A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones

There are two kinds of working mechanisms for the Stirling cycle, i.e., the positive and the reverse cycles, and a Stirling engine (SE) can be operated as a Stirling refrigerator (SR). This indicates that a probable practical method for evaluating the performance of a Stirling engine is to run it as...

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Autores principales:	Shulin Wang, Baiao Liu, Gang Xiao, Mingjiang Ni
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	stirling engine Stirling refrigerator analysis model p-V map working gas temperature Technology T
Acceso en línea:	https://doaj.org/article/44225e8e2eda457194b8ad6a7ae2e46c
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spelling	oai:doaj.org-article:44225e8e2eda457194b8ad6a7ae2e46c2021-11-11T15:51:21ZA Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones10.3390/en142170401996-1073https://doaj.org/article/44225e8e2eda457194b8ad6a7ae2e46c2021-10-01T00:00:00Zhttps://www.mdpi.com/1996-1073/14/21/7040https://doaj.org/toc/1996-1073There are two kinds of working mechanisms for the Stirling cycle, i.e., the positive and the reverse cycles, and a Stirling engine (SE) can be operated as a Stirling refrigerator (SR). This indicates that a probable practical method for evaluating the performance of a Stirling engine is to run it as a refrigerator, which is much easier to operate. For this purpose, an improved Simple model for both the positive and the reverse Stirling cycles, considering the various loss mechanisms and actual operating conditions, is proposed and verified by a self-designed Stirling engine. As to the positive cycle with helium and nitrogen at 2.8 MPa, the model errors range from 5.4–11.3% for the indicated power, and 1–10.2% for the cycle efficiency. As to the reverse cycle with helium and nitrogen, the errors of the predicted input power range from 7.9–15.3% and from 2.5–10.9%, respectively. The experimental cooling temperatures can reach −92.2 and −53.6 °C, respectively, for the reverse cycle with the helium and nitrogen at 2.8 MPa. This Stirling-cycle analysis model shows a good adaptability for both the positive and the reverse cycles. In addition, the p-V maps of the positive and reverse cycles are compared in terms of “pressure ratio” and “curve shape”. The pressure ratio of the reverse cycle is significantly higher than that of the positive one at the same mean pressure. A method is proposed to predict the indicated work of the positive Stirling cycles using the reverse ones. A mathematical model to predict the indicated power of the positive Stirling cycles based on the reverse ones is proposed: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><msub><mi>W</mi><mrow><mi>h</mi><mi>e</mi><mi>a</mi><mi>t</mi><mn>2</mn></mrow></msub></mrow><mrow><mo>−</mo><msub><mi>W</mi><mrow><mi>c</mi><mi>o</mi><mi>o</mi><mi>l</mi><mn>1</mn></mrow></msub></mrow></mfrac><mrow><mo>=</mo><mi mathvariant="normal">A</mi></mrow><mo>·</mo><msup><mrow><mo stretchy="false">(</mo><mfrac><mrow><msub><mi>T</mi><mrow><mi>g</mi><mi>e</mi><mn>2</mn></mrow></msub><mo>−</mo><msub><mi>T</mi><mrow><mi>g</mi><mi>c</mi><mn>2</mn></mrow></msub></mrow><mrow><msub><mi>T</mi><mrow><mi>g</mi><mi>c</mi><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>T</mi><mrow><mi>g</mi><mi>e</mi><mn>1</mn></mrow></msub></mrow></mfrac><mo>)</mo></mrow><mi>B</mi></msup></mrow></semantics></math></inline-formula>. The most critical issue with this method is to establish an associated model of the temperatures of the expansion and the compression space. This model shows a good adaptability for both the positive and the reverse cycles and can provide detailed information for deep discussion between the positive and the reverse cycles.Shulin WangBaiao LiuGang XiaoMingjiang NiMDPI AGarticlestirling engineStirling refrigeratoranalysis modelp-V mapworking gastemperatureTechnologyTENEnergies, Vol 14, Iss 7040, p 7040 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	stirling engine Stirling refrigerator analysis model p-V map working gas temperature Technology T
spellingShingle	stirling engine Stirling refrigerator analysis model p-V map working gas temperature Technology T Shulin Wang Baiao Liu Gang Xiao Mingjiang Ni A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones
description	There are two kinds of working mechanisms for the Stirling cycle, i.e., the positive and the reverse cycles, and a Stirling engine (SE) can be operated as a Stirling refrigerator (SR). This indicates that a probable practical method for evaluating the performance of a Stirling engine is to run it as a refrigerator, which is much easier to operate. For this purpose, an improved Simple model for both the positive and the reverse Stirling cycles, considering the various loss mechanisms and actual operating conditions, is proposed and verified by a self-designed Stirling engine. As to the positive cycle with helium and nitrogen at 2.8 MPa, the model errors range from 5.4–11.3% for the indicated power, and 1–10.2% for the cycle efficiency. As to the reverse cycle with helium and nitrogen, the errors of the predicted input power range from 7.9–15.3% and from 2.5–10.9%, respectively. The experimental cooling temperatures can reach −92.2 and −53.6 °C, respectively, for the reverse cycle with the helium and nitrogen at 2.8 MPa. This Stirling-cycle analysis model shows a good adaptability for both the positive and the reverse cycles. In addition, the p-V maps of the positive and reverse cycles are compared in terms of “pressure ratio” and “curve shape”. The pressure ratio of the reverse cycle is significantly higher than that of the positive one at the same mean pressure. A method is proposed to predict the indicated work of the positive Stirling cycles using the reverse ones. A mathematical model to predict the indicated power of the positive Stirling cycles based on the reverse ones is proposed: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><msub><mi>W</mi><mrow><mi>h</mi><mi>e</mi><mi>a</mi><mi>t</mi><mn>2</mn></mrow></msub></mrow><mrow><mo>−</mo><msub><mi>W</mi><mrow><mi>c</mi><mi>o</mi><mi>o</mi><mi>l</mi><mn>1</mn></mrow></msub></mrow></mfrac><mrow><mo>=</mo><mi mathvariant="normal">A</mi></mrow><mo>·</mo><msup><mrow><mo stretchy="false">(</mo><mfrac><mrow><msub><mi>T</mi><mrow><mi>g</mi><mi>e</mi><mn>2</mn></mrow></msub><mo>−</mo><msub><mi>T</mi><mrow><mi>g</mi><mi>c</mi><mn>2</mn></mrow></msub></mrow><mrow><msub><mi>T</mi><mrow><mi>g</mi><mi>c</mi><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>T</mi><mrow><mi>g</mi><mi>e</mi><mn>1</mn></mrow></msub></mrow></mfrac><mo>)</mo></mrow><mi>B</mi></msup></mrow></semantics></math></inline-formula>. The most critical issue with this method is to establish an associated model of the temperatures of the expansion and the compression space. This model shows a good adaptability for both the positive and the reverse cycles and can provide detailed information for deep discussion between the positive and the reverse cycles.
format	article
author	Shulin Wang Baiao Liu Gang Xiao Mingjiang Ni
author_facet	Shulin Wang Baiao Liu Gang Xiao Mingjiang Ni
author_sort	Shulin Wang
title	A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones
title_short	A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones
title_full	A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones
title_fullStr	A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones
title_full_unstemmed	A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones
title_sort	potential method to predict performance of positive stirling cycles based on reverse ones
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/44225e8e2eda457194b8ad6a7ae2e46c
work_keys_str_mv	AT shulinwang apotentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones AT baiaoliu apotentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones AT gangxiao apotentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones AT mingjiangni apotentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones AT shulinwang potentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones AT baiaoliu potentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones AT gangxiao potentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones AT mingjiangni potentialmethodtopredictperformanceofpositivestirlingcyclesbasedonreverseones
_version_	1718433295898771457

A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones

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