The effects of two gas flow streams with initial temperature and pressure differences in cold spraying nozzle

    The Effects of Two Gas Flow Streams with Initial Temperature and Pressure Differences in Cold Spraying Nozzle Wenyong Tang, Juanfang Liu, Qinghua Chen, Xueqing Zhang, Ziyun Chen PII: DOI: Reference:

S0257-8972(13)01171-7 doi: 10.1016/j.surfcoat.2013.12.019 SCT 19064

To appear in:

Surface & Coatings Technology

Received date: Accepted date:

15 May 2013 14 December 2013

Please cite this article as: Wenyong Tang, Juanfang Liu, Qinghua Chen, Xueqing Zhang, Ziyun Chen, The Effects of Two Gas Flow Streams with Initial Temperature and Pressure Differences in Cold Spraying Nozzle, Surface & Coatings Technology (2013), doi: 10.1016/j.surfcoat.2013.12.019

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ACCEPTED MANUSCRIPT The Effects of Two Gas Flow Streams with Initial Temperature and Pressure Differences in Cold Spraying Nozzle Wenyong Tang, Juanfang Liu, Qinghua Chen, Xueqing Zhang, Ziyun Chen

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College of Power Engineering, Chongqing University, 400030, Chongqing, China

Abstract：In order to inject powder into the nozzle in cold spraying, the pressure of the powder

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carrier gas at the nozzle inlet must be equal to or higher than the pressure of the propulsion gas,

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and the temperature of the powder carrier gas needs to be lower than the temperature of the propulsion gas to prevent from buildup or clogging by particles in the nozzle. The gas flow behavior resulting from the lower temperature and the higher pressure of powder carrier gas has

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an important effect on the particle acceleration in the nozzle. Several issues related to the gas flow will be examined through numerical simulation, including the initial pressure differential,

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the nozzle throat diameter, and the prechamber length between the injection tube outlet and the

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nozzle inlet. For different initial pressure differentials, nozzle throat diameters and prechamber

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lengths, the mixing conditions of the two gas flow streams in the nozzle are quite different and the negative effect of the inadequate mixing of the two gas flow streams in the nozzle on the

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particle acceleration is obvious. It is found that using lower differential pressure, larger nozzle throat diameter and longer prechamber for a certain diameter of powder injection tube can enhance the particle acceleration in the nozzle. Key words: Cold spraying; Powder carrier gas; Initial pressure differential; Prechamber

ACCEPTED MANUSCRIPT 1. Introduction Cold gas dynamic spraying (CGDS, often referred to as simply ‘cold spraying’) is a

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relatively new technique used to deposit materials onto the surface of a substrate [1]. In cold spraying process, high pressure gas is accelerated in a de Laval nozzle through an adiabatic

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expansion process of the gas. The pressure and temperature of the gas are dramatically

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decreased in the process. Based on the type of gas, pressure, and temperature the gas velocity can exceed 1000 m/s. The powder particles (usually 1 ~ 50µm in diameter) are introduced into the nozzle and are accelerated by the high speed gas of reduced temperature. As a consequence,

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the deleterious effects of high temperature oxidation, evaporation, melting, and other common problems for traditional thermal spray methods are minimized or eliminated [2]. In the

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process the particles are delivered from a powder feeder to a powder injection tube in the nozzle

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by a stream of powder carrier gas (as shown in figure 1). At the exit of the powder injection tube,

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the mixture of the particles and the powder carrier gas is injected into the main stream of propulsion gas. Then the particles are accelerated to reach the required velocities for successful

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bonding on the substrate located a certain distance away from the nozzle outlet [3, 4]. To achieve higher gas velocities in the nozzle, the pressurized propulsion gas is often preheated. And, in general, the powder carrier gas keeps unheated except for the application of cold spraying hard melting powder material, in which the two phase flow of carrier gas and solid particle is also heated to a higher temperature to improve the particle deposition [5]. In most of the applications of cold spray, the unheated lower powder carrier gas can prevent the carried powder particles from overheating. This can effectively reduce the possibility of the powder buildup or clogging in the powder injection tube and at the nozzle throat. In addition, the higher pressure of the powder carrier gas is to ensure a certain level of powder carrier gas

