prandtl number, Pr = m/a_Qc conduction heat flux_Qr radiation heat flux_QL heat transfer rate into the droplet surface

rs instantaneous outer radius of the droplet

�rs nondimensional radius of the droplet, �rs ¼ rs=r0

R universal gas constant

Red Reynolds number based on droplet radius and

relative velocity between the plasma and droplet

M Mach number

Nu Nusselt number

t time

T temperature�T nondimensional temperature, �T ¼ ðT � T0Þ=T0

u gas or plasma velocity in the x direction

u velocity vector

U axial velocity of the droplet

U1 axial plasma velocity

Td droplet temperature

rl radius of the liquid core

b non-dimensional surface regression rate = b ¼ 12

d�rs

dsv gas or plasma velocity in the y direction

Vpore velocity of vapor venting through the pore�Vr; �Vh liquid phase velocities within droplet

d thickness of the shell

@ differential operator

r gradient operator

v mass fraction in the before precipitation regime

vs mass fraction in the liquid core after precipitation

regime

�v nondimensional mass fraction, �v ¼ ðv� v0Þ=v0

g nondimensional radial coordinate, g ¼ r=rsm kinematic viscosity

c ratio of specific heats in Eq 13-18

l dynamic viscosity

q density

s nondimensional time, s ¼ aLt=r20

k mean free path of gas molecules, ak

ak, ae inverse effective Prandtl number for k and erespectively

n flattening factor

h spherical polar angle in droplet coordinates

Subscripts

0 initial value

0 total property in Eq 13-15

l, L liquid phase

v vapor phase

¥ far field

p particle

g gas phase

s splat or surface

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

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plasma generator as schematically shown in Fig. 2. Ionizedgases from the feed gas stream (Ar, He, N2, H2 mixtures)emerge from a plasma nozzle assembly at high velocitiesof the order of several hundred meters per second andtemperatures exceeding 10000 K (Ref 7). Modeling ofthese high-temperature gases containing ionized andneutral species and electrons constitutes a very challeng-ing task. Literature contains significant amount of work onthermo-fluid modeling of DC-arc plasmas (Ref 8-25). Thedetailed simulations include numerical solution of thechemically reacting flow (Navier-Stokes) equationsincluding the charged species. These equations includeconservation of mass, momentum and species with speci-fied chemical source terms and closure equations. Turbu-lence is accounted for by k-e or other subgrid models. Thegoverning equations take the following forms:

Continuity:@ðxnqÞ@t

þr � ðxnquÞ ¼ 0 ðEq 1Þ

Species:@ðxnqiÞ@t

þr � ðxnqiuÞ ¼ �r � ðxnJiÞ þ xn _qci

ðEq 2Þ

Momentum:@ðxnquÞ@t

þr � ðxnquuÞ

¼ �r pþ 2

3qk

� �þr � r (Eq 3)

Energy:@ðxnqeÞ@t

þr � ðxnqueÞ ¼ � prðxnuÞ � r � ðxnJTÞ

þ xnðUþ _Qc � _QrÞðEq 4Þ

In these equations, n = 0 for two and three dimensions inCartesian coordinates and n = 1 for two-dimensional axi-symmetric configuration with x representing the radialcoordinate. The symbols used in these equations aredefined in the nomenclature. These equations are sup-plemented by the reaction rates of the type,

Xr

arRr $X

p

bpPp ðEq 5Þ

with each reaction having a specified reaction rate thatdetermines the species production/depletion rates _qc

i .Typically the kinetic reaction rates are specified inArrhenius form and fast reactions are considered to be inequilibrium while the slower reactions proceed at theirkinetic rates. The system of equations is closed by speci-fying the diffusion fluxes for mass (Ji) and heat JTð Þ:Radiative losses are modeled as a temperature dependentenergy sink. Solution of the system of equations has beenimplemented in computational codes such as LAVA(Ref 8, 9). Figure 3 shows some results from Ramshawand Chang (Ref 8) on the radial and axial distributions ofplasma temperature for an axisymmetric Argon plasmaissuing into a room temperature Argon medium. In thisstudy, the computed temperature profiles were found tobe in reasonable agreement with the experiments per-formed by Dilawari et al. (Ref 10) at Idaho Nationallaboratories. One of the issues in comparisons of modelpredictions with experiments is the application of theappropriate boundary conditions in the model. Often,experiments do not provide sufficiently detailed inletmeasurements of velocities, temperatures, densities andspecies distributions (neutrals, ions and electrons) toprovide well-defined inlet conditions for the model. This is

Fig. 1 Solute containing droplet vaporization and precipitation routes: (A) uniform concentration of solute and volume precipitationleading to solid particles; (B) supersaturation near the surface followed by (I) fragmented shell formation (low permeability through theshell, (II) unfragmented shell formation (high permeability), (III) impermeable shell formation, internal heating, pressurization andsubsequent shell break-up and secondary atomization from the internal liquid; (C) elastic shell formation, inflation and deflation by solidsconsolidation


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not due to the lack of interest in measuring theseparameters, but the difficulty or inability of obtaining suchdata from experiments. One of the assumptions in many ofthe plasma simulations is the existence of local thermo-dynamic equilibrium (LTE) which simplifies the plasmathermal field description. In atmospheric pressure DC-arcplasmas that are typically employed in thermal sprayapplications, the justification for LTE has been made (Ref7). However, nonequilibrium effects have been alsostudied by Chang and Ramshaw (Ref 9) which show thatLTE approximation can break down under certain con-ditions and in some regions of a plasma jet.

Another issue with DC-arc plasma simulations is thearc root fluctuations creating unsteadiness at the plasmajet origin. These fluctuations with frequencies in the rangeof several kilohertz have been experimentally observedand modeled (Ref 11-13), an example of which is shown inFig. 4 from Ref 13. Complex inner geometry of DC-arcplasma chambers and the presence of an electrical arcwithin this chamber necessitate the injection of thermal

spray materials (powders or sprays) external to the plasmachamber. Typically, a droplet or particle laden jet of somecarrier gas is directed normal to the plasma jet axis inorder for the material to be entrained into the high-temperature plasma. This injection scheme naturallydistorts the axisymmetry of the plasma jet and inducesthree-dimensional effects. Li and Chen (Ref 16) modeledthe three-dimensional field of an Argon plasma jet andshowed that the carrier gas jet results in displacement ofthe plasma jet centerline from the axis with increasingcarrier jet velocity. Although the plasma temperaturedistributions do not seem to be greatly affected, the cal-culated particle temperature histories and their distribu-tions show significant variations. The radial location of theinjector with respect to the plasma jet orifice has beenshown to be a critical parameter in addition to the carriergas to plasma stream momentum ratio.

Simultaneous solution of the plasma flow field in thepresence of droplets is not feasible and typically plasmaflow field is first computed and the particle/droplet

Fig. 2 Internal geometry of a DC-arc plasma torch (from Sulzer Metco)

Fig. 3 Computed and measured plasma temperature profiles from Ref 8: (a) axial profile; (b) radial profile


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interaction is considered as a separate discrete phaseLagrangian model utilizing the plasma temperatures,velocities and plasma properties. This approach usuallyneglects the two-way coupling between the plasma gas andthe droplet liquid phases (i.e. influence of the discretephase on the plasma gas field) and only considers theinfluence of the plasma flow field on the injected particles/droplets. Literature contains a number of studies that dealwith the prediction of particle temperatures in plasmas(Ref 15-25). In many of these studies, the particle heattransfer is formulated in terms of heat conduction poten-tial and a temperature slip between particle and plasmagas. For small particles, the Knudsen number Kn = k/d,where k is the mean free path distance for gas moleculesand d is the particle diameter, could be large enough forthe continuum approximation for heat transfer not to holdtrue (i.e. Kn ‡ 1). In these situations, particle heat transfercalculations have to incorporate the slip flow and freemolecular flow regimes as appropriate. All computationsdeal with spherical particle heat up, melting and eventualvaporization and particles injected into the plasma takedifferent paths and consequently follow different tem-perature histories (Ref 23, 24). Depending on the materialparticles are composed of and the convective heat transferconditions, the Biot number Bi = hd/kp, where h is theconvective heat transfer coefficient, d is the particlediameter and kp is the particle thermal conductivity,determines the importance of the temperature gradientsinternal to the particle. In cases where Bi is small, theparticle internal temperature gradients are small andlumped capacity heat transfer analysis becomes appro-priate. When Bi > 0.1, the particle internal temperaturefield needs to be considered as a part of the computations.Effects of particle-particle interactions have also beenconsidered and quantified. A general modeling approachthat has been used in the field is schematically shown inFig. 5. It includes the modeling of gas dynamics of thethermal spray torch followed by predictions of dropletbreakup, droplet or particle transport (momentum, mass,

heat) processes and finally models of particle depositionand coating formation.

