Applied Experimental and numerical study of the additive layer manufactured inter-layer channel heat exchanger

In this paper the performance of a recently patented additive layer manufactured (ALM) concept inter-layer heat exchanger (HE) is evaluated experimentally and numerically. Two numerical HE models are developed using the conjugate heat transfer (CHT) methodology. The first is an idealised HE core model, consisting of a single period width HE corrugation section (termed superchannel). The second approach uses a fully detailed HE unit model which resolves the flow and heat transfer inside the complete HE unit. A close agreement was found between the HE unit simulations and the experimentally obtained results, such that the fully detailed HE model could be validated. It was also shown that, a full CHT approach is necessary to accurately evaluate complex inter-layer ALM HE core flow and heat transfer behaviour and can serve as an approach for optimising HE designs. The results also reinforce the occurrence of the inter-layer flow mixing inside the HE core of the same flow streams and allows the mass flow to redistribute inside the HE core which is impossible with the current HE generation geometries. The superchannel model results in a slight over-estimation in heat transfer ( 𝛥𝑇 ≈ 4 K on average) making the simplified model acceptable as a conservative estimate. Using validated simulations a parametric study was conducted by changing the solid properties of the full CHT HE model to aluminium to investigate the effects of a significantly more conductive material. This resulted in ≈3% higher heat transfer effectiveness ( 𝜖 ) of the HE unit. All the simulations were carried out using CFD package OpenFOAM.


Introduction
Heat Exchangers (HE) are the devices in which the heat is transferred between two or more fluid streams separated by a solid and are critical components in many industries, such as aerospace, automotive, power generation or chemical & process industry [1]. In high performance applications, such as aerospace and motorsport, the smallest overall HE size is critical since it enables the highest installed component density. This is normally achieved through increasing a number of the heat transfer surfaces (such as fins) and is referred to as compactness in the HE industry. The compactness of a HE is typically measured either using hydraulic diameter ( ℎ ) or the surface area density ( = ∕ ), measuring a ratio of heat transfer area to flow volume. To classify a HE as compact the values for liquids should be at least ℎ ≈ 8 mm and ≈ 400 m 2 ∕m 3 whilst for gasses they should be at least ℎ ≈ 5 mm and ≈ 700 m 2 ∕m 3 [2]. Traditionally, the heat transfer surfaces are assembled into HE cores using brazing and connected to fluid streams using headers which are welded on to the brazing or welding. This can provide improved structural integrity and a reduced likelihood of current HE manufacturing flaws, shown in [3]. SLM is also capable of producing solid surfaces at the HE relevant lengthscales (50 μm wall thickness reported in [9]) [10] making it advantageous for HE. Numerical analysis of compact HE is typically undertaken in two steps: firstly a small section of the HE core is analysed to obtain friction and heat transfer characteristics. These are then implemented in a simplified HE unit model which uses porous media and heat transfer effectiveness models to evaluate macro level flow and heat transfer performance [3,11,12]. In such scenarios, a periodic section of the HE corrugation is often used as introduced by Patankar et al. [13]. This method is computationally cheap and can be used in parametric studies [14,15], however, it has disadvantages for higher Reynolds number predictions [16]. More recently, the trend observed is to model larger sections of HE corrugation, which consist of a finite length HE corrugation channel [3,17,18]. This can provide a better understanding of flow and heat transfer development inside the channel and thus an overall more reliable HE performance prediction. Another emerging trend is to use the Conjugate Heat Transfer (CHT) methodology for compact HE and small sections of both plate-fin [19,20] and tubefin [21] HE being evaluated. The CHT methodology is undertaken to account the conduction with the fins and is reported to increase accuracy of predictions [20] compared to the traditional single computational domain approaches. A large computational domain for a plate-fin HE was also previously evaluated by the authors [3] in a numerical and experimental study which aimed at accounting the cross-flow heat transfer effects more fully in plate-fin HE applications.