ACCEPTED MANUSCRIPT flow for the injection of powder particles with a consistent powder mass flow rate, since for a certain diameter of the powder injection tube the powder carrier gas flow is primarily controlled

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by the initial pressure differential ∆P (∆P = P1 –P2, see Figure 1) between the powder carrier gas and the propulsion gas at the location of the powder injection tube exit [6]. Therefore, the gas

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flow in cold spraying nozzle is usually characterized by the two flow streams of the propulsion

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gas and the powder carrier gas with initial temperature difference ∆T (∆T = T2 –T1) and pressure difference ∆P.

However, most of the previous simulation studies ignore the pressure and temperature

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differences of the hot propulsion gas and the cold powder carrier gas. They only take the inlet parameters (pressure and temperature) of the hot propulsion gas as the nozzle inlet parameters

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in the simulation analyses [7-14]. Generally, a number of operating parameters affect powder

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particle deposition in cold spraying process to varying degrees through their influence on the

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velocity of sprayed particles [15]. The temperature of the propulsion gas is known as one of the primary parameters that controls particle velocity, and the effects of the powder carrier gas have

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not been examined in detail. Only an earlier study suggests that the cold powder carrier gas flow, as a secondary parameter in cold spraying process, can affect the coating formations [16]. In this study, the effects of the two flow streams of the propulsion gas and the powder carrier gas with initial temperature and pressure differences on the gas flow in the nozzle and the impact velocities of the particles are investigated through computational simulations. Several issues related to the powder carrier gas will be examined, which includes the initial pressure differentials between the cold powder carrier gas and the hot propulsion gas, the diameter ratio of the nozzle throat to the powder injection tube and the prechamber length of the two gas flow streams.

ACCEPTED MANUSCRIPT 2. Numerical analysis models The major aim of this paper is to investigate the axisymmetric gas flow of cold spraying

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nozzle and particle acceleration when the effect of cold powder carrier gas is taken into account. Two sets of parameters are involved in the simulation: the geometries of the nozzle; the

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pressure and temperature of the propulsion gas and the powder carrier gas. The 2D

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axisymmetric view of the nozzle configuration, the boundary conditions, and the meshing of the simulation domain are presented in Figure 2. The simulation domain is meshed by using Gambit2.3.16 with structured grids over the entire domain. The grid independence test

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indicates that the grid system with 400,000 cells is sufficient for a satisfactory solution. The relevant parameters of the nozzle and the powder injection tube are shown in Table 1. In the

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simulation the assumptions and related parameters are as follows: the copper powder is chosen

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as the spraying powder material, N2 is used as the propulsion gas and the powder carrier gas.

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The material properties of particle and gas are listed in table 2. The inlet boundary conditions of the propulsion gas and the powder carrier gas are set as pressure-inlet boundary conditions. The

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inlet pressure and temperature of the propulsion gas are 2.0MPa and 773K, respectively; the pressure of the powder carrier gas changes from 2.0MPa to 2.4MPa and the temperature of the powder carrier gas is 300K. The outlet of the computational domain is treated as pressure outlet with an atmosphere pressure. The reference temperature is 300K. Particles are introduced axially into the gas flow along the centerline at an initial temperature of 300K and the same velocity as that of powder carrier gas. Fluent (version 6.3) is used to predict the steady gas flow and the particle velocity, the gas is treated as compressible ideal gas, and the RNG k–ε model, proposed by Yakhot and Orszag [17], is chosen to simulate the turbulent flow. The RNG k–ε model has a similar form to the

ACCEPTED MANUSCRIPT standard k–ε model, while the RNG model is derived using a rigorous statistical technique (called renormalization group theory), which has an additional term in its equation that

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significantly improves the accuracy for rapidly strained flows. This feature makes the RNG k–ε model more accurate and reliable for a wider class of flows than the standard k–ε model. In the

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near wall zone, the non-equilibrium wall function is used for the near-wall flow treatment; the

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parameter y+ falls into the 30-60 range in this method [18]. In the present study, y+ was adapted into the 30-60 range. The corresponding governing equations of steady state are given as follow:

