Design and performance of a novel compact high-eﬀectiveness transparent-wall counter-ﬂow heat exchanger fabricated using additive manufacturing

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Introduction
There are numerous high-technology applications in which the science instruments need to be brought to low temperatures.Cryogenic cooling can be of interest for a number of reasons, ranging from thermal noise reduction to achievement of superconductivity or creation of ultra-cold test environments.For many applications, it is advantageous to locate the cooling source, e.g. a cryocooler at a distance away from the object to be cooled.Such "remote" cooling arrangements allow to reduce the disturbances transported from the cryocooler to a cooled object, which can be necessary for ultra-sensitive cold instruments, e.g.SQUID sensors in CERN's Antiproton Decelerator [2][3][4] and cryogenic mirrors of gravitational wave detectors (e.g.KAGRA [5][6][7] or the planned Einstein Telescope [8]).Moreover, the described spatial decoupling is useful when cooling has to be delivered to a harsh environment, e.g.HiRadMat and CHARM facilities at CERN [9][10][11].High magnetic fields and radiation levels inside these facilities may damage a cryocooler if it is located too close to the test areas, resulting in a deterioration of the cryocooler performance and reduction of its lifetime.
The remote cooling systems that consist of a cryocooler with a precooled fluid circulation loop were proposed in our previous work to address the aforementioned issues [12][13][14].Such an arrangement provides the needed spatial and mechanical decoupling between the cryocooler and the cooling interface while allowing to maintain an effective heat transfer between the two.The described remote cooling arrangements also form simpler cryogenic chains and require less cryogen compared to cooling solutions that use a bath with a cryogenic liquid.The latter aspect is important for the future large-scale cryogenic installations, which will provide cooling of superconducting radio-frequency (RF) cavities, RF-quadrupole structures and superconducting magnets in the next generation of particle accelerators, e.g. the Future Circular Collider [13,15].For these applications, it will be necessary to find a cooling solution that relies on a lower amount of cryogen, e.g.helium because its resources are limited.https://doi.org/10.1016/j.ijheatmasstransfer. 2023 Moreover, a wisely constructed remote cooling system allows to increase the power of the original cryocooler cooling source and to better distribute the cooling over a large area in a flexible manner.The resultant system with a cooling power of several Watts at 4.5 K can enable a more efficient pre-cooling of warmer stages of 3 He/ 4 He dilution refrigerators for novel quantum computers and offers a solution for cooling of rotating superconducting gantries for proton and heavy-ion cancer therapies [16][17][18].
The performance and often feasibility of the remote cooling systems is strongly dependent on effectiveness and compactness of the used counter-flow heat exchangers (CFHEXs).The high-effectiveness CFHEXs are also of key importance for the newly developed 40 K Reverse Turbo-Brayton (RTB) machines for applications in space, which enable ultra-low vibration cooling for the sensitive instruments (e.g.infrared detectors) as well as high-capacity broad-area cooling for zero-boil-off arrangements [19][20][21].Moreover, RTB coolers allow to reduce the complexity of the designed cryo-chains and can be further extended to a multi-stage configuration to achieve even higher cooling powers targeted by various space missions [22][23][24].The RTB technology has previously been demonstrated in flight on NASA's Hubble Telescope (cooling below 80 K) and on board the International Space Station within ESA's MELFI freezer (cooling to −80 • C) [25,26].A cryogenic RTB cooler does not yet exist in Europe and is currently under development within a Technology Research Programme of the European Space Agency.
A highly performant mesh-based CFHEX design was proposed for the remote cooling and RTB applications in earlier work [1,12].An effectiveness of 94.9% (corresponding to a number of transfer units, NTU of 19) in the 40 K-290 K temperature range has been experimentally achieved.This result outperformed the experimental NTU values of up to 16 reported in literature for mesh-based CFHEXs [27,28].The performance analysis of the constructed CFHEX suggested that an even higher effectiveness would be achieved if it were possible to fully eliminate the inner tube-to-mesh interface [1].This served as a motivation for the development of an innovative CFHEX concept with a transparent (in terms of thermal resistance) inner tube (or an inner wall1 ), which separates the fluid streams.In such a CFHEX, the mesh would traverse through the inner wall without being interrupted or cut, resulting in a lower thermal resistance between the two fluid streams and a tremendous increase in effectiveness.Even though the performance of such a CFHEX is evidently very promising, compact transparent-wall cryogenic CFHEXs of this type are not being presently accomplished as such a design presents a great manufacturing challenge.
This paper presents a novel compact transparent-wall CFHEX design with its challenging manufacturing methods and underlying testing.Two transparent-wall CFHEXs are sized and the experimental arrangements used to measure their performance are presented.The CFHEXs are tested with helium as the working fluid in the 4.8 K-290 K temperature, 1 bar-5 bar pressure and 50 mg/s-250 mg/s mass flow rate ranges. 2 Remarkable effectiveness values of 97.5 %-99.2 % (NTU=39-124) have been experimentally achieved with a pressure drop of less than 10 mbar per stream at the nominal operating conditions of the remote cooling system.The predicted and experimental results, notably the pressure drop and effectiveness of the constructed CFHEXs are presented and compared.

Remote cooling system
The newly developed high-effectiveness mesh-based CFHEXs are sized to enable the system that is depicted in Fig. 1.This system serves as a technology demonstrator of the remote cooling principle.The presented arrangement consists of a cooling source (i.e. a cryocooler) and a helium circulation loop.The latter is constructed to be operated at the nominal conditions of the remote cooling system, which are indicated in Fig. 1.The method used to define the operating conditions is described in the previous work [12].During the operation, a high-pressure (HP) helium stream at 5.3 bar enters the loop and passes through a series of pre-cooling counterflow (CFHEXs 1, 2 and 3) and cryocooler stage heat exchangers.Once the HP fluid exits the coldest CFHEX 3, it undergoes an isenthalpic expansion in a Joule-Thomson (JT) valve in which a twophase saturated fluid at around 4.5 K is produced (the exact temperature is determined by the outlet stream pressure and the pressure drop of the 2 Test temperature range is justified in Sec.7.2.return line).Due to the JT effect, the additional useful cooling power is generated and the heat can be deposited at the experimental cooling interface (CIF) at the saturation temperature until the dryout condition is reached.The cold returning low-pressure (LP) fluid at 1.3 bar is then used to pre-cool the incoming HP stream in the CFHEXs.The CIF can be located in a remote envelope at a distance away from the cryocooler, thereby demonstrating the remote cooling principle.Both remote and cryocooler envelopes are surrounded by radiation shields that are cooled to approximately 40 K by the 1 st stage of the cryocooler, are fully closed and covered with a 20-layer multi-layer insulation (MLI) blanket.
The CFHEXs in the arrangement in Fig. 1 need to be highly performant to achieve the temperature of 4.5 K at the remote CIF with the chosen cooling source.Their effectiveness should be above 93% at nominal operating conditions from [12], which translates into approximately 200 W of transferred heat in CFHEX 1, 35 W in CFHEX 2 and 5.7 W in CFHEX 3.
Such a remote cooling arrangement will operate successfully provided that the fluid at the JT valve is sufficiently cold to produce the cooling effect, and the LP fluid exiting the CIF is colder than the 2 nd stage of the cryocooler.If the LP fluid is warmer than the 2 nd stage (e.g. during cooldown), the mass at the CIF is large (e.g.cooling of heavy installations) and CFHEX 3 is highly effective, then it may become challenging to cool down the CIF.This can be the case because the returning LP flow would warm up the cold incoming HP stream in CFHEX 3, i.e. the CIF would be thermally decoupled from the 2 nd stage of the cryocooler.To address this issue, the system can be equipped with the bypass valve (see dashed line in Fig. 1).The latter allows to divert the incoming HP flow from CFHEX 3 until the CIF becomes sufficiently cold and, thus, to facilitate the cooldown.
The construction of CFHEX 1 of the remote cooling system has been presented in previous work [1].It has a mesh-based concentric geom-Fig.2. Schematic of the mesh-based hard-wall CFHEX design presented in [1,12].The mesh layers are stacked inside the HP and LP stream passages.etry shown in Fig. 2.This geometry will be referred to as a "hard-wall design" throughout this work.This design consists of two concentric tubes that form inner and outer passages for the HP and LP streams, respectively.Both passages are filled with layers of copper mesh that act as fins and increase the heat transfer area between the fluid and the CFHEX structure.
Moreover, the mesh stack in the CFHEX has a non-homogeneous thermal conductivity (high in-plane and low through-plane), which leads to an increased heat transfer in the radial and a low heat transfer in the axial CFHEX directions.As a result, the mesh-based inner structure allows to ensure that most of the heat is transferred between the flows and not along the structure of the CFHEX, which helps to achieve high effectiveness values.
CFHEX 1 reached an experimental effectiveness of 94.9% under the operating conditions of the remote cooling system, which allowed to transfer approximately 205 W of heat between the streams at nominal operating conditions.This result suggested that a cooling power of 0.8 W at 4.5 K could be achieved at the remote CIF provided all three CFHEXs maintain this high performance [1].
A further analysis has shown that an effectiveness of CFHEXs 2 and 3 has a stronger impact on capabilities of the remote cooling system than that of CFHEX 1.This is the case because CFHEXs 2 and 3 operate at a lower temperature level where the irreversible losses in the CFHEXs generate a larger entropy change and lead to a higher loss of cooling power [14].This served as a motivation to develop an even more effective design for CFHEXs 2 and 3, which will complete the remote cooling system.

