1. Introduction

2. Experimental Setup

2.1. Conveying Circuit

Experiments were conducted using circular, borosilicate glass pipes of $d=1.15\mathrm{mm}$ at different gas flowrates of $\dot{V}=[0.4,0.6,0.8]\mathrm{L}/\min$. The material is AISI 316L stainless steel, in the commercial form Oerlikon MetcoAdd 316L-D [18] with a nominal Particle Size Distribution (PSD) described by $D_{90}=106\mu m$ and $D_{10}=45\mu m$. These values can be compared with the PSD determined experimentally, in Figure 11.

The setup is sketched in Figure 4, where also the camera and lighting system are visible. Notice the vertical adjustment of the whole pipe, other adjustments were done by strategic placement of shims and adhesive tape. The pneumatic conveying circuit is presented in Figure 2.

The central part of the circuit is the borosilicate glass pipe, of which the wall thickness is $0.2\mathrm{mm}$.

2.1.1. Glass Pipe Coupler

The development of the system involved the design of the small-scale couplers for the pipe. Figure 3 shows the finished result, manufactured using Stereolitography 3D printing. The internal channels have larger nominal sizes to account for manufacturing tolerances. The couplers were printed in a batch and manually selected to ensure best fit with the pipe’s internal channel.

Figure 3. One of the couplers. The opening of the static pressure port in the manufactured part is barely visible to the naked eye. A section view presents the internal channels. The conic section is used to fit the coupler to the flexible pipe.

Figure 3. One of the couplers. The opening of the static pressure port in the manufactured part is barely visible to the naked eye. A section view presents the internal channels. The conic section is used to fit the coupler to the flexible pipe.

The same technology allowed to manufacture and iterate on a rotary valve feeder. This element shows areas of improvement, but it allowed to effectively feed the powder in the circuit for the short duration of the measurements.

The gas supply is provided by a high-pressure tank of clean, dry, pure nitrogen gas. This high purity gas supply ensures that the contamination from moisture or oils is not present, and completely avoids a compressor which might send vibrations down the gas line. A needle regulator was used to set the gas flowrate.

2.1.2. Sensors integration

The circuit schematic in Figure 2 shows that the pressure ports are connected to a Honeywell SSCDRRN100MDAA5 [19] piezo-resistive differential pressure sensor. The sensor provides a $0.5-4.5\mathrm{V}$ analog output, with a full scale of $\pm 10\mathrm{kPa}$. The 3D-printed couplers, see Figure 3, were designed to have a lateral port to measure the static pressure at the inlet and outlet of the pipe. A batch of couplers was printed, selecting those that provided best alignment of the central channel between the glass pipe and the coupler. Therefore, minimum disturbance is expected when measuring the static pressure.

The calibrated output values are updated at $1\mathrm{kHz}$, and recorded using a 14-bit USB oscilloscope. The sensor provides an accuracy of $\pm 0.25\%$ FSS (Full Scale Span) in the same measurement period. When accounting for other effects (temperature variation, voltage offset, calibration, orientation respective to gravity), the manufacturer declares a total error band of $\pm 2\%$ FSS. Consequently, while the absolute value of the differential pressure can be determined within $\pm 0.2\mathrm{kPa}$, the accuracy for tracking pressure changes over time remains at $\pm 0.025\mathrm{kPa}$.

The second channel of the oscilloscope was connected to a Vishay BPW34 photodiode, with a sensing area of $3\times 3\mathrm{mm}$. A simple voltage divider and amplifier was used as preconditioning circuit.

2.2. Camera Configuration

A Pantom VEO 640L high speed camera is visible in the setup of Figure 4. It carries a CMOS (global shutter) sensor, with $2560\times 1600\mathrm{px}$, each pixel is a square of side $10\mu m$. The camera has an electronic global shutter which duration can be selected independent of the fps. With good illumination the optimal balance was found at around $10\mu s$; longer times result in better illumination but the particles form a streak if they are moving too fast.