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Continuity equation

Momentum equation

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∂ ( ρui ) =0 ∂xi

Energy equation

(2)

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∂u ∂u ∂u k ∂ ∂ 2 ∂p ( ρu i u j ) = [ µ eff ( i + j ) − µ eff ]− ∂x j ∂x j ∂x j ∂xi 3 ∂x k ∂xi

(1)

(3)

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∂u ∂u j ∂ ∂ ∂T ∂ 2 ∂u k ( ρui c pT ) = [α T (µ eff )] + [µ eff ( i + )− ] ∂xi ∂xi ∂xi ∂x j ∂x j ∂xi 3 ∂xk

In real case of most cold spraying applications, the loading of particles within the carrier gas is small; the volume fraction of the powder within the gas phase is less than 10%. So that the particle can be treated as discrete phase dispersed in the continuous phase; particle-particle interactions and the effect of particles on the gas phase can be ignored [2]. In order to better understand the effect of powder carrier gas on particle acceleration, the motion of a single particle travelling along the centerline was simulated, where the effect of the decrease of gas velocity near boundary layers can be ignored and the transverse component of the gas velocity is assumed to be equal to zero. The trajectory of a discrete phase particle is obtained by integrating the force balance on the particle, which is written in a Lagrangian reference frame.

ACCEPTED MANUSCRIPT This force balance equates the particle inertia with the forces acting on the particle, and can be written (for the x direction in Cartesian coordinates) as：

dt

= FD (u − u p ) + FX

(4)

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du p

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Where FX is an additional acceleration (force/unit particle mass) term which represents the

FD =

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thermophoretic force, FD (u-up) is the drag force per unit particle mass and 18µ CD Re ρ P DP 2 24

(5) Here, u and up

are the velocities of the gas and the particles, respectively, µ is the molecular viscosity of the gas,

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ρ is the gas density, ρp is the density of the particle, and Dp is the particle diameter，Re is the relative Reynolds number which is defined as:

ρDP u − u p

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Re =

µ

(6) CD is the

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drag force coefficient, which can be computed by using Morsi & Alexander correlation [9, 11,

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13, 19] or Henderson correlation [2, 20, 21] in the simulations of cold spraying process. Ning et

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al [11] performed the comparison of accelerating processes for a spherical copper particle of 10

µm with smooth surface using drag coefficient of Morsi-Alexander and Henderson, and the result shows that no obvious difference of particle acceleration was observed in both nitrogen and helium gas flow and the Morsi and Alexander correlation is prior for the prediction of particle in-flight velocity for the typical particle size (5-25µm) of cold spray. In the present study, the Morsi and Alexander drag coefficient correlation is chosen for the simulation:

C D = a1 +

a2 a + 32 Re Re

(7) Here, a1, a2

and a3 are the constants that are applied for the smooth spherical particles over several ranges of

Re given by Morsi and Alexander [22].

ACCEPTED MANUSCRIPT The particle temperature during the accelerating process can be calculated as follows [18]:

m pC pp

dTp dt

= hAp (Tg − Tp )

(8) where the

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convective heat transfer coefficient, h, is related to thermal conductivity，λg ，of the gas and the

λg Nu dp

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h=

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diameter of particle by Nusselt number (Nu):

can be described as

Prandtl number, Pr, is given by:

Pr = ( µCpg ) / λg

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Nu = 2.0 + 0.6 Re1 / 2 Pr 1 / 3

(9) Nuselt number

(10)

(11)

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3. Results and discussion

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Where Cpg is the heat capacity of gas.