Improvements to the hard-wall mesh-based CFHEX
There are two main strategies to further increase the effectiveness of the hard-wall mesh-based CFHEX while maintaining its compact size and low pressure drop: a) decreasing axial conduction along the CFHEX to limit detrimental effects of the parasitic heat loads; b) decreasing or eliminating thermal resistance of the mesh-to-wall interface to increase the heat transfer between the two fluid streams.
The following subsections will describe in more detail various approaches that were taken to implement these two strategies.

Axial conduction
Axial conduction along the CFHEX deteriorates its effectiveness, which is especially important when a compact and highly effective cryogenic design is targeted due to short conduction lengths and large

Table 1
Static loss reduction (in brackets in green) that can be achieved by changing the geometry (e.g.tube wall thickness ) and materials of CFHEX 1 in cold conditions in the 60 K-293 K range [1] temperature gradients along the CFHEX.In previous work [1], a total static loss of 5.5 W in the 60 K-293 K range 3 was experimentally derived for a hard-wall design implemented as CFHEX 1.It was shown that the main contributing components to the static loss are the inner and outer tubes as well as the mesh because of its layer-to-layer contact.Axial conduction through these parts can be reduced by choosing less conductive materials where possible (without compromising the radial heat transfer) and by reducing the heat transfer areas for axial conduction.As an example, Table 1 summarises the contributions to static loss of different CFHEX 1 components and the reduction in the static loss of CFHEX 1 that can be achieved if a range of alternative materials and geometry options is used. 4 Manufacturing attempts showed that a 0.25 mm-thick stainless steel outer tube of the same length and inner diameter as that of CFHEX 1 can be machined without compromising the structural integrity of the design. 5This would allow for 0.9 W (16%) reduction in static loss.A lighter titanium outer tube would provide a similar reduction, and can be of interest for the space RTB application due to its mass-saving potential.A further mass and static loss reduction can be achieved by using a glass-fibre composite material, such as G10.This would also reduce an undesirable mesh-to-outer wall contact conductance due to a lower thermal conductance of a metal-dielectric interface.Therefore, the CFHEX effectiveness would further increase because less heat would be transferred via the outer wall.However, the differences in thermal dilatation between the fibre-glass reinforced composites and the commonly used metals can introduce a challenge when interfacing the CFHEX with the rest of the system (parts of the system, e.g.piping, connectors are often made of stainless steel and copper).Moreover, G10 can be subject to outgassing or helium diffusion in the warmer parts, which could be an issue for space as well as for high-vacuum applications.
Amongst the inner tube options presented in Table 1, one of the most promising candidates to reduce the axial conduction is a stainless steel inner tube, which provides around 1.5 W (27%) static loss reduction.However, using such an inner tube would introduce two stainless steel-to-copper mesh interfaces.The conductance of these is significantly lower than that of copper-copper mesh or bronze-copper mesh interfaces, which leads to a higher thermal resistance in the radial 3 The value of 5.5 W includes the contributions of inner and outer tubes, mesh stack, radiation and conduction through helium gas. 4 CFHEX 1 is used as an example as the experimental data for this design is available.The analysis of CFHEX 1 will help to identify the improvement areas for CFHEX 2 and 3 designs. 5The geometry of CFHEX 1 can be found in [1].
CFHEX direction and lower heat transfer between the CFHEX streams.Therefore, the overall effect of the stainless steel tube on the effectiveness is detrimental, unless the inner wall-to-mesh contact conductance can be improved [12,29].Alternatively, an epoxy inner tube would provide a similar static loss reduction, e.g.1.2 W for a 5 mm wall made of Stycast 2850FT with a thermal conductivity 6 of up to 1.3 W/m⋅K.However, such a solution would need to be introduced without penalising the fluid-to-fluid heat transfer across the inner tube.This design option will be discussed in the next section.The axial conduction through the mesh can be reduced by ensuring a low compression force (therefore, a low thermal conductance) between the mesh layers during the CFHEX assembly.A high interlayer compression could, in theory, have a positive impact on the effectiveness: it improves the inner wall-to-mesh contact conductance, which increases the heat transfer between the streams.However, despite this effect, the simulation and the experimental data suggest that excessive compression has an overall detrimental effect on the achieved effectiveness [1].Another way to reduce the axial conduction through the mesh is to introduce mesh layers made out of a less conductive material, e.g.stainless steel or plastic.This allows to create poorly conducting interfaces between the copper mesh and the chosen low-conductivity mesh, thus decreasing the effective axial conductivity of the mesh stack.It can be seen from Table 1 that introducing 30 equispaced stainless steel layers can reduce the static heat load by 1.3 W (24%).The axial conductivity of the copper mesh increases at higher temperatures, so it is recommended to increase the density of less conductive mesh layers towards the warm end of the CFHEX.
Overall, a 3.4 W-3.7 W (62 %-67 %) reduction in the total static loss in 60 K-293 K conditions could have been achieved for CFHEX 1 by using a 0.25 mm-thick outer stainless steel tube, an inner 5 mm-thick epoxy tube or 0.25 mm-thick stainless steel tube, and a copper mesh stack with 30 equispaced stainless steel layers.Such a reduction can lead to an increase in effectiveness of up to 1%, which corresponds to ≈ 6 NTUs.

Mesh-to-wall contact and novel strategies
Another important player in the performance of a mesh-based CFHEX is the thermal resistance of the inner wall-to-mesh interface.As an example, Fig. 3 shows the evolution of different components of the thermal resistance (between the HP stream and the centre of the in-Fig.3. Evolution of different components of the thermal resistance (between HP fluid and the middle of the inner wall) over the distance from the warm end of CFHEX 1 operating in the 50 K-290 K range.Data is obtained using the numerical model presented in [12].The components of radial resistance are depicted above the plot.(For interpretation of the colours in the figure(s), the reader is referred to the web version of this article.)ner wall) with the distance from the warm end of CFHEX 1 operating in the 50 K-290 K range.The inner wall-to-mesh interface contribution amounts to 55 %-71 % of the total resistance, and its elimination would increase the effectiveness of CFHEX 1 from 94.9% to 97.4% (i.e. increase corresponding to ≈ 19 NTUs) at the nominal system operating conditions.As a result, the ultimate step to improve the CFHEX effectiveness would be to fully eliminate the inner wall-to-mesh contact resistance.This type of CFHEX can be accomplished by letting the mesh traverse through the inner wall uninterrupted and will be referred to as a "transparent-wall" design in this work.
The assembly process of hard-and transparent-wall design ideas is visually presented in Fig. 4. The transparent-wall design presents a very challenging manufacturing task as the inner wall that separates the fluid passages may need to be constructed gradually as the mesh is placed in the outer tube.Several manufacturing processes were considered to accomplish this challenge.
One option would be to use 3D-printing.This technique allows to manufacture fine geometry features to a high precision as well as to optimise the shape of the flow channels to further enhance heat transfer [30].However, a number of difficulties would be encountered.Firstly, it would be necessary to 3D-print using two or more materials, which does not seem to be commercially available for the different materials of interest.Having multiple materials is important as the flow partition wall should have a low thermal conductivity, while the heat transfer matrix, i.e. mesh, should be as conductive as possible.
For smaller-scale CFHEXs, additive manufacturing presents a viable option.In this case, the partition wall can be made out of a poorly conducting epoxy glue, which is deposited on each mesh layer in the CFHEX.The overlapping contours of the epoxy would then form a solid partition between the flow passages, which results in the design shown in Fig. 5.A photo of a glued mesh stack is shown in Fig. 6.
An advantage of this approach is that epoxies are generally much less thermally conductive than metals, which is favourable for the reduction of static loss.This method also allows to maintain the mesh layers close to each other, hence a compact design can be achieved.However, the manufacturing process may become challenging for a number of reasons.Firstly, the epoxies have an associated curing time and pot life, which means that the assembly process should be carefully-timed such that the mechanical integrity and leak-tightness of the inner wall is not compromised.Moreover, an epoxy should remain mechanically sound at low temperature and elevated pressure conditions (differential pressure across the inner wall of up to 4.3 bar is targeted for the present system with operating pressures of  ℎ = 5.3 bar and   = 1.0 bar).The ways to address these and other challenges in the manufacturing process will be discussed in Sec.4.3.

