Mathematical modelling of high velocity oxygen fuel thermal spraying of nanocrystalline materials: an overview

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING Modelling Simul. Mater. Sci. Eng. 11 (2003) R1 R31 PII: S (03) TOPICAL REVIEW Mathematical modelling of high velocity oxygen fuel thermal spraying of nanocrystalline materials: an overview D Cheng 1, G Trapaga 2, J W McKelliget 3 andejlavernia 4 1 School of Nanosciences and Nanoengineering, University at Albany, Albany, NY 12203, USA 2 Cinvestav Unidad Queretaro, Libramiento Norponiente No Fracc. Real de Juriquilla, 76230, Queretaro, Qro., Mexico 3 Department of Mechanical Engineering, University of Massachusetts at Lowell, Lowell, MA 01854, USA 4 Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA Received 10 March 2002, in final form 4 August 2002 Published 28 October 2002 Online at stacks.iop.org/msmse/11/r1 Abstract An emerging application of nanocrystalline materials involves the deposition of nanocrystalline coatings using high velocity oxygen fuel (HVOF) thermal spraying. Since the physical, mechanical, and chemical characteristics of a nanocrystalline coating are critically influenced by the HVOF operating parameter, mathematical modelling is increasingly being used to establish a fundamental understanding of the process, to maximize coating performance, and to minimize the amount of experimentation required. In this paper, the modelling of HVOF thermal-spray processes, including combustion, gas dynamics, momentum, and thermal transfer between the particle and gas phase, as well as the impact of particles onto a substrate is reviewed. Particular attention is paid to topics that are particularly relevant to the thermal spraying of nanocrystalline coatings. Nomenclature A p c C D c h c p D p D E h projected area of particle thickness of flake drag coefficient heat transfer coefficient specific heat of particle particle diameter grain size aspect ratio of oblate spheroids static enthalpy /03/ $ IOP Publishing Ltd Printed in the UK R1

2 R2 Review Article H k K M n p q Q Re R p S a t T u V V v p We x total enthalpy freezing parameter thermal conductivity Mach number aspect ratio of a flake static pressure heat flux activation energy for isothermal grain growth Reynolds number radius of particle additional source term time temperature Cartesian component of the instantaneous velocity velocity vector x-component of V volume of particle Weber number radial coordinate Greek symbols ε dissipation rate of turbulent kinetic energy ε p surface emissivity of particle κ turbulent kinetic energy per unit mass µ fluid dynamic viscosity ρ mass density σ t surface tension coefficient τ Newtonian viscous stress tensor δ ij Kronecker delta degree of spreading ξ m Subscripts f g p t gas around particle gas particle turbulence Superscripts T transpose 1. Introduction In recent years, significant interest has been generated in the field of nanoscale, nanocrystalline or nanophase materials (in which the grain size is usually in the range of nm). This

3 Review Article R3 interest stems, not only from the outstanding properties that can be obtained by such materials, but also from the realization that early skepticism about the ability to produce high quality unagglomerated nanoscale powder was unfounded. There are literally dozens of methods utilized by over 60 companies involved in nanocrystalline materials in the United States alone, some of which are fully commercialized [1]. Accordingly, the focus is now shifting from synthesis to processing, i.e. the manufacture of useful coatings and bulk structures from these powders. The potential applications span the entire spectrum of technology, from thermal barrier coatings for turbine blades to wear resistant rotating parts. The potential economic impact is several billions of dollars per year [1]. The importance of the field can also be seen by the fact that, of the 25 most highly cited authors in the field of materials science and engineering, seven are engaged in research on nanoscale materials [2]. Significant progress has been made in various aspects of the processing of nanoscale materials. Most of this work has been focused on the fabrication of bulk structures [3 5]. However, the process most likely to have the greatest technological impact is the deposition of nanocrystalline coatings by thermally activated processes. These include the so-called thermal-spray processes such as the high velocity oxygen-fuel (HVOF) process, the plasma spray process, and others. A number of recent scientific meetings have been dedicated to the topic of thermal spraying of nanocrystalline materials [6]. Figure 1 shows a typical dark field transmission electron microscopy (TEM) image of nanocrystalline CoCr coating prepared by thermal spraying, illustrating an average grain size smaller than 100 nm [7]. HVOF spraying is one of the most important developments in the thermal-spray industry since the development of the original plasma spray technique. It is being used in an increasing variety of coating applications. Metallic, ceramic, and composite coatings are frequently applied to substrates in order to improve wear, abrasion, and corrosion resistance, as well as to deposit thermal and electrical barrier coatings. [8]. More recently, HVOF spraying has been successfully used as a means of producing nanocrystalline coatings [7 15]. HVOF is characterized by high particle velocities and relatively low thermal energy, when compared Figure 1. TEM dark images of thermal sprayed nanocrystalline CoCr coating [7].

4 R4 Review Article to plasma spraying. The extremely brief exposure of the precursor nanocrystalline particles to the HVOF flame appears to preserve the nanocrystalline structure in most of the particles deposited onto the substrate. Figure 2 shows schematic representations of two commonly used HVOF systems. In the Combustion Chamber, continuous combustion of oxygen and a hydrocarbon fuel (typically propylene, acetylene, propane, or hydrogen gas) occurs under high pressure (0.5 2 MPa). The hot combustion gases are then accelerated to supersonic velocities using a converging-diverging nozzle. With a carefully designed nozzle the gas exit velocity can be in excess of 2500 m s 1, more than five times the local sound velocity. These high gas velocities, when transferred to the injected particles, promote the formation of dense, homogeneous, and non-porous coatings. In general, the static pressure in the hot gas exiting the HVOF torch will not match the ambient atmospheric pressure. The high velocity free jet adjusts to the ambient pressure through a series of expansion and compression waves, known as shock diamonds. During expansion the Mach number increases and the temperature and pressure decrease; during compression, the reverse occurs, with the highest gas temperatures occurring in the compression waves. Luminescence of different gas species at high temperature renders the shock diamonds visible. Schlieren optical flow visualization studies reveal large turbulent eddy structures along the jet boundary [18, 19]. The high velocity, high temperature jet is cooled and slowed down by entrainment of the low velocity, low temperature air. The jet spreads, the radial dimensions of the shock pattern decrease, and the shock diamonds gradually disappear [18, 20]. After a certain number of expansion and compression waves, the static pressure in the jet equals the environmental pressure and the supersonic flow changes (a) (b) Figure 2. A schematic diagram of two commonly used HVOF systems, including combustion chamber, convergent divergent nozzle, and barrel; after [55].