Figure 4. Photo of the setup for the pneumatic conveying experiment.

Figure 4. Photo of the setup for the pneumatic conveying experiment.

The camera is equipped with a 25mm f/2.8 2.5-5X Ultra Macro lens. Compared with similar models, it has a good aperture (F2.8), meaning it is expected to deliver more light to the sensor compared to other alternatives. The aperture can be reduced (down to F16) to improve the depth of field. Given the camera’s sensor size of $25.6\times 16\mathrm{mm}$ (circa APS-C), pixel size of 10um. The recording window for the circular and square pipes was selected at $1280\times 400\mathrm{px}$, with a sample rate of $10000\mathrm{fps}$. At full acquisition window, the lens can provide an image:

Magnification	Field of View	Pixel Size
2.5x	10.24x6.4mm	4um
5x	5.12x3.2mm	2um

The camera is also mounted on a slider, which allows it to move closer or farther from the pipe in a precise manner, changing the focus. Especially with full aperture, the field of view is quite shallow, and it is crucial to put the focus plane on the center of the pipe. The pipe assembly is moved in order to align its mid-plane with the recording plane. The image is captured around the middle of the pipe length, limiting edge issues. The resulting pictures are of good quality and an example with minimal post-processing is shown in Figure 5.

Figure 5. Circular pipe (⌀ 1.15 $\mathrm{mm}$), 1280x400 $\mathrm{px}$, exposure 6.5 $\mu s$, aperture F8, sample rate $10000\mathrm{fps}$.

Figure 5. Circular pipe (⌀ 1.15 $\mathrm{mm}$), 1280x400 $\mathrm{px}$, exposure 6.5 $\mu s$, aperture F8, sample rate $10000\mathrm{fps}$.

Figure 6 presents a detail view of a group of medium sized particles, where the pixel size is approximately $3\mu m$. The image resolution allows a direct estimation of the PSD, given the expected particle diameters from the powder’s datasheet [18]. The exposure, or the time when light is actually collected by the sensor, must be relatively short to avoid blur in the direction of motion. An exposure of around $10\mu s$ almost completely eliminated the streaks while maintaining a good image luminosity with an aperture between F5.6 and F8.

Illumination of the section of interest is directly from the side opposite from the lens. A high powered LED light shines light towards the pipe and to the lens. It is extremely bright, and it is advisable to use some level of PPE when on. A layer of frosted acrylic sheet in front of the LED diffuses the light, resulting in sharper images and a more uniform background.

Figure 6. Detail view of four particles captured in Figure 5 (B).

Figure 6. Detail view of four particles captured in Figure 5 (B).

3. Particle Tracking

Figure 7. Image sequence from the recordings. The gas flow in this case is $0.4\mathrm{L}/\min$. Notice the particles’ movement relative to the vertical grid lines.

Figure 7. Image sequence from the recordings. The gas flow in this case is $0.4\mathrm{L}/\min$. Notice the particles’ movement relative to the vertical grid lines.

3.2. Tracking verification

The particle tracking software was tested on a simulated dataset to estimate the performance of the technique, having control on all possible variables. The model discussed in the article by Pedrolli et.al. [24] was adjusted to replicate the flow in conditions similar to the experiment. The simulation yielded a series of datasets containing particle positions and velocities recorded at intervals of ${10}^{-4}\mathrm{s}$, matching the framerate of the high-speed videos. These datasets serve as the baseline, or "ground truth," for assessing the error introduced during the particle tracking phase of the analysis.

Using Paraview [25], the simulation output was post-processed into a series of images, replicating those captured by the experimental setup. In these images, particles are depicted as dark circles against a white background, as shown in Figure 8 (A), occasionally overlapping. Overlapping particles pose a challenge for tracking. To address this, the chosen approach involves selecting only fully visible particles, employing the Kalman filter strategy implemented in TrackMate [21]. Figure 8 (B) illustrates the same frame as (A), overlaying the spots utilized in tracking and their corresponding tracks. It is worth noting that while the tracks may be incomplete, they provide sufficient data for velocity analysis.