Leak-tightness challenge
An epoxy inner wall can present a challenge in terms of leaktightness.There is a number of potential reasons for that: the deposited glue might not fill all the gaps between the mesh layers, or its contours deposited on the mesh layers might become misaligned.All this can create a gap in the epoxy wall through which the fluid can traverse between the flow passages, which results in various consequences for the remote cooling system behaviour.
First of all, a leak allows a part of the mass flow to bypass the CIF, which reduces the mass flow rate at the CIF and, hence, reduces the produced cooling power.Moreover, this bypassing flow will expand and the nature of this expansion (e.g.isenthalpic, isothermal) is not evident.This implies that the leaking fluid may warm up, remain at the same temperature or cool down (e.g.due to the JT effect) depending on the exact conditions.It should be noted that the remote cooling system is optimised to produce the maximum cooling effect by throttling helium at the JT valve.Therefore, throttling the leaking fluid at a different condition would be less efficient and would result in a lower cooling power at the CIF compared to nominal operation.In addition, less mass flow in the lower part of the CFHEX can lead to a loss in effectiveness because the CFHEX is designed to have a maximum effectiveness at the nominal operating mass flow rate.
Following this reasoning, the potential leak through the inner wall has a detrimental effect and should be minimised.For the designed remote cooling system, the maximum leak rate criterion of 1 × 10 −3 mbar⋅l/s could be set.This corresponds to approximately 0.1% loss of cooling power at the nominal mass flow rate, which is within the uncertainty to which the cooling power is measured.However, a leak rate through the inner wall of 1 ×10 −7 mbar⋅l/s was targeted for CFHEXs in the remote cooling system.This value corresponds to the typical diffusion rate of helium through epoxy at room temperature [31].Despite the fact that a higher leak-rate could be tolerated, a more stringent goal was set because a leak rate above 1 × 10 −7 mbar⋅l/s implies that the integrity of the inner wall has been somewhat compromised.This can lead to a growth of the leak as the CFHEX undergoes thermal cycling during the system operation, and, thus, to a deterioration in CFHEX and system performance.Moreover, leak-tightness is an even more significant factor in space applications, e.g.RTB coolers, where the CFHEX performance should be maintained after it has experienced high mechanical loads during the rocket launch.The next sections will elaborate on the steps taken to maintain the leak-tightness of the epoxy inner wall and thus, maximise the performance of the system.

Transparent wall verification
The selected epoxy has to meet a number of criteria: it has to maintain mechanical robustness in cryogenic conditions, to have a relatively long pot life (such that approximately 40 layers can be placed on top of each other before the curing process begins), to match the thermal dilatation of the copper mesh and to have an appropriate viscosity such that the deposited epoxy does not spread vastly across the mesh layers due to surface tension and does not cover the mesh heat transfer area.Amongst the available cryogenic epoxy glues, Loctite ® Stycast 2850FT 7was chosen due to its thermal expansion matching that of copper, its proven metal-glue adhesion and the availability of different catalysts, which allow to adjust the viscosity of the glue.Moreover, Loctite ® Stycast 2850FT maintains its performance at high operating temperatures8 (i.e. up to 90 • C-180 • C depending on the used catalyst), which allows considering this epoxy for space applications (e.g.RTB coolers [32]).From the available catalysts, a more viscous CAT 9 and a less viscous CAT 24LV were identified.A less viscous epoxy mix (using CAT 24LV) allows for an easier penetration of the glue through a mesh layer.However, a very low-viscosity epoxy tends to move due to gravity during the curing process and, hence, create leaks in the inner wall.A more viscous epoxy mix (using CAT 9) allows to maintain a desired partition profile, but it penetrates the mesh layers less easily, which should be addressed by implementing a suitable application procedure.
The leak-tightness of the Stycast epoxy wall was tested for each catalyst case and for various mesh sizes.An example of a sample used in these tests is depicted in Fig. 7.It consists of mesh layers glued to each other by depositing a circular epoxy contour on each subsequent layer in the way described in Sec.4.3.An arrangement used during the leak-tightness tests is shown in Fig. 8. Two KF flanges were glued to the top and bottom of the mesh stack.One of the KF interfaces was sealed with an end cap and the other one was used to connect a vacuum pump and a helium leak detector.In this arrangement, the leaks through the epoxy wall or KF flange-mesh interfaces could be detected.Similar interfaces will have to be accomplished for the final transparent-wall design to connect the stack to the rest of the remote cooling system.A sample was considered leak-tight if a leak rate below 1 × 10 −8 mbar⋅l/s was measured using helium as an externally applied test gas.If the leak test was successful, the test sample was pressurised via a KF interface as a next step.The test pressure was determined in line with the EN 13458 norm, i.e. 1.25 × 5.3 bar (as per nominal system operating pressure) for materials that become stronger at their operating conditions (i.e. at cold conditions for the remote cooling system).The sample was kept under this pressure for 2-3 hours to confirm that no pressure loss is observed, and then leak-tested again.In the course of testing it was concluded that CAT 9 provides the best wall leak-tightness under these conditions.The CFHEX will be subjected to numerous cooldowns within the remote cooling system and its HP passage is expected to operate under a variety of pressures (up to 5.3 bar for the remote cooling system from [12] and up to 25 bar for other cooling arrangements [12,33]).Therefore, the epoxy wall was thermally cycled and subjected to high pressures as a part of the verification test campaign.For this, a 100layer sample with epoxy wall made using CAT 9 was fabricated as depicted in Fig. 9a.The sample was leak-tested using a helium leak detector as shown in Fig. 9b, and then subjected to 5 thermal cycles from 293 K to 78 K.This was accomplished by immersing the prototype into a liquid nitrogen bath in a timeframe of around 5 minutes per cycle.The inner enclosure of the sample was then pressurised with helium gas to 5.3 bar for 1 hour at 78 K (as shown in Fig. 9c).The test was successful with no pressure loss observed, which was confirmed with the further leak detection.Throughout this validation as well as the tests described in Sec. 7, the transparent-wall arrangement has undergone approximately 40 thermal cycles and no thermal degradation has been observed.A high mechanical stability can be explained by the fact that the presence of the mesh inside the epoxy wall is effectively turning it into a copper-strand reinforced composite structure with a higher resistance to fatigue.Moreover, the sample was tested at a higher pressure of 50 bar once the qualification test campaign for use in the remote cooling system was completed.The sample has proven to maintain this pressure for a period of 3 hours and developed no leaks.This implies that the transparentwall design can also be used in high-pressure remote cooling systems such as those presented in the previous work [12].

