Abstract

Particle-to-supercritical carbon dioxide (sCO2) heat exchanger is a critical component in next-generation concentrating solar power (CSP) plants. The inherently low heat transfer between falling particles and sCO2 imposes a challenge toward economic justification of levelized cost of electricity produced through solar energy. Introduction of integrated porous media with the walls bounding particle flow has the potential to enhance the overall particle-to-sCO2 heat exchanger performance. This paper presents an experimental study on heat transfer characterization of additively manufactured lattice frame material based on Octet-shaped unit cell with particles and air as working fluids. The lattice structures were additively manufactured in stainless steel (SS) 316L and SS420 (with 40% bronze infiltration) via Binder jetting process, where the lattice porosities were varied between 0.75 and 0.9. The mean particle diameters were varied from 266 μm to 966 μm. The effective thermal conductivity and averaged heat transfer coefficient were determined through steady-state experiments. It was found that the presence of lattice enhances the effective thermal conductivity by 2–4 times when compared to packed bed of particles alone. Furthermore, for gravity-assisted particle flow through lattice panel, significantly high convective heat transfer coefficients ranging from 200 W/m2K to 400 W/m2K were obtained for the range of particle diameters tested. The superior thermal transport properties of Octet-shape-based lattice frame for particle flow makes it a very promising candidate for particle-to-sCO2 heat exchanger for CSP application.

1 Introduction

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 [612]. 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].

Figure 1 shows a typical CSP plant for power generation, where the present study is focused on the particle-to-sCO2 heat exchanger. The overall heat transfer coefficient of this heat exchanger is given as follows:
UHX=(1hsCO2+tHXkHX+RC+1hp)1
(1)
where the thermal resistances are comprised of convection due to sCO2(1/hsCO2), conduction in the wall separating hot and cold sides (tHX/kHX), particle contact resistance (Rc), and convection on the hot side due to falling particles (1/hp). The sCO2 flows through mini- or micro-channels offering superior convective transport, hence yielding significantly lower thermal resistance than that on the hot side due to falling particles. The present study is focused on improving the particle side thermal resistance through incorporation of porous media on the hot side.
Fig. 1
Concentrating solar power plant [2] and representation of particle-to-sCO2 heat exchanger; present study focused on particle side heat transfer enhancement
Fig. 1
Concentrating solar power plant [2] and representation of particle-to-sCO2 heat exchanger; present study focused on particle side heat transfer enhancement
Close modal

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 [1719]. 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.

2 Experimental Setups and Measurement Techniques

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.

2.1 Effective Thermal Conductivity Test Samples, Experimental Setup, and keff Measurement Procedure.

The lattice samples for keff 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 keff 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.

Fig. 2
Three samples of different porosities tested for effective thermal conductivity (dimensions in top figure in millimeters, scale in sample images in inches)
Fig. 2
Three samples of different porosities tested for effective thermal conductivity (dimensions in top figure in millimeters, scale in sample images in inches)
Close modal

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 keff 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 keff, other than the porosity itself. Hence keff results are reported as a function of measured porosities of the AM parts.

The effective thermal conductivity (keff) setup is shown in Fig. 3. A steady-state heat transfer experiment was developed to obtain the keff 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.

Fig. 3
(a) Experimental setup for keff determination and (b) unidirectional heat flow obtained via patch heater and cold sink
Fig. 3
(a) Experimental setup for keff determination and (b) unidirectional heat flow obtained via patch heater and cold sink
Close modal
The effective thermal conductivity (keff) was determined using Fourier's law of conduction (Eq. (2)). A constant heat flux boundary condition was maintained at the top wall of the sample while the bottom wall was glued firmly with the aluminum slab which served as the cold reservoir. Steady-state heat transfer experiments were conducted at three different heat flux values, and effective thermal conductivity was determined for each case, to ensure that the determined value was independent of the applied heat flux at the top wall. The net heat conducted across the one-unit cell thick sample was calculated by subtracting the stray heat loss from the total heat supplied.
keff=(qcond/A)ΔzΔT=({qtotalqloss}/A)ΔzT~topT~bot
(2)
qloss=kinstins[A(TTop,inTTop,out)+4bΔz(Tside,inTside,out)]
(3)
where, “A” is the lattice base area, “Δz” is the thickness of single unit cell of lattice, and “b” is the edge length of square cross sectioned lattice (Fig. 2). The stray heat loss venues involved the top wall insulation and the four side wall insulations. Thin thermocouples were secured at the inner and outer skins of the insulation to calculate the stray heat loss, with the knowledge of the thermal conductivity of the insulation material (Eq. (3)). This accounting of the heat loss ensured that the reported effective thermal conductivity is only a contribution of the unit cell topology, solid- and fluid-phase thermal conductivities, and lattices’ effective porosity.

