A Scalable Compact Additively Manufactured Molten Salt to Supercritical Carbon Dioxide Heat Exchanger for Solar Thermal Application

Solar thermal power generation with thermal storage offers the possibility of using a renewable resource for baseload or peak-load electrical power generation. Over the past decade, there has been an impetus to use the supercritical carbon dioxide (sCO₂) Brayton cycle for power generation. To couple the power cycle with the solar field and storage, three pathways are being explored by several research groups based on different receiver designs. These include the gas, liquid, and a solid particle medium pathway. The liquid pathway is mature, with roots in the Solar II demonstration project, and has been successfully commercialized over three decades [1–4]. However, in place of the nitrate salt mixture, to achieve higher turbine inlet temperatures of 700 °C, chloride salts are being considered for sCO₂ solar thermal cycles with the liquid pathway. A two-tank system is typically employed, with the molten salt (MS) pumped from the cold tank through the receiver and stored in a hot tank. An MS-sCO₂ primary heat exchanger is needed to transfer the heat into the power cycle. The inlet temperature of MS into this primary heat exchanger (PHE) from the hot tank would be 720 °C, and the sCO₂ inlet temperature would be 500 °C at a pressure of 200 bar. The pressure drop across the sCO₂ side is to be kept below 2 % of the line pressure (i.e., < 4 bar) from a cycle efficiency consideration. The PHE needs to be designed for high effectiveness as well as for a low exit temperature of MS to reduce parasitic losses in the receiver sub-system. In addition, the PHE must be able to resist corrosion of the MS. There is a dearth of literature on designs of PHEs that meet these challenging operating conditions and constraints. Printed circuit heat exchangers (PCHE) represent a common architecture for high-effectiveness and compact heat exchangers that lend to high conductance.

The PCHEs in literature have typically been designed and demonstrated for the 500–600 °C range on the high side. While the designs are applicable to higher temperatures, fabrication difficulties pertaining to etching and diffusion bonding need to be addressed. Aakre and Anderson [5] experimentally tested a 316L stainless steel diffusion-bonded heat exchanger using solar salt (0.6 NaNO₃—0.4KNO₃) on the hot side and 160 bar sCO₂ on the cold side. The temperature on the salt side remained below 550 °C, because of salt degradation around 600 °C. Yao et al. [6] designed a 316 stainless steel MS-to-sCO₂ pillow plate heat exchanger consisting of a pattern of concave and convex regions to enhance heat transfer through boundary layer thickness reduction. The heat exchanger was designed for MS entering at a temperature of 520 °C and exchanging energy with sCO₂ at an inlet temperature of 335 °C. Shi et al. [7] developed microlaminated heat exchanger for this application with rectangular parallel channels on the cold side and airfoil-shaped fins on the hot side. While the design was for chloride MS to sCO₂, they fabricated the device using stainless steel and demonstrated it at lower temperatures in Wang et al. [8] using a ternary salt (Hitec) and a synthetic oil. While the design shows improvement over traditional PCHE designs with zig-zag channels, it should be noted that the challenges for such a PHE are in using the microlamination method of chemical etching and diffusion bonding for nickel superalloys such as IN740H and H282 that are needed for this application owing to their superior creep strength. Caccia et al. [9] developed a design for a cermet PCHE for this application. The Zirconium–Tungsten composite material considered in this study allowed for heat transfer at temperatures ranging from 600 to 800 °C, an operating pressure of 200 bar on the sCO₂ side and 1 bar for the molten salt, and an allowable stress of 125 MPa giving a factor of safety of 3 with respect to the material flexure strength of 370 MPa. They reported power densities of around 8.2 MW/m³ for the core, assuming straight parallel channels having a semi-circular cross section. Montes et al. [10] investigated the optimization of the PCHE at the junction between a solar field and supercritical CO₂ power cycle under three different configurations recompression, intercooling, and partial-cooling. Their techno-economic analysis targeted an MS-to-sCO₂ printed circuit heat exchanger made of Haynes 242, and it was concluded that the investment cost for the solar plant could be significantly reduced by optimizing the heat exchanger. The authors were able to achieve an effectiveness of 0.83 and thermal power of 103.4 MW-th for the optimized heat exchanger for the partial-cooling cycle configuration. In this configuration, they also observed a reduction in costs from 40.456 million dollars for the baseline to 7.924 million dollars for the optimized PCHE.