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3.1 Effects of the nozzle initial pressure differential ∆P Figure 3 shows the gas temperature contours in the nozzle converging section for the

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conditions of different initial pressure differentials ∆P. In the figure, the diameter ratio of the nozzle throat to the powder injection tube, R, is 1.11; the initial pressure and initial temperature of the propulsion gas are 2.0MPa and 773K, respectively. When the initial pressure of the powder carrier gas is the same as that of propulsion gas (∆P=0), it is the lowest initial pressure differential to ensure a consistent powder mass flow rate; for the condition of ∆T=0, the temperature of the two phase flow of carrier gas and solid particle is heated to the initial temperature of the propulsion gas. This case (∆P=0 and ∆T=0) is the ideal spraying condition for cold spray, for which the powder carrier gas has no effect on the velocity of the gas flow in the nozzle and the impact velocity of the particles. Figure 3 (a) shows the temperature

ACCEPTED MANUSCRIPT distribution of the ideal spraying condition for comparison. In figure 3(b), 3(c) and 3(d), the initial temperature of the powder carrier gas is 300K (∆T=473K) and the initial pressure

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differentials ∆P are 0, 0.2MPa and 0.4MPa, respectively. It can be seen in figure 3 (b) that when the propulsion gas and the powder carrier gas have the same initial pressure (∆P=0), but

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different initial temperature (∆T=473K), the powder carrier gas stream is confined to the region

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around the nozzle centerline. Under this condition, the powder carrier gas has the lowest mass flow rate, and the percentage of the powder carrier gas mass flow rate in the total gas mass flow rate of the nozzle is only 2.1% (as shown in Table 3). The comparison between figure 3 (b) and

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figure 3 (a) indicates that when there is no initial pressure differential (∆P=0), the effect of the initial temperature difference (∆T=473K) between the two gas flow streams is not significant.

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In fact, ∆P must be larger than zero (∆P>0) and should not be too small to prevent the powder

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injection tube from buildup or clogging by particles since a slight pressure fluctuation of the

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propulsion gas or the powder carrier gas could result in ∆P<0 [6]. When increasing the initial pressure differential ∆P from 0 to 0.2MPa and 0.4MPa as listed

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in Table 3, the mass flow rate of the powder carrier gas (M1) significantly increases and the mass flow rate of the propulsion gas (M2), meanwhile, decreases to meet the thermodynamic limitation of the maximum mass flow rate at nozzle throat. In such a case, there exists not only the temperature difference but also the velocity difference between the powder carrier gas and the propulsion gas in the converging section of the nozzle. Consequently, the momentum exchange of the two gas flow streams enhances the mixing between them. It can be found from figure 3 (c) and 3 (d) that with increasing of the initial pressure differential ∆P; the cold powder carrier gas flow occupies more and more areas of the nozzle converging section near the nozzle throat. As a result, the increase of mass flow rate of the cold powder carrier gas will cause the

ACCEPTED MANUSCRIPT gas temperature to decrease at the nozzle throat. Comparing with the lines for the idea situation of ∆P =0 and ∆T=0 in figure 4 and figure 5, it can be seen that the effect degree of the

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temperature of the powder carrier gas on the velocity of the gas flow in the nozzle and the impact velocities of the particles on substrate are determined by the initial pressure differentials

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∆P. When ∆P=0, the lines for the situation of ∆T=473K are very close to the lines for the idea

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situation; this indicates that the effect of the temperature of the powder carrier gas on the velocity of the gas flow in the nozzle and the impact velocities of the particles are not significant. Whereas, when the initial pressure differential ∆P increases the velocity of the gas

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flow in the nozzle and the impact velocities of the particles are affected by the temperature of powder carrier gas to a large degree; it demonstrates that the velocity of gas flow in the nozzle

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and the impact velocities of the particles are greatly reduced by the cold powder carrier gas as

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the initial pressure differential ∆P increases.

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3.2 Effects of the diameter ratio of the nozzle throat to the powder injection tube In order to examine the effects of the diameter ratio of the nozzle throat to the powder

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injection tube, denoted by R, the simulation in this section keeps the following parameters invariant: (1) the temperature and pressure of the cold powder carrier gas and the hot propulsion gas; (2) the diameter of the powder injection tube; (3) the gas expansion area ratio of the nozzle outlet to the throat, and (4) the convergent and divergent length of the nozzle. In addition, the prechamber length of the two gas flow streams is zero, which means the exit of the powder injection tube locating at the inlet of the nozzle converging section. The variation of the diameter ratio (R) is through the diameter change of the nozzle throat. Since the maximum total gas mass flow rate in a converging/diverging nozzle is determined by the diameter and the sound speed at the nozzle throat, increasing the throat diameter will raise the maximum total

