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Computational Development of a Novel Aerosol Synthesis Technique for Production of Dense and Nanostructured Zirconia Coating

Mahrukh Mahrukh 1, 2, Arvind Kumar 3, Sai Gu 4,*, Spyros Kamnis 5

1 School of Energy, Environment & Agrifood, Cranfield University, Cranfield, Bedford, MK43 0AL, UK

2 Department of Mechanical Engineering, NED University of Engineering & Technology, University Road, 75270 Karachi, Pakistan

3 Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India

4, * Department of Chemical and Process Engineering, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, GU2 7XH, UK

5 Monitor Coatings Limited, 2 Elm Road, North Shields, Tyne & Wear, NE29 8SE, UK

* Corresponding author: Email: sai.gu@surrey.ac.uk, Tel. +44 01483 682676

ABSTRACT

The feasibility of a new processing method solution precursor high-velocity oxygen fuel spray (SP-HVOFS) is presented for the production of dense ZrO2-based nanostructured coatings, in which organometallic chemical precursor droplets are injected into the HVOF spray system. With the help of developed computational fluid dynamics (CFD) solver (Fluent), the evolution of particle volume, area, and number concentration is simulated considering nucleation, coagulation, and sintering. The aerosol model is validated with the experimental data available in the literature. When the oxygen-fuel gas flow rate (GFR) is increased, the (i) velocity and (ii) enthalpy of the HVOF flame is increased. The former reduces the particle residence time in the HVOF flame while the latter favours the sintering. Overall the results show that by controlling the GFR, single scale nanometre particles (~1-5 nm) can be fabricated without any agglomeration.

KEYWORDS: Liquid feedstock; Nanostructured coating; Solution precursor; Thermal Spray; Computational fluid dynamics

INTRODUCTION

Thermal spray processes are widely used for the generation of wear, corrosion or thermal resistant layers on machine parts for increasing their durability. The major advantages of these coating techniques are the usage of diverse ceramic and metallic materials 15. The technology of high-velocity oxygen-fuel (HVOF) thermal spraying is commonly used for spraying metallic particles; however with some modifications, it can be utilized for spraying ceramic particles 1,5. Further advancements in the coating industry are moving towards spraying nanoparticles for dense and thick coating with excellent bonding strength. The use of powder feedstock limits the size of injected particles and the thickness of the coating. Recently, liquid feedstock is utilized in HVOF spraying to generate dense coatings 510. The liquid feedstock is either suspension of nanoparticles or solutions. The former contains nano- or micro-sized particles in a solvent with dispersing agents while the solution precursors are made by dissolving metal salts or organometallic or liquid metal precursors in a solvent 1113.

The development of suspension and solution plasma spraying is briefly addressed in this work as the major topic focuses on the solution-based HVOF thermal spraying. The need for a discussion of suspension plasma spraying (SPS) and solution precursor plasma spraying (SPPS) is to compare the spraying process and coating outcomes. The literature related to suspension and solution HVOF spraying is minimal. Hence, it is required to consider the in-depth review of the SPS and SPPS processes to understand the behaviour of the suspension and solution breakup, evaporation, precipitation, and deposition processes.

The powder injection replacement with the liquid feedstock in the form of solution precursor is highlighted in the following as the research gap by presenting an in-depth literature review. However, the use of solution precursor thermal spraying over suspension thermal spraying purely depends on the application requirements. Though, solution precursor offers some key benefits over the suspension spraying. Supplementary work required for suspension spraying process includes the addition of suitable dispersion for making a stable suspension for controlling particles agglomeration (or settling down) in the reservoir; further constant stirring is essential to reduce this problem. The addition of a different product to the liquid phase is requisite to adjust the viscosity and/or surface tension of suspension. Also, viscosity increases with increment in the suspended particles, which in turn leads to the requirement of higher pumping power 1113. The thermal barrier coating (TBC) obtained by suspension plasma spraying show coating microstructure with medium porosity and high segmentation crack density 14.

Whereas the solution precursors are highly stabilized solutions, and its viscosity depends on the concentration of solution; no extra addition of dispersing agents or constant stirring is required for the precursor solution stabilization. Compared with the other thermal spray techniques, solution precursor thermal spraying allows an excellent chemical homogeneity of coatings 12. The solution precursor is mixed at the molecular level. Therefore, more stable phase composition and properties are expected in the sprayed coatings as compared to suspension spraying and conventional powder spraying 6. Furthermore, the solution precursor HVOF spraying eliminates the cumbersome process of nano-size powder manufacturing for using these nanoparticles in HVOF suspension or powder flame spraying processes. The coating generated by solution precursor spraying is denser, and no cracks are observed in the as-sprayed coating; also it is well bonded to the substrate 13.

The researchers studied the SPPS for in-situ particles generation and deposition of the coating layer on the substrate 15,16. The solution precursor plasma spraying involves on-site generation of fine particles (50500 nm) and splats formation of sizes from 2002000 nm, and shows nano-porosity and large homogeneous microstructure 16. The microstructure of TBC generated by SPPS has shown vertical cracks, dense ultrafine splats regions, and uniformly dispersed porosity 15.

Further, Bertolissi et al. 17 studied the size of the solution droplets in the SPPS by laser shadowgraphy technique. They examined the droplet breakup and solvent evaporation using water and ethanol solvents. It is evaluated that these processes are more efficient when the ethanol-based solution is injected into the plasma gas; whereas, residual liquid droplets are detected on the substrate with water-based solutions. It is concluded that residual liquid droplets at the substrate turned into non-pyrolized inclusions and later (by plasma heat) converted into the porous sponge-like structure in the deposit 17. In the SPPS coating processes, efficient heating of the precursor leads to dense deposits while increasing the amount of partially pyrolized precursor (poorly heated) leads to greater porosity 18. It is highlighted that primarily droplet injection density can control the amount of non-decomposed or partially pyrolized precursor droplets, spray droplets fragmentation and precursor concentration 13,15,19.

In the experiment reported by Ma et al. 7, the solution precursor is used for the coating of Inconel alloy layer for generating finely structured and highly bonded coatings using the solution precursor high-velocity oxygen-fuel spray (SP-HVOFS). The results showed that the coating obtained from SP-HVOFS process has better resistance to erosion and thermal shocks. It has good surface quality, adhesion, and ductility over the powder feedstock system 7. Chen et al. 5 studied the deposition of Al2O3-ZrO2 ceramic coatings by SP-HVOFS process. Both nanocrystalline ZrO2 and amorphous -Al2O3 are observed by as-sprayed coating characterization using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The coatings consist of ultrafine splats (25 m), spherical particles and hollow shell structures having high density with the thickness of 40 m 5.

In solution precursor, the process of droplets disintegration is dependent on the preparation of solution precursor. The main parameters required to maintain during the precursor preparation process are precursor viscosity, surface tension, the boiling point of the liquid solvent, solute chemistry and its solubility 13. The behaviour of small particles generated during the solution precursor flame spraying process depends on precursor droplet size distribution and injection velocities that need to be controlled during the process 12,13. These problems must be restrained by optimizing the process parameters which can be achieved by numerical modelling.

It is assumed that the nanoparticles synthesis inside the HVOF flame is similar to the flame spray pyrolysis (FSP). The numerical analysis of FSP is performed by Grohn et al. 20,21 in which they develop a model to predict the average primary ZrO2 particle diameters using monodisperse particle dynamics where the global chemical reactions are considered by which the immediate nanoparticle formation started upon precursor oxidation. The model is validated and showed that the increasing precursor concentration and/or decreasing dispersion gas flow resulted in the increase of product primary particle size. Moreover, Torabmostaedi et al. 22 pesented a numerical method by combining CFD with the particle dynamics to study the effect of processing parameters on the formation of nanoparticles by FSP for scaling up the synthesis of zirconia nanoparticles. A commercial CFD code is employed to simulate the gas flow field and droplet dynamics. They concluded that at higher precursor concentration, the primary particle diameter grew to 20 nm since higher particle concentration increased the coagulation and therefore enhanced the growth of primary particle at above the burner.

For a clear understanding of the numerical modelling of HVOF, and SP-HVOFS processes a brief literature review is presented here. The numerical modelling of HVOF conventional system with powder injection is performed by many researchers 2329. Li and Christofides 23 highlighted the multi-scale behaviour of the overall process inside the HVOF thermal spray torch. They divide the process dynamics into two main parts; first gas dynamics and the other particle dynamics (or in-flight particle behaviour). Both parts are highly dependent on the specific operating parameters of the HVOF torch. Gas dynamics shows different nature, such as varied temperature, pressure, and velocity, depending on the type of fuel used for combustion and oxygen-fuel ratio 25. Particle dynamics is dependent on the injection mass flow rate, particle size, and shape, injection velocity, the angle of spray and spray distance. For controlling the process having these parametric variations, CFD techniques are required to make the real process more efficient 23,25,26.

Till today, very few researchers have modelled the SP-HVOFS process. Modelling of the SP-HVOFS process has proved that droplets injected into the HVOF jet undergo strong shear breakup due to high relative velocities hence producing smaller secondary droplets 5,30,31. Use of atomization for solution precursor injection will further improve the solid particles morphologies hence forming dense coatings 30. Basu and Cetegen 30,31 modelled the injection of solution precursor droplet into the HVOF flame jet. This model covers the analysis of droplet breakup, vaporization, solute precipitation and pressurization in the liquid core surrounded by the solute. It is examined that the smaller droplets get evaporated rapidly and give out solid particles due to rapid heating while the larger droplets form precipitate shells with the liquid core inside. It is summarized that the coating generated by this approach is denser than the conventional process.

