Computational Development of a Novel Aerosol Synthesis Technique

Article pubs.acs.org/IECR

Computational Development of a Novel Aerosol Synthesis Technique for Production of Dense and Nanostructured Zirconia Coating Mahrukh Mahrukh,†,‡ Arvind Kumar,§ Sai Gu,*,∥ and Spyros Kamnis⊥ †

School of Energy, Environment & Agrifood, Cranfield University, Cranfield, Bedford MK43 0AL, United Kingdom Department of Mechanical Engineering, NED University of Engineering & Technology, University Road, 75270 Karachi, Pakistan § Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India ∥ Department of Chemical and Process Engineering, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU2 7XH, United Kingdom ⊥ Monitor Coatings Limited, 2 Elm Road, North Shields, Tyne & Wear NE29 8SE, United Kingdom ‡

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 favors the sintering. Overall the results show that, by controlling the GFR, single scale nanometre particles (∼1−5 nm) can be fabricated without any agglomeration.

1. INTRODUCTION

the solution precursors are made by dissolving metal salts or organometallic or liquid metal precursors in a solvent.11−13 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 behavior of the suspension and solution breakup, evaporation, precipitation, and deposition processes.

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.1−5 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 toward 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.5−10 The liquid feedstock is either suspension of nanoparticles or solutions. The former contains nano- or microsized particles in a solvent with dispersing agents while © 2016 American Chemical Society

Received: Revised: Accepted: Published: 7679

May 4, 2016 June 27, 2016 June 28, 2016 June 28, 2016 DOI: 10.1021/acs.iecr.6b01725 Ind. Eng. Chem. Res. 2016, 55, 7679−7695

Article

Industrial & Engineering Chemistry Research

generating finely structured and highly bonded coatings using the solution precursor high-velocity oxygen-fuel spray (SPHVOFS). 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 SPHVOFS process. Both nanocrystalline ZrO2 and amorphous γAl2O3 are observed by as-sprayed coating characterization using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The coatings consist of ultrafine splats (2−5 μm), spherical particles and hollow shell structures having high density with the thickness of 40 μm.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 behavior 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 modeling. 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 modeling of HVOF and SP-HVOFS processes, a brief literature review is presented here. The numerical modeling of HVOF conventional system with powder injection is performed by many researchers.23−29 Li and Christofides23 highlighted the multiscale behavior 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 inflight particle behavior). 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

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.11−13 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 nanosize 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 (50−500 nm) and splats formation of sizes from 200−2000 nm and shows nanoporosity 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 nonpyrolized 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 nondecomposed 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 7680

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

2. COMPUTATIONAL MODELING 2.1. Gas-Phase Flame Structure. Modeling of particle formation and growth in the SP-HVOFS process involves the coupling of the gas dynamics with the droplet/particle dynamics (see Figure 1). The gas dynamics of the SPHVOFS 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. In this method, the droplets of solution precursor, after being injected into the HVOF flame-jet, undergo several physical processes taking place simultaneously. The first stage is the aerodynamic breakup, as the slow moving droplets are entrained into the high-velocity jet and accelerate in the highvelocity gas stream (see Figure 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 (We < 100). The model is well adapted to the conditions of spraying and validated in the earlier studies; found in refs 33−36. 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 Figure 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 3000 to 4000 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

Till today, very few researchers have modeled the SPHVOFS process. Modeling 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 Cetegen30,31 modeled 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 a fewer number of works reported regarding experiments and modeling 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 SPHVOFS process. The novel numerical modeling 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 analyze the interaction between precursor droplets with combustion flame and to capture the aerosol dynamics during this interaction. The interaction is modeled without the adjustable parameters and need of experimental data by using commercial CFD software to predict zirconia nanoparticle characteristics. 7681

