A review of printed circuit heat exchangers for helium and supercritical CO2 Brayton cycles

Printed circuit heat exchangers (PCHEs) are a promising technology for helium and supercritical CO2 Brayton cycles due to their highly compact construction, very high heat transfer coefficients, capability to withstand high pressures and wide range of operating temperatures. The purpose of this review is to provide a comprehensive understanding of the performance of PCHEs based on available literature and survey of heat exchangers currently available on the market. First, the fundamental principles, including material selection, manufacturing and assembly, are introduced. Then, PCHEs with different flow passages are summarized and analysed along with their heat transfer and pressure drop characteristics. Next, geometric design optimisation of PCHEs is summarised and discussed, taking into consideration the complex relationships between heat transfer enhancement and pressure drop penalty, compactness and fluid inventory as well as capital cost. Finally, knowledge gaps are identified and suggestions for further research to address these for a wider range of applications are presented. The review covers relatively new heat exchangers on the market as well as designs that are still under development. Although extensive work has already been done in this field, and PCHEs are well established in the petrochemical industry, significantly more work is needed to increase their attractiveness for a wider range of applications. This work should be aimed at the optimisation of flow passage configurations in terms of thermohydraulic performance, complexity and manufacturing costs, development and selection of materials to increase further the range of high temperature and pressure operation, and the development of more generalised correlations for performance prediction and overall design optimisation.


Introduction
For power generation and heat to power conversion systems, advanced nuclear reactors have attracted the attention of various scholars in the field of future energy technologies, due to the global increase in electrical energy demand, environmental concerns, economic benefits and the multi-purpose potential application of this technology [1]. A gas-cooled fast reactor scheme from 4th generation nuclear systems is shown in Fig. 1. Its reference value of coolant inlet/outlet temperature and pressure is 490°C/850°C and at 90 bar, respectively. This can be achieved through the Rankine cycle with high pressure steam generators, the Brayton cycle with helium gas turbines, or the supercritical CO 2 Brayton cycle [2]. The helium Brayton cycle has been primarily envisioned for electricity production and actinide management due to its closed fuel cycle and excellent actinide management capability. Since helium typically has a low heat transfer capability due to its low volumetric thermal capacity and low thermal conductivity, a compact heat exchanger with a high surface-area-to-volume ratio is advantageous for thermal energy transfer [3,4]. Due to its potential for high electricity generation efficiency, the supercritical CO 2 Brayton cycle, has also attracted significant attention in recent years for high temperature heat to power conversion applications [5,6]. A supercritical CO 2 with low viscosity and high thermal conductivity can result in good compatibility with standard materials, lower compressive work, good tolerance and robustness with the turbine and compressor and good availability for heat sinks and sources due to the relatively low temperature required for maintaining the supercritical condition [7][8][9][10]. In such power generation and conversion systems, the efficiency of the electricity generation is critically dependent on heat exchangers, which are key components in transferring the thermal energy, and can be used as the heater, condenser, gas cooler and recuperator. Among the various types of heat exchangers, the printed circuit heat exchanger (PCHE) is a good candidate for heat sourcing and sinking of helium and supercritical CO 2 due to its favourable attributes of high compactness and structural rigidity, high efficiency and effectiveness, and its reliable performance under conditions of extreme pressure and temperature.
PCHE, also known as diffusion-bonded microchannel heat exchanger, or compact platelet heat exchanger, is a promising heat exchanger technology. The concept of the PCHE was originally invented at the University of Sydney in the early 1980s and was commercialised by Heatric in Australia in 1985 [11][12][13]. For PCHE, the flow passages are manufactured by photochemical machining into a flat plate, with the plates then stacked together and diffusion bonded. This manufacturing process is similar to that used for the manufacture of electronic printed circuit boards, hence the common description as PCHE. Photochemical machining, also known as photochemical milling or photo etching, is one of the least-well-known non-conventional machining processes. It employs chemical etching through a photoresist stencil to remove material over selected areas [14]. Diffusion bonding, also known as diffusion welding, is a solid-state welding technique by which two surfaces are bonded together under high temperature and mechanical pressure in a vacuum or non-oxygen environment wherein the atoms of two solid, metallic surfaces intersperse themselves over time [15]. As a result of these two advanced techniques, PCHEs have a compact and high-integrity core making them suitable for high pressure and high temperature applications. Recently, more manufacturers have also entered the compact heat exchanger market, including HEXCES, VPE and Alfa Laval. Fig. 2 shows a typical PCHE and its diffusionbonded core.
In recent years, new frontiers have been opened up for PCHE designs and applications, particularly for supercritical CO 2 and helium Brayton cycles. Several review papers have also been published in this area to present the state of the art. Ahn et al. [17] summarized the various layouts and development status of the supercritical CO 2 power cycle. Cheng et al. [18] and Cabeza et al. [19] reviewed the heat transfer and pressure drop of supercritical CO 2 flowing in channels, but both reviews were based only on results of experimental investigations and heat transfer correlations. Huang et al. [20] summarized the characteristics of flow and heat transfer in PCHEs based on experimental results and simulations but did not discuss material selection, manufacturing and assembly, and heat exchanger optimization methods. Overall, in previous works technical challenges related to the design and operation of PCHEs at high temperature and pressure have not been addressed in detail. PCHEs operating in these conditions require more detailed thermal and mechanical analysis and larger safety  1. A gas-cooled fast reactor scheme from 4th generation nuclear systems [1].

L. Chai and S.A. Tassou
Thermal Science and Engineering Progress 18 (2020) 100543 margins than conventional heat exchangers [21]. To contribute towards addressing these challenges, this review paper focuses on the fundamental principles of PCHE, including material selection, manufacturing and assembly, thermal and hydraulic performance, and optimization of the geometric design, all with the purpose of providing a comprehensive understanding of PCHEs, design considerations and their performance characteristics. Unlike the work of Huang et al. [20] that reviewed PCHEs by considering separately experimental studies and numerical simulations, the review in this paper considers in significant detail PCHE performance in terms of flow passage geometry and flow characteristics, material selection, manufacturing techniques and design optimisation.

