Granular Flow in Novel Octet Shape–Based Lattice Frame Material

Supercritical carbon-dioxide (sCO₂)-based Brayton cycle is a promising alternative to the traditional steam-powered Rankine cycle because of its potential for achieving high thermal-to-electric conversion efficiency of ∼50% [1]. The overall conversion efficiency of the power cycle can be improved by increasing the working fluid temperature at the turbine inlet (typically ≥700 °C). To this end, the power cycles are coupled with the solar energy field in concentrating solar power plants (CSPs) as shown in Fig. 1 [2].

The CSPs are an attractive technology as they feed on solar energy, a renewable source, and there has been a continuous effort to ensure their commercial scalability. In CSPs, the heat transfer fluid (HTF) flowing in a closed loop gets heated by the concentrated solar energy in the receiver section, and this thermal energy is eventually transferred to the working fluid (sCO₂) of the power cycle via a particle-to-sCO₂ heat exchanger. These HTFs also act as thermal energy storage (TES) systems which store the heat energy so that it can be dispatched as and when required, such as, in instances when solar energy is not readily available.

Molten salt and granular media are the most widely known HTFs for CSP application, and several heat exchanger (HX) designs such as shell-and-tube, shell-and-plate, and printed circuits have been investigated in the past based on these HTFs. Du et al. [3] investigated heat transfer characteristics of HITEC (NaNO₃–KNO₃–NaNO₂ eutectic) salt–oil pair in a shell-and-tube HX and provided empirical correlations to predict the thermal performance. He et al. [4] analyzed the turbulent heat transfer characteristics of molten HITEC salt and YD-350 synthetic oil pair in a shell-and-tube HX and reported that no significant heat transfer augmentation occurred when salt was replaced by water as HTF. Qian et al. [5] compared the thermal performance of molten salt and conductive 320-oil in baffled shell-and-tube HX, where molten salt provided higher heat transfer performance. Shell-and-tube HX design is one of the most primitive designs which suffers from fluid leakage, large volume, and inability to sustain high pressures [6]. Printed circuit HXs have considerable advantages over these traditional HXs in terms of specific areas for heat transfer, sustainability of high-pressure drops (up to 60 MPa), and relatively compact sizes [6].

Printed circuit HXs consist of a stack of plates etched with minichannels, where the contact between the plates is ensured through a diffusion bonding process. These minichannels are fabricated in various shapes such as straight, trapezoidal, serpentine, zig-zag, etc. [6]. Wang et al. [7] experimentally studied the heat transfer performance of airfoil finned printed circuit HX with HITEC molten salt on the hot side and YD-325 synthetic oil on the cold side. The heat transfer of the airfoil channel was ∼ 7 times higher than the straight channel due to disruptions of fluid flow by the fins. Nikitin et al. [8] experimentally determined the heat transfer and pressure drop characteristics of sCO₂ in a printed circuit HX having zig-zag channels with a semi-circular cross-section profile. The overall heat transfer coefficient for the zig-zag channel was obtained in the range of 300–650 W/m²K. Despite hosting several advantages over traditional shell-and-tube HXs, minichannels of printed circuit HXs have the drawback of potential plugging by the salt. Montes et al. [1] suggested a compact honeycomb HX where the molten salt flowed through a central tube and the sCO₂ was present on the outer trapezoidal ducts surrounding the tube. The proposed design prohibited the clogging of channels and avoided large mechanical stresses due to high pressures of sCO₂. Molten salts inherit some other limitations such as thermal instability, high melting points, and corrosive behavior [9]. Popular molten metals such as Nitrates have a maximum operating temperature limit of 560 °C, which prohibits the realization of turbine inlet temperatures ≥700 °C. On the other hand, solid particles as heat transfer media can have very high working temperatures (>1000 °C), high heat capacity, low-cost, and non-corrosive behavior [10]. Particle-to-sCO₂ heat exchangers have been actively investigated recently due to these advantages and two of the most widely researched concepts are—(a) fluidized bed, and (b) gravity-driven moving packed-bed.