3. Thermo-Fluid Modeling of High-Temperature Oxy-Fuel Flame Jets

HVOF flame process has been used as a primarymethod for generating metallic and in some cases ceramiccoatings in industrial applications. It has evolved as animproved method to modify surface properties enhancingthe product life, durability, thermal resistance and corro-sion resistance. Different industries such as aerospace,power generation and automotive are heavily dependenton HVOF thermal spray processes to generate functionalcoatings. Coatings produced by oxy-fuel spraying aretypically dense coatings. HVOF process is normally usedfor generating coatings with lower melting temperature,like WC-Co, Cr3C2-NiCr etc. (Ref 26). Wear resistantcoatings using tungsten carbide, cobalt or nickel basedmaterials are some common applications of HVOF pro-cess (Ref 27, 28). Because of its relatively low tempera-ture, HVOF process is rarely used for ceramic coatingapplication (Ref 26). There are however some exceptionswhere certain types of HVOF systems such as HV2000have been used for thermal barrier coating application.

Different designs of the HVOF torches have been usedin industry, although the core technology is similar in allcases. Figure 6 (Ref 29) shows a schematic of a HVOFtorch. It consists of a unit that incorporates a combustionchamber and a converging-diverging nozzle for acceler-ating the combustion products to supersonic speeds. Thecombustion process takes place inside the torch. The torchhouses three annular ports for injecting powder, fuel-oxygen mixture and air. Coating materials are injected inthe form of powder with a carrier gas (generally N2)through an axial inlet port. A water cooled jacket sur-rounds the nozzle to protect the torch from overheating.

Fig. 4 Arc and plasma jet dynamics: sequence of instantaneous heavy particle temperature distribution obtained numerically (num) andexperimentally (exp). Time intervals between frames is 100 ls for numerical results and 2 ms in the experiments from Ref 13


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Premixed fuel and oxygen are supplied into the HVOFcombustion chamber. In industry different types of HVOFtorches are used. Few of the commonly used torches areHV2000, JP-5000 by Praxair and Diamond Jet hybridtorch by Sulzer Metco. There are also different types offuels used for the HVOF process. Among gaseous fuels,propylene (C3H6) is the most common variety while ker-osene is preferred by many industries as an alternativeliquid fuel. Hydrogen has also been used in cases wherehigh temperatures and carbon free deposits are desired.

Depending on the applications, materials are injectedeither in the form of liquid precursors or in the form ofsolid particles. For ceramic coatings, generally solutionprecursor is preferred. In this case, liquid precursors areinjected as a spray of small droplets into the high-velocitycombustion gases. The droplet injectors are usually placedoutside the torch or very close to nozzle exit. In some

cases, liquid may be injected as a stream which undergoesbreakup into droplets in the high shear turbulent flow fieldof the HVOF jet. For metallic coatings, normally powderinjection is preferred. Powders containing micron-sizemetal or metal-alloy particles are injected into the torch.The quality and density of produced coatings depend ontemperatures and velocities that particles or dropletsattain before impacting on a substrate. It is important tonote that the particle/droplet temperature and velocity aredependent on fuel-oxygen ratio, mass flow rates of gasesas well as the powder/precursor type, injection location,spray distance, size and residence time of the particles ordroplets. As shown in Fig. 7 (Ref 29), there are multitudeof processes that ultimately affect the coating qualityincluding the dynamics of the HVOF jet. We will firstdiscuss the modeling of gas dynamics in an HVOF torch.The modeling of the HVOF gas dynamics includes heat,mass and momentum transport and combustion processes.The pre-mixed fuel and oxygen are injected into thecombustion chamber. The HVOF process is a multi-phaseprocess which involves discrete phase (particles or drop-lets) interacting with the continuum gas phase. Though gasdynamics and the particle dynamics influence each other,the particle effects on the gas phase are typicallyneglected. Particle loadings less than 4% by volume havebeen determined not to substantially affect the gasdynamics. Thus, the modeling typically considers onlyone-way coupling of the gas flow affecting the particles.

The modeling of combustion process within the torchcan be dealt with at different levels. The simplest modelassumes that the combustion of the fuel and oxidizer iscomplete and reaches chemical equilibrium. A moredetailed approach includes the overall chemical reactionrate between fuel and oxidizer and the corresponding heatrelease rate. A more comprehensive approach involvesmore detailed modeling of combustion process by areduced chemical kinetic mechanism. In thermal sprayprocess modeling, a computational approach that capturesthe gas composition, thermal and flow fields in a suffi-ciently accurate manner is adequate as computation ofdetailed gas species distributions may not add much to theaccuracy of the particle heat-up results.

Fig. 5 Modeling steps for thermal spray process utilizing solidor liquid feedstock

Fig. 6 Schematic of diamond jet hybrid HVOF process (Ref 29)


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The governing equations for gas phase modelinginclude mass, momentum [Compressible Navier Stokes]and energy conservation. However, the highly turbulentnature of the flow and consequently its high Reynoldsnumber make direct numerical simulation intractable.Therefore, turbulence closure models along with Reynoldsor Favre averaged governing equations are employed toobtain time averaged results and relevant flow statistics.The Reynolds averaging for any variable (like velocity,

temperature) is formulated as (Ref 30), / ¼ �/þ /0;

with �/ ¼ 1Dt

R t0þDt

t0/ dt and �/0 ¼ 0: On the other hand,

Favre average is formulated in a slightly different way as,

/ ¼ ~/þ /00;with ~/ ¼ q/�q and ~/00 ¼ 0: After incorporating

the time averaged quantities, the governing equationsreduce to (Ref 30),

Continuity

@�q@tþ @

@xið�q~viÞ ¼ 0 ðEq 6Þ

and momentum equation:

@ð�q~vjÞ@tþ @

@xið�q~vj~viÞ ¼ �

@�q@xjþ @

@xil@~vj

@xiþ @~vi

@xj� 2

3dji@~vl

@xl

� ��

þ @

@xi�qv00i v00j

� �j ¼ 1; 2; 3 (Eq 7)

where P, q and l are pressure, density and molecularviscosity of the gases. xi is the coordinate and the term�qv00i v00j is the Reynolds stress term indicating the effect ofturbulence. Closure of the Reynolds stress terms is takeninto account by considering RNG k-e model. Theseequations are generally of the form (Ref 30)

@ð�qkÞ@tþ @

@xið�q~vikÞ ¼

@

@xiakðlþ ltÞ

@k

@xi

� �þGk � �qe� YM

ðEq 8Þ

and

@ð�qeÞ@tþ @

@xið�q~vieÞ ¼

@

@xiaeðlþ ltÞ

@e@xi

� �þC1e

ek

Gk

�C2e�qe2

k�Re (Eq 9)

where e represents the turbulence dissipation, Gk desig-nates the generation of turbulence kinetic energy due tomean velocity gradient, YM models the effect of fluctua-tion dilatation to global dissipation, Re is the additionalterm in Eq 9 responsible for accuracy of the model inhighly strained flow field. ak and ae are inverse effectivePrandtl number for k and e, respectively.