In recent years, metal and ceramics additive manufacturing (AM) has been investigated as a viable technique for the fabrication of heat exchangers combining high effectiveness and compactness, especially in applications with extreme conditions and high strength requirements. Singh et al. [11] designed a ceramic heat exchanger for concentrating solar power (CSP) applications. The use of ceramics for this application was justified by their superior physical properties and corrosion/oxidation resistance that make them desirable candidates for surviving applications involving corrosive fluids at high temperatures (up to 750 °C). The modeled geometry was optimized not only for heat transfer performance but also for stress constraints imposed by high pressures and temperatures. One notable advantage of the AM process is the ability to design integrated headers—a feature that eases the scalability of the design while reducing cost and increasing the power density of heat exchangers. In a follow-on work [12], the group printed silicon carbide heat exchangers’ samples, characterized their properties, and experimentally validated the thermal performance using streams of cold and hot air at temperatures varying from 42 to 250 °C. Gerstler and Erno [13] presented a multi-furcating heat exchanger printed by the method of direct metal laser melting with aluminum, Titanium 6–4, cobalt chrome, and Inconel 718. The AM prototype was tested and compared to a conventional heat exchanger for aviation applications, and the authors showed that the AM heat exchanger was able to achieve the same thermal performance as the conventional one with 50 and 66 percent reductions in volume and weight, respectively. This AM heat exchanger also has the added advantage of increased reliability due to the absence of braze joints. Zhang et al. [14] experimentally validated the ability to use a compact AM heat exchanger for a high-temperature application. The prototype was an Inconel 718 manifold heat exchanger that used nitrogen at 600 °C and air at 38 °C. A good agreement between numerical and experimental results was observed, along with a 25% heat transfer density enhancement compared to plate-fin heat exchanger. Methods of heat transfer enhancement through additive manufacturing have been investigated for various applications. El Achkar et al. [15] studied the performance of an additively manufactured plate-fin heat exchanger for phase change applications. Ning et al. [16] compared the performance of three additively manufactured compact heat exchangers for industrial applications, with different levels of design complexity. The study concluded that the highest heat transfer improvement was observed with the most complex design whose printing was made possible by additive manufacturing. This thermal improvement comes, however, with the penalty of pressure losses up to twice those of the conventional design. Kelly et al. [17] demonstrated the use of binder jet additive manufacturing for the fabrication of a triply periodic minimal surface (TPMS) heat exchanger with an ultra-high-temperature ceramic. The team estimated an achievable 50 MW/m³ power density for their MS-sCO₂ heat exchanger. Tano et al. [18] described the design of a compact MS-sCO₂ PHE for this application, fabricated using Haynes 282 and metal AM (Fig. 1(a)). The design consisted of multiple pairs of mm-scale pin arrays on the sCO₂ (cold) side and parallel channels on the MS side. The sCO₂ headers were located outside the MS path, resulting in a partial cross-flow region for sCO₂ flow at the entrance and exit of the core (see Fig. 2(b)), and a counterflow region in the rest of the core. The feasibility of printing the features in the core, as well as surface roughness characterization, was shown. A correlation-based model was used to present a parametric study of the impact of flow and geometrical parameters on the performance and cost of the PHE. Results indicated that designs with an effectiveness of 90% and power densities of 10.8 MW/m³, including headers, can be obtained for an exit hot side temperature of 550 °C. Because of the low flowrates on the MS side (Re < 50), the PHE design was heat transfer limited on the MS side, requiring core lengths of 80 cm to obtain an effectiveness of 0.90 and a high power density of 11.4 MW/m³. Scalability was possible in the lateral direction by increasing the number of pairs of hot and cold flow paths; however, scalability was not possible in the vertical direction of the build due to the location of the sCO₂ headers. The design by Tano et al. [18] will be henceforth referred to as the Gen 1 design.

The objective of this work is to present a design that is more scalable and compact than the Gen 1 design by innovations in the header design and the MS channel flow path. The overall PHE design is first presented highlighting its unique attributes, followed by a description of the details of the header design. One of the key advantages of AM is that it permits an integrated header-core design that enables compact designs and the elimination of failure at the joint. Integrity of the header–core interface is demonstrated by pressure tests on a sub-scale PHE. A simplified thermofluidic model, developed in prior work [18], is used to assess the performance of the PHE core using correlations developed from experimental and computational fluid dynamics (CFD) simulations. A cost model, also developed in prior work [18], is used to assess the variation in cost based on these parameter variations. The PHE performance is discussed over a range of flow and geometric parameter variations. The impact of AM machine features and design on cost is assessed.

A comparative view of the two designs is presented in Fig. 1 with the Gen 1 and 2 PHEs in Figs. 1(a) and 1(b), respectively. Both models are designed with nominal dimensions to fit the base plate of an EOS M290 (EOS GmbH) laser powder bed fusion printer. Details of the sCO₂ and MS flows in the core are shown in Fig. 2. The modifications relative to the Gen 1 design shown in Figs. 1 and 2 address the low heat transfer rate on the MS side, which hinders the compactness of the PHE, and the scalability of the design in the vertical build direction. As shown in Figs 1(d) and 1(e), the rectangular channels on the MS side in the Gen 1 design were replaced by a 3D lattice of pins that provide additional surface area for heat transfer while increasing the residence time and mixing of the fluid in the channel. This design modification is intended to decrease the thermal resistance on the hot side of the PHE; however, the more intricate flow path in the lattice structure (see Fig. 2(e)) is anticipated to increase pressure drop when compared to the parallel channel path in the Gen 1 design shown in Fig. 1(d).

The second design change pertained to the headers, which are different in shape but also location. As illustrated in Fig. 2(d), the new sCO₂ headers are aerodynamically shaped and integrated into the MS flow passages. By comparing Fig. 2(b) with Fig. 2(f), the less efficient cross-flow zones observed in Gen 1 are minimized in the Gen 2 PHE. Furthermore, the integration of the headers in the flow path allows for the scalability of the unit. The Gen 1 design (Fig. 1(a)) can only be scaled up by adding more plates in the depth (horizontal scalability) but with the Gen 2 architecture, it is now possible to achieve vertical scalability by building the stacks on top of the other. The overall length of a single Gen 2 stack, which conforms to the dimensions of the EOS M290 build plate, is 24 cm, including the headers. The sCO₂ pin array plates are 18 cm in total length and include 2.3-cm-long diverging and converging sections near the headers followed by a 13.4-cm-long rectangular section that is 5 cm tall. Twenty-six such pin array plates are assembled in the width to make up the stack with a nominal rating of 20.7 kW under the current design conditions. The MS side channel width is 1.8 mm, with a lattice of slanted pin fins, tilted 45 deg in both the flow direction and the transverse direction to form the three-dimensional periodic flow network (see Fig. 2(e)).

Figure 3 shows a summary of the design methodology which includes structural, thermofluidic, and cost considerations. A unit cell of the core was used for mechanical simulations, while a correlation-based model was used for fluid flow and heat transfer. Headers for the sCO₂ side were designed to ensure uniform flow distribution across each pin array and between the pin arrays, while also satisfying structural integrity. A process-based cost model was used to assess the impact of variables on cost.

