CFD Simulations of Feeder Tube Pressure Oscillations and Prediction of Clogging in Cold Spray Nozzles

Abstract

Cold spray is an additive manufacturing method in which powder particles are accelerated through a supersonic nozzle and impinged into a nearby substrate. This method produces deposits with advantageous attributes, namely with low porosity and low residual stresses, which nearly match those of the bulk material. One challenge with cold spray is nozzle clogging, which occurs when particles bond to the inside of the nozzle, altering the cross-sectional area, increasing roughness on the nozzle inner surface, and causing a drop in the gas velocity, ultimately resulting in a lower quality deposit. Clogging puts certain combinations of materials and operational parameters out of practical reach. A CFD model of the cold spray nozzle is developed to study the flow of metal particles in the cold spray process, and we determine that the two-phase particle-laden flow from the feeder tube is inherently transient. CFD simulations demonstrate that pressure fluctuations in the particle feed system can cause the particles to disperse in the nozzle and ultimately lead to some particles bonding with the nozzle wall. The degree of clogging is found to be strongly dependent on the amplitude of these upstream pressure fluctuations and seemingly independent of the pressure oscillation frequency.

Introduction

Cold gas dynamic spraying (cold spray) is a metal deposition process with multiple industrial applications. It belongs to a wider family of thermal spray processes, which use high-temperature gases to apply metal coatings to parts. The main difference between cold spray and other thermal spray processes is that cold spray takes place at relatively low temperatures and at much higher particle velocities (Ref 1). Because the particles are cold-worked, their crystal structure is maintained and the bonding mostly occurs in the solid state, resulting in a deposit with low porosity and low residual stresses similar to the bulk material (Ref 2). Other thermal sprays largely rely on the rapid solidification of molten particles for bonding and therefore do not have the same advantages in terms of porosity and tensile properties. Cold spray can offer a more sustainable solution compared to other processes, as well (Ref 3). Because of these attributes, there is much interest in further developing the cold spray process for industry and manufacturing.

In this process, gas is accelerated through a converging–diverging de Laval nozzle which carries a metal powder. During the expansion of gas in the nozzle, particles are accelerated to supersonic speed and are impinged upon a nearby substrate. Particles will bond to the substrate if they reach a certain critical velocity, and the bonded particles accumulate to produce a deposit on the substrate. This process is illustrated in Fig. 1.

Fig. 1
figure1

Overview of the cold spray deposition process (Ref 4)

Cold spray is multipurpose in that it can enhance mechanical properties, allow the joining of two dissimilar metals, repair damaged parts, and additively manufacture parts. The cold spray process can be used in part fabrication, repair, and maintenance.

One major issue with cold spraying is nozzle clogging, which is especially problematic for low-melting point particles. With such low bonding energies, these particles tend to bond to the inner nozzle wall before they can exit. The particles will accumulate on the wall, effectively decreasing the inner diameter of the nozzle to the point that it clogs and cannot operate. Even as particles accumulate on the nozzle wall prior to the nozzle fully clogging, the gas flow velocity is compromised because the working diameter has decreased, resulting in lower particle exit velocities, thus jeopardizing their ability to bond to the substrate upon impact. The experiments in Ref 5 show that cold spray nozzles may clog in just 3 min. The present work is based on specific experiments (Ref 6) in which the nozzle clogged in precise regions, either just downstream of the throat (Fig. 2a) or about three eighths down the diverging section (Fig. 2b), depending on powder size distribution.

Fig. 2
figure2

Location of clog found in nozzles from experiments (Ref 6). (a) Clogging location with powder as received. (b) Clogging location with powder classified to remove fines

Clogging of cold spray nozzles is an expensive problem because nozzles are usually made from specialized materials such as tool steels, alloys, plastics, and cermets. The cost of nozzles makes their frequent replacement impractical. Clogging is also inconvenient because the operation window is drastically shortened, making it difficult to effectively spray a part and finish a task. Nozzles can be cleaned and restored to proper specifications, but this often requires difficult machining operations.

To better understand the clogging problem, a computational fluid dynamics (CFD) model has been created to simulate the gas dynamics and particle trajectories inside the nozzle. CFD simulations have been instrumental in improving the cold spray process in many regards and will continue to be essential for the development of cold spray as it overcomes nozzle clogging. Such simulations can help predict whether nozzles will clog, and the processes can be adjusted to ensure more effective operation.