2.2 Forced Convection Setup With Air as Working Fluid, and Heat Transfer Coefficient Calculation Procedure.

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.

Fig. 4
(a) Schematic of the experimental setup (not drawn to scale), (b) zoom-in view of heat transfer section, and (c) additively manufactured sandwich-type Octet panel in SS316L
Fig. 4
(a) Schematic of the experimental setup (not drawn to scale), (b) zoom-in view of heat transfer section, and (c) additively manufactured sandwich-type Octet panel in SS316L
Close modal

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.

An array of ten equi-spaced thermocouple slots were incorporated (in the AM phase itself) along the streamwise length of the samples with a depth of W/2 and W/6 into the span of both endwalls sandwiching the lattice section, where W is the width of the panel obtained after joining the smaller AM parts as described above. Under the assumption that the temperature distribution would be symmetric about the channel centerline in the streamwise direction, the representative wall temperature at a particular streamwise location was then obtained by calculating the area-averaged temperature based on the two measurements carried at the span of W/2 (centerline) and W/6. A trendline for streamwise variation of wall temperature was obtained for both top and bottom walls, to get a continuous variation Tw(x) from the discrete measurements. Convective heat transfer coefficient at these discrete locations along the streamwise direction is given as
h(x)=qconvTw(x)Tf(x)
(4)

The local fluid temperature Tf(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.

2.3 Particle Heat Transfer Test Facility and Heat Transfer Coefficient Calculation Procedure.

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.

Fig. 5
Particle heat transfer test facility
Fig. 5
Particle heat transfer test facility
Close modal

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.

To address the above aspect, a novel quasi-steady-state heat transfer methodology was devised exclusively for this part of the investigation, which could effectively provide local convective heat transfer coefficient where heat transfer was facilitated through falling particles. In this approach, first the hopper is filled with desired type of particles where the total mass of particles was decided such that a packed bed flow could be achieved at the heat transfer test section. Once the hopper was charged with particles, the heating process was started where all the eight patch heaters occupying the entire 150 × 250 mm2 panel on both left and right sides of sandwiched panel were heated. Once the steady-state heat transfer condition was achieved, the particle flow through the Octet panel was initiated by opening the gate valve installed at the bottom of the heat exchanger to 100%. Note that this facility also allows a fine control over the particle flowrate through the gate valve while still maintaining a packed moving bed through the Octet panel. In this study, the maximum possible particle mass flowrate was studied, hence 100% opening of the gate valve was set. Prior to the particle flow start, the data acquisition system was initiated which involved over 20 thermocouple measurements across the heat transfer test section, including a pair of temperature measurements for particle inlet and outlet. Once the particles started to flow through the Octet panel, the walls of the panel started to cool down rapidly to a local minima. At that point onwards, the particle and the wall temperatures continued to slowly increase for the remainder of the transient experiment. The reason behind this phenomenon is explained above. In the heat transfer coefficient calculation, the wall and particle temperatures during this slow heat ramp-up period were taken into consideration and the local instantaneous convective heat transfer coefficient was determined through the following equation:
h(x,t)=qconv(t)Tw(x,t)Tf(x,t)
(5)
where qconv(t) is the heat convected away from the walls via the particles in motion and this was obtained by subtracting the local heat losses from the backside of the eight patch heaters occupying and supplying constant heat flux on the left and right sides of the panel. The instantaneous local particle temperature Tf(x, t) was determined by linear interpolation between inlet and outlet particle temperature measurements, a procedure similar to the one followed for air-based experiments described above. Note that the temperature drop across the insulation material was measured at multiple locations along the streamwise length and also recorded along with the wall temperature at the same frequency throughout the transient operation. The heat loss however was minimal compared to the total heat supplied.

