Optimizing Power and Thermal Efficiency of an Irreversible Variable-Temperature Heat Reservoir Lenoir Cycle

• Main Authors: Ruibo Wang, Lingen Chen, Yanlin Ge, Huijun Feng
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Applied Sciences
• Subjects: finite-time thermodynamics; irreversible steady-flow Lenoir cycle; cycle power; thermal efficiency; heat conductance distribution; thermal capacity rate matching
• Online Access: https://www.mdpi.com/2076-3417/11/15/7171

Applying finite-time thermodynamics theory, an irreversible steady flow Lenoir cycle model with variable-temperature heat reservoirs is established, the expressions of power (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>P</mi></semantics></math></inline-formula>) and efficiency (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>) are derived. By numerical calculations, the characteristic relationships among <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>P</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> and the heat conductance distribution (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mi>L</mi></msub></mrow></semantics></math></inline-formula>) of the heat exchangers, as well as the thermal capacity rate matching (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>w</mi><mi>f</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub></mrow></semantics></math></inline-formula>) between working fluid and heat source are studied. The results show that when the heat conductances of the hot- and cold-side heat exchangers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>U</mi><mi>H</mi></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>U</mi><mi>L</mi></msub></mrow></semantics></math></inline-formula>) are constants, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mtext>-</mtext><mi>η</mi></mrow></semantics></math></inline-formula> is a certain “point”, with the increase of heat reservoir inlet temperature ratio (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>U</mi><mi>H</mi></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>U</mi><mi>L</mi></msub></mrow></semantics></math></inline-formula>, and the irreversible expansion efficiency (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula>), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>P</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> increase. When <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mi>L</mi></msub></mrow></semantics></math></inline-formula> can be optimized, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>P</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> versus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mi>L</mi></msub></mrow></semantics></math></inline-formula> characteristics are parabolic-like ones, there are optimal values of heat conductance distributions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mrow><msub><mi>L</mi><mi>P</mi></msub><mo stretchy="false">(</mo><mi>o</mi><mi>p</mi><mi>t</mi><mo stretchy="false">)</mo></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mrow><msub><mi>L</mi><mi>η</mi></msub><mo stretchy="false">(</mo><mi>o</mi><mi>p</mi><mi>t</mi><mo stretchy="false">)</mo></mrow></msub></mrow></semantics></math></inline-formula>) to make the cycle reach the maximum power and efficiency points (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>max</mi></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>max</mi></mrow></msub></mrow></semantics></math></inline-formula>). As <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>w</mi><mi>f</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub></mrow></semantics></math></inline-formula> increases, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>max</mi></mrow></msub><mtext>-</mtext><msub><mi>C</mi><mrow><mi>w</mi><mi>f</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub></mrow></semantics></math></inline-formula> shows a parabolic-like curve, that is, there is an optimal value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mrow><mi>w</mi><mi>f</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mo stretchy="false">(</mo><msub><mi>C</mi><mrow><mi>w</mi><mi>f</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub><mo stretchy="false">)</mo></mrow><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>) to make the cycle reach double-maximum power point (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mo stretchy="false">(</mo><msub><mi>P</mi><mrow><mi>max</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mi>max</mi></mrow></msub></mrow></semantics></math></inline-formula>); as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mi>L</mi></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>U</mi><mi>T</mi></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> increase, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mo stretchy="false">(</mo><msub><mi>P</mi><mrow><mi>max</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mi>max</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mo stretchy="false">(</mo><msub><mi>C</mi><mrow><mi>w</mi><mi>f</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub><mo stretchy="false">)</mo></mrow><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> increase; with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mo stretchy="false">(</mo><msub><mi>P</mi><mrow><mi>max</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mi>max</mi></mrow></msub></mrow></semantics></math></inline-formula> increases, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mo stretchy="false">(</mo><msub><mi>C</mi><mrow><mi>w</mi><mi>f</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>C</mi><mi>H</mi></msub><mo stretchy="false">)</mo></mrow><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> is unchanged.