Much of the past computational work in cold spray focused on comparing simulations to experiments to investigate particle velocity, substrate temperature, and impact characteristics. Champagne et al. (Ref 4) compared particle velocities from experiments to theoretical velocities from a one-dimensional mathematical model as well as a two-dimensional CFD model. They found that the one-dimensional model overpredicted the particle velocities while the two-dimensional model under-predicted the velocities. Sova et al. (Ref 7) completed a numerical study looking at the effects of powder injection location on the particle exit velocities. They found that particles injected upstream of the throat can reach critical velocities while particles injected downstream of the throat cannot. This is because the particles injected upstream of the throat have more distance to cover inside the nozzle before exiting and so are able to build momentum and accelerate to higher velocities. Sova et al. also showed that increasing the stagnation temperature along with preheating the particle feeder increased predicted particle velocities, shifting the particles closer to the deposition velocity window. Meyer and Lupoi (Ref 8) investigated the effect of nozzle size on deposition efficiency by performing experiments and CFD simulations of nozzles with various geometries. They found that out of the three nozzles studied, the nozzle with the smallest cross-sectional throat area had the smallest deposition efficiency. In a different study, Sova et al. (Ref 9) compared particle velocities between experiments and CFD simulations. In their work, they found that the particle velocities predicted by CFD simulations agreed well with measured particle velocities in experiments. With CFD simulations, Tang et al. (Ref 10) studied the interaction of the main gas stream with the powder carrier gas stream under several pressure and temperature inlet conditions. They studied the effects of throat-to-powder injection tube diameter ratio and the effects of prechamber length on particle and flow characteristics. Zhang et al. (Ref 11) completed a similar work to Tang et al., studying the effects of gas properties on deposition characteristics, as well as the particle impact velocities and temperatures.

Wang et al. (Ref 12) studied the clogging behavior of cold spray nozzles and the effectiveness of wall cooling to overcome this challenge. In their experiments, they showed that nozzles cooled externally by water deposited a higher coating mass than nozzles that were not cooled. This was because the cooled nozzles reduced clogging, thus allowing more particles to impinge the substrate. They used CFD to simulate the cooled nozzle with particle trajectories to show that wall cooling does not degrade the performance of the nozzle.

Yin et al. (Ref 13) studied the effects of injection pressure on particle acceleration, dispersion, and deposition in cold spray by conducting experiments and CFD simulations. They found that increasing the injection pressure can decrease the deposition efficiency as well as the coating strength. In addition, they used their CFD simulations to show that the turbulent kinetic energy (TKE) has a peak at the nozzle throat, as shown in Fig. 3(a). They determined the peak in TKE significantly contributes to particle dispersion in the diverging section. Lupoi and O’Neill (Ref 14) investigated particle trajectories in different cold spray nozzles with CFD simulations and experiments. They found that releasing particles in the diverging section produces a much narrower particle beam than releasing particles into the converging section. Their result was verified with CFD simulations by examining the particle tracks. Lupoi and O’Neill also showed that there is a peak in TKE at the throat of the nozzle, as shown in Fig. 3(b). They found that the particle beam width decreases by 42% when turbulence is not accounted for in the model, indicating that turbulence plays a major role in dispersion.

Fig. 3
figure3

Turbulent kinetic energy vs. axial position in works cited

Ozdemir and Widener (Ref 15) studied nozzle clogging in cold spray nozzles by performing experiments and CFD simulations. They varied the particle feeder tube diameter, its axial position, and its angle with respect to the centerline. They found that when the particle feeder tube is misaligned with the nozzle axis by as little as 1°, the particles will be redirected toward the nozzle wall in the diverging section. They also found that a particle feeder tube wider than the throat can lead to particles colliding with the nozzle wall in the diverging section. These collisions between the nozzle wall and the powder particles can lead to nozzle clogging.

In their experiments, Sova et al. (Ref 9) noted that even the lowest particle feed rates led to “pulsations of the particle jet and being provoked a rapid mechanical clogging of the nozzle by the particles.” To that point, the current work presents a CFD model, based on the experiments of (Ref 6) that isolates particle feeder tube pressure fluctuations as a root cause of particle dispersion and therefore nozzle clogging. These pressure fluctuations produce oscillations and turbulence such that particles collide and bond with the nozzle wall in the diverging section.

Methodology

ANSYS Fluent version 19.1 was used to conduct the CFD in this work. A 2D axisymmetric model was used to model the nozzle geometry in all simulations. After running a full 3D case using the LES turbulence model and comparing the results to those of the 2D model, we saw fit to use the axisymmetric model because there was, at most, a 3% difference in centerline velocity. Figure 4 shows the velocity profiles of the axisymmetric, 3D steady-state, and 3D LES simulations. There is negligible difference between the 2D and 3D simulations which used the k–epsilon turbulence model, while the LES turbulence model produced a slightly different velocity profile.