It may be noted that there are very less number of works reported regarding experiments and modelling of SP-HVOFS process, and more research is required in these areas. To date, no work has been reported to study the on-site formation and growth of nanoparticles for coating generation during the SP-HVOFS process. The novel numerical modelling of the nanoparticle synthesis inside the HVOF torch is performed first time in this piece of work. It is realized that the size of nanoparticles needs to be controlled for the specific coating requirement 12,31,32. In this work the gas flow rates (GFR) are regulated to control the size of nanoparticles for coating processes. The time-temperature history of the droplets and the nanoparticles in the HVOF flame are shown to control the size of resultant particulate deposits (i.e. primary particle and agglomerate size). The SP-HVOFS process includes complex stages of droplets fragmentation, precursor/solvent evaporation, chemical reactions, formation, nucleation and growth of nanoparticles while transferring heat, mass and momentum with the surrounding hot gas 30,31. This study is aimed at understanding the influence of the key aspects of SP-HVOFS process variables on the in-situ formation of nanoparticles. A CFD-based model for the SP-HVOFS process is proposed to analyse the interaction between precursor droplets with combustion flame and to capture the aerosol dynamics during this interaction. The interaction is modelled without the adjustable parameters and need of experimental data by using commercial CFD software to predict zirconia nanoparticle characteristics.

COMPUTATIONAL MODELLING

1.1. Gas-phase flame structure

Modelling of particle formation and growth in the SP-HVOFS process involves the coupling of the gas dynamics with the droplet/particle dynamics (See Fig. 1). The gas dynamics of SP-HVOFS process is a compressible reacting flow, contained with turbulence and subsonic/sonic/supersonic transitions. The computation of gas dynamics together with the droplet dynamics provides detailed information for the gas flow field that is required to predict the particle dynamics.

Figure 1. Schematic representation of SP-HVOFS process (Bottom) with CFD Temperature contours (Top)

In this method, the droplets of solution precursor, after being injected into the HVOF ame-jet, undergo several physical processes taking place simultaneously. The rst stage is the aerodynamic breakup, as the slow moving droplets are entrained into the high-velocity jet and accelerate in the high-velocity gas stream (See Fig. 1). Depending on the droplet initial size, thermophysical properties of the solution precursor and the surrounding gas conditions, droplets can undergo severe deformation and eventually break up into smaller droplets. The secondary breakup of droplets to smaller ones is modeled by the Taylor Analogy Breakup (TAB) model as the Weber number is less than 100 (). The model is well adapted to the conditions of spraying and validated in the earlier studies; found in 3336.

The second stage is the evaporation of micron-sized precursor droplets after which the formation of particles begins when the precursor gas is going through a chemical reaction (See Fig. 1). The high-temperature is needed to evaporate the precursor and to provide the conditions for the chemical reactions. The temperature of high-velocity flames varies from 30004000 K depending on the type of oxidizer, and the operating conditions 20,21,37,38. At the early stage, the particles are formed by gas-phase nucleation and grow by coagulation (particles collide with each other and stick to form agglomerates). Later, they coalesce into larger particles. The shape of the final product is determined by the rates of coalescence and coagulation. If the rate of sintering is faster than that of coagulation, the particles formed are spherical. Otherwise, irregularly shaped agglomerates are developed 39.

The SP-HVOFS method, which offers some unique advantages over the conventional particle fed HVOF coating, can be potentially used to deposit a wide variety of ceramic coatings for diverse applications 1,5. In this study, the coating material selected is Zirconia (ZrO2) which is widely used in coating applications as it has excellent thermal, mechanical and chemical stability. Moreover, Zirconia is popularly used as a biomaterial. The coatings generated by ZrO2 nanoparticles have high strength, high fracture toughness, high hardness, excellent wear resistance, and better friction behaviour. It is chemically durable, and thermally stable, having low thermal conductivity, high refractive index, and low optical absorption. ZrO2 coatings with nanocrystalline grain structure resulted in enhanced mechanical properties, and it is used in the variety of applications, such as TBC, and applications where improved tribological properties are needed 40,41. The solution utilized in this study is a mixture of 0.5 M zirconium n-propoxide (ZnP) 70wt.% in n-propanol diluted with ethanol for ZrO2 nanoparticle production.

For the supersonic combustion of methane inside the SP-HVOFS torch, a two-dimensional CFD-based model is employed using the Eulerian continuum approach. Then to capture the droplet dynamics in the domain, the Lagrangian model is coupled with the Eulerian continuum model for the description of multicomponent spray droplet break-up and atomization, transport, and evaporation. The evolution of particle volume, area and number concentration is simulated with the CFD-based model that accounts for nucleation, coagulation, and sintering of nanoparticles inside the SP-HVOFS flame. The flame combustion is modelled by using a single step reaction mechanism. The complete stoichiometric combustion reactions are expressed as:

Zirconium n-propoxide:

1-Propanol:

Ethanol:

Methane:

The eddy-dissipation model 4244 is used to express the reaction rate and to consider the interaction between eddy motion and chemical reaction. The equations for the chemical species, droplet species and radiation are fully explained by Torabmostaedi et al. 22 and are not repeated here for brevity. The employed mathematical models have been strongly tested against experimental and numerical data 20,23,27,22,4548.

1.2. Governing Equations

The governing equations for the two-dimensional model in the Cartesian tensor form are:

Mass conservation equation:

(1)

Momentum conservation:

(2)

Energy transport equation:

(3)

where the deviatoric stress tensor is given by

(4)

1.3. Turbulence Modelling

The utilization of SST turbulence model with the Eddy Dissipation (EDM) combustion model is presented for the first time in paper 49. In the present work, the SST model was employed for capturing the turbulence in the HVOF flame jet 4951. The transport equations of the SST model are given as 51:

(5)

(6)

In these equations,denotes the generation of turbulence kinetic energy due to mean velocity gradients.represents the generation of.anddenote the turbulence dissipation ofand.represents the cross-diffusion term.andare user-defined source terms.

1.4. Droplet Dynamics

After complete simulation of the gas phase, the precursor solution droplets are injected into the HVOF flame jet where they undergo several stages. The slow moving droplets are injected into the hot flame and are accelerated by the high-velocity gas stream. Firstly, they breakup due to the aerodynamic forces 34,36,51. The second stage consists of spherical particles or dropletsdispersed in the continuous phase.The trajectories of these discrete phase entities are computed with the heat and mass transfer to/from them. The coupling between the phases and its impact on both the discrete phase trajectories and the continuous phase flow can be included. Fluentsimulates the discrete second phase in a Lagrangianframe of reference. The Lagrangian discrete phase modelsfollow the Euler-Lagrange approach. The fluid phase is treated as a continuum by solving the time-averaged Navier-Stokes equations while the dispersed phase is solved by tracking a large number of particles, or droplets through the calculated flow field. The dispersed phase can exchange momentum, mass, and energy with the continuous phase 51.

2.4.1 Droplets Force Balance

The force balance in the Cartesian coordinates for the x-direction is written as 51:

(7)

where, is an additional acceleration force or droplet mass term; is the drag force per unit droplet mass which is given as

(8)

where, is the fluid phase velocity, is the droplet velocity, is the molecular viscosity of the fluid, is fluid density, is the density of the droplet, and is the droplet diameter. is the relative Reynolds number, defined as:

(9)

The drag coefficient,, is taken from 52:

(10)

where,

(11)

Haider and Levenspiel defined the shape factor, as 53:

(12)

where, is the surface area of a sphere having the same volume as a droplet, and is the actual surface area of droplets.

2.4.2 Droplet Breakup Model

The secondary breakup of droplets to smaller ones is modeled by Taylor Analogy Breakup (TAB) model as Weber number () is lower than 100 () 34,36,51. Different regimes of the droplets fragmentation are determined by using the critical value of We. The hydrodynamic force required for the deformation of droplets is related to the surface tension force acting to retain the droplet form by the Weber number (). Since the Ohnesorge number () remains much below 0.1 in the computational domain, the main parameter related to the breakup physics is the Weber number. The TAB model is well adapted to the conditions of spraying and validated in the earlier studies; found in reference 3436,46,54,55.

2.4.3 Droplet Heat-up and Vaporization Model

Droplet heat and mass transfer with continuous phase are modeled by considering three laws. The inert heating law 1 is applied when the droplet temperature is less than the vaporization temperature (= 271 K for liquid ethanol) 51,54,56,57. A simple heat balance Equation-13 is used to relate to the convective heat transfer, and the heat gained or lost by the droplet while moving through the continuous phase.

Law 1: For,

(13)

where and are mass, heat capacity, temperature and surface area of the droplet, respectively. Here, and are convective heat transfer coefficient and gas temperature.

The mass transfer law 2 is applied to predict the vaporization from a discrete phase droplet using Equation-14. This law is used when droplet temperature reaches the and continues until the droplet reaches the boiling point.

Law 2: For,

(14)

where,,, and are molar-flux of vapor, mass transfer coefficient, vapor concentration at the droplet surface and vapor concentration in the bulk gas, respectively. in Equation-14 is calculated from the Sherwood number (Sh) correlation 58,59

The droplet mass is reduced according to Equation-15:

(15)

where is molecular weight of species . During the activation of law 2, the droplets temperature is updated using heat balance Equation-16. It relates the sensible heat change in the droplet to the convective and latent heat transfer between the droplet and the continuous phase.

(16)

where is the rate of evaporation and is the latent heat.

For predicting the convective boiling of droplets, law 3 is applied. It uses the boiling rate Equation-17 and is activated when droplets reached the boiling point, ( = 351 K for liquid ethanol) 43,54.

Law 3: For,

(17)

where ,, and are thermal conductivity, heat capacity of the gas and droplet density, respectively.

The droplet with an injection temperature of 300 K enters into the hot CC for gradual evaporation and combustion with remnant oxygen left after premixed propane/oxygen burning. Since the Knudsen number (), the ratio of gas mean free path to droplet diameter (), is far less than the transition number 0.01, the discontinuous effects are neglected 60,61. It is also stated that the dependence of drag coefficient (CD) on the can be neglected in the case of HVOF spraying as shown by Sobolev et al. 62. The Reynolds number () varies from in the computation domain based on the characteristics of the gas dynamics.

1.5. Particle Dynamics

The CFD-based monodisperse aerosol model developed by Torabmostaedi et al. 22 is modified in this work for the synthesis of ZrO2 nanoparticles in SP-HVOFS process. Here, the equations of total particle number concentration, surface area concentration, and volume concentration undergo convection and diffusion in addition to being generated and depleted. This formulation is consistent with the monodisperse model proposed previously for the flame synthesis of nanoparticles 47,63.