Fluidized bed technology provides higher overall particle-to-wall heat transfer coefficient values, but the cost associated with the machinery required to supply fluidized gas and with the recuperative heat exchange devices to minimize convective heat transfer losses from the gas poses challenges in their commercial applications [11]. Gravity-driven moving packed-bed heat exchangers have become a viable alternative due to their simpler setup and lower operational costs [12]. However, the heat transfer coefficient values of the moving packed-bed HXs are lower than the fluidized beds, which is being countered by developing innovative HX designs by several researchers. Albrecht and Ho [12] investigated a counter-flow multi-bank shell-and-plate HX where sCO₂ flowed in a serpentine fashion via parallel plates and the particles moved in between the stacked plates under the influence of gravitational force. It was found that the thermal exchange in such configurations is limited by the low thermal conductivity of the particle bed. The authors in Ref. [12] proposed a reduced order modeling methodology to predict the heat transfer in HX and reported that an overall heat transfer coefficient of 400 W/m²K could be achieved for a particle channel width of 4 mm and particle diameter of 200 µm at CSP plant operating temperatures (500–800 °C). Baumann and Zunft [13] investigated crossflow shell-and-tube HX where the dense granular medium moved downward in a shell enclosing the tubes through which the working fluid of the power cycle passed. In such configurations, the heat transfer performance can deteriorate due to the stagnation zone on the upper vertex and the void zone in the wake of the tubes. The narrowing down of the horizontal tube pitch in Ref. [13] provided an increment in the overall heat transfer due to shorter particle–wall contact time.

The formation of the stagnation and void zones around the tubes in a shell-and-tube HX can be reduced by adopting more sophisticated tube designs as compared to the traditional circular ones. Tian et al. [14] proposed an elliptical-like combined tube shape constructed from the arrangement of three circular tubes. The stagnation and cavity zones in the novel elliptical-like tube were significantly lower than those in the conventional circular tubes resulting in the outside tube heat transfer performance due to particles similar to pure-elliptical configuration. The inside tube heat transfer of the elliptical-like configuration was compared with the corresponding elliptical- and circular-only configurations using the standard Gnielinski equation. For the same mass flowrate, the heat transfer coefficient was the highest for the elliptical-like configuration. In a recent study, Tian et al. [15] proposed a trapezoidal corrugated modification to the standard plates in a shell-to-plate HX where the trapezoidal bulge was reported to significantly improve the heat transfer between the particles and plate. The trapezoidal bulge enhanced particle–particle mixing and destroyed the thermal boundary layer development resulting in improved heat transfer in the downstream regions. The base angle of the trapezoidal bulge was reported to have a significant influence on the particle-to-wall heat transfer. Guo et al. [16] investigated the influence of the tube inclination on the particle-to-tube heat transfer. The contact resistance first increased and then decreased with the increment in the inclination angle. An optimum inclination angle of 15–37.5 deg was suggested by the authors to slow down the development of penetration resistance.

As discussed earlier, several novel HX designs have been explored in the past to improve the efficiency of the CSP plants. The granular flow and thermal exchange characteristics are being actively investigated through experimental and numerical means. Owing to the large capital investment required to conduct experiments, computational procedures have become a relatively more economical tool for testing and optimizing the new HX configurations and understating the intrinsic fundamental granular flow behavior. The discrete element method has become a very reliable and robust model in recent years to predict the macroscopic behavior of any granular system by resolving the particle–scale interactions. The concept of discrete element method (DEM) was first proposed by Cundall and Strack [17]. This method uses a Lagrangian framework to explicitly solve the trajectories of particles by evaluating the interparticle forces resulting from contact. The DEM theory is being currently employed by several researchers to model the granular interactions, and a discussion of some relevant studies is presented later.

Bartsch and Zunft [18] used DEM to model the dense granular flow field around the circular tubes in a moving packed-bed HX. The simulated results were in good agreement with the velocity profiles obtained from the particle image velocimetry (PIV) experiments. Yarrington et al. [19] measured the granular properties required as input in DEM simulations at elevated temperatures and consequently investigated its impact on the particles flowing down on an inclined plane. The free surface velocity magnitudes, flow volume fraction, average velocity magnitude, and mass flux contours were analyzed. Besides the simulation of moving packed-bed HXs in regard to the CSP plant applications, DEM is being extensively used to model the mixing and blending of particles in a rotating drum for chemical, pharmaceutical, ceramic, and fertilizer industries [20–22]. DEM is used in combination with computational fluid dynamics (CFD) to model the particle flow behavior in fluidized beds as well [23–25]. Guo et al. [26] employed DEM to investigate heat transfer in moving packed-bed tube HX, where the tubes were subjected to oscillations to improve the heat transfer. Tube oscillations improved thermal exchange by accelerating the particle update and improving the solid fraction in local zones. However, stronger oscillations led to the separation of particles from the tube, thereby deteriorating the heat transfer. Tian et al. [27] also investigated the effect of pin-fin and its oscillation on the gravity-driven granular flow. Several other researchers in the past have developed DEM codes to model the complex particle–particle heat transfer phenomenon [28–30].

