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Integral Process Modelling and Simulation for Solid-Particle-Forming Spray Processes

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Abstract

Solid particles are formulated in spray processes by atomization of a slurry or melt and successive solidification or drying of the droplets. The inter-correlations between the spray process conditions (atomizer types, raw material properties, operation conditions, etc.) and the powder product properties (particle size, morphology, structure, etc.) in spray processing of solid particles through integral process modelling and simulation are to be derived. A multiphase CFD-Continuum Model integrates different sub-process models dealing with various nozzle arrangements, liquid atomization, droplet spray, and particle consolidation phenomena. For quantitative descriptions of particle–droplet interactions in spray processes, particle–droplet collision model, and particle penetration model are developed based on numerical simulations. The integrative models are validated based on melt atomization process (two-phase) and spray process for composite-particle production (three-phase). The integral process model may be inverted to derive proper feed and process conditions for tailored particle production in a recursive design.

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Abbreviations

a :

Cube width [m]

a, b :

Constants [–]

A p :

Projection area [m2]

B :

Impact number [–]

Bo :

Bond number [–]

C :

Collection efficiency [–]

c :

Speed of sound [m/s]

C b, C d, C f, C k :

Coefficients in TAB model [–]

C D :

Liquid discharge coefficient [–]

C d :

Drag coefficient [–]

Co:

Courant number [–]

C p :

Specific heat capacity at constant pressure [J/kg K]

C v :

Specific heat capacity at constant volume

d or D :

Diameter [m]

d 50,3; d 32 :

Mass median diameter, MMD [m]; Sauter mean diameter SMD [m]

E k :

Kinetic energy [J]

f :

Volume fraction [–]

F b :

Buoyancy force [N]

F d :

Viscous drag force [N]

F g :

Gravitational force [N]

F s :

Surface tension force [N]

g :

Gravitational acceleration [m/s2]

h :

Film thickness [m]

k :

Turbulence kinetic energy [m2/s2]

K br, k 1, k 2 :

Coefficients in ETAB model [–]

K v :

Coefficient [–]

L :

Length [m]

m :

Mass [kg]

M :

Molecular weight [kg/mol]

\( \overset{.}{M} \) :

Mass flow rate [kg/s]

n :

Unit normal vector [–]

N p :

Particle number concentration [m−3]

Nu :

Nusselt number [–]

Oh :

Ohnesorge number [–]

p :

Pressure [Pa]; penetration depth [m]

Pr :

Prandtl number [–]

Q :

Particle–droplet collision number [–]

r :

Radius [m]

R :

Ideal gas constant [J/mol K]

Re :

Reynolds number [–]

St :

Stokes number [–]

t :

Time [s]

T :

Temperature [K]

U :

Velocity [m/s]

V :

Volume [m−3]

We :

Weber number [–]

x :

Droplet deformation [m]

X :

Area ratio of air core at nozzle exit to nozzle exit section

x, y, z :

Cartesian coordinates [m]

y :

Dimensionless droplet deformation [–]

α :

Spray angle [°]

δ :

Particle/droplet size ratio [–]

Δ :

Cell size [m]

ΔH f :

Latent heat [J/kg]

η :

Collision efficiency [–]

θ :

Solid–liquid contact angle [°]

κ :

Specific capacity ratio C p/C v [–]; interface curvature [m−1]

λ :

Thermal conductivity [W/m K]

μ :

Dynamic viscosity [Pa s]

μ, σ :

Coefficients in root and log normal distribution

ρ :

Mass density [kg/m3]

σ :

Surface tension [N/m]

τ E :

Eddy life time [s]

τ I :

Particle–eddy interaction time [s]

τ r :

Residence time in eddy [s]

φ :

Penetration angle [°]

ω :

Specific turbulence dissipation rate [s−1]; frequency [s−1]

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Acknowledgements

The authors express their gratitude to the DFG (Deutsche Forschungsgemeinschaft) for the financial support of this research within the SPP 1423 “Prozess–Spray.”

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Authors and Affiliations

  1. Foundation Institute of Materials Sciences (IWT), Bremen, Germany

    Xing-Gang Li, Sören Sander & Udo Fritsching

  2. Particles and Process Engineering, University Bremen, Bremen, Germany

    Xing-Gang Li, Sören Sander & Udo Fritsching

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  1. Xing-Gang Li
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  2. Sören Sander
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  3. Udo Fritsching
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Correspondence to Udo Fritsching .

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Editors and Affiliations

  1. Institute of Materials Science, University of Bremen, Bremen, Germany

    Udo Fritsching

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Li, XG., Sander, S., Fritsching, U. (2016). Integral Process Modelling and Simulation for Solid-Particle-Forming Spray Processes. In: Fritsching, U. (eds) Process-Spray. Springer, Cham. https://doi.org/10.1007/978-3-319-32370-1_18

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