In order for the header design to be viable, the sCO₂ headers would have to be made as compact as possible and of aerodynamic shape to reduce pressure drop on the MS side. The challenge with the compactness of the sCO₂ header are threefold: (1) there needs to be sufficient wall thickness to withstand the 200 bar internal pressure, (2) the flow distribution among multiple sCO₂ pin arrays needs to be uniform, and (3) the flow must be distributed uniformly across the lateral height within each pin array. Iterative simulations were performed between structural and fluid flow to determine the geometry of the header that would meet these requirements. The allowable stress in the design was restricted to a value of about 150 MPa, based on creep considerations using Haynes 282 [19] and the Larson Miller parameter approach [20] with a maximum temperature of 720 °C and a lifetime of 100,000 h. After conducting a static structural simulation of the header using linear periodic boundary conditions and applying the expected 200 bar pressure on the internal walls of the model, the final stress distribution showed a maximum equivalent stress of 168 MPa with most of the header subjected to stresses lower than 100 MPa.

Fluid flow simulations were performed in Ansys Fluent to ensure a uniform flow distribution from the sCO₂ header into each pin array. The modeled geometry is shown in Fig. 4(a). To manage the computational complexity of incorporating multiple pin array flow paths of the PHE core into the header flow distribution analysis, a porous media approach was employed, wherein the pressure drop in the core was modeled using inertial and viscous terms [21] based on CFD simulations of the pin array. The red boxed area in Fig. 4(a) identifies the region of the model defined as porous media. CFD simulations were run for different flowrates on a representative stripe of the pin array plate. A correlation between velocity and pressure drop was obtained. From this analysis, it was possible to derive the inertial and viscous parameters establishing an equivalence between the fluid flow in the pin array plate and in a section of porous media [18]. Due to the presence of bends and recirculation regions in the wake of the flow distribution features at the entrance of each pin array (see Fig. 2(f)), the k-omega shear stress transport (SST) turbulence model was used. Figure 4(b) shows the flow uniformity in terms of mass flowrate in each plate (primary ordinate) and the percent difference between the local and average mass flowrates (secondary ordinate) for total incoming flowrates of 50, 75, and 100 g/s. For reference, the 50 g/s incoming flowrate corresponds to a Reynolds number of 86,160 based on the inlet diameter and a Reynolds number based on the pin diameter of 1314 for the pin array. For all the flowrates considered, the mass flowrate into all pin arrays of the core was within 5% except for the one closest to the inlet, for which it was about 6 percent lower than average.

Upon verification of uniform flow into each sCO₂ pin array, the design of each pin array for flow uniformity across its width was performed. The final iteration of the design that ensured structural integrity and uniform flow distribution is shown in Fig. 4(c). Elongated ribs near the entrance of the pin array were added to ensure uniform flow distribution across the width. The streamwise velocity magnitude across the width of the pin array is plotted in Fig. 4(d) at three different axial locations corresponding to x/L = 0.1, 0.25 and 0.5. The percent difference relative to the mean velocity at the respective location is shown in the secondary ordinate in Fig. 4(d). In the diverging section near the inlet, at location x/L = 0.1, some flow non-uniformity is observed, with regions of higher velocity in the center of the pin array. However, once the flow enters the straight rectangular section of the pin array plate, the uniformity in flow distribution improves significantly at all locations across the plate height such that the highest value percent difference drops to below 3% (see x/L = 0.25 and 0.5 locations), indicating uniform flow distribution exists for a majority of the core.

One of the stated advantages of AM is the ability to design and fabricate integral header and core architectures for heat exchangers. In traditionally manufactured heat exchangers such as PCHE, the core is welded or brazed to the headers, and this could lead to potential failure locations at the header-core location, in addition to inefficient heat exchange in cross-flow sections. To experimentally verify the mechanical integrity of the integrated header-core architecture of the AM PHE, sub-scale PHEs specimens, with three pairs of hot and cold plates and headers, were designed and fabricated for accelerated testing at temperature. Additively manufactured 316L SS was used instead of H282 in order to accelerate time to failure and obtain results in a timely manner. Since the Larson–Miller analysis is an accurate description of the material behavior of metallic systems, the choice of material was dictated by testing expediency and powder availability. The design was intentionally weakened in the core to determine whether failure would occur at this weakened region or the header-core intersection. Both location and time to failure were of interest. If the failure occurred at the weakened section in the core rather than in the header-core section, it would corroborate the finite element analysis model and confirm that the PHE can be designed for the appropriate life considering the high-stress regions. If the time to failure at operating temperature matched the predicted lifetime based on a Larson Miller approach, confidence in the printing parameters and AM approach would be obtained.

Two different models of the sub-scale PHE were designed with varying degrees of weakened core regions. The first sub-scale PHE model for structural analysis, along with the imposed boundary conditions, is shown in Fig. 5(a) and the second design is shown in Fig. 5(d). For the first model, an entire row of pins was removed from the core, while for the second design, every other pin in the same row was removed. For both designs, a symmetry boundary was imposed on the top half pin plate and a 200 bar internal pressure was imposed on the sCO₂ pin arrays while atmospheric pressure was imposed on the MS side.

The results of the structural simulations in ANSYS Mechanical for the first design are shown in Figs. 5(b) and 5(c) and life estimations at different locations of Design 1 and 2 are summarized in Table 1. For the first design, the peak and average stresses in the unit are approximately 510 and 48 MPa, respectively, and it is seen that regions of higher stress in the 170 MPa range (and the peak of 220 MPa) exist at the entrance of the pin array in between the elongated flow distribution structures (see Fig. 5(b)). The stress in the region of the core with the removed row of pins is also similarly high; the regions of high stress are located in the surrounding pins facing the open row of pins. The high-stress regions in the pins surrounding the open core region are shown in Fig. 5(c). Based on the peak stress of 510 MPa in the design, the expected time for failure for a pressure of 200 bar and a temperature of 743 °C (highest operational temperature recorded during the experiment) was estimated to be less than 0.1 s, while the estimate based on the global average stress yield a rupture time of 8471 min (141 h). Since the high stresses observed in the simulation will relax in practice during the experiment, it was expected that the correct metric to predict the time to rupture of the unit should be a value bracketed by the 48 and 510 MPa stress estimates. To further this analysis, the average surface stress in the missing row region of each plate was calculated to estimate the expected life.

