MODELING OF FLAME SPRAYING OF POLYMER WIRE
WITH NANO FILLERS
Yu. Korobov
Ural State Technical University – UPI, Russia
M. Belotzercovski, A. Chekylaev
Joint Institute of Mechanical Engineering, Belarus
Abstract. A model of polymer wire flame spraying at axial wire feed is represented.
Stages of polymer melt forming, its removal from melting zone and subsequent
atomizing were considered. Continuous level-by-level removal of polymer melt was
accepted as boundary condition. Gas jet heat and dynamic influence upon atomizing
material was described. Forcing parameter's range of destruction-free polymer
forming is determined. As shown, stable spraying process is possible only at fixed
ratio of flow conditions. An original thermal spraying gun was developed basing on
modeling results analysis. Experimentally defined parameters of wire melting zone
are differed from calculated ones at 7…9 %. Comparison of coatings from powder
and wire showed that its mechanical properties are improved in case of wire with
nano fillers.
MODEL OF PROCESS
Thermal spraying of polymer coatings from powders has found a use for
protection of a surface of parts against corrosion and mechanical exposure [1]. An
addition of nano fillers into powders hardens coating and improves its adhesion to
metals. However segregation of components results in non-uniformity of structure,
decrease of strength and of operating characteristics of coatings. Besides close
limitations of fraction and humidity of powders increase costs reduce fabricability of
powder spraying. The indicated lacks are eliminated in case of wire materials, as it is
possible to introduce nano fillers during manufacturing of the wire. It provides the
uniformity of component's allocation and reduces costs in matching with powder
production. However now there is no equipment for polymer wire spraying.
To descript the process of polymer wire atomizing which is fed along an axis
of a high temperature gas jet a following model was offered. At wire heating the
melted layer of mean thickness  is formed on its surface (fig. 1). The dynamic effect
of the gas jet appears in interphase shearing stresses (τмф), which are generated owing
to a demonstration of internal friction force between solid and liquid phases at their
relative movement. If to accept, what at atomizing the pseudo-steady flow regime of
incompressible fluid takes place; their value depends, according to an equation of
Newton, on dynamic viscosity of a melt
 м ф    dw dx
Where μ - dynamic viscosity of a melt, Pas, dw/dx - velocity gradient of liquid layers
on a normal to a streamline, s-1.
The separation of a melt will happen, when the aerodynamic effect of a gas jet
per unit of area of adjoining layers will exceed surface tension force.
2-65
Liquid phase
Solid phase
Fig. 1. Scheme of melt layer flow.
The process of atomizing starts at violation of stability of wave flow, which
one is determined by amplitude of waves on a surface of a melt. Thus subjected to
velocity and flow regime of gas the demarcation of phases can have different wave
surface.
Gas jet energy transmitted to a melt should be in rather narrow range owing to
specificity of physical characteristics of thermoplastic polymers. On the one hand, it
should be enough to remove a melted layer of a small thickness. A reason is the
following: in a process of layer thickness growth a heat flow into a melt of polymer
and speed of its melting decrease rapidly [2]. On the other hand, the heat input excess
leads to polymer destruction, so coating quality will drop sharply.
Temperature and density of heat flow q depend on a composition of a
combustion mixture. At gas-flame processing the change of a composition of
combustion-mixture effects strongly on value of density of heat flow q, than on
temperature of a flame [3]. Therefore high temperature flame is characterized by
density of heat flow.
At steady process of wire atomizing, i.e. when the profiles of temperatures and
speeds in a layer do not depend on time, in a molten zone L the wire gains the shape
of the elongated cone. On a small section dL (dL < < L) we shall accept a cylindrical
form of wire surface. Besides the following assumptions are made: 1) on a segment
(L) parameters of the gas stream are constant and separation of a not molten wire is
eliminated; 2) the gravitational forces are neglected; 3) melt is incompressible liquid;
4) wire is solid homogeneous medium.
The flow regime of a melt layer is determined by Reynolds number [4]:
(1)
Re c  2,43( G2  23 /  мф 24 )1 / 11
Where: G2 - surface tension of a melt, J/m2; ρ2 - density of a melt, kg/m3;  м ф shearing stress on an interphase boundary, Pa;  2 - dynamic viscosity of a melt, Pa·s.
Laminar flow regime of a layer with vaves on a surface exists up to Reс = 400,
then a mode of developed turbulent flow of a melt comes.
Liquid layer depth is defined as [4]:
2
(2)
  47G2  22  2 мф
S 22
where: S2 – wave length, m.
Correlation between thermal and dynamic parameters of gas jet in case of
good quality- efficiency ratio was determined according to rate equality of wire feed
and melt removal.
The melt removal rate under condition of constant gas jet parameters on the
segment L, is determined by expression [4]:


2-66
Vтеч   м ф   min  2  2 
(3)
where: min - the minimum layer depth, at which one melt removal is possible, m.
During time t the gas jet with density of a heat flow q passes a following heat
quantity to the wire through a surface dF=2πrdL:
Q  2 qrtdL
(4)
where: r - wire radius, m
The time t is determined by an expression:
(5)
t  L min  rVпод 
Thus:
Q  2 q r L  min dL  rVпод 
(6)
Dividing expression (6) on a specific melting heat of polymer C, we shall
receive mass of the melt generating during time t:
m  2 q r L  min dL  rVподC 
(7)
where: C - specific melting heat of polymer, J/kg.
V распл  m  2
(8)
where: Vраспл - volume of a melt, м3.
Having substituted in (8) equation (7), we receive:
V распл  2 min qLdL  C 2Vпод 
(9)
Besides, Vраспл equals:
Vраспл=Vпр-Vтв
where: Vпр=r2πdL and Vтв=(r-min)2πdL are volume of the wire and volume of a solid
(unmelted) phase of the wire on the segment dL, accordingly.
Thus, Vраспл equals:
Vраспл= πdL(2  min r-  min 2)
(10)
Having equated (9) and (10), we receive after conversion:
 min  2r  2qL C 2Vпод 
(11)
Having substituted (11) in (3), we receive a quadric equation with respect to Vпод:
 мф
 м фqL
2
Vпод 
rVпод 
0
2
 2 C 2
As < r, the solution is corresponded to a sign "-" and Vпод equals:
 мфr
 qL
  мфr 
  мф

 
2 2
 2 C 2
 2 2 
2
Vпод
(12)
From a condition
 r 2  2   qL CC   0
we receive a ratio of thermal and dynamic parameters of a gas stream in a molten
zone of a wire L:
r 2 C мф  2
4  2 Lq
or
(13)
 мф  2
q
42 L
r C 2
The distribution of temperatures in the layer is described by a heat conduction
equation:
T
 2T
 a 2 , x  0, t  0;
t
x
where: a - temperature diffusivity coefficient of polymer, m2/s

 

2-67
Initial temperature:
T ( x ,0 )  T0 ,
Boundary conditions:
 T ( 0 ,t ) / x  q( t ) ; T (  ,t )  T0 ; T (  ,t ) / x  0
where:  - heat conduction of polymer, W/m·К.
Relation T  T ( x ,t ) is determined by using integral method of heat balance [5]:
T ( x,t )  T0  q( t ) ( t )  x
2 ( t )
2
(14)
1/ 2
 1 t

  6 a q ( t ) q( t )dt 
(15)


0
After inserting (t) from (15) to (14) the layer surface temperature is
determined as following:
t


T ( 0 ,t )  T0  3 / 2 ( a /  )q( t ) q( t )dt 
(16)
0


According to smallness of the value of (t), we shall consider a special case
when density of a heat flow is constant:
q(t) = const
It follows from equation (15):
 ( t )  6 at
(17)
It follows from equation (16):
(18)
T ( 0 , )  T0  3 / 2q a / 
Thus:
2
(19)
q
 T ( 0 ,t )  T0 
3at
The shearing stress on the interphase boundary depends on a regime of gas
flow which is determined by Reynold's number[7]:
For laminar flow (Re  2∙103):
 м ф  4 w1  1 RT
(20)
3
5
For a turbulent flow (2∙10 <Re  10 ):
 мф  0 ,03  1 w11.75  RT 0.25
(21)
where parameters of the gas flow are represented: w1, - speed, m\s;  - kinematics'
viscosity, m2/s; 1 - dynamic viscosity, Pa·s; RT - radius of a spray gun nozzle, m
Thus, Vпод is defined by substitution of equations (20) and (21) into (12).
For laminar flow regime:
2
 2w  r 
2 w1  1 r
4w  q L
Vпод 
  1 1   1 1 1
 2 RT
 2  2 RT
  2 RT 
For turbulent flow regime:
Vпод
(22)
2
7
7
1
1


4
4
4
0.015 w r   
 0.0151w1 r   1    0.0151w1 r    4 q1 L (23)

   
  
