Based on the finite time thermodynamics theory,the entransy theory and the entropy theory,the Stirling cycles under different conditions are analyzed and optimized with the maximum output power as the target in this p...Based on the finite time thermodynamics theory,the entransy theory and the entropy theory,the Stirling cycles under different conditions are analyzed and optimized with the maximum output power as the target in this paper.The applicability of entransy loss(EL),entransy dissipation(ED),entropy generation(EG),entropy generation number(EGN) and modified entropy generation number(MEGN) to the system optimization is investigated.The results show that the maximum EL rate corresponds to the maximum power output of the cycle working under the infinite heat reservoirs whose temperatures are prescribed,while the minimum EG rate and the extremum ED rate do not.For the Stirling cycle working under the finite heat reservoirs provided by the hot and cold streams whose inlet temperatures and the heat capacity flow rates are prescribed,the maximum EL rate,the minimum EG rate,the minimum EGN and the minimum MEGN all correspond to the maximum power output,but the extremum ED rate does not.When the heat capacity flow rate of the hot stream increases,the power output,the EL rate,the EG rate and the ED rate increase monotonously,while the EGN and the MEGN decrease first and then increase.The EL has best consistency in the power output optimizations of the Stirling cycles discussed in this paper.展开更多
A thermoelectric generation Stirling engine (TEG-Stirling engine) is discussed by employing a low temperature Stirling engine and the dissipative equation of motion derived from the method of thermomechanical dynamics...A thermoelectric generation Stirling engine (TEG-Stirling engine) is discussed by employing a low temperature Stirling engine and the dissipative equation of motion derived from the method of thermomechanical dynamics (TMD). The results and mechanism of axial flux electromagnetic induction (AF-EMI) are applied to a low temperature Stirling engine, resulting in a TEG-Stirling engine. The method of TMD produced thermodynamically consistent and time-dependent physical quantities for the first time, such as internal energy ℰ(t), thermodynamic work Wth(t), the total entropy (heat dissipation) Qd(t)and measure or temperature of a nonequilibrium state T˜(t). The TMD analysis produced a lightweight mechanical system of TEG-Stirling engine which derives electric power from waste heat of temperature (40˚CT100˚C) by a thermoelectric conversion method. An optimal low rotational speed about 30θ′(t)/(2π)60(rpm) is found, applicable to devices for sustainable, clean energy technologies. The stability of a thermal state and angular rotations of TEG-Stirling engine are specifically shown by employing properties of nonequilibrium temperature T˜(t), which is also applied to study optimal fuel-injection and combustion timings of heat engines.展开更多
Let Vk=u1u2……uk, ui＇s be i.i.d - U（0, 1）, the p.d.f of 1 - Vk＋l be the GF of the unsigned Stirling numbers of the first kind s（n, k）. This paper discusses the applications of uniform distribution to combinator...Let Vk=u1u2……uk, ui＇s be i.i.d - U（0, 1）, the p.d.f of 1 - Vk＋l be the GF of the unsigned Stirling numbers of the first kind s（n, k）. This paper discusses the applications of uniform distribution to combinatorial analysis and Riemann zeta function; several identities of Stifling series are established, and the Euler＇s result for ∑ Hn/n^k-l, k ≥ 3 is given a new probabilistic proof.展开更多
The thermoelectric energy conversion technique by employing the Disk-Magnet Electromagnetic Induction (DM-EMI) is examined in detail, and possible applications to heat engines as one of the energy-harvesting technolog...The thermoelectric energy conversion technique by employing the Disk-Magnet Electromagnetic Induction (DM-EMI) is examined in detail, and possible applications to heat engines as one of the energy-harvesting technologies are discussed. The idea is induced by the analysis of thermomechanical dynamics (TMD) for a nonequilibrium irreversible thermodynamic system of heat engines, such as a drinking bird and a low temperature Stirling engine, resulting in thermoelectric energy generation different from conventional heat engines. The current thermoelectric energy conversion with DM-EMI can be applied to wide ranges of machines and temperature differences. The mechanism of DM-EMI energy converter is categorized as the axial flux generator (AFG), which is the reason why the technology is applicable to sensitive thermoelectric conversions. On the other hand, almost all the conventional turbines use the radius flux generator to extract huge electric power, which uses the radial flux generator (RFG). The axial flux generator is helpful for a low mechanoelectric energy conversion and activations of waste heat from macroscopic energy generators such as wind, geothermal, thermal, nuclear power plants and heat-dissipation lines. The technique of DM-EMI will contribute to solving environmental problems to maintain clean and sustainable energy as one of the energy harvesting technologies.展开更多
In this paper,we give several identities of finite sums and some infinite series involving powers and inverse of binomial coefficients,which extends the results of T.Trif.
