Abstract

The direct measurement of particle temperatures in particle-laden flows presents a unique challenge to thermometry due to the flow's transient and stochastic nature. Previous attempts to measure the bulk particle temperature of a dilute particle plume or particle curtain using intrusive and non-intrusive methods have been mildly successful. In this work, a non-intrusive method using a high-speed infrared (IR) camera and a visible-light camera to yield an indirect particle temperature measurement technique is developed and tested. The image sequences obtained from the IR camera allow for the calculation of the apparent particle temperature, while the visible-light image sets allow for the calculation of the plume opacity as a function of flow discharge position. To extract the true particle temperature, a post-processing algorithm based on Planck's radiation theory was developed. The results were validated through a series of lab-scale tests at the University of New Mexico using a test rig capable of generating particle curtains at various temperatures. The temperature profiles extracted from the methodology presented were compared to the temperature data measured during experimental measurements yielding agreement of the bulk particle temperature of the plume within 10% error. The methods described here will be developed further to estimate the heat losses from the falling particle receiver at Sandia National Laboratories.

Introduction

Solid particle receivers for high-temperature concentrating solar power applications have attracted increasing interest over the past decade [1,2]. From numerical simulations [3] to receiver design and evaluations [4], teams world-wide have performed studies to characterize and assess the performance of particle receivers [5,6]. These receiver systems offer a promising pathway to successfully utilize the high-temperature heat (>700 °C) [7] absorbed from a solar thermal receiver to drive a supercritical carbon dioxide (s-CO2) Brayton power cycle by providing operating temperatures beyond 700 °C [8], which can yield ≥50% thermal-to-electric conversion efficiencies [1,2]. The falling particle receiver (FPR) at Sandia National Laboratories is a prime example of the capabilities of this technology [8,9].

However, during the on-sun operation of the FPR, particle egress through the front aperture has been observed, forming a particle plume that is carried by the wind; not only does this result in potential pollution hazards but also on loss of particle inventory in the system as well as heat and efficiency losses [10,11]. These events present a unique challenge for measurement techniques and devices due to the complexity of the multiphase flow, and also because the plumes (Fig. 1) are on the path of the concentrated irradiance. Moreover, since the particle egress from the system is extremely transient [12] and dependent on a variety of internal and external factors [13], intrusive methods such as thermocouples will not accurately measure the particle temperatures as they will only be in contact intermittently and temporarily with the particles that may strike them. Similarly, the thermocouples can be in direct exposure with the irradiance incident on the cavity and the hot air currents that egress from the cavity, as well the cold air currents entering the cavity, which can skew direct measurements [14]. Current variations of the “free-fall” configuration of the FPR have been numerically studied [15] through computational fluid dynamics models and forecasting techniques [16,17] as well as experimentally [18] at Sandia to further reduce the particle plume generation. Current studies include the addition of a multi-stage free-fall curtain [17] and the study of the effects of quartz window covers [19] to mitigate particle egress from the cavity. Therefore, addressing this issue is paramount for the receiver technology's success as the particle loss not only can impact the long-term operation of the system and reliability but also constitutes a receiver efficiency and overall efficiency of the solar plant.

Multiple studies can be found in the literature that highlight multiple attempts to measure particle temperature non-intrusively. Most of these techniques employ thermographic phosphors which are fluorescent at well characterized temperatures and are commonly used in combustion and energy sciences [20]. Kueh et al. presented a planar technique for measuring the temperature of radiatively heated particles suspended in a fluidized bed employing ZnO:Zn phosphors as tracer particles heated up to 500 K [21]. Similarly, Zhao et al. presented an enhancement of the technique using BaMgAl10O17 phosphors as they are able to operate at temperatures greater than 1000 K which could be a temperature applicable for FPRs [22]. Nonetheless, one main drawback is the need of a specific spectral range to activate the particles to emit the luminosity required for the measurement. On the other hand, camera-based thermography has also provided some attempts for non-intrusive temperature measurements of films [23] and liquids [24].