ACCEPTED MANUSCRIPT gas mass flow rate of the nozzle. As the diameter ratio (R) changes from 1.11 to 1.56, 2 and 2.44, the corresponding mass flow rate of the hot propulsion gas (M2) and the nozzle maximum total

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gas mass flow rate (M) are tabulated in Table 4 under the conditions of ∆P=0.2MPa and Di=1.8mm. As a result, the maximum total gas mass flow rate of the nozzle increases with the

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increasing diameter of the nozzle throat and, hence, the percentage of the mass flow rate of the

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cold powder carrier gas in the maximum total gas mass flow rate of the nozzle is reduced due to the unchanging mass flow rate (M1) of the cold powder carrier gas. Figures 6 and 7 depict the temperature and the velocity contours of different R in the whole

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computational domain, respectively. For the situations of the smaller diameter ratio, such as R=1.11 and 1.56, the mixing of the two gas flow streams in the converging section is stronger

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and thus the gas flow entering the nozzle throat can have more uniform temperature and

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velocity. The detail of the velocity vectors in in the converging section for R=1.11 and 1.56 are

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shown in Figure 8. For R=1.11, figure 8 (a) reveals that one vortex around the nozzle centerline in the converging section appears due to the intense momentum exchange. The backflow near

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the nozzle wall in the vortex strengthens the mixing of the two gas flow streams for more uniform temperature and velocity at the nozzle throat. When the diameter ratio is changed to 1.56, figure 8 (b) indicates there is no vortex in the converging section and the momentum exchange of the two gas flow streams weakens. For the situations of the larger diameter ratio, such as R=2 and 2.44, It is worth noting that the non-uniform gas flow due to inadequate mixing of the two gas flow streams will pass through the nozzle throat and remain a lower temperature and velocity region of the gas flow around the centerline in the nozzle as shown in figures 6 (c), (d) and 7 (c), (d). The lower temperature region of the gas flow can benefit for the temperature-sensitive powder materials since the injected powder particles from the injection

ACCEPTED MANUSCRIPT tube travel in the region around the centerline, the lower temperature of the gas flow in this region can keep the temperature-sensitive powder materials remaining a lower temperature for

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a better quality of powder coating. However, the lower gas velocity of the same region around the centerline will have an influence on the acceleration of powder particles traveling in the

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region because the lower the gas flow velocity around a particle, the lower the drag force acting

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on the particle for its acceleration. Figure 9 shows that the impact velocities and temperatures of 15µm copper particle on the centerline increase with diameter ratio R for the case of zero prechamber length, however, the change of the impact velocities and temperatures of the

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particle is not significant. Combining with the outcomes in figure 6, figure 7 and table 4, this result can be explained as following: when diameter ratio R is low, the mixing of the two gas

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flow streams in the converging section is stronger, however, the high percentage of the mass

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flow rate of the cold powder carrier gas in the maximum total gas mass flow rate of the nozzle

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will reduce the velocities of gas flow at the throat and in the following divergent section of the nozzle. As the diameter ratio R increases, on the one hand, the percentage of the mass flow rate

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of the cold powder carrier gas in the maximum total gas mass flow rate of the nozzle will decrease and the percentage of the mass flow rate of the hot propulsion gas in the maximum total gas mass flow rate of the nozzle will increase accordingly, but on the other the mixing of the two gas flow streams in the converging section becomes weak when there is no prechamber in front of the nozzle. Therefore, the injected cold carrier gas along the centerline will cause a lower temperature and velocity of the gas flow around the centerline in the divergent section of the nozzle. Thus, the increasing of the impact velocities of the particles on the centerline with the diameter ratio increasing is not significant. To examine the effect of the lower temperature and velocity of the gas flow around the centerline, the impact velocities and temperatures of

ACCEPTED MANUSCRIPT 15µm particles of which the entering positions at the exit of the powder injection tube is offset from the centerline are compared with that of 15µm particle on the centerline in figure 10.

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Apparently, the closer to the centerline the particle, the lower particle impact velocity and temperature .