Fig. 4
figure4

Centerline velocity vs. nozzle length

This figure indicates that the difference in results is not due to the inclusion of the third dimension, but rather the different turbulence models, since the two simulations that used the kε realizable model produced roughly the same result, even though they were solved for different dimensionality. It was not worth the enormously increased computational cost to capture a 3% (at most) difference in velocity between the k-ε realizable and the LES models. It is for similar reasons that the 2D axisymmetric model was used in all the aforementioned studies except (Ref 15). In the axisymmetric coordinate system, the governing equations of the flow can be expressed as follows:

Conservation of mass:

$$\frac{\partial \rho }{\partial t} + \frac{\partial }{\partial x}\left( {\rho v_{x} } \right) + \frac{\partial }{\partial r}\left( {\rho v_{r} } \right) + \frac{{\rho v_{r} }}{r} = 0$$
(1)

Conservation of momentum—axial direction:

$$\frac{\partial }{\partial t}\left( {\rho v_{x} } \right) + \frac{1}{r}\frac{\partial }{\partial x}\left( {r\rho v_{x} v_{x} } \right) + \frac{1}{r}\frac{\partial }{\partial r}\left( {r\rho v_{r} v_{x} } \right) = - \frac{\partial P}{\partial x} + \frac{1}{r}\frac{\partial }{\partial x}\left[ {r\mu \left( {2\frac{{\partial v_{x} }}{\partial x} - \frac{2}{3}\left( {\nabla \cdot \vec{v}} \right)} \right)} \right] + \frac{1}{r}\frac{\partial }{\partial r}\left[ {r\mu \left( {\frac{{\partial v_{x} }}{\partial r} + \frac{{\partial v_{r} }}{\partial x}} \right)} \right] + F_{x}$$
(2)

Conservation of momentum—radial direction:

$$\frac{\partial }{\partial t}\left( {\rho v_{r} } \right) + \frac{1}{r}\frac{\partial }{\partial x}\left( {r\rho v_{x} v_{r} } \right) + \frac{1}{r}\frac{\partial }{\partial r}\left( {r\rho v_{r} v_{r} } \right) = - \frac{\partial P}{\partial r} + \frac{1}{r}\frac{\partial }{\partial x}\left[ {r\mu \left( {\frac{{\partial v_{r} }}{\partial x} + \frac{{\partial v_{x} }}{\partial r}} \right)} \right] + \frac{1}{r}\frac{\partial }{\partial r}\left[ {r\mu \left( {2\frac{{\partial v_{r} }}{\partial r} - \frac{2}{3}\left( {\nabla \cdot \vec{v}} \right)} \right)} \right] - 2\mu \frac{{v_{r} }}{{r^{2} }} + \frac{2}{3}\frac{\mu }{r}\left( {\nabla \cdot \vec{v}} \right) + \rho \frac{{v_{z}^{2} }}{r} + F_{r}$$
(3)

where:

$$\nabla \cdot \vec{v} = \frac{{\partial v_{x} }}{\partial x} + \frac{{\partial v_{r} }}{\partial r} + \frac{{v_{r} }}{r}$$

Conservation of energy:

$$\frac{\partial }{\partial t}\left( {\rho E} \right) + \nabla \cdot \left( {\vec{v}\left( {\rho E + P} \right)} \right) = \nabla \cdot \left( {k_{\text{eff}} \nabla T - \mathop \sum \limits_{j} h_{j} \overrightarrow {{J_{j} }} + \left( {\overline{{\bar{\tau }}}_{\text{eff}} \cdot \vec{v}} \right)} \right) + S_{h}$$
(4)

Equation of state:

$$P = \rho R T$$
(5)

The nozzle geometry was based on an experimental nozzle design produced by the United Technologies Research Center (UTRC) and used in experiments by Siopis et al. (Ref 6). The dimensional details and zone names are given in Fig. 5. The inlets and outlets to the nozzle are shown in blue, the dashed line represents the axis of the nozzle, and the rest of the geometry was set as an adiabatic wall with the no-slip condition. An axis boundary condition was set for the axis of the nozzle. Particles were set to reflect off the feeder tube inlet so that they would remain in the domain during moments of backflow in the feeder tube. For all simulations, the density-based implicit solver was used with the first-order upwind spatial discretization scheme because the flow is supersonic, and a sufficient level of convergence was desired.

Fig. 5
figure5

Diagram of the nozzle used in the study (not to scale). Blue represents inlets/outlets to the domain. Key dimensions and zone names given in tables (Color figure online)

A mesh dependence study was conducted by simulating a steady-state solution with meshes ranging from 2500 to 135,000 cells and comparing the differences in flow properties. It was found that the meshes which contained 54,000 cells or more did not produce substantially different results, so the mesh of 54,000 cells was used. A layer of thin elements was also used near the wall of the nozzle to accommodate the boundary layer. The wall Yplus values of the mesh ranged from 0.5 to 70.