DOI: 10.1021/acs.iecr.6b01725 Ind. Eng. Chem. Res. 2016, 55, 7679−7695

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Industrial & Engineering Chemistry Research ⎛ ∂uj ∂u ⎞ 2 ∂u + i ⎟⎟ − μeff i δij (τij)eff = μeff ⎜⎜ ∂xj ⎠ 3 ∂xi ⎝ ∂xi

biomaterial. The coatings generated by ZrO2 nanoparticles have high strength, high fracture toughness, high hardness, excellent wear resistance, and better friction behavior. 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) 70 wt % in n-propanol diluted with ethanol for ZrO2 nanoparticle production. For the supersonic combustion of methane inside the SPHVOFS 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 breakup 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 SPHVOFS flame. The flame combustion is modeled by using a single step reaction mechanism. The complete stoichiometric combustion reactions are expressed as

2.3. Turbulence Modeling. The utilization of SST k − ω turbulence model with the eddy dissipation (EDM) combustion model is presented for the first time in this paper.49 In the present work, the SST k − ω model was employed for capturing the turbulence in the HVOF flame jet.49−51 The transport equations of the SST k − ω model are given as51

= ZrO2 + 12CO2 + 14H 2O 1‐propanol: C3H8O + 4.5O2 = 3CO2 + 4H 2O ethanol: C2H6O + 3O2 = 2CO2 + 3H 2O

methane: CH4 + 2O2 = CO2 + 2H 2O

The eddy-dissipation model42−44 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.20,23,27,22,45−48 2.2. Governing Equations. The governing equations for the two-dimensional model in the Cartesian tensor form are Mass conservation equation: (1)

Momentum conservation:

(5)

∂ ∂ (ρω) + (ρωuj) ∂t ∂xi μ ⎞ ∂k ⎤ ∂ ⎡⎢⎛ = ⎜μ + t ⎟ ⎥ + Gω − Yω + Dω + Sω σω ⎠ ∂xj ⎥⎦ ∂xj ⎢⎣⎝

(6)

g (ρd − ρ) ∂ud = FD(u − ud) + x + Fx ∂t ρd

∂p ∂ ∂ ∂ ∂ (ρui) + (ρuiuj) = − + (τij)eff + ( −ρu′iu′ j) ∂t ∂xj ∂xi ∂xj ∂xj

(7)

where Fx is an additional acceleration force or droplet mass term; FD(u − ud) is the drag force per unit droplet mass which is given as

(2)

Energy transport equation: ∂ ∂ (ρ E ) + [ui(ρE + p)] ∂t ∂xi ⎞ ∂ ⎛⎜ ∂T keff = + ui(τij)eff ⎟⎟ + Sh ⎜ ∂xj ⎝ ∂xj ⎠

∂ ∂ (ρ k ) + (ρkui) ∂t ∂xi μ ⎞ ∂k ⎤ ∂ ⎡⎢⎛ = ⎜μ + t ⎟ ⎥ + Gk − Yk + Sk σk ⎠ ∂xj ⎥⎦ ∂xj ⎢⎣⎝

In these equations, Gk denotes the generation of turbulence kinetic energy due to mean velocity gradients. Gω represents the generation of ω. Yk and Yω denote the turbulence dissipation of k and ω. Dω represents the cross-diffusion term. Sk and are Sω user-defined source terms. 2.4. 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. First, they breakup due to the aerodynamic forces.34,36,51 The second stage consists of spherical particles or droplets dispersed 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. Fluent simulates the discrete second phase in a Lagrangian frame of reference. The Lagrangian discrete phase models follow 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 as51

zirconium n‐propoxide: C12H 28O4 Zr + 18O2

∂ρ ∂ + (ρui) = 0 ∂t ∂xi

(4)

FD =

C Re 18μ + D 2 24 ρd dd

(8)

where u is the fluid phase velocity, ud is the droplet velocity, μ is the molecular viscosity of the fluid, ρ is fluid density, ρd is the density of the droplet, and dd is the droplet diameter. Re is the relative Reynolds number, defined as