Material selection
For helium and supercritical CO 2 cycles, the PCHE must be able to operate at elevated pressures and temperatures, limited by corrosion, oxidation and creep resistance of the selected materials [22]. For PCHE, the pressure and temperature differentials can result in high internal stresses, which can cause significant flow passage deformation leading to eventual failure of the PCHE [23]. Moreover, many current PCHEs employ 316/316L/347 stainless steel, which limits the operating temperature to 600-650°C due to creep and corrosion limitations [24]. For higher temperatures, PCHEs have to employ nickel-based alloys or titanium at much higher capital cost. Materials for diffusion-bonded PCHEs are summarized in Table 1. The choice depends on the requirements, including service conditions, pressure containment and corrosion, among others. In terms of safety considerations for PCHE applications in helium and supercritical CO 2 Brayton cycles, the research on material selection mainly focuses on thermal stresses and corrosion.
Creep is an important consideration in the design of PCHEs. Permanent creep deformation may occur in the compact flow passages, which can be detrimental on the thermohydraulic performance of the heat exchanger and may cause the compressor discharge gas passages to expand, thereby increasing the turbine backpressure and potentially impacting the safety of the whole system operation [25]. Oak Ridge National Laboratory (ORNL) and ATI Allegheny Ludlum have done much work on improving the performance of alloy materials for compact heat exchangers. Maziasz et al. [26][27][28][29] tested the creep resistance of a group of heat-resistant and oxidation/corrosion-resistant austenitic stainless alloys at high temperatures (650-800°C), covering Type 347 stainless steel and Alloy 120, 214, 230, 625, 740, 803, HR120 and AL20-25 + Nb. The results showed that standard 347 stainless steel cannot be used when the temperature exceeds 650°C, while alloys such as Alloy 214, 625, HR120 and AL20-25 + Nb can have very good properties for high temperatures, especially with careful control of microstructure during processing. Fig. 3 shows the SEM micrographs of standard 347 stainless steel and Alloy 625 to characterize the microstructural changes and to identify the precipitate phases forming during creep. For standard 347 stainless steel, Fe-Cr σ-phase at the grain boundary triple points formed after only 51.4 h creep at 704°C, while for Alloy 625, a relatively stable dispersion of Si-Mo-Cr-Ni M6C phase developed and remained stable along the grain boundaries even after 4510 h operation at 750°C and 100 MPa, indicating that Alloy 625 has significantly better creep resistance than the standard 347 stainless steel at temperatures higher than 700°C. Osman et al. [30] also found that thin foil specimens of 347 stainless steel had higher creep rates and higher rupture ductility than their bulk specimen counterparts and cannot be used at temperatures above 700°C. Evans et al. [31] employed both scanning and transmission electron microscopy to correlate microstructures with the creep behaviour of Alloy 625. A short-time heat treatment of the processed foils at 900°C was shown to produce the typical commercial foil microstructure and creep properties, indicating that Alloy 625 is an attractive potential alloy for use in the production of PCHEs for operation at high temperature. Li et al. [32] compared the maximum allowable stress of different materials such as Alloy 800H, HX, 230 and 617 at a high temperature (900°C) and suggested that Alloy 617 was the leading candidate material for high temperature heat exchangers. Klöwer et al. [33] also suggested Alloy 617 as a candidate material for 700°C power plants due to its combination of creep strength and good fabricability. However, Alloy 617 has not yet been approved by the ASME boiler and pressure vessel code  Table 1 Materials for diffusion-bonded PCHE. [34,35]. Work is on-going to develop a database for the composition refinement, mechanical properties, creep-fatigue, corrosion regimes, and microstructural and mechanical properties of Alloy 617 [36][37][38][39][40].
Corrosion is another important factor in material selection for PCHE, especially for supercritical CO 2 because helium is inert [41]. The previous research has focused on the oxidation performance and corrosion properties of compact heat exchanger materials in water vapour, moist air or exhaust gas. Comprehensive databases, selection rules, and design guidelines for high temperature alloys have been developed for thick-section pressure vessels and piping applications [24,26,27,42,43,44]. However, little research exists into the oxidation performance and corrosion properties at high temperatures for supercritical CO 2 . More recently, the University of Wisconsin-Madison, the Korea Advanced Institute of Science and Technology, and the National Energy Technology Laboratory, USA, have focused on research on the corrosion behaviour of alloys in supercritical CO 2 high-temperature environments. Anderson et al. [45,46] designed and constructed a facility for corrosion testing of materials in supercritical CO 2 environments at temperatures and pressures up to 650°C and 3925 psi, respectively. They first performed corrosion testing on ferritic steels NF616 and HCM12A, austenitic alloys IN 800H and 347 stainless steel, and a range of advanced concept alumina forming austenitic alloys in the temperature range of 450°C to 650°C and 3000 psi. Results showed that Cr and Al had profound influence on imparting corrosion resistance under these test conditions. Cao et al. [47] tested the corrosion behaviour of three austenitic alloys, 316SS and 310SS and Alloy 800H in supercritical CO 2 at 650°C and 20 MPa for 3000 h. Results showed that Alloy 800H exhibited the best corrosion resistance, followed by 310SS and 316SS, and that the oxidation of Alloy 800H and 310SS followed a diffusion-controlled parabolic growth law, while 316SS exhibited a higher oxide growth rate with more pronounced oxide spallation. Firouzdor et al. [48] studied the corrosion of four alloys at 650°C and 20 MPa up to 3000 h, specifically AL-6XN stainless steel and three nickel-based alloys, PE-16, Haynes 230, and Alloy 625. Results in Fig. 4 which presents a plan view of SEM images of the surface oxide morphology of Alloy 625 samples exposed to supercritical CO 2 for 500 h, 1000 h and 3000 h, show that Cr 2 O 3 oxide forms on the surface of the samples after 500 h exposure to high temperature and pressure CO 2 and protects the alloy from further corrosion. Lee et al. [49,50] investigated the corrosion and carburization behaviour of chromia-forming heatresistant alloys 800HT, 600 and 690, by exposing the alloys to 550°C, 600°C and 650°C at 20 MPa for 1000 h. For all alloys, a thin and continuous Cr 2 O 3 layer was formed on the surface, while the existence of an amorphous carbon layer was identified at the chromia/matrix interface. Below the amorphous C-layer, Cr-rich M 23 C 6 carbides were extensively formed in Alloy 800HT but not in Alloy 600 or Alloy 690. Rouillard et al. [51] studied the corrosion behaviour of different structural metallic materials for heat exchangers, typically one ferriticmartensitic steel T91 and several austenitic steels 316L, 253MA® and Alloy 800 under static supercritical CO 2 at 550°C and 250 bar. Results showed that the austenitic alloys were much more corrosion-resistant than T91. After 310 h, a thin protective Cr-rich oxide layer formed on the austenitic steels, whereas thicker, iron-rich, duplex scale grew on the ferritic-martensitic steel, which could be detrimental for the thermal conductivity of heat exchangers and, thus, the global cycle efficiency. Holcomb et al. [52] compared the oxidation behaviour of austenitic stainless steels and nickel-based alloys in supercritical water (726°C/208 bar) and supercritical CO 2 (730°C/207 bar). They found that nickel-based alloys in supercritical CO 2 did not exhibit much change with pressure, while nickel-based alloys in supercritical water had an increase in corrosion rate, with the log of the parabolic rate constant being proportional to pressure. Féron et al. [53] reviewed the corrosion behaviour of metals and alloys in supercritical fluids and concluded that oxidation and carburization in supercritical CO 2 may occur at between 450°C and 650°C for alloys. Nickel-based alloys with high chromium content were found to exhibit better corrosion resistance than stainless steel.

