Numerical analysis on interactions between fluid flow and structure deformation in platefin heat exchanger by Galerkin method
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Abstract
The fluidstructure interaction performance of platefin heat exchanger (PFHE) with serrated fins in large scale airseparation equipment was investigated in this paper. The stress and deformation of fins were analyzed, besides, the interaction equations were deduced by Galerkin method. The governing equations of fluid flow and heat transfer in PFHE were deduced by finite volume method (FVM). The distribution of strain and stress were calculated in large scale air separation equipment and the coupling situation of serrated fins under laminar situation was analyzed. The results indicated that the interactions between fins and fluid flow in the exchanger have significant impacts on heat transfer enhancement, meanwhile, the strain and stress of fins includes dynamic pressure of the sealing head and flow impact with the increase of flow velocity. The impacts are especially significant at the conjunction of two fins because of the nonalignment fins. It can be concluded that the soldering process and channel width led to structure deformation of fins in the exchanger, and degraded heat transfer efficiency.
1 Introduction
In large scale air separation equipment, the platefin heat exchanger (PFHE) working a key component plays an important role for improving heat transfer performance. In general, the PFHE has some specific advantages such as high heat exchange efficiency, compact structure etc., so that it is widely used in many fields such as aerospace, petrochemical engineering, deep hypothermia, and refrigeration for heat transfer among air, oil and water [1]. In compare with other kinds of heat exchanger, PFHEs have greater heat transfer area and higher efficiency, and therefore, attract lots of scholars [2, 3] to carry out researches on a wide range of issues including material and structures improvement, turbulent flow characteristics, temperature distribution, solving and optimizing algorithm etc.
Due to its narrow channel of the exchanger, the model of the minichannel can be used to analyze fluid flow and heat transfer characteristics approximately in order to use the heat transfer area sufficiently and improve heat transfer efficiency. Koh and Colony [4] simplified the minichannel of the porous medium and described the fluid flow in the mini channel by Darcy principle. Tien [5] investigated convective heat transfer boundary in minichannel and deduced numerical solutions of velocity and temperature by conjugation analysis method. Chen and Yang [6] simplified the minichannel heat exchanger as a porous media and then analyzed the velocity and temperature distribution by establishing doubleequation model and singleequation model. Bahrami and Tamayol et al. [7] proposed an approximation model and calculated pressure distribution in the minichannel with gliding flow, and investigated pressure variations with different geometry parameters.
Compared with the perforated fins and serrated fins, the plain fin has lower heat resistance and low heat transfer capacity. Therefore, the perforated fins and serrated fins are widely used in PFHE. For the enhanced heat transfer of rectangular cross section, Hooman [8] and Harley [9] investigated convective heat transfer and entropy variation of porous pipe with rectangular cross sections during constant wall temperature and uniform wall heat distribution. Mohammad [10] investigated heat transfer calculation method under cross section and the relationship among the local Nusselt number, average Nusselt number and aspect ratio of cross section. Furthermore, for the fluid flow of heat exchanger with different kinds of fins, reference [11, 12, 13, 14] discussed heat transfer characteristics with several kinds of fins commonly used including pin fins, herringbone fins, rectangular fins and circular fins with different parameters such as: fin space, heat exchange tube diameter and tube number etc. For the fluidstructure interaction, Jan [15] analyzed the fluidstructure interaction in cross flow heat exchanger and proposed a calculation method, finally improve calculation efficiency. Liu and Dong et al. [16] investigated 3dimensional heatforce interaction models and proposed a new method for solving complex boundary problem. Zhou [17] proposed a simplified calculation method of strain and stress in PFHE by assuming that fins are pieces of elastic spring and solved fatigue characteristics of temperature and pressure in miniheat exchanger of microchemical and thermal system.
Based on the literature review, it is found that the investigations on PFHE mainly include the performance of fins, the influence on heat transfer under cross sections and heat transfer enhancement of fins. However, the investigation on fluidstructure interactions is not enough. As we know, the fluidstructure interaction in the exchanger affects heat transfer efficiency and heat transfer performance of the exchanger, especially, for large air separation equipment, slight deformation of fins that was caused by fluid impact with low temperature results in different heat transfer performance. Meanwhile, in the PFHE, the diversity of fins also causes fluid flow and heat transfer variations, therefore, the traditional calculation on fluid flow and heat transfer efficiency can result in an inaccurate solution. In this paper, the serrated fin is adopted to analyze the deformation of fins and its effects on fluid flow in PFHE of large air separation equipment by minimum potential energy principle of tiny displacement theory. Besides, the influence on fluid flow and heat transfer in minichannel of PFHE by the deformation of fins when applying loads on fins of lateral direction is also investigated.
2 Model and flow pattern of PFHE
2.1 Model of PFHE
2.2 Flow pattern in PFHE
Generally, three kinds of flow patterns are commonly used in PFHE: cocurrent flow, countercurrent flow and cross flow. Temperature difference between top section and bottom section on different channels of the same layer distributes nonuniformly due to nonuniform flow distribution in inlet of the exchanger. For mass amount of fluid, the impact causes tiny deformation of fins and finally bring small influences of fluid flow and deformation. The flow variation causes slight fin deformation and finally, changes the heat transfer efficiency for each piece of fins. In order to solve the above problem, details on the mesh system were provided and finite element method (FEM) was adopted to analyze the interactions between serrated fins and fluid flow in PFHE and the maximum strain position for each piece of fins was achieved.
3 Analysis on fluid flow and fin deformation interaction
3.1 Load distribution on PFHE
3.2 Fluidstructure interaction calculation
 (1)
Fluid Domain
In eq. (1), u, v and w represent fluid velocity along x, y and z direction respectively, ρ represents fluid density, P represents dynamic pressure.
In eq. (7), φ represents a general variable, Γ_{φ} represents generalized diffusion coefficient, S_{φ} represents generalized source term.
The turbulent model that can be used in high strain and mass flow conditions based on renormalization group can be written as:
In eq. (8) and eq. (9), k represents turbulent kinetic energy, ε represents turbulence dissipation rate.
 (2)
Boundary Conditions:
In eq. (22) and eq. (23), Λ is the coordinate transformation matrix.
 (3)
Structure Domain
In eq. (25), r is displacement vector, M_{s} is mass matrix, C_{s} is structure damping matrix, K_{s} is structural stiffness matrix, f_{p} is node vector, f_{o} is pressure vector.
In eq. (27), N_{se} represents the shape function of fins.
4 Results and discussion
In this section, the interactions between serrated fins and fluid flow in PFHE under different velocities were analyzed, besides, flow characteristics and serrated fin deformation were carried out.
In order to validate the performance of the leading flow structure with specificshaped hole in inlet of PFHE, the status detection and data processing system was established. The leading flow and enhanced heat transfer experimental facility are consisted by air loop system, heat exchange system and data processing system. The air loop system is composed by wind compressor, wind channel, dedusting and purification devices. The heat exchange system is composed by test model, moisture separator, saturated vapor producer and drainage system. The data processing system is composed by a data processing computer and several monitoring probes. The monitoring probes include the flow meters, thermocouples, pressure and differential pressure transducers.
4.1 Analysis on fluid flow
4.2 Analysis on structure deformation
5 Conclusion