The rate of change of particle number concentration, N is given by

(18)

The first two left-hand side terms in Equation-18 describe the convection and diffusion of the particles in the turbulent flow. The particle formation rate,, is calculated based on the mass flux imbalance in each grid cell 47

(19)

where is the Avogadro number, is the cell volume, is the molecular weight of ZnP, is the number of cell faces, is the signed (positive for out- and negative for in-flow) mass flux through cell face , and is the mass fraction of the precursor at cell face . The second term on the right-hand side in Equation-18 has the Fuchs interpolation function () for Brownian coagulation in the free molecule and continuum regime 39,64 which is used to calculate the collision kernel for irregularly shaped aggregates.

The sintering effect on the agglomerate surface area is given by Koch and Friedlander, 65,

, (20)

The total agglomerate volume concentration,, is provided by Kruis et al., 39,

, (21)

The primary particle diameter, , number of primary particles per agglomerate, , and collision aggregate diameter, , are 39,

(22)

where is the fractal dimension which is set as 1.8, a commonly-used value for aggregates generated in high-temperature aerosol processes 39,66. Similar to the previous study of Torabmostaedi et al. 22,48,67, the relation is given by Kobata et al. 68 is used here to determine the time needed for two zirconia particles to sinter by grain boundary diffusion:

, (23)

where (K) is the gas temperature which is found from CFD simulation, is the grain boundary width which is m 69, (m2 s-1) is the grain boundary diffusion coefficient given by 70,71,

, (24)

and (N m-1) is the surface tension according to Rsner-Kuhn et al., 72,

, (25)

The term in Equation-23 is the molar volume of zirconia ( m3 mol-1). This sintering rate, among others, is selected based on the comparison of model predictions with the measured ZrO2 primary particle diameters made by preindustrial-scale flame spray pyrolysis (FSP) 22.

Equations (1)-(25), along with the chemical species, droplet species and radiation 22 form the complete set of equations of the CFD-monodisperse model and are solved using FLUENT's pressure-based 2D axisymmetric solver and Green-Gauss Node based gradient option. The monodisperse model equations are written in C++ programming language, and the code is coupled with the main flame dynamics module of the CFD solver as a user defined function (UDF). A second-order upwind discretization scheme is used since it ensured the accuracy, stability and convergence.

RESULTS AND DISCUSSIONS

1.6. Model validation

The gas dynamics and monodisperse aerosol model (i.e., using a separate Fortran code) is validated in our previous study 22. To put the current aerosol modelling (i.e. using a coupled CFD-based monodisperse model through UDF) into the prospect with respect to the available literature; the aerosol model is tested against the experimental and numerical data reported by Grhn et al. 21 for the synthesis of ZrO2 nanoparticles in a similar solution precursor flame spray pyrolysis (SP-FSP) system. This study is chosen for validation since a similar modelling approach is used in their study.

As shown in Fig. 2, the particles are collected by a vacuum pump on a glass microfiber filter. The final primary particle size is calculated based on the measured specific surface area (SSA) of the ZrO2 powder by N2 adsorption at 77 K using the BrunauerEmmettTeller (BET) equation theory 21. Also, particles are sampled thermophoreticallyon carbon-coated copper grids (Plano, mesh 300) on the centre axis at 42010-2m height above the burner (HAB) using 20100ms grid residence time in the flame. The precursor solution is fed through the central capillary of the nozzle at the feed rate of 4 mL/min for 0.5 and 1 M ZnP concentration in ethanol, resulting in the ZrO2 production rate of 4.11110-6kg/s and 8.22210-6kg/s (14.8 g/h and 29.6g/h), respectively. A concentric two-phase nozzle is used to spray the metal-containing liquid mixture. 35L/min of dispersion oxygen is introduced into the surrounding annular gap at an angle of 45 with the centre capillary. The gap width (x, see Fig. 2) is adjusted to assure critical flow conditions for all experiments. Methane and oxygen are supplied through an annulus surrounding the nozzle to form a diffusion flame to ignite and sustain the main flame. More details of the experimental apparatus and procedures can be found in the cited reference 21.

Figure 2. Schematic view of SP-FSP nozzle configuration

Figure 3 demonstrates the comparison of the predicted zirconia primary particle diameters (solid lines) for different precursor concentration of 0.51 M production rate of 2.66676.2510-6kg/s (9.622.510-3g/h). The measured TEM is presented by triangular symbols, BET by the square symbol, and the numerical data from Grhn et al. 21 by the dotted lines for the primary particle diameter. Model predictions are mixing-cup averages for beams with 510-2m diameter (i.e., the radius of the domain) going through the flame at different HAB to be consistent with measurements and numerical data.

, (26)

where is the primary particle diameter, and are the facet velocity vector and the facet area vector, respectively.

As can be seen in Fig. 3, the results from the present model are in good agreement with the BET and TEM measurements. In the present work, only 2% deviation is observed from BET data while the numerical results in 21 show under prediction of about 79%. Also, comparison of the predicted diameters with the TEM measurement shows better agreement than the model in 21 (see Fig. 3a and 3b).

The improvement of the present model compared to that developed by Grhn et al. 21 can be attributed due to the use of the SST turbulence model instead of Realizable turbulence model that may have improved the gas flow prediction and ultimately the particle size evolution.

(a) (b)

Figure 3. Comparison of the present model with measured and numerical results reported in reference 21. Evolution of the primary particle diameter at 5 l min-1 dispersion gas feed rate is shown for (a) 0.5 M and (b) 1 M ZnP concentration in ethanol

1.7. The Numerical predictions of SP-HVOFS process dynamics

The evolution of primary particle diameters is simulated for zirconia nanoparticle synthesis in SP-FSP system using the numerical models. The simulation results showed that the numerical predictions are in reasonable agreement with on-line characterizations and numerical data 21 at different production rates and precursor concentration. Thus, the model can be used for equipment design and process optimization in SP-HVOFS process.

(a)

(b)

Figure 4. (a) The schematic representation of the SP-HVOF torch illustrating geometric domain with the boundary conditions. [Three sections I-Combustion chamber (CC), II-Barrel, III-Free jet region, sections -I, -II, and -III for SP-HVOFS torch is used throughout the text] (b) the zoomed view of DJ2700 torch grid

The HVOF gun geometry employed in this study is Diamond Jet DJ2700-torch (Sulzer Metco, Wohlen, Switzerland) 33,34. The operating parameters along with the schematic representation of the computational domain are shown in Fig. 4a and Table 1. The total inlet radius of the combustion chamber (CC) is RCC=9.1 mm, with length LCC=23.8 mm (named as section-I). The radius at nozzle throat is RT= 4.2 mm, with the extended diverging section acting as the barrel of the gun with length LB= 66.2 mm (section-II) and exit radius of RB=6.215 mm. The free jet domain length (LFJ) is set to 500 mm (section-III), to see the particle growth in the far field region after the guns outlet. The torch geometry considered in the numerical simulations is axisymmetric. The mesh consisted of 53947 numbers of nodes, and it is very fine inside the torch and in the regions of flame jet ejection into the atmosphere (Fig. 4b). The premixed oxygen-methane is axially injected into the DJ2700 gun; the resulting hot combustion gases are accelerated inside the convergent-divergent (C-D) nozzle and flows through the barrel section towards the exit of the gun. The formation of shock diamonds is observed after ejection of flow in the free jet region (Fig. 1).

Table 1. Geometric Parameters and Working Conditions of DJ2700 HVOF torch

Geometric Parameters

Symbol

Dimension (mm)

(I) Combustion chamber length

LCC

23.8

Combustion chamber radius

RCC

9.10

Nozzle throat radius

RT

4.20

(II) Barrel length

LB

66.2

Barrel exit radius

RB

6.22

(III) Free jet length

LFJ

500

Working Conditions

Case

1

2

3

4

Oxygen flow rate (kg/s)

0.0035

0.007

0.014

0.021

Fuel flow rate (kg/s)

0.0015

0.003

0.006

0.009

Droplet diameter and initial temp.

50m, 300K

Droplet flow rate and initial velocity

3.82110-4 kg/s, 15 m/s

Solution precursor mass composition

72.3 % Ethanol, 19.4 % ZnP, 8.3 % n-propanol

Precursor concentration

0.5 M ZnP solution

The lowest to highest oxygen-fuel GFR selected for this study is designated as Case 1, 2, 3, and 4, respectively (Table 1). The initial precursor droplet diameter is 50 m with an injection temperature of 300 K, and velocity of 15 m/s. The droplet flow rate is 3.82110-4 kg/s that gives zirconia production rate of 2.77810-5 kg/s (or 100 g/h). The solution precursor carrying mixture of 0.5 M zirconium n-propoxide (ZnP 70 wt. % in n-propanol) diluted in ethanol has mass composition of about 72.3 % ethanol, 19.4 % ZnP, and 8.3 % n-propanol solutions (Table 1). These multicomponent droplets are injected axially into the CC after complete simulations of combustion and turbulence of gaseous flow inside the torch.

In SP-HVOFS process, the physical and chemical properties of nanoparticles are dependent on a large number of parameters, such as combustion gas temperature, pressure, velocity, C-D nozzle design, oxygen-fuel injection flow rates and feeding ratio, fuel and precursor properties and their concentration 5,30,31. In this study, the effects of different oxygen-fuel GFRs on the gas dynamics and production of the ZrO2 nanostructured coating are analysed during the SP-HVOFS process.

1.8. Effect of gas flow rates on the HVOF gas dynamics

The combustion process inside the HVOF gun is mainly dependent on the CC design, total oxygen-fuel GFR, and oxygen-fuel gas ratio 23,38,45. Four different levels of oxygen-fuel GFR are considered with the constant oxygen-fuel ratio of O/F= 2.333, to analyse the effects of increasing oxygen-fuel GFR on the combustion gas and particle dynamics inside SP-HVOFS process (Table-1, Case 1to4).

