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Rate capability and Ragone plots for phase change thermal energy storage

Nature Energy volume 6, pages 295–302 (2021)Cite this article

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Abstract

Phase change materials can improve the efficiency of energy systems by time shifting or reducing peak thermal loads. The value of a phase change material is defined by its energy and power density—the total available storage capacity and the speed at which it can be accessed. These are influenced by material properties but cannot be defined with these properties alone. Here we show the close link between energy and power density by developing thermal rate capability and Ragone plots, a framework widely used to describe the trade-off between energy and power in electrochemical storage systems (that is, batteries). Our results elucidate how material properties, geometry and operating conditions influence the performance of phase change thermal storage. This research sets a clear framework for comparing thermal storage materials and devices and can be used by researchers and designers to increase clean energy use with storage.

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Fig. 1: Schematics of electrochemical and thermal energy storage devices, showing analogous inputs and outputs.
Fig. 2: Rate capability and Ragone plots for electrochemical and thermal energy storage.
Fig. 3: Thermal resistances and their relationship to temperature profiles in the PCM.
Fig. 4: Effect of thermal conductivity on device performance for PCM thickness of 3.5 cm.
Fig. 5: Effect of PCM thickness on Ragone curves for two thermal conductivities.
Fig. 6: Effect of material properties on gravimetric and volumetric Ragone plots for building cooling energy storage.

Data availability

All data generated or analysed during this study are included in the published article, its Supplementary Information and Source Data files

Code availability

The numerical model developed for this work was generated in MATLAB R2019b. Unrestricted access to the source code is available at https://github.com/NREL/ThermalRagone.

References

  1. Cabeza, L. F., Castell, A., Barreneche, C., de Gracia, A. & Fernández, A. I. Materials used as PCM in thermal energy storage in buildings: a review. Renew. Sustain. Energy Rev. 15, 1675–1695 (2011).

    Article  Google Scholar 

  2. Kalnæs, S. E. & Jelle, B. P. Phase change materials and products for building applications: a state-of-the-art review and future research opportunities. Energy Build. 94, 150–176 (2015).

    Article  Google Scholar 

  3. Mavrigiannaki, A. & Ampatzi, E. Latent heat storage in building elements: a systematic review on properties and contextual performance factors. Renew. Sustain. Energy Rev. 60, 852–866 (2016).

    Article  Google Scholar 

  4. Souayfane, F., Fardoun, F. & Biwole, P.-H. Phase change materials (PCM) for cooling applications in buildings: a review. Energy Build. 129, 396–431 (2016).

    Article  Google Scholar 

  5. Xiao, Q., Fan, J., Li, L., Xu, T. & Yuan, W. Solar thermal energy storage based on sodium acetate trihydrate phase change hydrogels with excellent light-to-thermal conversion performance. Energy 165, 1240–1247 (2018).

    Article  Google Scholar 

  6. Sharan, P., Turchi, C. & Kurup, P. Optimal design of phase change material storage for steam production using annual simulation. Sol. Energy 185, 494–507 (2019).

    Article  Google Scholar 

  7. Laughlin, R. B. Pumped thermal grid storage with heat exchange. J. Renew. Sustain. Energy 9, 044103 (2017).

    Article  Google Scholar 

  8. Amy, C., Seyf, H. R., Steiner, M. A., Friedman, D. J. & Henry, A. Thermal energy grid storage using multi-junction photovoltaics. Energy Environ. Sci. 12, 334–343 (2019).

    Article  Google Scholar 

  9. Datas, A., Ramos, A., Martí, A., del Cañizo, C. & Luque, A. Ultra high temperature latent heat energy storage and thermophotovoltaic energy conversion. Energy 107, 542–549 (2016).

    Article  Google Scholar 

  10. Albertus, P., Manser, J. S. & Litzelman, S. Long-duration electricity storage applications, economics, and technologies. Joule 4, 21–32 (2020).

    Article  Google Scholar 

  11. Ling, Z. et al. Review on thermal management systems using phase change materials for electronic components, Li-ion batteries and photovoltaic modules. Renew. Sustain. Energy Rev. 31, 427–438 (2014).

    Article  Google Scholar 

  12. Barako, M. T. et al. Optimizing the design of composite phase change materials for high thermal power density. J. Appl. Phys. 124, 145103 (2018).

