Heat Transfer Characteristics of Particle and Air Flow Through Additively Manufactured Lattice Frame Material Based on Octet-Shape Topology

Supercritical carbon dioxide (sCO₂)-based Brayton cycle has the potential for higher efficiency (>50%) compared to steam-based Rankine cycles at concentrated solar power (CSP) relevant temperatures [1] due to its high-temperature operability. The sCO₂ process has relatively simpler turbomachinery and offers lower installment, maintenance, and operational costs [2]. CSP Gen3 technology identifies three pathways, viz. molten salt, gas-phase, and falling particles [2] to develop sCO₂-based heat exchangers that can operate efficiently at CSP relevant temperatures while being both reliable and cost effective. Liquified nitrate salts can be operated at temperatures up to 565 °C [3] while chloride salts can go up to 700 °C under practical considerations [2], however, corrosion to stainless steel (SS) medium is of major concern in the case of chloride salts [4]. In context with the above drawbacks of molten salt, particles are considered an attractive solution. Particles such as bauxite and silica sand can be directly heated up to 1000 °C and above, in the receiver section through a heliostat field [5]. There have been several investigations on particle-based receiver designs [6–12]. Heated particles can then be driven with the help of gravity from the central receiver to a particle storage container or directly to a heat exchanger.

Particle-to-sCO₂ heat exchangers have been identified as one of the most crucial components demanding innovation to achieve the CSP levelized cost of electricity targets of $0.05/kWh by 2030 [2]. The simplest particle heat exchangers can be in the form of tube bundles, where the fluid such as air or water passes inside the tubes and a heated packed bed of particles is driven around the tubes, thus heating the fluid. This type of heat exchanger is known to have a highly localized heat transfer coefficient in which only the sides of the tubes benefit from the movement of the packed bed while the top and bottom of each tube get lower heat transfer [13]. More efficient heat exchangers such as shell-and-plate and shell-and-tube have also been considered for particle-to-fluid applications. Tian et al. [14] suggested a novel tube shape for implementation in shell-and-tube particle heat exchanger, where the elliptical-shaped tube enhanced heat transfer at the top and bottom of the tube (compared to circular shape) by 42% and 53%, respectively. Experimental study done by Maskalunas et al. [15] showed that the heat transfer coefficient between silica particles and the surface of a parallel plate heat exchanger can vary between 200 W/m²K and 250 W/m²K. Parallel plate heat exchangers can be easily manufactured from high performance materials such as stainless steel and zirconium carbide composite for high temperature and pressure applications. These materials can be diffusion bonded to create very compact heat exchangers known as PCHEs [4]. In an evaluation study, based on factors such as thermal transport capabilities, heat exchanger's structural integrity and its manufacturability, as well as scalability and erosion characteristics, shell-and-plate design was demonstrated to be the best [16].

To this end, a novel enhanced heat transfer concept is developed for the falling particle channel side of the particle-to-sCO₂ heat exchanger for potential employment in a shell-and-plate type heat exchanger (Fig. 1). The convective heat transfer coefficient on the falling particle side is enhanced by packing the parallel plates with Octet-shaped lattices. The Octet unit cells and the enclosing plates were additively manufactured in SS316L and SS420 (with 40% bronze infiltration) via Binder jetting technology. The Octet lattice has been chosen after carrying out direct simulations which quantified its superior heat transfer enhancement characteristics compared to other common unit cell topologies [17–19]. The goal of this paper is to: (a) determine the effective thermal conductivity of lattice structures with void space occupied by particles of different sizes and (b) determine the convective heat transfer coefficient for air and particles flow in large panel of Octet lattice manufactured additively via Binder jetting.

The following sections present details of different experimental setups employed to measure effective thermal conductivity of lattices made from Octet unit cells where void space is packed with particles of varying diameters. A forced convection setup to quantify the overall convective heat transfer coefficient of sandwich-type Octet panel with air as the working fluid is discussed. Finally, a unique test facility was built to carry out particle-based heat transfer experiments. After this section, the results are presented and analyzed. The paper concludes with major findings from this comprehensive experimental program and path forward based on these findings.