The average stress in row #3 of Table 1 was calculated as the average equivalent stress in the weakened region. It includes both the stress at the surface of the pins and in the solid. As another measure of the local stress, the surface stress at the surface of the pins in the top, middle, and bottom pin arrays in the weakened regions are reported in rows 4–6 of Table 1. The average stress in this region was 77 MPa with local surface-averaged values of 150, 177, and 167 MPa for the stress-concentration region in the top, middle, and bottom plates, respectively. Given the location of the absolute maximum stress and the local peak in each plate, the expectation of failure for this design was in the core region with the missing row of pins. Among the three local results considered, the average surface stress in the middle and bottom plates gave the most realistic estimate of time to rupture of 58 and 85 min, which compare well with the experimental results described in the following section.

The stress distribution in the second design is shown in Fig. 5(e). As with the first design, it is seen that there are regions of high stress near the entrance to the pin array in between the elongated flow distribution structures and the peak stress in this region is similar to that in the first design. The high-stress regions in the core row with every other pin removed are shown in Fig. 5(f). As with the first design, the high-stress zones are in the pins surrounding the regions where the pins have been removed. The peak stress in this region is 376 MPa with an average of 115 MPa in the middle plate. Compared to the first design, the second design exhibits less stress variation from one plate to an adjacent one. Based on the average surface stresses in this region, the time to failure for a pressure of 200 bar and temperature of 743 °C was estimated to be 10.6 h.

The two designs were printed using SS316 in a Trumpf TruPrint 3000 laser powder bed fusion printer. The majority of the volume was printed with laser power, scanning velocity, hatch spacing, and layer thickness of 220 W, 700.0 mm/s, 150 μm, and 30 μm, respectively, with additional contour, up-skin, and down-skin laser scans. A porous, net-like structure was printed below the specimens to support the bottom surface of the specimens during printing.

A picture of the pressure and temperature test facility is shown in Fig. 6. The facility consisted of a 500,000 BTU/h (165 kW) Maxon^® burner (Honeywell Process Solutions, Phoenix, AZ) that was connected to a test chamber using 21-in. circular stainless steel ducting lined with high-temperature rigid insulation. The circular duct wall was equipped with an active cooling scheme consisting of water-cooled copper coils integrated around the ducting, a water pump, and a small air-cooled radiator to dissipate the heat from the water. The test chamber was 3 ft × 3 ft × 2 ft (width × height × depth) and was made with ¼” wall thickness steel plate with high-temperature insulation lining the inner walls. The chamber was mounted on a strut channel frame with locking castors. The back and top walls were adjustable to permit the placement of the test article to be tested and for exhausting the combustion gases, respectively. The test article to be pressure tested was placed within the chamber, and it was connected to a high-pressure nitrogen source with high-pressure-rated tubing integrated with an electronically controlled pressure regulator and an electronically controlled three-way solenoid valve assembly. The solenoid valve assembly could be used to isolate the test article from the nitrogen cylinder upon application of pressure. Furthermore, it could be used to relieve pressure and re-pressurize the test article during cyclic pressure testing. A proportional-integral-derivative (PID) controller on the burner was wired to the control station located in an adjacent office space container where the experiments were monitored remotely. The burner controller enabled the adjustment of the fuel–air ratio and hence the test chamber set temperature.

During the pressure test, since the units were not stress-relieved, the test specimens were left attached to the build plate and sectioned apart as individual pieces for ease of testing. The experiments started by pressurizing the units at ambient temperature with a hold time at each set pressure. During the hold time, the unit was isolated from the pressure source to monitor the pressure for any decay indicative of a leak. All the above units passed the pressure test at ambient with 30 min hold time at the max pressure of 200 bar.

The elevated temperature testing started with the weakest design (Design 1), and a target temperature and pressure of 720 °C and 200 bar, respectively. The Design 1 unit was placed in the burner chamber, and five k-type thermocouples were inserted at different locations of the unit (as shown in Fig. 6). The time series of this unit body temperature (the average of all five thermocouples) and the unit internal pressure throughout the first round of testing are plotted in Figs. 7(a) and 7(b) shows a picture of the failed unit. First, the unit was heated up to the target temperature of 720 °C at atmospheric pressure. The unit was then pressurized in steps of 50 bar and 15 min hold time until the target value of 200 bar was achieved. The test proceeded until any potential failure sign could be noticed.

The first unit withstood a cumulative testing time of around 150 min before failing, with the last 35 min being at the highest pressure of 200 bar. Failure was characterized by an abrupt decay in the pressure observed while the unit was still at the target temperature, which is an indication of a leak. The test was stopped, and after the cool-down process, the unit was removed from the chamber for inspection. No visible sign of defect was observed on the external walls, but after pressurizing the unit with compressed air (6.9 bar) and applying soapy water, the approximate location of the leak was revealed to be adjacent to the location of the missing rows at the center of the part and between the sCO₂ plates (see Fig. 7(b)). The test was conducted a second time with a second identically printed sub-scale unit to ensure the repeatability of the experiment. The unit failed after about 57 min at the highest temperature and pressure. The leak test revealed that this unit failed at the core region and away from the header core. The second sub-scale design with alternate pins missing in two rows (Fig. 5(d)) was also pressure tested at temperature. Over a span of two days, the unit was under 200 bar pressure at 730 °C for over 11 h without any loss of pressure, at which point the test was concluded.

When compared with the simulation results, these experimental results reveal the following: (i) The prediction of failure location for the first design is consistent between the simulation and experiments and (ii) the predicted lifetime with the LMP approach using the maximum stress is an underestimate of the actual failure time while using the average stress is an overestimate. A local average of the surface stresses near the weakened location from the mechanical simulations seems to be the most accurate metric to predict the time to rupture. The experimental results also established confidence in the printing parameters and process.