Manufacturing and assembly
The manufacturing process of PCHE begins with thin sheets of metal that are photochemically etched with specific design patterns before the individual platelets are accurately assembled and joined by a diffusionbonding process to form a compact, strong, all-metal structure containing complex internal passages that allow for precise flow control, fluid manifolding and metering features [54]. The manufacturing process is shown in Fig. 5. Firstly, photo etching creates unique platelet designs including channels, ridge, wall, side, end margin, and block end. This process employs corrosive oxidation of selected areas of metal and does not alter the internal structure of the metal or metal properties such as hardness, grain structure and ductility. The fluid flow passages of PCHE are mostly made of near-semicircular channels, with etch depth varying from 0.1 mm to 2.5 mm, and channel width varying from 0.2 mm to 5 mm. The passage shape may be corrugated or straight, depending on many factors, such as the working fluid to be used, the heat load, and the pressure drop requirements. The flexibility of the etching process can use any angle increments (1°or less) over a wide range, unlike fins, which are usually manufactured at set angles [56]. Secondly, platelets are accurately stacked in a clean-room environment by maintaining heat and pressure in a controlled atmosphere to remove surface impurities and to promote grain growth across the interface between components. Then, diffusion bonding is applied to form a monolithic part where the bonding of flow plates, taking place in a high-temperature, high-pressure environment with no melting or deformation of channels, ensures flow integrity and complete bonding of all plates throughout the stack. This process uses no interlayer, flux, or braze alloy, and the interfacial area between two metal flow plates becomes welded together as atoms intertwine with one another, allowing for the incredibly precise construction of the internal flow passages within the block. As a result, this creates an extremely highintegrity solid block of the parent metal that contains the internally bound flow channels running throughout the core of the block [57,58]. Table 2 lists the diffusion-bonding process parameters. Among these parameters, three bonding variables, the bonding temperature, the bonding pressure and the holding time, primarily govern the success or failure of diffusion bonding. The bonding temperature is typically 0.6-0.7 of the absolute melting point of the material being bonded. The bonding pressure must be sufficiently low with respect to the yield strength of the material so that no large-scale deformation of the parts to be joined occurs. Holding times can vary from a few minutes to several hours [59,60]. The final process is assembly with the inlet/ outlet flow distribution headers, which are welded on to the diffusionbonded blocks. In this process, much attention should be given to large thermal gradients and possible residual stresses from the welding process, which can result in separation in adjacent areas between the header and the diffusion-bonded weld joint. To reduce/avoid any potential thermal gradients and localized thermal stresses during welding, brazing may be employed to join external flanges and headers to the diffusion-bonded assembly.

Thermohydraulic performance
So far, there are four main types of PCHE flow passage that have been developed: straight channel, zigzag (or wavy) channel, channel with S-shaped fins, and channel with airfoil fins, as shown in Fig. 6. In this section, we will focus on the thermohydraulic performance of these four types of PCHE.