Effective thermal conductivity experiments were carried out on the additively manufactured lattice frames for two different cases: (a) void space was occupied by air and (b) void space was occupied by particles. Further, convective heat transfer capabilities of single cell thick lattice for air and particle flows have been investigated experimentally. Three different experimental setups were built to measure the previously-mentioned quantities.

The lattice samples for k_eff experiments were made from a 5 × 5 array of Octet-shaped unit cells in the span and single unit cell in the thickness as shown in Fig. 2. The Octet unit cell could be contained in a cube of edge length Δz = 10 mm. The overall dimensions of each sample were 50 mm × 50 mm × 10 mm. Three samples having as-designed lattice porosities (ɛ) of 0.75, 0.8, and 0.886 were tested for effective thermal conductivity evaluation. However, the actual measured porosities of the additively manufactured lattices were 0.733, 0.798, and 0.884, respectively. Porosity of lattice structures has a dominant effect on the k_eff for a given solid-fluid pair, hence it is imperative that accurate measurement of porosity be carried out in such studies since deviations from as-designed and additive manufacturing (AM)-assisted samples are frequent.

As mentioned above, the actual porosities differed from the intended ones, and the deviation is attributed to the AM process—a trend observed in many prior research efforts [20,21]. It is noted that the AM samples have inherent roughness and defects at both the fibers and endwall, however, the measurement of porosity of such structure accounts for all the defects [22]. For k_eff experiments in particular, the void space is occupied by stagnant air/particles, hence the AM induced defects are not expected to have an added contribution on k_eff, other than the porosity itself. Hence k_eff results are reported as a function of measured porosities of the AM parts.

The effective thermal conductivity (k_eff) setup is shown in Fig. 3. A steady-state heat transfer experiment was developed to obtain the k_eff of additively manufactured samples. A unidirectional heat flow was achieved from top plate to bottom plate of the sample, where Octet-shaped unit cells were sandwiched between the two plates. A cold thermal reservoir was created with the help of an ice-water slurry which was periodically stirred to avoid thermal stratification. An aluminum slab (10 × 10 × 2.5 cm³) was then partially submerged into the chilled reservoir which acted as a near-constant cold reservoir, owing to its large thermal mass.

Figure 4 shows the schematic of the experimental facility used in the present study where air was the working fluid under forced convection scenario. Air was drawn from a compressed air tank maintained at ∼1 MPa. A pressure regulator was installed downstream of the compressor to adjust the mass flowrate to a desired value. Air was then directed to an orifice plate for flowmetering. Differential pressure across the orifice plate static air pressure upstream of the orifice plate and air temperature were measured using Dwyer 477AV-2 (0–10 kPa), Dwyer DPG-002 (0–100 kPa), and fast response T-type thermocouple, respectively. These pressure and temperature measurements were then fed into an in-house matlab code to determine the mass flowrate. The metered flow was then passed through a control valve regulating the flow into the test section. The transition of the flow from circular pipe to square duct was executed with the help of a trapezoidal shaped diffuser.

Figure 4 also shows the schematic of the heat transfer test section. The sandwich panel was heated with patch heaters attached to both the top and bottom walls using thermally conductive silicone compound (CHEMPLEX^® 1381 DE). Rubber foam thermal insulation with thermal conductivity of 0.037 W/mK and thickness of 3.2 mm was pasted on the surface of the heaters. T-type thermocouples were used to measure the temperature inside each thermocouple slot which was very close to the solid-fluid interface and this temperature was treated as the representative wall temperature in the convective heat transfer coefficient calculations. A constant heat flux type thermal boundary condition was created with the help of the patch heaters mentioned above, where the heating power was controlled with variable transformers having voltage indicators.

The sandwich panel featuring an array of Octet unit cells had top and bottom walls of 15 cm × 25 cm dimension and thickness was 1 cm (excluding the top and bottom wall thicknesses). Hence, the flow channel had high aspect ratio (width/height) of 15. It is generally challenging to achieve a uniform hydrodynamically developed flow at the entrance of the test section with such a high aspect ratio. To address this, a ∼33 cm long plexiglass duct was installed between the heat transfer test section and the trapezoidal diffuser.

