Abstract

Particle Image Velocimetry (PIV) measurements are commonly used to determine velocity fields from a flow, given that sufficient tracers can be added and tracked to determine their motion. While these types of measurements are typically completed using high-speed cameras to capture the trajectories of the tracer particles, the experiments performed at the University of New Mexico generated extensive time-resolved infrared temperature image (i.e., thermogram) sets of a free-falling particle curtain captured at 300 Hz. The camera used for such measurements was high-speed infrared camera that provides a resolution of 640 × 512. The thermogram sets acquired have been extensively analyzed with two commonly used commercial PIV analysis packages, DaVis and PIVlab. The comparison between the two software packages showed consistent velocity fields and contours, along with corresponding average velocity as functions of discharge position. As expected, the vertical velocity component of these gravity-driven curtains follows a trend that resembles a free-falling sphere rather than a falling sphere experiencing drag. The study also found that the discharge velocity showed negligible effects due to the inlet particle temperature of the curtain. These results will be applied to the development of a methodology to estimate the mass flowrate of particle curtains and plumes using a novel non-intrusive image correlation methodology.

Introduction

The interest in solid particle receivers for concentrating solar power (CSP) applications has grown in recent years [19] as this technology enables the coupling of a solar thermal receiver with a supercritical carbon dioxide (s-CO2) Brayton cycle capable of operating at temperatures beyond 700 °C and ∼50% conversion efficiencies [1]. One example is the falling particle receiver at Sandia National Laboratories [1,2,4,7,8] which uses Silica-based bauxite particles of a sub-millimeter size [4,7,8,10] distribution that flow across an aperture while they are heated directly using a concentrated light beam from the heliostat field [10].

Nonetheless, during operation, the Sandia team learned that particle plumes are ejected from the aperture operation as shown in Fig. 1. This could be attributed to the complex dynamics of multiphase flow combined with turbulence and sudden changes in wind speed and direction, as well as air temperature inside the cavity. These particle losses can accumulate during operation times and can lead to increased O&M costs as they must be replenished to safely operate the receiver. This paper summarizes the imaging method to characterize the bulk velocity and egress rate of these particle plumes which will lead to the estimation of the mass loss per hour of operation of the particle receiver at Sandia.

Fig. 1
Particle egress captured from the falling particle receiver aperture during testing. The plume can be observed within the region inside the rectangle highlighted in the left part of the image.
Fig. 1
Particle egress captured from the falling particle receiver aperture during testing. The plume can be observed within the region inside the rectangle highlighted in the left part of the image.
Close modal

Experimental Setup

The experimental setup used for these experiments was developed at the University of New Mexico (UNM) Solar Simulator Lab as shown in Fig. 2. First, an actuated tube furnace is used to heat up the particles to the desired temperature for the experiment. The top hopper is equipped with an exchangeable bottom-perforated plate which allows particles flow control, and it is restrained by a sling gate to start and stop particles flow.

Fig. 2
Experimental setup used. The components are the following: (a) tube furnace, (b) top hopper, (c) bottom hopper, (d) cooled panel, (e) metallic mesh, and (f) sliding gate.
Fig. 2
Experimental setup used. The components are the following: (a) tube furnace, (b) top hopper, (c) bottom hopper, (d) cooled panel, (e) metallic mesh, and (f) sliding gate.
Close modal

The bottom hopper collects falling particles and is equipped with thermocouples to measure the final temperature of the particles after falling. A cooled panel is intended to provide a low, constant background temperature for the falling particle curtains from the top hopper to the bottom hopper. A metallic mesh is used to restrain the flow and provide a semi-uniform plume of falling particles. Finally, the camera used for this experiment is a high-speed infrared (IR) camera with a 100-mm lens, which operates at a speed of 300 Hz, at a resolution of 640 × 512 pixels, situated five meters from the particle curtain to emulate the mounting distance of the camera at Sandia’s falling particle receiver. It should be noted that at this distance, the pixel size is estimated to be 750 µm [10].