In this study, a previously designed, manufactured [10] and recently patented [22] concept titanium SLM HE is evaluated experimentally and numerically to establish flow resistance and thermal performance characteristics. A fully detailed ALM HE CFD model, employing the CHT methodology is developed and validated using the experimental results. These results are then compared to a more idealised numerical model consisting of a single corrugation period width HE core (superchannel) for heat transfer predictions. Finally, using the validated inter-layer HE unit model a parametric study is undertaken to evaluate the HE performance with aluminium as the HE material to investigate whether any thermal gains are obtained.

Experimental approach
An experimental study was conducted to evaluate the concept interlayer HE which geometry is described in detail in [10]. It was manufactured using SLM out of commercially pure titanium ( Fig. 1a) with its relevant properties given in Table 1. This material was selected working in collaboration with the SLM specialist based on a number of factors. Firstly, CpTi has good printability, reliability and repeatability characteristics when used in SLM. Secondly, despite having lower thermal conductivity than materials such as Aluminium or Copper, it is used in the heat transfer industry in heavy duty applications where weaker and softer materials cannot withstand the lifecycle. Also, it was noted that no inter-layer fluid leakages were observed after the build. The concept HE unit consists of four cold and three hot layers which use a counter-flow oriented inter-layer HE corrugation with a mean hydraulic diameter of ℎ = 2.8 mm (channel height of 5.5 mm, distance between elipses of 2 mm, and ellipse width and length of 2 and 4 mm), uniform wall thickness of 0.5 mm and surface area density of = 818 m 2 ∕m 3 , shown schematically in Fig. 1b. The surface density of the proposed ALM structure is similar to plate-fin HE and classifies it as compact for both gasses and liquids according to Shah [23]. In contrast to plate-fin corrugations the proposed structure enables the maldistributed flow entering the heat exchanger core to re-distribute across the layers through the inter-layer structure. Maldistributed flow is a common issue in high performance applications such as aerospace and motorsport occurring due to space limitations resulting in restricted header design which leads to non-uniform heat exchanger matrix utilisation. The proposed design in turn has potential for improved utilisation of heat exchanger core volume, enabling either more heat transfer capacity or a smaller heat exchanger for a given application. The HE was tested in an experimental setup as shown in Figs. 1c and 1d with air used as a working fluid for both flow streams. Note, that Fig. 1c shows the uncovered HE unit, which was insulated using Silicon Carbide sheets and experiments were run inside a chamber to further minimise heat loss. To simplify the experiments the hot flow side of the HE was run at a constant Reynolds number of ≈ 28760 ( = ∕ ). This is equal to ≈ 670 assuming even flow distribution at the HE core inlet ( = ℎ ∕ ). The cold fluid stream was varied between 6120 ≤ ≤ 55914 (108 ≤ ≤ 980) with ten separate measurement points recorded.
During the experiments the hot stream air was heated up to ≈ 363 K using a 750 W heater whilst the cold stream was supplied with ambient air (on average ≈ 290 K). The flow on each fluid side was measured using rotameters (KDG Instruments series 2000) which have a +∕−2.5% accuracy. Pressure was measured using FC034 pressure transducers, having a +∕−0.5% measurement accuracy. Calibrated type K mineral insulated thermocouples were used for measuring the temperature at the inlet and outlet of both fluid streams with a tolerance of ±1.5 K. To ensure repeatability of the experiments, certain points were repeated three times. The thermal experimental uncertainty was measured using heat balance, shown in Fig. 3a and obtained by: (1) E. Greiciunas et al.  where ℎ is the heat emitted by the hot stream and is the heat absorbed by the cold stream. This formulation means that a scenario in which the heat balance is below 100 (more heat absorbed than emitted) is not physical since some heat loss to the environment is expected despite insulating the HE. It should also be noted that the error bars placed on the measured heat balance (Fig. 3a) show the maximum possible error due to the measurement accuracy of the experimental equipment described above. However, this level of error is unlikely as indicated by the repeated experimental points in Fig. 3a, where on average the fluctuation between the experimental heat balance is <5%. This confirms a good repeatability level of the experiments which were completed over a time span of two weeks. It should be noted that the highest repeatability error was found at the lower Reynolds numbers, which likely arises from difficulty measuring the very small mass flow in the test rig. The pressure for both fluids was measured at the inlet to each HE stream. To calculate the pressure drop this pressure was subtracted from the atmospheric pressure measured during the experiments, shown in Fig. 3b. This measurement technique resulted in the need to apply experimental correction since due to the setup, a pressure drop occurs as a result of the sudden expansion in the pipe diameter at the outlet section of the experimental rig. It occurs at a location where the flow exits the HE header ( = 13 mm) and enters the rubber ducting connected on the outer diameter of the HE header surface ( = 27 mm) (Figs. 1a and 1c). The contribution of this additional pressure loss was taken into account by using the well established analytical formula for a head loss in a pipe, taken from White [24]: where was taken as a mean velocity at the inlet to the HE (worked out from the mass flow) and = 0.6 was selected based on [24]. Note, that the K coefficient does not account for the slight turn in the outlet tubing, leading to a potential slight under-estimation of the pressure drop in that section. The corrected pressure drop data in Fig. 3b and shows the increasing influence of the pressure drop in the pipe expansion section compared to the pressure drop in the HE unit and it should be noted for any future experimental setup design.