Upon verification of the design of the header for flow uniformity and stresses in the prior sections, thermofluidic modeling and process-based cost modeling of the PHE core were performed. The correlations in the thermofluidic model were validated through pressure drop and heat transfer experiments on additively manufactured pin arrays for the cold side. Simulations were used to determine the flow and heat transfer characteristics on the hot side. The reliability of these correlations and simulations will also be validated in future work by conducting experiments on the full-scale PHE.

The correlation-based thermofluidic model presented by Tano et al. [18] for the core design shown in Fig. 2(a) was modified to reflect the changes made to the design in the PHE core. The objective of this simplified numerical model was to evaluate the thermofluidic performance of the heat exchanger over a wide design space efficiently. The inlet temperature and pressure of the fluid streams were kept fixed at 720 °C and pressure of 1 bar for the molten salt, and 500 °C and 200 bar for the sCO₂. As shown in Fig. 8, the PHE was divided into three main sections- diverging entrance section, a converging exit section, and the main counterflow region. The entrance and exit regions were not truly in cross-flow with MS; however, 5% of the length at the entrance and exit was modeled as cross-flow to account for a slight reduction in effectiveness in these sections relative to a pure counterflow design. The main counterflow section was further discretized to incorporate the effect of temperature-dependent properties.

A similar equation can be written for the cold side. The thermal resistance to heat flux on the hot side R_h″, and the heat transfer coefficient on the cold side, obtained from CFD and experiments, respectively, are discussed in Sec. 5.2. The local temperatures on the hot and cold sides were obtained through an iterative process. First, a guess was made on the outlet sCO₂ temperature, and the average temperatures on the hot and cold sides are obtained for the cross-flow 2 region. Next, a differential equation solver in matlab was used to obtain the temperature distribution in each control volume of the counterflow region, and finally, a procedure analogous to that used in the cross-flow 2 domain was employed to calculate the average temperatures in the cross-flow 1 section. At this stage, the inlet sCO₂ temperature could be calculated, and the result was compared to the known inlet temperature. The iterative process was terminated when the two values were within the specified tolerance of 0.01 °C.

Experimental testing of pin arrays with supercritical carbon dioxide: The heat transfer correlation used in the thermofluidic model on the sCO₂ side was experimentally verified using the setup illustrated in Fig. 9. The design of AM pin array heat sink used for sCO₂ heat transfer characterization is shown in Fig. 9(b). The pin array was laid out on a 5 cm × 10 cm footprint area connected to plena with fluidic ports to measure temperature and pressure on either side.

The line schematic of the CO₂ loop is depicted in Fig. 9(d). The main components of the test assembly included a tank containing liquid CO₂, a circulating pump designed specifically for high-pressure liquid CO₂ application and a preheater that converted liquid CO₂ to a supercritical state and sensibly increased the temperature to a desired inlet temperature before it entered the heat sink which rested on top of a heat flux meter. This flux meter provided heat to the test section through a set of cartridge heaters inserted at the bottom and controlled by an AC variable transformer (see Fig. 9(c)). When the heated CO₂ exited the heat sink, it was sent to a coil heat exchanger immersed in a glycol bath and cooled by a chiller. Upon becoming a liquid, the flow was directed through a Coriolis flowmeter and eventually back to the liquid CO₂ tank located upstream of the CO₂ pump. The fluxmeter and heat sink assembly were thoroughly insulated to minimize heat losses during the experiments.

The dimensions of two AM pin array heat sinks tested in this study are listed in Table 2. The pin fin rows, as shown in Fig. 2(c), were arranged in a staggered arrangement with respect to the flow direction. The non-dimensional heat transfer coefficient, Nusselt number, as a function of Re_Amin for the flowrates considered in the experiment as well as a comparison with three correlations in the literature—Prasher et al. [23], vortex and non-vortex shedding correlations by Rasouli et al. [24] are shown in Fig. 10. The Prasher et al. [23] correlation was developed for micro pin fin heat sink with staggered circular and square pin fins, and the Rasouli et al. [24] correlations were established using PF-5060 and LN₂ flows through diamond-shaped pin fin heat sinks (Table 3). The heat sink HS2 has dimensions designed so that vortex shedding was expected while HS1 has an aspect ratio that prevents the onset of vortex shedding at any location. As seen in Fig. 10, for the range of tested Reynolds numbers, the Nu number showed an increasing trend as predicted by the correlations, and for any given Re_Amin, the HS2 (designed to develop vortex shedding) resulted in higher Nu compared with HS1.

Comparing experimental results with predicted values by the correlations, it can be seen that the Prasher et al. [23] correlation better predicts heat transfer in cases where vortex shedding is expected, while the Rasouli et al. [24] non-VS correlation is more accurate for non-vortex shedding scenarios.

The results of pressure drop experiments in non-dimensional form (friction factor) are presented in Fig. 11 along with predictions from various pin array correlations from the literature. The literature correlations are listed in Table 3. The experimental friction factor in HS1 and 2, in agreement with correlation predictions, has a decreasing trend with an increase in Re_Amin. Compared with predicted values, it can be concluded that none of the correlations considered has an acceptable predictive capability, except the one presented by Rasouli et al. [24]. This correlation was developed based on results from eight-pin array heat sinks with diamond pin shape, machined on aluminum substrate with 2 cm × 2 cm footprint area. Seven of the eight samples had an aspect ratio between 1.5 and 3.2. The aspect ratio of HS2 falls in this range, and the friction factor is hence predicted with better accuracy (Fig. 11(b)) compared to HS1, whose aspect ratio is outside the range. The Rasouli et al. [24] correlation was therefore selected to predict the friction factor of the sCO₂ in the thermofluidic model.

Rasouli et al. [24] noted that for the tall and sparse pin arrays, enhancement in heat transfer was observed due to vortex shedding downstream of the pins while this effect was suppressed for denser or shorter pin arrays.