The gas temperature (TG), pressure (PG), velocity (VG) and Mach (MG) number increases with increase in GFR, as presented in Figs. 57. As shown in Fig. 5, the maximum TG without multicomponent droplets injection is observed in the combustion chamber (3000K4000K in section-I for all GFR ) 20,21,37,38, after that, it decreases gradually inside the barrel (section-II) and some peaks are observed in the shock jet (section-III). After the injection of precursor droplets, the value of TG goes down in the CC (T is 750to1000K for Case 1 and 4, respectively). It is because heat is extracted from the gas for evaporating the precursor droplets, as seen in Fig. 6 and Fig. 7a.

Figure 5. Variation of gas temperature without droplets injection along centreline axis, for Case 1 (solid line), Case 2 (dotted line), Case 3 (Dashed line), and Case 4 (Dash-dot-dot line) [This description for legend is applicable in all graphical representations]

The map of TG in Fig. 6 shows the high and the low-temperature regions from the gun inlet to some extent in the free jet section-III (near guns exit region as demonstrated by a star). Lower temperatures are detected at the oxygen-fuel inlets, and point of droplets injection in section-I. After the immediate start of droplets evaporation, a sudden drop in the TG is detected at droplets injection port (along the guns axis). Then TG begins to increase inside the CC and the barrel due to accelerating rates of oxygen and fuel and multicomponent vapours combustion (section-I & -II, Fig. 6 and 7a). Higher GFRs (Case 3 and 4) augmented the combustion temperature in sections -I and II, and due to the burning of the flammable precursors vapours, more heat is added. For each case, the temperature rise is observed after ejection of the flow in the atmosphere. This fluctuating temperature rise is due to the formation of shock jets at the exit of the torch as seen in section-III (Fig. 6 and Fig. 7a).

The gas pressure (PG) is also dependent on the injection of oxygen fuel mass flow rates. The highest combustion inlet pressure value of 0.7723 MPa (7.723 bars) is observed for Case 4, and the lowest value of 0.0586 MPa (0.586 bars) is observed for Case 1 in section-I (Fig. 7b). For each case pressure sharply declines in the CC and the barrel sections. Furthermore, for Cases 2, 3 and 4, the barrel exit pressure is less than the atmospheric pressure and the flow is under-expanded, which forms a Mach-disc at the downstream of the barrels exit (Fig. 7b). The flow settles down in the free jet region after series of shock waves 23. These high pressure combustions in the HVOF torch increase the flame energy transfer and improve the overall flow dynamics.

Figure 6. Gas temperature maps for Cases 1 to 4 [Section-I-Combustion chamber (CC), Section-II-Barrel, Section-III-Part of Free jet region]

Similarly, the gradual increase in VG is identified inside the C-D nozzle, and the barrel section, while high values are observed in the shock jet. Figure 7c and 7d show the centreline profiles of gas velocity and Mach number for internal and external flow fields for different cases. The velocity field is varying for each case due to enhancement in the rate of combustion and it gets accelerated inside the C-D nozzle. The minimum velocity values are detected for Case 1, and highest velocity values are observed for Case 4. The reason for this is obvious, as more kinetic energy is added to the gas during high rates of combustion with increased GFR. Moreover, the Mach number profiles are demonstrating the increased energy carried by the combustion gas for higher oxygen-fuel flow rate cases. For Case 1, subsonic flow is observed at the C-D nozzle throat, MG 1.0 at gun ejection (Fig. 6, and 7c). These high gas temperatures, pressure, velocities and Mach number will affect the precursor droplet evaporation, particle formation, and particle growth inside the SP-HVOFS torch; it is discussed in the subsequent two sections.

Figure 7. Variation of (a) gas temperature, (b) gas pressure (c) gas velocity, and (d) gas Mach Number along centreline axis for Cases 1to4

1.9. Effect of gas flow rates on precursor droplet dynamics and ZrO2-nanopartiles formation

In the SP-HVOFS gun, the chemical reaction started immediately as the precursor droplets absorb heat from the surrounding hot gas and get converted into vapours (section-I). The evaporation of the precursor liquid is dependent on the combustion temperature, and under high GFRs, the liquid boils rapidly and evaporation rate increases. Similarly, in SP-HVOFS process, the evaporation rate is augmented by increasing oxygen-fuel flow rates. In Case 1, the highest rate of evaporation is detected in the C-D nozzle throat region along the gun axis while the precursor droplet evaporation continues in the barrel (section-II, Fig. 8a). Whereas for Case 4, high rate of evaporation is observed inside the barrel, and the maximum amount of ZnP precursor droplets get evaporated inside barrels mid-section (along the guns axis; Fig. 8b). In barrel section-II, the evaporation of precursor droplets is less in Case 1 as compared to Case 4 due to lower gas temperatures (TG) as observed in Fig. 7a. Generally, the higher evaporation is detected for Case 1 than for Case 4 in the torch. The understanding developed for the difference in rate of evaporation has two points: (i) higher gas temperature with increased GFR augmented the rate of evaporation to some extent in the CC and the barrel in Case 4; (ii) the large gas velocities reduced the interaction time between the gas and droplets in Case 4 that leads to a smaller amount of overall evaporation as compared to Case 1.

It is mentioned that high evaporation rate will eventually increase the average particle growth rate and size 73. Here for the SP-HVOFS process, the contours plot in Fig. 8a, 8b illustrates that particle formation rate is decreased for higher GFRs (Case 4) as compared to the lower GFR (Case 1) due to less residence time available for the precursor vapours to interact with fast moving hot gas (as mentioned earlier). Due to these higher relative velocities, the process of evaporation decreases in the fast moving supersonic HVOF flame-jet in Case 2, 3 and 4 as compared to subsonic flow (Case 1). In Case 1, the precursor vapours got sufficient reaction time to interact with the combustion gases and formed the required ZrO2 species. In Fig. 8a, at the nozzle throat highest rate of formation is identified and after the throat region, the formation rate decreases because of less available TG, which is much lower as compared to Case 4 (temperature difference between Case 1 and 4 is TG = 1614K, Fig. 7a). The opposite behaviour in ZrO2 formation is observed for Case 4 that is the highest rate of particle formation is witnessed after the throat region (as seen in Fig. 8b). The formation of particles continues in section-III for both cases until all the precursor vapours converted into ZrO2 species (i.e., in the free jet section-III which is not shown in Fig. 8).

The particles formation start where the oxygen-fuel combustion streams and precursor vapour streams get mixed inside the combustion chamber, while the turbulence mixing occurs near the centreline axis of the torch as the precursor droplets are injected axially into the CC (from a central hole/opening). The mass fraction of Zirconium n-propoxide and Zirconia (normalized by their maximum values) is shown for Cases 1 and 4 in Fig. 8c, and 8d, respectively. It clearly shows more formation of Zirconia near the nozzle throat and in the barrel inlet sections, as excessive mass fractions of Zirconia is present near these regions (surrounding gun axis). A significant amount of ZnP appears in section-I and then it reduces gradually after the C-D nozzle throat that confirms the formation of Zirconia particles inside the SP-HVOFS gun (Fig. 8c, 8d). Similarly, as the evaporation/formation rate more mass fraction of Zirconia is observed in the combustion chamber and the barrel section for Case 1 when compared with Case 4, as in Case 4 ZnP has less interaction time available in high-temperature regions. Also, in Case 4, the droplets/vapours fly away without prior evaporation and chemical formation hence less mass fractions are detected in the CC.

Figure 8. Normalized contour plot of ZnP mass fraction and droplet evaporation rate (top) and ZrO2 mass fraction and nanoparticles formation rate (bottom) for Case 1 (a) and (c), Case 4 (b) and (d)

For Cases 1to4, Fig. 9 shows the normalized contours of precursor droplets Sauter mean diameter (SMD) inside the torch. The precursor droplet diameter decreases with droplets fragmentation as it travels inside section-I and -II. In Case 1, due to the presence of the low-temperature field, the droplets will not fully evaporate and remain present till the exit of the barrel section (Fig. 9a). The droplets disintegration and evaporation rates increase with increment in the GFR as gas temperature, and pressure is augmented; hence, droplets starts disappearing in the middle of the barrel in Cases 2 and 3 (Fig. 9b, and 9c). It is caused by the interaction of precursor droplets with higher GFR combustion gases having more kinetic energy and enthalpy. Therefore, the reduction of droplet size occurs by the augmentation in relative velocities.

Figure 9. Sauter mean diameter (SMD) of the precursor droplets inside the SP-HVOFS torch

It is clearly seen in Fig. 9c and Fig. 9d that high rate of combustion increases gas turbulence near droplets injection region, which caused abrupt mixing of the hot gas and the precursor droplets that intensifies the droplet breakup phenomenon. Moreover, an increase in the ratio of oxidant mixture to the mass of injected precursor is another dominant factor in reducing the droplet size near injection regions inside the CC. Smaller droplets with less precursor mass and having high kinetic energies (Case 4, Fig. 9d) would leave the SP-HVOFS torch at a faster rate without complete evaporation. These droplets and vapours carrying higher kinetic energies will lower the formation and growth of nanoparticles in the higher GFR cases (details are discussed in next section-3.5.1).

1.10. Effect of increasing oxygen and fuel gas flow rates on the nanoparticles synthesis in SP-HVOFS torch

3.5.1 Process physics, with number, area, and volume concentration of nanoparticles

It is stated that particle formation occurring directly from the vapours take place via homogeneous nucleation 73. The local cooling rate, the residence time distribution, and the number density in the nucleation and growth zones are the primary factors which affect the nucleation and growth of nanoparticles in the SP-HVOFS process. Furthermore, as stated earlier, different process parameters, such as process gas-type, gas-temperature, gas-pressure, gas-velocity, gas-flow rate, and droplets evaporation rate need to be controlled to get the required formation, and size of nanoparticles.