Numerical solution methodology
Numerical simulations undertaken in this study are an extension of the single fluid domain analysis undertaken in [10]. In this study, CFD simulations of the inter-layer ALM HE were undertaken with the CFD code OpenFOAM using steady-state incompressible continuity of mass, momentum and energy equations for the fluid domain [25]:  where -mean RANS velocity vector, -fluid pressure, -fluid temperature, -fluid density. = + , where is the dynamic turbulent viscosity and calculated based on the − turbulence model [26] used in this paper and ) and is the turbulent Prandtl number taken to be 0.85 in RANS simulations. Note that + adaptive wall treatment was used. All the predictions in this article used smooth no-slip wall assumption (since surface roughness data of the prototype was not available) and the CHT formulation, thus, included resolving heat transfer in the solid region, separating the hot and cold HE flows. This was undertaken solving the heat conduction equation: The steady-state assumption was maintained throughout all the simulations as it has been previously shown to produce accurate predictions of pressure drop and temperature change in studies [3,10] for the Reynolds number range at which the HE unit was experimentally tested. It is, however, acknowledged that there could be unsteady flow features as indicated in [16] together with experimental [27,28] and numerical studies [4,17,29] which provide insight into these transient effects. The effect of the unsteady flow features is considered small for the HE of this study. The simulations were discretised using two levels of approximation provided in Table 2 whilst the meshing was completed using a combination of the inbuilt blockMesh and snappyHexMesh tools within OpenFOAM, ensuring that default mesh quality conditions (non-orthogonality, skewness, aspect ratio) in OpenFOAM were met.

Computational domains and grid independence
In this section the fully detailed HE model including CHT (cold and hot fluid domains separated by a solid) is undertaken (Figs. 2a,  2b and 2c). The fully detailed model approach produces results in good agreement with experiments and enables the observation and evaluation of the complex flow through the inter-layer HE corrugation. This approach is contrary to the normal practice of simplifying the flow and heat transfer inside the HE unit with porous media and heat transfer effectiveness models [10]. To check the accuracy of the solutions a range of HE unit meshes were created and compared to the first experimental test point (Table 3) using second order dominant discretisation ( Table 2). Medium and fine meshes show both convergence in terms of temperature and pressure between the solutions. Additionally an acceptable agreement to the experimental data is also shown (note that potential experimental inaccuracies are more likely for the first point (Fig. 1a), driven by low mass flow rate on the cold side). Fine resolution HE unit mesh was selected for further simulations -further increase in mesh resolution was treated as an overly high computational cost.
The superchannel model (Fig. 4a) is the second HE core model used in this study and consists of one corrugation period width slice of the HE core following the methodology in [10]. It produces idealised HE core thermal performance and pressure drop predictions since the model does not take into account the maldistributed flow as it enters the HE core. The meshing controls of from the HE unit model were used for the smaller superchannel model which also uses the CHT methodology. This ensures comparability between the superchannel and HE unit models through maintaining the same mesh resolution. To estimate the HE unit flow resistance together with the superchannel model thermal predictions, the cold HE side outlet header was modelled (Fig. 2d). Again, the same meshing controls as for the HE unit model were applied, which maintains the solution similarity with the other two models. This is done since [10] showed that the pressure drop for this HE is dominated by the outlet HE header effects. This two model approach allows a computationally cheaper estimate of the HE unit performance, however, it is also important to understand the inaccuracy it produces which is studied in the next section.