The particle-to-sCO₂ heat transfer is influenced by several factors such as particle-side bulk thermal conductivity, particle–wall contact resistance, particle size, channel width, interstitial gas, particle velocity, and particle residence time [31–33]. As discussed earlier, several types of HX concepts have been reported which can potentially augment the thermal exchange from the particle-side channel. In this study, the authors propose a novel gravity-driven moving packed-bed HX with an Octet lattice framework packed between the plates of the channel on the falling-particle side. Octet has been investigated extensively in the past for its superior mechanical properties [34,35]. The past work by our group focused on experimentally and numerically analyzing the convective heat transfer augmentation capabilities of fiber-based lattices from both Cubic and Octahedron families in forced convection channel configurations with both air and water as the working fluid [36–40]. A thorough flow and heat transfer investigation has been conducted to characterize the flow patterns and thermal exchange dynamics rendered by four different topologies, namely, Octet, Tetrakaidecahedron, Cube, and FD-Cube, subjected to both laminar and turbulent flow conditions. Extensive experimental and numerical investigation was conducted recently to establish the stagnant thermal conductivities of the aforementioned lattices with water and air filled in their void volume [41,42]. Amongst these four investigated topologies, Octet provided the highest interfacial heat transfer coefficient values on the fibers whereas effective thermal conductivity was found to be independent of lattice topology for porosity ≥0.8. From prior investigations, it has been well established that Octet exhibits superior interfacial heat transfer and mechanical properties [43]. These previous findings are a motivation to extend the utilization of unique fiber-based Octet topology to granular flow systems employed in CSP plants. Recently, Aider et al. [44] experimentally evaluated the convective heat transfer coefficient of an Octet lattice moving packed-bed heat exchanger (OLHX) additively manufactured in 420 stainless steel and found that the particle flow through OLHX channel provided a heat transfer coefficient of 400 W/m²K at lattice porosity of 0.88. Moreover, the effective thermal conductivity of Octet–particles combination configurations was about 4–8 times higher than the corresponding particles-only configurations. OLHX therefore has the potential to reduce the particle-side thermal resistance and provide enhanced heat transfer owing to a large wetted specific area. The current study aims at experimentally visualizing the flow of particles and eventually developing a DEM framework to simulate the granular flow through OLHX. The mass flowrates of the particles under free-fall through OLHX were measured through experiments. The results from DEM simulations were compared to the experimental data in terms of the mass flowrate as well as local flow features. The particle-side heat transfer coefficient is critical in determining the viability of granular-based heat exchange technology in CSP plants as dictated by the $/kWh metrics, and the proposed OLHX can be optimized to meet these cost and power requirements of power plants.

Figure 2 shows the schematic of the experimental setup used for granular flow visualization in OLHX, and Fig. 3 provides the details of the corresponding computational domain used in the DEM simulations. The OLHX consisted of a single-cell thick Octet lattice packed in an enclosure made of 12.7-mm-thick acrylic sheets. The acrylic panels provided the required transparent access to record the granular flow motion using a GoPro camera at 30 Hz. The setup consisted of a large hopper formed by bending mild steel sheets riveted at junctions to act as buffer storage for the desired number of particles before they were released to flow through the lattice under the influence of gravity. At the beginning of every test-run (t = 0), the lattice exit (shown in Fig. 2) was sealed with cardboard sheet, and the particles were poured from the top into the hopper such that the whole Octet lattice section and a certain known height of the hopper were charged with stagnant particles. The cardboard sheet at the lattice exit was then instantly removed to allow the particles to fall into a container underneath the exit. A stopwatch was used to monitor the time during the free-fall and the time when all the particles had drained out of the OLHX was recorded. The particles collected underneath the OLHX exit were then measured on a high-precision weighing scale to evaluate the mass of the particles. The measured mass of the particles and the recorded time were finally used to evaluate the time-averaged mass flowrate of particles. Each run was repeated several times to ensure the repeatability of results and accuracy of the procedure adopted.