3 Particle Size Distribution and Particle Packing in Additive Manufacturing Lattice Parts

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].

Fig. 6
Particle size distribution
Fig. 6
Particle size distribution
Close modal

4 Uncertainty Analysis

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.

5 Results and Discussion

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

5.1 Effective Thermal Conductivity (keff).

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 keff 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 keff 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 keff 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 keff was a strong function of solid-phase intrinsic thermal conductivity and the lattice porosity. A suitable normalization of keff/ks collapses different ks samples onto one curve. A comparison is shown for keff/ks 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.

Fig. 7
Effective thermal conductivity of Octet lattice (void space occupied by air)
Fig. 7
Effective thermal conductivity of Octet lattice (void space occupied by air)
Close modal

The third set of keff 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 keff 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.

Fig. 8
Effective thermal conductivity of Octet lattice (void space occupied by particles) and keff enhancement factor (η) with respect to packed bed of particles
Fig. 8
Effective thermal conductivity of Octet lattice (void space occupied by particles) and keff enhancement factor (η) with respect to packed bed of particles
Close modal

Figure 8 also presents the relative enhancement in keff values (η = (keff)voidparticles/(keff)packed bed) for the lattice when particles were packed in void space in reference to a packed bed of particles. This enhancement in keff 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.

5.2 Forced Convection With Air as Working Fluid.

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 (keff), 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.

Fig. 9
Heat transfer coefficient in the periodic regime, variation presented with respect to average air flow velocity (measured at the inlet of the porous section) (channel diameter-based Reynolds numbers varied between 3000 and 13,000 for SS316L and SS420 samples)
Fig. 9
Heat transfer coefficient in the periodic regime, variation presented with respect to average air flow velocity (measured at the inlet of the porous section) (channel diameter-based Reynolds numbers varied between 3000 and 13,000 for SS316L and SS420 samples)
Close modal

5.3 Forced Convection With Particle as Working Fluid.

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 [1719,27].

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 (dp—266 μm), CARBOBEAD-CP 30/60 (dp—397 μm), and CARBOBEAD HSP 20/40 (dp—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.

Fig. 10
Transient convective heat transfer coefficient at five different locations in the streamwise direction for three particle types (Octet panel porosity of 0.88, SS316L): (a) CP 40/100, (b) CP 30/60, and (c) HSP 20/40
Fig. 10
Transient convective heat transfer coefficient at five different locations in the streamwise direction for three particle types (Octet panel porosity of 0.88, SS316L): (a) CP 40/100, (b) CP 30/60, and (c) HSP 20/40
Close modal
Fig. 11
Time-averaged heat transfer coefficient in the periodic heat transfer regime, variation presented with respect to particle diameter
Fig. 11
Time-averaged heat transfer coefficient in the periodic heat transfer regime, variation presented with respect to particle diameter
Close modal

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.

Fig. 12
(a) Time-averaged convective heat transfer coefficient variation with streamwise location and (b) enhancement factor of heat transfer coefficient with respect to streamwise location
Fig. 12
(a) Time-averaged convective heat transfer coefficient variation with streamwise location and (b) enhancement factor of heat transfer coefficient with respect to streamwise location
Close modal

6 Conclusions

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.

Acknowledgment

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.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

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

Nomenclature

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)

hp =

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

hsCO2 =

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

keff =

effective thermal conductivity (W/mK)

kHX =

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

kins =

thermal conductivity of the insulation (W/mK)

ks =

solid-phase intrinsic thermal conductivity (W/mK)

qcond =

net heat conducted across the sample (W)

qloss =

stray heat losses (W)

qtotal =

net heat supplied to the lattice (W)

tHX =

thickness of the contacting channel wall (m)

tins =

thickness of the insulation (m)

RC =

particle contact resistance (m2K/W)

Tf =

working fluid temperature (°C)

Tside,in =

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

Tside,out =

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

TTop,in  =

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

TTop,out =

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

Tw =

wall temperature (°C)

UHX =

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)

Greek Symbols

ε =

porosity

η =

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

Abbreviations

sCO2 =

supercritical carbon dioxide

AM =

additive manufacturing

CSP =

concentrated solar power plant

PCHE =

printed circuit heat exchanger

SS =

stainless steel

TIG =

tungsten inert gas

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