(3)

where the deviatoric stress tensor is given by 7682

DOI: 10.1021/acs.iecr.6b01725 Ind. Eng. Chem. Res. 2016, 55, 7679−7695

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Industrial & Engineering Chemistry Research Re =

ρdd|ud − u| μ

vapor concentration in the bulk gas, respectively. kc in eq 14 is calculated from the Sherwood number (Sh) correlation58,59 The droplet mass is reduced according to eq 15:

(9)

The drag coefficient, CD, is taken from

52

md (t + Δt ) = md (t ) − NA i d M w Δt

b3Red 24 CD = (1 + b1Redb2) + Red b4 + Red

where Mw is molecular weight of species i. During the activation of law 2, the droplet’s 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.

(10)

where b1 = exp(2.3288 − 6.4581⌀ + 2.4486⌀ 2 b2 = 0.0964 + 0.5565⌀

md cd

b3 = exp(4.095 − 13.8944⌀ + 18.4222⌀ 2 − 10.2599⌀3 (11) 53

(12)

Ohnesorge number (Oh =

μ ρσd

ρc vrel 2d σ

(17)

where K∞, c∞, and ρd 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 (Kn = λ/dd), the ratio of gas mean free path (λ) to droplet diameter (dd), 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 Kn can be neglected in the case of HVOF spraying as shown by Sobolev et al.62 The Reynolds number (Re) varies from 2.09 × 105 to l.18 × 105 in the computation domain based on the characteristics of the gas dynamics. 2.5. 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 SPHVOFS 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

). Since the

) remains much below 0.1

(Oh ≪ 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 refs 34−36, 46, 54, and 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 (Td) is less than the vaporization temperature (Tvap = 271 K for liquid ethanol).51,54,56,57 A simple heat balance Equation-13 is used to relate Td to the convective heat transfer, and the heat gained or lost by the droplet while moving through the continuous phase. Law 1: For Td < Tvap md cd

dTd = hAd (T∞ − Td) dt

(13)

∂ ⎛ ∂N ⎞ 1 ⎜ρuiN − Γk ⎟ = I − β(ρN )2 ∂xi ⎝ ∂xi ⎠ 2

where md, cd, Td, and Ad are mass, heat capacity, temperature and surface area of the droplet, respectively. Here, h and T∞ 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 eq 14. This law is used when droplet temperature reaches the Tvap and continues until the droplet reaches the boiling point. Law 2: For Tvap ≤ Td < Tboil Ni = kc(Ci ,s − Ci , ∞)

(16)

⎡ d(dd) c (T − Td) ⎤ 4K∞ = (1 + 0.23 Red ) ln⎢1 + ∞ ∞ ⎥ ⎣ ⎦ ρd c∞dd dt L

where s is the surface area of a sphere having the same volume as a droplet and S 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 (We) is lower than 100 (We < 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 (We =

dTd dmd = hAd (T∞ − Td) + L dt dt

where dmd is the rate of evaporation and L is the latent heat. dt 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 (Tboil = 351 K for liquid ethanol).43,54 Law 3: For Td ≥ Tboil

b4 = exp(1.4681 + 12.2584⌀ − 20.7322⌀ 2 + 15.8855⌀3

Haider and Levenspiel defined the shape factor, ⌀ as s ⌀= S

(15)

(18)

The first two left-hand side terms in eq 18 describe the convection and diffusion of the particles in the turbulent flow. The particle formation rate, I, is calculated based on the mass flux imbalance in each grid cell47 I=

(14)

where Ni, kc, Ci,s, and Ci,∞ are molar-flux of vapor, mass transfer coefficient, vapor concentration at the droplet surface and

−NA VcellM Z

n

∑ miX Z,i i=1

(19)

where NA is the Avogadro number, Vcell is the cell volume, MZ is the molecular weight of ZnP, n is the number of cell faces, mi is 7683

