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Theoretical model to estimate fluid distribution in compact heat exchangers

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Abstract

One of the limitations to design a compact heat exchanger is the phenomenon of fluid maldistribution. Most research considers a uniform fluid distribution in the channels, which can be considered a wrong approximation, since the non-uniform fluid distribution can seriously affect the performance. There are few experimental and numerical studies related to fluid distribution in a compact heat exchanger, however, currently, there is no mathematical model capable of predicting the fluid distribution within the channels. The present work developed the first theoretical model capable to estimate the flow distribution inside compact heat exchanger channels. The model is based on the concept of the shape factor, relating the radiation ratio between surfaces with the mass flow rate. The model considers geometric parameters to estimate the fluid distribution, such as channel position, channel cross-sectional area, fluid inlet surface area, and inlet header depth. In order to verify the model's accuracy, comparisons with experimental and numerical data available in the literature were performed, besides, a test facility was produced and used to test two header configurations. The average error of the model was approximately 9%, having a better performance than the hypothesis of uniform distribution, which presented an average error of 13%. However, in cases where fluid maldistribution was pronounced, the model exhibited significantly better results, reducing the error from 29%, uniform distribution hypothesis, to 11%. This demonstrates that the model can be applied to estimate fluid distribution inside de core and enhance the design of heat exchangers.

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Availability of data and materials

The data that support the findings of this study are available from the corresponding author, M. V. V. Mortean upon reasonable request.

Abbreviations

A :

Cross-sectional area [m2]

β :

Correction factor [-]

CHE :

Compact heat exchanger [-]

CoV :

Coefficient of variation [-]

D :

Inlet tube diameter [mm]

d :

Channel diameter [mm]

E b :

Emissive power of black surface [W/ m2]

\(\triangle\;{P}\) :

differential pressure [kPa]

\(\overline{F}\) :

average of the standard shape factors [-]

F :

initial shape factor [-]

F c,ij :

adjusted shape factor [-]

F p :

standard shape factor [-]

F T :

sum initial shape factors [-]

L :

length of longest header edge [mm]

L d :

header diagonal length [mm]

\(\dot{m}\) :

mass flow rate [kg/s]

\(\overline{\dot{m}}\) :

average mass flow [kg/s]

N :

number of channels [-]

PCHE :

printed circuit heat exchanger [-]

PHE :

plate heat exchanger [-]

q'' :

heat flux [W/m2]

\(\sigma\) :

standard deviation of fluid non-uniformity [-]

T :

Temperature [°C]

V :

Velocity [m/s]

Z :

header depth [mm]

Subscript channel :

Channel

i :

surface number

j :

surface number

in :

Inlet

out :

Outlet

References

  1. Shah RK, Sekulić DP (2003) Fundamentals of heat exchanger design. John Wiley & Sons, Hoboken, NJ

    Book  Google Scholar 

  2. Sarmiento APC, Soares VHT, Carqueja GG et al (2020) Thermal performance of diffusion-bonded compact heat exchangers. Int J Therm Sci 153:106384. https://doi.org/10.1016/j.ijthermalsci.2020.106384

    Article  Google Scholar 

  3. Hein LL, Mortean MVV (2021) Theoretical and experimental thermal performance analysis of an additively manufactured polymer compact heat exchanger. Int Commun Heat Mass Transfer 124:105237. https://doi.org/10.1016/j.icheatmasstransfer.2021.105237

    Article  CAS  Google Scholar 

  4. Lee S-M, Kim K-Y (2014) A Parametric Study of the Thermal-Hydraulic Performance of a Zigzag Printed Circuit Heat Exchanger. Heat Transfer Eng 35:1192–1200. https://doi.org/10.1080/01457632.2013.870004

    Article  ADS  CAS  Google Scholar 

  5. Alvarez RC, Sarmiento APC, Cisterna LHR et al (2021) Heat transfer investigation of a 90° zigzag channel diffusion-bonded heat exchanger. Appl Therm Eng 190:116823. https://doi.org/10.1016/j.applthermaleng.2021.116823

    Article  CAS  Google Scholar 

  6. Lasbet Y, Auvity B, Castelain C, Peerhossaini H (2007) Thermal and Hydrodynamic Performances of Chaotic Mini-Channel: Application to the Fuel Cell Cooling. Heat Transfer Eng 28:795–803. https://doi.org/10.1080/01457630701328908

    Article  ADS  CAS  Google Scholar 

  7. Hesselgreaves JE (2001) Compact heat exchangers: selection, design, and operation. Pergamon, Amsterdam, New York

    Google Scholar 

  8. Zilio G, Teixeira MJ, Mortean MVV et al (2022) Structural analysis of compact heat exchanger samples fabricated by additive manufacturing. Int J Press Vessels Pip 199:104714. https://doi.org/10.1016/j.ijpvp.2022.104714