Previous work by Ortega et al. [10,11] highlights the initial steps of a non-intrusive imaging method development to extract the true particle temperature from thermography measurements using a visible-light camera (Nikon D3500 with 70–300 mm Nikkor lens) coupled with a high-speed Infrared (IR) camera (ImageIR8300 with 100 mm lens). The focus of their work was to develop a lab-scale system which allows for the measurement of a particle plume under a controlled environment to develop a measurement technique which could be applicable for the FPR on-sun tests. However, as shown in Fig. 2, higher irradiance levels require a larger number of heliostats to achieve this which can yield a spot over 2 m in diameter. Therefore, to avoid any potential irradiance spillage intercepting the cameras during on-sun operation, the team decided to constraint the cameras to be mounted 5 m away from the center of the aperture. It was determined that the field of view corresponding to an individual pixel of the IR camera positioned 5 m away from the aperture was much larger than the mean particle diameter [10,11]. This means that the temperature measurements directly from the IR camera represent the apparent temperature, but not the true temperature of the particles [10,25]. Substantial work has been done to address the issue of low resolution of thermometry at longwave infrareds [26] as well as the enhancement of feature recognition in thermal images (i.e., thermograms) using specialized algorithms for: IR image reconstruction [27], characteristic enhancement of low-resolution thermal stereo images [28], as well as pixel smoothing techniques for temperature averaging [29]. However, little to no work has been done to address the issue of sub-pixel scale averaging that can occur when the object of interest is smaller than the pixel size. In this work, a novel non-intrusive particle temperature extraction method developed by the University of New Mexico and Sandia National Labs is presented. The analysis can be used to estimate the average particle temperature within a particle plume using a combination of IR and visible-light cameras which can be applied to measurements under high-temperature and high-irradiance conditions such as the on-sun tests of the FPR at Sandia.

Theory

Ho and Ortega et al. compared five different methods which could have been applied to establish a basis for the methodology [11]; however, the energy balance approach using two cameras collecting data at known time frames was selected based on their analysis. Starting from a power balance approach, every pixel from the IR camera receives radiative power from the background and the particles for the same amount of time, if any, contained within the field of view of the pixel (Fig. 3) as shown in Eq. (1). Expanding this equation in terms of heat flux (i.e., irradiance) and solving for the irradiance received by the pixel yields Eq. (3).
Q˙px=Q˙p+Q˙bk
(1)
q˙pxApx=q˙pAp+q˙bkAbk
(2)
q˙px=1Apx(q˙pAp+q˙bkAbk)
(3)
where Q˙ is the total power, q˙ is the irradiance (i.e., heat flux), and A is the area covered by the individual components represented as subscripts: pixel (px), particle (p), and background (bk). The area ratios in Eq. (3) can then be substituted using the opacity relationship shown in Eq. (4). Since the area occupied by the background is the inverse of the area occupied by the particle, so that Ap = 1 − Abk, when Eq. (4) is substituted into Eq. (3), the irradiance balance can be expressed as Eq. (5) where ωp is the opacity of the particles within a pixel.
ωp=ApApx
(4)
q˙px=q˙pωp+q˙bk(1ωp)
(5)

Following, Planck's radiation law can be applied into this model to describe the model into temperature terms. While the Stefan–Boltzmann's is a simplified approach to solve for the particle temperature, it represents the total hemispherical irradiance over the entire electromagnetic spectrum, which will overestimate the energy measured by the IR camera sensor which operates between 2 and 5.7 µm [25].

Planck's Radiation Law.

Planck's radiation law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium using Eq. (6) [30]. Similarly, the hemispherical gray body irradiance over a spectrum of interest can be estimated by integrating Planck's equation over the relevant spectral range using Eq. (7) [30]. For this study, λ1 = 2 µm and λ2 = 5.7 µm since this is the operating range of the IR camera used in this work. Similarly, the emissivity value is assumed to be that of a gray hemispherical emitter (i.e., constant with uniform magnitude in all directions) since at the present time, the radiative properties of the particles have not been studied. Therefore, ɛ(λ, T) = ɛ = 0.9. It can be observed that the irradiance is a function of temperature, which means an iterative numerical solver will be required to solve for temperature.
B(λ,T)=2hc2λ51ehc/λKT1
(6)
q˙=πλ1λ2ε(λ,T)B(λ,T)dλ
(7)

Here, B is the spectral radiance of the body, λ is the specific wavelength, T is the specific temperature, h is Planck's constant, c is the speed of light, K is the Boltzmann constant, and ε is the emissivity. For our case, λ1 = 2 μm and λ2 = 5.7 μm.

Model Development.

