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Thin Solid Films 506–5

Effect of surface roughness on splat shapes

in the plasma spray coating process

M. Raessi, J. Mostaghimi *, M. Bussmann

Centre for Advanced Coating Technologies, Department of Mechanical and Industrial Engineering, University of Toronto, Canada

Available online 19 September 2005

Abstract

We used a three-dimensional model of droplet impact and solidification to simulate the effect of surface roughness on the impact

dynamics and the splat shape of an alumina droplet impinging onto a substrate. The substrate surface was patterned by a regular array of

cubes spaced at an interval twice their size. Three different cube sizes were considered, and the results were compared to the case of droplet

impact onto a smooth substrate. To understand the effect of solidification on the droplet impact dynamics and splat morphology, the

simulations were run with and without considering solidification. Comparing the results, we have concluded that solidification plays a major

role in determining splat shape on a rough surface. We also present results of the distribution of voids between the splat and the substrate.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Surface roughness; Droplet impact; Numerical model; Solidification

1. Introduction

Thermal-sprayed coatings are applied to protect sub-

strates against wear, corrosion, and thermal shock. In

thermal spray processes, a hot gaseous jet is used to melt

and accelerate the powder of a metallic or ceramic coating

material. The hot jet draws energy from either a plasma or a

combustion source. During these processes, a spray of

molten (or partially molten) droplets, or particles is directed

at a substrate. As the droplets impact the substrate, they

spread and solidify, each forming a so-called splat. A

coating forms as a result of the accumulation of many such

splats.

Among many experimental and numerical studies that

have been done on droplet impact and solidification, only a

few have considered the effect of surface roughness. For

instance, Ahmed and Rangel [1] numerically studied the

impingement and solidification of an aluminum droplet on

uneven substrates, using a two-dimensional axi-symmetric

model. Their results show that droplet impact onto an

0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.tsf.2005.08.140

* Corresponding author.

E-mail address: mostag@mie.utoronto.ca (J. Mostaghimi).

uneven substrate is almost always accompanied by splash-

ing. However, the degree of splashing decreases with the

increase in surface roughness height. Fukanuma [2]

presented a formula which describes the flattening process

of a droplet onto a rough surface, and concluded that the

flattening ratio and the flattening time decreases with

increasing roughness. Liu et al. [3] numerically studied

the impact of a droplet onto substrates with wavy surfaces;

however, their two-dimensional axi-symmetric model did

not include solidification. They found that for wavelengths

of the surface larger than the droplet diameter, droplet

spreading ended with breakup.

This paper then, presents the results of three-dimensional

numerical simulations of droplet impact and solidification

onto substrates with rough surfaces. The effect of surface

roughness on splat morphology and the bonding between

the splat and the substrate are studied.

2. Numerical method

The three-dimensional numerical model of droplet

impact and solidification which is used in this study was

developed by Bussmann et al. [4] and Pasandideh-Fard et al.

07 (2006) 133 – 135

Fig. 1. Computer-generated images of 40 Am diameter alumina droplets at 2055 -C impacting with a velocity of 65 m/s onto alumina substrates initially at 25

-C, characterized by different values of surface roughness.

M. Raessi et al. / Thin Solid Films 506–507 (2006) 133–135134

[5]. Detailed discussion of the model is in [4,5] and is not

repeated here.

Equations of conservation of mass and momentum

governing the liquid phase in the presence of a solid phase

are

lYI HV

Y� �

¼ 0

fl HVY

� �

fltþ HV

YIlY

� �VY ¼ �H

qlYpþHyl2V

Y þ Hq

Fb

Y

where VYrepresents the velocity vector, p the pressure, q the

density, t the kinematic viscosity, and Fb

Yany body forces

acting on the fluid. In these equations, H denotes the

liquid–solid fraction, and it is equal to one within the liquid

phase and zero within the solid phase. The free surface of

Fig. 2. (a) Comparison of alumina splats on different surface conditions in the prese

roughness with and without solidification.

the liquid is defined by using the ‘‘Volume of Fluid’’ (VOF)

method, in which a scalar function f is defined equal to one

within the droplet material (liquid or solid) and equal to zero

without. Since f is passively advected with the flow, it

satisfies the advection equation which in the presence of the

solid phase is

flf

fltþ HV

YIlY

� �f ¼ 0:

The energy equation which is solved for heat transfer and

phase change is [5]

qflh

fltþ q V

YIlY

� �h ¼l

YI kl

YT

� �

where h represents the enthalpy, k the conductivity, and T

the temperature. To solve the energy equation, the enthalpy

nce of solidification. (b) Comparison of splat shape on a substrate with 3 Am

Fig. 3. Cross section of an alumina splat on a substrate with 3 Am roughness in the directions shown in Fig. 2(b). The cubes on the substrate and the splat are

shown in black and gray, respectively.

