Micro-structured heat exchanger for cryogenic mixed refrigerant cycles

Mixed refrigerant cycles (MRCs) offer a cost- and energy-efficient cooling method for the temperature range between 80 and 200 K. The performance of MRCs is strongly influenced by entropy production in the main heat exchanger. High efficiencies thus require small temperature gradients among the fluid streams, as well as limited pressure drop and axial conduction. As temperature gradients scale with heat flux, large heat transfer areas are necessary. This is best achieved with micro-structured heat exchangers, where high volumetric heat transfer areas can be realized. The reliable design of MRC heat exchangers is challenging, since two-phase heat transfer and pressure drop in both fluid streams have to be considered simultaneously. Furthermore, only few data on the convective boiling and condensation kinetics of zeotropic mixtures is available in literature. This paper presents a micro-structured heat exchanger designed with a newly developed numerical model, followed by experimental results on the single-phase pressure drop and their implications on the hydraulic diameter.


Introduction
In recent years, the application of MRCs as a reliable and ecient refrigeration method for hightemperature superconductors in cables, fault current limiters, etc. has been reviewed [13]. MRCs consist of a Linde-Hampson refrigeration cycle operated predominately in the two-phase region of wide-boiling mixtures. This enables low temperature gradients among the uid streams in the main heat exchanger and thus an increased process eciency [4]. As low temperature gradients necessitate large heat transfer areas, micro-structured heat-exchangers are well suited due to their high volumetric heat transfer areas.
In recent work, a correlation-based, numerical heat exchanger model has been presented, capable of calculating heat transfer and pressure drop of zeotropic uid mixtures simultaneously along the length of the heat exchanger [5]. Utilising this model, a micro-structured heat exchanger was designed for future use in MRCs. The counter-ow heat exchanger was produced by diusion welding of 60 micro-structured sheets (stainless steel grade 1.4571). A schematic representation of these metal sheets is presented in gure 1. Each sheet was structured by etching 50 parallel, S-shaped channels with 400 µm width, 200 µm depth and 20 cm length. Additionally, the sheets  comprise four positioning holes for sheet alignment and four cut out areas forming the headers.
The sheets were stacked face-to-face prior to diusion bonding to form round channels of 400 µm diameter. In total, the heat exchanger consists of two passages with 750 channels each. The vapour-headers are designed signicantly larger than the liquid-headers to account for the density change due to evaporation and condensation. The area ratio was estimated following the design rule given by Kays et al. [6]: where A depicts the cross-section area and ρ the uid density. Both isotropic wet-chemical etching and face-to-face stacking typically do not yield exact channel geometries. While isotropic etching tends to produce elliptical channels rather than perfectly circular ones [7], diusion bonding of face-to-face stacked micro-structured sheets can lead to a parallel oset between the channels. Hence, the resulting channel geometry can dier signicantly from the specied one. In order to assess the magnitude of this deviation, the single-phase laminar pressure drop is investigated at room temperature. Since the Poiseuille law provides an analytical solution for the pressure drop in the laminar ow regime, an accurate estimate of the eective hydraulic diameter can be derived. The pressure drop model used to correlate the generated data and the inuence of the manufacturing process on the channel geometry are described in section 2. The experimental procedure of the pressure drop measurements is presented in section 3. In section 4 the results are presented and discussed. Finally, the paper is summarised in section 5.

Theoretical framework
In this section, the equations used to model the single-phase pressure drop in the heat exchanger are outlined and the eect of the manufacturing steps on the channel geometry is discussed. can be derived from the cross-section area A and the circumference C: In the laminar ow regime the friction factor is dened by the Poiseuille law as where Re is the Reynolds number and η is the dynamic viscosity of the uid. For the two 45 • bends of the S-shaped channels, an equation derived by Hausen [8] based on data by White [9] is used to calculate the friction factor where R is the radius of the bend. The pressure drop at the entrance and exit of the heat exchanger core is calculated according to Kays et al. [6]: with where σ depicts the ow area ratio and K c and K e the contraction and expansion coecients for laminar ow taken from gure 5-2 in Kays et al. [6]. The uid properties of the test uids, helium and air, were calculatd with REFPROP [1012] using the local pressure and the average of inlet and outlet temperatures.

Channel geometry
In order to quantify the eect of the manufacturing process on the hydraulic diameter, three inuences are discussed: • wet-chemical etching, • parallel oset of the micro-structured sheets and • surface roughness of the channel walls.
The isotropic wet-chemical etching process typically yields elliptical rather than circular channels (cf. gure 2) [7]. The manufacturing tolerances of the etching process are specied with ± 60 µm and ± 30 µm for the channel width and height, respectively. This results in a ± 60 µm uncertainty of the hydraulic diameter.
The change in hydraulic diameter caused by a parallel oset x os of two structured sheets stacked face-to-face is given by As illustrated in gure 2, the hydraulic diameter is reduced due to an increase in circumference while the ow area remains constant. The diameter tolerance of the positioning hole for sheet alignment is given with + 80 µm. In case of a circular channel with a 400 µm diameter, a parallel oset of + 80 µm results in a reduction of the hydraulic diameter by − 45.2 µm.
On account of the small hydraulic diameters utilised in compact heat exchangers, the roughness introduced to the channel walls through etching can lead to high relative roughness values. Therefore, the surface roughness can inuence the pressure drop even in the laminar ow regime. Kandlikar et al. [13] have proposed to consider roughness eects by modifying the ow diameter based on constrictions caused by the surface roughness. The constricted ow diameter d h,cf is given by where is the average roughness height. Therefore, a typical worst case estimate of 5 µm average roughness height reduces the hydraulic diameter by − 10 µm.
Considering all the eects mentioned above yields a hydraulic diameter of 400 + 60 −115.2 µm.