For reacting flows as in HVOF, mass conservation ofthe each species can be written as (Ref 30),

@ð�qYjÞ@t

þ @

@xið�qYj~viÞ ¼ �

@

@xiJj

� �þ Rj

j ¼ 1; 2; 3 . . . N � 1 (Eq 10)

Ji is the diffusion flux of ith species calculated by Maxwell-Stefan equation and N is total number of species involvedin the process. Rj is the rate of production of species ‘‘j’’.The energy equation can be formulated as (Ref 30),

@ð�qHÞ@t

þ @

@xj½~vjð�qH þ �pÞ�

¼ @

@xi

"acpðlþ ltÞ

@T

@xiþ ~vjðlþ ltÞ

@~vi

@xjþ @

~vj

@xi� 2

3dji@~vl

@xl

� �

�XN

j¼1

JjHj

#þ SE (Eq 11)

where T is the temperature and H is total enthalpy, SE

stands for source terms like heat generation. The totalenthalpy can be defined as (Ref 30)

H ¼X

j

YjHj: ðEq 12Þ

The computational time increases significantly withincrease in number of species. Many studies hence haveimplemented the eddy dissipation model to simplify theproblem. Eddy dissipation model assumes infinitely fastreaction process and the reaction rate is limited by tur-bulent mixing rate of fuel and oxidants. With the eddydissipation model, proper analysis of Arrhenius rate is notrequired. In general, considering the length of the com-bustion section, the residence time for combustion process

Fig. 7 Processes in an HVOF torch (Ref 29)


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is sufficiently long to achieve chemical equilibrium(Ref 30).

To simplify computational analysis, some studies con-sider only the expansion of hot combustion gases throughthe torch which can be modeled by considering ideal gasand isentropic relations. The primary equations in thiscase are (Ref 31),

P0

P¼ 1þ 1

2ðc� 1ÞM2

� � cc�1

ðEq 13Þ

q0

q¼ 1þ 1

2ðc� 1ÞM2

� � 1c�1

ðEq 14Þ

T0

T¼ 1þ 1

2ðc� 1ÞM2

� �ðEq 15Þ

where P, T and q are pressure, temperature and density,respectively. Subscript ‘‘0’’ denotes stagnation conditionsand c is specific heat ratio. The velocity of the gas phase(v) can be calculated by considering local Mach number(M) from

v ¼M cP=q½ �1=2 ðEq 16Þ

The Mach number (M) can be found using area ratio. Thisequation takes the form (Ref 31),

A1

A2¼M2

M1

1þ 12ðc� 1ÞM2

1

1þ 12ðc� 1ÞM2

2

" #ðcþ 1Þ=2ðc� 1ÞðEq 17Þ

where A1 and A2 are cross-sectional area of two points andcorresponding Mach numbers are M1 and M2. The massflow rate of the gas can be calculated using the equation(Ref 31),

_mg ¼P0ffiffiffiffiffiffiT0

p At c�Mpr

R:

2

ðc� 1Þ

� � cþ1c�1ð Þ

" #1=2

ðEq 18Þ

Here, �Mpr is average molecular weight of the gas phaseand R is the universal gas constant. At is the throat area ofthe torch (Ref 31).

Depending on the equivalence ratio of fuel and oxygenmixture, the product gases attain a high temperature(Ref 32). In case of gaseous fuel like propylene, the com-plete global chemical reaction can be written as, C3H6 +4.5O2 = 3CO2 + 3H2O. At high temperatures attained inoxy-fuel combustion, significant dissociation of species canoccur and chemical equilibrium composition contains spe-cies other than the complete combustion products. Figure 8shows the adiabatic flame temperature variation as afunction of mixture equivalence ratio (fuel-oxygen ratiodivided by the stoichiometric fuel-oxygen ratio) at threedifferent mixture pressures. It is found that the peak tem-peratures are shifted slightly to fuel-rich conditions andtemperatures increase with higher chamber pressures.

Depending on the torch design, Mach number of thegas flow can reach up to 2 at the exit plane of the nozzle.Different types of nozzles can be operated at differentpressure ratios making the emerging gas jet over-expanded, expansion matched or under-expanded (Ref 27).

After exiting the nozzle, the gas expands in the atmo-sphere entraining stagnant ambient air. Depending on thecontrol parameters like mass flow rate and torch design,shock diamonds may or may not be present inside oroutside the nozzle.

Hassan et al. (Ref 33) presented a three-dimensionalgas dynamics model of HVOF process. In this work, theauthors used a 3D computational model to analyze thegas dynamics of a Metco Diamond Jet rotating wire torch.The dimensions of the torch are shown in Fig. 9. Com-mercial CFD code (CFD-Ace) was used to solve a pres-sure-based Favre-averaged Navier-Stokes equations topredict the gas flow field with k-e model for turbulenceclosure. The combustion modeling used an approximate,one-dimensional equilibrium chemistry code to formulatea single step reaction of propylene and calculation ofequilibrium composition. From the reported results, itwas found that the temperature of the combustionchamber reaches as high as 3150 K. The Mach numbercontour plots suggest that near the sharp corner of thetorch, flow separation occurs, while near the axis of the

Fig. 8 Computed chemical equilibrium temperatures forpropylene-oxygen combustion (Ref 45)

Fig. 9 Schematic of the interior of the three-dimensionalHVOF thermal spray torch (Ref 33)


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flow field, Mach number increases to as high as 1.3.Figure 10 shows the temperature profile outside thenozzle. The temperature of the flow field exhibits decayafter the nozzle exit. The gas issuing out of the nozzleexpands through a series of shock waves known as shockdiamonds. The entrainment of surrounding air ensuresmixing of hot gases with cold atmosphere, resulting in arapid decay of velocity and temperature of the gases.Though the maximum temperature of the gases at the exitof the nozzle is around 2500 K, it cools down to 900 K atthe substrate location.

Among others, Gu et al. (Ref 32) also presented acomprehensive CFD model of the gas phase. In thiswork, the authors used a 2D computational model tostudy the gas dynamics phenomena involved in theHVOF coating processes. The model assumes a steadystate, highly turbulent, fully compressible, high speedflow following combustion in the chamber. The keyobjective of the model was to analyze the effect ofequivalence ratio on the gas dynamics of the combustionproducts. Initially, the model reported a baseline casewith flow rates values of 150, 555 and 35 scfh respectivelyfor fuel (C3H8), O2 and carrier gas (N2). The inlet tem-perature was considered to be 288 K. Under this baselinecondition, the flow had an equivalence ratio of 0.8making the flame fuel-lean. The streamlines of the gasphase inside the combustion chamber depict that the gastends to flow from the wall toward the center of thetorch and subsequently accelerate toward the nozzle. Theisotherms within the combustion chamber show thatthe temperature increases to as high as 3180 K. Theisotherms also confirm that the highest temperaturezones are centered near the fuel/oxygen inlet while thepowders and carrier gas remain in comparatively coolerzone. Figure 11 (Ref 32) represents the iso-Mach numbercontours from the exit of the nozzle, which is marked asx = 0 in the figure. It shows that the flow is under-expanded. Simulation also predicted few shock waves,downstream of the nozzle. The authors systematicallyvaried the gas flow rates and equivalence ratio tounderstand the effect of these parameters on the gasdynamics. The simulations showed that for constant gas

flow rate, the maximum temperature attained by thecombustion products changes with equivalence ratio.Globally the results also depicted that with higher gasflow rate the temperature also increases. Figures 12 and13 (Ref 32) show temperature and velocity profiles alongthe centerline for different flow conditions of air-fuelratios with total flow rates indicated in parentheses. Itappears that the flow rates do not have much effect onthe centerline temperature and velocity. However, themaximum velocity was attained for the condition corre-sponding to the highest gas flow rate and fuel-rich flame.On the other hand, with lowest gas flow rate and leanestflame, lowest velocity was attained. Pressure profile alongthe centerline for different flow conditions shows thatwithin the nozzle, the pressure is as high as 2 to 3 atm,which indicates the need of pressurized feeding of pow-ders. At the exit of the nozzle, the pressure is around5 9 104 Pa above atmospheric, suggesting that the flow isunder-expanded. It was also noticed that the pressureincreases with increase in gas flow rate. However, thechange in equivalence ratio did not have much effect onthe pressure field.