As was the case in the experiments conducted by Siopis et al. (Ref 6), the fluid used in the simulations was helium, and its density varied with the ideal gas law. Only the flow domain was simulated in this work. The sprayed powder was simulated as a copper nickel alloy that consisted of particles with diameters distributed randomly with equal likelihood from 5 to 50 microns. The particle density was 8.94 g/cc, and the particle specific heat was 380 J/kg K. Although the experiments in Ref 6 did not have particle diameters equally distributed, this was done for the sake of making conclusions about the likelihood of collisions and bonding based on diameter. The particle diameter range was roughly 5 to 50 microns in the experiments (Ref 6). Several turbulence models were tried and considered by solving a steady-state solution with them, and after comparison, the realizable k-ε turbulence model with standard wall functions was deemed most appropriate because it provided the most physically likely results for axial TKE with a peak in the throat, similar to Ref 13, 14. Yin et al. (Ref 16) found in their review that RANS turbulence models were the most frequently used out of the studies they investigated, which puts this work in line with others like it. Specifically, most of the aforementioned works implemented the kε turbulence model.

The discrete phase model (DPM) with Lagrangian one-way coupling was used to inject and track particles inside the cold spray nozzle. Because the volume fraction of solid particles to driving gas is less than 10%, one-way coupling between the fluid and particles is a valid assumption (Ref 17). Particle–particle collisions are also negligible under such conditions (Ref 17) and therefore were not accounted for in these simulations. The DPM model solves a force balance equation iteratively to find each particle’s trajectory. This force balance equation is written as:

$$\frac{{{\text{d}}\overrightarrow {{u_{p} }} }}{{{\text{d}}t}} = \frac{{\vec{v} - \overrightarrow {{v_{p} }} }}{{\tau_{r} }} + \frac{{\vec{g}\left( {\rho_{p} - \rho } \right)}}{{\rho_{p} }} + \vec{F}$$
(6)

where the quantity τr is the drag force term written as:

$$\tau_{r} = \frac{{\rho_{p} d_{p}^{2} }}{18\mu }\frac{24}{{C_{\text{D}} \text{Re}_{p} }}$$
(7)

The coefficient of drag, CD, is responsible for the particles’ acceleration down the nozzle. This term was approximated with the “High-Mach-number” drag law, which is based on a correlation given by Clift et al. in Ref 18, and shown in Eq 8:

$$C_{\text{D}} = \frac{24}{{\text{Re}_{p} }}\left( {1 + 0.15\text{Re}_{p}^{0.687} } \right) + \frac{0.42}{{1 + 4.25*10^{4} \text{Re}_{p}^{ - 1.16} }}$$
(8)

The particles were tracked stochastically using the discrete random walk (DRW) model. This model is used to account for the random turbulent effects that act on the particles in the flow. When updating the particle positions, the DRW model will add random fluctuations to the particle velocities to represent turbulent effects. By computing the particle trajectories a sufficient number of times, the turbulent effects on particle dispersion will be included in the particle trajectories (Ref 19).

When a particle collides with a wall, the way to determine if the particle bonds to it is by computing the critical velocity for bonding and comparing it to the actual impact velocity. An approximation for critical velocity is given by Schmidt et al. (Ref 20):

$$v_{\text{crit}} = \sqrt {\frac{{F_{1} 4\sigma_{\text{TS}} \left( {1 - \frac{{T_{\text{i}} - T_{\text{R}} }}{{T_{\text{m}} - T_{\text{R}} }}} \right)}}{\rho } + F_{2} c_{p} \left( {T_{\text{m}} - T_{\text{i}} } \right)}$$
(9)

This approximation has been widely used by researchers in past works, including Siopis et al. (Ref 6). The critical velocity ratio is defined in Schmidt et al.’s work as the particle impact velocity divided by the particle critical velocity:

$${\text{CVR}} = \frac{{v_{\text{impact}} }}{{v_{\text{crit}} }}$$
(10)

A CVR ≥ 1 means that the particle impact velocity is greater than or equal to the critical velocity required for bonding and thus indicates that the particle bonds to the wall. In theory, the vimpact should be the component of velocity normal to the smooth wall. This is not realistic though, because on the length scale of one particle diameter (on the order of 10 microns), the nozzle wall has roughness. Thus, it was assumed that any collision with the wall was a head-on collision, and therefore, the total velocity magnitude was used for the vimpact, rather than the component which is normal to the wall. Additionally, it was found by Nardi et al. (Ref 21) that particles impacting at angles significantly shallower than 90° can produce higher bond strength deposits than those produced at 90°, so using the magnitude rather than the normal component can help model a bond occurring at a steep angle. No bonding was predicted in simulations where the normal component of vimpact was used, but upon using the magnitude of vimpact, a prediction of bonding was obtained. It should be noted here that the numerous phenomena responsible for particle–wall bonding inside the nozzle are not fully known, and thus, we are forced to make several simplifying assumptions in this study regarding the bonding requirements inside the nozzle. Future work should be dedicated to studying impact phenomena and tribochemistry between the particles and nozzle wall.