Firstly, the process physics for the nanoparticles nucleation is explained here and then the terminologies are used in the subsequent part of the manuscript. The growth of nanoparticles continues through nucleation by acquiring more atoms through coalescence, coagulation, and sintering. In coalescence the particles collide with each other and lose their kinetic energy; also, it is referred to as sintering and diffusion of species within particles where contact is made 73. The coalescence takes place in high-temperature zones (section-I and -II of SP-HVOFS torch). Coagulation is a stepwise process wherein two nuclei meet and are joined, causing sintering due to processes such as Brownian motion, and it decreases the number of particles in the flow 73. Furthermore, the Brownian motion is the random motion of particles suspended in a fluid resulting from their collision with the quickatomsormoleculesin the gas or liquid 73. Sintering is the process of compacting and forming a solid mass of material by heat and/or pressure without melting it to the point of liquefaction. At sufficiently high temperatures, particles coalesce (sinter) faster than they coagulate, and spherical particles are produced. If the density of the particles is relatively small and the collection time is short, then the particle agglomerates are smaller in size 73.

In the SP-HVOFS torch, the magnitude of particle volume concentration (V), number concentration (N), and area concentration (A) rises due to the interaction of the precursor droplets with the combustion gases in the increasing flame temperature zones (section-I and II). Fig. 10 shows the graphs and contours plots of V, N, and A in the SP-HVOFS gun for Case 1. The volume concentration of particles keeps increasing inside the torch as shown in the contour plot of V (Fig. 10a). The gases carrying ZnP vapours and ZrO2 particles ejected out from the torch exit, at x=0.09 m in the free jet section-III. The volume concentration reached its peak value equal to 1.6110 m/kg in the free jet region along the gun central axis (at about 0.0622 m away from the torch exit, Fig. 10a) and then started to decrease as the precursor mass fraction is reduced in these regions.

Figure 10. Variation of (a) particle volume concentration, V (b) particle number concentration, N and (c) particle area concentration, A, for Case 1

The coalescence rate depends on the particle number concentration and the residence time in the hot zone 73. The number concentration (N) has high values inside the torch (at the throat and in section-II) as seen in contours plot of Fig. 10b and further downstream at gun exit it decreases as the process of sintering (coalescence) is strengthening in these sections. The highest value for N is 16.21020 numbers/kg observed at the nozzle throat and the start of the barrel section-II. At guns exit, the value of N decreases gradually from 6.111020 to 2.31020 numbers/kg till x=0.128 m in the free jet region due to the increase in coagulation and coalescence of ZrO2 seed particles. The formation of ZrO2 particle from ZnP vapours further rises to x=0.151 m in section-III, which enhances the value of N to 8.8641020 numbers/kg and after this point a sharp decline is observed indicating that sintering is augmented in this region.

Similarly, the area concentration (A) has the increasing and decreasing values observed during the flight of ZrO2 seed particles in the SP-HVOFS torch (Fig. 10c). Firstly, the value of A is increased in the torch as the surface area is increasing due to the dominating formation of new particles. At x=0.151 m agglomeration starts as a sharp decrease in A is detected. After this point the sintered particles coagulate and form hard and soft agglomerates, it is further explained in part-b.

Figure 11. Comparison of (a) particle volume concentration, V (b) particle number concentration, N and (c) particle area concentration, A, along gun axis for Cases 1 to 4

For Case 1 to 4, Fig. 11 shows the comparison graphs of V, N, and A along the SP-HVOFS guns central axis. It is observed that ZrO2 particle formation is highly influenced by the variation in GFR, gas temperature, pressure, and velocity. The main reason behind volume reduction for higher GFR is that when more gas is added it enhances the combustion, but at the same time it dilutes precursor concentration in the overall flow, and hence nanoparticles formation is decreased (see Fig. 11a). The increase in volume concentration (V) of nanoparticles indicates that the chemical reaction for converting ZnP into ZrO2 is ongoing in section-I and -II of the SP-HVOFS torch (Fig. 11a). The gases carrying ZnP vapours and ZrO2 particles ejected out from the torch exit (at x=0.09 m). In Case 1 and 2, the value of V reached its peak in the free jet region along the gun central axis and then started to decrease. The decreasing value of V indicates that quantity of ZnP vapours is decreased as it is consumed in the formation of ZrO2 seed particles.

In section-II, the values of volume concentrations for Cases 3 and 4 is much higher than Cases 1 and 2, because the nanoparticles formation rate is increased for high GFR in the barrel section (Fig. 11a). Further, V starts to decrease more sharply for Case 4 than that for Case 3; it depicts that ZrO2 seed particles flight speed is higher in high-temperature zones than that in other cases and which leads to less formation of ZrO2 in this region (due to less interaction time). Moreover, the nanoparticles formation process in Case 4 is not as smooth as it appears in Cases 1, 2 and 3, the increase in turbulence and thermal energy/enthalpy induces random motion of ZnP vapours and abrupt formation of ZrO2 particles.

The fluctuating values of A and N (increasing and decreasing) inside section-I and -II indicates that most of the produced ZrO2 seed particles are colliding with each other, and they get sintered wherever the temperature is favourable (Fig. 11b, 11c). Increasing N indicates that most of the produced ZrO2 seed particles are separated after nucleation while decreasing N demonstrates that ZrO2 particles may aggregate within the high-temperature surroundings. Mostly high values of N are concentrated along the axis of the SP-HVOFS gun as the solution precursor is injected axially into the gun from a central opening and particle formation is higher in these areas.

In all cases, the highest values for N are observed inside the torch nozzle throat region while the value of N decreases gradually at guns exit (x=0.09 m) due to increasing coagulation and coalescence of ZrO2 seed particles. The ZrO2 particles formation from ZnP vapours further rises in section-III (free jet region), which enhances the value of N and after this point, a sharp decline is observed indicating that aggregation is increased in this section. Along the gun axis, the position of N peak value for each case is different, as seen in Fig. 11b. The value of N decreases up to the domain outlet indicating that aggregation is still occurring. In the overall process, the gas temperature and velocity regulate the sintering and coagulation processes and thus controls the value of N. In Case 4, at high temperature (TG in Fig. 7a and N in Fig. 11b) in the mid of barrel section a sudden increase in the particle number is observed, while at low temperatures the particle number density (N) decreases. This high gas temperature region (as seen in Fig. 7a as a sudden increase in TG, and in Fig. 6 Case 4 sharp red colour in contour map in HVOF flame-jet along the central axis) proves the abrupt increment in the ZnP vaporization. However, the enormous increase in gas velocity (VG in Fig. 7b) decreases the interaction (residence) time between the precursor vapours and the combustion gas inside the SP-HVOFS torch. It reduces the overall particle number concentration (N in section-III showed in Fig. 11b) and reduces particle growth in Cases 3 and 4 (details discussed in part-b).

Similarly, the increment in the value of A identifies that there are increasing numbers of ZrO2 seed particles in the process, but there is no obvious sintering. However, the sintering is intense in zones having favourable conditions for the sintering process, and it reduces the value of A. The particle area concentration (A) is also influenced by the increment in GFR, and higher values are observed for Cases 3 and 4. As seen in Fig. 11c particle surface area reached its highest value in the combustion sections, as these regions support the chemical reaction of ZnPtoZrO2 formation. At a high-temperature inside guns section along the central axis, the particles coagulate and sintered that decrease the particle area concentration. These fluctuations in the value of A continue in section-II, and it indicates that coalescence and sintering are dominant in these regions.

For Case 1 and 2 higher values of A are detected inside the barrel up to the free jet region at x=0.15 and 0.16 m, respectively; after that A starts to decrease and its value declines from x=0.30 m in section-III (Fig. 11c). From this point, the sintered particles coagulate and form hard- and soft agglomerates; it is further explained in part-b. In Cases 3 and 4, particle surface area reached its highest value in the barrel midsection as these zones support the required chemical reaction for the formation of ZrO2. In high-temperature zones along the central axis, the precursor droplets evaporate, and precursor vapours react with the remanent oxygen to form ZrO2 that increases the particle area concentration. Then similar to V, A decreases from the mid of section-II it indicates that coalescence and sintering are dominant in these regions of the torch. For Cases 3 and 4, area concentration values decreased in section-III and this reduction is caused by the less formation of ZrO2 seed particles due to less interaction with the surrounding air. Hence, higher GFR reduced V and affected N, A in a similar manner (Fig. 11a, 11b, and 11c).

3.5.2 Effect of increasing gas flow rates on the particle growth and agglomeration

In the SP-HVOFS torch, the process of coagulation and sintering starts simultaneously as the precursor droplets converted into vapours (in section-I). Here increment in GFR increases the dilution of aerosol particles, and thus reduces the overall particle concentration in the flow. It further intensifies the gas velocities which reduce particle residence time in high-temperature regions. Due to these reasons, the rate of sintering is reduced, and it decreases the growth of primary particle diameter (). Further, the collision between the particles is not always successful. If the kinetic energy of the particles during collision is larger than the energy induced by the van der Waals interactions, then they will get separated after the collision (no sintering); otherwise, they will coagulate together 74. In SP-HVOFS process, the combustion gas velocity determines the residence time of the primary particles in torchs different sections-I and -II. As shown earlier in Fig. 7c, the higher gas kinetic energy will lower the residence time of particles in high-temperature zones, which leads to the lower growth of primary particles, and accordingly, smaller size nanoparticles are obtained in Cases 3 and 4. This elevated kinetic energy is the result of an increase in oxygen-fuel availability in the reaction zone, which intensifies the mixing of fuel and oxygen in the burning section-I and enhances the rate of combustion. Moreover, nanoparticles agglomeration is also reduced when GFR increases as the particle-to-particle interaction and collision time is shortened.

Furthermore, the particle formation increases with the increment in the evaporation rate which is due to high combustion rates and higher enthalpy of the flame 73. In the SP-HVOFS process, the contour plots are shown in Fig. 8a and 8b illustrated the greater formation rate of ZrO2 particles for higher GFR Case 4 as compared to lower GFR Case 1. It is attributed to the high thermal energy/enthalpy available for Case 4 that augmented the droplet evaporation and the chemical reaction for particle formation. However, in Cases 3 and 4, ZrO2 seed particles have less growth because of less residence time for nanoparticles to collide with each other and get sintered. As the nucleated particles are moving fast inside the torch, the rate of aggregation is also reduced. Whereas, in Cases 1 and 2, the sintering, the aggregation and the growth of nanoparticles continued by acquiring more atoms. For all cases, maximum sintering occurs in section-I and -II due to favourable high-temperatures.