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3.3 Effects of the prechamber length

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The original design consideration of the prechamber is to increase the residence time of the particles in the hot propulsion gas flow before entering the nozzle, thereby enabling them to achieve higher temperatures prior to their acceleration in the nozzle [23]. But the particle

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temperature must not exceed the temperature resulting in the clogging of particles in the nozzle. Prechamber length, Lp, is the distance between the exit of the powder injection tube and the

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inlet of the nozzle converging section. Except for raising the temperatures of sprayed particles,

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prechamber, certainly, will also alter the mixing state of the two gas flow streams before

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entering the nozzle throat and will influence the velocity of the gas flow and the velocities of the particles in the nozzle.

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To explain the effects of the prechamber length on the impact velocities of the particles, the cases shown in figure 6 (d) and figure 7 (d) with Lp=0 are also shown in figure 11 as the comparison reference, in which the lower temperature and lower velocity region in the diverging section near the nozzle throat is quite distinct. Under the same conditions, the temperature contours and the velocity contours corresponding to the three different Lp of 10mm, 30mm and 50mm are presented in the figures of 11 (b), 11 (c) and 11 (d) and the figures of 12 (b), 12 (c) and 12 (d), respectively. According to the figures, the longer prechamber (30mm and 50mm) can provide more time and space for the mixing of the two gas flow streams and thus the gas flow at the nozzle throat can have more uniform temperature and velocity distributions. The

ACCEPTED MANUSCRIPT quite uniform distributions of temperature and velocity at the nozzle throat can be seen in figure 13 (a) and figure 14 (a). The gas temperature and gas velocity distributions (shown in figure 13

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and figure 14) of the cross-sections at the nozzle throat and two other different locations (40mm and 120mm downstream from nozzle throat) in the nozzle diverging section also show that the

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longer the prechamber, the more uniform distributions of temperature and velocity in the area

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around the centerline at the nozzle throat and in the following diverging section. The effects of the prechamber length on the impact velocities of 5µm and 15µm particles are shown in figure 15 for the initial pressure differentials ∆P=0.2MPa. When the diameter ratio

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is low (R=1.11), the change of the impact velocities of the particles with the increase of the prechamber length are not obvious. As the value of the diameter ratio increases, the rise of the

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impact velocities of the particles with the increasing of the prechamber length becomes more

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and more significant. When examining the impact velocity change of the highest value of

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diameter ratio in figure 15(a) and (b), it can be seen that the phenomenon of the lower temperature and lower velocity region around centerline in the diverging section, which is

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shown in in figure 11 (a) and in figure 11 (b) for zero of prechamber length, is an important factor to influence the particle acceleration in the nozzle diverging section. The reason is the same as that of the description about the effect of diameter ratio on the impact velocities of the particles in the above section. The phenomenon will vanish when the prechamber length reaches to an appropriate value for the adequate mixing of the two gas flow streams. When considering the required heating temperature of the particles in the prechamber the appropriate length of prechamber should be determined by the particle heating up temperature as well as the adequate mixing state of the two gas flow streams. Figure 16 is the diagram of particle impact temperatures of 5µm and 15µm particles. The

ACCEPTED MANUSCRIPT increasing of the impact temperature for the 5µm particle with the increasing of the prechamber length is not as much as that of the impact temperature for 15µm particle under the same

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conditions. The reason is that the smaller particles have lower thermal capacity and the temperature increased in prechamber for the smaller particles will be easily cooled down by the

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rapidly expanded gas flow stream in de Laval nozzle. Thus, the particle pre-heating of

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prechamber is more effective to larger particles for the increasing of particle impact temperatures. 4. Conclusions

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In this study, the numerical simulation of cold spraying investigates the effect of the cold powder carrier gas on the velocity of the gas flow in the nozzle and the impact velocities of the

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particles under different conditions. The examined conditions related to the powder carrier gas

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include the initial pressure differentials between the cold powder carrier gas and the hot

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propulsion gas, the diameter ratio of the nozzle throat to the powder injection tube and the prechamber length of the two gas flow streams. The following conclusions can be obtained:

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(1) the effect degree of the cold powder carrier gas on the velocity of the gas flow in the nozzle and the impact velocities of the particles on substrate are determined by the initial pressure differentials ∆P. For ideal case of ∆P=0, the effect of the cold powder carrier gas on the velocity of the gas flow in the nozzle and the impact velocities of the particles are not significant. However, when the initial pressure differential ∆P increases, the velocity of the gas flow in the nozzle and the impact velocities of the particles are affected by the temperature of powder carrier gas to a large degree. The velocity of gas flow in the nozzle and the impact velocities of the particles are greatly reduced by the cold powder carrier gas as the initial pressure differential ∆P increases.