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Industrial & Engineering Chemistry Research the signed (positive for out- and negative for in-flow) mass flux through cell face i, and XZ,i is the mass fraction of the precursor at cell face i. The second term on the right-hand side in eq 18 has the Fuchs interpolation function (β) for Brownian coagulation in the free molecule and continuum regime39,64 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 Friedlander65 ρ(A − Nas) ∂ ⎛ ∂A ⎞ ⎜ρuiA − Γk ⎟ = Ia0 − ∂xi ⎝ ∂xi ⎠ tsin

3. RESULTS AND DISCUSSION 3.1. 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 modeling (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 Gröhn 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 modeling approach is used in their study. As shown in Figure 2, the particles are collected by a vacuum pump on a glass microfiber filter. The final primary particle size

(20)

The total agglomerate volume concentration, V, is provided by Kruis et al.39 ∂ ⎛ ∂V ⎞ ⎜ρuiV − Γk ⎟ = Iv0 ∂xi ⎝ ∂xi ⎠

(21)

The primary particle diameter, dp, number of primary particles per agglomerate, np, and collision aggregate diameter, dc, are39 dp =

6V 6V , np = , dc = d pn p(1/ Df ) A πd p 3

(22)

where Df is the fractal dimension which is set as 1.8, a commonly used value for aggregates generated in hightemperature 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: tsin =

0.013RTrp 4 wDgbγ Ω

Figure 2. Schematic view of SP-FSP nozzle configuration.

(23)

where T (K) is the gas temperature which is found from CFD simulation, w is the grain boundary width which is 5 × 10−10 m,69 Dgb (m2 s−1) is the grain boundary diffusion coefficient given by70,71 ⎛ −2.33 × 105 ⎞ Dgb = 9.73 × 10−7 exp⎜ ⎟ RT ⎠ ⎝

is calculated based on the measured specific surface area (SSA) of the ZrO2 powder by N2 adsorption at 77 K using the Brunauer−Emmett−Teller (BET) equation theory.21 Also, particles are sampled thermophoretically on carbon-coated copper grids (Plano, mesh 300) on the center axis at 4−20 × 10−2 m height above the burner (HAB) using 20−100 ms 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 4.111 × 10−6 kg/s and 8.222 × 10−6 kg/s (14.8 g/h and 29.6 g/h), respectively. A concentric two-phase nozzle is used to spray the metalcontaining liquid mixture. 3−5 L/min of dispersion oxygen is introduced into the surrounding annular gap at an angle of 45° with the center capillary. The gap width (x, see Figure 2) is adjusted to ensure 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 3 demonstrates the comparison of the predicted zirconia primary particle diameters (solid lines) for different precursor concentration of 0.5−1 M production rate of 2.6667−6.25 × 10−6 kg/s (9.6−22.5 × 10−3 g/h). The measured TEM is presented by triangular symbols, BET by the square symbol, and the numerical data from Gröhn et al.21 by the dotted lines for the primary particle diameter. Model

(24)

and γ (N m−1) is the surface tension according to Rösner-Kuhn et al.72 γ = (1517 − 0.44(T − 2125)) × 10−3

(25)

The term Ω in eq 23 is the molar volume of zirconia (Ω = 2.01998 × 10−5 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 radiation22 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. 7684

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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.

predictions are mixing-cup averages for beams with 5 × 10−2 m diameter (i.e., the radius of the domain) going through the flame at different HAB to be consistent with measurements and numerical data. ⎯→ n ∑i = 1 d pvi⃗ · A i dmix − cup = → ⎯ n ∑i = 1 vi⃗ · Ai (26)

→ ⎯ where dp is the primary particle diameter vi⃗ , and Ai are the facet velocity vector and the facet area vector, respectively. As can be seen in Figure 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 in21 show under prediction of about 7−9%. Also, comparison of the predicted diameters with the TEM measurement shows better agreement than the model in ref 21 (see Figure 3a,b). The improvement of the present model compared to that developed by Gröhn et al.21 can be attributed due to the use of the SST k − ω turbulence model instead of Realizable k − ε turbulence model that may have improved the gas flow prediction and ultimately the particle size evolution. 3.2. 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 online characterizations and numerical data21 at different production rates and precursor concentration. Thus, the model can be used for equipment design and process optimization in SP-HVOFS process. 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 Figure 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 gun’s outlet. The torch geometry considered in the numerical simulations is axisymmetric. The mesh consisted