The friction factor was predicted using the Rasouli et al. [24] correlations

Due to the complex nature of the 3D lattice architecture on the hot side, CFD simulations were performed to obtain the thermal resistance for various Reynolds numbers. Figure 12 shows the simulation setup that consists of two computational domains—the fluid domain with MS and the solid domain of Haynes 282. A representative stripe of the array of slanted pin fins was modeled in lieu of the complete array to reduce the computational time. A constant heat flux of 40,000 W/m² was imposed on the top and bottom faces based on the estimated thermal rating of the full-scale PHE. The side faces were defined as symmetry boundaries. The flowrate at the inlet was varied to obtain simulation results as a function of the Reynolds number. The molten salt, whose temperature-dependent properties were obtained from Wang et al. [28], is a composition of 20 mol% NaCl, 40 mol% KCl, and 40 mol% MgCl₂. The simulations were performed using the k-omega SST turbulence model, and convergence was deemed achieved when all residuals were lower than 10⁻⁶ except the turbulent kinetic energy, which was of the order of 10⁻⁴.

For the two channel heights considered, a second-order polynomial was used to relate the thermal resistance to the Reynolds number, and a piecewise model was used for the friction factor as a function of the Reynolds number. The resulting correlations based on CFD simulations for two channel heights are listed in Table 4. Figure 13 shows that for both channel heights; the friction factor decreases sharply at low Re_Amin and at a slower rate after a Re_Amin of 12 and 17 for 1.8 and 1.0 mm channels, respectively. The friction factor increases by 43% from 35.7 for a 1.8 mm gap to 51.2 for 1.0 mm at Re_Amin of 20. The percent increase drops to 32% at Re_Amin of 35. The thermal resistance of the 1.8 mm channel is however higher, such that going from the 1.8 to 1.0 mm channel, the value of R″_h decreases by 27% on average over all Re_Amin. The resistance of the 1.8 mm channel decreases more rapidly with Re_Amin than the other configuration such that the percent change from 1.8 mm to 1.0 mm channel is only 16% at a Reynolds number of 35.

A process-based cost model (PBCM) was developed to estimate the heat exchanger cost (in $/kW-thermal or $/kW-th) for every variation of geometric and flow parameters considered [29]. The estimation process was performed by evaluating the constituent cost at every step of the production line including expenses associated with the material, equipment, labor, consumables, facility, utilities, and overhead. The model determines the overall cost after consideration of parameters for the PHE design, the facility operation, each step of the production and the individual expenses they generate. The PBCM consisted of the four following steps. First, a laser powder bed fusion is employed to print the heat exchanger layer by layer by melting metal powder under the action of a laser and allowing the melt pool to solidify according to the desired design. Next, a heat treatment step was implemented to relieve the stress generated in the printed element during the repeated melting-cooling sequences. The third step consisted of removing the base plate and supporting elements by means of a computer-controlled bandsaw. Finally, the heat exchanger was internally cleaned and smoothed by flowing an abrasive medium through the internal passageways. The cost estimate presented in Sec. 6 uses a AM printing parameter set of 700 mm/s velocity, 330 W power, and 0.11 mm hatch spacing. This conservative parameter set was selected because it consistently achieved high part density, low surface roughness, and good dimensional tolerance [18]. A discussion of increasing laser speed on the cost is discussed in the last section. A detailed description of the cost model is found in the study by Ziev et al. [29].

Based on the thermofluidic and cost models described in Sec. 5, a parametric study was conducted on the geometrical and flow parameters of the PHE to identify tradeoffs and design geometries that would lead to high power densities. The parameters were varied sequentially, holding all others at a baseline value, to isolate their impact on the performance. The varied parameters and their baseline values are summarized in Table 5. The baseline values for the hot and cold channel width (W_c and W_h) are the result of a compromise between the fin efficiency and the channel gap that will minimize manufacturing-induced flow obstruction. The pin diameter (D_pin), transverse pitch ratio (β_T), and wall thickness (t_w) were set from simulations on mechanical stress. The range of surface roughness was based on measurements of as-printed parts (upper limit) and the potential for reduction in roughness with surface treatments such as abrasive flow machining or other chemical treatments (lower limit). While all parameters were varied, only results for the parameters with the most impact on performance are presented in this section.

Figure 14 shows the impact of varying the flowrate of the MS (hot) stream relative to the sCO₂ (cold) stream, represented as heat capacity rate ratio C_r on the performance of the PHE with the baseline geometry indicated in Table 5. The impact of varying C_r on exit fluid temperatures and effectiveness is shown in Fig. 14(a), while the pressure drop and cost (in $/kW) are shown in Fig. 14(b). The sCO₂ flowrate is kept at 80 g/s, and the arrows on Fig. 14 show the direction of increasing the MS flowrate. The PHE with a 1.8 mm channel gap width on the hot side is represented by the filled symbols, and the 1.0 mm gap width PHE is depicted with hollow symbols. At an equal overall width of the PHE, the 1.0 mm gap will result in more plates and an increased heat transfer surface area compared to the 1.8-mm gap configuration. The PHEs with the two different channel gap widths show a similar trends in terms of effectiveness and outlet temperatures (Fig. 14(a)), and thermal rating (Fig. 14(b)). The 1.0-mm channel PHE has an effectiveness that varies from 0.81 to 0.90 compared to that from 0.79 to 0.89 for the 1.8-mm channel case. The better thermal performance of the 1.0 mm channel PHE is observed in the form of higher thermal rating (Fig. 14(b)) and power density. For example, at a C_r ratio of 0.93, the thermal rating and power density are 20.2 kW and 18.6 MW/m³ compared to 19.9 kW and 15.3 MW/m³, respectively, for the 1.8 mm case. This trend can be explained by the higher fin efficiency on the hot side for the 1.0 mm channel and the increased local velocity with narrower MS channels. The abrupt change in effectiveness observed at the two highest C_r ratios is due to a switch in C_min along the PHE. As the MS flowrate increases, however, C_min is consistently on the sCO₂ side for the subsequent cases. Figure 14(a) shows that an increase in MS flowrate is accompanied by an increase in T_co because the thermal resistance on the hot side decreases (as illustrated in Fig. 13). However, the increased velocity results in a decrease in residence time, which results in an increase in T_ho. A tradeoff exists between a high effectiveness and a lower T_ho, which is a desired feature to minimize parasitic losses in the system.