Straight-channel PCHE
A summary of studies on the thermohydraulic performance of straight-channel PCHEs is shown in Table 3 in chronological order.
Mylavarapu et al. [61,62,63] designed and built a high-temperature helium test facility at Ohio State University in 2008, with the primary purpose of investigating the heat transfer and pressure drop characteristics of PCHE. The test facility was designed to facilitate operation at temperatures and pressures up to 900°C and 3 MPa, respectively. A straight-channel PCHE, having ten hot and ten cold plates with twelve channels in each plate, was fabricated using Alloy 617 plates as shown in Fig. 7. A simplified steady state laminar PCHE computational model was developed, consisting of ten hot-side and ten cold-side plates, each 1.6 mm thick, with one straight channel per plate. Numerical investigations were conducted for various hydrodynamic entrance region parameters, such as incremental pressure drop number, apparent Fanning friction factor and hydrodynamic entrance length in a semi-circular duct. Results showed a much earlier Reynolds number of about 1700, marking the onset of transition from laminar to the transition flow regime and the non-dimensional hydrodynamic entrance length

Material
Determining the required temperature and time for a diffusion joint to form. Time Determining the required time for diffusion welding. Temperature Diffusion welding occurring in the same range as recrystallization, about 0.6-0.7 melting temperature on an absolute temperature scale. Pressure A certain amount of pressure needed to produce intimate contact between opposing asperities. Surface preparation A thin layer of electroplated or vacuum-deposited material to protect the surface. . For transition and turbulent flow through straight semi-circular channels, the correlations given by Gnielinski [69] and Abraham et al. [70] were suggested for estimating the Nusselt number and the Fanning friction factor. The Gnielinski correlation [69] was developed for circular pipes for 2300 ≤ Re ≤ 5 × 10 6 Chen et al. [65] developed two heat transfer correlations for their tested PCHE based on the steady-state experimental data using a direct method and an indirect method. The heat transfer correlation with a power function of the Reynolds number for a total of 182 data points on both the hot and cold sides, was proposed as The heat transfer correlation from a nonlinear regression approach for a total of 76 data points on both the hot and cold sides, were obtained as As shown in Fig. 8, comparison of the overall heat transfer coefficients (U) obtained from these developed correlations with experimental data shows good agreement. It should be pointed out that the conclusions above about equations 1-5 are from their operating temperature and pressure respectively larger than 85°C and 1 MPa, which are far away from the helium critical point (-267.96°C and 0.2276 MPa). When the operating condition near the critical or pseudo critical points, the above equations may not be applicable and should be modified by the effect of variable physical properties.
Researchers from Korea, China and India also studied the thermohydraulic performance of straight-channel PCHE, both experimentally and numerically. For experimental studies, Seo et al. [10] built an experimental rig, fabricated a straight-channel PCHE and carried out the thermohydraulic performance analyses for Reynolds numbers in the range of 100-850. Results showed that average heat transfer rate and overall heat transfer coefficient of the counter-current configuration were 6.8% and 10-15% higher, respectively, than those of the parallel flow. Increasing Reynolds number was shown to lead to improved heat transfer performance, but also to a larger pressure drop, while increasing inlet temperature did not affect the heat transfer performance but did slightly decrease the pressure drop. Empirical heat transfer correlations of the hot and cold sides using the modified Wilson plot method were proposed as  (6) and the Fanning friction factor correlation, represented by the function of the Reynolds number was developed as follows: The heat transfer correlations can be predicted from the experimental data within ± 7% error, while the friction factor correlation can be predicted within ± 8% error. Chu et al. [4] conducted a supercritical CO 2 experimental system and manufactured a straightchannel PCHE. They tested the effects of thermal properties, operating pressure and the pseudocritical point of CO 2 on the thermohydraulic performance of their PCHE and concluded that supercritical CO 2 had better heat transfer capability than water fluid, with the higher-pressure conditions leading to improved overall heat transfer performance, but operation at the transcritical state significantly reduced the thermohydraulic performance. The Nusselt number and Darcy friction factor correlations were fitted by experimental data in order to simplify the design process as follows.
For water turbulent flow: Re Pr 0.122 0.56 0.14 (8) For CO 2 in both the supercritical and transcritical states: For numerical simulation, Aneesh et al. [66] carried out three-

Fig. 7.
A straight-channel PCHE tested at Ohio State University [61]. dimensional (3D) steady-state conjugate heat transfer simulations to examine the effect of variation of thermophysical properties and operating conditions on thermohydraulic performance, using helium as the working fluid and Alloy 617 as the solid substrate. Results showed the almost same performance for the aligned and staggered arrangements of the hot and cold channels in the PCHE and a better performance for single than double banking. Kim et al. [67] proposed a mathematical expression for the conduction and convection thermal resistances of cross, parallel, and counterflow PCHEs with straight channels, based on an extensive numerical study. In their model, the conduction heat transfer between the hot and cold channels in the PCHE was characterized by the conduction shape factor and the convection heat transfer performance in the semicircular channels was also expressed as a function of Graetz number ( = Gz ). Fig. 9a and 9b show the effect of channel size and channel length, respectively, on the heat transfer effectiveness of the PCHE for three flow types. Among the three flow types, the counterflow type shows the best thermal performance, followed by the crossflow type, while the parallel flow type shows the worst performance.

