MODELING OF FLAME SPRAYING OF POLYMER WIRE WITH NANO FILLERS
Yu. Korobov
Ural StateTechnicalUniversity – 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 powdershardens coating and improves its adhesion to metals. However segregation of components results in non-uniformityof structure, decrease of strength and of operating characteristics of coatings. Besides close limitations of fraction and humidity of powdersincrease costs reducefabricability of powder spraying. The indicated lacks are eliminated in case of wire materials, as it is possible to introducenano fillers during manufacturing of thewire. It provides the uniformityof component's allocationand reduces costs in matching with powder production. However now there is no equipment for polymer wirespraying.
To descript the process of polymer wire atomizing which isfed 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 thegas 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
Whereμ - dynamic viscosity of a melt, Pas, 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 areaof adjoining layers will exceed surface tension force.
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. Thussubjected tovelocity 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 growtha 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 combustionmixture. At gas-flame processing the change of a composition of combustion-mixture effects stronglyon 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 elongatedcone. On a small sectiondL (dLL) we shall accepta cylindrical formof wire surface. Besides the following assumptions are made: 1) on a segment (L) parameters of the gas stream are constantand separation of a not molten wire is eliminated; 2) the gravitational forces are neglected; 3) melt is incompressible liquid; 4) wireis solid homogeneous medium.
The flow regime of a melt layer is determined by Reynolds number[4]:
(1)
Where: G2 - surface tension of a melt, J/m2;ρ2 - density of a melt, kg/m3; - shearing stress on aninterphase boundary, Pa; - 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 meltcomes.
Liquid layer depth is defined as [4]:
(2)
where: S2– wavelength, m.
Correlationbetween thermal and dynamic parameters of gas jet in case of good quality- efficiency ratiowas determined according to rate equalityof wire feed and melt removal.
The melt removalrate under condition of constant gas jet parameters on the segment L, is determined by expression [4]:
(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 qpasses a following heat quantity to thewire through a surface dF=2πrdL:
(4)
where: r - wire radius, m
The time t is determined by an expression:
(5)
Thus:
(6)
Dividing expression (6) on a specific melting heat of polymer C, we shall receive mass of the melt generating during time t:
(7)
where:C - specific melting heat of polymer, J/kg.
(8)
where: Vраспл - volume of a melt, м3.
Having substituted in (8) equation (7), we receive:
(9)
Besides, Vраспл equals:
Vраспл=Vпр-Vтв
where: Vпр=r2πdLand Vтв=(r-min)2πdL are volume of thewire and volume of a solid (unmelted) phase of thewire on the segment dL,accordingly.
Thus, Vраспл equals:
Vраспл= πdL(2r-2)(10)
Having equated (9) and (10), we receive after conversion:
(11)
Having substituted (11) in (3), we receive a quadric equationwith respect toVпод:
As < r, the solution is corresponded to a sign "-" and Vпод equals:
(12)
From a condition
we receive a ratio of thermal and dynamic parameters of a gas stream in a molten zone of a wire L:
or (13)
The distribution of temperatures in the layer is described by a heat conduction equation:
,
where: - temperature diffusivity coefficientof polymer, m2/s
Initial temperature:
,
Boundary conditions:
; ;
where: - heat conduction of polymer, W/m·К.
Relation is determined by using integral method of heat balance [5]:
(14)
(15)
After inserting (t)from (15) to (14)thelayer surface temperature is determined as following:
(16)
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 followsfrom equation (15):
(17)
It followsfrom equation (16):
(18)
Thus:
(19)
The shearing stress on theinterphase boundary depends on a regime of gas flow which is determined byReynold's number[7]:
For laminar flow (Re2∙103):
(20)
For a turbulent flow (2∙103Re105):
(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, Vподis defined by substitution of equations (20) and (21) into (12).
For laminar flow regime:
(22)
For turbulent flow regime:
(23)
Experiment results and discussion
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. Burningof 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 -105Вт/м2 (is determined by calorimetric test).
ab
Fig. 2. Wire spray gun. а) exterior; b) process of spraying.
A polymer wireof d = 3 mm from a polyamide ПА 6 was usedin experiment. The expression for required length of a molten zone of the wireLis obtained experimentally[9]:
(24)
where: d - diameter of sprayedwire, m; Z - parametercharacterizing process of thermoexchange between a stuff and heat source in unit of time (for polymers Z=5, s-1).The following values were taken: С =270∙103J/kg,μ =110 Pa·s, Tпл = 393 К, G=0,015 J/m2, =1,2·10-7m2/s, 0,5 W/(m·K) [10]. Calculatedlength of a molten zone of the wireis 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 freeat removalof shearing stress. As a result in the moment of liquid layer separationthe elastic forces save the shape of the melt on a caught-onsurface. The measurements of a wavelength 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).
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 rateVподis 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), thelayer depth of the melt in a molten zone L was evaluated. Thusτмфwas characterize from (21), as Reynold's number for thegas is Re= 1,5∙105(advanced turbulent flow regime):
According to equation (2) =240mkm, According to equation (11) =260 mkm. The calculation error of equation (11) is 7,7 %.
Agraphic chartof wire feed ratechange upon exposure of constructiveparameters was drawn according to equation (23) and subjected toexperimental data(fig. 4).As seen there is a strictly marked border which separates an area of parameters ensuring qualitative atomizing.
Fig.4. Relation of wire feed rateupon density of a heat flow (Q) and flow rate of combustion products (Wг). Wire - polyamide ПА 6,d = 3 mm.
Comparative tests of coatingswere conducted with usage of a powder polymers flame spraying gun "TERCO-P" and designed wire flame spraying gun. Outcomes have shown that addingnano 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 feedingmaterial and nano filler addition.
Studied characteristic / Values for coatings from different materialsPowder ПА-6,
200+50 mkm / Powder ПА-6,
200+50 mkm
+ carbonic filler, 5+5 mkm / Wire ПА-6,
d = 3mm
+ carbonic filler, 5+5 mkm
Adhesion strength, MPа / 7,2…7,7 / 8,3…8,6 / 9,5…10,1
Brinell hardness, MPа / 70 / 80 / 80
Coefficient of dry friction,
V = 0,65 m/s / Р=10 MPа / 0,20 / 0,15 / 0,13
Р=5 MPа / 0,25 / 0,08 / 0,07
Conclusions
1. The area of parameters ensuring qualitative atomizingand absence of polymer destruction is stationedfor polymer wire flame spraying.
2. The original polymer wire flame spraying gunis 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 thewire gives the best results, as compared with the powder.
References
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