The two PHE designs are comparable in terms of pressure drop on the cold side (Fig. 14(b)); the slight difference observed (6760 Pa for 1.8 mm hot side versus 6783 Pa for 1.0 mm) results from the counteracting effects of lower flow per plate in the 1.0 mm PHE and a higher temperature and thus viscosity on the sCO₂ side. The pressure drop on the hot side, however, is several times greater for the narrower channel. For example, at a C_r of 0.93, the pressure drop through the 1.0 mm gap width is 7 kPa compared to 1.36 kPa for the 1.8 mm gap width. At a constant hot channel gap width, the volume of the heat exchanger remains unchanged; hence, the trends in cost (in $/kW-th) reflect the power rating variations. As the MS mass flowrate increases from 97 to 141 g/s, the power rating increases from 19.5 to 21.5 kW translates into a cost reduction from $460/kW-th to $419/kW-th for the 1.8-mm hot channel PHE. In the 1.0 mm case, a cost reduction from $434/kW-th to approximately $400/kW-th is achieved with a power rating enhancement from 19.9 to 21.7 kW.

Figure 15 shows the PHE performance as a function of L_HX, the total length of the PHE core. The exit temperatures of the streams and effectiveness trends with core length are shown in Fig. 15(a) while the pressure drops, thermal rating, and cost (in $/kW-th) are shown in Fig. 15(b). As the length increases, there is more surface area and residence time for heat exchange between the two streams as shown by the increase in temperature difference with T_ho decreasing from 552 to 542 °C and T_co increasing from 704 to 716 °C. The effectiveness increases 12% from 0.84 to 0.94 with core length. Although the thermal rating increases from 20.4 to 21.7 kW as L_HX changes from 16 to 35 cm, the volumetric power density decreases from 17.3 to 9.3 MW/m³ due to the increase in core volume from 1.18 to 2.32 dm³. The pressure drop follows a linear increase from 1360 to 2824 Pa on the hot side and 6327 to 11,400 Pa on the cold side. The non-monotonic trend in cost can be explained in terms of the different growth rates of the power rating and PHE volume with L_HX. As the length increases, so does the heat exchanger volume and the expenses related to material cost, and the other processing parameters. The additional cost is justified by the associated increase in power rating, as evidenced by the initial decrease in cost per kW. However, a point is reached at L_HX of 20 cm, where the power rating gain comes with a larger increase in material volume, thereby causing a rise in $/kW-th cost beyond L_HX of 20 cm from $434/kW-th for L_HX of 20 cm to $445/kW-th for L_HX of 36 cm.

The impact of the overall width (number of plates) on the PHE performance is shown in Fig. 16. The exit temperatures of the streams and effectiveness trends with core width are shown in Fig. 16(a) while the pressure drop, thermal rating, and cost (in $/kW) are shown in Fig. 16(b). The residence time increases with the number of plates in the PHE, since the total flowrate gets subdivided into more streams, and the PHE effectiveness increases from 0.848 to 0.88. The thermal rating improves from 20.5 to 21.1 kW, but the additional pairs of hot and cold streams translate into a volume increase, which causes a drop in power density from 19 to 10.9 MW/m³. The pressure drop decreases on both hot and cold sides due to a decrease in mass flowrate through each plate in the core with an increase in the overall width while keeping the total MS and sCO₂ flowrates constant. A cost reduction from $439/kW-th to $427/kW-th is observed because the increase in material cost associated with adding more plates is lower than the increase in power rating.

Figure 17 illustrates the influence of the peak-to-valley roughness R_z on the thermal performance of the heat exchanger. The R_z range was selected to span the values obtained from sample measurements on the sCO₂ side, before and after abrasive flow machining, and was modeled so that R_z effectively results in a reduction in the height of the pin array on the cold side. Due to the complex nature of the flow path through the 3D lattice on the MS side, the impact of surface roughness was not modeled on this side. The reduction in the minimum cross-sectional flow area A_min due to the channel constriction by surface roughness appears to have a prominent effect on the thermal performance by increasing the heat transfer coefficient on the cold side and reducing the thermal resistance. As a result, the effectiveness increases from 0.85 to 0.88 and the rating from 20.6 to 21.1 kW. The pressure drop on the cold side, however, increases significantly from 6.4 kPa to 11.8 kPa due to the constriction in the open channel area.

The effect of various parameters was considered in this study and based on the findings, it can be suggested that the most effective way to combine the advantages of high power density, low pressure drop and high effectiveness is by increasing the number of plates (larger W_max). Increasing the length of the PHE does increase the thermal performance of the PHE and lower the cost, but only up to the point when the increase in material volume and associated manufacturing costs match the gain in thermal performance, after which there is only a marginal increase in thermal rating and the trend in cost (in $/kW-th) reverses. The effect of increasing the flow length in the PHE has the adverse effect of increasing the pressure drop whereas an increase in the number of plates, at a constant mass flowrate lowers the pressure losses. The effect of surface roughness is less straightforward to incorporate at the design stage because roughness is not a parameter that can easily be monitored and predicted before printing. Further study is required to formulate accurate design guidelines, but a reasonable operation window can be specified based on the average size of the powder and available surface smoothing methods.