The authors (Ref 32) also performed a study on theeffect of torch design on the gas-dynamics. The simula-tions showed that with shorter span of combustion

Fig. 10 Gas temperature contour in the plane of symmetry of the aircap and exterior (Ref 33)

Fig. 11 Iso Mach number lines at the downstream of nozzle.X = 0 corresponds nozzle exit (Ref 32)


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chamber, the particles have shorter time to accelerate,which will result in longer residence time. Although thegas temperature decreases slightly with shorter combus-tion chamber length, the slow moving particles tend to beheated for longer time, increasing the possibility of oxi-dation before reaching the substrate.

4. Modeling of Particle or Droplet Heat-up

Once the thermal and flow fields of a DC-arc plasma orHVOF jet are computed, these results can be utilized todetermine particle or droplet heat-up behavior. In the caseof particle injection, the particles attain different velocitiesand temperatures before impacting on a substratedepending on the particle loading rate, injection location,

particle properties, size distribution and effects of turbu-lent transport. In case of solution precursor droplets, thedroplets undergo precipitation and shell formation fol-lowed by shell rupture as described earlier. Eventuallydepending on the initial droplet size and concentration ofsolute in the droplet, they become fully pyrolized orremain in un-pyrolized condition.

In this study, it is realized that the aerodynamic pro-cesses of very short timescale have already produceddroplets of stable sizes that will not undergo further break-up. All the droplets introduced into the plasma undergorapid heating resulting in solvent vaporization andincreased concentration of solute near the droplet surface.At a critical value of solute concentration, precipitationoccurs, resulting in the formation of a solid shell aroundthe liquid core. The precipitation leading to shell forma-tion is assumed to be instantaneous based on the super-saturation concentration value of the solute based on theliterature data (Ref 34, 35). The binary (solute + solvent)droplets are assumed to be injected axially or transverselyinto a high-temperature plasma jet where solvent portionof the droplet vaporizes with simultaneous reduction indroplet size and increase in the solute concentration. Thedroplets are assumed to be composed of precursor (solute)dissolved in a solvent with a prescribed initial precursormass fraction. Droplet motion in the hot convective gasenvironment is governed by the droplet momentumequation given by (Ref 36, 37),

@U

@t¼ 3CD

8rs

q1qL

U1 �Uj j U1 �Uð Þ ðEq 19Þ

@V

@t¼ 3CD

8rs

q1qL

V2 ðEq 20Þ

where U, V are the droplet velocities in x and y directions,CD is the drag coefficient due to the relative motion

Fig. 12 Variation of gas temperature with distance along the centerline (symmetry axis) of the computational domain for different gasratio at flow rates of 590 and 705 scfh (Ref 32)

Fig. 13 Variation of gas velocity with distance along the cen-terline (symmetry axis) of the computational domain for gasratios, shown at flow rates of 590 and 705 scfh (Ref 32)


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between the droplet and the surrounding hot gases withU¥ being the streamwise local plasma flow velocity. Thechange in the droplet radius is given by,

drsdt¼ � _m

4pqLr2s

ðEq 21Þ

where _m is the mass rate of vaporization, qL is the liquiddensity and rs is the radius of the droplet. The drag coef-ficient, CD, is modified for the surface blowing effects asfollows,

CD ¼24

Reð1þ BMÞðEq 22Þ

where BM is the Spalding�s mass transfer number. Themass vaporization rate, _m, can be expressed in terms ofeither mass or heat transfer as (Ref 36, 37),

_m ¼ 2pqgD12rsSh� lnð1þ BMÞ ðEq 23aÞ

_m ¼ 2pkg

CP;vrsNu� lnð1þ BTÞ ðEq 23bÞ

In these equations, Nusselt number Nu* and Sherwoodnumber Sh* are based on a nonvaporizing sphere andmodified for vaporization effects because of the varyingfilm thickness around the droplet. When the mass vapor-ization rate from Eq 23a and 23b are equated, a rela-tionship between the droplet surface temperature andsurface solute vapor concentration just above the liquidsurface is obtained. This relationship along with athermodynamic relation for vapor-liquid equilibrium(Clapeyron equation) and the Rault�s law for the mixturefacilitate the iterative solution for the droplet surfacevapor mass fraction and temperature. These quantities arecalculated at each step along the droplet trajectory andcoupled with the solution of species and energy equationswithin the droplet.

Within the droplets, the energy and species transportare computed to determine the distributions of thesequantities. The most detailed transport within thedroplet includes the effects of convection induced by theshear at the liquid-gas interface on the droplet surface.This shear induces an internal recirculatory flow withinthe droplet that is characterized by a spherical Hill�svortex whose strength is computed as a function of theslip velocity between the droplet and the gas stream.The general form of the species and energy equationsaccounting for the internal recirculation can be writtenin spherical polar coordinates and nondimensional formas (Ref 36, 37),

LeL�r2s

@�vz

@sþ 0:5PeLLeL �Vr�rs � LeLbg �@�vz

@g

þ 0:5PeLLeL�Vh�rsg

@�vz

@h¼ 1

g2

@

@gg2@�vz

@g

� �

þ 1

g2sinh@

@hsin h

@�vz

@h

� �

ðEq 24aÞ

and

�r2s

@ �T

@sþ 0:5PeL �Vr�rs � bg �@ �T

@gþ 0:5PeL

�Vh�rsg

@ �T

@h

¼ 1

g2

@

@gg2@

�T

@g

� �þ 1

g2 sin h@

@hsin h

@ �T

@h

� �(Eq 24b)

subject to the initial and boundary conditions,

s ¼ 0! �vz ¼ 0 and �T ¼ 0

g ¼ 1! @�vz

@h¼ 0;

Z p

0

@�vz

@gsin h dh ¼ _m

2prsqLDzavz;o

and@ �T

@h¼ 0;

Z p

0

@ �T

@gsin h dh ¼

_Q

2prskLT0

h ¼ 0; p! @�vz

@h¼ 0 and

@ �T

@h¼ 0

The boundary conditions at the droplet surface (g = 1)correspond to uniform droplet surface temperature (i.e.Ts = Ts(t)) and the total heat flux received by thedroplet at its surface. All the symbols are defined in thenomenclature.

Some sample results are shown in Fig. 14 for a 20 lmdroplet injected into DC-arc plasma at two time instantsalong its trajectory (Ref 36). It is seen that the internalcirculation inside the droplet can result in significant sol-ute concentration and in moderate temperature variations.Such data are needed when solute precipitation in thedroplets is to be predicted. Sometimes, the computationaloverhead to compute the internal droplet temperature andconcentration variations may not be justified particularlyfor those cases where many droplet calculations are nee-ded to develop statistics. In such cases, spherically sym-metric model without internal droplet circulation can beutilized. In this case, the governing equations reduce to(Ref 38, 39):

LeL�r2s

@�vz

@s� 0:5LeL

drsdt

g@�vz

@g¼ 1

g2

@

@gg2@�vz

@g

� �ðEq 25aÞ

�r2s

@ �T

@s� 0:5

drsdt

g@ �T

@g¼ 1

g2

@

@gg2@

�T

@g

� �ðEq 25bÞ

with the initial and boundary conditions as,

�v

�T

8<:

9=;ðs ¼ 0Þ ¼ 0 and

@

@g

�v

�T

8<:

9=;��g¼0

¼ 0

and@

@g

�v�T

��g¼1

¼_m

2prsqLDsvz;o

_QL

2prskkT0

8<: (Eq 26)

where _QL is the heat flux to the droplet, kL is the liquidconductivity, qL is liquid density, Ds is the mass diffusivityof solute in solvent.

The models described above allow the computation ofthe solute concentration and temperature within thedroplets. This information is needed for determination of


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the precursor precipitation time and the regions of thedroplets that undergo precipitation. Clearly, this requiresa model of precipitation kinetics and is probably theweakest link in modeling of the liquid precursor basedthermal spray modeling. The current state of knowledge inprecipitation of liquid precursors is discussed in the nextsection of this paper. It is however predicted that dropletscan undergo precipitation near their surface due to con-centration of the solute there and this causes shell-typeparticle morphologies to form.

