Technical Papers
May 21, 2020

Numerical Study of Pressure Drop in Stirling Engine Regenerator

Publication: Journal of Energy Engineering
Volume 146, Issue 4

Abstract

The regenerator of a β-type Stirling engine is simulated with computational fluid dynamics. Emphasis is given to the drop in pressure caused by friction during gas flow through the regenerator matrix. The primary results include the temporal variation of the mass-flow rate and velocity in different levels of the regenerator. A time interval of between 5% and 10% of the engine cycle was found, during which gas is flowing inward to or outward from the regenerator from both its sides. Both gas velocity and pressure drop per unit length is found to increase in hotter sections. The friction factor is extracted and correlated with Reynolds number. Furthermore, two correction factors are applied to the coefficients of viscous and inertial resistance of the Ergun equation. Finally, the temporal and spatial change of the pressure drop is examined for the studied engine. An equation that well estimates the value of the pressure drop for a given time and regenerator length is presented. The derived equation can be used as input data to improve a simple analytical model.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

The model used in the work presented in the paper is an ANSYS Fluent setup. There is no code available, but the setup parameters can be provided by the author if requested. It must be noted, however, that most of the setup parameters are defined and listed in the paper. The derived correlations are a result of the editing of the data produced by the simulation. The files representing the way of this editing can be provided upon request.

Acknowledgments

The authors Panagiotis Bitsikas and George Dogkas would like to thank the National Technical University of Athens for the financial support in the form of scholarship.