Manufacturing method of transparent-wall CFHEXs
The baseline transparent-wall CFHEX consists of an outer tube, which is filled with layers of wire mesh screens.Each screen is joined to the subsequent screen using epoxy glue, which forms the inner wall of the CFHEX in an additive manufacturing manner.The leak-tightness of the inner wall in such a design heavily relies on the manufacturing process, which has to consider a variety of factors, e.g.glue pot life and curing time, as well as distribution and eccentricity of the deposited wall contours.
The transparent-wall CFHEX was fabricated in the following steps.First, the outer tube was thoroughly cleaned.The mesh layers were cut into a circular shape with the dimensions of the outer tube using an electrical discharge machining process to ensure the required dimension tolerances.Further, the mesh layers were chemically cleaned in an ultrasonic bath to achieve a good adhesion between the epoxy and the mesh (which reduces the probability of a leak through the inner wall) and to ensure a clean heat transfer surface later on.It was also found that at least 3-4 mesh distances between the mesh wires should be filled with the epoxy glue at each point of the inner wall profile to achieve a leak-tight design.In addition, it was ensured that every wire within the profile of the partition is visibly covered with epoxy, and that the glue penetrates through the mesh to form a continuous pattern on the other side of the mesh layer.Eccentricity and consistency of the position of the inner wall contour on the mesh layers were also found to be important for the leak-tightness of the design.An automated epoxy distribution can be envisaged for future production.
The additive manufacturing proceeded in the following steps.Each mesh layer was pushed down the supported outer shell until it touched the previous mesh layer.A lower compression of the mesh layer stack allows to reduce the contact conductance between the mesh screens and, hence, to reduce static heat load and to increase the effectiveness of the CFHEX.Therefore, the mesh layers were carefully positioned on top of each other to avoid excessive compression.However, a certain amount of compression force was applied during the assembly process to ensure that the mesh layers are flat such that the integrity of the epoxy wall is maintained.
The viscosity of the epoxy increases noticeably after approximately 40 minutes of gluing and its quality decreases, thus the CFHEX manufacturing was accomplished in batches.Several dozens of mesh layers were placed in the outer tube until the glue would start to become more viscous, and then a time period of 24 hours was allowed to pass for the epoxy to cure at room temperature.A weight was placed on the last mesh layer to ensure that the position of the mesh stack remains unchanged during the curing process.The use of an epoxy with a longer pot life would allow to extend the application intervals.Moreover, the use of cryogenic epoxies that harden under the ultraviolet light could significantly ease the additive manufacturing and allow for a continuous assembling of the CFHEX.
Once the entire mesh stack was placed in the outer tube, the transition pieces were glued to the top and bottom mesh layers.These pieces facilitate the integration of the CFHEX in the remote cooling system, and their geometries were adjusted in line with particular interfaces.

Transparent-wall CFHEXs for the remote cooling system
The transparent-wall CFHEXs 2 and 3 of the remote cooling system from Fig. 1 were modelled and sized for their respective operating con- Copper mesh dimensions Medium mesh from Table 3 Fine mesh from  ditions following the process described in [12].The resultant CFHEX dimensions are summarised in Table 2.
A transparent-wall design during its assembly is depicted in Fig. 10.The 0.25 mm-thick stainless steel outer tube was chosen for both CFHEXs based on the arguments outlined in Sec.3.1.A subsequently finer mesh was chosen for CFHEXs 2 and 3 to enhance the heat transfer between the streams as indicated in Table 2.The pressure drop increases as the mesh becomes finer [12].This happens because the hydraulic diameter of the finer mesh is smaller (see Eq. ( 1)) and there is more contact between the fluid and the mesh matrix.However, this trend could be accepted because the pressure drop decreases towards Fig. 10.Photo of a transparent-wall design (CFHEX 3) during the assembly process with approximately 3/4 of the mesh stack placed in the outer tube.lower temperatures and the predicted values for both CFHEXs 2 and 3 are well below 100 mbar, which was a nominal value assumed in the system studies [12].Low-conductivity stainless steel mesh layers were introduced along the length of CFHEXs 2 and 3. Initially, plastic layers were considered as they would reduce axial conductivity even further due to the presence of dielectric metal-plastic interfaces of poor thermal conductivity.The samples shown in Fig. 11 were fabricated to assess the leak-tightness of glued plastic mesh and copper-plastic mesh stacks.Several leak tests were successful, which proves that an introduction of plastic interlayers could be an interesting option for future CFHEX designs.However, the metallic alternative (i.e.stainless steel mesh layers) was selected for the first prototypes of the already challenging transparent-wall designs to minimise the risk of inner wall leakage.This choice was made since the successful leak-tight adhesion of metal and epoxy was repeatedly demonstrated in the verification tests (see Sec. 4.2).The size of stainless steel mesh layers was chosen to be similar or larger than the copper mesh size, such that no additional pressure drop is introduced.The inner wall of both CFHEXs was made out of Loctite ® Stycast 2850FT epoxy with CAT 9.This choice was justified in Sec.4.2.The transparent-wall designs from Table 2 are predicted to provide an increase in effectiveness of over 4% with respect to the hard-wall design.

Experimental arrangements
The novel transparent-wall design is aimed to be tested across a wide range of operating conditions to demonstrate that it can satisfy the cooling needs of current and future cryogenic applications.With this purpose in mind, the setups described in Sec.6.1 and 6.2 were built to characterise the performance of the transparent-wall CFHEXs in the 4.5 K-290 K temperature and 1 bar-5 bar pressure ranges.

CFHEX test in the 10 K-290 K range (CFHEX 2)
The constructed transparent-wall CFHEX 2 was tested under two different temperature conditions using the arrangements depicted in Fig. 12.The figure depicts the test arrangement and the instrumentation around the CFHEXs; a detailed description of the fluid supply and circulation system can be found in [12].
As indicated in Fig. 12, both experimental arrangements are equipped with quite a few temperature (TT), absolute pressure (PT) and differential pressure (PDT) sensors to characterise the performance of CFHEX 2. Pressures are measured using Rosemont and WIKA tronic pressure transducers.Temperatures are acquired by a combination of Pt1009 (for  > 260 K), TVO 10 and Cernox11 (for  < 80 K) sensors using a four-wire measurement technique.Fluid stream temperatures at specific locations are measured on thin stainless steel piping and an indium foil is placed at the sensor-pipe interface to improve thermal contact.Sensors and relevant setup parts are covered with MLI.Additionally, the lower part of the setup containing CFHEXs 2 and 3 is surrounded with a fully closed radiation shield.It is pre-cooled at the 1 st stage of the cryocooler and covered with a 20-layer MLI blanket to reduce the radiative heat load.A total radiation heat load of around 15 mW was estimated during static loss tests.The wires of all sensors are heat-sunk at the appropriate thermalisation pads as well as on the respective nearby piping to intercept remaining heat inleaks.
Experimental data are acquired using a LabVIEW 12 program and processed using a Python script [34].Typical temperature errors during the measurements amount to ±0.14 K at 290 K, ±0.12 K at 50 K and ±0.015K at 10 K. Typical absolute pressure measurement errors are ±0.04 bar at 5 bar and ±0.02 bar at 1 bar HP and LP stream pressures, respectively.Uncertainty values of ±0.2 mbar (HP) and ±1 mbar (LP) are estimated at a pressure drop measurement of 4 mbar.The mass flow rate uncertainty amounts to ±3 mg/s at 250 mg/s.
In the arrangement from Fig. 12a, the high-pressure fluid is supplied to the system and is passed via both CFHEXs 1 and 2 before being precooled at the 1 st stage of the cryocooler and by a JT expansion.This arrangement allows to create the fluid inlet temperatures of ≈ 290 K and ≈ 50 K at the warm and cold ends of CFHEX 2, respectively.Therefore, the performances of the hard-and transparent-wall designs can be compared under similar temperature conditions.In this arrangement, heater EH210 in combination with a temperature controller is used to regulate the temperatures of the 1 st stage of the cryocooler, whereas heaters EH110 and EH510 are used to maintain constant CFHEX 2 inlet flow temperatures.
In the arrangement of Fig. 12b, the fluid flow is cooled at both cryocooler stages.The stage temperatures are controlled using the heaters EH210 and EH410 in combination with a temperature controller.This allows to create the 10 K-50 K operating range for CFHEX 2, and hence measure its performance in the nominal conditions of the remote cooling system.