Once the furnace has been loaded with particles, it is preheated to the desired temperature. Once that temperature has been achieved, the particles are poured into the top hopper and a particle plume (i.e., curtain) will be generated. During the tests, thermogram sequences are collected as shown in Fig. 3.

Fig. 3
Sample thermogram for particles preheated at 100 °C and discharge rate of 6.2 g/s. It should be noted that the IR pixels may contain 1 or more particles based on the resolution of the camera.
Fig. 3
Sample thermogram for particles preheated at 100 °C and discharge rate of 6.2 g/s. It should be noted that the IR pixels may contain 1 or more particles based on the resolution of the camera.
Close modal

The main reason to use this high-speed IR camera was to extract the plume’s temperature as a function of time; nonetheless, if the temporal resolution is adequate, an estimation of the bulk particle motion can be extracted from the image sequences collected. This means that the IR camera will serve to not only measure the particle temperatures but also measure the mean particle velocity as a function of discharge position.

Methodology

To process the thermogram sequences, the particle image velocimetry tourniquet (PIV) can be applied to determine a correlation between the thermograms in the sequence. If successful, this would mean that a separate high-speed camera will not be necessary to conduct the on-sun measurements at Sandia’s falling particle receiver.

Particle Image Velocimetry.

PIV is an imaging method that extracts complete velocity vector fields in one and two dimensions from a time-resolved image sequence. These vector fields are obtained by analyzing the region of interest (ROI) for a set of consecutive images in which the motion of a pixel cluster can be observed (Fig. 4). While processing the data, a PIV software can identify a cluster of pixels in motion, by using a signal obtained via direct Fourier transform (DFT) or a series of algorithms denominated by a fast Fourier transform (FFT) method, depending on the software of choice. Lastly, using calibration factors, such as pixel-to-distance ratios and time resolution between images, as well as other user pre-specified conditions for the analysis, the software reinterprets the velocity vector of each cluster. Having multiple clusters within an image set will generate a velocity field for the entire ROI for the entire set. Using the discrete form of a Fourier transform (i.e., DFT or FFT) approach in order to obtain images where the frequencies of particles of interest remain, and the rest is filtered out. A more extensive explanation on how the Fourier Transform is used for PIV is provided by LiQun et al. [11].

Fig. 4
Correlation of particles within a region of interest to extract vector fields. These vector fields are then converted to velocity based on the reference scale and time between the image pair.
Fig. 4
Correlation of particles within a region of interest to extract vector fields. These vector fields are then converted to velocity based on the reference scale and time between the image pair.
Close modal

PIVlab Analysis Toolbox.

PIVlab is a matlab toolbox with a graphical user interface from which most of the functions related to PIV can be accessed (PIVlab requires the matlab image processing toolbox to run). The PIVlab Graphic User Interface (GUI) makes these types of analyses easily accessible to everyone as it requires the three main steps to perform an analysis (image pre-processing, image sequence evaluation, and post processing) [12].

Due to its user-friendly interface and its accessibility, PIVlab has become a popular tool for PIV analysis, and it has been used in multiple studies from the study of “gas migration regimes and outgassing in particle-rich suspensions” [13], the study of “transition from turbulent to coherent flows in confined 3D active fluids” [14], and “particle velocimetry analysis of immiscible two-phase flow in micromodels” [15].

PIVlab Image Pre-processing.

First, a ROI containing the curtain of falling particles was established to perform all the subsequent calculations as shown in Fig. 5.

Fig. 5
Establishing the image region of interest for the PIV analysis
Fig. 5
Establishing the image region of interest for the PIV analysis
Close modal

The pre-processing setup was followed by a calibration process to provide a conversion factor from pixel distance to physical distance as well as the interval of time between each image. This calibration was achieved using the perforations on the structure shown on the right side of the image. These perforations are 50.8 mm (2”) apart from each other (Fig. 6).