 
2
2
2
 RT 
 RT  
 RT  2  2



7
4
1 1
1
4
EXPERIMENT RESULTS AND DISCUSSION
2-68
The calculations have shown that the ratio of thermal and dynamic parameters
of a gas stream on the condition (13) is fitted at usage of a high temperature gas jet,
accelerated up to supersonic level. Burning of propane-air mixture in the activated
combustion chamber of designed spray gun was used to realize this condition [8] (fig.
2). The modes of atomizing have ensured speed of a gas jet -1200 m/s (is determined
by calculation with taken gas parameters at combustion chamber: temperature
Тк=2000 К, pressure Рк=0,4 MPа); density of a heat flow -105 Вт/м2 (is determined by
calorimetric test).
a
b
Fig. 2. Wire spray gun. а) exterior; b) process of spraying.
A polymer wire of d = 3 mm from a polyamide ПА 6 was used in experiment.
The expression for required length of a molten zone of the wire L is obtained
experimentally [9]:
Zd   Tпл 
L
4 a  q 
2
(24)
where: d - diameter of sprayed wire, m; Z - parameter characterizing process of
thermoexchange between a stuff and heat source in unit of time (for polymers Z = 5, s1
). The following values were taken: С =270∙103 J/kg, μ =110 Pa·s, Tпл = 393 К, G
=0,015 J/m2, a =1,2·10-7 m2/s,   0,5 W/(m·K) [10]. Calculated length of a molten
zone of the wire is L = 12,5 mm.
The nature of waves of the melt is determined by the following. At stationary
flow of the polymer melt there is an elastic deformation, from which one the given
melt is became free at removal of shearing stress. As a result in the moment of liquid
layer separation the elastic forces save the shape of the melt on a caught-on surface.
The measurements of a wave length have shown that in an initial molten zone S is of
11…13 mm and it is decreased as separation area is brought nearer (fig. 3).
S1
S2
2-69
Fig. 3. Changes of a wavelength of the melt ПА-6 in a molten zone, the scale
is 1 mm.
On calculations according to equations (3) and (23) wire feed rate Vпод is 0,020
and 0,019 m\s, respectively. From experience the steady and qualitative melting is
provided at Vпод = 0,021 m\s. The further increase of Vпод results in separation of a
not molten wire from area L. A divergence of outcome is 9,5 %.
Using values of S and Vпод in equations (2) and (11), the layer depth of the melt
in a molten zone L was evaluated. Thus τмф was characterize from (21), as Reynold's
number for the gas is Re = 1,5∙105 (advanced turbulent flow regime):
According to equation (2)  min =240 mkm, According to equation (11)  min =
260 mkm. The calculation error of equation (11) is 7,7 %.
A graphic chart of wire feed rate change upon exposure of constructive
parameters was drawn according to equation (23) and subjected to experimental data
(fig. 4). As seen there is a strictly marked border which separates an area of
parameters ensuring qualitative atomizing.
Uneffective
sputtering
zone
Vпод,
m/s
Q, W/m2
x 10-4
Wг, m/s
Fig. 4. Relation of wire feed rate upon density of a heat flow (Q) and flow rate of
combustion products (Wг). Wire - polyamide ПА 6, d = 3 mm.
Comparative tests of coatings were conducted with usage of a powder polymers
flame spraying gun "TERCO-P" and designed wire flame spraying gun. Outcomes
have shown that adding nano fillers into polymer improves quality of coating, and
usage of a wire gives the best results, as compared with the powder (tab. 1).
Table 1. Change of polymer coating properties subject to type of feeding material and
nano filler addition.
Studied characteristic
Values for coatings from different materials
Powder ПА-6,
Wire ПА-6,
Powder ПА-6,
+50
200
mkm
d = 3mm
200+50 mkm
+
carbonic + carbonic filler,
filler, 5+5 mkm
5+5 mkm
Adhesion strength, MPа
7,2…7,7
8,3…8,6
2-70
9,5…10,1
Brinell hardness, MPа
70
80
80
Coefficient Р =10 MPа
of
dry
friction,
Р = 5 MPа
V = 0,65 m/s
0,20
0,15
0,13
0,25
0,08
0,07
CONCLUSIONS
1. The area of parameters ensuring qualitative atomizing and absence of
polymer destruction is stationed for polymer wire flame spraying.
2. The original polymer wire flame spraying gun is designed according to
modeling of process. The experimentally evaluated parameters of wire fusion zone
differ from computational ones on 7... 9 %.
3. The adding of nano fillers into polymers at flame spraying improves quality
of coating, and usage of the wire gives the best results, as compared with the powder.
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