CFHEX tests below 10 K (CFHEX 3)
As a following step, CFHEX 3 was integrated into the experimental setup, thus completing the remote cooling system, which is shown in Fig. 13.This test arrangement allows to demonstrate that the transparent-wall CFHEX design is functional at temperatures down to 4.5 K and lower, and to evaluate its performance in these challenging conditions.The critical temperature sensors are placed at the inlets and outlets of CFHEX 3 to experimentally derive its effectiveness.In this arrangement, the setup was modified such that the differential pressure sensor PDT910 measures the pressure drop of the LP passage of CFHEX 3, as opposed to the arrangements in Fig. 12 where the pressure drop of the entire LP return line was measured.The pressure pick-up at the LP flow outlet of CFHEX 3 is accomplished using a "pressure measurement capillary" as shown in Fig. 10.Moreover, the setup is equipped with a carefully designed Cooling InterFace (CIF).It is formed of a 1.4 m wound copper tube with inner and outer diameters of 3 mm and 4 mm, respectively.The tube is brazed onto a 0.5 mm-thick cylindrical surface with an outer diameter of 8 cm.This allows to equip the CIF with a Kapton heater EH550 and temperature sensors TT220, TT221 and TT920 to assess the cooling power deposited at the CIF at a given temperature.Thus, the cooling performance of the constructed system can be characterised.Similarly to previous experimental setups, all sensor wires are heat-sunk at appropriate locations to reduce external heat inleaks to the sensors.With this purpose in mind, additional thermalisation pads are introduced in the setup as shown in Fig. 13.A typical temperature error during the measurements at 4.5 K would amount to ±6 mK.

Experimental results
The primary goal of the experimental campaign is to characterise the performance of the two transparent-wall designs in different conditions, and hence validate the correlated numerical model developed previously as a sizing tool for high-effectiveness mesh-based designs [12].The following aspects can be verified during the testing: 1. Friction factor.Based on the analysis of the measured performance of CFHEX 1, a new friction factor dependency for the coarse mesh was proposed in the previous work [1].Finer mesh were used in CFHEXs 2 and 3, therefore the applicability of the proposed friction factor fit to other mesh sizes can be investigated by analysing the measured pressure drop of the CFHEXs under different conditions.

Fluid-to-mesh heat transfer and mesh-to-wall interface conductance.
The thermal contact resistance between the inner wall and the mesh is no longer present in the transparent-wall design.This suggests that a deviation between the predicted and measured effectiveness values would be mainly due to the differences in the assumed and real fluid-to-mesh heat-transfer coefficient.As a result, the effectiveness analysis of the transparent-wall designs will allow to confirm the correlation factors for fluid-to-mesh heat transfer and mesh-to-wall interface conductance, which were proposed in the previous work [1].3. Axial conduction.The effectiveness analysis will confirm if the axial conduction was reduced by introducing the stainless steel mesh and applying a lower compression force during the CFHEX assembly.
Finally, the CFHEXs can be characterised under the nominal operating conditions to verify if the transparent-wall approach improves their performance in practice.

Pressure drop
The available fluid pressure across the JT expansion (which dictates the lowest temperature that can be achieved at the CIF of the remote cooling system) is defined by the characteristics of the used warm pump and the pressure drop of the CFHEXs.Therefore, a low pressure drop, especially for the LP stream, is targeted from a system performance perspective.
The pressure drop Δ is defined as: where  is the friction factor between the fluid and the mesh,   is the frontal area faced by the fluid flow,   and  ℎ are the porosity and the hydraulic diameter of the mesh, respectively, and  is the length of the mesh stack in the direction of the fluid flow.ṁ,  and  are the mass flow rate, density and velocity of the fluid passing through the mesh, respectively.The friction factor depends on the Reynolds number  =  ℎ ∕ and can be described in a simple form as: where  is a geometry-dependent coefficient and the exponent  depends of the fluidic effects and the flow regime [37].Other forms of  −  dependency can be found in [35].The hydraulic diameter of the mesh is low and lies close to its wire diameter.As a result, small laminar flow passages are formed between the wires, and thus  lies close to 1.The mesh geometry parameters, i.e. wire diameter and pitch define its porosity   , which influences the coefficient .In the   = 50 %-70 % range of interest, a higher porosity results in a lower friction factor [35].
At the start of the experimental campaign, the pressure drop Δ of CFHEX 2 was measured at warm conditions (the cryocooler was switched off) with helium and argon as working fluids.The tests were performed in the configuration from Fig. 12a.During the tests, the temperature of the fluid remained around 293 K and the values of  and  could be calculated from the measured Δ values and fluid conditions using Eq. ( 1).Fig. 14 shows the experimentally derived  −  dependency obtained during warm tests together with the experimentally obtained data for coarse mesh in CFHEX 1, which is presented in [1, Fig. 5].Based on the explanation above, the coarse and medium with similar porosities mesh used in CFHEXs 1 and 2, respectively, would have a similar friction factor.However, as seen in Fig. 14, a higher friction factor (by about a factor of two in Fig. 14) was experimentally derived for the coarse mesh in CFHEX 1.This is caused by the fact that the mesh was overcompressed in the experiments with CFHEX 1 [1].This resulted in its lower porosity that translated into a higher friction factor, which is coherent with the results on Fig. 14.In the present experiment with CFHEX 2, a great care was taken to avoid over-compression between the medium mesh layers, as described in Sec.4.3.
A further effect, which resulted in a difference in  −  relations for CFHEXs 1 and 2 is the inaccuracy in the estimation of the HP and LP fluid passage area in the transparent-wall design.This is the case because the epoxy that forms the inner wall tends to spread slightly across the mesh after being deposited.A cross-section of a transparentwall sample is shown Fig. 15 for visualisation.An uncertainty of ±1 mm is attributed to the measured inner diameter of the epoxy inner tube, which suggests that the value lies in the 16.5 mm-18.5 mm range.The experimentally derived friction factors for the 16.5 mm and 18.5 mm Fig. 14.Variation of friction factor with Reynolds number for different gases at warm conditions.Points and lines represent the experimental data and fitted/calculated dependencies, respectively.Experimental data are measured using helium, neon, argon and nitrogen gases for the mesh with dimensions indicated in the legend (  is a wire diameter,  is pitch as per Table 3).These results are compared to the dependencies from literature [35][36][37].Medium mesh data assume two different inner diameters of the epoxy inner tube: 16.5 mm and 18.5 mm.The  −  relations in Fig. 14 are also compared to dependencies presented in literature [35][36][37].It can be seen that the experimentally derived  values for medium mesh from the tests with argon and with helium follow the same tendency.Therefore, the tests confirm that  solely depends on the non-dimensional parameter .A similar conclusion was drawn from the testing of CFHEX 1 with coarse mesh [1] where the tests were performed with four different fluids (helium, argon, nitrogen, neon) and all the obtained friction factor values followed the trend presented in Fig. 14.It can also be seen that  for coarse mesh is closer to the dependency for woven mesh screens from Barron [35], whereas  for medium mesh lies closer to the classic laminar flow dependency, i.e. 64∕.
The inner diameter of the epoxy wall was estimated to lie closer to 16.5 mm on average, and the fit to this experimental data is shown in Fig. 14.Based on this result and the data from [1], the two proposed  −  dependencies for coarse and medium mesh can be summarised as follows: • Coarse mesh with   = 0.62:  = 86.2⋅ ( −0.74 ) from [1]; • Medium mesh with   = 0.64:  = (45∕) ⋅ (1 + 0.036 ⋅  0.87 ).The experimentally derived  −  fit for medium mesh can now be used to predict the pressure drop at colder conditions.
As the next step, CFHEX 2 was tested in the operating temperature range of CFHEX 1 using the setup in Fig. 12a.Such a test allows to directly compare Δ of both designs as well as to verify that the proposed  −  fit for medium mesh is applicable for predictions at lowtemperature conditions.Fig. 16 shows the variation of pressure drop Δ ℎ with absolute pressure  ℎ in the HP passage for CFHEXs 1 and 2. The measured Δ ℎ is slightly higher in CFHEX 2.Even though the latter is shorter than CFHEX 1, it has a smaller HP passage area, which results in a higher  2 ∕2 term in Eq. ( 1).This, along with a smaller hydraulic diameter  ℎ of the medium mesh, explains its higher pressure drop.However, it is worth noting that CFHEX 2 was designed to operate at lower temperatures, i.e. 10 K-50 K where the pressure drop will be lower due to lower flow velocity.Therefore, a design with a larger wetted area, and thus a higher heat transfer, to maximise the effectiveness could be afforded.
Furthermore, the Δ of CFHEX 2 can be predicted using the newly proposed  −  fit for medium mesh to verify its applicability for cold conditions.Fig. 17 shows the experimental data together with calculated Δ ℎ values based on the proposed  −  fits for coarse and medium mesh in the 60 K-290 K and 10 K-50 K conditions (see Fig. 12 for experimental arrangements).It can be seen that the  −  fit for medium mesh produces a closer agreement between the experimental data and predictions than the fit for coarse mesh.The small differences between the simulations and test data can be due to variation of the HP passage area along the CFHEX.This effect is more pronounced towards the low temperatures (e.g. in the 10 K-50 K range) when low Δ ℎ values are measured, which is confirmed by the results shown in Fig. 17b.Overall, the Δ ℎ values are predicted within ±1 mbar using the proposed  −  fit for medium mesh.
Fig. 18 shows Δ variation with mass flow rate ṁ in both passages in the 42 K-285 K operating range together with the numerical predictions that are based on the  −  fit for the medium mesh.The LP side pressure drop for CFHEX 2 was calculated by subtracting the predicted Δ  of CFHEX 1 from the Δ measured using PDT910 over the LP return line 13 (see Fig. 12).Similar to the Δ ℎ −  ℎ variations, a good agreement between the predictions and the experimental data can be observed.

