Skip to main content
SpringerLink
Log in

Beta Stirling refrigerator performance using a tubular heat exchanger with elliptical tube layouts and a cylinder with different bores

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

The Stirling cycle is regarded as one alternative to the compressive cooling cycle. The current study examines the performance of a beta Stirling refrigerator with a cylinder with different bores. Bores differ in terms of the diameters of the compression and expansion cylinder. The refrigerator comprises a twin shell and tube condenser, and evaporator. The evaporator and condenser tubes show an elliptical cross-section. The elliptical ratios in the evaporator and condenser (1, 0.75, 0.50, 0.25, 0.20) with a fixed cross-section area are compared. A wire mesh regenerator uses as the regenerator. The selection of the working fluid is helium. The current work prepares a spreadsheet program to overcome the reversed Stirling refrigeration cycle. The suitable dimensions of the refrigerator to obtain a high cooling load are determined. The results recommended that using tubes with elliptical cross-sections in both evaporator and condenser enhances the COP of the refrigerator by about 33% (COP = 1.3). Also, using tubes having elliptical cross-sections in both evaporator and condenser enhances the cooling load of the refrigerator by about 24% at a 0.2 elliptical ratio. Furthermore, the use of different bores of refrigerator cylinder increases the cooling load of the refrigerator by about 25% when the expansion to compression bore ratio is 1.5. Additionally, the use of different bores of refrigerator cylinder increases the COP of the refrigerator by about 40%, especially at low pressures at expansion to compression bore ratio of 2.0. The proposed refrigerator can achieve a cooling capacity of 450 W at COP = 0.9 under a charged pressure of 5 bar. Comparing the current work and earlier studies shows that the proposed refrigerator achieves a 60% improvement in cooling load at the same pressure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

A :

Surface area (m2)

ɸ C :

The bore of the compression cylinder (m)

ɸ E :

The bore of the expansion cylinder (m)

G :

Gear bore (m)

\(f\) :

Coefficient of friction

\(h\) :

The coefficient of heat transfer (W m−2 K−1)

\(i\) :

Number of wire mesh (pores inch−1)

K :

Coefficient of minor losses

\(k\) :

The thermal conductivity (W m−1 k−1)

L :

The length (m)

\(m\) :

The mass (kg)

m . :

The rate mass flow (kg s−1)

N :

The speed (rpm)

NTU:

The number of units transferred

P :

Driven power (W)

\(p\) :

The pressure (Pa)

Q . :

The rate of heat transfer (W)

R :

Constant of specific gas (Jkg−1 K−1)

\(r\) :

Crank radius (m)

L 1, L 2 , L3, L 4 :

The length of the links of the drive mechanism m

Re :

The Reynolds number

S :

The stroke (m)

St :

Stanton number

T :

The temperature (K)

\(t\) :

The time (s)

U :

The coefficient of overall heat transfer (W m−2 K−1)

V :

The volume (m3)

v :

The velocity (m s−1)

\(x, \, y\) :

Coordinates (m)

a :

Major diameter

b :

Minor diameter

\(\varepsilon\) :

Regenerator effectiveness

ξ :

Equivalent diameter (b + a) (m)

ɸ :

The bore of the cylinder

θ :

Crank angle (°)

θ 1,θ 2 :

The angle of connecting rod (°)

\(\mu\) :

Fluid viscosity (kg m−1 s−1)

\(\rho\) :

Fluid density (kg m−3)

Ψ:

Regenerator porosity

Ζ :

Elliptical ratio \(\left( {b/a} \right)\)

C:

Compression space

ch:

Charging

cl:

Clearance

Co:

Condenser

cw:

The cooling water

D:

The displacer piston

E:

Space of expansion

Ev:

The evaporator

h:

Hydraulic

max:

Maximum

min:

Minimum

In:

Inner

Out:

Outer

p:

The piston

pol:

The positive overlap between piston and displacer

R:

The regenerator

Sc:

Schmidt

sw:

Swept

T:

Tube

T :

Total

th:

Thermal

tp:

Transport port

w:

The regenerator wire

References

  1. Eid E. Performance of a beta-configuration heat engine having a regenerative displacer. Renew Energy. 2009. https://doi.org/10.1016/j.renene.2009.03.016.

    Article  Google Scholar 

  2. Gothe S, Begot S, Lanzetta F, Gavignet E. Design manufacturing and testing of a Beta Stirling machine for refrigeration applications. Int J Refrig. 2020. https://doi.org/10.1016/j.ijrefrig.2020.03.005.