The samples used in this part were made by reticulating Octet unit cell in span where the sample was one-unit cell thick. The sample was additively manufactured from SS316L and SS420 using binder jetting technology. The bed size of the 3D printer limited the maximum size of the lattice which can be printed in one run. Therefore, the sandwich panel shown in Fig. 4 was obtained by 3D printing different smaller sections and then joining them together. For the SS316 panel, all the parts were joined together using tungsten inert gas (TIG) welding. TIG welding works by creating a very high-temperature plasma that melts and joins the panel parts together creating a seamless SS316 panel. The additively manufactured SS420 lattice panel parts were joined together by soldering. Since SS420 material is infiltrated with bronze, tin metal can easily bond to the SS420 panel parts.

The steady-state heat transfer experimental procedure included heating both top and bottom panels via the glued patch heaters. The experimental procedure included first heating the top and bottom plates and allowing them to reach a primary steady-state in absence of air flow. This step was followed by allowing desired airflow through the test section and allowing the setup to reach a second steady-state. At this stage, the measurements of flow inlet temperature, wall temperature at discrete locations, and temperature drop across the insulation were carried out. Note that the panel was 15 cm wide and 25 cm long, and a representative wall temperature would only be found by measuring local wall temperatures at several discrete locations on both the top and bottom walls.

The local fluid temperature T_f(x) was determined by linear interpolation between inlet and outlet air temperature measurements. The linear interpolation is justified due to the constant heat flux boundary condition on the two opposite walls of the channel. The local convective heat transfer coefficient (h(x)) obtained from above procedure was then used to calculate a representative heat transfer coefficient for each row of unit cells in the streamwise direction. In this paper, we have presented convective heat transfer coefficient for air-based experiments in the periodic heat transfer regime.

The heat transfer test section described in Sec. 2.2 (Fig. 4) was used in the experiments for determination of convective heat transfer coefficient with particles as working fluid. Unlike air-based convection experiments, the particles which carry heat from the test section had to be transported back into the system. To this end, a bucket elevator system was designed, developed, and built for these experiments. Bucket elevator works by rotating a set of buckets attached to a chain or a belt, and by doing so, the buckets scoop the particles from the bottom of the elevator casing and discharge them at the top.

The actual assembled test facility, assembly CAD model, instrumented heat transfer test section, and schematic representation of heat transfer scenario involving falling particles are shown in Fig. 5. Particles are first stored at room temperature in the top hopper while the top and bottom walls of the sandwich panel were being electrically heated with a set of patch heaters. The particles were held until the panel walls reached a temperature of ∼100 °C. A gate valve was installed right downstream of the heat transfer section, which facilitated the on/off type flow of particles across the heat transfer test section. Once the desired panel wall temperatures were achieved, the gate valve was flipped and the elevator was started at the same time, to allow the transport of the spent particles back into the top hopper via a series of equi-spaced buckets.

It should be noted that particle heat transfer experiments are different from the air-based experiments in the sense that the working fluid was recirculated and fed back into the heat transfer section. Due to convection, particles carry away some heat from the heated walls and the same batch of particles is transported back into the hopper above the test section via the bucket elevator. During the transport in the buckets, the particles loose some heat to the laboratory ambient, however, in our initial testing and the design of heat transfer experiments, we observed that the particle temperatures continue to keep increasing as they are recirculated for a prolonged duration. Further, it was decided that bucket elevator-based experiments should not be allowed to run for very long periods of time, as particles can get destroyed/crushed during the transport, which may inherently change the particle size distribution with time, and a satisfactory steady-state could never be achieved, both in the sense of heat transfer and the working fluid rheological properties. Furthermore, for each set of experiments, fresh batch of particles was used to ensure that the rheological properties of the particles are same, and that the morphed or destroyed particles are not used.

The particles used in the experiment were made from sintered bauxite. Three different particle batches were tested: CARBOBEAD-CP 40/100 with a mean particle diameter of 266 μm, CARBOBEAD-CP 30/60 with a mean particle diameter of 397 μm, and CARBOBEAD HSP 20/40 with a mean particle diameter of 966 μm. Particle size analysis was performed using Anton Paar PSA 1190 LD particle size analyzer.