Zigzag (or wavy)-channel PCHE
A summary of studies on the thermohydraulic performance of zigzag (or wavy) channel PCHEs is shown in Table 4 in chronological order.
In 2004, an experimental facility was built at the Tokyo Institute of Technology to investigate the thermohydraulic parameters of supercritical CO 2 for PCHE with zigzag channels. Nikitin et al. [71][72][73] investigated both experimentally and numerically the heat transfer and pressure drop characteristics of the zigzag-channel PCHE. The tested overall heat transfer coefficient varied from 300 to 650 W/(m 2 K), while the compactness of the heat exchanger core was about 1050 m −1 and the maximum power density approached 4.4 MW/m 3 . Based on the experimental and numerical results, empirical correlations for heat transfer coefficient and pressure drop factor were proposed using a power function as illustrated below: The calculation of Re is based on the channel hydraulic diameter. It can be noted that all four correlations are independent of Pr. However, the heat transfer coefficient should be associated with Pr, as a result of the change in the ratio of momentum diffusivity to thermal diffusivity, and so the above four correlations are not universal and their application is limited to the same geometry parameters and operating conditions as those of Nikitin et al. [71][72][73]. Ngo et al. [60,74] also realised this problem and ascribed these independencies to the narrow range of 0.75 < Pr < 1.04. To address this, a zigzag PCHE was investigated by varying Pr widely, from 0.75 to 2.2. The results confirmed Nusselt number dependence on Pr. However, the Fanning friction factor was found to be independent of Pr.
As shown in Fig. 10a and 10b, these empirical correlations can predict the overall heat transfer coefficient and pressure drop very well, with a standard deviation of ± 3% and ± 13.5%, respectively. Following on from the work at Tokyo Institute of Technology, Lee and Kim [79][80][81][82] from Inha University focused on the effects of the geometric parameters of zigzag flow channels on the performance of a PCHE based on 3D Reynolds-averaged Navier-Stokes analysis with the shear stress transport (SST) turbulence model. The studied geometric parameters included the channel angle, the ellipse aspect ratio of the channel, the ratios of the pitch and depth of the ribs to the hydraulic diameter of the channel, and four different shapes of channel cross section (semicircular, rectangular, trapezoidal, and circular) and configuration. The results demonstrated that the rectangular channel showed the best thermal performance coupled with the worst hydraulic performance, while the circular channel showed the worst thermal performance.
In 2008, a helium test loop was constructed at Korea Advanced Institute of Science and Technology to investigate the thermohydraulic performance of PCHE for application to helium high temperature gascooled reactors. Kim where ν s /ν b is the surface to bulk mean ratio of the viscosity. Finally, they used the numerical code to develop models for Fanning factor and Nusselt number for various geometries, including angle (from 5°to 45°), pitch length (between 12.3 mm and 24.6 mm), and diameter (from 1.51 mm to 2 mm) and developed correlations for Nusselt number and Fanning friction factor using local information produced by the numerical results, in the following form: where the constants a, b, c and d relate to the PCHE geometry and include the effects of angles, pitch, and hydraulic diameter. The relationship of Nusselt number to Reynolds number, and Fanning factor multiplied by Reynolds number to Reynolds number for a pitch of 24.6 mm and different channel angles is shown in Fig. 11a and b, respectively. Kim et al. [89] created a k-ɛ SST turbulence model with CO 2 real gas properties to develop Nusselt number and Fanning friction factor It should be noted that equations 27-30 are again independent of Pr, limiting their application to similar geometry parameters and operating conditions as those used by Kim et al. [89].
Researchers from USA, China and India have also carried out research in this field. For experimental studies, Chen et al. [88] fabricated a reduced-scale zigzag-channel PCHE using Alloy 617 plates for the heat exchanger core and experimentally investigated its pressure drop and heat transfer characteristics in the high-temperature helium test facility of Ohio State University. The maximum channel Reynolds number was approximately 3558, covering the laminar flow and laminar-to-turbulent flow transition regimes. Based on the experimental data, the heat transfer and pressure drop correlations were developed using the nonlinear regression method: These two correlations only apply to the similar geometry parameters and operating conditions as those used for their development. Comparisons between the experimental data of the zigzag channels and the results obtained from the straight-channel PCHE by Figley et al. [64] indicated that the zigzag channels can lead to two to three times higher heat transfer coefficient in the laminar flow regime and one-anda-half to three times higher in the transition flow regime compared to straight channels. For numerical studies, Ma et al. [86] and Khan et al. [87] conducted a 3D, laminar, incompressible and steady state model, respectively, to test the local heat transfer and pressure drop mechanism of zigzag-channel PCHE. They found that the local Nusselt number and friction factor at high temperature matched well with those at low temperature for Reynolds numbers larger than 900, and that the heat transfer and pressure drop both increased with an increase in the inclined angle within the range of 0-45°. Baik et al. [7] investigated the thermal performance of wavy-channel PCHE and the effects of the waviness factors, including the amplitude and the period, on the thermal performance. They concluded that wavy-channel PCHE can have significantly higher thermal performance than the straightchannel ones, mainly due to the increased area for heat transfer. To improve the performance of the zigzag-channel PCHE, Lee et al. [90] proposed a zigzag-type PCHE with inserted straight channels, as shown in Fig. 12, and conducted 3D numerical analysis with re-normalization group (RNG) k-ɛ model to examine its thermohydraulic performance. Through a comparison of the dimensionless factors, including Fanning friction factor, Colburn-j factor, and volume-goodness factor ( = G v j f 1/3 ), the zigzag channel with the inserted straight channel showed an advanced thermohydraulic performance that was better than the regular zigzag or wavy channel. For example, for straight-channel lengths varying between 0.5 mm and 2 mm, the heat transfer characteristics of 1 mm straight channels were quite similar to those of the zigzag channel, but the Fanning friction factors were reduced by 60% for all of the mass flow rates, resulting in a volume-goodness factor that was improved by 26-28% compared to that of the original zigzag channel. Yoon et al. [91] conducted two laminar CFD models for investigation of the effects of geometric parameters such as relative length ratio, zigzag angle and radius of curvature of bend on thermohydraulic performance. A single channel isothermal model was used to investigate friction factors, while a two-channel model was used to study the Nusselt number in zigzag channels and the effect of temperature-dependent fluid properties on the pressure loss. The results showed that the friction factor of the zigzag channel was mainly influenced by the zigzagchannel geometry, while Nusselt number was dependent on the overall heat exchanger design, including the plenum sections. Based on the extensive CFD analysis database, Nusselt number and Fanning friction factor correlations were developed by implementing a least squares method: for  Fig. 12. Zigzag-channel PCHE (a) zigzag channel, (b) with inserted 1 mm straight channels and (c) wavy channel [90].

Table 5
Representative thermohydraulic performance studies of PCHEs with S-shaped fins. is the relative length. These friction factor correlations are valid for 50 ≤ Re ≤ 2000, 5 < θ < 45°, 4.09 ≤ l R / D ≤ 32.73. For the above correlations, the unit of zigzag angle (θ) in the correlations is in radians.