Fig. 6
PIVlab calibration used to establish the physical conversion parameters
Fig. 6
PIVlab calibration used to establish the physical conversion parameters
Close modal

Lastly, the image sets were evaluated by applying the pre-established PIV settings under the analysis tab of PIVlab. During this step, the FFT window deformation PIV algorithm was selected with multiple passes and interrogation windows with 50% steps. The interrogation windows used were square areas with a side length of 32 and 16 pixels for passes 1 and 2, respectively (Fig. 7).

Fig. 7
Image evaluation setting for correlation interrogation window
Fig. 7
Image evaluation setting for correlation interrogation window
Close modal

PIVlab Image Sequence Evaluation.

Once the pre-processing parameters have been established, the sequence can be evaluated, and for every image pair, a velocity vector field can be obtained as shown in Fig. 8.

Fig. 8
Vector fields obtained for every pair of images in the sequence used in the analysis
Fig. 8
Vector fields obtained for every pair of images in the sequence used in the analysis
Close modal

PIVlab Image Post-processing.

Applying the pre-established temporal and spatial scales, the average velocities of the vectors can then be scaled, and the average velocity can then be extracted from the image pairs from a polyline selected in the image as shown in Fig. 9.

Fig. 9
Velocity as a function of discharge position can be extracted from the vector fields using the pre-specified linear paths. Three positions were used to extract the velocity profiles from the velocity vector field.
Fig. 9
Velocity as a function of discharge position can be extracted from the vector fields using the pre-specified linear paths. Three positions were used to extract the velocity profiles from the velocity vector field.
Close modal

Particle Egress Rate Calculation.

Continuing with the work presented by Ortega et al. [16], PIVlab was applied to estimate the plume average velocity. Furthermore, to estimate the mass flowrate, it must be defined using Eq. (1)
m˙b=ρbAcVb
(1)
where ρb is the bulk density, Ac is the cross-sectional area of the flow, and Vb is the bulk velocity of the flow. As previously shown, the bulk velocity can be extracted from the thermogram sets. Similarly, the cross-sectional area of the flow can be estimated using the images from which the width, wc, and thickness, tc, of the plume can be quantified, as shown in Eq. (2)
m˙b=ρbwctcVb
(2)

Nonetheless, there is no direct or indirect way to measure the bulk density of the plume. Therefore, if the bulk density of the plume on Eq. (3) is substituted into Eq. (2), the mass flowrate equation now becomes Eq. (4)

ρb=φρp
(3)
m˙p=φρpwctcVb
(4)
where ρp is the particle density and φ is the volume fraction of the particles within the plume. While we cannot directly measure the particle volume fraction, there are several indirect ways to find this value.

Modified Beer’s Law.

Beer’s law is a simple ratio that states that the opacity, ω, is a function of the light intensity with a medium (I) and without a medium (Io) as stated in Eq. (5)

ω=1IIo
(5)
A modified version of this equation was presented by Kim et al. and shows a correlation between opacity, ω, volume fraction, φ, particle diameter, dp, and curtain thickness, tc [17]
ω=1e3φtc2dp
(6)
Rewriting Eq. (4) with Eq. (6), we obtain Eq. (7) which shows the mass flowrate as a function of two constants, the particle diameter, and density as determined by Ortega et al. [18] and Ho et al. [7], respectively. Similarly, three measurable variables, the plume width measured from the thermograms as shown by Ortega et al. [10], the average particle velocity obtained through PIV, and the plume opacity obtained from the visible-light images employing the technique by Ortega et al. [10]
m˙p=23dpρpwcVbln(1ω)
(7)

Experimental Results and Discussion

A set of tests was performed consisting of pre-heating about 5 kg of particles to six different set temperatures (i.e., 100 °C, 200 °C, 300 °C, 450 °C, 600 °C, and 750 °C) to later be used to generate free-falling particle curtains. While the particles were deposited in the top hopper, thermocouples were used to record the particle temperature during operation. As the particles were discharged, they flowed over the restraining mesh which is used to generate a uniform curtain that was imaged by the IR camera as shown in Fig. 2.