5 Review Article R5 Figure 3. Images of shock diamonds of a Hobart-Tafa JP-5000 HVOF equipment operated at chamber pressures of (a) 0.65 and (b) 0.91 MPa [21]. to a subsonic flow. Figure 3 shows the images of shock diamonds of a Hobart-Tafa JP-5000 (Hobart-Tafa Technologies, Inc., Concord, NH) operated at chamber pressures of (a) 0.65 MPa and (b) 0.91 MPa, respectively [21]. In general, a higher chamber pressure results in a longer supersonic core. This is primarily due to an increase in static pressure at the barrel exit. The nanoscale powder particles are injected into the gas jet inside the torch and are simultaneously heated and propelled towards the substrate. With the relatively low temperature of the HVOF flame (about 3000 K), as compared to plasma spraying, for example (about K) [22], the particles are made highly plastic and superheating or vaporization of individual particles is prevented [23]. During the deposition of carbide coatings these lower temperatures lead to a reduction in carbide depletion. Additional advantages of the HVOF process over conventional plasma spraying include higher coating bond strength, higher deposition rates, higher hardness, lower oxide content, and improved wear resistance due to a homogeneous distribution of particles [24, 25]. The microstructure and physical properties of the nanocrystalline coatings produced in the HVOF process are determined by the physical and chemical state of the particles as they impinge upon the substrate. This, in turn, depends upon a large number of fundamental process parameters such as gun design, fuel/oxygen ratio, gas jet formation, position of substrate relative to the gun, particle size and shape, materials, injection method, and so on. To improve and optimize the quality of the coatings it is necessary to quantify the effect of these fundamental process parameters and to relate them, through the physics of the process, to the chemical and physical properties of the coating. The traditional approach to the problem of process optimization usually involves direct experimental measurement coupled with one-factor-ata-time methods, Taguchi methods, and factorial design. This approach is generally expensive and may not lead to a fundamental understanding of the physics of the thermal-spray process. In addition, the results obtained may only be applied to existing well-known systems with a limited number of dominant parameters and for rather small variations of these parameters. The optimal solution could be in question when, for example, a new powder fraction or nozzle is used.

6 R6 Review Article Ideally, the experimental programme would involve continuous, in situ, monitoring of the particle flux, velocity, temperature, and size distribution just prior to impact on the substrate. Experimental techniques such as dual focus laser velocimetry, photographic measurement, and pressure measurements, have been tried to determine the dynamic parameters of gas and sprayed particles in flight [19 23]. Despite the numerous efforts reported to date, in situ measurements remain far from being implemented in practical applications as a result of their complexity and high expense. Nevertheless, the modern diagnostic and in situ measurement techniques have the potential to provide valuable data to validate another promising approach, mathematical modelling. Mathematical modelling and computer simulation represent very promising complements to the experimental approach. A well-validated simulation model contributes to the scientific understanding of the system, provides a basis for extrapolation, and may suggest regions where further experimentation might be fruitful. The results of modelling studies will make it possible to predict the velocity, temperature, and composition of the powder particles impinging onto the substrate. In addition to providing fundamental insight into the processes taking place, the development of a mathematical model may be economically appropriate, in particular, taking into consideration the fact that in situ measurements of the thermal interaction parameters are both difficult and expensive. From a modelling point of view the HVOF system is very complex, involving the interaction between a gas phase and a liquid or solid phase, turbulence, heat and mass transfer, chemical reaction, and supersonic/subsonic flow transitions. In the past few years, computational fluid dynamic (CFD) methods have been used to provide insight into the complex flow behaviour during HVOF thermal spraying [30 35]. Some models have been successfully applied to the deposition of nanocrystalline coatings [13,37,38], providing fundamental insight into the process and providing valuable guidelines for controlling the coating quality. In general, the modelling methodology used to predict the in-flight behaviour of particles during nanocrystalline HVOF are the same as those used for conventional materials and described in earlier sections. However, special attention should be paid to microstructural stability since it is precisely the scale of the microstructure which gives these materials their unique properties. Available studies show that the particles used to deposit nanocrystalline coatings typically involve the following: (1) an irregular morphology such as flakes, agglomerates or hollow particles; (2) a two-phase mixture of solid and liquid phases. Accordingly, their in-flight and impingement behaviour departs from the conventional case, where droplets are typically spherical and molten. In this paper the modelling of HVOF thermal spraying processes, including combustion, gas dynamics, the in-flight behaviour of the powder particles, and the impingement of droplets, is reviewed. In order to assess our current understanding of the mathematical modelling of nanocrystalline coatings, the general models concerning the HVOF processes will be overviewed first. Special topics concerning nanocrystalline coatings are then discussed in light of recent results. 2. Gas phase dynamics Early modelling work involving simplified one-dimensional models was developed by several groups and has been reviewed by Sobolev and Guilemany in 1996 [42]. More recent analyses have used modern CFDs methods to simulate complex physical processes in two or three dimensions. In this paper only two- or three-dimensional models will be reviewed. In the CFD approach fluid flows are simulated by numerically solving partial differential equations that govern the transport of quantities such as mass, momentum, and energy. Turbulent mixing, chemical reactions and radiation are also modelled. Though different