Effectiveness
The effectiveness is one of the most important characteristics of the CFHEX as it strongly influences performance of the remote cooling and other CFHEX-based systems [13].Therefore, experiments were conducted to validate the numerical predictions of the effectiveness of the transparent-wall design and to determine its performance for a range of conditions.
The effectiveness  is defined as the ratio between the actual rate of enthalpy exchange between the two streams the CFHEX Ḣ and thermodynamically maximum possible rate Ḣ [38].It can be expressed as: The effectiveness of a given stream can be expressed using the enthalpy approach as: for a CFHEX in which the mass flow rate is the same for both fluid streams.In Eqs. ( 4) and ( 5), ℎ is the specific enthalpy of the HP or LP stream calculated at the pressure indicated by the subscript and at the temperature  stated in brackets (e.g. ℎ, = inlet  of the HP stream,  , = outlet  of the LP stream).For a perfectly insulated CFHEX,  ℎ and   should be equal.However, heat is transferred between the CFHEX and the surroundings, as well as conducted along the CFHEX structure during the tests, which leads to a difference between these two effectiveness values.Fortunately, the average value   = ( ℎ +   )∕2 is insensitive to the heat transfer between the CFHEX and the surroundings, hence it can be used to assess the intrinsic performance of the CFHEX [39].The transparent-wall CFHEX 2 was tested in two different temperature conditions for the following reasons: 1. measurements in the 42 K-285 K range allow to compare the effectiveness of CFHEX 2 to that of CFHEX 1 in a similar temperature range, and to confirm that the transparent-wall approach leads to an improved CFHEX performance, and 2. measurements in the 11 K-50 K range allow to characterise the behaviour of CFHEX 2 in its nominal operating conditions.
The effectiveness of the CFHEX mainly varies with the mass flow rate as was shown in previous work [1].This variation for CFHEX 2 in the two listed temperature conditions is shown in Fig. 19.
A maximum effectiveness of 97.5±0.2% was achieved in the 42 K-285 K operating range as it can be seen in Fig. 19a.An increase of 2.6% in effectiveness compared to the hard-wall CFHEX 1 of similar dimensions was achieved.This translates into a tremendous rise in NTU from 19 to 39.This achievement confirms that the eliminated wall-tomesh contact and a lower compression force between the mesh layers during assembly (described in Sec.4.3) can significantly improve the effectiveness of compact CFHEXs.
The solid lines in Fig. 19a represent the predictions of the numerical model from [12] with no additional correlation factors.The difference between the predictions and the experimental data must be due to the incomplete heat transfer and possible flow maldistribution as discussed in the previous work [1] where a correlation factor 0.8  was proposed.The predictions using this correlation factor are represented with the dashed lines in Fig. 19a and are in better agreement with the experimental data.
It can also be seen that the spread between the experimentally derived  ℎ and   is lower than between the predicted  ℎ and   .This can be to the measurement constraints, e.g. the LP outlet flow temperature  , was measured at a location, which is slightly upof the point where the LP stream exits the mesh.This resulted in a lower recorded  , , thus a lower measured   , and a smaller spread between  ℎ and   .Overall, the small spread between  ℎ and   compared to hard-wall CFHEX 1 (results in [1]) indicates that the static losses have been reduced in the transparent-wall design.
Fig. 19b shows the variation of effectiveness with mass flow rate in the 11 K-50 K operating temperature range.Only  ℎ is shown in the plot because  , (which is needed to derive   ) was not accessible in the experiment due to direct integration of CFHEX 2 into the compact assembly with the adjacent CFHEX 1 (see Fig. 13b).The depicted  ℎ represents the lowest and, therefore, the most conservative effectiveness value.
In the 11 K-50 K range, an effectiveness of 98.2±0.7% was achieved as it is seen from Fig. 19b.This value is maintained over a larger range of mass flow rates (above 100 mg/s), which highlights the indisputable advantage of the wall-to-mesh interface elimination.
The effectiveness in the 11 K-50 K range is higher than that in the 42 K-285 K range due to a lower axial conductivity of the CHFEX materials at lower temperatures, a lower temperature gradient along the CFHEX and a peak in radial conductivity of the copper mesh at around 25 K [29].All these factors contribute to a higher predicted and measured effectiveness.
A difference between the experimental and predicted  ℎ at lower ṁ may indicate the presence of minor heat inleaks from the surroundings.This is due to the fact that, in the current CFHEX configuration, the LP flow shields the HP flow from the external parasitic heat loads.The heat inleak from the surroundings warms up a colder LP flow in the outer CFHEX passage, thus less cooling is available for the HP flow.This translates into a lower  ℎ , especially at lower ṁ where the same heat inleak would lead to a greater reduction in the HP flow cooling.Moreover, the observed trend can indicate the presence of incomplete heat transfer effects that become prominent at lower mass flow rates and are not described by the numerical model [12].However, an effectiveness of 96.3±0.9% was achieved even at low ṁ values.Similarly to the 42 K-285 K test results, the correlation factor 0.8  provides a good agreement with experimental data.
For high-effectiveness CFHEXs, a small difference in the  value translates into to a large difference in performance in terms of the number of transfer units.For instance, an effectiveness increase from 98.0% to 98.5% corresponds to 18 NTUs, and this effect would be even larger for a higher .This emphasises the importance of providing a precise effectiveness value when characterising a high-performance CFHEX.However, this can be a challenging task: for example, it can be seen that the higher  values in Fig. 19b have a larger uncertainty than the values in Fig. 19a.This is the case for the designed CFHEXs because temperature sensor errors are large compared to total measured temperature differences in the tests with a lower Δ between the CFHEX ends (e.g.Δ = 39 K in the 11 K-50 K range whereas Δ = 243 K in the 42 K-285 K range).One way to reduce this error in the 11 K-50 K condition and to improve the accuracy of experimental  values could be to directly measure the temperature differences between the fluid flows at the CFHEX ends (e.g. with a calibrated thermocouple) instead of measuring the absolute stream temperatures (as described in Sec. 6).This reduces accumulated errors and improves the accuracy of the measurements.
In general, a high  of 97.5±0.2%measured during the tests with a larger Δ of 243 K between the CFHEX ends (Fig. 19a) serves as a confirmation that a higher  should be achieved in the 11 K-50 K range where the Δ and axial conduction are lower, and the radial heat transfer is higher (see previous paragraphs).Therefore, this result provides a solid ground to suggest that 98.2% value is reliable.An ultimate way to validate the measured effectiveness values is to assess if the resultant cooling power of the entire remote system is in line with expected values.Such an experimental study was performed previously [14] and its results confirm the reliability of high effectiveness values reported in this paper.