Figure 4. (a) 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.

of 53 947 numbers of nodes, and it is very fine inside the torch and in the regions of flame jet ejection into the atmosphere (Figure 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 toward the exit of the gun. The formation of shock diamonds is observed after ejection of flow in the free jet region (Figure 1). The lowest to highest oxygen-fuel GFR selected for this study is designated as cases 1, 2, 3, and 4, respectively (Table 1). The initial precursor droplet diameter is 50 μm with an injection temperature of 300 K and velocity of 15 m/s. The droplet flow rate is 3.821 × 10−4 kg/s that gives zirconia production rate of 2.778 × 10−5 kg/s (or 100 g/h). The solution precursor carrying mixture of 0.5 M zirconium npropoxide (ZnP 70 wt % in n-propanol) diluted in ethanol has 7685

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TG without multicomponent droplets injection is observed in the combustion chamber (3000−4000 K 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 (ΔT is 750−1000 K for cases 1 and 4, respectively). It is because heat is extracted from the gas for evaporating the precursor droplets, as seen in Figures 6 and 7a.

Table 1. Geometric Parameters and Working Conditions of DJ2700 HVOF Torch geometric parameters

symbol

dimension (mm)

(I) combustion chamber length combustion chamber radius nozzle throat radius (II) barrel length barrel exit radius (III) free jet length

LCC RCC RT LB RB LFJ

23.8 9.10 4.20 66.2 6.22 500 case

working conditions oxygen flow rate (kg/s) fuel flow rate (kg/s) droplet diameter and initial temp. droplet flow rate and initial velocity solution precursor mass composition precursor concentration

1

2

3

4

0.0035 0.007 0.014 0.021 0.0015 0.003 0.006 0.009 50 μm, 300 K 3.821 × 10−4 kg/s, 15 m/s 72.3% Ethanol, 19.4% ZnP, 8.3% n-propanol 0.5 M ZnP solution

Figure 6. Gas temperature maps for cases 1−4 [section I, combustion chamber (CC); section II, barrel; and section III, part of free jet region].

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 analyzed during the SPHVOFS process. 3.3. 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 oxygenfuel GFR are considered with the constant oxygen-fuel ratio of O/F = 2.333, to analyze the effects of increasing oxygen-fuel GFR on the combustion gas and particle dynamics inside SPHVOFS process (Table 1, cases 1−4). The gas temperature (TG), pressure (PG), velocity (VG), and Mach (MG) number increases with increase in GFR, as presented in Figures 5−7. As shown in Figure 5, the maximum

The map of TG in Figure 6 shows the high and the lowtemperature regions from the gun inlet to some extent in the free jet section III (near gun’s 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 vapors combustion (section I and II, Figures 6 and 7a). Higher GFRs (cases 3 and 4) augmented the combustion temperature in sections I and II, and due to the burning of the flammable precursor’s vapors, 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 (Figures 6 and 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 bar) is observed for case 4, and the lowest value of 0.0586 MPa (0.586 bar) is observed for case 1 in section I (Figure 7b). For each case pressure sharply declines in the CC and the barrel sections. Furthermore, for cases 2−4, 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 barrel’s exit (Figure 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. 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,d shows the centerline 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

Figure 5. Variation of gas temperature without droplets injection along centerline 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]. 7686

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Figure 7. Variation of (a) gas temperature, (b) gas pressure, (c) gas velocity, and (d) gas Mach Number along centerline axis for cases 1−4.

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) and case 4 (b) and (d).