Validation of the numerical results with the experiments
In this section the results of the two numerical HE models are presented and compared to the experimental work. Firstly, the HE unit pressure drop is compared in Fig. 4b and it can be seen clearly that both full HE unit models predict pressure drop very close to the experimentally measured values. Interestingly, the pressure drop of both discretisation accuracy approaches produce almost an identical response. This is in contrast to the previous findings in [16] where a two dimensional sinusoidal corrugation was evaluated and led to a higher pressure drop. However, in the current study the pressure drop is measured at the HE unit level and was shown to be highly dominated by the outlet header effects [10] which could have reduced the importance of more accurate discretisations.
This can be further seen when looking at the cold flow outlet HE header (Fig. 2d) pressure drop in Fig. 4b. This simplified model uses a uniform velocity inlet to the domain and in turn directs more mass flow through the outer layers of the HE core where the passage of the flow is more difficult. This in turn leads to an increased pressure drop overprediction (up to 60%) using the outlet HE header alone (further highlighting the pressure drop inefficiencies inside the outlet header design). It should be noted though that this is a proof of concept HE, and the design is not claimed to be an optimum at this stage. Additionally, as this reduced complexity model provides a significant computational saving, it is considered to be a potentially useful option for a conservative pressure drop estimate, especially in the more optimised HE header design cases.
Mass flow redistribution inside the HE core (Figs. 5a-5b) is another area of interest and is critical for evaluating the performance of the concept inter-layer corrugation. Here the HE core layers are numbered 1-4 bottom to top for the cold HE side (Fig. 2a) and 1-3 bottom to top for the hot HE side (Fig. 2c). For the cold HE side (Fig. 5a), the performance is very similar to the results obtained in the previous numerical study [10] where it was found that almost double the initial mass flow into the outer HE core layers is absorbed (Layers 1 and 4) across the range of 108 ≤ ≤ 979. A similar trend is also observed on the hot side of the HE (Fig. 5b) which was kept almost at a constant flow rate during experiments. In this case the flow direction is the opposite (as the HE is counter flow) and there are three hot HE core layers which are surrounded by the cold flow. Thus, in Fig. 5b the mass flow redistribution between the layers can be observed in Layers 1 and 3 reaching almost double the initial entrained mass flow. This   would not have been possible on both sides of the HE without the interlayer passages. It reinforces the potential advantages of the inter-layer channels (previously studied in [10]).
In terms of the thermal performance it is firstly compared qualitatively in 4c where during the last experimental point the thermal HE insulation was removed and the thermal image was taken using a FLIR thermal camera. This is not a fully accurate experimental result due to the thermal leakage to the environment and relatively low image resolution of the camera (640 × 480). However, the image provides a good indication of heat transfer distribution across the HE unit and allows to directly compare it with the solid HE unit computational domain results at the same experimental point (in terms of showing the hot and cold regions of the HE unit which should be minimised to achieve better overall HE unit efficiency). Overall, close agreement can be seen between the numerical and experimental results which reinforces confidence in the numerical simulation. Further comparison of the thermal results is shown in Figs. 5c and 5d. Here both the superchannel and the full HE unit models are compared across the experimental dataset for cold and hot HE sides (the cold flow was varied 108 ≤ corrug cold ≤ 979 whilst the hot flow was maintained at corrug hot ≈ 670). Several interesting trends can be observed and are discussed below.