The particle size distribution is shown in Fig. 6. For other thermo-physical and spectral properties of these particles, the readers are referred to Refs. [8,23,24].

The uncertainty analysis for each of the reported quantities was carried out using the sequential perturbation method prescribed by Moffat [25]. The uncertainty in the reported fiber diameters was ∼3% which is a direct contribution of the device used for the measurement. The uncertainty for a typically value of reported values of effective thermal conductivity was ∼3%. The uncertainty in typical values of Nusselt number and air flow Reynolds number is ∼3% and ∼4%, respectively.

In this section, we are presenting experimental results on effective thermal conductivity and convective heat transfer coefficient for air and particles as working fluids.

Effective thermal conductivity experiments were carried out for three cases: (a) packed bed of particles (without lattice), (b) lattice with void space occupied by air, and (c) lattice with void space occupied by particles. Each configuration was tested at three different heat flux levels to ensure that the reported k_eff values were independent of the heating conditions. Note that the wall temperatures at these three different heat flux levels was ranging between 20 °C and 50 °C, hence radiation effects and other solid-phase thermo-physical property changes can be ignored. The packed bed k_eff was similar for all particles with diameters varying between 266 μm and 966 μm with an averaged value of ∼0.4 W/mK.

The second set of experiments was conducted on Octet lattice with void space occupied by air. Figure 7 shows the k_eff values for the samples printed in SS316L and SS420 as shown in Fig. 2. The thermal conductivity of solid-phase was measured to be ∼13 W/mK and ∼20.8 W/mK for SS316L and SS420 materials, respectively. It was found that k_eff was a strong function of solid-phase intrinsic thermal conductivity and the lattice porosity. A suitable normalization of k_eff/k_s collapses different k_s samples onto one curve. A comparison is shown for k_eff/k_s versus ɛ with the generalized correlation prescribed recently by Kaur et al. [22] for porous media with porosities greater than 0.8. The comparison was found acceptable for this porosity range.

The third set of k_eff experiments was conducted on lattices with void space being occupied by the particles with diameters varying from 266 μm to 966 μm (Fig. 8). There was a clear decreasing trend in the k_eff value with increasing lattice porosity, which is again consistent for the case when void space was occupied by air, indicating that particles do not alter the dominant impact of fibers and their intrinsic thermal conductivity values, even though particles are nearly 16 times more thermally conductive than air.

Figure 8 also presents the relative enhancement in k_eff values (η = (k_eff)_{void→particles}/(k_eff)_{packed bed}) for the lattice when particles were packed in void space in reference to a packed bed of particles. This enhancement in k_eff is one mode which implicitly affects the overall thermal transport between the hot and cold sides. Further, a rapid decline in η was observed with increasing lattice porosity. The enhancement levels were similar for different particle sizes for the three lattice porosities and varied from 2 to 4 times compared to the particle packed bed configurations (absence of lattice) for SS316L, while η for SS420 was found to vary between 4 and 8 for three different particle sizes occupying the void space.

This subsection presents steady-state experimental results on local convective heat transfer coefficient offered by Octet unit cells when packed between two parallel plates (integrally manufactured) with air as the convective agent (Fig. 9). The panel is shown in Fig. 4 and was formed by joining smaller pieces together as the maximum printable size was limited by the manufacturing method. The heat transfer development with increasing streamwise distance from the inlet section was presented by the authors in Ref. [26], where a periodic heat transfer (when unit cell-based h does not change with increasing distance) was observed after 40% of the channel length. Figure 9 shows the h values for the two panels made from SS316L and SS420 in this periodic heat transfer regime. Note that these values are conservative in nature and are presented to allow a direct comparison between two different plates and for heat exchangers made from Octet unit cells which are sufficiently larger in size. In practical scenarios, designers should leverage the high heat transfer values obtained in the developing flow regime as shown by Aider et al. [26]. Similar to prior heat transfer quantity (k_eff), SS420 sample had higher heat transfer compared to SS316L sample, due to the conjugate heat transfer effects which depend on the solid-phase intrinsic thermal conductivity. Both the h trends demonstrated a power law dependence on the working fluid flow velocity. Cooling designers can use these trends in the design of heat exchangers which are based on air.

