Numerical modeling of recuperative cryogenic matrix heat exchangers and the experimental validation

https://doi.org/10.1016/j.ijthermalsci.2016.01.014Get rights and content

Highlights

  • A numerical model to predict the thermal performance of MHEs is developed.

  • The model considers the effects of both axial/radial conduction and heat leakage.

  • The axial conduction deteriorates the MHE performance at low mass flow rate.

  • The effects of the axial conduction via the outer wall are important.

Abstract

The recuperative matrix heat exchanger (MHE) has advantages of large specific surface area, compactness, high effectiveness, and low flow resistance, which make it promising for applications in Joule-Thomson cryocooler and reverse Brayton cryocooler. In this study, a numerical model is developed to predict the thermal performance of MHEs. The effects of axial conduction of both inner and outer walls as well as radial heat conduction through mesh-screens and the heat leakage are considered. The temperature distribution over the fluids and mesh screens in MHEs can be determined using this model. The model is validated by analytical solution of effectiveness-NTU method and the results of the experimental tests on two MHEs with different structures at cryogenic temperature. Using the proper correlations for heat transfer coefficients, the relative deviations of the ineffectiveness predictions from experimental results are below 13.2% in the mass flow range of 0.4 g/s – 2.1 g/s. The numerical results show that the axial conduction of inner and outer walls has similar effects on the thermal performance of MHEs. The increase of axial conduction can substantially lower the effectiveness of the MHEs at mass flow rates below 1 g/s, while the influence of the number of transfer unit (NTU) on the MHE effectiveness becomes dominant at mass flow rates above 1 g/s.

Introduction

Matrix heat exchangers were first developed and studied by McMahon in 1950 [1]. A typical MHE consists of numerous high thermal conductivity perforated plates (or wire-screen) and low thermal conductivity spacers. The alternate spacer-plate units are bonded together to form the inner channel and the outer channel. This type of exchanger could largely enhance the heat transfer capability in radial direction, meanwhile, reduce the heat transfer in axial direction. Due to the advantages of compactness, lightweight and high effectiveness, MHEs have been widely used in helium liquefiers and small/miniature cryocoolers [1], [2].

Previous studies have been focused on heat transfer and flow resistance of wire mesh-screens. Kays and London [3] carried out the experimental study on MHEs with stacked mesh screens structure and obtained the heat transfer and friction correlations under different porosities. Park and Ruch [4] reported the experimental studies on the heat transfer and flow friction correlations of a type of MHEs with inline stacked and staggered stacked plain-weave screens. Tian and Kim [5] experimentally investigated the thermal performance of wire-screen meshes and found that the overall thermal performance index of wire-screens had approximately 2–5 times larger than that of copper foams with similar pore sizes. Xu [6] presented the analytical solutions of the effective thermal conductivity of the plane mesh-screens and revealed that the anisotropy metal mesh-screen could reach 78.5% of the thermal conductivity of the bulk metal material.

The effectiveness analysis based on analytical solution of effectiveness-NTU method is the primary approach in the thermal design and analysis of heat exchangers, and many studies using this method have been reported to determine the effectiveness of MHEs [7]. Venkatarathnam [8] developed a closed-form expression to calculate the MHE effectiveness in terms of heat resistances and finite plate number. Jones [9] proposed an analytical method to determine the temperature distribution and effectiveness for high-NTU MHE, which included the effects of the axial conduction in the flow channels as well as the metal wall between the channels. Nellis [10] presented an analytical solution for the effectiveness of heat exchanger subjected to external heat flux based on effectiveness-NTU method. Mathew [11] analyzed the thermal performance of microchannel heat exchangers with heat leakage based on the effectiveness-NTU method. Narayanan and Venkatarathnam [12], [13] obtained the analytical solution of effectiveness subjected to heat leakage and axial heat conduction only through outer wall for balanced flow.