Previous velocity measurements and simulation results [7] have shown how a group of particles flowing continuously will have a velocity profile that resembles free-fall as opposed to that of a sphere experiencing drag as shown in Fig. 10. Ultimately, the main goal was to obtain velocity fields that matched those of previous experiments done with PIV and curtains of falling particles. From their results, the velocity region for the experiment is expected to have a maximum velocity ∼2.2 m/s due to the fall distance of ∼0.25 m. Similarly, the curtain’s width was estimated to be approximately 50 mm [10].

Fig. 10
Measured, modeled (ANSYS Fluent), and analytical particle velocities. The box in the lower left corner of the plot represents the region corresponding to the experiments conducted for this study [7].
Fig. 10
Measured, modeled (ANSYS Fluent), and analytical particle velocities. The box in the lower left corner of the plot represents the region corresponding to the experiments conducted for this study [7].
Close modal

Velocity Profile Uniformity.

First, the uniformity of the velocity profile is assessed to compare the particle velocities at different regions within the curtain as shown in Fig. 9. The results shown in Fig. 11 display the velocity profiles at the three regions selected in Fig. 9. By ensuring that the velocity profiles are similar, it can then be assumed that the velocity profile at the centerline of the curtain represents the average velocity of the curtain. From here we can also see that as the particles’ discharge position increases, the profile tends to deviate from the analytical free-fall curve. This can be correlated to the fact that as the particles accelerate downwards, air entrains the curtain and spreads the particles away from each other, hence increasing the effect of drag on the curtain.

Fig. 11
Discharge velocities estimated through PIV at the three positions selected
Fig. 11
Discharge velocities estimated through PIV at the three positions selected
Close modal

Velocity Profile Variation With Particle Temperature.

The velocity profiles of a low (100 °C), medium (450 °C), and high (750 °C) temperature curtain were extracted to compare the effects of the plume temperature on the curtain velocity. As seen before, although not very significant, drag forces begin to play a role in the discharge velocity as the curtain flows downstream. On the other hand, as the temperature of the air surrounding the particles increases, the density decreases, and this could lead to some differences in the velocities measured.

Comparing the discharge velocity profiles in Fig. 12 as a function of particle temperature, it appears that the particle temperature does not have a noticeable effect on the discharge velocity profile. This could roughly mean that the bulk fluid (air) temperature remains at a similar value throughout the tests.

Fig. 12
Discharge velocities estimated through PIV at the different temperatures
Fig. 12
Discharge velocities estimated through PIV at the different temperatures
Close modal

On the other hand, a similar trend that deviates from the free-fall profile can be observed as before. These means that drag forces become a factor as the curtain accelerates downward permitting the entrainment of air, which spreads the particles within it away from each other, hence increasing the effects of drag. It can be said that the effect of drag is not as significant as for the single sphere in free-fall under drag (Fig. 10) but it is present due to the low mass flowrate of particles in the curtains tested.

Comparison of DaVis and PIVlab.

PIVlab and DaVis are two commercial platforms used for PIV analysis. PIVlab has gained popularity on this field due to its user-friendly interface and its accessibility as a free matlab toolbox. On the other hand, DaVis is a commercial suite with multiple applications that require data visualization. Even when both, PIVlab and DaVis, required the user to follow a similar pre-processing progression to perform a PIV analysis, PIVlab has a more intuitive interface than DaVis. On the other hand, DaVis has been an industry standard and provides great accuracy and reliability for PIV and particle tracking velocimetry (PTV) studies. Both tools employ an FFT-based analysis to complete the correlation studies. Therefore, it was decided that DaVis would be an ideal tool to validate the velocity profiles obtained from PIVlab.