PCHE with S-shaped fins
A summary of studies on the thermohydraulic performance of PCHEs with S-shaped fins is shown in Table 5 in chronological order.
In 2005, researchers from Tokyo Institute of Technology developed a PCHE with S-shape discontinuous fins and tested its thermohydraulic parameters using supercritical CO 2 . Tsuzuki et al. [92,93] carried out supercritical CO 2 turbulence CFD studies with an RNG k-ɛ model to investigate the thermohydraulic performance of PCHE with S-shaped fins. They considered different fin shapes and angles, assuming that the supercritical CO 2 was in local equilibrium for thermodynamic and transport properties [98]. Results showed that the fin angle greatly affected the pressure drop but it did not significantly affect the heat transfer performance. Using the relationship of heat transfer rates per unit volume against the pressure drop per unit length, they obtained an optimal flow channel configuration that had only one-fifth of the pressure drop of the conventional zigzag configuration with equal heat transfer performance. Ngo et al. [60,74] manufactured a PCHE with Sshaped fins and carried out tests in a supercritical CO 2 test loop to confirm its performance. A conventional PCHE with zigzag fins was also designed for comparison, which had the same free flow area, hydraulic diameter, and fin angle. Experimental results showed that the pressure drop factor of the PCHE with S-shaped fins was 4-5 times lower and the Nusselt number 24-34% lower than those of the zigzag fins, depending on the Reynold number, as shown in Fig. 13. Based on the experimental results, Nusselt number and Fanning factor empirical correlations were developed as follows: The calculation of Re was based on the channel hydraulic diameter. As shown in Fig. 14, these empirical correlations can predict the overall heat transfer coefficient and pressure drop well, with a standard deviation of ± 2.3% and ± 16.6%, respectively. Ngo et al. [94] determined the optimal fin and plate configuration for a PCHE with Sshaped fins using 3D CFD simulation and evaluated the thermohydraulic performance of the heat exchanger in a residential heat pump application [99]. Comparison with a conventional heat exchanger, the PCHE showed 3.3 times higher compactness, 37% lower pressure drop on the CO 2 side and ten times smaller volume on the water side. Comparison between experimental and numerical results of the performance of the PCHE showed a deviation of < 5% [100,101]. Tsuzuki et al. [95] used the validated RNG k-ɛ turbulence model for the development of supercritical CO 2 correlations around the pseudocritical point, where fluid properties change radically. Simulations with 20 different temperatures were performed with the fluid inlet temperature set 2 K lower or higher than the constant wall temperature for the cold and hot sides respectively. Based on the numerical results, Nusselt number correlations were developed for the cold (water)/hot (CO 2 ) sides: The deviations of the correlations were 1.47% for the water side and 0.90% for the CO 2 side. It should be noted that equations 38-41 were based on a single PCHE and thus only apply to PCHEs with similar geometric parameters. To further investigate the S-shaped fin effects, Tsuzuki et al. [96] conducted numerical parametric surveys with an RNG k-ɛ turbulence model to elucidate how the fin shape affects the thermohydraulic performance. The studied fin parameters including fin angle, overlapping length, fin width, fin length, and edge roundness. Fin angle proved to be the most effective parameter, a narrower fin can produce more heat transfer area per unit volume, but has worse fin efficiency than wider fins, while a longer fin can reduce the pressure drop that occurs due to the stream bend. Fin roundness at the head and tail edge of the fins has only minimal effect on heat transfer performance but greatly affects pressure drop. Methods to reduce pressure drop always lead to heat transfer deterioration and therefore, optimization parameters should be carefully selected considering thermohydraulic performance and manufacturing costs.
Following the work of Tsuzuki et al. [96], Zhang et al. [97] from the Ohio State University used multi-objective evolutionary algorithms for S-shaped fin optimization based on CFD simulations of nine S-shaped fin channel design models to maximize the heat exchanger thermal effectiveness and to minimize the overall pressure drop across the heat exchanger core. The selected shape factors for the S-shaped fin channel optimization were the fin angle and fin length and the objective functions were selected to be the heat transfer effectiveness and the pressure drop across the core. The optimization results indicated that the smallfin-angle channels with large fin length were able to reduce the pressure drop, while the large-fin-angle channels with small fin length were favourable in increasing the heat exchanger thermal effectiveness. They recommended the use of an S-shaped fin channel with 11.6°fin angle and 6.08 mm fin length for low pressure drop applications and 60°fin

PCHE with airfoil fins
A summary of studies on the thermohydraulic performance of PCHEs with airfoil fins is shown in Table 6 in chronological order.
In 2008, researchers from Pohang University of Science and Technology first proposed a PCHE model with several airfoil shape fins (NACA 0020 model). Kim et al. [75] numerically investigated the thermohydraulic performance of PCHE with airfoil fins compared with the continuous zigzag configuration. The results showed that the PCHE  [60].

Table 6
Representative thermohydraulic performance studies of PCHEs with airfoil fins.