For investigating the agglomeration and the non-agglomeration phenomena for an aerosol synthesis process in SP-HVOFS torch the starting point of hard- and soft agglomerates during the process is highlighted. The hard-agglomerates region starts when reaches a value of 1.01. The beginning of soft-agglomerate formation starts when ( is the final value of the primary particle diameter), after this point sintering is negligible and colliding particles are held together by physical (van der Waals) forces and not by the chemical or the sintering bonds 2022. Figure 12a shows the profiles of primary and collision particle averaged diameters along the gun central axis for Cases 1 and 2. The final primary particle size of ZrO2 nanoparticles are decreased from 11.31 to 6.91 nm as GFR is increased from 0.005 to 0.01 kg/s (in Case 1 and 2, respectively). The formation of hard-agglomerates begins at an axial distance of 0.078 m away from the guns exit for Case 1 (as marked by first vertical-solid-line). While for Case 2 this position moved to 0.099 m in the free jet region (as marked by second vertical-dashed-line). The percentage difference between the region of hard-agglomerate formation in Case 1 and Case 2 is 14%. Case 2 has a wider region of hard-agglomerates with smaller collision diameters as compared to Case 1. It is the evidence of change in process physics while increasing GFR. The particle size obtained at the end of the hard-agglomerate regions is decreased from 11.265 to 6.932 nm (at 0.352 m and 0.406 m) for Case 1 and 2, respectively.

Figure 12. Comparison of primary (), and collision () particle diameter for (a) Case 1 and 2, (b) Case 3 and 4

The beginning of soft-agglomerate formation is assumed at that point where the growth of primary particle becomes constant as22. In this region, the atmospheric air surrounding the free jet lowers the gas temperature and dilutes the particles flow; hence sintering reduces which begins soft-agglomerate formation. The diameter of soft-agglomerates at 0.5 m away from the gun exit decreases from 15.416 to 9.094 nm as the GFR is increased from Case 1 to 2 (41% reduction). The final value of the primary particle diameter is found to be 11.313 nm for Case 1, while for Case 2 it is equal to 6.915 nm (38.8% reduction).

Similar graphs are produced for Cases 3, and 4 (Fig. 12b), and the difference in nanoparticles sizes is clearly observed between Case 1, 2 and Case 3, 4. An enormous decrease in the particle growth is noticed when the GFR increased from Case 1 to 4. In Cases 3 and 4, at the gun exit primary particle grows to 1.616 and 1.461 nm, respectively; which is much smaller than the particle size observed for Case 1 and 2 (Fig. 12, Table 2). It happens as the precursor mass in the SP-HVOFS torch is diluted by the higher oxygen-fuel quantity. Therefore, an increment in the gas to the particle volume ratio occurred, and this would lower the particle collision rate which reduced the particles diameter in Case 3 and 4. Moreover, as stated earlier, ZrO2 seed particles relative velocity is enhanced in Case 3 and 4 (as kinetic energy of the gas is increased by the higher rate of combustion). It reduces the residence time of nucleated particles inside the guns high-temperature zone that diminished the sintering rate and hence is reduced.

For Cases 3 and 4, reduction in coagulation, coalescence, and sintering phenomena occurs as the gas temperature, gas pressure, and gas velocity is getting higher, and sintering time is decreasing with the increasing GFR (see Fig. 12b). Some growth in ZrO2 nanoparticles size is detected in the free jet section-III and the particles size increases up to 4.016 and 3.205 nm for Case 3, and 4, respectively. For Case 3, the hard-agglomerates region starts at x=0.241 m (as marked by vertical-solid-line) in the free-jet section-III away from guns exit. The value of agglomerate diameter detected at the end of this hard-agglomerate region is. After reaching a point, x=0.493 m, hard-agglomerate formation ends and the region of soft-agglomeration started (as marked by vertical-hollow-line), this agglomeration continues until the domain-outlet (x=0.59 m). The final agglomerate size is, and the final value of primary particle diameter () is found to be 4.973 nm for Case 3. In Case 4, hard-agglomerates formation starts earlier than Case 3 at x=0.223 m, while the very small soft-agglomerates region is noticed at the end of the domain (x=0.522 m). The final sizes observed for Case 4 are and. Based on these results, it is concluded that primary particle size and hard-agglomerate regions are strongly affected by changing the GFR.

Table 2 illustrates the nanoparticles size at different locations inside the SP-HVOFS gun for various GFR. The particle growth is reduced with increasing GFRs. Six lines are drawn at six different locations (at x=0.0119 m, 0.0238 m, 0.0569 m, 0.090 m, 0.340 m, 0.590 m) in SP-HVOFS torch to analyse the variation in primary particle diameter () of ZrO2 nanoparticles formed by using four different GFR. By assuming Case 1 as a reference case, the percentage variation in is studied. At the combustion chamber mid region, the reduction in is 3% for Case 2, in comparison to Case 1. Very small variation in primary particle size is observed when Case 1 and Case 2 data is analysed in section-I and -II of the torch (as shown in Table 2 and in Fig. 12a). The difference is significant in the free-jet spray region after the gun exit as the flow is supersonic for Case 2. As the primary particle size reduces due to less interaction of particles and dilution caused by the surrounding gas, (Fig. 12a clearly shows this variation in and for Case 1 and 2, respectively), increase of GFR from Case 1 to 2 leads to a 38.5% reduction in primary particle diameter in the free-jet spray region after the gun exit.

When Case 3 and 4 are compared with Case 1, the percentage difference in is 24% for Case 3 and 57% for Case 4, respectively in the CC-mid section-I. This reduction in nanoparticle size intensifies as the flow moves along the SP-HVOFS torch. Finally, at the outlet, the percentage reduction in reaches its highest value of 56% and 62% in Case 3, and 4, respectively (Table 2). The reason for this is obviously the reduced amount of interaction time in the high combustion zones of the torch at higher GFR. Hence, a smaller amount of sintering and aggregation is observed for Case 3 and 4.

Table 2. Primary particle diameter for different gas flow rates

SECTIONS

x (m)

Case

1

2

3

4

Primary particle diameter (nm)

(I) CC-mid

0.0119

1.791

1.739

1.369

0.772

Throat

0.0238

1.611

1.631

1.266

0.922

(II) Barrel-mid

0.0569

1.627

1.658

1.447

1.320

Barrel-exit

0.090

1.839

1.770

1.617

1.461

(III) Free-Jet-mid

0.340

10.503

5.947

3.583

2.743

(III) Free-Jet-end

0.590

11.313

6.915

4.973

4.334

Figure 13. Contours of primary particle diameter, (top), and collision particle diameter, (bottom) for (a) Case 1 and (b) Case 4

The distribution map of and for Case 1 and 4 are shown in Fig. 13. It is observed that and decreases as per increment in the GFR (from Case 1 to Case 4). Further, the values of and are significantly different in Case 1, whereas in Case 4 the agglomerates has the similar size as that of primary particles; only 1% increase is detected in for the hard-agglomerate region in section-III. In Fig. 13, the black line in section-III is showing the beginning of hard- and soft-agglomerate regions in the spraying process. It can be seen that hard-agglomerate formation starts earlier in Case 1 and the total region of soft-agglomerate formation is considerably bigger as compared to Case 4. As the gas flow dynamics is much faster for Case 4, it minimises the interaction of ZnP precursor vapours and ZrO2 particles with the hot gas throughout the process. Therefore, the agglomeration is delayed and very small particle size is obtained. It is concluded that by further increasing the GFR, non-agglomerated particles can be obtained with much smaller nanoparticles size.

The domain studied in the present work is elongated to observe the size of nanoparticles formed during the flight from guns exit up to the substrate. It is observed that if the density of the particles is relatively small, and the spraying distance (between torch and substrate) is short, then the nanoparticles agglomerates are small 73, or for high GFR non-agglomerated particles can also obtain. It is seen in Figs. 12 and 13 that collision diameter keeps increasing until the domain-outlet. Hence, maintaining a proper distance between the SP-HVOFS gun and the substrate can be an important factor for the desired size and types of (hard-, soft-, or non-agglomerated) nanoparticles formation for coating generation. Accordingly, deposition of hard- or /soft-agglomerated large or/small size nanoparticles on the substrate can be obtained. For example, for producing the dense and fine layer, the substrate must be placed nearer to the guns exit so that smaller size and non-agglomerated nanoparticles coating can be obtained 73.

In summary, increasing oxygen-fuel GFRs considerably affected the (i) gas velocity and (ii) gas enthalpy of the HVOF flame-jet. The increased gas velocity reduces the particle residence/interaction time in the HVOF flame while the higher gas-enthalpy favours the sintering. Moreover, the overall results showed that by controlling the GFR, nanometre size particles (~1-5 nm) can be produced without any agglomeration. Furthermore, the present study reveals that three kinds of control can be devised, either (a) regulating GFR or (b) maintaining a proper spray distance or (c) adjusting both, to effectively generate the required type of nanostructured, homogenous coating.

CONCLUSION

The size of the nanoparticle is needed to be controlled to obtain the desired coating for a particular application. In the present work, nanostructured coating process by the SP-HVOFS technique using Zirconia nanoparticles is modelled, and the gas flow rates (GFR) are regulated to control the size of the nanoparticles. The monodisperse aggregate model is validated for the synthesis of ZrO2 nanoparticles in the SP-FSP process and subsequently used for analysing particles growth in the SP-HVOFS process. The following conclusions are drawn from the present work:

The gas dynamics and the growth of ZrO2 nanoparticles in the SP-HVOFS process are highly influenced by changing the oxygen-fuel GFR.

By increasing the GFR the gas enthalpy, gas temperature, gas pressure, gas velocity, and the gas Mach number increases significantly.