7 Review Article R7 methods are used, the following assumptions are commonly made in HVOF modelling [39]: The flame gas obeys the ideal gas law. Area changes are considered to be adiabatic and frictional effects are neglected, i.e. laws of isentropic flow of compressible fluids may be applied. The rise of the gas temperature due to combustion follows laws of heat transfer to a perfect gas flowing within a constant area duct without friction (Rayleigh). The spray powder particles are spheres. Chemical reactions of the exhaust gases with surrounding media and particles with gases are not considered. Vaporization and evaporation of the particles is negligible. Principles of heat transfer apply to heat exchange between hot exhaust gases and spray powder particles; hot exhaust gases and nozzle wall; impinging hot gas stream onto substrate and coating; and impinging molten/heated particles and solidified particles or substrate Combustion model When modelling combustion in thermal-spray processes, it is crucial to compare the results of numerical simulations with experimental measurements. In the absence of direct access to species, velocity, and temperature measurements in the combustion chamber model validation has to be performed using predicted and measured characteristics of the free jet that discharges from the nozzle. The most common assumption used when modelling combustion in HVOF thermal-spray devices is that the chemical reaction rates are much faster than the timescales associated with the gas dynamics. In particular, the Damkohler number, which describes the ratio of fluid timescales to chemical reaction timescales, is much smaller than unity. The consequence of this assumption is that the combustion is in a state of local thermodynamic and chemical equilibrium and that the reactions complete immediately upon entering the computational domain. This assumption provides an approximation of the combustion process and is easier to handle than other complex combustion mechanisms, and their associated reaction kinetics [20, 31, 40 42]. Smith et al [43] were the first to apply a one-dimensional equilibrium chemistry model, originally developed for the prediction of rocket performance, to HVOF combustion and it has been used subsequently by several groups. The reaction is normally expressed as a net reaction in the form of: Fuel + xoxygen Products, (1) where only the main combustion products, about seven to nine species, are considered. Swank et al [31] conducted experiments to study gas combustion behaviour. The results from this study revealed much higher values of enthalpy, gas temperature, and gas velocity at the gun exit than those obtained from numerical simulations using the equilibrium model. This significant deviation indicates that the combustion products are far from equilibrium compositions. Hence, in an effort to improve the simulations, a single one-dimensional model for the frozen combustion flow has been employed, which proved to be the more suitable model in predicting the values of enthalpy, gas temperature and gas velocity at the gun exit [31]. Despite this modification, correct prediction of the gas flow field in the combustion chamber was not achieved since it failed to account for the gradual ignition of the incoming oxygen fuel stream.

8 R8 Review Article Chang and Moore [35] included more reactions and species in the combustion model so as to predict a more accurate flow field with regard to energy release and flame speed in the combustion chamber and the gas flow field in the nozzle. Since the combustion mechanisms and reaction kinetics of even simple hydrocarbons like methane (CH 4 ) are not completely understood, detailed modelling of combustion of higher hydrocarbons, like acetylene, ethylene, propane, or kerosene in industrial applications remains an elusive goal Governing equations The equations governing gas flow in an HVOF torch express the physical laws of conservation of mass, momentum, energy, and individual chemical species. If the continuum hypothesis is valid mass conservation is expressed in terms of the continuity equation: ρ t + ( ) ρuj = ṁ, (2) x j where u j is the jth Cartesian component of the instantaneous velocity, ρ is the fluid density, and m represents the rate of mass generation in the system. The momentum equations are t (ρu i) + (ρu i u j ) = p + τ ij + ρf i, (3) x j x i x j where p is the static pressure, τ ij is the viscous stress tensor, and f i is the ith component of the body acceleration. For Newtonian fluids τ ij can be related to the velocity gradients through ( ui τ ij = µ + u ) j 2 x j x i 3 µ u k δ ij, (4) x k where µ is the fluid dynamic viscosity and δ ij is the Kronecker delta symbol. Substitution of equation (4) into (3) results in the Navier Stokes equations: t (ρu i) + (ρu i u j ) = p + { ( ui µ + u j x j x i x j x j x i ) 2 3 µ u k x k δ ij } + ρf i. (5) The energy equation is a mathematical expression of the first law of thermodynamics. For high-speed compressible flows, where there is extensive interchange between thermal and kinetic energy, the total enthalpy form of the energy equation is usually used. The total, or stagnation, enthalpy is defined as H = h + u j u j 2, (6) where h is the static enthalpy, defined as T h = c p dt. (7) T ref The energy equation takes the form t (ρh ) + (ρu j H) = ( k T ) + p x j x j x j t + (τ ij u j ) (J ij h i ) + S a + ρf i u i. (8) x i x j Here, J ij is the total (concentration and temperature driven) diffusive mass flux for the species, S a represents additional energy sources, and k is the thermal conductivity.

9 Review Article R Turbulence models The time-dependent transport equations given above are equally applicable to both laminar and turbulent flow. Turbulent flows, however, are inherently unsteady and contain a wide range of time and length scales. Direct numerical simulations of turbulent flows using the transient form of the equations requires prohibitively short time steps and excessively fine grids. For most engineering calculations it is more appropriate to apply a time-averaged form of the Navier Stokes equations, including some appropriate assumptions about the turbulence structure. A discussion of different time-averaged turbulence models can be found in [44]. The k ε turbulence model is a two equation model that employs partial differential equations to govern the transport of the turbulent kinetic energy, k, and its dissipation rate, ε. The standard k ε model based on Launder and Spalding [45] is most frequently used to model the flow fields of a thermal spraying device. In this model, the square root of k is taken to be the velocity scale, while the length scale is modelled as µ k 3/2 l = C3/4. (9) ε The expression for eddy viscosity is ν t = C µk 2. (10) ε The modelled equations for k and ε are t (ρk) + (ρu j k) = ρp ρε + [( µ + µ ) ] t k, (11) x j x j σ k x j t (ρε) + ρpε ρε 2 (ρu j ε) = C ε1 C ε2 x j k k + [( µ + µ ) ] t ε, (12) x j σ ε x j where C µ, C ε1, C ε2, σ k, σ ε are five constants and the production P is defined as ( µi P = ν t + µ j 2 ) µ m µi δ ij 2 x j x i 3 x m x j 3 k µ m. (13) x m This model is a semi-empirical model based on the Reynolds-averaging technique of the Navier Stokes equations and is only valid for fully turbulent flow. The improved Renormalization Group (RNG) k ε model employs an analytical approach to the Navier Stokes equations. Additional terms and functions appear in the transport equations for k and ε. This model accounts for effects of swirl, low Reynolds number effects, separated flows, and time-dependent flows, and provides analytical formulae for turbulent Prandtl numbers. The RNG model, however, is susceptible to instability. For practical computational use, the standard k ε model is more stable than the RNG k ε model. As the flow field is straight, fully turbulent and has no swirling areas, the standard k ε model does not seem to have disadvantages and will lead to a satisfying solution to the HVOF thermal spraying applications. For high-speed flows the rate of turbulent dissipation decreases as the Mach number increases. If this effect is not included in the k ε model, then high-speed turbulent jets are predicted to decay more rapidly than observed in experiments. Since the HVOF thermal spraying flows of interest occur at relatively high Mach number, where the compressibility is important, the compressibility corrections were made by Oberkampf et al [46].