Firstly, the dynamic pressure on both sides of a single fin distributes nonuniformly. In PFHE, the dynamic pressure on the two sides of the exchanger is larger than that on the middle part of the fin. The results show that the disturbing effect at the two sides of fins results in the dynamic pressure is larger than that at the middle part.

Secondly, the fluid flow in the exchanger was influenced by obstacles coming from the fins because of certain thickness and the nonalignment of fins. Besides, the fluid flow in PFHE shows that the velocity and dynamic pressure vary periodically normal to the direction of fluid flow. Therefore, the dynamic pressure distributed nonuniformly and brought net difference of dynamic pressure.

Thirdly, the net pressure difference between the two sides of fins in the exchanger causes tiny deformation of fins. The analysis on the net value of strain and stress distribution on the two sides of fins show that the maximum value of strain and stress on fins is on the rise with fluid velocity, meanwhile, the minimum value of strain and stress of fins decreased.
Notes
Acknowledgements
This paper is supported by the National Natural Science Foundation of China (No. 51705297) and Natural Science Foundation of Shandong Province, China (Grant No. ZR2016EEP09). Besides, we would also like to show our appreciation to Mr. WEI Zhenwen, the chairman of Doright Corporation, for his kindly help during the leading flow and enhanced heat transfer experiment period.
Compliance with ethical standards
Conflict of interest
The authors have no financial or other relationship that might be perceived as leading to a conflict of interest that could affect authors’ objectivity. Besides, this manuscript has not been published elsewhere and it has not been submitted simultaneously for published elsewhere.
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