    Article  Google Scholar 

  13. Yang, T. et al. A composite phase change material thermal buffer based on porous metal foam and low-melting-temperature metal alloy. Appl. Phys. Lett. 116, 071901 (2020).

    Article  Google Scholar 

  14. Zhou, D., Zhao, C. Y. & Tian, Y. Review on thermal energy storage with phase change materials (PCMs) in building applications. Appl. Energy 92, 593–605 (2012).

    Article  Google Scholar 

  15. Mohamed, S. A. et al. A review on current status and challenges of inorganic phase change materials for thermal energy storage systems. Renew. Sustain. Energy Rev. 70, 1072–1089 (2017).

    Article  Google Scholar 

  16. Sharma, A., Tyagi, V. V., Chen, C. R. & Buddhi, D. Review on thermal energy storage with phase change materials and applications. Renew. Sustain. Energy Rev. 13, 318–345 (2009).

    Article  Google Scholar 

  17. Kenisarin, M. M. High-temperature phase change materials for thermal energy storage. Renew. Sustain. Energy Rev. 14, 955–970 (2010).

    Article  Google Scholar 

  18. Pielichowska, K. & Pielichowski, K. Phase change materials for thermal energy storage. Prog. Mater. Sci. 65, 67–123 (2014).

    Article  Google Scholar 

  19. Gur, I., Sawyer, K. & Prasher, R. Searching for a better thermal battery. Science 335, 1454 (2012).

    Article  Google Scholar 

  20. Ragone, D. V. Review of battery systems for electrically powered vehicles. SAE Tech. Pap. Ser. https://doi.org/10.4271/680453 (1968).

    Article  Google Scholar 

  21. Li, Y., Tan, B. & Wu, Y. Mesoporous Co3O4 nanowire arrays for lithium ion batteries with high capacity and rate capability. Nano Lett. 8, 265–270 (2008).

    Article  Google Scholar 

  22. Qie, L. et al. Nitrogen-doped porous carbon nanofiber webs as anodes for lithium ion batteries with a superhigh capacity and rate capability. Adv. Mater. 24, 2047–2050 (2012).

    Article  Google Scholar 

  23. Colclasure, A. M. et al. Electrode scale and electrolyte transport effects on extreme fast charging of lithium-ion cells. Electrochim. Acta 337, 135854 (2020).

    Article  Google Scholar 

  24. Ji, H. et al. Ultrahigh power and energy density in partially ordered lithium-ion cathode materials. Nat. Energy 5, 213–221 (2020).

    Article  Google Scholar 

  25. Shamberger, P. J. Cooling capacity figure of merit for phase change materials. J. Heat Trans. 138, https://doi.org/10.1115/1.4031252 (2015).

  26. Shao, L. et al. Figure-of-merit for phase-change materials used in thermal management. Int. J. Heat. Mass Transf. 101, 764–771 (2016).

    Article  Google Scholar 

  27. Yazawa, K., Shamberger, P. J. & Fisher, T. S. Ragone relations for thermal energy storage technologies. Front. Mech. Eng. 5, https://doi.org/10.3389/fmech.2019.00029 (2019).

  28. Christen, T. Ragone plots and discharge efficiency-power relations of electric and thermal energy storage devices. J. Energy Storage 27, 101084 (2020).

    Article  Google Scholar 

  29. Ji, H. et al. Enhanced thermal conductivity of phase change materials with ultrathin-graphite foams for thermal energy storage. Energy Environ. Sci. 7, 1185–1192 (2014).

    Article  Google Scholar 

  30. Liu, L., Su, D., Tang, Y. & Fang, G. Thermal conductivity enhancement of phase change materials for thermal energy storage: a review. Renew. Sustain. Energy Rev. 62, 305–317 (2016).

    Article  Google Scholar 

  31. Kumar, N., Hirschey, J., LaClair, T. J., Gluesenkamp, K. R. & Graham, S. Review of stability and thermal conductivity enhancements for salt hydrates. J. Energy Storage 24, 100794 (2019).

    Article  Google Scholar 

  32. Kholmanov, I., Kim, J., Ou, E., Ruoff, R. S. & Shi, L. Continuous carbon nanotube–ultrathin graphite hybrid foams for increased thermal conductivity and suppressed subcooling in composite phase change materials. ACS Nano 9, 11699–11707 (2015).