Reference Test section description Test conditions Measured characteristics Typical description
Hot-side configuration with airfoil fins can achieve the same heat transfer performance with a pressure drop only one-twentieth that of a zigzag-channel PCHE. They attributed the equal heat transfer performance to the enhancement of the heat transfer area and the uniform flow configuration, while the reduction of pressure drop was due to the suppression of the generation of separated flow, owing to the streamlined shape. Kim et al. [106] performed sensitivity analysis with various design parameters to configure the optimal arrangement of airfoil fins by using CFD analysis for a supercritical CO where Re min is the Reynolds number at the minimum flow area and the calculations of Nu and Re are based on the channel hydraulic diameter. These three equations were developed for a specific PCHE and thus only applied to the geometry investigated. As mentioned earlier, airfoil fins can have improved thermohydraulic performance over zigzag fins when applied to PCHE with supercritical CO 2 as the working fluid. To further improve the thermohydraulic performance of PCHEs, researchers from Xi'an Jiaotong University in China focused on optimization and novel airfoil fin shapes. Xu et al. [103,104] numerically investigated the effects of airfoil fin arrangements on heat transfer and flow resistance with SST k-ε model and constant temperature boundary condition (60°C) for the top wall, bottom wall and fins. Comparison of parallel and staggered arrangements showed that the difference in Nusselt numbers between the two arrangements were quite small. However, the pressure drop per unit length in the staggered arrangement was much smaller than that of the parallel arrangement, concluding that staggered fin arrangement leads to better thermohydraulic performance compared to parallel fin arrangement. To further reduce the flow resistance, they recommended a sparse arrangement of fins and modified the head of the airfoil fin to be swordfish shape, as shown in Fig. 15. Ma et al. [105] investigated the manufacture of airfoil PCHE plate and the effect of the fillets formed on the end walls of airfoil fin during the photochemical etching process. They found that the fin end-wall fillet can increase the heat transfer and pressure drop because of small vortices formed at the leading and trailing edges of the fins. Chu et al. [108] investigated the geometrical parameters of airfoil fins (fin length, fin width, transverse pitch and longitudinal pitch) on the thermohydraulic performance of PCHE. Local thermohydraulic results showed that the heat transfer rate decreases due to the strong variation in the properties of supercritical CO 2 , but that the pressure loss remained almost constant along the main flow direction. Study of the pitch parameters indicated that a parallel distribution of airfoil fin can enhance the heat transfer with higher flow resistance, while a staggered distribution can improve the comprehensive heat transfer performance. Based on the numerical results, the Colburn factor and Darcy friction factor correlations of PCHE with distributed airfoil fins were fitted as follows: where Re in is the inlet Reynolds number. These correlations can predict the numerical results with a maximal error of < 5% within the range of applied Reynolds number. It can be found that these two correlations are independent of Pr, which make them be only applied to the same operating conditions as Chu et al. [108].

Optimisation
Heat exchanger optimization is an important field, full of challenges, involving many different optimization criteria. For supercritical CO 2 power cycles, heat exchanger design optimization is particularly important due to their high capital and operating costs [109]. In recent years, many researchers have undertaken significant work on the optimization of PCHE devices.
Lee and Kim [83] defined an objective function for the Euler number and the effectiveness of the heat exchanger for a geometric design of zigzag channel PCHE. The function included the ratio of the radius of the fillet to the hydraulic diameter of the channels, the ratio of wavelength to the hydraulic diameter of the channels, and the ratio of wave height to the hydraulic diameter of the channels. Following this, they updated their optimization method to a multi-objective genetic algorithm to find the Pareto optimal front [80]. This method employed two non-dimensional objective functions related to heat transfer performance and friction losses for a geometric design, including the cold channel angle and the ellipse aspect ratio of the cold channel. Kim et al. [106] suggested an objective function of Nusselt number to Euler number for the optimization design of PCHE with airfoil shaped fins, including staggered pitch, horizontal pitch and vertical pitch. Based on their objective functions, they obtained some optimal geometric designs for PCHE. Rajabifar et al. [110,111] and Chai et al. [112] also recommended the use of the ratio of Nusselt number to Euler number as Fig. 15. Motivation of optimization for PCHE with airfoil fins [103].