To gather information about the particle–wall collisions inside the nozzle, a user-defined function (UDF) was implemented as a custom boundary condition on all walls past the feeder tube exit, namely the prechamber wall, the “step” between the prechamber and converging wall, the converging wall, and the diverging wall. This UDF recorded the axial position, particle diameter, and bonding CVR of each particle–wall collision. The data from this UDF were used to determine which particles bonded or reflected, with what diameter, and at what location in the nozzle. Particles that collided with a CVR > 1 were terminated and no longer tracked.

To test the hypothesis that transient feeder tube fluctuations are a cause of particle dispersion, three types of simulations were run. First, a completely steady-state calculation was performed. Second, a transient calculation was performed, but with constant inflow boundary conditions. Finally, nine transient calculations were performed with a time-varying pressure at the feeder tube inlet with three different pressure wave amplitudes and three wave frequencies to isolate the respective effects that wave amplitude and frequency have on particle dispersion and bonding.

Boundary conditions at the inlets (feeder tube and annulus) were fixed at a pressure of 4 MPa for the steady-state simulation along with the transient case with constant inflow conditions. All simulations were solved with 400 °C inlets. To simulate the nine different pressure fluctuations in the feeder tube inlet, the inlet total pressure was changed to a custom UDF, which simulated a pressure that varied sinusoidally with time according to the following equation:

$$P = P_{\text{avg}} + P_{\text{amplitude}} \cdot \sin \left( {2\pi \omega t} \right)$$
(11)

In this equation, the average pressure Pavg was kept at 4 MPa, the amplitudes Pamplitude used were 50 kPa, 25 kPa, and 10 kPa, and the frequencies ω used were 25 Hz, 50 Hz, and 100 Hz. We do not have measurements of these oscillations, so the values of frequency and amplitude were selected to give a sufficient range that conclusions could be made about the respective effects of frequency and amplitude on particle dispersion. The boundary condition applied to the atmosphere was a pressure outlet and was set to standard atmospheric conditions—zero gauge pressure and 27C.

Results and Discussion

Steady-State Model

Contours of the helium gas flow were obtained from the steady-state model to understand the flow characteristics inside the nozzle, and they are presented in Fig. 6. As expected, the velocity near the inlet is low, while the temperature and pressure are high. The velocity increases toward the throat and continues to increase supersonically until the outlet, after which point the flow decelerates to zero at the substrate. Small Mach diamonds are observed just outside of the nozzle exit, and a bow shock is observed just prior to the substrate because the supersonic compressible flow is decelerating to subsonic velocities. Once the flow contacts the substrate, the flow disperses radially into the atmosphere at low velocity. In the diverging section within the boundary layer, a lower velocity is observed which is due to the no-slip condition on the nozzle wall.

Fig. 6
figure6

Steady-state contours

Not surprisingly, the pressure starts high and smoothly decreases as the flow moves from the inlet to the outlet, while the temperature decreases in proportion to the increase in velocity. The temperature in the boundary layer is relatively high compared to that of the bulk fluid because of viscous heating in that region.

In each simulation, 500,000 particles were injected into the domain at room temperature. All injections consisted of the particles being generated inside the feeder tube and occupying the entire feeder tube volume. To generate particles as if they were realistically occupying the 3D feeder tube space uniformly, particles were generated with more likelihood by a factor of the square root of radial position.

The particle pathlines for the steady-state solution are provided in Fig. 7, where particles are observed to start at a low velocity and build momentum throughout the length of the nozzle. The particle beam width increases in the prechamber until some particles collide with the converging wall and begin their supersonic journey down the diverging section. The beam width narrows at the throat because all the particles must squeeze through that small hole, but it then widens again in the diverging section until the particles reach the substrate. The particle–wall collisions from this steady-state solution are presented in Fig. 8, where it is observed that all collisions in the nozzle occur prior to the throat and at CVRs below 1. The particles have been grouped by size in this figure to show the consistent behavior that smaller particles attain higher velocities. This phenomenon occurs because, as the particles build momentum down the nozzle, their velocities increase according to their mass. Experiments show that particles bond in the diverging section (Ref 6, 22), which necessarily means they disperse in that section. Because all the CVRs are below 1 in the steady-state solution, it is determined that the steady-state solution does not properly account for the physics responsible for particle dispersion in the diverging section, since it predicts no clogging.

Fig. 7
figure7

Particle pathlines—low to high velocity (blue to red). Range from 0 to 1700 m/s (Color figure online)

Fig. 8
figure8

Steady-state particle–wall collisions

Figure 9(a) shows the axial TKE in the nozzle modeled in this study, where a peak at the throat similar to the results shown in Fig. 3(a) and (b) is observed. Figure 9(b) shows how the TKE varies radially in the nozzle and confirms a maximum value at the throat. It is worth noting from Fig. 9(b) that there is much more turbulence near the wall than on the axis, and several orders of magnitude are more in the throat at the wall than in the throat on the axis. This means that, when particles collide with the wall in the converging section near the throat, in situations like what Fig. 8 describes, those particles experience extreme turbulence that can send them toward the wall in the diverging section, where clogging occurs (Ref 6, 22). It also means that as particles begin to disperse radially, they enter areas with more and more turbulence, continually giving them a greater chance to be pushed toward the wall.