The Octet lattices used in the experiments were additively manufactured in resin using an in-house Form 3 SLA printer (from Formlabs). The total length of each lattice in the mean-flow direction was 100 mm, and the width of the lattice was 50 mm (shown in Fig. 3). The lattice was single-cell thick where each repeating unit cell had dimensions of 10 mm × 10 mm × 10 mm, resulting in total ten cells along the streamwise direction and five along the channel span. Different views of the Octet topology are also shown in Fig. 3. Three porosities of the Octet lattice were investigated experimentally and numerically, namely, 0.75, 0.80, and 0.88. The corresponding fiber diameters were 1.55 mm, 1.36 mm, and 1 mm, respectively. The dimensional scales of the lattice section in the computational domain were exactly the same as that of the experiments. However, the large computational time and memory requirements prohibited the simulation of the exact same mass of particles as filled during experiments. A relatively lower mass of particles was simulated (due to the computational cost of DEM) due to which a scaled-down version of the hopper was modeled as shown in Fig. 3. The hopper in the computational domain resembled a frustum with a rectangular base. The width and depth of the base where it connected with the lattice section were 50 mm and 10 mm, respectively, in order to completely conform to the lattice entrance. The total height of the hopper was 120 mm which opened to a rectangular cross section of 80 mm × 40 mm on the top.

Unlike experiments, the covering lid was placed at the junction of the frustum base and the lattice entrance (shown in red color in Fig. 3) in computations. The lattice was bounded by walls of zero-thickness on the four sides in simulations. In the first step, the particles were injected from the top of the hopper and allowed to accumulate down on the lid under the influence of gravity. When the required amount of particle mass was injected into the hopper, the particles were allowed to settle down for some time to ensure that the mass flowrate during free-fall was calculated from the initial resting state of the particle just like in experiments. Figure 4 shows the resting particles filled in the hopper before the free-fall. Once the particles were settled, the lid below them was removed, and they were allowed to fall through the Octet lattice under the gravitational force.

Three different batches of sintered bauxite CARBOBEAD particles were experimentally investigated. Figure 5 shows the distribution profiles from the particle-size analysis performed using Anton Paar PSA 1190 LD. The investigated particles and the corresponding mean diameters are provided in Table 1. The flow of particles (three different diameters) was experimentally investigated for three different Octet lattice porosities; however, the simulations were performed using only CARBOBEAD-CP 30/60 particles for all three porosities of the lattice.

In the present study, the DEM simulations were performed using the open-source code liggghts (LAMMPS Improved for General Granular and Granular Heat Transfer Simulations) [45], which predicts the motion of a particle using the Newtons’ law of motion as given below [46].

In the above-given formulae, Y is Young's modulus, G is the shear modulus, ν is Poisson's ratio, and e represents the coefficient of restitution. The superscript asterisk (*) refers to the effective properties. The shear force accounting for the tangential displacement between two interacting particles for the duration of contact time is a “history effect.” The tangential overlap was truncated to fulfill the criteria F_t ≤ μ_sF_n, where μ_s is the coefficient of static sliding friction and F_n is the normal force.

For the angular motion, the net torque is contributed by the torque from the tangential force and the rolling friction. Two rolling friction models from the current code library, namely, constant directional torque (CDT), and elastic–plastic spring-dashpot (EPSD2) were used in the current study.

The correct evaluation of forces as per the equations presented in this section requires accurate a priori determination of several input properties such as Young's modulus, Poisson's ratio, and coefficients of sliding friction, rolling friction, and restitution. The properties and other numerical inputs adopted in the simulations of the current study are discussed in Sec. 5.

The parameters provided as input to evaluate particle–particle, particle–fiber, and particle–channel wall interactions are provided in Table 2. Both the fiber surfaces and channel walls were provided with the same material properties. The variables particle–particle sliding friction, rolling friction, and restitution coefficients were adopted from a recent study by Bagepalli et al. [48], where the authors experimentally measured the mechanical properties of CARBOBEAD-CP 30/60 proppants. The authors also reported the contact properties of particles against alumina- and resin-walls. The coefficient of sliding friction and rolling friction between particle–alumina wall was 1.0 and 0.41, respectively, whereas the coefficient values for the particle–resin wall were 0.80 and 0.40, respectively. The particle–wall sliding friction values of 0.25 and 0.30 were used in DEM simulations by Gallego et al. [49] when the walls were considered to be made of steel and methacrylate, respectively, while the glass beads were the falling granular medium.