ACCEPTED MANUSCRIPT (2) Under the condition of zero prechamber length, the mixing of the two gas flow streams in the converging section becomes weak as the diameter ratio R increases. As a result, the

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injected cold carrier gas along the centerline will cause a lower temperature and lower velocity of the gas flow around the centerline in the divergent section of the nozzle. Thus,

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increasing the diameter ratio cannot significantly increase the velocity of the gas flow and

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the impact velocities of the particles on the centerline when there is no prechamber in front of the nozzle.

(3) Prechamber in front of nozzle not only raise the temperature of the particles before entering

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the nozzle but also alter the mixing state of the two gas flow streams. The effect degree of the prechamber length on the velocity of gas flow in the nozzle and impact velocities of the

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particles is dependent on the value of the diameter ratio R. For the higher value of diameter

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ratio, elongating the prechamber can reduce the lower temperature and lower velocity

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region around the centerline in the diverging section and can increase the velocity of gas flow in the nozzle and impact velocities of the particles. The particle pre-heating of

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prechamber is more effective to larger particles for the increasing of particle impact temperatures. The appropriate length of prechamber is determined by the required heating up temperature of particles as well as the adequate mixing state of the two gas flow streams. Acknowledgements The research was supported by National Natural Science Foundation of China (No. 51206196).

ACCEPTED MANUSCRIPT References

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[1] A. P. Alkimov, A. N. Papyrin, V. F. Kosarev, N. I. Nesterovich, M. M. Shushpanov, United States Patent No. 5302414, 1994.

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[12] V. K. Champagne, D. J. Helfritch, S. P. G. Dinavahi, P. F. Leyman, J. Therm. Spray Technol. 20 (2010) 425-431. [13] S. Yin, X. F. Wang, W. Y. Li. Surf. Coat. Technol. 205 (2011) 2970-2977. [14] J. J. Park, M. W. Lee, S. S. Yoon, H. Y. Kim, S. C. James, S. D. Heister, S. Chandra, W. H. Yoon, D. S. Park, J. Ryu. J. Therm. Spray Technol. 20 (3) (2011) 514-522. [15] Z. B. Zhao, B. A. Gillispie, J. R. Smith, Surf. Coat. Technol. 200 (2006) 4746-4754. [16] T. Han, Z. Zhao, B. A. Gillispie, J. R. Smith, J. Therm. Spray Technol. 14 (3) (2005) 373-383. [17] Y. V. Yakhot, S. A. Orszag, J. Sci.Comput. 1 (1986) 3-51. [18] FLUENT 6.3.26 User Guide Manual. [19] J. Pattison，S. Celotto, A. Khan, W. O'Neill. Surf. Coat. Technol. 202 (2008) 1443–1454. [20] H. Tabbara , S. Gu. AIChE J., 58 (11) (2012) 3533–3544.

ACCEPTED MANUSCRIPT [21] B. Jodoin, F. Raletz, M. Vardelle. Surf. Coat. Technol.200 (2006) 4424–4432. [22] S. A. Morsi, A. J. Alexander, J. Fluid Mech. 55 (1972) 193-208.

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[23] V. F. Kosarev, S. V. Klinkov, A. A. Sova, Recent Pat. on Eng. 1 (2007) 35-4.

ACCEPTED MANUSCRIPT Figure captions Fig.1 Schematic of cold spraying system.

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Fig.2 2D axisymmetric view of the nozzle configuration, the boundary conditions and the meshing.