Fig. 9
figure9

Turbulent kinetic energy in present nozzle—axial and radial

The high values of turbulence in the steady-state solution both at the throat and near the walls, however, are evidently not the sole cause of particle dispersion because, as demonstrated in Fig. 8, there are zero particle–wall collisions downstream of the throat in this model. Although it has been established that the increased turbulence at the throat contributes to dispersion (Ref 13, 14), there is still more physics to be accounted for if the full effect of dispersion is to be observed.

In their study (Ref 15), Ozdemir and Widener also used a steady-state solution for the gas flow through a cold spray nozzle to simulate particle trajectories. They concluded that particle dispersion and particle–wall collisions in the diverging section can be caused by the feeder tube diameter being larger than the throat diameter. They simulated a nozzle with a feeder tube diameter-to-throat diameter ratio of 2.4:1, which showed the highest level of particle–wall impacts in the diverging section. The nozzle used in this study has a feeder tube diameter-to-throat diameter ratio of 1.4:1. Since the steady-state simulation conducted in the present study did not produce any collisions in the diverging section of the nozzle, it is concluded that the feeder tube diameter-to-throat diameter ratio is not high enough for Ozdemir and Widener’s conclusions to apply.

Transient Model with Constant Pressure in Feeder Tube

In this second simulation, the first-order implicit transient formulation was used with constant pressure inlets set to 4 MPa. This simulation was conducted to determine whether the physics responsible for particle dispersion are present in a transient scenario while maintaining constant inflow conditions.

Once the solution progressed sufficiently that the initial transient noise subsided and the inlet pressure settled to 4 MPa, the 500,000 particles were injected incrementally in groups of 50,000 to simulate a constant stream of particles entering the nozzle feeder. Figure 10 shows the resulting particle–wall collisions, and the results are similar to those of the steady-state simulation—collisions exclusively occur prior to the nozzle throat and at CVRs less than one. It is thus concluded that a transient simulation with a constant inlet pressure cannot predict the realistic particle dispersion that leads to clogging in the diverging section, and that transient simulations with fluctuating inlet pressures should be investigated.

Fig. 10
figure10

Transient particle–wall collisions at constant inflow

It should be noted that the 3D LES case that was conducted to establish dimensional independence of the solution was solved with these same inlet boundary conditions, and that it produced no collisions in either the converging or diverging sections, nor did it produce any particles that adhered to the nozzle wall.

Transient Model with Pressure Fluctuations in Feeder Tube

Pressure fluctuations were simulated by applying the pressure UDF to the feeder tube inlet boundary. In the nine transient simulations with pressure oscillations, the same 500,000 particles from the prior transient simulation (with constant inflow conditions) were injected into the domain incrementally in groups of 50,000. These ten injections were evenly spread out in time across the pressure wave, as shown in Fig. 11. In each simulation, two injections occurred at the lowest point on the pressure wave while two injections occurred at the highest point. This was done so that the results could be representative of particles traveling on all parts of the pressure wave. The injection points were adjusted depending on the frequency of the oscillations so that all injections were conducted in like fashion according to the frequency of the pressure oscillation in the feeder tube.

Fig. 11
figure11

Feeder tube inlet total pressure vs. flow time with injection locations

Although the total pressure in the nozzle was governed by the UDF which generated a sine curve (see Eq 11), it is observed that the sections of the curve below Pavg have kinks once per period, which is contrary to a perfect sine curve. This inconsistency is due to backflow in the feeder tube during the time that feeder tube pressure drops below that of the annulus. The annulus inlet is held at a constant 4 MPa during these simulations, so when the feeder tube pressure drops below that of the annulus, the flow is directed into the feeder tube from the annulus. This backflow imposes on the sinusoidal boundary and manifests in a suppressed sine curve during the times that pressure drops below 4 MPa. Even though there is a kink in the curve, the pressure still oscillates clearly and sufficiently to determine the effect that the oscillations have on particle dispersion.

Particles were injected only once the transient noise subsided and the pressure stabilized to its operational condition. For example, small oscillations can be seen on the lower part of the curve at 0.015 s, which is why injections did not begin until 0.035 s when the pressure became settled.

The resulting particle–wall collisions from the nine transient simulations with oscillating pressures are summarized in Fig. 12 and 13. In all these solutions, bonding is successfully predicted in the diverging section, which means the physics responsible for dispersion in the diverging section are accounted for with the incorporation of an oscillating pressure. Like the prior two cases, the smaller particles collide with faster velocities than the larger ones, but these transient models predict more collisions in the converging section than the prior two.