In this section, we explore the impact of changing PHE design and printing process parameters on cost. The cost in $/kW-th presented in the parametric study is based on the conservative set of parameters and a single-laser machine (print speed of 700 mm/s). However, high part density is obtained at higher print speeds and laser powers. A porosity map was generated from a build using H282 with various speeds and laser powers (see Fig. 18) with the motivation of operating within a “process window” for which low porosity is maintained regardless of small variations in local process conditions. Fourteen cube specimens printed with various speeds and laser powers were cross-sectioned, and around 20 to 50 optical micrographs were each taken from different parts of the cubes. The porosities which showed up as dark regions in the micrographs were segmented out, and the amount of bright region in the set of micrographs collected from a given cube was regarded as the part density for the given set process parameters. From the map, it is seen that very low porosities of 0.03%, obtained at the conservative printing speed of 700 mm/s can also be obtained at higher speeds of 959 mm/s and 1366 mm/s. Figure 19 shows a cost comparison between Gen 1 [18] and Gen 2 PHEs for two printing speeds (959 and 1366 mm/s) and three commercially available machines: the EOS M290 which is a single-laser machine currently used for the printing of the articles tested in this study, the EOS M400–4 machine with four lasers, and the SLMNGXII600 twelve-laser machine equipped with a system that reduces the setup/teardown and heat-up/cool-down time.

The results reveal that switching to the Gen 2 PHE design results in more than two-fold cost reduction for all the printers investigated. The cost reductions are primarily driven by reduced material used per kW and reduced printing costs per kW. The reduced printing costs per kW are related to the reduced material used because melting less material requires less time. Additionally, printing at higher speeds and with more advanced printers that have more lasers reduce printing costs by reducing the time required to melt the material. These reductions in cost show diminishing returns with respect to printing speed because the print time-related costs only account for a portion of the total cost. Costs associated with machine setup, pre-heating, cooldown and part removal time and post-processing costs are not affected by the reducing in printing time. It is seen that the Gen 2 design reduces the PHE cost by 2.8 times for the baseline print speed of 959 mm/s. A further 22 percent decrease in cost, to $185/kW-th, can be obtained by using the twelve-laser machine.

Design of a compact, scalable additively manufactured (AM) primary heat exchanger for solar thermal applications was presented. The design is compared against a recent design in literature from Tano et al. [18], referred to as Gen 1 design. The key design novelties include (a) a lattice structure in the MS flow, which increases the heat transfer rate on the side with the largest thermal resistance, and (b) incorporation of sCO₂ headers within the MS path. The latter results in a near-counterflow arrangement for the PHE and a design that can be scaled in two dimensions.

The structural integrity of the header-core junction was assessed and validated by conducting experiments at a pressure of 200 bar and a temperature of 730–743 °C on AM 316 stainless steel printed sub-scale specimens. A comparison between the structural simulations and the experimental results revealed that the maximum stress used as design parameter is quite conservative. A more realistic value to consider is an average surface stress localized around the stress-concentration zone.

Thermofluidic and process-based cost models were used to determine the impact of variation of geometric and flow parameters on the performance and cost of the PHE. The results show that a factor of 2.8 times reduction in cost can be achieved by the Gen 2 design, with power densities as high as 18.6 MW/m³ (including headers) for an effectiveness of 0.88.

Pathways to cost reduction by increase in print speed and industrial-scale AM machines were presented. The largest cost reduction is achieved by the design changes, followed by increase in print speed from 700 mm/s to 959 mm/s. While the presented design was for MS to sCO₂, the design can be readily adapted for solid particle medium to sCO₂ heat exchangers, with particles flowing through the lattice channels.

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-EE0008536. Simulations of the unit cell core were performed using computational resources sponsored by the Department of Energy's Office of Energy Efficiency and Renewable Energy and located at the National Renewable Energy Laboratory. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

There are no conflicts of interest.

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

f =

Darcy friction factor

h =

average heat transfer coefficient (W/m²-K)

t =

thickness (m)

C =

heat capacity rate (W/K)

H =

height (m)

L =

length (m)

$m˙$ =

mass flowrate (kg/s)

R″ =

thermal resistance (K-m²/W)

c_p =

specific heat capacity (J/kg-K)

k_w =

wall conductivity (W/m-K)

A_cr =

footprint of cross-flow region, L_crH (m²)

A_min =

minimum flow area within the pin array (m²)

A_pin =

pin half surface area, =0.5πD_pinH_pin (m²)

A_surf =

pin array footprint area (m²)

A_w =

wall surface area not including the pins (m²)

C_r =

heat capacity rate ratio

D_Amin =

heat sink hydraulic diameter based on A_min and P_min (m)

D_h =

hydraulic diameter based on pin fin size (m)

D_pin =

pin fin diameter (m)

P_min =

wetted perimeter associated to A_min (m)

N_plates =

number of plates in the heat exchanger

N_pin =

number of pin fins in the array

N_row =

number of pin fins rows in the flow direction

R_z =

peak-to-valley roughness (µm)

S_L =

longitudinal pitch (m)

S_T =

transverse pitch (m)

W_max =

overall width of heat exchanger core (m)

AM =

additive manufacturing

H282 =

Haynes 282

HX =

heat exchanger

IN740H =

Inconel 740H

MS =

molten salt

Nu_Amin =

average Nusselt number based on D_Amin

Nu_Dh =

average Nusselt number based on hydraulic diameter

NTU =

number of transfer units

PCHE =

printed circuit heat exchanger

PHE =

primary heat exchanger

Pr =

Prandtl number

Re_Amin =

Reynolds number based on D_Amin

Re_Dh =

Reynolds number based on hydraulic diameter

sCO₂ =

supercritical carbon dioxide

UA =

overall heat transfer conductance (W/K)

α =

aspect ratio, $=Hpin/Dpin$

β =

pitch ratio, =S_L/T/D_pin

ɛ =

heat exchanger effectiveness

  η_pin =

fin efficiency

c =

cold

co =

cold outlet

cr =

cross-flow

h =

hot

ho =

hot outlet

versus =

vortex shedding

w =

wall