Our preliminary flow visualization experiments carried out on particles flowing through Octet lattice revealed that the particle flow behavior around the fiber and endwall was similar to that of airflow. Similar flow stagnation and separation characteristics were observed for particles flowing through Octet unit cell, which was found to be similar to that of airflow, as shown in our prior publications [17–19,27].

However, it should be noted that particles moving through porous media, despite having similar flow characteristics as that of air or water flow through them, will not necessarily impart similar heat dissipation qualitatively. The stagnation zone observed in particle flow results in particle trapping resulting in lower particle refresh rate, which contributes to reduced heat transfer. Particle flow around the circular fibers in turn enhances heat transfer due to higher local particle speeds.

To characterize the heat transfer for particles, a novel quasi-steady-state heat transfer technique was used to determine time-dependent local convective heat transfer coefficient by carrying out measurements for over 30 min during the slow heat ramp-up phase of the experiment as described in Sec. 2.3. Figure 10 shows the transient heat transfer coefficient calculated at different streamwise locations for the three particle diameters flowing through Octet panel made with SS316L. Similar transient behavior was observed for SS420 panel as well and was presented in Ref. [26]. The results in Fig. 10 are presented over a time period in which the system was considered to be in quasi-steady-state, and it should be noted that both the wall temperatures at different streamwise locations as well as the particle inlet and outlet temperatures were steadily increasing with time. However, their cumulative effect resulted in a time-independent behavior in h which is both expected and desired behavior in heat transfer experiments. The time-averaging of the presented h values in Fig. 11 was carried out for the phase in which time-independent behavior in h was observed. Figure 11 presents the time-averaged h values in the periodic heat transfer regime for both Octet panels made from SS316L and SS420 [26], as a function of particle diameter. The particle flowrates for CARBOBEAD-CP 40/100 (d_p—266 μm), CARBOBEAD-CP 30/60 (d_p—397 μm), and CARBOBEAD HSP 20/40 (d_p—966 μm) were 95.25 g/s, 116.94 g/s, 139.65 g/s, respectively. Note that the flowrates of particles were similar for both SS316L and SS420 panels since they were of similar porosities.

The convective heat transfer coefficient was found to be decreasing with increasing particle size. The difference between SS316L and SS420 was found to be minimal for particle heat transfer in contrast with air-based heat transfer. This is attributed to high heat carrying capacity of particles in comparison with air—this is an interesting finding, since material choice in CSP heat exchangers is critical due to the necessity of bonding hot and cold sides together. Diffusion bonding method is a popular method for bonding hot and cold sides together and this technology is demonstrated for SS316L material. For near-term CSP goals, it is recommended that SS316L-based enhanced heat transfer concepts could be explored further, due to concept scalability and reliability.

Note that the particle heat transfer results presented in Fig. 11 are for channels with distance between parallel plates equal to 10 mm. In order to demonstrate the efficacy of the Octet lattice in reference to the state-of-the-art parallel plate with absence of any enhanced heat transfer concept, separate experiments were conducted for parallel plates in the test facility shown in Fig. 5. The distance between the two parallel plates was kept the same as 10 mm. For brevity, comparison plots are presented for SS316L case only, where parallel plates were also built from SS316L. Figure 12 presents a developing heat transfer behavior for lattice and parallel plate configurations for the flow of three particles through them. The particle heat transfer experiments carried out for parallel plates covered a wide range of particle flowrates. For each streamwise location, a relationship was established for h and the average flow velocity of particles (u). The parallel plate heat transfer data presented in Fig. 12 were obtained for the mass flowrates that were observed for the Octet panel particle experiments. Hence, a fair comparison between Octet panel versus parallel plate could be carried out where the distance between parallel plates in the two configurations as well as the mass flowrate were the same. A clear effect of particle diameter was observed on heat transfer for both lattice and parallel plate configurations. An interesting finding of this study is that in the entrance region, parallel plate configurations exhibited higher heat transfer in comparison to the Octet panels. In the periodic heat transfer regime, the gain in heat transfer due to Octet panel could be observed. For the largest particle size, the Octet and plane channel exhibited similar heat transfer, however, for the other two smaller particle sizes, nearly 30–40% gain in convective heat transfer was observed for the Octet panel.