As shown in Fig. 13, the velocity profiles, although with more variations than the ones obtained from PIVlab, closely resemble those obtained from Fig. 12. This gives the team confidence to say that the velocities obtained from PIVlab are promising and accurate.

Fig. 13
Discharge velocities estimated through PIV at the different temperatures using DaVis
Fig. 13
Discharge velocities estimated through PIV at the different temperatures using DaVis
Close modal

Average Particle Mass Flowrate.

To estimate the mass flowrate of the particles, there two main measurements must be completed based on Eq. (7). First is the bulk particle velocity which is estimated through PIV tools as described in this work. Moreover, the particles are used as tracers to estimate the behavior of the entire plume; therefore, the velocity of the particles is assumed to be the same as the entire plume. Last, the plume opacity estimation is required to complete this calculation as described by Ortega et al. [10] as shown in Fig. 14.

Fig. 14
(a) Image taken with Nikon Camera for a 5.2 g/s curtain and (b) opacity profile as a function of discharge position
Fig. 14
(a) Image taken with Nikon Camera for a 5.2 g/s curtain and (b) opacity profile as a function of discharge position
Close modal

After estimating the opacity, applying the PIV technique described is used to estimate the bulk particle velocity, and applying Eq. (7), the mass flowrate can be calculated as shown in Figs. 15 and 16 where a conservative agreement between the measured average mass flowrate using the scale and the estimated mass flowrate can be observed during experiments using the method presented.

Fig. 15
(a) Image taken with Nikon Camera for a 5.2 g/s curtain and (b) comparison of mass flowrate measured and estimated using Eq. (7)
Fig. 15
(a) Image taken with Nikon Camera for a 5.2 g/s curtain and (b) comparison of mass flowrate measured and estimated using Eq. (7)
Close modal
Fig. 16
(a) Image taken with Nikon Camera for a 3.5 g/s curtain and (b) comparison of mass flowrate measured and estimated using Eq. (7)
Fig. 16
(a) Image taken with Nikon Camera for a 3.5 g/s curtain and (b) comparison of mass flowrate measured and estimated using Eq. (7)
Close modal

Conclusions and Discussion

In this paper, the team has shown that it is possible to extract mean velocity values from a high-speed thermogram sequence through PIV analysis. As shown in Fig. 11 through Fig. 13, the discharge velocity profiles resemble the free-fall profile much closer than that of a sphere under drag (see Fig. 10).

This demonstrates that the thermogram sequences obtained from the IR camera allow for a reliable estimation of the bulk velocities of a particle curtain despite the resolution limitations. However, this is very promising because this means that a single camera is capable of providing temperature and velocity data from the same image captures.

Furthermore, a technique to estimate the mass flowrate of a particle curtain/plume is presented in this work. The cases presented show an agreement between the measured mass flowrate and the values estimated through the imaging analysis. The disparity in the values is due to the simplification of the mass flowrate equation by making it one-dimensional (1D) and reducing the thickness and volume fraction measurement to a single measurement of plume opacity. However, the current model used (i.e., modified Beer’s law model) can yield the most accurate measurements at the moment.

Future studies will include the development of generalized volume fraction to opacity correlation which accounts for more variables such as particle size distribution, particle morphology, and particle radiative properties.

Acknowledgment

The authors thank Matthew Bauer and Andru Prescod from DOE for their management and support of this work, which was funded by DOE’s Solar Energy Technologies Office (Award No. 33869). Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-NA0003525.

Funding Data

  • U.S. Department of Energy (DOE) Solar Energy Technologies Office (Award No. 33869).

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

I =

light flux after medium (lux)

dp =

median particle diameter (m)

tc =

curtain/plume thickness (m)

wc =

curtain/plume width (m)

Ac =

cross-sectional area (m2)

Io =

light flux before medium (lux)

Vb =

bulk curtain/plume velocity (m/s)

Greek Symbols

ρb =

bulk curtain/plume density (kg/m3)

ρp =

particle density (kg/m3)

φ =

particle volume fraction

ω =

opacity

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