Now that an irradiance model is chosen, and Eq. (5) can be rewritten in terms of the fraction of the irradiance coming from the particles which can be described as shown in Eq. (8). Here the pixel and background irradiances are calculated using Eqs. (6) and (7) as functions of temperature measured by the IR camera. Moreover, if the opacity can be measured from the visible-light camera, the expected particle irradiance from the particles within every pixel can be computed as highlighted on the diagram in Fig. 4.
q˙p=q˙px(1ωp)q˙bkωp
(8)

A bisection root-finding method was developed to iterate inside a loop which will be used to find the particle temperature which yields the expected particle irradiance to maintain the balance in the irradiance equation. This is done by applying a bisection root-finding method which starts under the assumption that the particle temperature will be between the pixel temperature and a large temperature outside of the range of analysis (i.e., 1200 °C) and the loop will run for up to 1000 iterations or until the temperature variation is under 0.1 °C.

Experimental Setup

A lab-scale test rig was designed and built at the University of New Mexico (UNM) Solar Simulator Lab as shown in Fig. 5. The experimental arrangement is composed of three main components: (1) an instrumented small particle receiver (SPR) used to generate particle curtains with similar mass flowrates to those of the plumes as estimated by Sandia [12], (2) an actuated tube furnace used to preheat the particles to a set temperature, and (3) a solar simulator which can be used to emulate the heat fluxes which particle plumes are exposed to as they flow out of the system (to be used in future experiments).

Before every test, the furnace will preheat the particles to the temperature of interest. Once the particles are ready, the tube furnace is raised, and the particles are poured into the top hopper. When the hopper's sliding gate is opened, the particle flow starts, and thermocouple and weight data are recorded. While the particles flow steadily (i.e., constant mass discharge rate) through the system, both cameras collect image sequences as the particles discharge losing heat to the ambient air (i.e., transient heat loss). To ensure that the exposure settings will allow the calculation of the curtain opacity, a light-emitting diode (LED) panel was installed behind the curtain to generate sufficient contrast of the particles and the background as shown in Fig. 6.

The particles used in this work are CarboHSP 40-70 with a median diameter of ∼330 µm and playground sand with a median diameter of ∼380 µm after it was sieved out to remove particles greater than 1 mm. For this study, three temperatures were considered, 200 °C (low), 450 °C (medium) and 750 °C (high), to assess the effects of temperature and particle type (i.e., topology, size distribution, etc.) on the effectiveness of this technique to extract the true particle temperature.

Opacity Measurements From Visible-Light Images.

As described by Beer's law, the opacity of a participating medium can be measured based on the amount of interference that this produces on a reference light source, and it is best described as Eq. (9) where Io is the intensity of the light with no interference and I is the intensity of the light with interference due to a medium [31].
ωp=IoIIo
(9)

As shown by Ortega et al. [10], the visible-light images are treated as grayscale 16-bit images with intensities ranging from 0 (black) to 65,535 (white). The calculation of Eq. (9) is performed in two simple steps. First, when the reference image is compared to the image with the particle curtain, the numerator, as seen in Fig. 7, simply becomes a negative of the image with particles. When divided by the reference image, as seen in Fig. 8, the image remains the same, except that the values of the pixels are no longer intensity values but opacity values ranging from 0 (empty) to 1 (fully opaque). Lastly, the average opacity as a function of discharge position can be found by discretizing an image into sub-regions where the average opacity can be calculated as seen in Fig. 9. The data can be fitted with a power-law function which can be used for the particle temperature calculations.

Apparent Particle Temperature From Thermograms.

Different from the visible-light images, the thermograms collected already are matrices with temperature values which simplify the process of obtaining an apparent temperature profile. Once the set is loaded, an average apparent temperature profile can be obtained for every thermogram in the sequence by averaging every row of values which will yield a profile as a function of discharge position. Based on frame rate of the cameras, for a 2-min span of data there are approximately 554 thermograms per 1 visible image, therefore, the average apparent temperature value at every row should also include the temporal variation of every camera capture. This means that the profile developed accounts for the spatial variation of temperature as well as the temporal variation for the entire sequence of 554 thermograms as shown in Fig. 10. It should be noted that while the particle discharge is steady, the transient temperature of the curtain decreases as it flows down due to heat losses to the ambient which makes this problem time-dependent. Similarly, it is important to highlight that the apparent or pixel temperature depends on the sensitivity of the IR camera and the particle flow conditions. If these conditions are not able to meet the sensitivity threshold of the IR camera (i.e., yielding sufficient temperature difference for the camera to distinguish a change from the background), the measurements will not be possible, and the technique cannot be applied. This means that there is dependency on the IR camera pixel size, particle size, and temperature which the user should consider beforehand.

True Particle Temperature Extraction.