Figure 8. Example snapshot of the Simulated Particle Tracking (sPT). (A) shows particles represented as uniformly colored dark circles. The tracking result in (B) highlights the tracked spots and their respective tracks (backwards in time). The shaded representation in (C) displays particle overlapping, with darker particles being farther from the observer.

Figure 8. Example snapshot of the Simulated Particle Tracking (sPT). (A) shows particles represented as uniformly colored dark circles. The tracking result in (B) highlights the tracked spots and their respective tracks (backwards in time). The shaded representation in (C) displays particle overlapping, with darker particles being farther from the observer.

The tracking information was exported from TrackMate as CSV files containing all the Spots, Edges, and Tracks. Tracks consist of a series of edges, each defined by an origin and target spot. These elements are interconnected through identifier numbers (IDs), with edges containing the IDs of their respective origin and target spots.

Matlab scripting was the tool of choice to analyze the results, and get to the values of interest. Most relevant for the LMD process is the instantaneous mass flowrate of metallic powder. The resulting values are depicted in Figure 9 and Figure 10. The values labelled as OpenFoam data refer to the direct extraction of particle diameters and velocities from the simulation. Both the results of the tracking and the simulation’s raw dataset were processed the same way, for consistency. The area concentration from the particle tracking is the direct measurement of the dark spots against the light background, essentially equivalent to counting the black vs white pixels of the binary map represented in Figure 8 (A).

Figure 9 displays the difference between the ground truth (OpenFOAM data) and the simulated Particle Tracking. In both cases, area and volume fraction concentrations, there is a discrepancy. The volume fraction discrepancy was plotted as a function of the volume fraction $\varphi$ determined using the Particle tracking and the expected one determined by the simulation. This results in a clear linear relationship. This is easily explained by the occlusion phenomena (see Section 3.1), therefore the line passes through the origin since the occlusion error should tend to zero for very low concentrations. Compared to the work by Spinewine et.al. [23], in this case the concentration is much lower, therefore the linear fit will be used directly to correct the volumetric concentration and then calculate the mass flowrate.

Knowing the bulk density of the material ${\rho }_s$, the mass flowrate of the solid particles is calculated as

$$\dot{m}={\rho }_s(V_{t}ot·\varphi )\widehat{v_Z}$$

(1)

where $\widehat{v_Z}$ is the average velocity of the particles along the pipe, determined using the particle tracking of Figure 8. Without applying the correction on the volume this results in the mass flowrate reported in Figure 10. This diagram also reports the average particle velocity and the standard deviation intervals in of the velocities in the frame, which coincide almost perfectly (the average error is less than $1\%$). The flowrate corrected using the linear fit is not represented in the figure as the two lines effectively overlap, and the error is also less than $1\%$.

Figure 9. Simulated: solids concentration in the simulated flow, both as projected area (A) and volumetric (B). The values coming from the Particle Tracking method is compared with those of the raw dataset. All data was filtered with a $2\mathrm{ms}$ moving average. (C) the error in the estimated volume fraction is fitted by a line passing through the origin.

Figure 9. Simulated: solids concentration in the simulated flow, both as projected area (A) and volumetric (B). The values coming from the Particle Tracking method is compared with those of the raw dataset. All data was filtered with a $2\mathrm{ms}$ moving average. (C) the error in the estimated volume fraction is fitted by a line passing through the origin.

Figure 10. Simulated: particle average velocity and standard distribution in the observed section of the simulated flow over time (A), and calculated mass flowrate (B). The data was filtered with a $2\mathrm{ms}$ moving average. This data was not corrected with the information of Figure 9.