    Article  Google Scholar 

  33. Liu, M., Ma, Y., Wu, H. & Wang, R. Y. Metal matrix–metal nanoparticle composites with tunable melting temperature and high thermal conductivity for phase-change thermal storage. ACS Nano 9, 1341–1351 (2015).

    Article  Google Scholar 

  34. Wu, S. et al. High-performance thermally conductive phase change composites by large-size oriented graphite sheets for scalable thermal energy harvesting. Adv. Mater. 31, 1905099 (2019).

    Article  Google Scholar 

  35. Sekulic, D. P., Sciubba, E. & Moran, M. J. Entransy: a misleading concept for the analysis and optimization of thermal systems. Energy 80, 251–253 (2015).

    Article  Google Scholar 

  36. Py, X., Olives, R. & Mauran, S. Paraffin/porous-graphite-matrix composite as a high and constant power thermal storage material. Int. J. Heat. Mass Transf. 44, 2727–2737 (2001).

    Article  Google Scholar 

  37. Thomas, B. R. & Linden, D. in Linden’s Handbook of Batteries 4th edn, 3.1–3.22 (McGraw-Hill Education, 2011).

  38. Zimny-Schmitt, D. Utility Rate Database (US Department of Energy’s Energy Information Administration, 2020); https://openei.org/wiki/Utility_Rate_Database

  39. Nellis, G. & Klein, S. Heat Transfer (Cambridge Univ. Press, 2009).

  40. Minkowycz, W. J., Sparrow, E. M. & Murthy, J. Y. Handbook of Numerical Heat Transfer 2nd edn (John Wiley & Sons, 2006).

  41. Patankar, S. V. Numerical Heat Transfer and Fluid Flow (Hemisphere Publishing Corporation, 1980).

  42. Bell, I. H., Wronski, J., Quoilin, S. & Lemort, V. Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library coolProp. Ind. Eng. Chem. Res. 53, 2498–2508 (2014).

    Article  Google Scholar 

  43. Hahn, D. W. & Özisik, M. N. in Heat Conduction 3rd edn, 467–470 (John Wiley & Sons, 2012).

  44. Buildings Energy Efficiency Frontiers and Innovation Technologies (BENEFIT) DE-FOA-0002090 (US Department of Energy, Office of Energy Efficiency and Renewable Energy, 2019).

Download references

Acknowledgements

This work was authored by the National Renewable Energy Laboratory (NREL), operated by Alliance for Sustainable Energy, LLC, for the US DOE under contract no. DE-AC36-08GO28308. Funding provided by US DOE Building Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the US Government. We thank S. Mumme from the DOE Building Technologies Office for his support and insight on this paper. We also thank J. Vidal and M. Bianchi from NREL for their feedback on our work.

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Authors and Affiliations

  1. National Renewable Energy Laboratory, Golden, CO, USA

    Jason Woods, Allison Mahvi, Anurag Goyal, Eric Kozubal, Adewale Odukomaiya & Roderick Jackson

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  1. Jason Woods
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Contributions

J.W. developed the concept of thermal rate capability and Ragone plots and oversaw the project, A.M. developed the numerical model, performed experiments on the thermal storage device, analysed the data and created the figures, A.G. and E.K. helped design the thermal storage device experiments and contributed to developing the concept, A.O. measured material properties and contributed to developing the concept, R.J. helped develop the idea and provided guidance during the project. J.W. and A.M. wrote the paper.

Corresponding author

Correspondence to Jason Woods.

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The authors declare no competing interests.

Additional information

Peer review information Nature Energy thanks Patrick Shamberger and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–8, Notes 1–6, Tables 1 and 2 and references.

Supplementary Video 1

The PCM phase and the PCM and fluid temperatures when the baseline device is discharged at 1 C.

Supplementary Video 2

The PCM phase and the surface heat flux at y = 0 when the baseline device is discharged at 1 C.

Supplementary Table 1

The raw experimental data used to generate Supplementary Figs. 3 and 4.

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Woods, J., Mahvi, A., Goyal, A. et al. Rate capability and Ragone plots for phase change thermal energy storage. Nat Energy 6, 295–302 (2021). https://doi.org/10.1038/s41560-021-00778-w

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