However, the analytical solution of effectiveness-NTU method could not easily handle some cases such as unbalanced flow and axial conduction both inner and outer walls [13]. Recently, numerical methods have been developed to better describe the heat transfer characteristics inside MHEs. Nellis [14] developed a numerical model which could takes axial conduction, heat leakage and variable fluid properties into account. Based on this model, an improved prediction on the temperature distribution and effectiveness was obtained for the perforated-plate MHEs [15]. Chen et al. [16] presented the numerical analysis and experimental results of the metal-wire mesh-screen MHEs at liquid-nitrogen temperature, revealing the effects of the axial thermal conductivity and variable fluid properties on the heat transfer performance of the MHEs. Venkatarathnam [13] studied the axial heat conduction through both inner and outer walls based on the numerical method. They found the degradation of effectiveness due to axial heat conduction through the outer wall could not be ignored. However the radial thermal resistance between the stream to outer wall and stream to inner wall need empirical estimation. Gupta [17], [18] performed numerical study to investigate the performance of heat exchanger subjected to ambient heat leakage and axial conduction.

Due to the complicated structures of mesh screens, the modeling of matrix heat exchangers primarily relies on the distributed-parameter models and heat transfer correlations. Many details have been ignored in the previous studies, e.g. the axial conduction through the outer wall, the stacked structure of both the inner and outer walls, and the details of radial conduction along mesh screens. However, the outer wall and inner wall are connected by the mesh-screen and spacer along the channel as shown in Fig. 1, and the outer wall and inner walls have the similar temperature variations in flow direction. Moreover, the mesh-screens are usually treated as the fins in the previous studies, and only the fin efficiency is used to account for the convection area and conduction along the mesh screens [4], [8], [14], [16]. Consequently, heat transfer between inner wall and outer wall would ‘break’. Instead, the radial thermal resistance between the stream and the outer/inner wall requires empirical estimations [13].

In this study, the radial heat transfer along mesh-screens and the axial heat conduction through both the inner and outer walls are included in the two-dimension numerical model of MHEs. The numerical model is validated by the analytical solution of effectiveness-NTU method under various conditions. The predictions of MHE ineffectiveness are in good agreement with the experimental results of the MHEs tested in the temperature range from 100 K to 300 K. The results in present study show an important role of the axial conduction in the outer wall and the radial conduction in the mesh screens. Including the details such as the axial conduction, radial conduction, and stacked wall structures, the improved model can be used in the optimization of channel geometry.

Section snippets

Numerical simulation

The schematic of MHE is shown in Fig. 1. Since the MHE is axisymmetric about the centerline, half of the MHE was used in the 2D numerical model as shown in Fig. 2.

MHEs have two pathways of heat transfer which are conduction through solids and the convection of fluids in the channels. The solids consist of mesh screens, spacers, and epoxy adhesive. The MHE can be divided into N cells in the axial direction, and M cells in the radial direction. Each of the mesh screen or spacer constitutes at

Calculation of thermal resistance and heat transfer coefficients

The dimensionless thermal resistance in x direction is determined byRi,jx=(cg)minπ/4((r(j)+Δr/2)2(r(j)Δr/2)2)δixλi,jxwhere r(j) is the radial coordinate, and Δr is the radial length of the cell. λi,jx is the effective thermal conductivity in axial direction, e.g. the conductivity of mesh screen and spacer. The former consists of the normal-direction thermal conductivity of the mesh screen with epoxy adhesive filled (Eq. (33)), while the latter consists of the spacer and the epoxy adhesive

Results and discussion

The predictions using the model presented in this study are compared with the experimental results for the two MHEs with different outer wall diameter. The experimental apparatus and procedures have been presented in our previous studies [22], [23]. The schematic of experimental apparatus are shown in Appendix. The key parameters of the MHE samples studied in this paper are listed in Table 2. Both of them are consisted of copper mesh-screens and stainless steel spacers (0Cr18Ni9). The

Conclusions

This paper presents a numerical model for MHEs which can take into account the effects of the axial conduction of both the inner and outer walls, the radial conduction of each mesh-screen, and the heat leakage. The governing equations with dimensionless variables were presented. Based on the numerical model, the temperature distribution inside the MHE can be obtained for the fluids, both inner and outer walls in axial direction, and each mesh-screen in radial direction. The model was validated

Acknowledgments

This project was supported by the Shaanxi International Science and Technology Cooperation Projects (2014KW09-01) and the Fundamental Research Funds for the Central Universities (2012JDGZ03).

References (23)

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