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, Figure 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 barrel’s midsection (along the gun’s axis; Figure 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 Figure 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

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 along the barrel axis and no shock diamonds are formed at the barrel exit (Figure 6). The supersonic jet, with visible shock diamonds, is appeared for cases 2−4 as MG > 1.0 at gun ejection (Figures 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. 3.4. Effect of Gas Flow Rates on Precursor Droplet Dynamics and ZrO2 Nanoparticles Formation. In the SPHVOFS gun, the chemical reaction started immediately as the precursor droplets absorb heat from the surrounding hot gas and get converted into vapors (section I). The evaporation of the precursor liquid is dependent on the combustion 7687

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Industrial & Engineering Chemistry Research 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 Figure 8a,b 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 vapors 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 2−4 as compared to subsonic flow (case 1). In case 1, the precursor vapors got sufficient reaction time to interact with the combustion gases and formed the required ZrO2 species. In Figure 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 ΔTG = 1614 K, Figure 7a). The opposite behavior 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 Figure 8b). The formation of particles continues in section III for both cases until all of the precursor vapors converted into ZrO2 species (i.e., in the free jet section III which is not shown in Figure 8). The particles formation start where the oxygen-fuel combustion streams and precursor vapor streams get mixed inside the combustion chamber, while the turbulence mixing occurs near the centerline 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 Figure 8c,d, 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 (Figure 8c,d). 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/vapors fly away without prior evaporation and chemical formation hence less mass fractions are detected in the CC. For cases 1−4, Figure 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 sections I and II. In case 1, due to the presence of the low-temperature field, the droplets will not fully evaporate and remain present until the exit of the barrel section (Figure 9a). The droplets disintegration and evaporation rates increase with increment in the GFR as gas temperature, and pressure is augmented; hence, droplets start disappearing in the middle of the barrel in cases 2 and 3 (Figure 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 Figure 9c,d 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, Figure 9d) would leave the SP-HVOFS torch at a faster rate without complete evaporation. These droplets and vapors carrying higher kinetic energies will lower the formation and growth of nanoparticles in the higher GFR cases (details are discussed in the next section 3.5.1). 3.5. 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 vapors 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 SPHVOFS 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. First, 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 7688

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

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 (Figure 10c). First, 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. For cases 1−4, Figure 11 shows the comparison graphs of V, N, and A along the SP-HVOFS gun’s central axis. It is observed that ZrO2 particle formation is highly influenced by the

collision with the quick atoms or molecules in 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 (sections I and II). Figure 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 (Figure 10a). The gases carrying ZnP vapors 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 1.61 × 10−6 m3/kg in the free jet region along the gun central axis (at about 0.0622 m away from the torch exit, Figure 10a) and then started to decrease as the precursor mass fraction is reduced in these regions. 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 Figure 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 16.2 × 1020 numbers/kg observed at the nozzle throat and the start of the barrel section II. At gun’s exit, the value of N decreases gradually from 6.11 × 1020 to 2.3 × 1020 numbers/kg until 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 vapors further rises to x = 0.151 m in section III, which enhances the value of N to 8.864 × 1020 numbers/kg and after

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 1−4. 7689

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Industrial & Engineering Chemistry Research

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 favorable 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 Figure 11c particle surface area reached its highest value in the combustion sections, as these regions support the chemical reaction of ZnP to ZrO2 formation. At a high-temperature inside gun’s 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 (Figure 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 vapors 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 (Figure 11a−c). 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 vapors (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 (dp). 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 torch’s different sections I and II. As shown earlier in Figure 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 oxygenfuel 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, nanoparticle’s agglomeration is also reduced when GFR increases as the particle-to-particle interaction and collision time is shortened.