    Article  Google Scholar 

  3. Le’an S, Yuanyang Z, Liansheng L, Pengcheng S. Performance of a prototype Stirling domestic refrigerator. Appl Therm Eng. 2009. https://doi.org/10.1016/j.applthermaleng.2008.02.036.

    Article  Google Scholar 

  4. Kongtragool B, Wongwises S. A review of solar-powered Stirling engines and low temperature differential Stirling engines. Renew Sustain Energy Rev. 2003. https://doi.org/10.1016/S1364-0321(02)00053-9.

    Article  Google Scholar 

  5. Cheng C, Yu Y. Numerical model for predicting thermodynamic cycle and thermal efficiency of a beta-type Stirling engine with rhombic-drive mechanism. Renew Energy. 2010. https://doi.org/10.1016/j.renene.2010.04.002.

    Article  Google Scholar 

  6. Dong S, Shen G, Xu M, Zhang S, An L. The effect of working fluid on the performance of a large-scale thermoacoustic Stirling engine. Energy. 2019. https://doi.org/10.1016/j.energy.2019.05.142.

    Article  Google Scholar 

  7. Doğan B, Ozturk M, Erbay L. Effect of working fluid on the performance of the duplex Stirling refrigerator. J Clean Prod. 2018. https://doi.org/10.1016/j.jclepro.2018.04.076.

    Article  Google Scholar 

  8. Solmaz H, Ardebili SM, Aksoy F, Calam A, Yilmaz E, Arslan M. Optimization of the operating conditions of a beta-type rhombic drive Stirling engine by using response surface method. Energy. 2020. https://doi.org/10.1016/j.energy.2020.117377.

    Article  Google Scholar 

  9. Batooei A, Keshavarz A. A gamma type Stirling refrigerator optimization: an experimental and analytical investigation. Int J Refrig. 2018. https://doi.org/10.1016/j.ijrefrig.2018.05.024.

    Article  Google Scholar 

  10. Eid EI, Khalaf-Allah RA, Soliman AM, Easa AS. Performance of a beta Stirling refrigerator with tubular evaporator and condenser having inserted twisted tapes and driven by a solar energy heat engine. Renew Energy. 2018. https://doi.org/10.1016/j.renene.2018.09.044.

    Article  Google Scholar 

  11. Tekin Y, Ataer O. Performance of V-type Stirling-cycle refrigerator for different working fluids. Int J Refrig. 2010. https://doi.org/10.1016/j.ijrefrig.2009.08.011.

    Article  Google Scholar 

  12. Ataer OE, Karabulut H. Thermodynamic analysis of the V-type Stirling-cycle refrigerator. Int J Refrig. 2005. https://doi.org/10.1016/j.ijrefrig.2004.06.004.

    Article  Google Scholar 

  13. Hachem H, Gheith R, Aloui F, Nasrallah S. Optimization of an air-filled beta type Stirling refrigerator. Int J Refrig. 2017. https://doi.org/10.1016/j.ijrefrig.2017.02.019.

    Article  Google Scholar 

  14. Dai D, Liu Z, Yuan F, long R, Liu W, . Finite time thermodynamic analysis of a solar duplex Stirling refrigerator. Appl Therm Eng. 2019. https://doi.org/10.1016/j.applthermaleng.2019.04.098.

    Article  Google Scholar 

  15. Cheng C, Huang C, Yang H. Development of 90-k Beta type Stirling cooler with rhombic drive mechanism. Int J Refrig. 2018. https://doi.org/10.1016/j.ijrefrig.2018.11.027.

    Article  Google Scholar 

  16. Dogan B, Ozturk M, Erbay L. Effect of working fluid on the performance of the duplex Stirling refrigerator. J Clean Prod. 2018. https://doi.org/10.1016/j.jclepro.2018.04.076.

    Article  Google Scholar 

  17. Gadelkareem T, Eldein Hussin A, Hennes G, El-Ehwany A. Stirling cycle for hot and cold drinking water dispenser. Int J Refrig. 2019. https://doi.org/10.1016/j.ijrefrig.2018.11.033.

    Article  Google Scholar 

  18. Djetel-Gothe S, Begot S, Lanzetta F, Gavignet E. Design, manufacturing and testing of a Beta Stirling machine for refrigerator applications. Int J Refrig. 2020. https://doi.org/10.1016/j.ijrefrig.2020.03.005.

    Article  Google Scholar 

  19. Du T, Chen Q, Du W, Cheng L. Performance of continuous helical baffled heat exchanger with varying elliptical tube layouts. Int J Heat Mass Transf. 2019. https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.142.