In the current study, alumina particles interacted with steel surface in the hopper, resin wall in the lattice volume, and acrylic glass on the bounding walls in the experimental setup. However, all the surfaces in a simulation were attributed the same sliding friction coefficient value for particle interaction. Three different cases of particle–wall sliding friction (0.3, 0.5, and 1.0) covering a wide range of values as reported in the literature discussed earlier were simulated in order to calibrate it against the current experimental data.

The considered time-step (δt) should be smaller than the particle's contact duration [52]. A common guideline is to adopt δt of about 20% of t_Ray for a stable solution; however, larger time-steps can be adopted if the achieved particle velocities in the computational domain are not expected to be very large. In the current study, δt = 5 × 10⁻⁶ was specified in all the simulations. The value of Young's modulus significantly influences the time-step size because larger the Young's modulus smaller is the time-step required to resolve particle–scale interactions. Researchers generally use a reduced elastic modulus magnitude as compared to the actual Young's modulus of particles [46,52] to reduce the computational time. Zhou et al. [53] investigated the sensitivity of angle of repose of monosized spheres to various factors such as particle characteristics, material properties, and geometrical constraints. Young's modulus range of 10⁵–10⁸ N/m² was investigated which showed no obvious effect on the angle of repose. The major controlling factors for translational and rotational motion of particles were found to be sliding and rolling frictions. Yan et al. [54] performed a parametric multi-level sensitivity analysis to understand the effect of DEM input particle properties on the bulk response for system involving discharge of particles from a flat bottom cylindrical container onto a plate. With all other parameter fixed, change in Young's modulus from 0.02 GPa to 200 GPa demonstrated small influence on the final shape of pile of material and average velocity of particles near the orifice. However, computational time increased from 0.4 h for Young's modulus value of 0.02 GPa with time-step size of 5 × 10⁻⁶ s to 240 h for Young's modulus value of 200 GPa at time-step size of 5 × 10⁻⁸ s. Xu et al. [55] investigated the effects of material properties on granular flow in a silo. The authors found that material modulus with artificial value of 1/1000 of the actual value yielded no significant difference in flow pattern and discharge rate suggesting that soft-sphere approach (lower modulus values) can be used to predict of behavior of hard particles to save computational time.

Yarrington et al. [19] and Bagepalli et al. [48] reported Young's modulus value of alumina particles to be ∼ 209 GPa which would require a very small time-step. Instead, Young's modulus of 1 × 10⁷ Pa was used in the current study to reduce the overall computational cost.

As discussed in Sec. 5, three different values (0.3, 0.5, and 1.0) of particle–wall sliding friction coefficient were investigated numerically. The mass-flowrate characteristics of CP 30/60 particles using these three values in OLHX having a porosity of 0.88 is presented in Fig. 7, where all the simulation results correspond to the EPSD2 rolling friction model. The time t = 0 in these plots corresponded to the initiation of injection into the hopper. The same amount of time was provided for particle filling and resting in all the simulations before they were released for the free-fall. The mass flowrate measured from the experiments for the considered lattice porosity was 38.98 g/s. The simulated mass of the particles falling through OLHX provided a steady-mass flowrate for a considerable time indicating that 100 g was sufficient to analyze the flow behavior without the start- and end-effects. Significant deviation in mass flowrates was observed for the three different particle–wall sliding friction coefficients. As the coefficient of sliding friction decreased, the predicted mass-flowrate value increased. For the current setup, the best agreement with the experimental data was provided by a friction coefficient value of 0.5. Therefore, this value was used for the rest of the simulations.