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 Figure 11a). The increase in volume concentration (V) of nanoparticles indicates that the chemical reaction for converting ZnP into ZrO2 is ongoing in sections I and II of the SP-HVOFS torch (Figure 11a). The gases carrying ZnP vapors and ZrO2 particles ejected out from the torch exit (at x = 0.09 m). In cases 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 vapors 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 (Figure 11a). Further, V starts to decrease more sharply for case 4 than that for case 3; it depicts that ZrO2 seed particle’s 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 vapors and abrupt formation of ZrO2 particles. The fluctuating values of A and N (increasing and decreasing) inside sections 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 favorable (Figure 11b,c). 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 gun’s exit (x = 0.09 m) due to increasing coagulation and coalescence of ZrO2 seed particles. The ZrO2 particles formation from ZnP vapors 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 Figure 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 Figure 7a and N in Figure 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 Figure 7a as a sudden increase in TG, and in Figure 6 case 4 sharp red color 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 Figure 7b) decreases the interaction (residence) time between the precursor vapors and the combustion gas inside the SP-HVOFS torch. It reduces the overall particle number concentration (N in section III showed in Figure 11b) and 7690

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regions is decreased from 11.265 to 6.932 nm (at 0.352 and 0.406 m) for cases 1 and 2, respectively. The beginning of soft-agglomerate formation is assumed at that point where the growth of primary particle becomes constant as dp = 95%dpf.22 In this region, the atmospheric air surrounding the free jet lowers the gas temperature and dilutes the particles flow; hence sintering reduces which begins softagglomerate formation. The diameter of soft-agglomerates (dp) 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 (dpf) 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 (Figure 12b), and the difference in nanoparticles sizes is clearly observed between case 1 and 2 and case 3 and 4. An enormous decrease in the particle growth is noticed when the GFR increased from cases 1−4. 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 cases 1 and 2 (Figure 12, Table 2). It happens as the precursor mass in the SP-

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 SPHVOFS process, the contour plots are shown in Figure 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 favorable high-temperatures. For investigating the agglomeration and the nonagglomeration 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 dc/dp reaches a value of 1.01. The beginning of softagglomerate formation starts when dp = 95%dpf (dpf 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.20−22 Figure 12a shows the profiles of primary (dp) and

Table 2. Primary Particle Diameter for Different Gas Flow Rates case 1 sections

x (m)

(I) CC-mid throat (II) barrel-mid barrel-exit (III) Free-Jet-mid (III) Free-Jet-end

0.0119 0.0238 0.0569 0.090 0.340 0.590

2

3

4

primary particle diameter (nm) 1.791 1.611 1.627 1.839 10.503 11.313

1.739 1.631 1.658 1.770 5.947 6.915

1.369 1.266 1.447 1.617 3.583 4.973

0.772 0.922 1.320 1.461 2.743 4.334

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 particle’s diameter in cases 3 and 4. Moreover, as stated earlier, ZrO2 seed particle’s relative velocity is enhanced in cases 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 gun’s high-temperature zone that diminished the sintering rate and hence dp 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 Figure 12b). Some growth in ZrO2 nanoparticles size is detected in the free jet section III and the particle’s size increases up to 4.016 and 3.205 nm for case 3, and 4, respectively. For case 3, the hardagglomerates region starts at x = 0.241 m (as marked by vertical-solid-line) in the free-jet section III away from gun’s exit. The value of agglomerate diameter detected at the end of this hard-agglomerate region is dc = 4.775 nm. After reaching a point, x = 0.493 m, hard-agglomerate formation ends and the region of soft-agglomeration started (as marked by verticalhollow-line), this agglomeration continues until the domain− outlet (x = 0.59 m). The final agglomerate size is dcf = 5.239 nm, and the final value of primary particle diameter (dpf) 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

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

collision (dc) 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 gun’s 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 cases 1 and 2 is 14%. Case 2 has a wider region of hard-agglomerates with smaller collision diameters (dc) 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 7691

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

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 minimizes the interaction of ZnP precursor vapors 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, nonagglomerated 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 gun’s 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 nonagglomerated particles can also obtain. It is seen in Figures 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 nonagglomerated) 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 gun’s exit so that smaller size and nonagglomerated 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 favors the sintering. Moreover, the overall results showed that by controlling the GFR, nanometer 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, homogeneous coating.