Subsequent to shell formation, further heating of theparticle containing a liquid core can lead to either venting ofthe vapor inside the shell if the shell is porous or internalpressurization and eventual rupture of the shell. This por-tion of the process can be modeled as follows. The particlemotion through the hot plasma is still governed by Eq 19and 20 except that the particle size is now fixed at the outerdiameter of the precipitate shell. The Nusselt number forthe porous and nonporous shells is obtained as described inBasu and Cetegen (Ref 38). The model for the particleinterior is divided into three zones: solid shell, liquid coreand vapor annulus. In each region, the energy equation is ofthe same form as Eq 25 with a moving interface between theliquid core and the vapor film. The enthalpy carried by thevapor escaping through the pores is accounted for inthe model as detailed in Basu and Cetegen (Ref 38).Depending on the type of shell formed, one may or may nothave any venting effect through the pores in the shell.However, for the general case of a shell porosity ðeÞ, one canwrite the following mass balance equation for the vapor.

_mv ¼ � _ml � _mout ðEq 27Þ

where _mv is the vapor mass generation rate within theshell, _ml is the rate of change remaining core liquid massand _mout is the rate of vapor mass leaving the porous shell.After some algebraic manipulations with the ideal gas lawassumption, this reduces to:

dpv

dt¼ RTv

Vv4pr2

l qv

drldt

�� 4pr2

l ql

drldt� qvAporeVpore

� �

ðEq 28Þ

where Vpore is the velocity of the gas venting through thepores of the shell estimated from Karman-Cozeny equa-tion while Apore is the total area of the pores. qv and ql

denote the densities of the vapor and liquid phase while rl

is the radius of the liquid core. Equation 28 gives anexpression for internal pressure rise as a function of thevapor velocity escaping through the pores and the rate atwhich the liquid front is receding toward the dropletcenter. Internal pressurization of the shell due to vapori-zation of the liquid within it can lead to shell rupture orinflation depending on the shell type that forms duringprecipitation. This obviously depends on the solute andsolvent characteristics and the thermo-physical conditionsunder which the precipitation occurs.

The interaction between particle and gas phase can bemodeled similarly by solving momentum and energyequation for the particle phase. The primary governingequations for the particles in Lagrangian form are(Ref 31),

mpdv

dt¼ 1

2CDqgAPðvg � vpÞ vg � vp

�� ðEq 29Þ

Fig. 14 Temperature and solute concentration distributions within a 20 lm diameter droplet injected into a DC-arc plasma from Ref 36


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dxp

dt¼ vp ðEq 30Þ

mpCpp

dTp

dt¼ hA0spðTg � TpÞ þ Sh ðTp 6¼ TmÞ

0 ðTp ¼ TmÞ

�

ðEq 31Þ

DHmmpCpp

dfpdt¼ hA0spðTg � TpÞ þ Sh ðTp ¼ TmÞ

0 ðTp 6¼ TmÞ

�

ðEq 32Þ

Here subscripts p, g and m stand for particle, gas phaseand melted phase respectively. m is the mass, t is time, CD

is drag coefficient, v is axial velocity, x is axial distance, As

is surface area, Cp is specific heat and constant pressure.f is the fraction of molten mass. Sh is source term forradiative heating. In case where radiation is neglected,Sh = 0. The convective heat transfer coefficient can becalculated by correlations. Most of the researchers use,Ranz-Marshal relation given by h = kg/dp(2 + 0.6Re1/2Pr1/3).Reynolds number and Prandtl number in this case aredefined as, Re = qgdp|vp � vg|/lp and Pr = Cpplp/kg. kg isthermal conductivity of the gas phase and dp is the diameterof the particle. Solving these equations coupled with the gasphase (described earlier) results in the instantaneousvelocity and temperature of the particle (Ref 31).

5. Precursor Chemistries andPrecipitation Kinetics for LiquidPrecursors

The weakest link in the modeling of liquid precursorbased thermal spray process is the detailed description ofthe precipitation of solute in a droplet. Currently, thespray pyrolysis literature contains the most extensivestudies. Both experimental and modeling studies exploredconditions under which different types of particles areformed. Zhang et al. (Ref 40) and Jain et al. (Ref 41)reviewed this subject presenting both experimental dataand modeling results pointing to the different morpholo-gies. Che et al. (Ref 42) carried out studies in which theparticle structure was controlled by reactions within thedroplets in spray pyrolysis. They achieved dense or hollowsingle crystal or layered particle structures by carefullycontrolling the reactions within droplets, sintering andphase transformations. Zhang et al. (Ref 40) studiedexperimentally the formation of zirconia from differentzirconium salts and determined the conditions and pre-cursor solutions that yield solid particles. Nimmo et al.(Ref 43) studied generation of zirconia from zirconiumnitrate sprayed with a diameter of less than 5 lm into acontrolled heating furnace. They were able to producetetragonal phase ultrafine zirconia powers under certainoperating conditions.

Linn and Gentry (Ref 44) performed an experimentalstudy of single droplet precipitation of different aqueoussolutions of calcium acetate, sodium acetate, sodium car-bonate, ammonium chloride, lithium manganous nitrate

and barium alumino silicate. They found that after aperiod of uniform shrinkage due to evaporation in a hotgas environment, crystallization, crust formation andfracture of the crust were observed. Ammonium chlorideand lithium manganous nitrate showed bubbling andinflation of the precursor droplets after the initialshrinkage. While these studies illustrate the differentnucleation mechanisms and in some cases inflation ofdroplet upon heating, these experiments were conductedat low heating rates where droplets were suspended in arelatively low gas temperature environment (with respectto flame or a plasma) and low velocities. Since the pre-cipitation morphology is strongly dependent on thedroplet heating rates, the actual processes taking place ina droplet can be altered significantly. Modeling of pre-cipitation of solute salts in a liquid droplet has been pri-marily based on the homogeneous nucleation hypothesis(Ref 34, 35). It is assumed that onset of precipitationoccurs when the solute concentration reaches a super-saturation level and engulfs all regions of the droplet thatexceed the equilibrium saturation concentration. Whilefundamental studies of precipitation onset in solutiondroplets have been undertaken (Ref 34, 35), these studieshave revealed that the parameters affecting the precipi-tation onset are difficult to determine even for the simplesingle component solutions under well-controlled condi-tions. Models based on the minimization of the Gibbsenergy have been considered to predict the onset ofprecipitation. In practice, validity of homogeneous pre-cipitation hypothesis is in question firstly due to the morelikely possibility of the heterogeneous precipitation as aresult of impurities and secondly because of the effects ofvery rapid heating of droplets.

Precipitation of the solute salts in these and othermodels is based upon attainment of super-saturationconcentration of the solute before the onset of precipita-tion followed by precipitation in all regions of the dropletthat are above the equilibrium saturation concentration.This assumption of homogeneous precipitation has beenused widely in modeling, yet its validity for differentmaterial systems and droplet heating conditions is notknown. Ozturk and Cetegen (Ref 36) and Basu andCetegen (Ref 38, 39) used this concept of homogenousprecipitation in their models and showed that largedroplets typically form shell type precipitates, which aredetrimental to the final coating quality as they areembedded as unmolten fragments in the coating. Smallerdroplets are not only better entrained but tend to volumeprecipitate. This volume precipitation and subsequentintense heating usually results in molten splats on thesubstrate resulting in denser coatings. Some sample resultsare shown in Fig. 15 (Ref 36).

6. Modeling of Coating DepositionProcess

The coating generation process is an interactionbetween molten droplet/particle and substrate surface or


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previously deposited materials on the surface. This inter-action is also responsible for porosity development in thecoating. Most of the models dealing with coating evolutionassume that the coating generation is a consequence ofindividual molten droplet splats impacting the surfaceindependently. The temperature, velocity and size ofparticles determine thickness of each splat which dictatesthe coating density. The size of particles before impact canbe expressed as a distribution function (Ref 31),

f ðdpÞ ¼1ffiffiffiffiffiffi

2pp

rdp

exp �ðlnðdpÞ � lÞ2

2r2

!;

where l, r2 are two parameters corresponding mean andvariance of ln(dp). Most of the available works alsoassume that a particle after impacting the substrate takesshape of a flattened cylinder and the flatness can beexpressed by,

n ¼ Ds

dp¼ 2

dp

ffiffiffiffiffiffiAs

p

r;

where Ds is the diameter of the splat and As is the surfaceof the splat. Considering the volume conservation, theheight of the splat can also be calculated (Ref 31). Theflattening factor (n) depends on many parameters like,Reynolds number, Peclet number and Weber number.However, many researchers used a simplified formulation,n = 1.2941Re0.2. Simulation of these parameters for eachand every droplet results in a stochastic coating pattern(Ref 31).