10 R10 Review Article 2.4. Numerical schemes In a high-speed compressible flow, the accuracy, numerical stability, and boundedness of the solution depends critically on numerical schemes used to resolve the conservation equations. The first-order upwind-differencing scheme (UDS) and the hybrid-differencing scheme (HDS) are the techniques most commonly used to difference the conservation equations. The UDS scheme simply applies the value from the upstream cell to the cell face. HDS uses UDS in high convection regions, and the purely diffusive second-order central-differencing scheme (CDS) in low convection regions. HDS is bounded and highly stable, but also highly diffusive when the flow direction is skewed relative to the finite volume mesh. This makes it difficult to capture discontinuities, such as the shock diamonds in the free jet of the HVOF. The HDS is only marginally more accurate than the UDS since the second-order CDS is restricted to low convection regions. Although, in principle, it is possible to reduce numerical diffusion through a process of grid refinement it is found that both UDS and HDS are rather sluggish to grid refinement and, for most engineering problems, it is necessary to resort to schemes with higher order truncation errors. Linear higher order schemes, such as CDS, and the well-known QUICK scheme, increase the accuracy of solution, but may still suffer from the boundedness problem, i.e. the solution may display unphysical oscillations around steep gradients, or unacceptable negative values for species concentrations and certain turbulence quantities. Therefore, highly accurate schemes, such as total variation diminishing (TVD) [47 49], MUSCL [50], PPM [51], and ENO [52] have been developed and have proved to be capable of capturing supersonic shocks with relatively few cells. One excellent example was given by Sinha et al using a characteristicbased upwind (Roe/TVD) scheme and the standard k ξ turbulence model. As shown in figure 4, the numerical results agree very well with the experimental data on the intensity and position of the diamond shocks [53]. It should be pointed out that the above schemes have mainly be used in the modelling of room-temperature air jets. In the modelling of the HVOF processes, however, most of the schemes used are only of first and second order. For example, Oberkampf and Talpallikar [46] used different schemes for different equations. A second-order upwind scheme was used for the convection terms in the continuity and momentum equations, while a first-order upwind Figure 4. Comparisons of pressures along the axis of a jet for an underexpanded Mach 2 nozzle expanding into air, obtained by experiment ( ) and simulation (- ---)[53].

11 Review Article R11 (a) (b) Figure 5. Flooded Mach number contour over the calculation domain (a) and Mach number profiles along the centreline (b): a result from third-order Osher Chakravarthy scheme [38]. scheme was used for the convection terms in the energy, turbulence, and mixture fraction equations. Eidelman et al [34] tried to use the MUSCL scheme to capture HVOF shock diamonds; however, only two diamonds were observed in their results. Only recently a thirdorder Osher Chakravarthy scheme was able to successfully capture five shock diamonds in the HVOF process, as shown in figure 5 [38]. Compared with the approximately eight diamonds observed experimentally, however, there is apparently much work to be done to increase the accuracy. The reason few higher order schemes have been used might be due to their numerical stability. Actually, in [38], much efforts were devoted to obtaining a convergent numerical solution when the third-order scheme was applied, because of the complexity of HVOF processes. To obtain more accurate numerical results for the gas flow in HVOF systems, more efforts should be devoted to choosing, or developing new precise numerical schemes and developing skills in resolving the stability problems Results of gas dynamics modelling Several groups reported their modelling results in the open literature. Thorpe and Richter [19] conducted the first quantitative analysis of the gas dynamics of HVOF thermal spraying. They analysed the internal and external flow of a newly designed HP/HVOF torch from Hobart TAFA Technologies. Power et al [54] and Smith et al [43] performed the first simulation of the HVOF process using modern CFD techniques. They performed separate axisymmetric analyses of the internal and external flow in a Metco Diamond Jet torch. Oberkampf and Talpallikar [20] performed a CFD analysis of a similar torch using a commercial computer code, CFD-ACE. They modelled the HVOF process with full coupling between the internal and external flow fields. Figure 6 shows the computed static temperature distribution inside the nozzle. The peak combustion temperature for this simulation is 3100 K and occurs close to the oxygen propylene

12 R12 Review Article Figure 6. Temperature contours inside the nozzle of a Metco Diamond type torch [20]. Figure 7. Mach number contours over computational domain for a Metco Diamond type torch [20]. gas inlet. The gas temperature decreases gradually with axial distance. The chemistry model assumed an instantaneous reaction of the pre-mixed oxy-propylene stream as soon as it entered the computational domain. An improved combustion model should use finite rate chemistry to model the gradual ignition of the oxy-fuel stream. However, the computational time for such a solution would increase substantially. Figure 7 shows the contours of the local Mach number for the torch. Inside the nozzle, the velocity of the gas mixture is low, but it is accelerated to M = 1 at the nozzle exit. Upon entering the ambient environment, the gas flow immediately expands in order to match the ambient pressure at the contact boundaries, and is accelerated during expansion. The gas mixture is alternately accelerated and decelerated due to repeated expansion and compression until, finally, it decays to a subsonic velocity after several cycles. It is obvious from these contours of the Mach number that an annulus of supersonic flow persists even through the compression waves associated with the shock diamonds. Richter [55] used the commercial CFD program RAMPANT to model the combustion and gas flow of HVOF processes with the two different gun configurations shown in figure 2. It was reported that in both cases the combustion is essentially completed by the time the exhaust