    Article  CAS  Google Scholar 

  9. da Silva RPP, Mortean MVV, de Paiva KV et al (2021) Thermal and hydrodynamic analysis of a compact heat exchanger produced by additive manufacturing. Appl Therm Eng 193:116973. https://doi.org/10.1016/j.applthermaleng.2021.116973

    Article  CAS  Google Scholar 

  10. Dixit T, Al-Hajri E, Paul MC et al (2022) High performance, microarchitected, compact heat exchanger enabled by 3D printing. Appl Therm Eng 210:118339. https://doi.org/10.1016/j.applthermaleng.2022.118339

    Article  CAS  Google Scholar 

  11. Yang Y, Li H, Xie B et al (2022) Experimental study of the flow and heat transfer performance of a PCHE with rhombic fin channels. Energy Convers Manage 254:115137. https://doi.org/10.1016/j.enconman.2021.115137

    Article  CAS  Google Scholar 

  12. Chang H, Han Z, Li X et al (2022) Experimental study on heat transfer performance of sCO2 near pseudo-critical point in airfoil-fin PCHE from viewpoint of average thermal-resistance ratio. Int J Heat Mass Transf 196:123257. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123257

    Article  Google Scholar 

  13. Ning J, Wang X, Sun Y et al (2022) Experimental and numerical investigation of additively manufactured novel compact plate-fin heat exchanger. Int J Heat Mass Transf 190:122818. https://doi.org/10.1016/j.ijheatmasstransfer.2022.122818

    Article  Google Scholar 

  14. Aneesh AM, Sharma A, Srivastava A et al (2016) Thermal-hydraulic characteristics and performance of 3D straight channel based printed circuit heat exchanger. Appl Therm Eng 98:474–482. https://doi.org/10.1016/j.applthermaleng.2015.12.046

    Article  CAS  Google Scholar 

  15. Mylavarapu SK, Sun X, Glosup RE et al (2014) Thermal hydraulic performance testing of printed circuit heat exchangers in a high-temperature helium test facility. Appl Therm Eng 65:605–614. https://doi.org/10.1016/j.applthermaleng.2014.01.025

    Article  CAS  Google Scholar 

  16. Zhang L, Yang P, Li W et al (2022) A new structure of PCHE with embedded PCM for attenuating temperature fluctuations and its performance analysis. Energy 254:124462. https://doi.org/10.1016/j.energy.2022.124462

    Article  CAS  Google Scholar 

  17. Sarmiento APC, Milanez FH, Mantelli MBH (2021) Theoretical models for compact printed circuit heat exchangers with straight semicircular channels. Appl Therm Eng 184:115435. https://doi.org/10.1016/j.applthermaleng.2020.115435

    Article  Google Scholar 

  18. Strobel M, Mortean MVV (2022) Pressure drop and fluid maldistribution analysis of a compact heat exchanger manufactured by 3D printing. Int J Therm Sci 172:107331. https://doi.org/10.1016/j.ijthermalsci.2021.107331

    Article  CAS  Google Scholar 

  19. Baek S, Lee C, Jeong S (2014) Effect of flow maldistribution and axial conduction on compact microchannel heat exchanger. Cryogenics 60:49–61. https://doi.org/10.1016/j.cryogenics.2014.01.003

    Article  ADS  CAS  Google Scholar 

  20. Chu W, Bennett K, Cheng J et al (2018) Numerical study on a novel hyperbolic inlet header in straight-channel printed circuit heat exchanger. Appl Therm Eng 146:805–814. https://doi.org/10.1016/j.applthermaleng.2018.10.027

    Article  CAS  Google Scholar 

  21. Kitto JB, Robertson JM (1989) Effects of Maldistribution of Flow on Heat Transfer Equipment Performance. Heat Transfer Eng 10:18–25. https://doi.org/10.1080/01457638908939688

    Article  ADS  CAS  Google Scholar 

  22. Strobel M, Mortean MVV (2022) Analysis of Flow Maldistribution in Compact Heat Exchangers. J Fluids Eng. https://doi.org/10.1115/1.4054917

    Google Scholar 

  23. Bassiouny MK, Martin H (1984) Flow distribution and pressure drop in plate heat exchangers—I U-type arrangement. Chem Eng Sci 39:693–700. https://doi.org/10.1016/0009-2509(84)80176-1

    Article  CAS  Google Scholar 

  24. Thonon B, Mercier P, Feidt M (1992) Flow Distribution in Plate Heat Exchangers and Consequences on Thermal and Hydraulic Performances. In: Roetzel W, Heggs PJ, Butterworth D (eds) Design and Operation of Heat Exchangers. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 245–254

    Chapter  Google Scholar 

  25. Singh S, Ghosh SK (2022) Influence of chevron angle and MWCNT/distilled water nanofluid on the thermo-hydraulic performance of compact plate heat exchanger: An experimental and numerical study. Powder Technol 405:117515. https://doi.org/10.1016/j.powtec.2022.117515