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 dcf = 4.372 nm and dpf = 4.334 nm. 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, and 0.590 m) in SP-HVOFS torch to analyze the variation in primary particle diameter (dp) of ZrO2 nanoparticles formed by using four different GFR. By assuming case 1 as a reference case, the percentage variation in dp is studied. At the combustion chamber mid region, the reduction in dp is 3% for case 2, in comparison to case 1. Very small variation in primary particle size is observed when cases 1 and 2 data is analyzed in sections I and II of the torch (as shown in Table 2 and in Figure 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, (Figure 12a clearly shows this variation in dp and dc for cases 1 and 2, respectively), increase of GFR from cases 1 to 2 leads to a 38.5% reduction in primary particle diameter in the free-jet spray region after the gun exit. When cases 3 and 4 are compared with case 1, the percentage difference in dp 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 SPHVOFS torch. Finally, at the outlet, the percentage reduction in dp reaches its highest value of 56% and 62% in cases 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 cases 3 and 4. The distribution map of dp and dc for cases 1 and 4 are shown in Figure 13. It is observed that dp and dc decreases as per increment in the GFR (from cases 1−4). Further, the values of dp and dc 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 dc for the hardagglomerate region in section III. In Figure 13, the black line in section III is showing the beginning of hard- and soft-

4. CONCLUSION The size of the nanoparticle is needed to be controlled to obtain the desired coating for a particular application. In the 7692

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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

present work, nanostructured coating process by the SPHVOFS technique using zirconia nanoparticles is modeled, 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 analyzing particle’s growth in the SPHVOFS process. The following conclusions are drawn from the present work: 1. The gas dynamics and the growth of ZrO2 nanoparticles in the SP-HVOFS process are highly influenced by changing the oxygen-fuel GFR. 2. By increasing the GFR the gas enthalpy, gas temperature, gas pressure, gas velocity, and the gas Mach number increases significantly. 3. 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. 4. The higher gas velocities increase the relative velocities of ZnP vapors and ZrO2 seed particles that reduce the residence time of the vapors and particle in the hightemperature regions of the SP-HVOFS torch. Hence, the size of the primary particle diameter (d p ) and agglomerated particle diameter (dc) decreases. 5. High combustion rates associated with higher GFR reduced the process of nucleation, sintering, and agglomeration in the SP-HVOFS process. 6. 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, nonagglomerated nanoparticles can be obtained with much smaller particle size. 7. 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 nonagglomerated) 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, homogeneous 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.

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Nomenclature

A = total agglomerate area concentration, m2/kggas as = surface area of completely fused aggregate, m2 ao = monomer surface area, m2 dc = collision aggregate diameter, nm dp = primary particle diameter, nm Df = fractal dimension Dgb = grain boundary diffusion, m2/s I = particle formation rate, s−1 m−3 mi = mass flux through cell face i, kg/s Mz = molecular weight of ZnP, kg/mol NA = Avogadro number, 1/mol N = particle number concentration, 1/kggas n = number of cell np = number of primary particles per agglomerate μ Oh = = Ohnesorge number (Oh) ρσd

R = universal gas constant, J mol−1K−1 ρd |u − u| Re = d μd = Reynolds number rp = primary particle radius, nm tsin = sintering time, s T = gas temperature, K Vcell = cell volume, m3 V = particle volume concentration, m3/kggas vo = volume of ZrO2 monomer, m3 ρ v 2d

We = c relσ = Weber number (We) w = grain boundary width, m XZ,i = mass fraction of ZnP precursor at cell face i Greek symbols β collision kernel between agglomerates, m3/s γ surface tension, N/m ρ gas density, kg/m3 ρp density of particles, kg/m3 Ω molar volume, m3/mol subscripts i = cell face p = particle

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel. +44 01483 682676. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge the financial support from the U.K. 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.

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ABBREVIATIONS BET Brunauer−Emmett−Teller CC combustion chamber C−D convergent−divergent CFD computational fluid dynamics DJ diamond jet

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