7. Some Results from Previous Studies

In this section, some results from previous studies arehighlighted for plasma and HVOF flame jet thermal sprayprocesses. Figure 16 shows some sample results from

Yu (Ref 45) on particle velocities and temperatures fordifferent particle sizes in a DC-arc plasma as determinedfrom experiments. Clearly large variations of particletemperatures, velocities and sizes exist in thermal sprayprocesses and these contribute to the microstructuralfeatures of the deposited coatings. In addition to theparticle state variations, variation of particle trajectorieswithin a plasma jet leads to dispersion of particle positionsat different jet cross sections as shown in Fig. 17 (Ref 16).Dispersion is also affected by the degree of swirl asswirling flow has a tendency to have a larger degree ofdispersion at farther downstream positions as shown inthis figure as well. Figure 18 shows the effects of particlecarrier gas flow rate on particle trajectories, velocities,temperatures and vaporization rates (Ref 21). The particlepenetration into the plasma increases with increasingcarrier gas flow rate and peak particle temperatures arealso higher for the higher carrier gas flow rates employedin this study. There is typically an optimum carrier gasflow rate for particles to penetrate into the plasma jet andundergo sufficient degree of heating in the plasma.Figure 19 (Ref 25) shows another example of particleheating in a DC-arc plasma. In this case, a 30 lm zirconiaparticle is injected into a DC-arc plasma. Both surface andcore temperature evolution is shown on the left panel. Theinternal particle temperature rises with increasing timewithin the particle as shown on the right panel.

An important aspect of particle heat-up in a plasma orHVOF flame jet is the treatment of heat transfer from thegas stream into the particle or droplet. As mentionedearlier, noncontinuum effects may be prevalent in somecases. Figure 20 (Ref 19) shows the ratio of heat fluxeswith and without the Knudsen effect in the conductionregime. While the noncontinuum effects may not be sig-nificant for larger diameter particles, they can be signifi-cant for small particles.

There have not been many studies of droplet injectioninto plasmas in the past. There are some recent modeling

Fig. 15 Precipitation zones within the droplets for (a) axially injected 20 lm droplet 0.4 ms after injection, (b) transversely injected20 lm droplet 0.4 ms after injection, (c) axially injected 5 lm droplet 0.2 ms after injection, and (d) axially injected 10 lm droplet0.36 ms after injection (Ref 36)


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studies of liquid precursor droplet injection into plasmas(Ref 14, 36, 38, 39). In these studies, droplet break-up andevolution of solute concentrations within injected dropletswere considered. Figure 21 shows the Weber numbervariations along droplet trajectories in a plasma jet asreported in Ref 14. From the Weber numbers, the pro-pensity of the droplets for break-up is evaluated as highWeber number regions are those where droplet break-upis expected.

Li et al. (Ref 29) performed a computational study onin-flight behavior of particles during HVOF process. Thetorch shown in Fig. 6 (Ref 29) was designed in such a waythat the Mach number at the exit of the nozzle to bearound 2. Maximum gas velocity with this nozzle can goup to 2000 m/s. The gas dynamics of the combustionprocess has been modeled using the similar methodologiesas described earlier. The particle heating formulationneglected temperature variation within the particle.

The turbulent nature of the HVOF gas flow fieldintroduces indeterminism with respect to particle track-ing and hence a stochastic method was adopted, whereinstantaneous velocity is always represented as the sum

of the average velocity and the fluctuating component ofthe fluid velocity. Temperature distribution within theflow field shows that the maximum temperature isaround 2500 K and it is located in the core of the jet.The velocity profile of the gas field along the radialdirection at different axial planes is shown in Fig. 22(Ref 29). The authors also reported the effect of injec-tion location on particle velocity. Figure 23 (Ref 29)depicts the axial velocity profiles of five different sizedparticles injected from different locations. The resultsshowed that despite being injected at different axiallocations, the same sized particles always attain similarvelocities and temperatures before impacting on thesubstrate. The authors in this work also performed astatistical analysis of the distribution of particle impactvelocity and temperature for a wide range of particlesizes and injection locations. The analysis depicted that90% of the total volume of particles impact the substratewithin a 2 mm radius from the center. Residence times ofthe particles were around 2 to 4 ms, while the axialvelocity and temperature at the time of impact werearound 94 m/s and 1176 K, respectively.

Fig. 16 Particle velocity and temperatures as a function of particle size at an axial distance of 10.2 cm at three radial locations (Ref 45)


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Bartuli et al. (Ref 46) conducted a detailed parametricstudy for liquid fuel HVOF process for nano WC rein-forced cobalt coating. For assessing the effect of sprayparameters on the microstructure, a computational modelwas used to simulate the combustion process and inter-action of the WC-Co particles with the exhaust gases.Additionally, experimental work was performed to vali-date the model and compare the coating quality with theconventional micro-sized power coatings. In this work,commercially available spraying equipment (JP-5000,Tafa Inc., Praxair Surface Technologies, Concord, NH)

with a kerosene-oxygen mixture as fuel was used forexperimentation. For computations, k-e turbulence modelwas adopted. Single-step reduced chemistry model wasused for the combustion process.

Optimal spraying conditions are found to be functionsof parameters like fuel (kerosene) flow rate, length of thetorch barrel and spraying distance. The oxygen flow ratewas maintained at 2000 scfh. The temperature and velocitydistribution of the combustion gas inside the torch for allthe different fuel flow rates show that the static temper-ature of gas phase is highest for a kerosene flow rate of

Fig. 17 Comparison of the predicted particle distributions at three successive sections with and without swirl from Ref 16


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6.0 gph while the velocity profile remains largely unaf-fected. The effect of three different barrel sizes on theparticle (WC-Co particles of average size of 48 lm)velocity and temperature was also studied. The simulation

results are illustrated in Fig. 24 (Ref 46). The results showthat inside the nozzle, longer barrel length leads to highervalues of peak velocity and temperature. It is claimed thatthis information can be utilized for optimization of the

Fig. 18 Dependency of in-flight behavior for zirconia particles of 30 lm as a function of carrier gas flow rates: (a) particle trajectories,(b) particle velocity, (c) particle temperature and (d) evaporation rates from Ref 21

Fig. 19 Axial evolution of zirconia particle temperature and the temperature distribution within the particle at different time instantsfor a 30 lm particle from Ref 25


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control parameters for minimum thermal interaction ofparticle and combustion flame reducing the chances ofdecarburization grain growth leading to adhesive coatings.