    Article  CAS  Google Scholar 

  26. Li W, Hrnjak P (2021) Single-phase flow distribution in plate heat exchangers: Experiments and models. Int J Refrig 126:45–56. https://doi.org/10.1016/j.ijrefrig.2021.01.026

    Article  Google Scholar 

  27. Tereda FA, Srihari N, Sunden B, Das SK (2007) Experimental Investigation on Port-to-Channel Flow Maldistribution in Plate Heat Exchangers. Heat Transfer Eng 28:435–443. https://doi.org/10.1080/01457630601163769

    Article  ADS  CAS  Google Scholar 

  28. Ranganayakulu C, Seetharamu KN (1997) The combined effects of inlet fluid flow and temperature nonuniformity in cross flow plate-fin compact heat exchanger using finite element method. Heat Mass Transf 32:375–383. https://doi.org/10.1007/s002310050134

    Article  ADS  CAS  Google Scholar 

  29. Schab R, Kutschabsky A, Unz S, Beckmann M (2023) Numerical investigation of tubeside maldistribution in shell-and-tube heat exchangers. Heat Mass Transfer. https://doi.org/10.1007/s00231-023-03385-5

    Article  Google Scholar 

  30. Huang L, Lee MS, Saleh K et al (2014) A computational fluid dynamics and effectiveness-NTU based co-simulation approach for flow mal-distribution analysis in microchannel heat exchanger headers. Appl Therm Eng 65:447–457. https://doi.org/10.1016/j.applthermaleng.2014.01.046

    Article  CAS  Google Scholar 

  31. Qian H, Hrnjak P (2021) Void fraction in vertical intermediate and inlet headers of microchannel heat exchangers: Experiments and models. Appl Therm Eng 199:117498. https://doi.org/10.1016/j.applthermaleng.2021.117498

    Article  CAS  Google Scholar 

  32. Ahmad M, Berthoud G, Mercier P (2009) General characteristics of two-phase flow distribution in a compact heat exchanger. Int J Heat Mass Transf 52:442–450. https://doi.org/10.1016/j.ijheatmasstransfer.2008.05.030

    Article  CAS  Google Scholar 

  33. Vist S, Pettersen J (2004) Two-phase flow distribution in compact heat exchanger manifolds. Exp Thermal Fluid Sci 28:209–215. https://doi.org/10.1016/S0894-1777(03)00041-4

    Article  CAS  Google Scholar 

  34. Kim S, Choi E, Cho YI (1995) The effect of header shapes on the flow distribution in a manifold for electronic packaging applications. Int Commun Heat Mass Transfer 22:329–341. https://doi.org/10.1016/0735-1933(95)00024-S

    Article  Google Scholar 

  35. Chu W, Bennett K, Cheng J et al (2019) Numerical study on a novel hyperbolic inlet header in straight-channel printed circuit heat exchanger. Appl Therm Eng 146:805–814. https://doi.org/10.1016/j.applthermaleng.2018.10.027

    Article  CAS  Google Scholar 

  36. Incropera FP, DeWitt DP (2007) Fundamentals of heat and mass transfer, 6th edn. John Wiley, Hoboken, NJ

    Google Scholar 

  37. Gross U, Spindler K, Hahne E (1981) Shapefactor-equations for radiation heat transfer between plane rectangular surfaces of arbitrary position and size with parallel boundaries. Letters in Heat and Mass Transfer 8:219–227. https://doi.org/10.1016/0094-4548(81)90016-3

    Article  ADS  Google Scholar 

  38. Peng X, Li D, Li J et al (2020) Improvement of Flow Distribution by New Inlet Header Configuration with Splitter Plates for Plate-Fin Heat Exchanger. Energies 13:1323. https://doi.org/10.3390/en13061323

    Article  CAS  Google Scholar 

  39. Strobel M (2019) Análise da perda de carga e má distribuição em trocador de calor compacto fabricado por impressão 3D, Undergraduate Thesis, Universidade Federal de Santa Catarina, Joinville

  40. Ma T, Zhang P, Shi H et al (2020) Prediction of flow maldistribution in printed circuit heat exchanger. Int J Heat Mass Transf 152:119560. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119560

    Article  Google Scholar 

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Authors and Affiliations

  1. Thermal Fluid Flow Group T2F, Joinville Technology Center, Federal University of Santa Catarina, Joinville, SC, Brazil

    M. V. V. Mortean, G. F. Luvizon & D. Baraldi

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  1. M. V. V. Mortean
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  2. G. F. Luvizon
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  3. D. Baraldi
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Contributions

M. V. V. Mortean: Methodology, Investigation, Validation, Writing—review & editing. G. F. Luvizon: Methodology, data curation and Software. D. Baraldi: Writing – review & editing.

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Correspondence to M. V. V. Mortean.

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Mortean, M.V.V., Luvizon, G.F. & Baraldi, D. Theoretical model to estimate fluid distribution in compact heat exchangers. Heat Mass Transfer 60, 419–432 (2024). https://doi.org/10.1007/s00231-023-03437-w

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