13 Review Article R13 gases have accelerated to sonic velocity at the nozzle throat. Increasing the mass flow rates of fuel and oxygen into the combustion chamber results in an increase in combustion pressure. Moderate increases have little effect on the gas velocities and result in only a small increase in temperature. A substantially larger mass throughput, i.e. in the case of gun (a), results in a longer supersonic jet which extends further towards the substrate than that of gun (b). A sensitivity study by Cheng et al [56] investigated the effect of operational parameters on gas dynamics during HVOF thermal spraying. The calculated results showed that the most sensitive parameters affecting the process are propylene flow rate, total flow rate of oxygen and propylene (oxy-fuel flow rate), total inlet gas flow rate, and barrel length. The results show that increasing the total inlet gas flow rate has limited effect on the gas velocity and temperature inside the nozzle, for the parameter range investigated. However, increasing the total inlet gas flow rate increases the total thermal and momentum inertia. Moreover, the flame gas is maintained at a high velocity and temperature for a longer distance. Increasing the oxy-fuel flow rate significantly increases flame velocity and temperature, particularly after exiting the nozzle. The effect of propylene flow rate is significant and complex. In order to minimize the extent of oxidation of the sprayed powder particles, and to achieve a high flame temperature and velocity, the overall injected stream should be adjusted to be propylene-rich. The nitrogen flow rate significantly affects the gas flow on the inside of the gun. On the basis of the calculated results it is evident that in order to obtain maximum gas velocity and temperature, the nitrogen flow rate should be kept to a minimum, provided that particles can be delivered to the gun in a smooth manner. By minimizing the entrainment of the surrounding air, a nozzle with longer barrel length achieves a relatively high gas velocity and temperature for a longer distance. The calculated results qualitatively agree with available experimental results. Up to now, no experimental data could be found in the open literature about the gas dynamics of HVOF processes, due to the difficulties in measuring the temperature, pressure, and velocity of the gas flame because of its higher temperature characteristics. Therefore, direct validation of the models still needs to be done with the availability of experiment data. One indirect way to validate the mathematical model is to use the model to simulate a similar air nozzle, where the measurement of pressure along the flow is feasible [53,56]. The other method is by comparison of the number and distance of simulated diamond shocks with experimental observations. The latter methods have been described in section 2.4, and show discrepancies between simulation results and experimental results. Improved combustion model (finite rate chemistry), improved turbulent model (RNG k ε model) and higher numerical schemes should give better numerical results. However, those measures will substantially increase computation time and lead to numerical instability. 3. Particle models Models describing the in-flight behaviour of particles during plasma spraying are in an advanced stage of development and are well documented [42, 57, 58]. Modifications of these models have been applied to the HVOF process. Mathematical models of the dynamic and thermal behaviour of in-flight particles utilize either the Eulerian or the Lagrangian approach. The Eulerian approach uses a frame of reference fixed in the laboratory and represents the gas/particle mixture as a two-phase flow. The two phases are considered as separate fluids each occupying a fraction of a control volume. This method is particularly useful when the fraction of particles is large. A direct numerical simulation of the two-phase turbulent flow system requires solving the instantaneous compressible Navier Stokes equation for the gas flow followed by simulating the motion of

14 R14 Review Article a large number of particles in the resolved instantaneous gas field. This method requires a large capacity and very fast computers. It is not practical at the present time for engineering applications and is seldom used to model the HVOF processes. Instead, the Lagrangian approach is frequently used. With the dilute assumption, the Lagrangian approach considers the volume occupied by particles as negligible. In this approach, the semi-coupled or decoupled method can be used to solve the governing equations. From the viewpoint of solution methods of governing equations for two-phase systems, three types of models may be considered: coupled, semi-coupled [35,46,59] and decoupled [36,60]. Since the coupled method, Eulerian approach, is seldom used in HVOF processes, only decoupled and semi-coupled methods are discussed Decoupled model (Lagrangian approach) When the particle loading is very low, one can assume that the presence of particles will have a negligible effect on the gas velocity and temperature field in the barrel and in the jet. This means that the governing equations can separately be described for gases and particles. If the number of particles in the unit volume is also small, one can also assume that the particles are collisionless in flow. As a result of these assumptions, the two-phase problem can then be decoupled, and one can simulate the gas flow first and then study the flow of different particles through the established flow pattern. Usually, the most convenient methods for collisionless particle modelling is the Lagrangian formulation, where the simulation of particle motion is performed for every particle or group of particles [18]. Also, Lagrangian particle flow formulation allows a clear definition of the particle boundary conditions, in particular, for the particles reflecting from the walls. Such a simulation is extremely difficult to perform when an Eulerian approach is used for the particle descriptions. The simulation of the particle flow field consists of calculating particle trajectories and temperature histories in the gun barrel and in the jet. Particle motion in the turbulent gas is predicted by means of a Lagrangian stochastic model (LSD) [61,62]. There are two elements in the LSD model: the description of the turbulent field and integration of the particle motion equations. Numerical solution of the gas fluid equations provides the fields of mean velocity components as well as turbulent kinetic energy κ and dissipation rate of turbulent kinetic energy ε. From k and ε, the scales in time and space of large turbulence eddies can be evaluated. The fluid instantaneous velocity is obtained by adding the fluctuating velocity resulting from large turbulent eddy to the mean velocity. The velocity and temperature of the powder particles are noted as important parameters characterizing the in-flight behaviour of the powder particles. Generally, the following factors are thought to govern the movement of the powder particles [63]: (i) drag force, (ii) force due to pressure gradients, (iii) force due to added mass, (iv) Basset history term, and (v) external potential forces (gravitational, electrical, among others). In principle, among the factors that affect the movement of particles during the HVOF process, only the drag force plays a dominant role, other factors can be neglected in most cases [64]. Therefore, the motion equation describing the velocity of the particle is expressed as dv p v p ρ p = 1 dt 2 A pc D ρ g (V g V p ) 2, (14) where v p is the volume of the particle and A p the projected area of the particle. C D is the drag coefficient depending on Reynolds number, Re = ρ g D p (V p V g )/µ g (µ g is the dynamic viscosity of the gas). It should be kept in mind that in a specified flow the appropriate selection