Figure 10. Simulated: particle average velocity and standard distribution in the observed section of the simulated flow over time (A), and calculated mass flowrate (B). The data was filtered with a $2\mathrm{ms}$ moving average. This data was not corrected with the information of Figure 9.

4. Results

4.1. Particle Size Distribution

The PT algorithm uses the spot area and other metrics to find the most likely trajectories. As indicated, all this information is available in the output files. When determining the Particle Size Distribution, it is appropriate to use the method described in Appendix B to correct for the occlusion. Finding a PSD skewed towards larger particle size is to be expected, but the largest assemblies of particles that would cause noticeable outliers are avoided. The PSD is evaluated on the total recorded number of spots, reported in Table 1.

Figure 11 reports the PSD measured in the $0.8\mathrm{L}/\min$ test, and is repeatable across different runs. The experimentally measured values $D_{90}^{exp}=114\mu m$ and $D_{10}^{exp}=49\mu m$ are very similar to the one expected for the powder MetcoAdd 316L-D [18] ($D_{90}=106\mu m$ and $D_{10}=45\mu m$). This encouraging result shows that the setup is indeed able to accurately capture the particles. Figure 11 also reports $D_{50}^{exp}=74\mu m$.

Figure 11. Particle Size Distribution (PSD) measured in the experiments.

Figure 11. Particle Size Distribution (PSD) measured in the experiments.

The accuracy of this measurement is very dependent on the sharpness of the original images, and on the parallax error. The camera setup can be improved by a telecentric lens, and secondarily by a parallel rays light source. Nonetheless, the PSD is essentially spot-on with the values declared by the manufacturer.

4.2. Mass flowrate estimation

Figure 12 reports the final results of the particle tracking, calculated using Equation 1. Considering the established flow for $t\ge 0.3\mathrm{s}$, the particles’ average velocity remains relatively constant, with a narrow distribution. Indeed there is a small dependency on the particle loading, as a denser flow determines a slightly lower average velocity, but in this case the flowrate variation is to be attributed for the most part to the variation of particle concentration.

Figure 12. Particle tracking result for a conveying flow of nitrogen of $0.8\mathrm{L}/\min$, corresponding to an average gas velocity of $12.8\mathrm{m}/\mathrm{s}$. The diagram reports the particles’ velocity distribution and volumetric concentration, averaged over the recorded frame ($L=3\mathrm{mm}$) and over a moving time window ($1\mathrm{ms}$). These are used to calculate the mass flowrate.

Figure 12. Particle tracking result for a conveying flow of nitrogen of $0.8\mathrm{L}/\min$, corresponding to an average gas velocity of $12.8\mathrm{m}/\mathrm{s}$. The diagram reports the particles’ velocity distribution and volumetric concentration, averaged over the recorded frame ($L=3\mathrm{mm}$) and over a moving time window ($1\mathrm{ms}$). These are used to calculate the mass flowrate.

4.3. Flow fluctuations

Considering Figure 13, we can evaluate the average of the mass flowrate. The deviation from the average mass flow rate is expressed in terms of the Root Mean Square (RMS), a statistical measure that quantifies the spread or variability of a set of values, or a continuous function, around the average. Assuming a finite number n of virtual measurements, the i-th mass flow rate measurement ${\dot{m}}_i$ and the average at the outlet ${\dot{\overline{m}}}_{out}$, the RMS value is defined as:

$${\dot{m}}_{RMS}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left({\dot{m}}_i-{\dot{\overline{m}}}_{out}\right)}^2}$$

(3)

The results are reported on the same figure, and can be compared in Table 2. The intensity of flow irregularities is very close in magnitude to what was determined using CFD-DEM, though with an imperfect match.

Figure 13. Powder mass flowrate determined using PT for three conditions. The resulting average and RMS values are determined for what are considered as established flow conditions, or $t\ge 0.3\mathrm{s}$.