Fig. 12
figure12

CVR vs. axial position of particle–wall collisions for nine oscillating pressures

Fig. 13
figure13

Bonded particles from nine oscillatory simulations

An obvious trend observed from Fig. 12 and 13 is that as pressure wave amplitude increases, bonding increases. Evidently, more particles are dispersed in the diverging section when the pressure wave amplitude is larger. A related trend was found by Fukumoto et al. (Ref 23), who determined that larger inlet pressures resulted in higher deposition efficiencies—in this case of the present study, the deposition efficiency refers to that of the particles on the nozzle wall. Figure 13 indicates that, at high enough amplitudes and with particle diameters greater than 20 microns, there may be a correlation between lower frequencies and higher amounts of bonding, but a larger sample of particles should be modeled to determine if this trend is a case of sample variability or a consistent phenomenon.

Although particles of all sizes are shown to bond in this study, Fig. 12 demonstrates that the largest particles, with diameters ranging from 35 to 50 microns, all have CVRs close to one. This indicates that those particles are on the cusp of bonding, and that copper nickel alloy particles with diameters slightly larger than 50 microns would not bond at all in a repeat experiment. Such sizes are not typical in cold spray, but it is worth noting that by using larger particles, clogging could be prevented.

It should be noted that 50 kPa is only about 1% of the operating inlet pressure (4 MPa), and a fluctuation of that magnitude still caused a significant amount of clogging. These results show that very small oscillations in the feeder tube cause a severe amount of clogging.

These nine oscillatory simulations may have isolated a root cause of clogging, but there is a discrepancy between the clogging predicted by these simulations and that was observed in experiments. In the results from Ref 6, clogging was found in a narrow region of the diverging section (see Fig. 2). The simulations, however, predict collisions that lead to clogging along nearly the whole length of the diverging section (see Fig. 12).

An inconsistency between the experiments in Ref 6 and the models in this work are the inlet boundary conditions. In cold spray experiments, the feeder tube is set to a certain volumetric flow rate, while the annulus is set to a certain temperature and pressure. The temperature difference between the feeder tube and the annulus is known to cause mixing and turbulence, which causes dispersion among the particles. The reason the inlet temperatures were both set to 400 °C in this work is because it was already known that the mixing of the hot and cold gases causes dispersion. If the inlets were simulated at their realistic temperature conditions, the particle dispersion data would be the result of both mixing and feeder tube oscillations. The primary goal of this work is to determine the effect that feeder tube oscillations alone have on particle dispersion, and thus, it was desirable to set both inlets to the same temperature to isolate oscillation effects.

The feeder tube oscillations that manifest in experiments, therefore, are actually flow rate oscillations, not pressure oscillations. Although we hypothesize that the total pressure does oscillate with the flow rate, it is the oscillating flow rate which causes the pressure to oscillate, not the other way around. As was previously mentioned, the oscillatory pressure in this work results in backflow, which is not realistic in cold spray. A future study is in progress which will incorporate a mass flow condition at the feeder tube inlet with realistic temperature differences between the inlets to obtain an overall more realistic prediction of clogging for the experiments in Ref 6. The oscillatory flow rate would not result in backflow because, even when the flow rate is at a minimum, the flow would still be moving forward, just slower. Again, the pressure oscillations in this work were implemented to observe the effect of oscillations alone on particle dispersion, which would not be possible if a cold mass flow condition were used, because then the mixing of hot and cold gases would contribute to dispersion as well.

It seems unlikely, however, that by incorporating more factors that are known to cause clogging, namely the temperature difference between the feeder tube and the annulus, and that the models will result in a smaller prediction of the expanse of clogging. Rather, it seems likely that adding factors responsible for clogging will increase the modeled prediction of clogging. Regardless, the inconsistency in the inlet conditions between the experiments and the present models ought to be pointed out.

Another factor that may be responsible for this overprediction in the clogging expanse is the lack of local temperature effects included in calculating the critical velocity. In past works, it has been shown that increasing substrate temperature increases deposition efficiency. For example, Fukumoto et al. (Ref 23) show that deposition efficiency increases with substrate temperature as well as inlet pressure. The higher wall temperature increases the energy available for bonding and thus reduces the required particle kinetic energy for bonding. Conversely, lower surface temperatures are detrimental to bonding, which means that in areas where the nozzle is cooler, particles are less likely to bond. This is the motivation behind nozzle cooling, which has proven to successfully prevent clogging (Ref 5).

Since the tungsten-carbide nozzle inner wall gets slightly cooler down the length of the nozzle (Ref 12), it may be that the particles cannot bond as effectively farther downstream in the diverging section. If a parameter like the CVR in Schmidt et al.’s work were developed to account for substrate temperature, the simulations may yield the results that better align with those of experiments. It is unknown to what extent the results would change if the wall temperature were accounted for, but that is one possible reason for the overprediction. In general, the phenomena responsible for particle–wall bonding inside the nozzle are not well known, and future studies should be dedicated toward investigating particle and nozzle behavior during impact and bonding, along with studying the tribochemistry related to particle–wall bonding in cold spray.