15 Review Article R15 of the drag coefficient is still one of the unresolved problems in the field of gas particle flows [65]. Regarding the thermal behaviour of the powder particles during the HVOF process, the powder particle temperature, T p, as a function of time, t, and radial coordinate, x, can be described by a heat conduction equation: ( x n T p λ p x ), 0 x R p, t > 0, (15) T p ρ p c p = 1 t x n x where c p is the specific heat of the particles, and λ p is the heat conductivity of the particles. The boundary conditions describing the centre and the surface of the particles are as follows: and T p (0,t)= 0 (16) x λ p T p t (R p,t)= c h (T f T p (R p, t)), (17) where T p (x, 0) = T p0, and the coefficient of heat transfer, c h, can be determined by the Ranz Marshall semi-empirical equation [66]: N u = c hd p λ = 2+0.6Re 1/2 Pr 1/3, Pr = c f η f λ f. (18) It is thought that during the HVOF spraying process the surface temperature of a homogeneous particle can become as high as the melting temperature of that material [42]. Hence, subsequent propagation of the melting front towards the particle centre is controlled by the so-called Stefan heat balance condition [67]. Inserting the effective specific heat into the heat conductivity equation (15), it becomes ρ p c p (T p ) T p x = 1 x n ( ) x n T p λ p, 0 x R p, t > 0, (19) x x ( ) p (T p ) = 1+q p cp 1 (1 k) 1 (T k T 1 ) 1 Tk T (2 k)/(1 k) 1, T s T p T 1, (20) T p T 1 (T p ) = 1, T p >T 1 T p <T s. (21) The boundary and initial conditions for equation (19) are the same as in equation (15). Yang and Eidelman [36] used the decoupled model to simulate the gas flow field, particle temperature and particle velocity histories, and particle temperature and velocity profiles in the HVOF thermal spraying of Inconel 718. The model was validated by experimental measurement of the gas velocity and particle velocity and excellent agreement between simulations and measurements was obtained for both gas and particle flow fields, as shown in figure 8. The simulated results also show that the velocity and temperature distributions of particles are critically determined by their sizes. These quantitative results offer a comprehensive, fundamental analysis of the HVOF thermal-spray system and allow the researcher or engineer to design optimal injection conditions for different particle and flow regimes Semi-coupled model (Lagrangian approach) For the semi-coupled method, the dilute assumption also means that the particulate phase occupies a negligible volume fraction of the flow and that the particles are collisionless. The coupling between the two phases is accomplished by adding source terms in the gas phase equations. This technique usually incorporates a statistical model to take into account the

16 R16 Review Article (a) (b) Figure 8. Velocity (a) and temperature (b) distributions of gas and Inconel 718 particles with different sizes at the jet centreline for the case of an 8 in gun barrel ( : experimentally measured gas velocity; : calculated velocities for gas; : 10 mm; : 20 mm; +: 40 mm, and : 60mm particles, respectively;, experimentally measured velocity for 40 mm particles) [36]. non-uniform distribution effect of particle sizes and the sum over all particles in the appropriate computational cell. The detailed methodology for formulating the source terms can be found in [35, 59]. In [68], a fully consistent numerical simulation of HVOF spraying with injected Inconel 718 particles has been presented with the application of a semi-decoupled model. The transient solution using a stochastic particle model provided insight into the statistical distribution of particle temperature, velocity, size, and degree of melting. As shown in figure 9, the following results could be obtained: Particle acceleration and heating strongly depend on the particle size. Most particles did not reach the melting temperature. Particles are only partially molten even at the melting temperature. Particle heating and melting strongly depend on the particle size. Small particles have higher velocities and higher temperatures as expected. Heavier (larger) particles penetrate further into the gas due to their larger mass and momentum. Lopez et al [69] used a semi-coupled model to simulate the gas/particle dynamics of a wire-feed HVOF thermal-spray torch in two dimensions. Particle velocity distributions were measured using a Laser Two-Focus (L2F) velocimeter. Table 1 shows a direct comparison of the numerically predicted and experimentally measured particle velocities at three coincident locations. The predictions compare very well with the measured particle velocities. In the case of numerical solutions, for the coupled and semi-coupled methods, governing equations are simultaneously solved for the two phases. It is accordingly preferable to consider the gas flow as steady. However, it is relatively difficult to model the thermal behaviour of a particle; in particular, it is difficult to deal with the melting front propagation and the latent heat effect in a particle. On the contrary, the decoupled method is applicable to steady or unsteady equations and able to model the solidification and melting problems in an individual particle. Therefore, the choice of model strongly depends on the problems to be addressed and the equations for the gas phase.

17 Review Article R17 (a) (b) (c) (d) Figure 9. Distributions of particle axial velocity (a), particle temperature (b), particle degree-ofmelting, and particle size at the exit of the torch at t = 2 ms during thermal spraying of Inconel 718 coatings [68]. Table 1. Measured and predicted particle velocities, after [69]. Positions Measured Predicted (mm) V (m s 1 ) V (m s 1 ) Impingement, flattening, and solidification of droplets It is well established that the most critical factors governing the quality of as-sprayed materials are bonding and porosity among deposits, and these are closely related to the interaction behaviour of droplets on a substrate surface. In thermal-spray processes, the transient behaviour associated with the spreading and consolidation of sprayed droplets on a target substrate is of critical importance. The physical phenomena occurring during droplet impingement involve fluid flow, heat transfer, and rapid solidification. These phenomena take place simultaneously on a microscopic scale while droplets with different solid fractions at high velocities impact on a microscopically non-flat liquid, mushy or solid surface layer on the substrate. The droplet/substrate and droplet/droplet interactions critically determine the morphological characteristics and adhesion of the resultant splats and, hence significantly affect the microstructure and mechanical properties of as-sprayed materials. In order to realize in situ,