    Article  Google Scholar 

  20. Hoseinzadeh S, Heyns PS. Thermo-structural fatigue and lifetime analysis of a heat exchanger as a feedwater heater in power plant. Eng Fail Anal. 2020. https://doi.org/10.1016/j.engfailanal.2020.104548.

    Article  Google Scholar 

  21. Adelekan DS, Ohunakin OS, Oladeinde MH, Jatinder G, Atiba OE, Nkiko MO, Atayero AA. Performance of a domestic refrigerator in varying ambient temperatures, concentrations of TiO2 Nano lubricants and R600a refrigerant charges. Heliyon. 2021. https://doi.org/10.1016/j.heliyon.2021.e06156.

    Article  PubMed  PubMed Central  Google Scholar 

  22. Wiriyasart S, Suksusron P, Hommalee C, Siricharoenpanich A, Naphon P. Heat transfer enhancement of thermoelectric cooling module with nanofluid and ferrofluid as base fluids. Case Stud Therm Eng. 2021. https://doi.org/10.1016/j.csite.2021.100877.

    Article  Google Scholar 

  23. Sheikholeslami M, Farshad SA, Said Z. Analyzing entropy and thermal behavior of nanomaterial through solar collector involving new tapes. Int Commun Heat Mass. 2021. https://doi.org/10.1016/j.icheatmasstransfer.2021.105190.

    Article  Google Scholar 

  24. Sheikholeslami M, Farshad SA. Investigation of solar collector system with turbulator considering hybrid nanoparticles. Renew Energy. 2021. https://doi.org/10.1016/j.renene.2021.02.137.

    Article  Google Scholar 

  25. Sheikholeslami M, Jafaryar M, Said Z, Alsabery AI, Babazadeh H, Shafee A. Modification for helical turbulator to augment heat transfer behavior of nanomaterial via numerical approach. Appl Therm Eng. 2021. https://doi.org/10.1016/j.applthermaleng.2020.115935.

    Article  Google Scholar 

  26. Sheikholeslami M, Farshad SA, Ebrahimpour Z, Said Z. Recent progress on flat plate solar collectors and photovoltaic systems in the presence of nanofluid: a review. J Clean Prod. 2021. https://doi.org/10.1016/j.jclepro.2021.126119.

    Article  Google Scholar 

  27. Ghanbari AT, Hoseinzadeh S, Sohani A, Shahverdian MH. Applying homotopy perturbation method to provide an analytical solution for Newtonian fluid flow on a porous flat plate. Math Meth Appl Sci. 2021. https://doi.org/10.1002/mma.7238.

    Article  Google Scholar 

  28. Getie MZ, Lanzetta F, Bégot S, Admassu BT, Hassen AA. Reversed regenerative Stirling cycle machine for refrigeration application: a review. Int J Refrig. 2020. https://doi.org/10.1016/j.ijrefrig.2020.06.007.

    Article  Google Scholar 

  29. Djetel-Gothe S, Bégot S, Lanzetta F, Gavignet E. Design, manufacturing and testing of a Beta Stirling machine for refrigeration applications. Int J Refrig. 2020. https://doi.org/10.1016/j.ijrefrig.2020.03.005.

    Article  Google Scholar 

  30. Yang Z, Liu S, Li Z, Jiang Z, Dong C. Application of machine learning techniques in operating parameters prediction of Stirling cryocooler. Cryogenics. 2021. https://doi.org/10.1016/j.cryogenics.2020.103213.

    Article  Google Scholar 

  31. Cheng C, Huang J. Development of a 100-K pneumatically driven split-type cryogenic Stirling cryocooler based on experimental and numerical study. Cryogenics. 2020. https://doi.org/10.1016/j.cryogenics.2019.102998.

    Article  Google Scholar 

  32. Eid EI, Abdel-Halim M, Easa AS. Effect of opposed eccentricity on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations. Heat Mass Tran. 2014. https://doi.org/10.1007/s00231-014-1408-z.

    Article  Google Scholar 

  33. Yang LH, Xu L, Wang WC, Wang SH. Building information model and optimization algorithms for supporting campus facility maintenance management: a case study of maintaining water dispensers. KSCE J Civ Eng. 2021. https://doi.org/10.1007/s12205-020-0219-7.

    Article  Google Scholar 

  34. Çağlar A. Design and experimental investigation of a novel thermoelectric water dispenser unit. Appl Therm Eng. 2018. https://doi.org/10.1016/j.applthermaleng.2018.11.028.