Performance below 10 K (CFHEX 3)
The transparent-wall CFHEX 3 was tested at the lowest temperature range (below 10 K) by means of its integration in the remote cooling setup.During all the tests, the pressure on the LP line was maintained at 1.7 bar: this setting allowed to cover the widest range of mass flow rates given the performance limitations of the used circulating pump.Due to this, the cold end of the CFHEX remained at the corresponding saturation temperature of 4.8 K. Tests with a nominal cold-end temperature of 4.5 K were performed at system level (results can be found in Points and lines represent the experimental and simulation data, respectively.The sources of the friction factor and correlation parameters used for the simulation are indicated in brackets.The maximum  ℎ ,   and ṁ measurement uncertainties are ±42 mbar, ±15 mbar and ±3 mg/s, respectively. [14]), and no significant change in effectiveness and pressure drop performance was observed in these conditions.
The results of the CFHEX 3 test campaign are shown in Fig. 20.Fig. 20a depicts the pressure drop of each stream as a function of the mass flow rate.The test was performed in the configuration from Fig. 13.It can be seen that a maximum pressure drop of 0.8 mbar and 1.1 mbar was measured at 2.2 bar (HP) and 1.7 bar (LP) fluid flow pressures, respectively.Based on this result, the numerical studies suggest that at the 5.3 bar and 1.0 bar nominal operating pressures this would lead to HP and LP pressure drop values of 0.34 mbar and 0.3 mbar, respectively.Such low Δ will allow to reach a lower LP pressure and, hence, operate the system at temperatures well below the nominal temperature of 4.5 K at the CIF.The solid and dashed lines represent Δ predictions based the experimentally derived  −  dependencies from Fig. 14 for coarse and medium mesh, respectively.The CFHEX 3 design uses the fine mesh from Table 3 and it can be seen that the  −  fit for medium mesh provides a better Δ prediction than  −  fit for coarse mesh.It can be seen that  −  fit for medium mesh provides a good agreement for the HP stream pressure drop.The predictions for Δ  also lie within the error bars.However, the measured Δ  is generally slightly higher than the predicted value.This can be due to a possible presence of small amount of mist flow inside the LP passage of CFHEX 3 (see the discussion in the next paragraphs), which is not considered in the numerical simulations for a single phase flow.
The variation of CFHEX 3 effectiveness with mass flow rate is shown in Fig. 20b.Only  ℎ data is presented for the same reasons as those outlined in Sec.7.1.2.Fig. 20b depicts  ℎ derived using two different methods.Effectiveness calculated using the classic definition from Eq. ( 4) is indicated by black points.In this calculation, helium at the LP inlet is assumed to be in the single-phase gas condition.Interestingly, the  ℎ derived using this method amounts to values above 100% for the mass flow rates above 150 mg/s.This can be associated with a high ± 1.5% measurement error, however an alternative explanation can be offered by looking into the test procedure.
During the effectiveness measurement run the inlet temperatures of the high-and low-pressure streams were conditioned to be at a constant value.The high-pressure inlet flow was kept at 10 K by means of a heater EH410 on the 2 nd stage of the cryocooler (see Fig. 13a), while the low-pressure inlet was kept at 4.8 K by expanding the flow into the two-phase state in the JT valve before it entered the cooling interface, where some heat was deposited to bring the fluid to the gaseous state.This was the only method of controlling the LP inlet temperature in the given system configuration and it offered a great temperature stability because helium was brought to its saturation temperature at a welldefined stable pressure.However, the heat deposited at the CIF might not be sufficient to bring the two-phase flow downstream the JT valve into a single-phase gas state, i.e. the exact vapour quality of the helium flow exiting the CIF / entering the CFHEX 3 is unknown when the LP inlet temperature is conditioned in such a way.This gives a reason to suggest that a mist flow enters the CFHEX 3, which is also in line with a slightly higher pressure drop in the LP passage shown in Fig. 20a.The mist flow provides an additional available enthalpy for cooling (i.e.latent heat of evaporation).As a result, the HP outlet flow is colder than it would have been if the LP flow was a single phase vapour.This leads to a higher calculated effectiveness, which is seen in Fig. 20b (black points).
However, since the pressure downstream the JT valve and the heating power deposited at the CIF are known, it is possible to estimate the vapour fraction and, therefore, the enthalpy of the LP inlet flow, corresponding to ℎ  ( , ) term in Eq. ( 4).The enthalpy of the two-phase helium can be much lower than that of single-phase vapour helium at 4.8 K, thus the real Δ Ḣ in Eq. (3) ( = Δ Ḣ ∕Δ Ḣ ) is higher than in the case where single-phase vapour fluid is assumed.The effectiveness values calculated using this method are shown in Fig. 20b (green points) together with the corresponding simulation results (dashed line) with the correlation parameter 0.8  .The numerical predictions lie within the measurement error and show a good agreement with the test data.The approximation of the vapour fraction considers that a JT expansion is ideal and isenthalpic, and that the only heat absorbed by the flow is the heating power at the CIF.This results in the lowest ℎ  ( , ) and, thus, the most conservative  ℎ approximation.As discussed previously,  ℎ is the lower of the two effectiveness values, thus the overall effectiveness will be equal to or higher than the values in Fig. 20b.As it can be seen from the green points in Fig. 20b, a maximum effectiveness of 99.2±1.5% was achieved by CFHEX 3 at a mass flow rate of 150 mg/s, and the effectiveness of above 98.5±1.5% was measured at all other mass flow rates.Similarly to CFHEX 2, a higher measurement error is related to a low measured Δ between the CFHEX ends.However, there are strong reasons to suggest that 99.2% value is reliable for a number of reasons.Firstly, the axial conductivity of the mesh stack and the used materials is very low below 10 K, while the radial conductivity of copper is still relatively high.As a result, a great decou-A.Onufrena, T. Koettig, B. Naydenov et al. pling between in-plane and out-of-plane mesh conductivity as well as overall reduction of static loss is achieved.Moreover, CFHEX 3 is only 27% shorter than CFHEX 2 whereas the temperature gradient along its structure is around 7 times smaller, which suggests that a higher effectiveness is expected.Moreover, a pressure drop associated with a shorter CFHEX operated below 10 K is comparatively low, which allowed to use a finer mesh with a larger heat transfer area to further enhance the performance.
An effectiveness of 99.2% (being the lowest of the two  ℎ and   values as discussed previously) with such a low pressure drop is a remarkable achievement because the effectiveness of the coldest CFHEX has the largest implications on the available cooling power of the remote cooling system.In addition, the ability of the CFHEX to make use of vaporisation enthalpy (i.e.capture the mist flow that was not fully evaporated in the CIF) to pre-cool the incoming HP stream increases the overall performance of the remote cooling system.

Outcomes of CFHEX design
The effectiveness variation with mass flow rate of all three CFHEXs in the remote cooling system is shown in Fig. 21.It can be seen that all the CFHEXs have an optimum performance in the 125 mg∕s-180 mg∕s range where the nominal design point of the system lies.Moreover, every constructed CFHEX outperformed its predecessor in terms of maximum effectiveness, i.e.  CFHEX1 <  CFHEX2 <  CFHEX3 .This is a very beneficial trend because a) the entropy production due to irreversibilities in the system increases towards the low temperatures.Since CFHEX 3 has the highest effectiveness and a relatively low pressure drop, its losses due to entropy production are minimised [14].This has a strong and positive impact on the overall system performance, and b) this trend implies that the lessons were learnt at each CFHEX construction stage, new ways to improve the existing technology were discovered and applied to the existing designs.
The maximum effectiveness values of 94.9±0.5% (NTU of 19±2), 98.2±0.7% (NTU of 64±25) and 99.2±1.5% (NTU of ≈ 124) were achieved for CFHEXs 1, 2 and 3, respectively, in their nominal operating temperature conditions.Moreover, an effectiveness of 97.5±0.2%(NTU of 39±3) was achieved for CFHEX 2 in the 42 K-285 K range.All this is an experimental proof of the great potential of mesh-based CFHEXs and of the unique mesh-based transparent-wall design.The stated effectiveness values were achieved with combined pressure drop values of Δ  < 16 mbar for CFHEX 1, Δ  < 1.5 mbar for CFHEX 2 and Δ  < 1.2 mbar for CFHEX 3 at the nominal operating conditions of the system, 14 i.e. ṁ =150 mg/s, 5.3 bar inlet and 1.0 bar outlet pressures.The constructed CFHEXs were integrated in the remote cooling system to boost the power of the cryocooler cooling source.The resultant system performance is described in detail in [14] and serves as a confirmation of the reliability of measured effectiveness and pressure drop values.