An experimental investigation was carried out to evaluate the heat transfer performance of Octet-shaped unit cells for their capabilities to provide convective heat transfer enhancement with air and particles as the working fluids. Octet panels were manufactured via Binder jetting method using stainless steel 316L and SS420 materials. The effective thermal conductivity and averaged heat transfer coefficient were obtained experimentally for the cases where the void space was occupied by air and particles. The following major conclusions have been drawn from this work:

• Packing the void space of Octet lattice with particles results in thermal conductivity enhancements ranging from 2 to 4 and 4 to 8 times that of the packed bed of particles, for SS316L and SS420 materials. Maximum benefits were observed for the lowest lattice porosity.

• For airflow velocities ranging from 3 m/s to 12 m/s, the convective heat transfer coefficients in the periodic heat transfer region varied between 200 W/m²K and 600 W/m²K for the two materials.

• For particle flow through Octet lattice of porosity 0.88, the convective heat transfer coefficient was ∼400 W/m²K for CP 40/100 for both the solid-phase materials.

• When compared to parallel plate configuration, the SS316L Octet panel resulted in heat transfer coefficient enhancement of 40–50% for CP 40/100 and CP 30/60 particles, however, no enhancement was observed for the largest particle size (HSP 20/40).

The enhancement levels obtained for the thermal transport quantities through incorporating lattice structures when compared to empty channel, is significant. Additive manufacturing or other manufacturing methods will have a promising role to play to increase the particle-to-sCO₂ heat exchanger effectiveness, through inclusion of enhanced heat transfer concepts, such as porous media or pin fins. Future work will include a demonstration of enhanced overall heat transfer coefficient of porous media enabled particle-to-sCO₂ heat exchanger tested at CSP relevant conditions.

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 United States 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.

h =

heat transfer coefficient (W/m²K)

A =

base area of the lattice (m²)

B =

width of the lattice (m)

W =

total width of the samples used in convective experiments (m)

h_p =

heat transfer coefficient due to convection by particles (W/m²K)

$hsCO2$ =

heat transfer coefficient due to convection by sCO₂ (W/m²K)

k_eff =

effective thermal conductivity (W/mK)

k_HX =

thermal conductivity of the contacting channel wall (W/mK)

k_ins =

thermal conductivity of the insulation (W/mK)

k_s =

solid-phase intrinsic thermal conductivity (W/mK)

q_cond =

net heat conducted across the sample (W)

q_loss =

stray heat losses (W)

q_total =

net heat supplied to the lattice (W)

t_HX =

thickness of the contacting channel wall (m)

t_ins =

thickness of the insulation (m)

R_C =

particle contact resistance (m²K/W)

T_f =

working fluid temperature (°C)

T_side,in =

inner-side temperature of the insulation covering the side of lattice (°C)

T_side,out =

outer-side temperature of the insulation covering the side of lattice (°C)

T_Top,in  =

inner-side temperature of the insulation covering the top of lattice (°C)

T_Top,out =

outer-side temperature of the insulation covering the top of lattice (°C)

T_w =

wall temperature (°C)

U_HX =

overall heat transfer coefficient of heat exchanger (W/m²K)

$T~bot$ =

mean temperature at the bottom wall of the lattice (°C)

$T~top$ =

mean temperature at the top wall of the lattice (°C)

x′ =

non-dimensional streamwise location (x/L)

$qconv″$ =

net convected heat flux (W)

ΔT =

temperature difference (°C)

Δz =

thickness of the lattice section (m)

$ε$ =

porosity

η =

relative k_eff enhancement of particle-lattice combination configuration with respect to particles-only packed bed

sCO₂ =

supercritical carbon dioxide

AM =

additive manufacturing

CSP =

concentrated solar power plant

PCHE =

printed circuit heat exchanger

SS =

stainless steel

TIG =

tungsten inert gas