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Numerical Optimization of Quenching Efficiency and Particle Size Control in Flame Synthesis of ZrO2 Nanoparticles

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Abstract

The development of a new quenching design combining rapid cooling with an expansion for controlling the size of nanoparticles synthesized at industrial scale by flame spray pyrolysis was investigated. The design of the quenching device was supported by simulations using a coupled computational fluid dynamics-monodisperse aerosol model to reduce the size of the primary particles and their agglomerate diameters while conserving the production yield at the filter above the burner. The results showed that quenching the spray flame in an open environment led to lower production yield due to the negative velocity of quenching gas which diverted the particles to the bottom of reactor. An additional upstream air flow could help to increase the particle production yield at high air flow rates, while it had a negative effect on the penetration depth of quenching gas inside the main flame which resulted in higher flame heights. The new design showed that adding an enclosure around the burner and quenching ring can significantly increase the quenching efficiency and reduce the particle size. The technique to control the particle size was also studied in this paper.

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Abbreviations

a :

Area of agglomerate particle, m2

a s :

Area of a completely fused (spherical) aggregate of volume v a

A :

Dimensionless coefficient in eddy dissipation model

A d :

Surface area of the droplet, m2

B :

Dissipation term

c :

Particle velocity, m/s

c p :

specific heat capacity, J/(kg K)

C :

Scaling constant

C D :

Drag coefficient

C i,s :

Concentration of component i on the droplet surface

C i,∞ :

Concentration of component i in the bulk

d :

Droplet diameter, m

d o :

Orifice diameter, m

d i :

Initial droplet size, m

D :

Particle diffusion coefficient, m2/s

D i,m :

Diffusion coefficient of vapor in the bulk, m2/s

D dg :

Droplet to gas density ratio

D ω :

Cross diffusion term

e * :

Sensible enthalpy, J/kg

E :

Total enthalpy, J

f :

Stoichiometric mass requirement of oxidant to consume 1 kg of fuel

F :

Force, N

g :

Gravitational acceleration, m2/s

g t :

Gas transition parameter, m

\(\tilde{G}_{k}\) :

Generation of k

G ω :

Generation of ω

g :

Gravitational acceleration, m2/s;

h :

Convective heat transfer coefficient, W/(m2 K)

h v,i :

Latent heat of vaporization, J/kg

H :

Dimensionless coefficient in eddy dissipation model

I :

Radiation intensity

J :

Diffusion flux

k :

Kinetic energy, m2/s2

k b :

Boltzmann constant, J/K

K :

Thermal conductivity, W/(m/K)

Kn :

Knudsen number

m :

Mass, kg

\(\dot{m}\) :

Mass flow rate/vaporization rate, kg/s

M w :

Molecular weight, g/mol

n :

Refractive index

N :

Number concentration of the particles per unit mass of gas, #particles/kggas

p :

Pressure, Pa

Pr :

Prandtl number

r c :

Collision radius of an aggregate, m

r p :

Radius of primary particle, m

R :

Universal gas constant, J/(mol K)

R i :

Reaction rate

Re :

Reynolds number

Re d :

Reynolds number based on droplet diameter

\(\vec{s}^{\prime}\) :

Scattering direction vector

S :

Source term

Sc :

Schmidt number

t :

Time, s

T :

Temperature, K

v :

Velocity, m/s

v a :

Volume of agglomerate particle, m3

We :

Weber number

x :

Mole fraction

Y :

Mass fraction

z :

Absorption coefficient, m−1

β:

Collision kernel between agglomerates, m3/s

γ:

Surface tension, N/m

ɛd :

Droplet emissivity

μ:

Dynamic viscosity, kg/(m s)

ρ:

density, kg/m3

σ:

Stefan-Boltzmann constant, W/(m2 K4)

σs :

Scattering coefficient, m−1

τ:

Deviatoric stress tensor

ω:

Specific dissipation rate, s−1

Γ:

Effective diffusivity

Φ:

Phase function

Ω′:

Solid angle

eff:

Effective value in reference to the addition of turbulent and non-turbulent contribution of a variable

d:

Droplet

g :

Gas

k:

Kinetic energy

mix:

Mixture

P:

Particle

R:

Radiation

sin:

Sintering

∞:

Continuous phase

ω:

Specific dissipation rate, s−1

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Acknowledgments

This work was supported by the European Community’s Seventh Framework Program under Grant No. CP-FP 228885-2.

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Authors and Affiliations

  1. School of Engineering, Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK

    Hosein Torabmostaedi

  2. Faculty of Science, Engineering and Computing, Kingston University, London, SW15 3DW, UK

    Hosein Torabmostaedi & Tao Zhang

Authors
  1. Hosein Torabmostaedi
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Corresponding author

Correspondence to Tao Zhang.

Appendix

Appendix

Model Validation

The accuracy of the 3D model developed in this work (quenching device incorporated in the mesh but no quenching gas applied) for prediction of the flame height and particle size was examined by comparing the simulated results with those calculated in our previous work (Ref 7) and measured by Mueller et al. (Ref 19). Figure 16 shows the flame heights of three simulated flames at feed rates of 6.8, 54.1, and 81.1 mL/min using 1 M ZnP concentration in ethanol. The dispersion gas flow rate and its pressure drop were kept constant at 50 L/min and 1 bar, respectively, for all precursor feed rates. Increasing the solution feed rate increased the supplied fuel energy to the flame which resulted in higher flame height. Comparing the flame heights, good agreement was found between the 3D model (this work), the 2D model,7 and the measured values obtained by Mueller et al. (Ref 19).

Fig. 16
figure 16

Comparison of 3D (this work) and 2D (Ref 7) simulation results with experimental data (Ref 19) for flame height as a function of precursor feed rate at 1 M ZnP concentration in ethanol

Full size image

Figure 17 shows the comparison between numerical (3D and 2D model) and measured (Ref 19) data for BET-equivalent average diameter of the zirconia primary particles as a function of production rate at 1 M precursor concentration. The results from the 3D model were in good agreement with the previously calculated (Ref 7) and the measured (Ref 19) results. Increasing the production rate from 50 to 300 g/h increased the primary zirconia particle diameter from 6.7 to 19.4 nm (solution feed rates were from 6.8 to 81.1 mL/min using 1 M ZnP in ethanol, which were dispersed by 50 L/min oxygen at 1 bar pressure drop), while the measured values were 6 to 19 nm, respectively. The validated 3D model was then used to optimize the quenching efficiency in FSP.

Fig. 17
figure 17

Comparisons of 3D (This work), 2D (Ref 7) and experimental data (Ref 19) for primary particle diameter as a function of production rate at 1 M ZnP concentration in ethanol

Full size image

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Torabmostaedi, H., Zhang, T. Numerical Optimization of Quenching Efficiency and Particle Size Control in Flame Synthesis of ZrO2 Nanoparticles. J Therm Spray Tech 23, 1478–1492 (2014). https://doi.org/10.1007/s11666-014-0148-4

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  • DOI: https://doi.org/10.1007/s11666-014-0148-4

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