Conclusions
A novel transparent-wall mesh-based CFHEX design has been proposed for low-temperature remote cooling and low-vibration on-ground and spaceborne applications.The CFHEX has a general concentric-tube geometry in which the low-and high-pressure stream passages are filled with metal mesh layers to enhance the heat transfer and effectiveness of the CFHEX.The first hard-wall prototype of a mesh-based CFHEX was Fig. 21.Effectiveness variation with helium mass flow rate for all three CFHEXs under different temperature conditions.Effectiveness measurements of CFHEX 1 are described in detail in [1].
presented in [12].In the novel transparent-wall design, the mesh traverses without interruption through the inner tube made out of epoxy.In this way, the mesh-to-inner wall interface is fully eliminated, which leads to a significant boost in effectiveness.
An elaborate fabrication procedure has been developed to accomplish this challenging design.It was demonstrated that a leak-tight partition between the streams can be constructed using additive manufacturing techniques.The correlated numerical model from [12] was then adapted to size two transparent-wall CFHEXs for the operation in 10 K-50 K and 4.5 K-10 K temperature ranges.They were fabricated and integrated in the remote cooling system prototype to experimentally evaluate their performance.
The transparent-wall designs were tested across the 4.8 K-290 K temperature range, and their performance was compared with the predictions of the correlated numerical model [12].The heat transfer correlation factor 0.8  proposed in [12] has been validated, and it is shown to produce reliable effectiveness predictions.The constructed transparent-wall CFHEXs reached remarkable effectiveness values of 97.5±0.2%(NTU of 39±3), 98.2±0.7% (NTU of 64±25) and 99.2±1.5% (NTU of ≈ 124) in the 42 K-285 K, 11 K-50 K and 4.8 K-10 K temperature ranges, respectively, with helium as a working fluid.The reliability of the high effectiveness values reported in this work was confirmed by measuring the overall performance of the remote cooling system [14].
Moreover, the effectiveness of the coldest CFHEX 3 was experimentally evaluated for the two-phase LP inlet flow condition.It was shown that in this condition the CFHEX was able to recuperate the additional enthalpy, which became available due to the latent heat of evaporation, and to use it for further cooling of the HP flow.This behaviour of the CFHEX is beneficial at a system level because the cooling power, which was not used at the CIF, can be recovered.
The pressure drop of the transparent-wall CFHEX was also measured, which allowed to derive a friction factor model for medium mesh.This friction factor was found to be close to a laminar flow dependency and lower than that of the coarse mesh.A higher experimentally derived friction factor for coarse mesh might be due to over-compression of the mesh in the measured stack and deformation of mesh wires.The measurement results also revealed the difficulty of estimating the dimensions of the epoxy wall in the novel CFHEX.The derived friction

Fig. 1 .
Fig. 1.Schematic of the constructed remote cooling system based on a fluid circulation loop and a cryocooler cooling source.The nominal operating conditions and the relevant temperatures are stated.

Fig. 4 .
Fig. 4. Schematic representation of an assembly process of (a) hard-wall and (b) transparent-wall designs.

Fig. 5 .
Fig. 5.A schematic representation of the transparent-wall design with inner epoxy wall and additional low-conductivity mesh layers in between the copper mesh layers as discussed in Sec.3.1.Inner and outer tube wall thicknesses are exaggerated in the schematic.

Fig. 6 .
Fig. 6.A stack of glued copper mesh layers that represent the inner structure of the transparent-wall CFHEX.The circular epoxy contours deposited on each mesh layer form an inner partition wall.

Fig. 7 .
Fig. 7. Test samples with layers of copper mesh joined to each other by deposition of a circular epoxy pattern that resembles the inner wall.Prototype (a) shows the circular epoxy pattern and the inner wall diameter corresponds to that of KF16 flange.In the prototype (b), two KF16 flanges are attached to the glued mesh stack as interfaces for further leak and pressure tests.

Fig. 8 .
Fig. 8. General geometry of a test specimen to test the leak-tightness of an epoxy wall.

Fig. 9 . 2
Fig. 9. (a) 100-mesh layer prototype for leak-tests with the cap glued to its top and KF16 flange for pump or gas bottle connection at the bottom.(b) The prototype from (a) connected to a leak-detector to test the integrity of the epoxy wall.(c) The prototype from (a) in a bath of liquid nitrogen with helium at 5 bar(g) on the inner side of the epoxy wall.

Fig. 11 .
Fig. 11.Samples consisting of (a) plastic mesh only, and (b) alternating copper and plastic mesh layers for leak testing of plastic-plastic and metal-plastic glued interfaces, respectively.

Fig. 12 .
Fig. 12. Schematic of the test arrangements for CFHEX 2 performance characterisation with fluid inlet flow temperatures of (a) ≈ 290 K at the warm and ≈ 50 K at the cold CFHEX end (in this arrangement JT2 only has a function of pressure reduction and   ≈ 0), and (b) ≈ 50 K at the warm and ≈ 10 K at the cold CFHEX end.The fluid temperature conditions are ensured by means of a two-stage GM cryocooler, regulated by electric heaters (EH) and measured with temperature sensors (TT).The fluid pressure and pressure drop are measured with absolute (PT) and differential (PDT) pressure transducers.The pressure drop in the system is regulated using a JT2 hand-valve.

Fig. 13 .
Fig. 13.(a) Schematic of the remote cooling system with integrated CFHEX 3, and (b) photo of the constructed remote cooling system.The locations of CFHEX 1, 2 and 3, top of the thermal radiation shield (TS), stage HEXs 1 and 2 are shown.The constructed remote CIF is located 0.7 m (piping length) away from the 2 nd stage of the cryocooler cooling source.The heat transferred through the wires of the temperature sensors is intercepted at the thermalisation pads TP1, TP2 and TP3 at the temperature levels near 50 K, 10 K and 4.5 K, respectively.

Fig. 15 .
Fig. 15.Cross-section of a transparent-wall CFHEX sample.Inner diameter measurement uncertainty is estimated to be ± 1 mm.

Fig. 16 .
Fig. 16.Pressure drop variation with helium inlet pressure for CFHEX 1 and 2. Warm and cold end temperatures of high-pressure stream are around 290 K and 60 K, respectively.

Fig. 17 .
Fig. 17.Variation of pressure drop of CFHEX 2 with inlet pressure for different helium mass flow rates in the (a) 60 K-290 K and (b) 10 K-50 K temperature ranges.The source of the friction factor (determined in warm conditions) is indicated in Mesh geometries can be found in Table

Fig. 18 .
Fig. 18.HP and LP pressure drop variation with helium mass flow rate in CFHEX 2. The warm and cold CFHEX end temperatures during the test are 285 K and 42 K, respectively,  ℎ = 3.0 bar and   = 1.7 bar.

Fig. 20 .
Fig. 20.Variation of (a) pressure drop and (b) effectiveness of CFHEX 3 with mass flow rate. ℎ, = 10 K,  , = 4.8 K,  ℎ = 2.2 bar and   = 1.7 bar during the test.Points and lines represent the experimental and simulation data, respectively.The sources of the friction factor and correlation parameters used for the simulation are indicated in brackets.The maximum  ℎ ,   and ṁ measurement uncertainties are ±42 mbar, ±15 mbar and ±3 mg/s, respectively.

steel, 𝒕 = 𝟎.𝟕𝟎 mm (reference)
. (For interpretation of the colours in the table, the reader is referred to the web version of this article.)

Table 3
Different copper mesh dimensions considered for the CFHEX design.Porosity   = 0.62 is considered for all mesh options.