Figure 13. Powder mass flowrate determined using PT for three conditions. The resulting average and RMS values are determined for what are considered as established flow conditions, or $t\ge 0.3\mathrm{s}$.

4.4. Photodiode calibration

The values measured by the photodiode and the differential pressure sensor are reported in Figure 14. The figure shows an evident correlation of all the signals, which suggests the possibility to calibrate inexpensive and small sensors to determine the powder flowrate in positions close to the nozzle.

The signal from the photodiode was directly scaled to the mass flowrate by matching on the average values of the two signals between $0.3\mathrm{s}$ and $0.7\mathrm{s}$. This resulted in an extremely good agreement, with the signals almost superimposed, as shown in Figure 15. Evaluating the calibrated flowrate in the stable conditions, or for $0.3\mathrm{s}\le t\le 0.7\mathrm{s}$, returns $\mathrm{RMS}=11.7\%$, only slightly lower compared to the value determined using PT.

Figure 14. Particles’ mass flowrate, for a conveying flow of nitrogen of $0.8\mathrm{L}/\min$, corresponding to an average gas velocity of $12.8\mathrm{m}/\mathrm{s}$. The pressure measurement and transmitted luminosity are included, each on the respective axis.

Figure 14. Particles’ mass flowrate, for a conveying flow of nitrogen of $0.8\mathrm{L}/\min$, corresponding to an average gas velocity of $12.8\mathrm{m}/\mathrm{s}$. The pressure measurement and transmitted luminosity are included, each on the respective axis.

Figure 15. Particles’ mass flowrate measured using Particle Tracking (PT) and the photodiode signal, linearly calibrated, for a conveying flow of $0.8\mathrm{L}/\min$. The lower panel reports a detail, showing proper signal synchronization.

Figure 15. Particles’ mass flowrate measured using Particle Tracking (PT) and the photodiode signal, linearly calibrated, for a conveying flow of $0.8\mathrm{L}/\min$. The lower panel reports a detail, showing proper signal synchronization.

Even if the acquisition rate was higher, at $50\mathrm{kHz}$, the measurement performed via the photodiode shows less steep changes than PT, deriving the physical construction of the device itself. A diode with lower parasitic capacitance, and a better preconditioning circuit, can certainly improve the response time of the sensor, capturing faster varying phenomena. It is unlikely that the photodiode sensing element size, which is $3\times 3\mathrm{mm}$, caused this smoothing: when analyzing the high-speed video, the observed pipe length was a similar value.

4.5. Pressure measurement

The pressure sensor is an internally compensated and calibrated Integrated Circuit (IC), the values over time are reported in Figure 16. The average values for $t\ge 0.3\mathrm{s}$ are calculated, as well as the initial values for the empty pipe.

Figure 16. Measured pressure drop along the pipe. The slope is calculated for the nominal pipe length.

Figure 16. Measured pressure drop along the pipe. The slope is calculated for the nominal pipe length.

The experimental values are higher than those obtained by the CFD-DEM simulation [24], reported in Table 3. The simulations are conducted with the hypothesis of laminar flow and Argon gas. Also, the experimental values might be afflicted by localized pressure drops in proximity of the ports, given the couplers geometry of Figure 3, which deviates from the ideal.

The signal is directly affected by the volumetric fraction present in the pipe, but the faster variations are not captured. The differential sensor, connected at the entrance and exit of the pipe, measures the average drop necessary to convey the powder present in the whole pipe. Therefore, even if the sensor declares a response time of $1\mathrm{ms}$, the faster variations are averaged over the whole pipe length.

One issue to be aware of when deploying such sensors is that the static port, visible in the coupler of Figure 3, is a few tenths of a mm wide and could become clogged. On the other hand, a visible amount of fine particles were able to pass through the small orifice, and make their way through the connecting transparent silicone tube. This could cause issues on the delicate MEMS, which can work in humid conditions, but is not qualified in terms of dust protection.

5. Discussion

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