Once the coefficient of sliding friction was fixed as 0.5, the effect of the rolling friction model on the mass flowrate was analyzed. Figure 8 shows the temporal variation of the mass flowrates of CP 30/60 particles in OLHX having porosity of 0.88 for two rolling friction models, namely, EPSD2 and CDT. No significant difference in the mass-flowrate characteristics was observed for the two rolling friction models. During the steady-rate condition, i.e., between 3 s and 4.5 s, the value of EPSD2 was slightly lower and CDT was slightly higher than the mean experimental value. Since the choice of the rolling friction model did not significantly influence the prediction of final mass-flowrate value, EPSD2 was chosen to conduct further simulations.

Figure 9 shows the image of particles taken during experiments at instants when the particles were in steady-fall condition. Also presented is the zoomed-in image of the front side of the acrylic panel of OLHX having 0.88 porosity with CP 30/60 particles to better understand the granular motion.

From the front view, three distinct flow characteristics were observed, i.e., (a) stagnant zone upstream of the fiber junctions, (b) cone-shaped void zone in the wake of the fibers, and (c) unobstructed wavy-type motion of particles on lateral sides of the fibers. The upstream stagnation of particles and downstream void due to particle separation is a common characteristic of granular flow around tubes in a shell-and-tube type heat exchanger. The downstream regions of fibers typically remain devoid of contact with the heated particles leading to weaker heat transfer. The overall conjugate heat transfer coefficient of OLHX depends on the effective thermal conductivity of the system and interfacial heat transfer coefficient values. The interfacial heat transfer coefficient depends on the flow fields rendered by the moving media in the lattice. The local heat transfer coefficient distribution around a discrete arrangement of circular tubes arranged normally and inclined to the mean-flow direction is reported in the literature. However, the current OLHX represents a relatively complex scenario where all the cylindrical fibers of the repeating unit cell are placed at a different angle to the encountering particles. The solid fibers attached to the bounding walls when fabricated in metal will develop thermal gradients internally leading to interesting thermal exchange dynamics with the particles. Figure 10 shows the images of OLHX (ɛ = 0.88) during the discharge of particles CP 30/60 colored by the local flow velocities obtained from the simulations. The particles on the lateral side of the fibers had relatively larger flow velocities which corresponded to the speeding wavy motion in Fig. 9. The zoomed-in view in Fig. 10(b) clearly demonstrates regions underneath the fibers junctions which were devoid of the particle contact. It is noted that not only the downstream fiber regions suffered from poor contact but also certain sections of the front- and side-acrylic walls (Fig. 10(c)). Therefore, the heat transfer coefficient values would have non-uniform distribution on the walls connected to the sCO₂-side channel exhibiting regions of locally high and low heat transfer magnitudes. Moreover, the fiber–fiber junctions and fiber–channel wall junctions provided accommodation to the particles for accumulation as demonstrated in the post-free-fall image in Fig. 11. The particles collected in the junctions would not allow these spots to be updated with the fresh heated particles which will affect the heat transfer negatively in these regions over time.

The temporal evolution of mass-flowrate profiles for CP 30/60 particles at three different lattice porosities is provided in Fig. 12. For the same total mass of particles, the mass flowrate was maximum for the highest porosity value of 0.88. Therefore, the particles drained out of 88% porous OLHX in the least time span. The lowest porosity value of 0.75 provided the maximum hindrance to the free flow of the particles resulting in the maximum discharge time.

Figure 13(a) shows mass flowrates obtained from the experimental runs of three different particle batches as a function of lattice porosity. The trends with respect to the porosity variation were similar for particles of different diameters, where the mass flowrate increased with increasing porosity. The difference in mass flowrates of CP 40/100 and 30/60 particles remained almost the same across the entire porosity range. The gap between mass flowrates for HSP 20/40 particles with respect to the other batches decreased as the lattice porosity increased. The larger porosity of the lattices ensures greater voidage volume for the particles to fall freely resulting in increased flow velocities in the domain resulting in relatively larger mass flowrates. However, it should be noted that the stagnant effective thermal conductivity would decrease with increasing porosity too. Figure 13(b) shows the comparison of experimental mean mass-flowrate data with the numerically predicted values as a function of porosity for CP 30/60 particles. Overall, the predicted values were in good agreement with the corresponding experimental data, especially for the higher porosities. The simulated mass had spherical particles of uniform diameter as opposed to the distribution profile provided in Fig. 5. This is expected to influence the mass-flowrate values predicted via simulations.