Figure 2 shows that the clogging location is greatly influenced by particle size in experiments (Ref 6). It is clear from Fig. 12 that smaller particles reach critical velocity before larger ones, which means smaller particles bond before larger ones. When the small particles begin accumulating early in the nozzle, particles of all sizes begin accumulating onto those. The simulations in this work do not account for particle accumulation effects in the nozzle, but this may have a significant impact in experiments, which may be another reason for the overprediction in the modeled clogging expanse. This hypothesis is reinforced by comparing the difference between Fig. 2(a) and (b). When the fine particles are injected along with large ones, the fines drive the location of clogging closer to the throat, but when the fines are removed and only larger particles are injected, the clogging location is driven farther down the nozzle. Figure 12 also indicates that larger particles cause clogging farther down the nozzle, while smaller ones begin to clog closer to the throat. To reconcile Fig. 2 and 12, the location of clogging seems to depend on where the smallest particles begin to bond. Small particles do not necessarily bond more than others (see Fig. 13), but because they bond first, they drive the clogging upstream.

It is worth mentioning that although this was not the case for the experiments in Ref 6, some materials foul throughout the entire diverging section, not only in a small expanse (Ref 22). If a cold spray system with nozzle and feedstock materials that are known to clog throughout the entire diverging section were modeled as they are in this work, the current model may predict both the clogging expanse and mass of particles responsible for clogging more accurately.

Discrepancies aside, the transient simulations with pressure oscillations successfully predict particle–wall collisions and bonding in the diverging section of the nozzle, whereas the simulations with constant inflow conditions did not. With this finding, a root cause of particle dispersion and therefore clogging has been identified, which satisfies the primary goal of this work.

Conclusions

CFD simulations were performed to identify the cause of particle dispersion and therefore nozzle clogging in cold spray. The models were based on specific experiments (Ref 6). A steady-state model was initially investigated, which failed to predict the particle–wall collisions that those experiments reported downstream of the throat. This motivated a transient investigation of particle behavior with inlet conditions held at constant pressure, which also failed to predict collisions in the diverging section. Finally, nine transient simulations were conducted with pressure oscillations in the feeder tube at three wave amplitudes and three wave frequencies, all of which successfully predicted bonding in the diverging section. It is therefore concluded that pressure oscillations in the feeder tube are a root cause, but certainly not the only cause, of particle dispersion and bonding in cold spray.

The pressure waves disperse the particles in proportion to the wave amplitude: Larger wave amplitudes result in larger amounts of bonding in the diverging section. There does not seem to be any correlation between the pressure oscillation frequency and the degree of clogging.

The pressure oscillations only went up to as high as 1% of the average pressure, and the models still predicted substantial amounts of clogging. To extend these conclusions, oscillations in the feeder tube can be due to vibrations, fluid–structure interactions, turbulence, or other factors still not identified—oscillations are not just limited to pulsations in the feeder gas flow. In whatever form, oscillations in the feeder tube region, even if they are very small, are detrimental in that they promote the onset of clogging aggressively. Work could be done to limit such oscillations in the feeder tube region to alleviate the issue of clogging in cold spray.

Abbreviations

C D :

Coefficient of drag

c p :

Specific heat

d :

Diameter

E :

Energy

F :

Force

F1, F2 :

Empirical factors

g :

Gravity

J j :

Diffusion flux of species

k :

Thermal conductivity

P :

Pressure

Re:

Reynold’s number

R :

Individual gas constant

r :

Radial dimension

t :

Time

T i :

Particle impact temperature

T m :

Melting temperature

T R :

Reference temperature (293 K)

T :

Temperature

v :

Flow velocity

v crit :

Critical velocity

v impact :

Impact velocity

x :

Axial distance

μ :

Viscosity

ρ :

Density

σ TS :

Tensile strength

σ U :

Yield stress

τ :

Stress

τ r :

Drag force

eff:

Effective

p:

Particle

CVR:

Critical velocity ratio

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Acknowledgments

The authors acknowledge the contributions from the ARL, UTRC, and MGHPCC computing resources. Funding was provided from the Army Research Laboratory under Contract W911NF-15-2-0024.

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Liebersbach, P., Foelsche, A., Champagne, V.K. et al. CFD Simulations of Feeder Tube Pressure Oscillations and Prediction of Clogging in Cold Spray Nozzles. J Therm Spray Tech 29, 400–412 (2020). https://doi.org/10.1007/s11666-020-00992-0

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Keywords

  • cold spray
  • computational fluid dynamics
  • clogging
  • feeder tube oscillations
  • particle dispersion
  • particle–wall collisions