Both models (HE unit and superchannel) were discretised to both first and second order accuracy which revealed an interesting difference between them. For the HE unit predictions higher accuracy discretisation led to a larger thermal prediction (up to ≈ 2.5 K at the last experimental point) with increasing cold side flow rate. This difference also starts to become noticeable from 300 ≈ corrug cold ≈ 400, close to the previously suspected onset of the transitional flow occurring in HEs [3,10,16]. The first order dominant discretisation was shown previously [16] to omit this flow regime occurring, producing a steadystate response. This onset of the transitional flow is also thought to lead to increasing disagreement between experiments and HE unit predictions in terms of the overall on both fluid sides which remains within the experimental error bars for the cold side and just outside ( ≈ 2 K) from the error bars on the hot side. The challenge of measuring the low experimental mass flow is also a potential secondary reason why the temperature change might had a lower predicted value. This can be a factor on the hot side especially as the flow measurement was calibrated at room conditions.
In contrast, no difference is observed when comparing the predictions of the first and second order accuracy dominant discretisations using the superchannel model (Figs. 5). This is an unexpected result, however, it perhaps indicates that the effect of the discretisation may only become significant in more complex flow scenarios (e.g the full HE unit case discussed above). The unsteady flow occurrence is thought to also have a smaller effect on this particular HE within the Reynolds numbers tested. This is based on the previous results [10] where it was shown that at least to = 1000 both steady state and transient predictions lead to very similar results of pressure drop and temperature change. The thermal predictions using the superchannel model are also constantly higher than with the HE unit model and this increases at higher Reynolds number. This is expected and was also observed in the previous study [10] and occurs because the superchannel model is and does not take into account the complex inlet HE header effects. However, superchannel is seem to be a very useful HE core model since it leads to significant computational cost reduction.
Additionally, the superchannel model shows the potential of the HE core if it was equipped with more efficient headers (this in theory shows that an additional 5 could be lost/gained by the cold/hot HE sides respectively at the highest Reynolds number).
To summarise, the CFD is in a good agreement with the experimental results for pressure drops across the Reynolds number range tested. For the temperature change the agreement on both cold and hot HE sides is good, especially taking into account both experimental and numerical challenges for resolving the flow in the transitional Table 4 Relevant properties of the AlSi10Mg which could be used to manufacture the prototype HE, taken from EOS (SLM manufacturer) website [30].  Reynolds regime. Both first and second order dominant discretisation schemes can be applied for analysing the HE, but it should be kept in mind that at the higher Reynolds numbers the first order approach is likely to lead to some solution inaccuracies. First order dominant discretisation schemes could be useful for estimating flow and heat transfer through complicated HE corrugations or when used for large computational domains where the faster convergence is advantageous from a pragmatic perspective.

Effect of higher conductivity material for the heat transfer efficiency
Achieving good model agreement with the experimental data provided confidence to carry out a parametric study of the HE unit. One particular concern raised during both manufacture and testing was the usage of commercially pure Titanium due to its non-optimal thermal properties (Table 1). Thus, it was decided to study a scenario in which the HE unit would be manufactured using an Aluminium powder (AlSi10Mg). Its properties were taken from one of the HE manufacturers and summarised in Table 4. It also should be noted that the thermal properties of the Aluminium ALM powder are also very similar to ones of conventional HE aluminium [3] which shows potential of the technology for the next generation HE. Comparing the commercially pure titanium (Table 1) and Aluminium (Table 4), it can be easily observed that the Aluminium has significantly higher potential for heat transfer which can be compared using the material thermal diffusivity [31]: with the results provided in Table 5. It can be clearly seen that the overall potential for the Aluminium to transfer more heat is more than of an order higher and one could intuitively expect significantly more efficient heat transfer. Thus, the material properties were implemented into the superchannel and HE unit models to evaluate whether using Aluminium would enhance the heat transfer for the HE unit. The simulations in this case were completed using the dominant second order accuracy for both Aluminium and Titanium ( which for the two HE sides becomes: where =̇, ℎ =̇ℎ and = min( , ℎ ). The two expressions (Eq. (10)) enable evaluation of the heat transfer efficiency for both models with the data shown in Fig. 6. Contrary to the original expectation, only a relatively low increase in the heat E. Greiciunas et al. transfer effectiveness is observed (on average a 3% increase). However, it is thought that this can be explained by the low wall thickness used for the HE unit (uniform 0.5 mm in both HE header and HE core) which in turns reduces the importance of the separating material. Furthermore, the inter-layer heat exchanger has no secondary heat transfer surfaces (fins) which makes the heat transfer more efficient and the role of highly conductive material less critical. The supporting evidence for this can be found in heat exchanger literature such as Shah and Sekulic [31] and Kays and London [32]. The example HE sizing calculations using the analytical − HE model in Kays and London [32] does not even take into account the thermal primary heat transfer surface solid resistance into account and assumed it negligible. It is only used in the later literature, however, described as a minor diffusive loss as in Shah and Sekulic [31] and they also emphasise that the role of the primary surface conduction becomes significant only in cases of low conductivity materials (e.g. ceramics and plastics) or high wall thickness. However, in both books [31,32] the analytical HE models do take into account the fin efficiency (for the concept HE design it is unity). Thus, it could potentially be expected that for current generation HE, such as plate-fin HE, change in material would make a more significant difference due to the dominance of the secondary heat transfer surfaces, especially for thicker surfaces. Additionally, in [31] it is stressed that the heat transfer resistance in the fluid film is typically a dominant force. Such results were observed in an study by Luo and Roetzel [33] where performance of an aluminium and stainless steel plate-fin HE was modelled and found that conduction played a much smaller role in the case of Aluminium finned structure whilst for the stainless steel structure (thermal conductivity is comparable to titanium) stronger fin conduction resistance effect is reported. No fins are present in the proposed inter-layer HE, making it an overall inherently more efficient HE (already in addition to the counter-flow orientation). Furthermore, elimination of fins should also minimise the transient heat transfer effects, occurring due to a change in flow conditions. However, the findings of Luo and Roetzel [33] also provide a reason why some improvement in heat transfer effectiveness is found and is at ≈3%. In the case of the HE unit (Fig. 2a-2c) -the flow entering both hot and cold flow HE core sections is maldistributed. This creates sections inside the HE core where the heat transfer is not optimised (e.g. in regions where flow recirculates). This in turn leads to higher importance of efficient lateral solid conduction for those regions, making Aluminium HE more efficient.

Conclusions
The recently patented concept titanium inter-layer HE, manufactured using the SLM method, was evaluated experimentally producing a comprehensive dataset and modelled using CFD. It should be noted that this HE is an initial concept and it is not aimed to be an optimised design for a specific application. Two HE models were developed using a CHT methodology: firstly, a fully detailed HE unit model was developed in order to capture the complex flow and heat transfer in full detail. The second model used the simplified single corrugation width HE core model (termed superchannel) for thermal predictions and the outlet HE header to account for the pressure drop contribution. The main findings of the study are: • A very close agreement is found between the HE unit model and the experiments in terms of the pressure drop performance across Reynolds number range. In terms of the thermal performance, a good agreement was found between the HE unit model and the experiments with most of the prediction points lying within the experimental error bounds. The results provide a validation of the full CHT HE numerical model. • The superchannel model consistently provided slightly higher thermal transfer rates in terms of since it provides an idealised heat transfer scenario where no maldistribution inside the inlet HE header occurs. However, the superchannel model is still valuable since it shows the maximum thermal efficiency this HE core could obtain and is significantly computationally cheaper than the complete HE model. Simulating the outlet HE header separately produced an increasingly higher pressure drop compared to the experiments (up to ≈ 60%). However, since simulating the HE header separately is significantly faster computationally and over the lifetime of the HE, its pressure drop of the HE is expected to increase significantly ( [34][35][36] reported fouling related pressure drop increase up to 200%), the separate HE header model can still be used as a conservative pressure drop estimate.
• A study was conducted by altering the solid domain from titanium to aluminium to evaluate the HE performance using a more thermally conductive material. On average, approximately a 3% increase in heat transfer effectiveness was observed. The thermal conduction was found to have a smaller influence than originally expected and is thought to relate to: firstly, the proposed inter-layer HE corrugation eliminates secondary heat transfer surfaces (fins) which reduces the role of solid conduction. Secondly, the low uniform (0.5 mm) overall wall thickness, which further minimises the role of solid conduction.

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.