Dongmo et al. (Ref 47) performed a detailed compu-tational study to model the HVOF process using alumina(Al2O3) powder. They also used commercial Spray-Watch� system to experimentally validate their model. Inthis work, a 3D model was developed to simulate thecombustion and gas dynamics processes during the HVOFprocess. This model also investigated the interactions ofparticles and combustion gases. The torch has beenmodeled as TopGun-G (GTV mbH, Luckenbach,Germany). Similar to most of the models described ear-lier, this work uses Eulerian and Lagrangian approaches tosolve the velocity and temperature fields of the gas andparticle fields, respectively. Reynolds and Farve-averagedNavier-Strokes� equations along with k-e turbulencemodel were adopted. Commercially available ANSYS-CFX 11 software was used. The parameter values con-sidered for this simulation are stated in Table 1 (Ref 47).In this work, gaseous propane was used as the fuel. Thedistribution of all the species involved in the combustionprocess along the centerline is shown in Fig. 25(a) and (b)

Fig. 20 Heat transfer under noncontinuum conditions (Q2 withKnudsen effect, Q0 without Knudsen effect)\(Ref 19)

Fig. 21 Variation of Weber number along droplet trajectories of water droplets 20, 40 and 60 lm diameter from Ref 14

Fig. 22 Velocity distribution of the gas phase along the radialdirection at different axial planes (Ref 29)

Fig. 23 Profiles of axial velocity of particles of five differentsizes injected from different axial locations (Ref 29)


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(Ref 47). Figure 26 (Ref 47) shows the pressure and Machnumber distribution along the centerline inside and out-side of the torch. For the converging nozzle, the velocity aswell as Mach number of the exhaust gas increases reachinga supersonic level. The simulation results also depicted thepresence of diamond shocks. The model also predicted theaxial velocities and the temperature for different sizedparticles. The results depict that particles having sizessmaller than 20 lm undergo rapid decay in velocity andtemperature outside the torch. They do not reach thesubstrate at the point of impact. This finding has also beenconfirmed by measurements using SprayWatch� system.In summary, the authors put forward a numerical modelfor HVOF process using propane as fuel and alumina aspowder. The results show that the particles of size less

than 20 lm are not suitable for coating as their low massand inertia do not allow them to reach the substrate withdesirable velocity and temperature characteristics. Othersignificant works in this category include the work ofTawfik and Zimmerman (Ref 48) who proposed a one-dimensional single-phase, nonadiabatic frictional flow withvariable specific heats to model the flow inside the nozzleof the HVOF torch and the supersonic jet plume outsidethe nozzle. Though this model is simple in construction, itwas validated by a series of experiments and provided alow cost-effective analysis contrary to the more compu-tationally intensive models described earlier. The particleinteraction was modeled using a Lagrangian approachwith a lumped capacitance model for heat transfer. Thefuel used was kerosene with Inconel and WC as the

Fig. 24 (a) Average velocity and (b) average temperature profiles of Ref 46 particles (WCCo, 48 lm average size) inside and outside ofthe barrels of different lengths

Table 1 Parameters for the HVOF computational domain using oxy/fuel ratio 0.8 (Ref 47)

Inlet C3H8/O2 Inlet N2 Inlet Al2O3 Wall Free jet Substrate

Mass flow, g/s 5.143 9 10�3 2.065 9 10�3 0.068 … … …Temperature, K 300 300 300 460 298 298Pressure, Pa … … … … 105 …

Fig. 25 (a) Mass fraction of the CO2 within the torch, (b) mass fraction of all the species along the centerline (Ref 47)


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injected particles. Their simulations indicated that heattransfer between the gas and the particle is more efficientthan momentum transfer resulting in faster rise in particletemperature. Particles for a diameter range of 38-50 lmexhibit a highest temperature of around 2500 R with anaverage velocity of 3500-5000 ft/s.

Lau et al. (Ref 49) proposed a mathematical modelpredicting the particle behavior of nanocrystalline Nipowders during HVOF spray. They used a similarLagrangian description of the particle interaction withinthe flame. The gas flow was modeled as ideal gas in africtionless adiabatic duct. Their work indicated thatfraction of the Ni-agglomerates did not melt during theHVOF process. Particles of 36 lm in size attain only 30%of the HVOF flame temperature during impact on thesubstrate. Particles with diameter of 15 lm reach a tem-perature of 1440 K during impact on the substrate.Eidelman and Yang (Ref 50) developed a three-dimensionalmodel to simulate an HVOF process for nanoscale coat-ing. They used traditional Favre averaged compressibleNavier-Stokes equations with k-e turbulence model for thecontinuum gas flow. Particle interaction with nozzle walland the gas phase was formulated using a Lagrangianapproach with key assumptions such as no temperaturevariation inside the particle, no intra-particle interactionand uniform particle properties. They observed thatWC-Co particles of greater than 60 lm in size cannot beaccelerated to greater than 33% of the maximum gasphase velocity and lead to porous coatings. Particlessmaller than 10 lm were also found to decelerate in thestagnation zone and lead to very poor coating quality.

Basu and Cetegen (Ref 51) were the first to formulate amodel for a new process of high-temperature coating,where liquid ceramic precursors can be injected into

high-velocity oxy-flame to generate a high-quality denseoxide coating. The model incorporated the thermo physicalphenomena that precursor droplets undergo when they areinjected axially into the high-velocity flame. The processeswithin the droplet would be different from those duringplasma spray as HVOF process is generally characterizedby higher velocity and lower temperature as compared toDC-arc plasma. The modeling of HVOF jet was based onthe consideration that the products from the combustion ofstoichiometric mixture of oxy-propylene emerge out of thenozzle. The gaseous jet of HVOF was solved using k-eturbulence model using the commercial FLUENT com-putational fluid dynamics code. The droplets injected intothe flame underwent the processes of initial aerodynamicbreak-up, heating and surface evaporation with soluteprecipitation and internal vaporization and shell rupture.The precursor used for this study was zirconium acetatewith mass fraction of 0.2. The aerodynamic break-up phe-nomenon was predicted using Taylor Aerodynamic Break-up (TAB) model. The model predicted that the axiallyinjected (droplets are injected inside the HVOF flame jet)droplets were broken into smaller droplets of sizes rangingfrom 0.5 to 1 lm. However, in case of transverse injection(droplets are injected downstream) they experienced lowervelocities and lesser amount of droplet break-up. Figure 27(Ref 51) shows the droplet size distribution after aerody-namic break up in case of axial and transverse injection.

The second phase of the droplet processes consideredvaporization and precipitation. These authors and others(Ref 36, 52, 53) reported that the evaporation processincreases the solute concentration within the droplet in aplasma and HVOF jet. At some point, the solute con-centration increases the supersaturation limit triggeringprecipitation. The model of Basu and Cetegen (Ref 51)

Fig. 26 Contour plots of (a) static pressure and (b) Mach number along the centerline (Ref 47)


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showed that the time involved in this precipitation processis longer than that in case of plasma injection. Figure 28(Ref 51) shows the variation of solute mass and temper-ature within droplets whose initial diameters were 5 and20 lm. It shows that the gradient of mass-fraction isgreater than the gradient of temperature profile, indicat-ing the higher thermal diffusivity than mass diffusivity. Italso indicates that the smaller droplets tend to volumet-rically precipitate while the larger droplets tend to formshell-type morphology.

A study of post-precipitation stage for the droplets of10 and 20 lm was carried out by Basu and Cetegen forboth plasma and HVOF (Ref 38, 51). The trapped liquidwithin the shell vaporizes to increase the internal pressure.The model showed that for both plasma and HVOFdepending on the porosity of the formed shell, the internalpressure increases resulting in the rupture of the shell.This result also indicated that the time scale involved forthis process is microseconds whereas the time scale for theprecipitation process is of the order of milliseconds.

8. Multi-Scale Modeling of Thermal SprayProcess

The studies described in previous sections portray onlytwo important parts of the thermal spray processes,

namely gas dynamics and particle/droplet transport pro-cesses. In order to describe the whole thermal spray pro-cess starting from gas dynamics to coating generation, amulti-scale modeling approach is necessary. There are fewworks in the literature that reported on modeling of thewhole thermal spray process. In this section, some of thesemodels are described briefly. The major work on multi-scale modeling of industrial HVOF thermal spray wascarried out by Li et al. (Ref 30). In this work a DiamondJet Hybrid HVOF thermal spray process for generatingWC-12% Co coating was designed and modeled. Li et al.(Ref 30) focused on the multi-scale modeling and analysisof gas dynamics, in-flight behavior of particles and micro-structure of generated coatings. Computational domainfor this work includes both inside and outside of thenozzle. Eulerian approach was used in this model to solvethe thermal and flow field of the gas phase, while theparticle velocity, temperature and degree of melting weredetermined from a Lagrangian approach. Reynolds andFavre-averaged Navier-Stokes� equations were solved formodeling the gas dynamics. Nonequilibrium wall functiontreatment was used in renormalization group turbulencemodel to solve for the gas dynamics of flow at highReynolds number with large pressure gradients within thenozzle. The eddy dissipation model was used for modeling