The increase in gas enthalpy and gas temperature in the SP-HVOFS process augmented the rate of evaporation of precursor solution and the rate of formation of ZrO2 nanoparticles.

The higher gas velocities increase the relative velocities of ZnP vapours and ZrO2 seed particles that reduce the residence time of the vapours and particle in the high-temperature regions of the SP-HVOFS torch. Hence, the size of the primary particle diameter () and agglomerated particle diameter () decreases.

High combustion rates associated with higher GFR reduced the process of nucleation, sintering, and agglomeration in the SP-HVOFS process.

Furthermore, the increase in the oxygen-fuel flow rates diluted the injected precursor and thus reduces particle concentration in the process and decreased the rate of particle collision. As a result, non-agglomerated nanoparticles can be obtained with much smaller particle size.

Maintaining a proper distance between the SP-HVOFS gun and the substrate can be a key factor in obtaining the desired size and types of (hard-, soft- or non-agglomerated) nanoparticles for coating formation.

The important aspects of the present work are that by controlling the GFR and by maintaining proper spray distance the generation of required nanostructured, homogenous coating can be achieved. In future experimental and numerical studies, more parameters would be controlled to improve the nanoparticles synthesis process inside the SP-HVOFS torch.

ACKNOWLEDGMENT

The authors would like to acknowledge the financial support from the UK Engineering and Physical Sciences Research Council (EPSRC) project grant: EP/K027530/1, and the research studentship from the NED University of Engineering and Technology, Pakistan.

ABBREVIATIONS

BET

Brunauer-Emmett-Teller

CC

Combustion Chamber

C-D

Convergent-Divergent

CFD

Computational Fluid Dynamics

DJ

Diamond Jet

FSP

Flame spray pyrolysis

GFR

Gas Flow Rate

HVSFS

High-Velocity Suspension Flame Spraying

HVOF

High-Velocity Oxygen-Fuel

HAB

Height Above Burner

SP-FSP

Solution Precursor Flame Spray Pyrolysis

SP-HVOFS

Solution Precursor High-Velocity Oxygen Fuel Spray

SSA

Specific surface area

SPS

Suspension plasma spraying

SPPS

Solution precursor plasma spraying

TAB

Taylor Analogy Breakup

TBC

Thermal Barrier Coating

TEM

Transmission Electron Microscopy

XRD

X-ray diffraction

ZnP

Zirconium n-Propoxide

NOMENCLATURE

= total agglomerate area concentration, m2/kggas

= surface area of completely fused aggregate, m2

= monomer surface area, m2

= collision aggregate diameter, nm

= primary particle diameter, nm

= fractal dimension

= grain boundary diffusion, m2/s

= particle formation rate, s-1 m-3

= mass flux through cell face i, kg/s

= molecular weight of ZnP, kg/mol

=Avogadro number, 1/mol

= particle number concentration, 1/kggas

= number of cell

= number of primary particles per agglomerate

= Ohnesorge number ()

R = universal gas constant, J mol-1K-1

= Reynolds number

= primary particle radius, nm

= sintering time, s

= gas temperature, K

= cell volume, m3

= particle volume concentration, m3/kggas

= volume of ZrO2 monomer, m3

= Weber number ()

w = grain boundary width, m

= mass fraction of ZnP precursor at cell face i

Greek symbols

= collision kernel between agglomerates, m3/s

= surface tension, N/m

= gas density, kg/m3

= density of particles, kg/m3

= molar volume, m3/mol

Subscripts

= cell face

= particle

REFERENCES

(1) Dobbins, T. A.; Knight, R.; Mayo, M. J. HVOF Thermal Spray Deposited Y2O3 -Stabilized ZrO2 Coatings for Thermal Barrier Applications. J. Therm. Spray Technol. 2003, 12, 214.

(2) Schwetzke, R.; Kreye, H. Microstructure and Properties of Tungsten Carbide Coatings Sprayed with Various High-Velocity Oxygen Fuel Spray Systems. J. Therm. Spray Technol. 1999, 8, 433.

(3) Sudaprasert, T.; Shipway, P. H.; McCartney, D. G. Sliding Wear Behaviour of HVOF Sprayed WC-Co Coatings Deposited with Both Gas-Fuelled and Liquid-Fuelled Systems. Wear 2003, 255, 943.

(4) Erne, M.; Kolar, D. Thermal Spraying of Oxide Ceramic and Ceramic Metallic Coatings. In Ceramic Coatings - Applications in Engineering; Feng, S., Ed.; InTech, 2012; pp 167194.

(5) Chen, D.; Jordan, E. H.; Gell, M. Solution Precursor High-Velocity Oxy-Fuel Spray Ceramic Coatings. J. Eur. Ceram. Soc. 2009, 29, 3349.

(6) Puranen, J.; Laakso, J.; Kylmlahti, M.; Vuoristo, P. Characterization of High-Velocity Solution Precursor Flame-Sprayed Manganese Cobalt Oxide Spinel Coatings for Metallic Sofc Interconnectors. J. Therm. Spray Technol. 2013, 22, 622.

(7) Ma, X. Q.; Roth, J.; Gandy, D. W.; Frederick, G. J. A New High-Velocity Oxygen Fuel Process for Making Finely Structured and Highly Bonded Inconel Alloy Layers from Liquid Feedstock. J. Therm. Spray Technol. 2006, 15, 670.

(8) Rauch, J.; Bolelli, G.; Killinger, A.; Gadow, R.; Cannillo, V.; Lusvarghi, L. Advances in High-Velocity Suspension Flame Spraying (HVSFS). Surf. Coatings Technol. 2009, 203, 2131.

(9) Killinger, A.; Kuhn, M.; Gadow, R. High-Velocity Suspension Flame Spraying (HVSFS), a New Approach for Spraying Nanoparticles with Hypersonic Speed. Surf. Coatings Technol. 2006, 201, 1922.

(10) Bolelli, G.; Cannillo, V.; Gadow, R.; Killinger, A.; Lusvarghi, L.; Rauch, J. Properties of High-Velocity Suspension Flame Sprayed (HVSFS) TiO2 Coatings. Surf. Coatings Technol. 2009, 203, 1722.

(11) Pawlowski, L. Suspension and Solution Thermal Spray Coatings. Surf. Coatings Technol. 2009, 203, 2807.

(12) Fauchais, P.; Vardelle, A. Solution and Suspension Plasma Spraying of Nanostructure Coatings. In Advanced Plasma Spray Applications; Hamid, J., Ed.; 2012; pp 149188.

(13) Fauchais, P.; Montavon, G. Latest Developments in Suspension and Liquid Precursor Thermal Spraying. J. Therm. Spray Technol. 2010, 19 (1-2), 226.

(14) Vassen, R.; Stuke, A.; Stver, D. Recent Developments in the Field of Thermal Barrier Coatings. J. Therm. Spray Technol. 2009, 18, 181.

(15) Gell, M.; Jordan, E. H.; Teicholz, M.; Cetegen, B. M.; Padture, N. P.; Xie, L.; Chen, D.; Ma, X.; Roth, J. Thermal Barrier Coatings Made by the Solution Precursor Plasma Spray Process. J. Therm. Spray Technol. 2008, 17, 124.

(16) Govindarajan, S.; Dusane, R. O.; Joshi, S. V. In Situ Particle Generation and Splat Formation during Solution Precursor Plasma Spraying of Yttria-Stabilized Zirconia Coatings. J. Am. Ceram. Soc. 2011, 94, 4191.

(17) Bertolissi, G.; Chazelas, C.; Bolelli, G.; Lusvarghi, L.; Vardelle, M.; Vardelle, A. Engineering the Microstructure of Solution Precursor Plasma-Sprayed Coatings. J. Therm. Spray Technol. 2012, 21, 1148.

(18) Jordan, E. H.; Xie, L.; Gell, M.; Padture, N. P.; Cetegen, B.; Ozturk, A.; Roth, J.; Xiao, T. D.; Bryant, P. E. C. Superior Thermal Barrier Coatings Using Solution Precursor Plasma Spray. J. Therm. Spray Technol. 2004, 13, 57.

(19) Saha, A.; Seal, S.; Cetegen, B.; Jordan, E.; Ozturk, A.; Basu, S. Thermo-Physical Processes in Cerium Nitrate Precursor Droplets Injected into High-Temperature Plasma. Surf. Coatings Technol. 2009, 203, 2081.

(20) Grhn, A. J.; Pratsinis, S. E.; Antoni, S.-F.; Raffaele, M.; Wegner, K. Scale-up for Nanoparticle Synthesis by Flame Spray Pyrolysis: The High-Temperature Particle Residence Time. Ind. Eng. Chem. Res. 2014, 53, 10734.

(21) Grhn, A. J.; Pratsinis, S. E.; Wegner, K. Fluid-Particle Dynamics during Combustion Spray Aerosol Synthesis of ZrO2. Chem. Eng. J. 2012, 191, 491.

(22) Torabmostaedi, H.; Zhang, T.; Foot, P.; Dembele, S.; Fernandez, C. Process Control for the Synthesis of ZrO2 Nanoparticles Using FSP at High Production Rate. Powder Technol. 2013, 246, 419.

(23) Li, M.; Christofides, P. D. Modeling and Control of High-Velocity Oxygen-Fuel (HVOF) Thermal Spray: A Tutorial Review. J. Therm. Spray Technol. 2009, 18, 753.

(24) Li, M.; Shi, D.; Christofides, P. D. Model-Based Estimation and Control of Particle Velocity and Melting in HVOF Thermal Spray. Chem. Eng. Sci. 2004, 59, 5647.

(25) Li, M.; Shi, D.; Christofides, P. D. Diamond Jet Hybrid HVOF Thermal Spray: Gas-Phase and Particle Behavior Modeling and Feedback Control Design. Ind. Eng. Chem. Res. 2004, 43, 3632.

(26) Shi, D.; Li, M.; Christofides, P. D. Diamond Jet Hybrid HVOF Thermal Spray: Rule-Based Modeling of Coating Microstructure. Ind. Eng. Chem. Res. 2004, 43, 3653.