We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the firs...We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.展开更多
Thermochemical recuperation heat recovery is an advanced waste heat utilization technology that can effectively recover exhaust waste heat from oxy-fuel Stirling engines.The novel combustor of a Stirling engine with t...Thermochemical recuperation heat recovery is an advanced waste heat utilization technology that can effectively recover exhaust waste heat from oxy-fuel Stirling engines.The novel combustor of a Stirling engine with thermochemical recuperation heat recovery system is expected to utilize both reformed gas and diesel fuels as sources of combustion.In this research,the effects of various factors,including the H_(2)O addition,fuel distribution ratio(FDR),excess oxygen coefficient,and cyclone structure on the temperature distribution in the combustor,combustion emissions,and external combustion system efficiency of the Stirling engine were experimentally investigated.With the increase of steam-to-carbon ratio(S/C),the temperature difference between the upper and lower heating tubes reduces and the circumferential temperature fluctuation decreases,and the combustion of diesel and reformed gas remains close to complete combustion.At S/C=2,the external combustion efficiency is 80.6%,indicating a 1.6%decrease compared to conventional combustion.With the increase of FDR,the temperature uniformity of the heater tube is improved,and the CO and HC emissions decrease.However,the impact of the FDR on the maximum temperature difference and temperature fluctuation across the heater is insignificant.When the FDR rises from 21%to 38%,the external combustion efficiency increases from 87.4%to92.3%.The excess oxygen coefficient plays a secondary role in influencing temperature uniformity and temperature difference,and the reformed gas and diesel fuel can be burned efficiently at a low excess oxygen coefficient of 1.04.With an increase in the cyclone angle,the heater tube temperature increases,while the maximum temperature difference at the lower part decreases,and the temperature fluctuation increases.Simultaneously,the CO and HC emissions increase,and the external combustion efficiency experiences a decrease.A cyclone angle of 30°is found to be an appropriate value for achieving optimal mixing between reformed gas and diesel fuel.Th展开更多
Regenerators play a vital role in enhancing the overall performance of Stirling engines.Hence,this paper performed an energy and exergy analysis to elucidate the significance of regenerator characteristics concerning ...Regenerators play a vital role in enhancing the overall performance of Stirling engines.Hence,this paper performed an energy and exergy analysis to elucidate the significance of regenerator characteristics concerning system performance,contributing to the optimal regenerator’s design and selection.The relationship between regenerator structure,regenerator exergy destruction,and output power,thermal efficiency,and exergy efficiency for Stirling engines was established by integrating the thermal model of Stirling engines with a mathematical model of regenerators.In contrast to cross-flow and parallel-flow regenerators,a novel concept of inclined-flow regenerators,featuring a matrix surface inclined in the direction of gas flow,was developed to achieve higher and more balanced engine output power and energy utilization efficiency.A comprehensive investigation was conducted into the effects of matrix structure types and regenerator geometries on the performance of both regenerators and engines.The results reveal that,following structural optimization,Stirling engines equipped with the inclined-flow regenerator demonstrate a substantial 16.6%,38.3%,and 37.2%increase in power output,thermal efficiency,and exergy efficiency,respectively,compared to those equipped with cross-flow regenerators.In contrast,when compared to engines fitted with parallel-flow regenerators,they experience a 13.5%reduction in power output but achieve remarkable enhancements of 45.4%and 36.7%in thermal and exergy efficiency,respectively.This study introduces new insights into selecting regenerator structures for enhancing the output performance of Stirling engines.展开更多
The reduction of oxygen consumption is a key factor to improve the energy density of underwater Stirling engine.A series of fundamental experiments are carried out to elucidate the spray characteristics of soybean oil...The reduction of oxygen consumption is a key factor to improve the energy density of underwater Stirling engine.A series of fundamental experiments are carried out to elucidate the spray characteristics of soybean oil/2,5-dimethylfuran(DMF)blended fuel in an underwater Stirling engine.Spray characteristics such as spray penetration,spray angle,spray area,and light intensity level under low injection and ambient pressures are obtained using image post-processing method.The results show that the effects of injection pressure,ambient pressure,and nozzle diameter on the transient spray characteristics of underwater Stirling engine are similar to those of diesel engine.However,in the steady spray process,the injection pressure has little effect on spray near angle,and the spray far angle increases with the increase of the injection pressure.Compared with the spray far angle at injection pressure of 3 MPa,the spray far angle at 5 MPa and 7 MPa increased by 11.38%and 18.14%respectively.The addition of DMF can obviously improve the atomization of soybean oil/DMF blended fuel.The spray angle of blended fuel in transient process increases with the increase of the DMF concentration.The spray near angle has exceeded that of diesel(46.21°)when the DMF volume fraction exceeds 25%.The spray far angle is equivalent to that of diesel when the DMF volume fraction reaches 75%.Moreover,the spray with gas ejection no longer keeps conical,the droplet diameter distribution is more dispersed,and the droplet diameter is smaller.展开更多