M. Raessi et al. / Thin Solid Films 506–507 (2006) 133–135 135

transforming model [6] is used to convert the energy

equation to one with a single dependent variable:

the enthalpy. The main advantage of this method is

that it represents the energy equation for both phases

simultaneously.

These governing equations are solved using a finite

volume technique on a three-dimensional Cartesian struc-

tured grid. According to the problem geometry, symmetry

boundaries are utilized to reduce the problem size and

therefore to save computational time. Along symmetry

boundaries, fluid flow obeys free slip and no-penetration

conditions, and an adiabatic thermal boundary condition is

applied. Numerical computations were performed on an

AMD Athlon 1.4 GHz PC; the average CPU time was 36 h.

3. Results and discussion

Fig. 1 shows simulated images of 40 Am diameter

alumina droplets, initially at 2055 -C, impinging with an

impact velocity of 65 m/s onto smooth and rough alumina

substrates. Each column shows a droplet during successive

stages of impact. For the rough substrates, the surface is

patterned by cubes which are regularly spaced at an interval

twice their size. Three different cube sizes of 1, 2, and 3 Amwere considered. In Fig. 1(a) to (d), the fluid flow, heat

transfer and phase change are modeled. The splat shape on

the smooth substrate (Fig. 1(a)) differs little from the shape

on the 1 Am rough substrate (Fig. 1(b)). But as the

roughness size increases further to 2 and 3 Am, the splat

shape changes substantially. In particular, on the 3 Am rough

substrate, the droplet is blocked at t =0.8 As from spreading

along the 45- diagonal and effectively the liquid flow is

channeled in two directions. To understand the effect of

solidification, Fig. 1(e) presents results of fluid flow without

solidification for the case of 3 Am roughness.

In Fig. 2(a), a quarter of the final shape of the alumina

splats is depicted for different substrate surface conditions.

As the size of the surface roughness increases from 0

(smooth) to 1 and 2 Am, the splat radius also increases.

However, on the 3 Am rough substrate, the extent of

spreading along the horizontal and vertical axes is approx-

imately equal to that on the smooth substrate. Fig. 2(a) also

clearly depicts the effect of roughness size on the splat

morphology.

The upper half of Fig. 2(b) shows an alumina splat on the

substrate of 3 Am roughness at t=5 As, for the case when

solidification is modeled. For comparison, the lower half of

Fig. 2(b) shows the droplet shape on the same substrate and

at the same time, but without solidification. Comparing the

two cases, the effect of solidification on the splat shape is

very well seen. It must be mentioned that without solid-

ification, the droplet recoils further until it reaches to its

equilibrium configuration which is not shown here.

Finally, Fig. 3 shows the cross sections of the alumina

splat on the 3 Am rough substrate, along directions A-A

(horizontal) and B-B (45- diagonal) shown in Fig 2(b). The

cubes on the substrate and the splat are shown in black and

gray, respectively. The splat appears to bond more com-

pletely with the substrate along the diagonals, as the voids

beneath the splat are smaller along section B-B than along

section A-A.

4. Conclusion

The effect of substrate roughness on an alumina splat

shape was studied. We concluded that droplet solidification

is the main mechanism responsible for changing the splat

shape. An increase in roughness size up to a certain value

increases the splat diameter. For the case of a splat on a

substrate of 3 Am roughness, voids between the splat and the

substrate are seen to be smaller along the 45- diagonal thanalong the horizontal direction.

References

[1] A.M. Ahmed, R.H. Rangel, Int. J. Heat Mass Transfer 45 (2002) 1077.

[2] H. Fukanuma, in: C.C. Berndt (Ed.), Thermal Spray: Practical Solutions

for Engineering Problems, Cincinnati, U.S.A., October 7–11, 1996, 9th

National Thermal Spray Conference Proceeding, ASM International,

1996, p. 647.

[3] H. Liu, E.J. Lavernia, R.H. Rangel, Acta Metall. Mater. 43 (1995) 2053.

[4] M. Bussmann, J. Mostaghimi, S. Chandra, Phys. Fluids 11 (1999) 1406.

[5] M. Pasandideh-Fard, S. Chandra, J. Mostaghimi, Int. J. Heat Mass

Transfer 45 (2002) 2229.

[6] Y. Cao, A. Faghri, W.S. Chang, Int. J. Heat Mass Transfer 32 (1989)

1289.