References

ANSYS. 2013. ANSYS fluent theory guide, release 15.0. Canonsburg, PA: ANSYS.
Barreno, I., C. S. Costa, M. Cordon, M. Tutar, I. Urrutibeascoa, X. Gomez, and G. Castillo. 2015. “Numerical correlation for the pressure drop in Stirling engine heat exchangers.” Int. J. Therm. Sci. 97 (Nov): 68–81. https://doi.org/10.1016/j.ijthermalsci.2015.06.014.
Borbilas, N. 2004. “Thermodynamic analysis of Stirling cycle.” [In Greek.] Ph.D. thesis, Dept. of Mechanical Engineering, National Technical Univ. of Athens.
Caughley, A., M. Sellier, A. Tucker, and M. Gschwendtner. 2012. “CFD modelling of a diaphragm Stirling cryocooler.” In Proc., 17th Int. Cryocooler Conf. Oak Park, IL: Cryogenic Society of America.
Cha, J. J. 2007. Hydrodynamic parameters of micro porous media for steady and oscillatory flow: Application to cryocooler regenerators. Atlanta: Georgia Institute of Technology.
Chen, W. L. 2017. “A study on the effectes of geometric parameters in a low-temperature-differential γ-type Stirling engine using CFD.” Int. J. Heat Mass Transfer 107 (Apr): 1002–1013. https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.007.
Chen, W. L., K. L. Wong, and Y. F. Chang. 2014a. “A computational fluid dynamics study on the heat transfer characteristics of the working cycle of a low-temperature-differential γ-type Stirling engine.” Int. J. Heat Mass Transfer 75 (Aug): 145–155. https://doi.org/10.1016/j.ijheatmasstransfer.2014.03.055.
Chen, W. L., K. L. Wong, and Y. F. Chang. 2015a. “A numerical study on the effects of moving regenerator to the performance of a β-type Stirling engine.” Int. J. Heat Mass Transfer 83 (Apr): 499–508. https://doi.org/10.1016/j.ijheatmasstransfer.2014.12.035.
Chen, W. L., Y. C. Yang, and J. L. Salazar. 2015b. “A CFD parametric study on the performance of a low-temperature-differential γ-type Stirling engine.” Energy Convers. Manage. 106 (Dec): 635–643. https://doi.org/10.1016/j.enconman.2015.10.007.
Chen, W.-L., K. L. Wong, and H. E. Chen. 2014b. “An experimental study on the performance of the moving regenerator for a γ-type twin power piston Stirling engine.” Energy Convers. Manage. 77 (Jan): 118–128. https://doi.org/10.1016/j.enconman.2013.09.030.
Cheng, C. H., and Y. F. Chen. 2017. “Numerical simulation of thermal and flow fields inside a 1-kW beta-type Stirling engine.” Appl. Therm. Eng. 121 (Jul): 554–561. https://doi.org/10.1016/j.applthermaleng.2017.04.105.
Costa, C. S., I. Barreno, M. Tutar, J. A. Esnaola, and H. Barrutia. 2015. “The thermal non-equilibrium porous media modelling for CFD of woven wire matrix of a Stirling regenerator.” Energy Convers. Manage. 89 (Jan): 473–483. https://doi.org/10.1016/j.enconman.2014.10.019.
Costa, C. S., H. Barrutia, J. A. Esnaola, and M. Tutar. 2013. “Numerical study of the pressure drop phenomena in wound woven wire matrix of a Stirling regenerator.” Energy Convers. Manage. 67 (Mar): 57–65. https://doi.org/10.1016/j.enconman.2012.10.014.
Costa, C. S., M. Tutar, I. Barreno, J. A. Esnaola, H. Barrutia, D. Garcia, M. A. Gonzalez, and J. I. Prieto. 2014. “Experimental and numerical flow investigation of Stirling engine regenerator.” Energy 72 (Jul): 800–812. https://doi.org/10.1016/j.energy.2014.06.002.
Dang, H., and Y. Zhao. 2016. “CFD modeling and experimental verification of a single-stage coaxial Stirling-type pulse tube cryocooler without either double-inlet or multi-bypass operating at 30–35 K using mixed stainless steel mesh regenerator matrices.” Cryogenics 78 (Sep): 40–50. https://doi.org/10.1016/j.cryogenics.2016.06.001.
Gedeon, D., and J. G. Wood. 1996. Oscillating-flow regenerator test rig: Hardware and theory with derived correlations for screens and felts. Albany, OH: National Aeronautics and Space Administration.
Guzzetti, A. 2013. CFD modeling of a beta-type Stirling engine. Milan, Italy: Polytecnico Di Milano.
Ibrahim, M., and R. Tew. 2012. Stirling convertor regenerators. Abingdon, UK: Taylor and Francis.
Kraitong, K. 2012. Numerical modelling and design optimisation of Stirling engines for power production. Newcastle, UK: Univ. of Northumbria at Newcastle.
Kuban, L., J. Stempka, and A. Tyliszcak. 2019. “A 3D-CFD study of a γ-type Stirling engine.” Energy 169 (Feb): 142–159. https://doi.org/10.1016/j.energy.2018.12.009.
Mahkamov, K. 2006. “Design improvements to a biomass Stirling engine using mathematical analysis and 3D CFD modelling.” J. Energy Res. Technol. 128 (3): 203–215. https://doi.org/10.1115/1.2213273.
Martini, W. R. 1983. Stirling engine design manual. Washington, DC: US Dept. of Energy.
Martins, N., B. Brunone, S. Meniconi, H. Ramos, and D. Covas. 2017. “CFD and 1D approaches for the unsteady friction analysis of low Reynolds number turbulent flow.” J. Hydraul. Eng. 143 (12): 04017050. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001372.
Moujaes, S., and S. Aekula. 2009. “CFD predictions and experimental comparisons of pressure drop effects of turning vanes in 90° duct elbows.” J. Energy Eng. 135 (4):119–126. https://doi.org/10.1061/(ASCE)0733-9402(2009)135:4(119).
Moujaes, S., and R. Jagan. 2008. “3D CFD predictions and experimental comparisons of pressure drop in a ball valve at different partial openings in turbulent flow.” J. Energy Eng. 134 (1): 24–28. https://doi.org/10.1061/(ASCE)0733-9402(2008)134:1(24).
Rogdakis, E., P. Bitsikas, G. Dogkas, and G. Antonakos. 2019. “Three-dimensional CFD study of a ß-type Stirling engine.” Therm. Sci. Eng. Prog. 11 (Jun): 302–316. https://doi.org/10.1016/j.tsep.2019.04.012.
Rogdakis, E. D., G. D. Antonakos, and I. P. Koronaki. 2016. “Influence of a regenerator on Stirling engine performance.” J. Energy Eng. 142 (2): E4016002. https://doi.org/10.1061/(ASCE)EY.1943-7897.0000338.
Simon, T. W., and J. R. Seume. 1988. A survey of oscillating flow in Stirling engine heat exchangers. Rep. No. Albany, OH: National Aeronautics and Space Administration.
Tew, R., K. Jeffries, and D. Miao. 1978. A Stirling engine computer model for performance calculations. Albany, OH: National Aeronautics and Space Administration LReC.
Thomas, B., and D. Pittman. 2000. “Update on the evaluation of different correlations for the flow friction factor and heat transfer of Stirling engine regenerators.” In Proc., Energy Conversion Engineering Conf. and Exhibition. New York: IEEE. https://doi.org/10.1109/IECEC.2000.870632.
Urieli, I., and D. Berchowitz. 1983. Stirling cycle engine analysis. Bristol, UK: Adam Hilger.
Versteeg, H. K., and W. Malalasekera. 2016. An introduction to computational fluid dynamics, the finite volume method. Translated by A. Vronteli and K. Yakinthos. Thessaloniki, Greece: Tziolas.
Xiao, G., H. Peng, H. Fan, U. Sultan, and N. Mingjiang. 2017a. “Characteristics of steady and oscillating flows through regenerator.” Int. J. Heat Mass Transfer 108 (May): 309–321. https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.096.
Xiao, G., U. Sultan, N. Mingjiang, H. Peng, X. Zhou, S. Wang, and L. Zhongyang. 2017b. “Design optimization with computational fluid dynamics analysis of β-type Stirling engine.” Appl. Therm. Eng. 113 (Feb): 87–102. https://doi.org/10.1016/j.applthermaleng.2016.10.063.

Information & Authors

Information

Published In

Go to Journal of Energy Engineering
Journal of Energy Engineering
Volume 146Issue 4August 2020

History

Received: Sep 11, 2019
Accepted: Feb 26, 2020
Published online: May 21, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 21, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

Panagiotis Bitsikas [email protected]
Ph.D. Student, Laboratory of Applied Thermodynamics, School of Mechanical Engineering, Thermal Engineering Section, National Technical Univ. of Athens, Heroon Polytechniou 9, Zografou Campus, Athens 15780, Greece (corresponding author). Email: [email protected]
Emmanouil Rogdakis
Professor, School of Mechanical Engineering, Thermal Engineering Section, National Technical Univ. of Athens, Heroon Polytechniou 9, Zografou Campus, Athens 15780, Greece.
George Dogkas, Ph.D.
Laboratory of Applied Thermodynamics, School of Mechanical Engineering, Thermal Engineering Section, National Technical Univ. of Athens, Heroon Polytechniou 9, Zografou Campus, Athens 15780, Greece.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share