Fig. 27 Diameter distribution of (a) 5 lm axially injected and(b) 30 lm transversely injected droplets after shear break-up(Ref 51) Fig. 28 Temperature and solute mass fraction profiles at the

onset of precipitation for a droplet with initial size of (a) 5 lmand (b) 20 lm (Ref 51)


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the chemistry. A first order upwind differencing schemewas used to solve for coupled mass, momentum andenergy equation while second order upwind scheme wasemployed to capture the shock diamond that occurs in theexternal field. A fourth order Runge-Kutta method wasused to solve for the velocity, temperature and meltingdegree of the particle. For predicting the microstructure ofthe coating, a stochastic approach was adopted. Thepowder particles were injected at the central inlet nozzle.N2 was used as the particle carrier gas. The interactionbetween the hot combustion gases and particle results inmomentum and energy transfer which leads to accelera-tion and heating of particles. Eventually, the particles inmolten or semi-molten state exit the nozzle with a veryhigh momentum and impact the cold and stationary sub-strate. The combustion process created an elevated tem-perature of 3000 K and the pressure of 6 9 105 Pa insidethe combustion chamber. Table 2 compiles the conditionsunder which the parametric study was conducted byLi et al. (Ref 30).

In the simulation, the jet is over-expanded at the nozzleexit. For a small initial distance at the centerline, theconcentration of N2 carrier gas is higher but all the otherspecies are almost absent. Due to rapid mixing and tur-bulence, the concentration of the carrier gas decreases andother species concentrations gradually increase within thenozzle. Outside the nozzle, due to entrainment of thestatic air, O2 and N2 contents increase rapidly. The verylow mass fraction of propylene indicates a high degree ofcomplete combustion inside the chamber. For the baselinecondition in Table 2, the results show that the velocity andtemperature profile also change with different spray dis-tance. It can be noted that for each spray distance there isan optimum particle size for which the temperature ishighest. It also shows that the velocity and temperatureincrease with increasing spray distance. The authors alsoreported that the effect of injection velocity is negligibleon the impact velocity and temperature of the particle.Their analysis also showed that for industrial applications,the equivalence ratio should be around 1.2 for maximummass flow rates.

Simulation of the coating microstructure was based onthe energy conversion during the impact of the heatedparticles with the substrates, which dictates the tempera-ture and degree of melting of the particles. The idealcondition of 100% melting of the particles would result insurface coating which is homogenous. However, when thepresence of semi-molten or un-melted particles is taken

into consideration, roughness and porosity increases in themicrostructure. Figures 29 and 30 (Ref 30) suggest thepresence of un-melted particles. For low melting ratio,the lower flow rates increase the porosity of the coatingwhile for higher melting ratio, the lower flow rates reducethe porosity in the microstructure. Their results also pre-dicted that very small sized particles are not effective forcoating generation. The injection velocity did not have asignificant effect on the coating and also the carrier gasflow rate must be kept to a minimum value to allow suf-ficient residence time for heat transfer between the par-ticle and combustion gases. Similar such works werereported by Chandra et al. (Ref 54-56) for plasma andHVOF deposition. These models were also stochastic innature and predicted the porosity, thickness and rough-ness of the coatings as a function of particle size, velocity,temperature, stand-off distance and injection methodol-ogy. To our knowledge, there has been no study per-formed on the multi-scale modeling of droplets in HVOFand plasma including stochastic analysis of the coatingformation.

Table 2 Specified gas flow rate for parametric analysisof Diamond Jet hybrid HVOF gun (Ref 30)

CasePropylene,

scfhOxygen,

scfhAir,scfh

Nitrogen,scfh _m, g/s /

1 (baseline) 176 578 857 28.5 18.10 1.0452 176 578 428 28.5 13.73 1.1863 176 867 857 28.5 21.35 0.7564 264 867 1286 28.5 27.01 1.045

Fig. 29 Simulated (a) microstructure and (b) pore distributionin the coating made of particles of nonuniform molten states,which are deposited under baseline condition reported in Table 2(Ref 30)


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9. Conclusions and Recommendations

Thermal spray process has been typically modeled asthree physically distinct segments: gas dynamics, gas-particle or gas-droplet interactions and coating deposition.Review of literature suggests that sophisticated models ofboth plasma and HVOF flame jets have been formulated.These models range from those that simulate the evolu-tion of high-temperature jets with plasma or flame com-positions to those that simulate the plasma andcombustion process in detail. Powder or liquid sprayinjection into a plasma or a HVOF flame jet have beenmostly modeled as the discrete phase of droplets andparticles being heated in the computed thermal environ-ment of a DC-arc plasma or HVOF flame jet. This type oftreatment assumes that the discrete phase has very little orno effect on the flow and thermal fields of the plasma orHVOF flame jet, an assumption that is only valid fordilute particle or droplet regimes. In thermal sprayapplications where a larger amounts of powders or liquidprecursors are to be processed, the dilute regimeapproximations will fail and the two-way coupling of thegas flow field with particles need to be taken into account.

Eulerian-Lagrangian approach has been used to modelthe gas and particle interaction. The particle loading rateand the size distribution of the particles have a strongeffect on the final temperature, velocity and melting ratioprior to impact on a substrate. Many authors havereported that most of the particles get deposited very nearto the center of the jet. The coating develops when onemolten particle gets deposited on another. The modelingthe pattern of the coating is stochastic in nature, whichinvolves statistical determination of splat size, coatingthickness and porosity of the coating. It has been reportedby many authors that size distribution, feeding-rate ofparticles and temperature of the flow fields have effects onthe porosity and coating density.

In case of precursor droplets, the temperature andvelocity of the gas fields also affect the internal liquidcirculation and temperature distribution within droplets.Larger droplets usually undergo aerodynamic break-up.The droplets subsequently undergo fast vaporization andprecipitation forming solid particles. The results show thatthe high velocity of HVOF jet facilitates the aerodynamicbreak up to higher degree, resulting in smaller dropletsthat are injected axially along the centerline of the high-temperature jet and can undergo faster vaporization andmost likely generating splats of fully molten particles.However, for transverse injection, smaller droplets maynot be properly entrained into the gas jet and hence canresult in poor coating quality due to unpyrolized materialarriving on the coating surface.

In the modeling of liquid precursor droplets beingprocessed in a plasma or HVOF flame jet, one of themajor knowledge gaps is the existence of comprehensiveprecipitation models that can be incorporated into heatand mass transfer models for liquid droplets of the typediscussed in this article. For example, the current state-of-the-art in precipitation modeling of droplets in thermalsprays is limited to a homogeneous precipitation aroundprecursor droplets that are based on studies at slowheating rates. The kinetics of solute precipitation experi-enced at rapid heating rates in plasmas and HVOF flamejets is an area that needs to be addressed in the future.

There are only few works available on the multi-scalemodeling which involves end-to-end analysis of the ther-mal spray process. Modeling of the process that includessimulations of plasma or HVOF flame and at the sametime calculate particle or droplet heat-up states in a cou-pled manner and also handle the deposition and coatingformation would be desirable in the future. Such modelscan address the need for understanding multi-dimensionaleffects of each control parameter as well as determiningthe optimum conditions for particular coating micro-structural requirement. With the advances in computa-tional power and development of more sophisticatedmodel components, the models of this type are envisagedto be important tools in the thermal spray field in thefuture. Finally, more detailed experimental results areneeded to validate these models. With the advancement ofoptical diagnostic techniques, it is anticipated that moredetailed experimental results will be available in thefuture.

Fig. 30 Simulated (a) microstructure and (b) pore distributionin the coating made of particles of nonuniform molten states,which are deposited under condition in case 4 reported in Table 2(Ref 30)


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Acknowledgments

The authors acknowledge the past financial support bythe Office of Naval Research under the direction ofDr. Larry Kabacoff. Many useful discussions took placeduring the course of our modeling studies with our col-leagues Professors Maury Gell, Nitin Padture andEric Jordan. We are also grateful to Kaushik Saha andAbhishek Saha for their help in the literature search.

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