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Fig.3 Temperature contours in the portions of the nozzle for the different ∆P, (a) without the

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powder carrier gas (b) ∆P=0 (c) ∆P=0.2MPa (d) ∆P=0.4MPa, the average temperatures of the gas at the nozzle throat are marked in the figure.

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Fig.4 Gas velocity along the nozzle central line for the different ∆P and ∆T. Fig.5 Effect of powder carrier gas on copper particle impact velocity.

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Fig.6 Temperature contours for different R (a) R=1.11 (b) R=1.56 (c) R= 2 (d) R =2.44. Fig.7 Velocity contours for different R (a) R=1.11 (b) R=1.56 (c) R = 2 (d) R =2.44.

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Fig.8 Velocity vectors in the converging section of the nozzle, (a) R=1.11 (b) R =1.56.

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Fig.9 Effect of the diameter ratio R on 15µm copper particle impact velocity and temperature.

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Fig.10 Effect of the particle inlet position on 15µm copper particle impact velocity and temperature, the horizontal ordinate indicate the cross section of the powder injector, R=2.44. Fig.11 Gas temperature contours under different distance between the injector and nozzle inlet at the R=2.44 (a) 0mm, (b)10mm, (c)30mm and (d) 50mm. Fig.12 Gas velocity contours under different distance between the injector and nozzle inlet at the R=2.44 (a) 0mm, (b)10mm, (c)30mm and (d) 50mm. Fig.13 Gas temperature on the different cross sections, (a) at nozzle throat; (b) at 40mm downstream from nozzle throat, and (c) at 120mm downstream from nozzle throat. Fig.14 Gas velocity on the different cross sections, (a) at nozzle throat; (b) at 40mm downstream from nozzle throat, and (c) at 120mm downstream from nozzle throat.

ACCEPTED MANUSCRIPT Fig.15 Effect of the prechamber length on particle impact velocity under different R (a) 5µm copper particle, (b) 15µm copper particle. ∆P=0.2MPa.

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5µm copper particle, (b) 15µm copper particle. ∆P=0.2MPa.

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Fig.16 Effect of the prechamber length on particle impact temperature under different R (a)

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Figure 16a

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Figure 16b

ACCEPTED MANUSCRIPT Highlights The powder carrier gas effects in cold spraying process were examined.




The gas flow fields are influenced by the initial gas pressure differential.




The higher initial gas pressure differential the lower particle velocity.




Larger nozzle throat diameter and longer prechamber can increase particle velocity.

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ACCEPTED MANUSCRIPT Table 1 Parameters of the nozzle and the powder injector Geometry characteristic

Value

Diameter of the powder injector Di (mm) Diameter of the nozzle throat Dt (mm) Diameter ratio of the nozzle throat to the powder injection tube R= Dt / Di

1.11, 1.56, 2, 2.44

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0,10,20,30,50 18

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20, 150

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9 30

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Length of prechamber Lp (mm) Diameter of nozzle inlet Din (mm) Lengthes of nozzle converging and diverging section Lc, Ld (mm) Nozzle expansion ratio α Standoff distance SOD (mm)

1.8 2, 2.8, 3.6, 4.4

ACCEPTED MANUSCRIPT Table 2 Material properties for particle and gas Properties

Cu 3

8978 381 387.6

Ideal gas law 1040 0.0242

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Density kg/m Specific heat (Cp) J/kg·K Thermal conductivity, W/m·K

Nitrogen

ACCEPTED MANUSCRIPT Table 3 Gas mass flow rate in the nozzle under different ∆P M2/g·s-1

M/g·s-1 12.12 11.87 11.75

M1·M -1/% 2.4 55.4 76.1

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11.83 5.29 2.80

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0 0.2 0.4

M1/g·s-1 0.29 6.58 8.95

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∆P/MPa

ACCEPTED MANUSCRIPT Table 4 Gas mass flow rate in the nozzle under different R M1/ g·s-1

M2/ g·s-1

M/ g·s-1

M1·M -1/%

1.11 1.56 2 2.44

6.58 6.58 6.58 6.58

5.29 13.37 25.65 40.89

11.87 19.95 32.23 47.47

55.4 33.0 20.4 13.9

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