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Numerical Study of the Plasma Flow Field and Particle In-flight Behavior with the Obstruction of a Curved Substrate

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Abstract

A three-dimensional numerical model is developed using computational fluid dynamics software FLUENT v6.3.26 to investigate the influence of curved substrate on the plasma flow fields and subsequent in-flight particle behavior. The curved substrates have two different dimensional shapes and are positioned in two orientations (convex or concave). It is found that inclusion of the substrates with different shapes in different directions significantly affects the plasma flow fields at the vicinity of the substrate, although the most upstream region of the plasma field remains unaffected. Plasma temperature and velocity contours and flow vectors in the computational domain, especially at regions near substrates are presented. Investigations on the size effect on the in-flight particle parameters are carried out, which show that smaller particles tend to acquire higher velocities and temperatures. Moreover, smaller particles are more susceptible to the flow change by the substrate inclusion. However, for the size range of the zirconia feedstock we used later, there is no obvious effect of the substrate inclusion on the particle distribution on the substrate surface.

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Abbreviations

a :

empirical constant (9.81)

A p :

surface area of the particle (m2)

C :

specific heat capacity (J/kg K)

C μ :

empirical constant (0.09)

C 1s :

empirical constant (1.44)

C 2s :

empirical constant (1.92)

C ∞ :

specific heat capacity of the plasma (J/kg K)

C p :

specific heat capacity of yttria-stabilized zirconia (J/kg K)

C D :

drag coefficient

D :

diffusion coefficient (m2/s)

D p :

particle diameter (m)

E :

arc voltage (V)

F D :

viscous drag force of the particle (N)

G K :

product of the eddy viscosity and viscous dissipation terms

H :

enthalpy (J/kg)

h :

heat transfer coefficient (W/m K)

h lt :

latent heat of vaporization (J/kg)

I :

arc current (A)

I t :

turbulent intensity (%)

m p :

mass of particle (kg)

k p :

thermal conductivity of yttria-stabilized zirconia (J/kg K)

k ∞ :

thermal conductivity of plasma (J/kg K)

K :

von Kármán constant (0.42)

L :

length of the curved substrate

p :

pressure (Pa)

\( P_{\text{in}}^{\text{W}} \) :

constant heat source (W/m3)

\( \dot{q} \) :

heat flux (W/m2)

Q c :

convective heat transfer (J)

R1:

inner radius of the curved substrate

R2:

outer radius of the curved substrate

Re d :

Reynolds number based on the particle diameter (m/s)

S φ :

source term

T b :

boiling point of yttria-stabilized zirconia (K)

T m :

melting point of yttria-stabilized zirconia (K)

T E :

plasma temperature at an element point adjacent to the wall (K)

T i :

initial particle temperature (K)

T p :

particle temperature (K)

T w :

plasma temperature on the substrate wall (K)

T ∞ :

local temperature of the plasma (K)

u, v, w :

velocity components in x, y, and z directions, respectively (m/s)

U :

velocity magnitude (m/s)

U E :

plasma velocity at an element point adjacent to the wall (m/s)

V :

volume (m3)

V :

plasma velocity vector (m/s)

\( {\bar{\mathbf{V}}} \) :

mean velocity vector (m/s)

V′ :

velocity vector fluctuation (m/s)

V n :

volume fraction for species n

V p :

particle velocity vector (m/s)

W :

width of the curved substrate

W p :

energy increase of the particle (J)

X p :

position of the particle motion

y :

distance from element to the wall (m)

Y n :

mass fraction for species n

y E :

distance from adjacent element point to the wall (m)

∞:

far field region

l:

laminar state

p:

particle

t:

turbulent state

mix:

mixture properties

α:

thermal diffusivity (m2/s)

ε:

turbulent kinetic energy dissipation rate (m2/s2)

η:

torch efficiency (%)

Γφ :

diffusion coefficient

κ:

turbulent kinetic energy (m2/s2)

κE :

turbulent kinetic energy at adjacent element point to the wall (m2/s2)

μ:

dynamic viscosity (kg/ms)

νp :

kinematic viscosity (m2/s)

φ:

process variable

ρ:

density of plasma (kg/m3)

ρp :

density of zirconia (kg/m3)

τW :

wall shear stress (Pa)

Pr :

Prandtl number

Re :

Reynolds number

U*:

dimensionless mean velocity

y*:

dimensionless distance from element to the wall

\( y_{\text{T}}^{*} \) :

dimensionless thermal sublayer thickness

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Division of Engineering Mechanics, Nanyang Technological University, 50, Nanyang Ave., Singapore, 639798, Singapore

    Te Ba & Heong Wah Ng

  2. Institute of High Performance Computing, 1, Fusionpolis Way, No. 16-16, Connexis, Singapore, 138632, Singapore

    Chang Wei Kang

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  1. Te Ba
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Correspondence to Heong Wah Ng.

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Ba, T., Kang, C.W. & Ng, H.W. Numerical Study of the Plasma Flow Field and Particle In-flight Behavior with the Obstruction of a Curved Substrate. J Therm Spray Tech 18, 858–874 (2009). https://doi.org/10.1007/s11666-009-9395-1

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  • DOI: https://doi.org/10.1007/s11666-009-9395-1

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