18 R18 Review Article continuous control over the microstructure and ultimate mechanical properties of as-sprayed materials, it is necessary to ascertain the inherent relationship between the microstructure and the processing parameters, such as substrate surface condition, initial droplet size and velocity, as well as materials properties. Therefore, a comprehensive understanding of the complex physical phenomena during droplet impingement and effects of the processing parameters is highly desirable. The first numerical study on the transient flow behaviour of a single liquid droplet impinging onto a flat surface, into a shallow or deep pool was performed by Harlow and Shannon [70]. In their work, the full Navier Stokes equations were solved numerically in cylindrical coordinates using the marker-and-cell technique [71]. However, the effects of the surface tension and viscosity, that are important to the deformation behaviour of the molten droplets, were not taken into consideration. Kitaura et al [72] improved the method of Harlow and Shannon by considering the effects of the surface tension and viscosity, and applied the method to a single droplet impinging onto a hot flat surface. In both studies, however, interactions between multiple droplets during spreading were not taken into account. In addition, the impact speed, density, viscosity and surface tension of the liquid droplets (e.g. water) that were used in these studies were significantly lower relative to those present normally in spray deposition processes. Nevertheless, these pioneering studies did provide valuable insight into the problem of droplet impingement. The deformation and solidification behaviour of a single molten droplet on a cold surface was investigated by Madejski [73]. A simplified model was developed which considered inertial, viscous, and surface tension effects to predict the final splat diameter and height. Solidification during droplet spreading was determined by incorporating the one-dimensional Stefan solution into a macroscopic flow model. He predicted asymptotic values for the degree of spreading ξ m of the impinging droplets for different ranges of freezing parameter k, Reynold number Re, and Weber number We (table 2). A recent analytical investigation [74] modified some of the assumptions of Madejski s model and addressed the effects of different solid fractions of a droplet in flight. Using Madejski s model, however, the details of the transient deformation behaviour during droplet spreading, especially during the interaction of multiple droplets, cannot be determined. Trapaga and Szekely [75] conducted a mathematical study of the isothermal impingement of liquid droplets in spray processes using the commercial package FLOW-3D. In a subsequent study, heat transfer and solidification phenomena were also addressed [76]. The results of these studies provided detailed information on the spreading process for a single droplet on a flat surface, and related the final splat diameter to operational parameters, such as initial droplet velocity, initial droplet diameter, and droplet material properties. Although experimental investigations of droplet spreading behaviour have received increasing attention, for example, using high-speed two-colour pyrometers [77], the experimental observation of droplet impingement and solidification by Trapaga et al [76] using high-speed videography is Table 2. Asymptotic equations proposed by Madejski [73] for the estimation of the degree of spreading ξ m for different ranges of the parameters k, Re, and We. ξ m = We/3 k = 0 = Re 1, We > 100 a ξ m = (Re ) 1/5 k = 0 = We 1, Re < 100 a ξ m = Re 1/5 k = 0 = We 1, Re > 100 a (3ξm 2 /We) + (1/Re)(ξ m/1.2941) 5 = 1 k = 0, We > 100, Re > 100 a ξ m = k k>0, We 1 = 0, Re 1 = 0 b a Fluid flow. b Fluid flow and solidification.

19 Review Article R19 indeed unique. However, only preliminary numerical results regarding the interaction of two droplets, one droplet into a liquid pool or onto a fibre, were presented in these studies. Liu et al [78,79] performed a numerical study of the interaction between multiple flattening droplets on a flat surface. They solved the full Navier Stokes equations, coupled with the volume of fluid (VOF) technique, using the program RIPPLE [80]. A two-domain method was employed to treat the thermal field and solidification problem within the flattening droplet and to track the moving solid/liquid interface. A Stefan solution of the solidification problem was incorporated into a two-phase flow continuum model to simulate the flow problem with a growing solid layer. These studies not only provided detailed information of interaction processes of multiple molten droplets, but also improved our understanding of the effects of important processing parameters on the spreading and interaction behaviour. In addition, the numerical results provided insight into the formation of vortices and ejection of liquid from a surface during impingement of multiple droplets. Consequently, these studies form a basis for exploring the mechanisms that govern the micro-pore evolution during discrete droplet processes. Most of the above studies ignored the effect of the roughness of the deposition surface on the spreading of the droplet. Under the practical conditions that are present in spray deposition processes, however, the physical phenomena of droplet spreading and consolidation take place at a microscopically rough and non-flat surface on a target substrate. In addition, droplets may not impact normal to the substrate surface. In more recent studies, the numerical modelling of the transient deformation behaviour of molten droplets during impingement onto a rough and non-flat surface, are performed [81, 82]. Bussmann et al [82] developed a three-dimensional model (also based on the code RIPPLE) of droplet impact onto an inclined plane and onto a sharp edge. Surface tension was modelled as a volume force acting on fluid near the free surface. Contact angles were applied as boundary conditions at the contact line. The results of simulations of both impact scenarios yielded reasonable agreement with experiment (figures 10 and 11). These results are quite different from droplet impact normal to a flat surface, where a single droplet spreads axisymetrically and eventually forms a thin, flat splat [83]. Liu et al [81] simulated droplet impact on wavy surfaces. Single droplets were shown to spread along the surface and to eventually form a thin, non-flat, splat. When the wavelength of the surface is larger than the droplet diameter, the spreading process exhibits a periodic repetition of an acceleration deceleration behaviour and ends with a violent liquid break-up (figure 12(a)). When the wavelength of the surface is smaller than the droplet diameter, the surface plays a hindering role in the spreading process (figure 12(b)). A final splat diameter of up to about seven times the initial droplet diameter is obtained over a large range of microseconds, depending on the surface conditions, impact velocities, droplet diameters and material properties. Although the impingement of droplets has been intensively studied, the modelling is limited to droplets with simple geometries (spheres). In HVOF thermal spray, however, it is not unusual for the impinging particles to be solid or a mixture of solid and liquid, often with an irregular shape [14]. Therefore, the modelling of impingement and deformation of these particles needs to be addressed in detail in future work. 5. HVOF synthesis of nanocrystalline coatings Recently, there has been increasing interest in the manufacture of nanocrystalline coatings by HVOF spraying. More than 50 volume per cent of atoms could be associated with grain