Figure 14 shows the experimentally obtained mass flowrates for three different porosities of the Octet lattice as a function of particle diameter. At a fixed porosity, the mass flowrate diminished with increasing particle diameter. The smaller diameter particles at any fixed porosity will have a tendency to movei faster in the porous volume and subsequently have more frequent interactions with the fibers of the lattice oriented at different angles. In the case of OLHX where the fiber network can be very dense for lower porosities, the scale of particles with respect to the fiber dimensions can be a very critical parameter of investigation. The previous study by the authors [44] showed that the particles with smaller diameters provided a higher overall heat transfer coefficient for OLHX at a fixed porosity.

The experimental and DEM-based numerical investigation is conducted for flow in a novel Octet lattice moving packed-bed heat exchanger (OLHX) in this study with potential applications in CSP-based power generation. The OLHX packed beds demonstrate high effective thermal conductivity and overall heat transfer coefficients; therefore, it is imperative to gain in-depth knowledge of how it modifies the granular flow field. In the present study, experimental flow visualization was conducted on three different porosities, namely, 0.75, 0.80, and 0.88, of OLHX for three different CARBOBEAD particle batches—(a) CP 40/100, (b) CP 30/60, and (c) HSP 20/40. The DEM framework to simulate the granular flow through the OLHX was then developed in the open-source ligggths software, the results from which provided good agreement with the corresponding experimental data. This framework will be further developed to investigate the heat transfer in complex OLHX configurations. Major conclusions from this flow analysis study are highlighted as follows:

• For a fixed particle diameter, the mass flowrate increased with increasing OLHX porosity. For a fixed porosity of the OLHX, the mass flowrate decreased with increasing particle diameter. The enhanced particle flow velocities coupled with frequent interactions with the fiber network are expected to provide high overall heat transfer coefficient values.

• The experimental images showed cone-shaped void zones downstream of fibers, stagnation areas upstream of junctions, and wavy-type unobstructed motion around fibers. The DEM simulations were able to capture all these important flow features of the experimental results.

• DEM images clearly demonstrated regions of the fiber network as well as channel walls which were completely devoid of the particle contact. These regions will provide very low thermal exchange opportunity leading to non-uniform heat transfer coefficient distribution on the fibers as well as channel walls in contact with the working fluid of the power cycle.

• The images of the OLHX domain post-completion of simulations showed the accumulation of the particles on the junctions of fibers with other fibers as well as with the channel walls. These regions did not have very frequent updates of the fresh incoming particles which can prove to be the hot spots for poor thermal exchange over time.

• The DEM simulations were conducted with the assumption of particles being spherical and having uniform fixed diameters which was different from the measured morphological characteristics of the particles used in experiments. Modeling of real-like particle distribution can further improve the accuracy of the DEM simulations.

This material is based upon work supported by the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under the Solar Energy Technologies Office Award Number DE-EE0009377. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

There are no conflicts of interest.

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

e =

coefficient of restitution

g =

gravitational force

m =

mass of the particle

s =

skin parameter

v =

velocity

x =

particle position

F =

force acting on the particle

G =

shear modulus

I =

moment of inertia

R =

radius of the particle

T =

torque acting on the particle

Y =

Young's modulus

d_f =

fiber diameter

d_p =

mean particle diameter

k_n =

elastic constant for normal contact

k_t =

elastic constant for tangential contact

t_Ray =

Rayleigh time-step criteria

v_n =

normal component of the relative velocity

v_t =

tangential component of the relative velocity

S_n =

material constant in normal direction

S_t =

material constant in tangential direction

β =

material constant used to calculate interacting forces in LIGGGHTS

ɛ =

porosity

δ_n =

normal overlap distance between two particles

δ_t =

tangential displacement between two particles

γ_n =

viscoelastic damping constant for normal contact

γ_t =

viscoelastic damping constant for tangential contact

μ_s =

sliding friction coefficient

μ_r =

rolling friction coefficient

ν =

Poisson's ratio

ρ =

density of the particle

ω =

angular velocity

* =

effective properties

CDT =

constant direction torque

CSP =

concentrated solar power plant

DEM =

discrete element method

EPSD =

elastic–plastic spring dashpot

HTF =

heat transfer fluid

HX =

heat exchanger

OLHX =

Octet lattice moving packed-bed heat exchanger

sCO₂ =

supercritical carbon-dioxide

TES =

thermal energy storage