    Article  Google Scholar 

  35. Formosa F, Despesse G. Analytical model for Stirling cycle machine design. Energy Convers Manag. 2010. https://doi.org/10.1016/j.enconman.2010.02.010.

    Article  Google Scholar 

  36. Atrey M, Bapat S, Narayankhedkar K. Cyclic simulation of Stirling cryocoolers. Cryogenics. 1990. https://doi.org/10.1016/0011-2275(90)90313-2.

    Article  Google Scholar 

  37. Sarafraz MM, Safaei MR, Tian Z, Goodarzi M, Bandarra Filho EP, Arjomandi M. Thermal assessment of nano-particulate graphene-water/ethylene glycol (WEG 60:40) nano-suspension in a compact heat exchanger. Energies. 2019. https://doi.org/10.3390/en12101929.

    Article  Google Scholar 

  38. Sarafraz MM, Safaei MR, Goodarzi M, Yang B, Arjomandi M. Heat transfer analysis of Ga–In–Sn in a compact heat exchanger equipped with straight micro-passages. Int J Heat Mass Tran. 2019. https://doi.org/10.1016/j.ijheatmasstransfer.2019.05.057.

    Article  Google Scholar 

  39. El-Ehwany A, Hennes G, Eid E, El-Kenany E. Development of the performance of an alpha-type heat engine by using elbow-bend transposed fluids heat exchanger as a heater and a cooler. Energy Convers Manag. 2011. https://doi.org/10.1016/j.enconman.2010.08.029.

    Article  Google Scholar 

  40. Cheng C, Yang H, Keong L. Theoretical and experimental study of a 300-W beta-type Stirling engine. Energy. 2013. https://doi.org/10.1016/j.energy.2013.06.060.

    Article  Google Scholar 

  41. Hoseinzadeh S, Ghasemiasl R, Havaei D, Chamkha AJ. Numerical investigation of rectangular thermal energy storage units with multiple phase change materials. J Mol Liq. 2018. https://doi.org/10.1016/j.molliq.2018.08.128.

    Article  Google Scholar 

  42. Li ZX, Khaled U, Al-Rashed AA, Goodarzi M, Sarafraz MM, Meer R. Heat transfer evaluation of a micro heat exchanger cooling with spherical carbon-acetone nanofluid. Int J Heat Mass Tran. 2020. https://doi.org/10.1016/j.ijheatmasstransfer.2019.119124.

    Article  Google Scholar 

  43. Bahmani MH, Sheikhzadeh G, Zarringhalam M, Akbari OA, Alrashed AA, Shabani GA, Goodarzi M. Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger. Adv Powder Technol. 2018. https://doi.org/10.1016/j.apt.2017.11.013.

    Article  Google Scholar 

  44. Bahmani MH, Akbari OA, Zarringhalam M, Ahmadi G, Goodarzi M. Forced convection in a double tube heat exchanger using nanofluids with constant and variable thermophysical properties. Int J Numer Method Heat. 2020. https://doi.org/10.1108/HFF-01-2019-0017.

    Article  Google Scholar 

  45. Hoseinzadeh S, Sohani A, Shahverdian H, Shirkhani A, Heyns S. Acquiring an analytical solution and performing a comparative sensitivity analysis for flowing Maxwell upper-convected fluid on a horizontal surface. Therm Sci Eng Prog. 2021. https://doi.org/10.1016/j.tsep.2021.100901.

    Article  Google Scholar 

  46. Tyagi S, Kaushik S, Singhal M. Parametric study of irreversible Stirling and Ericsson cryogenic refrigeration cycles. Energy Convers Manag. 2002. https://doi.org/10.1016/S0196-8904(01)00181-9.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Department, Faculty of Technology and Education, Suez University, Suez, Egypt

    Eldesouki I. Eid, Reda A. Khalaf-Allah, Asmaa I. Albadry & Ammar S. Easa

Authors
  1. Eldesouki I. Eid
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reda A. Khalaf-Allah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Asmaa I. Albadry
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ammar S. Easa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reda A. Khalaf-Allah.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eid, E.I., Khalaf-Allah, R.A., Albadry, A.I. et al. Beta Stirling refrigerator performance using a tubular heat exchanger with elliptical tube layouts and a cylinder with different bores. J Therm Anal Calorim 147, 7523–7538 (2022). https://doi.org/10.1007/s10973-021-11021-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-021-11021-9

Keywords

Search

Navigation