L. Chai and S.A. Tassou
Thermal Science and Engineering Progress 18 (2020) 100543 the objective function for the optimisation process. However, they did not present evidence of defined weighting of their objective function, assigning the same weight to heat transfer and pressure drop even though each made a different contribution to the overall performance of the heat exchanger, as pointed out by Kwon et al. [107]. Considering the convenience of the objective function for optimization design of PCHE and also the different contribution of heat transfer and pressure drop, Guo and Huai [113,114] where R g is the ideal gas constant for CO 2 . The local entropy generation rates were then integrated to determine the total entropy generation rate which was used as the objective function to study the influence of constraints such as mass flow rate, total length of heat transfer channel, thickness of the cold plate and the thermal conductivity of the plate on the overall performance of the PCHE. Facing the challenge of optimal design of PCHE, some researchers introduced the cost-based objective functions which gave reasonable weighting to heat transfer and pressure drop. Kim and No [78] employed the sum of the capital cost and operating cost as the objective function for optimization of the design of a zigzag-channel PCHE. Yoon et al. [102] used the objective functions of the total cost with the operating condition to compare straight channel, zigzag channel, S shape and airfoil fin PCHEs. Kwon et al. [107] also suggested the use of a costbased objective function for optimization of PCHE for the recuperator of a small-scale Brayton cycle. However, the problem of the cost-based objective function is that the capital cost and operating cost change significantly depending on the application and it is difficult to evaluate the accurate heat transfer and pressure drop contributions to the overall performance of the heat exchanger because of the uncertainties in empirical correlations.
PCHE is also a type of microchannel heat exchanger, and the zigzag configuration, S-shaped fins, and airfoil fins can be thought as passive methods for heat transfer enhancement. Therefore, the optimization used for microchannel heat exchanger with passive structures can be suitable for PCHE. Several experimental, numerical and theoretical studies have been carried out for the optimal design, and the optimization usually imposes severe constraints on the heat exchanger and system design for a given heat transfer rate. These constraints included the mass flow rate, pressure drop, fluid temperature rise, and temperature difference between fluid inlet and surface [116]. The optimal design methods are usually based on a given thermal resistance or a given pumping power or a given fluid flow rate. Singhal and Garimella [117,118], Gosselin and Bejan [119], and Canhoto and Reis [120] performed optimization methods based on the minimization of pumping power requirement to evaluate the heat transfer performance for a given thermal resistance. Tsai and Reiyu [121] and Liu and Garimella [122] established theoretical optimization models based on thermal resistance minimization to predict microchannel heat exchanger performance for a given pumping power. Promvonge et al. [123], Xia et al. [124,125], Chai et al. [126,127], and Zhang et al. [128] used the performance evaluation criteria to comprehensively access the heat exchanger for a given pumping power. The performance evaluation criterion (η) is defined as the ratio of the heat transfer coefficient of the optimal geometry to that of the reference at an equal pumping power by Webb [ where  [133], and Chai et al. [127] developed optimization methods based on entropy generation minimization proposed by Bejan [115] to study the optimization of thermal and hydraulic resistances for a given fluid flow rate or a Reynolds number. In addition to the optimization methods mentioned above, some interesting work has been done using genetic algorithms for optimization design of compact heat exchangers. Xie et al. [134] applied a generalized procedure based on ɛ-NTU and the genetic algorithm technique for the optimization of a plate-fin compact heat exchanger. The minimum total volume and total annual cost of the heat exchanger were taken as objective functions and the geometries of the fins were fixed while three shape parameters were varied for the optimization objectives, with or without pressure drop constraints. They concluded that the genetic algorithm could provide a strong auto-search and combined optimization capability in the design of heat exchangers. Mishra et al. [135] proposed a genetic-algorithm based optimization technique for crossflow plate-fin heat exchangers using offset-strip fins.
The optimization programme minimized the number of entropy generation units for a specific heat duty under given footprint constraint.
Their results demonstrated the application and importance of a design approach based on the second law of thermodynamics as well as the suitability of the genetic algorithm for optimization of complex heat exchangers. However, they also suggested that the optimum design was highly sensitive to some of the geometric parameters and that a small deviation from the optimum value may give a large degradation in performance. Bacellar et al. [136] presented a multi-objective genetic algorithm along with a segmented ε-NTU approach method for a multiscale analysis with topology and shape optimization for a full-scale heat exchanger design. The objective function was the entropy generation index ( = = NTU N UA S S gen ) from Ogiso [137], and the total fluid pumping power was used as a direct measure of the energy cost to deliver the objective function. They tested how the entropy generation varied with the different surfaces and how it affected the overall performance and obtained an optimally designed heat exchanger, which had a potential size reduction of more than 50%, with a similar reduction in pumping power compared to the baseline microchannel heat exchanger. The general flowchart of the optimization procedure for PCHE is shown in Fig. 16 and the general flowchart of the genetic algorithm is shown in Fig. 17.

Conclusions
Printed Circuit Heat Exchangers (PCHEs) extend the applications of compact heat exchangers where pressure, temperature or corrosion prevent the use of conventional heat exchangers. The all-welded construction of PCHEs manufactured from high-strength and corrosionresistant alloys makes them suitable for very high-temperature and high-pressure applications, while their highly compact construction and exceptionally high heat transfer coefficients make them a good choice for demanding thermal energy transfer applications. This paper provides a comprehensive review of PCHEs, covering material selection, manufacturing and assembly, types of flow passages, thermohydraulic performance, heat transfer and pressure drop correlations, as well as geometric design optimisation methods. The paper provides a good review of state of the art and identifies gaps for further research and development.
The main summary of the review is as follows: (i) PCHEs relate to high-strength, high-temperature materials. At operating temperatures lower than 650°C, 316/316L/347 stainless steel can be employed for the manufacture of PCHEs whereas for operating temperatures higher than 650°C, nickel-based alloys, such as Alloy 625 or 617, can safely be employed but at much higher capital cost. (ii) Creep and corrosion are the two most important factors influencing material selection, but very little experimental data is available for helium or supercritical CO 2 in high-temperature environments. (iii) Photochemical machining and diffusion bonding are the two main processes of PCHE manufacture. Photochemical machining provides flexibility in thermohydraulic design, and diffusion bonding forms a compact, strong, all-metal heat exchanger core. (iv) Four main types of PCHE flow passages that Fig. 17. General flowchart of genetic algorithm [136].

L. Chai and S.A. Tassou
Thermal Science and Engineering Progress 18 (2020) 100543 include: straight channel; zigzag (or wavy) channel; channel with Sshaped fins; and channel with airfoil fins, have been developed and tested at test facilities in the USA, Japan, Korea and China using helium and supercritical CO 2 as the working fluids. Their thermohydraulic performance has been investigated both experimentally and numerically. The test conditions for helium were 900°C and 3.0 MPa, while for supercritical CO 2 test conditions were 500°C and 20 MPa. Generally, PCHEs with airfoil fins showed best performance, followed by S-shaped fins and zigzag (or wavy) channel PCHEs. (v) Several authors have developed empirical correlations for the prediction of average heat transfer and pressure drop characteristics. However, most of the correlations were developed for a specific flow passage and using thermophysical properties corresponding to the average temperature and pressure at inlet and outlet conditions. (vi) Several optimization techniques for PCHE design have also been developed, usually based on the relationship between the Euler and Nusselt numbers and the cost-based objective function consisting of the capital cost of the PCHE and operating costs by assigning relative weighting factors to heat transfer and pressure drop for different operating conditions. Recommendations for further work to fill knowledge gaps include: a) Refinement of the composition of materials to improve mechanical properties and corrosion resistance for both helium and supercritical CO 2 for operation at temperatures and pressures, above 650°C and 200 bar respectively. b) Further optimisation of the geometry of PCHEs to simplify the design without compromising performance, in order to reduce the number and complexity of the fabrication steps and overall cost of manufacture. c) More experimental and numerical studies are required to enable accurate local heat transfer and pressure drop data to be obtained for the development of more universal correlations that are able to cover a wide range of geometry and flow parameters to facilitate the design and performance prediction of PCHEs.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.