Experimental method
A schematic representation of the experimental set-up used to investigate the pressure drop is shown in gure 3. The ow rate of the test medium (dry air or helium) is regulated with a hand valve. Before entering the test section, the temperature of the gas is controlled with a water bath. The gas temperatures up-and downstream of the heat exchanger (TI 1 & 2) are measured with a Pt-100 Class B platinum thermometer and a Endress+Hauser TMT84 temperature transmitter. The absolute pressure in the laboratory and the relative pressure before the heat exchanger (PI 3) are both determined with Endress+Hauser PMC731 pressure transmitters. Since each heat exchanger passage is equipped with only one pressure port at either the liquid-or vapourheader, the pressure drop of the heat exchanger core cannot be measured directly. Additionally, the liquid-and vapour-header are equipped with dierent diameter tubing. Therefore, the tubing pressure drop on the liquid-and vapour-side can each only be determined with passage 1 or 2, respectively. Endress+Hauser PMD235 dierential pressure transmitters are used to measure the pressure dierence between the up-and downstream pressure ports (PDI 4) and between either the upstream pressure port and the upstream header (PDI 5-1) or the downstream header and the downstream pressure port (PDI 5-2), depending on ow direction. In order to isolate the core pressure drop from the tubing pressure drop, the experimental values for the liquid-and vapour-side tubing are interpolated and subtracted from the PDI 4 data. The gas ow rate is offset etching Each data point is the average of 100 measurements taken at a 5 Hz sampling rate. All uncertainties are given as expanded uncertainties according to the guide to the expression of uncertainty in measurement (GUM) [14], using both Type A and Type B contributions with a coverage factor of k = 2.
During the course of the experiments, the pressure drop of both heat exchanger passages is determined in either ow direction and with gaseous helium and air. Helium ow rates of 0.05 1 g/s and air ow rates of 0.25 4 g/s were achieved, resulting in Reynolds numbers of 10 250 and 60 1100, respectively.

Results and discussion
A comparison of the experimentally determined Darcy friction factors with Poiseuille's law (cf. equation 4) is depicted in gure 4. For this comparison, the eect of the 45 • bends as well as the entrance and exit losses are subtracted from the experimental core pressure drop. The experimental data based on the nominal diameter exhibit a signicant parallel oset from the prediction of laminar theory. This indicates that all data points correspond to the laminar ow regime, but the eective channel geometry deviates substantially from the specied one. Figure 5 illustrates that the model under-predicts the experimental data by up to 65 %. In order to estimate the uncertainty of the predicted pressure drop, the ideal gas law is used to calculate the gas density and the pressure dependence of the gas viscosity is neglected. In this comparison, the uncertainty of the hydraulic diameter estimated in section 2.2, accounts for over 99 % of the error bars of the calculated pressure drop. The uncertainties due to temperature, pressure and mass ow measurements evaluate to only 0.0 0.7 mbar, 0.1 1.8 mbar and 0.1 3.2 mbar, respectively. This highlights the high degree of sensitivity of the pressure drop regarding the hydraulic diameter.
To account for the eects mentioned in section 2.2, eective hydraulic diameters for both passages are determined by tting the pressure drop model to each individual experimental   Additionally, it is interesting to note that, on average, the Poiseuille law makes up 97.4 % of the total pressure drop. The 45 • bends and the entrance and exit eects account for only 1.5 % and 1.1 %, respectively. As the Poiseuille law is of analytical origin, the plausibility of the eective hydraulic diameter can be assumed.

Summary and conclusions
In this paper a micro-structured heat exchanger for MRC applications is presented. The heat exchanger was designed with a correlation-based numerical model, capable of predicting heat transfer and pressure drop of zeotropic uid mixtures. As an initial assessment of both heat exchanger and model performance, the single-phase pressure drop is determined with helium and air at room temperature. Experimental pressure drop values range from 0.05 to 0.9 bar with Reynolds numbers of 101100.
The experiments reveal a signicant discrepancy between the specied and the actual channel geometry. Manufacturing tolerances, parallel oset of the micro-structured sheets and surface roughness are identied as the most signicant inuences on the hydraulic diameter. Employing eective hydraulic diameters of 324.4 +3.8 −6.3 µm and 321.5 +3.0 −5.0 µm for passage 1 and 2, respectively, the experimental data is predicted within a ±10 % error band. The eective hydraulic diameter provides the basis for future experimental investigations of heat exchanger and model performance. Since most heat transfer and pressure drop correlations are based on the hydraulic diameter, an accurate estimate of the hydraulic diameter is a precondition for a comparison between model and experiments in an MRC setup.