With the opacity and pixel temperature functions known and an established background temperature, the average particle temperature as a function of discharge position can be estimated using the model depicted in Fig. 4. It should be remembered that the average particle temperature represents the estimated particle temperature at any given discharge position to maintain the irradiance balance equation requirements. Similarly, while convection is indeed a factor that contributes to the time-dependent temperature variation due to heat losses, air can be considered to be a non-participating medium in radiation heat transfer. This means that regardless of the type of heat loss experienced by the particles, they will be emitting at a different temperature and this can be captured by the IR camera used in this work. Therefore, an irradiance balance model is applicable [32]. Lastly, to validate the results, the average particle temperatures extracted are compared with the semi-empirical particle temperatures calculated using a lumped capacitance exponential decay model as highlighted by Cengel and Ghajar for a single particle using the temperatures recorded at the top and bottom hoppers as seen in Fig. 11 [33].

Results and Model Validation

Previous results obtained by Ortega et al. showed that the Stephan–Boltzmann's model overestimates the estimated particle temperature (see Fig. 11) because it considers the spectral emittance over the entire electromagnetic spectrum [25]. On the other hand, the IR camera used in this has a limited operating spectral range [25]. Therefore, the experimental and Planck's-based model results were reanalyzed for carbo and sand particles at different temperatures. The measured temperature profiles were obtained empirically using a lumped capacitance model. On the other hand, the extracted particle temperatures are the average particle temperature values obtained by processing the image sequences at a corresponding time with the measured profile. The results for the comparison can be seen in Fig. 12. While similar amounts of carbo and sand particles were preheated to the same temperature for the same duration, it is clear by comparing Figs. 12(a)12(d) that the sand particles tend to cool at a faster rate compared to carbo particles. This is most likely due to the vast number of smaller particles of sand (i.e., based on particle size distribution) which are flowing through the system which make the flow more prone to losing heat faster. On the other hand, the particle size distribution is much narrower for carbo particles [34]. Aside from this, the team attempted to produce a measurement for sand particles at 750 °C without success. It was observed that the friction factor of the sand increases and the particles at high temperature would not flow out of the tube furnace when it is hot. Nonetheless, there is substantial evidence that the method can estimate the particle temperature within 10% error from the empirical values as seen in Fig. 12. When interpreting the data in this figure, we must note that the analytical curves in most cases lie within the uncertainty corridor of the experimental readings, with the uncertainty dominated by the data variability. We also report the r2 measure of agreement between the model curve and the average measured values, which shows improvement with increasing preheat temperature.

Conclusions and Closing Remarks

This paper presents the advancements towards the development of a novel non-intrusive methodology to indirectly measure particle temperature using infrared thermometry for particle plumes. The theoretical development is presented with sufficient evidence for the selection of the approach. A test rig was designed and built to generate experimental cases which helped the validation of the technique using two types of particles preheated at different temperatures operating under a steady discharge condition with variable temperature throughout the measurements. Overall, the particle temperature measurements obtained applying the methodology described show an agreement with direct measurements within 10% error as seen in Fig. 12. This means that this analysis can be applicable to ceramic/oxide solid particles of any kind within the sensitivity threshold of the IR camera, and it is agnostic to the temperature conditions if the known values required are pre-determined. Future studies will be required to assess the capabilities of the methodology employing various particles and determine whether the method maintains a low uncertainty level. Similarly, a sensitivity study will be performed in the future to assess the importance of the individual variables used in the methodology.

The method developed will serve as a basis to develop a measurement technique to estimate the true temperature of the particle plumes which egress from the FPR aperture during on-sun tests. By knowing the true temperature of the particles within the plume, the heat losses of the system can be estimated. While this work presents an image post-processing method, the team strives to develop an in situ measurement technique which can yield particle temperature measurements in real-time.

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 #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.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

Data provided by a third party are listed in Acknowledgment.

Nomenclature

q˙ =

irradiance (W m−2)

A =

projected area (m2)

B =

spectral radiance of body (W m−2 s r−1)

D =

particle diameter (mm)

I =

light intensity

Q˙ =

power (W)

T =

temperature (K)

Greek Symbols

ɛ =

emissivity

λ =

wavelength (m)

φ =

plume volume fraction

ω =

opacity of media

Subscripts

bk =

background

o =

initial

p =

particle

px =

pixel

Constants

c =

speed of light constant (2.998 × 108 m s−1)

h =

Planck's constant (6.626 × 10−34 J s)

K =

Boltzmann's constant (1.381 × 10−23 m2 kg s−2 K−1)

σ =

Stefan–Boltzmann's constant (5.6704 × 10−8 W m−2 K−4)

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