20 R20 Review Article Figure 10. Normal view of the impact of a 2 mm diameter water droplet at 1 m s 1 onto a 45 stainless steel incline. Photographs at the left, simulation results at the right [82]. boundaries or interfacial boundaries when the grain size is small enough [84]. Thus, a significant amount of interfacial component between neighbouring atoms associated with grain boundaries contributes to the unique properties of nanocrystalline materials, such as high hardness, high strength, and high corrosion resistance [84]. Since the pioneering work of Kear et al [9] and Tellkamp et al [10], advances have been made towards the synthesis of nanocrystalline feedstock powders, suitable for HVOF thermal spraying; the development of new material systems, having the potential of producing nanocrystalline coatings with superior physical and mechanical properties; the synthesis of nanocrystalline coatings from nanocrystalline feedstock powders;

21 Review Article R21 Figure 11. Perspective view of the impact of a 2 mm diameter water droplet at 1.2 m s 1 onto a 1 mm high stainless steel edge. Photographs at the left, simulation results at the right [82]. increased fundamental understanding on the formation of nanocrystalline coatings during HVOF spraying; and modelling of the HVOF process to optimize the experimental parameters. The development of nanocrystalline HVOF coatings is driven by the need to enhance the physical characteristics of engineered coatings (e.g. hardness, bond strength, corrosive behaviour, etc), as well as the potential to develop coatings with heretofore-unobtainable microstructures (e.g. with grain sizes <100 nm) [85, 86]. Preliminary research results [9, 10] are encouraging, and potential industrial applications are rapidly expanding. It is also apparent, however, that in order to fully exploit the potential of this technology a firm understanding of

22 R22 Review Article (a) (b) Figure 12. Deformation sequence of a single tungsten droplet impinging onto a solid, waved surface layer on a substrate: (a) wavelength larger than droplet diameter, (b) wavelength smaller than droplet diameter [81]. the relevant fundamental physical phenomena involved will have to be established. This will be a challenge to the scientific community as a result of the complex interaction between the fluid, thermal, and solidification phenomena that are present during the thermal spraying of nanocrystalline materials. The complexity of the HVOF process poses a challenge in predicting the behaviour of HVOF sprayed nanocrystalline coatings, both experimentally and theoretically. In principle, however, it is evident that the behaviour of the nanocrystalline powders during HVOF will be influenced by: (i) the inherent thermal stability of the sprayed materials, (ii) the thermal environment present during the HVOF process, and (iii) the thermal history of the particle powders (liquid or solid) following impingement, initially on a surface and subsequently on each other. In reference to the development of nanocrystalline coatings, mathematical modelling may be used for the following: to provide fundamental insight into the mechanisms that govern microstructural evolution; to provide guidance in the establishment of HVOF experimental parameters that will be required to generate optimal combinations of microstructure and physical behaviour; to allow the manufacture of nanostructured coatings with complex physical and chemical arrangements (i.e. graded or layered in two or three dimensions) Momentum and thermal transfer during flight In related studies, Eidelman et al [37] used a three-dimensional CFD model, consisting of a conservative equation and constitutive relations for both gas and particle phases, to simulate the HVOF spraying of nanocrystalline coatings. As a result, process optimization, new process and coating tool design, and control design for the thermal spraying system were evaluated. In the case of thermal spraying of nanocrystalline WC/Co, the results of this study show that the deposition of a high density coating requires the preparation of µm WC/Co agglomerates which should be stable and not disintegrate under conditions of a supersonic flow. In addition, the results show that a low temperature exposure tends to prevent grain growth, particle disintegration resulting from Co melting and substrate overheat [37].

23 Review Article R23 As stated in section 3.2, to render the problem tractable, the particle is often assumed to be a sphere. In practice, especially during thermal spraying of nanocrystalline materials, powders with irregular morphologies are often used as feedstock materials (see figure 13). Even a spherical particle may change its morphology during flight in the jet. The geometrical factor will greatly affect the mechanical and thermal behaviour of in-flight particles. These factors should be included in the modelling work for thermal spraying of nanocrystalline materials to obtain more precise results. In related studies, Lau et al [14, 87] selected a route to simulate the HVOF spraying process for producing nanocrystalline coatings from cryomilled nanocrystalline Ni feedstock powders, in which a number of issues relative to the specific characteristics of the cryomilled nanocrystalline feedstock powders (not spherical), such as powder aspect ratio, were addressed. During mechanical milling, the continuous welding and fracturing of the as-received spherical powder particles results in the formation of flake-shaped agglomerates. In order to account for the geometry of the irregular flakes, the particle area in equation (14) is expressed as the shape of two faces of an ellipse: A p = 2πr 2 n, (22) where r is the radius of the particle and n the aspect ratio. The volume, v p is then expressed by the following equation: v p = A p c, (23) where c is the thickness of the flakes. The dimensional characteristics of methanol milled and cryomilled Ni powders are shown in table 3. The results of the modelling studies are presented in figure 14. The model predicts a sharp increase in initial velocity and temperature for both (a) (b) 200 µm 200 µm Figure 13. Examples of different morphologies of feedstock powders for HVOF thermal spraying. (a) Nanocrystalline Al powders; (b) nanocrystalline Ni powders. Table 3. The dimensional characteristics of methanol milled and cryomilled Ni powder. Milling environment Agglomerate size Thickness (mm) (mm) Milling time Aspect (h) a d 10 a d 50 a d 90 d 10 d 50 d 90 ratio Methanol Liquid nitrogen a d 10, d 50, d 90 particle size corresponding to 10, 50, and 90 weight per cent of the cumulative particle size distribution.