(27) Kamnis, S.; Gu, S. Numerical Modelling of Propane Combustion in a High-Velocity Oxygenfuel Thermal Spray Gun. Chem. Eng. Process. Process Intensif. 2006, 45, 246.

(28) Kamnis, S.; Gu, S. 3-D Modelling of Kerosene-Fuelled HVOF Thermal Spray Gun. Chem. Eng. Sci. 2006, 61, 5427.

(29) Kamnis, S.; Gu, S.; Lu, T. J.; Chen, C. Computational Simulation of Thermally Sprayed WC-Co Powder. Comput. Mater. Sci. 2008, 43, 1172.

(30) Basu, S.; Cetegen, B. M. Modeling of Liquid Ceramic Precursor Droplets in a High-Velocity Oxy-Fuel Flame Jet. Acta Mater. 2008, 56, 2750.

(31) Cetegen, B. M.; Basu, S. Review of Modeling of Liquid Precursor Droplets and Particles Injected into Plasmas and High-Velocity Oxy-Fuel (HVOF) Flame Jets for Thermal Spray Deposition Applications. J. Therm. Spray Technol. 2009, 18, 769.

(32) Fauchais, P.; Montavon, G.; Lima, R. S.; Marple, B. R. Engineering a New Class of Thermal Spray Nano-Based Microstructures from Agglomerated Nanostructured Particles, Suspensions and Solutions: An Invited Review. J. Phys. D. Appl. Phys. 2011, 44, 093001.

(33) Gozali, E.; Kamnis, S.; Gu, S. Numerical Investigation of Combustion and Liquid Feedstock in High Velocity Suspension Flame Spraying Process. Surf. Coatings Technol. 2013, 228, 176.

(34) Gozali, E.; Mahrukh, M.; Gu, S.; Kamnis, S. Numerical Analysis of Multicomponent Suspension Droplets in High-Velocity Flame Spray Process. J. Therm. Spray Technol. 2014, 23, 940.

(35) Zeoli, N.; Gu, S.; Kamnis, S. Numerical Modelling of Metal Droplet Cooling and Solidification. Int. J. Heat Mass Transf. 2008, 51, 4121.

(36) Tabbara, H.; Gu, S. A Study of Liquid Droplet Disintegration for the Development of Nanostructured Coatings. AIChE J. 2012, 58, 3533.

(37) Dongmo, E.; Wenzelburger, M.; Gadow, R. Analysis and Optimization of the HVOF Process by Combined Experimental and Numerical Approaches. Surf. Coatings Technol. 2008, 202, 4470.

(38) Gu, S.; Eastwick, C. N.; Simmons, K. A.; McCartney, D. G.; McCartney, G.; McCartney, D. G. Computational Fluid Dynamic Modelling of Gas Flow Characteristics in a High-Velocity Oxy-Fuel Thermal Spray System. J. Therm. Spray Technol. 2001, 10, 461.

(39) Kruis, F. E.; Kusters, K. A.; Pratsinis, S. E.; Scarlett, B. A Simple Model for the Evolution of the Characteristics of Aggregate Particles Undergoing Coagulation and Sintering. Aerosol Sci. Technol. 1993, 19, 514.

(40) Roest, R.; Atanacio, A. J.; Latella, B. A.; Wuhrer, R.; Ben-Nissan, B. An Investigation of Sol Gel Coated Zirconia Thin Films on Anodised Titanium Substrate by Secondary Ion Mass Spectrometry and Scanning Electron Microscopy. Mater. Forum 2007, 31, 160.

(41) Thakare, V. Progress in Synthesis and Applications of Zirconia. Int. J. Eng. Res. Dev. 2012, 5, 25.

(42) Magnussen, B. F.; Hjertager, B. H. On Mathematical Models of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion. In 16th Symposium on Combustion.The Combustion Institute; 1976; Vol. 16, pp 719729.

(43) Kuo, K. K. Principles of Combustion, 2nd ed.; John Wiley & Sons, Inc., 1986.

(44) Fukumoto, K.; Ogami, Y. Simulation of CO-H2-Air Turbulent Nonpremixed Flame Using the Eddy Dissipation Concept Model with Lookup Table Approach. J. Combust. 2012, 2012, 1.

(45) Dongmo, E.; Gadow, R.; Killinger, A.; Wenzelburger, M. Modeling of Combustion as Well as Heat, Mass, and Momentum Transfer during Thermal Spraying by HVOF and HVSFS. J. Therm. Spray Technol. 2009, 18, 896.

(46) Gozali, E.; Mahrukh, M.; Gu, S.; Kamnis, S. Numerical Investigation on Effects of Nanoparticles on Liquid Feedstock Behavior in High-Velocity Oxygen Fuel (HVOF) Suspension Spraying. Surf. Coatings Technol. 2015, 280, 370.

(47) Grhn, A. J.; Buesser, B.; Jokiniemi, J. K.; Pratsinis, S. E. Design of Turbulent Flame Aerosol Reactors by Mixing-Limited Fluid Dynamics. Ind. Eng. Chem. Res. 2011, 50, 3159.

(48) Torabmostaedi, H.; Zhang, T. Computational Study of the Effect of Processing Parameters on the Formation and Growth of ZrO2 Nanoparticles in FSP Process. Chem. Eng. Process. Process Intensif. 2014, 78, 1.

(49) Saqr, K. M.; Wahid, M. A. Comparison of Four Eddy-Viscosity Turbulence Models in the Eddy Dissipation Modeling of Turbulent Diffusion Flames. Int. J. Appl. Math Mech. 2011, 7, 1.

(50) Menter, F. R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA J. 1994, 32, 1598.

(51) Ansys. Ansys Fluent Theory Guide. V14.5 ed. SAS IP, Inc. 2012, pp 1735.

(52) Morsi, S.; Alexander, A. An Investigation of Particle Trajectories in Two-Phase Flow Systems. J. Fluid Mech 1972, 55, 193.

(53) Haider, A.; Levenspiel, O. Drag Coefficient and Terminal Velocity of Spherical and Nonspherical Particles. Powder Technol. 1989, 58, 63.

(54) Gozali, E.; Kamnis, S.; Gu, S. Numerical Investigation of Combustion and Liquid Feedstock in High-Velocity Suspension Flame Spraying Process. Surf. Coatings Technol. 2013, 228, 176.

(55) Gozali, E.; Kamnis, S.; Gu, S. Analysis of Liquid Feedstock Behavior in High-Velocity Suspension Flame Spraying for the Development of Nanostructured Coatings. In Proceedings of the International Thermal Spray Conference; 2013; pp 418423.

(56) Bovat, P. M. Computational Analysis of Water Atomization in Spray Desuperheaters of Steam Boilers, Rensselaer Polytechnic Institute, 2013.

(57) Hu, D. Comparison of Numerical and Experimental Results of Four Liquid Spray Combustors, Louisiana State University and Agriculture and Mechanical College, 2002.

(58) Ranz, W. E.; Marshall, W. R. Evaporation from Drops. Part I. Chem. Eng. Prog. 1952, 48, 141.

(59) Ranz, W. E.; Marshall, W. R. Evaporation from Drops. Part II. Chem. Eng. Prog. 1952, 48, 173.

(60) Fauchais, P. L.; Heberlein, J. V. R.; Boulos, M. I. Thermal Spray Fundamentals: From Powder to Part; Springer: London, 2014.

(61) Sobolev, V. V.; Guilemany, J. M.; Nutting, J. Gas-Particle Interactions during Spraying. In High Velocity Oxy-Fuel Spraying Theory, Structure-Property Relationships and Applications; Shrikant, J., Ed.; W. S. Maney and Son Ltd, 2004; pp 2961.

(62) Sobolev, V. V.; Guilemany, J. M.; Garmier, J. C.; Calero, J. A. Modelling of Particle Movement and Thermal Behaviour during High-Velocity Oxy-Fuel Spraying. Surf. Coatings Technol. 1994, 63, 181.

(63) Schild, A.; Gutsch, A.; Mhlenweg, H.; Pratsinis, S. E. Simulation of Nanoparticle Production in Premixed Aerosol Flow Reactors by Interfacing Fluid Mechanics and Particle Dynamics. J. Nanoparticle Res. 1999, 1, 305.

(64) Seinfield, J. H. Atmospheric Chemistry and Physics of Air Pollution; John Wiley & Sons: New York, 1986.

(65) Koch, W.; Friedlander, S. K. Particle Growth by Coalescence and Agglomeration. J. Aerosol Sci. 1990, 21, 73.

(66) Seto, T.; Hirota, A.; Fujimoto, T.; Shimada, M.; Okuyama, K. Sintering of Polydisperse Nanometer-Sized Agglomerates. Aerosol Sci. Technol. 1997, 27, 422.

(67) Torabmostaedi, H.; Zhang, T. Effect of Nozzle Geometry and Processing Parameters on the Formation of Nanoparticles Using FSP. Chem. Eng. Res. Des. 2014, 92, 2470.

(68) Kobata, A.; Kusakabe, K.; Morooka, S. Growth and Transformation of TiO2 Crystallites in Aerosol Reactor. AIChE J. 1991, 37, 347.

(69) Brossmann, U.; Wurschum, R.; Sodervall, U.; Schaefer, H.-E. Oxygen Diffusion in Ultrafine Grained Monoclinic ZrO2. J. Appl. Phys. 1999, 85, 7646.

(70) Madeyski, A.; Smeltzer, W. W. Oxygen Diffusion in Monoclinic Zirconia. Mat. Res. Bull. 1968, 3, 369.

(71) Mueller, R.; Jossen, R.; Kammler, H. K.; Pratsinis, S. E.; Akhtar, M. K. Growth of Zirconia Particles Made by Flame Spray Pyrolysis. AIChE J. 2004, 50, 3085.

(72) Rsner-Kuhn, M.; Hofmeister, W. H.; Kuppermann, G.; Bayuzick, R. J.; Frohberg, M. G. Investigations of the Influence of Oxygen on the Surface Tension of Zirconium by the Oscillating Drop Technique.