In order to improve the performance and service life of the Leningrader seal of the Stirling engine piston rod,interference,pre-load and friction coefficient were taken as influencing factors,and the curved surface re...In order to improve the performance and service life of the Leningrader seal of the Stirling engine piston rod,interference,pre-load and friction coefficient were taken as influencing factors,and the curved surface response method was adopted to reduce the contact stress of sealing surface and von Mises stress of the sealing sleeve as the response index,with the optimization goal of reducing wear and extending life.The above three key parameters are analyzed and optimized,the influence of each parameter on the sealing performance and service life is obtained,and the best combination scheme of the three is determined.The results show that the interaction between pre-tightening force and interference fit has the greatest impact on contact stress.The interaction between interference fit and friction coeffi-cient has the most significant effect on von Mises stress.The optimized parameters can reduce the maximum contact stress and maximum von Mises stress of the sealing sleeve by 26.3%and 20.6%,respectively,under a media pressure of 5-9 MPa.Test bench verification shows that the leakage of the optimized sealing device in 12 h is reduced by 0.44 cc·min^(-1)(1 cc=1 cm^(3)).The wear rate of the sealing sleeve is 1.08%before optimization and 0.45%after optimization,indicating that the optimized parameters in this paper are effective.展开更多
基金supported by the Tsinghua University Initiative Scientific Research Program
文摘Based on the finite time thermodynamics theory,the entransy theory and the entropy theory,the Stirling cycles under different conditions are analyzed and optimized with the maximum output power as the target in this paper.The applicability of entransy loss(EL),entransy dissipation(ED),entropy generation(EG),entropy generation number(EGN) and modified entropy generation number(MEGN) to the system optimization is investigated.The results show that the maximum EL rate corresponds to the maximum power output of the cycle working under the infinite heat reservoirs whose temperatures are prescribed,while the minimum EG rate and the extremum ED rate do not.For the Stirling cycle working under the finite heat reservoirs provided by the hot and cold streams whose inlet temperatures and the heat capacity flow rates are prescribed,the maximum EL rate,the minimum EG rate,the minimum EGN and the minimum MEGN all correspond to the maximum power output,but the extremum ED rate does not.When the heat capacity flow rate of the hot stream increases,the power output,the EL rate,the EG rate and the ED rate increase monotonously,while the EGN and the MEGN decrease first and then increase.The EL has best consistency in the power output optimizations of the Stirling cycles discussed in this paper.
文摘A thermoelectric generation Stirling engine (TEG-Stirling engine) is discussed by employing a low temperature Stirling engine and the dissipative equation of motion derived from the method of thermomechanical dynamics (TMD). The results and mechanism of axial flux electromagnetic induction (AF-EMI) are applied to a low temperature Stirling engine, resulting in a TEG-Stirling engine. The method of TMD produced thermodynamically consistent and time-dependent physical quantities for the first time, such as internal energy ℰ(t), thermodynamic work Wth(t), the total entropy (heat dissipation) Qd(t)and measure or temperature of a nonequilibrium state T˜(t). The TMD analysis produced a lightweight mechanical system of TEG-Stirling engine which derives electric power from waste heat of temperature (40˚CT100˚C) by a thermoelectric conversion method. An optimal low rotational speed about 30θ′(t)/(2π)60(rpm) is found, applicable to devices for sustainable, clean energy technologies. The stability of a thermal state and angular rotations of TEG-Stirling engine are specifically shown by employing properties of nonequilibrium temperature T˜(t), which is also applied to study optimal fuel-injection and combustion timings of heat engines.
基金the Mathematical Tianyuan Foundation (Grant No.A0324645) of China
文摘Let Vk=u1u2……uk, ui＇s be i.i.d - U（0, 1）, the p.d.f of 1 - Vk＋l be the GF of the unsigned Stirling numbers of the first kind s（n, k）. This paper discusses the applications of uniform distribution to combinatorial analysis and Riemann zeta function; several identities of Stifling series are established, and the Euler＇s result for ∑ Hn/n^k-l, k ≥ 3 is given a new probabilistic proof.
文摘The thermoelectric energy conversion technique by employing the Disk-Magnet Electromagnetic Induction (DM-EMI) is examined in detail, and possible applications to heat engines as one of the energy-harvesting technologies are discussed. The idea is induced by the analysis of thermomechanical dynamics (TMD) for a nonequilibrium irreversible thermodynamic system of heat engines, such as a drinking bird and a low temperature Stirling engine, resulting in thermoelectric energy generation different from conventional heat engines. The current thermoelectric energy conversion with DM-EMI can be applied to wide ranges of machines and temperature differences. The mechanism of DM-EMI energy converter is categorized as the axial flux generator (AFG), which is the reason why the technology is applicable to sensitive thermoelectric conversions. On the other hand, almost all the conventional turbines use the radius flux generator to extract huge electric power, which uses the radial flux generator (RFG). The axial flux generator is helpful for a low mechanoelectric energy conversion and activations of waste heat from macroscopic energy generators such as wind, geothermal, thermal, nuclear power plants and heat-dissipation lines. The technique of DM-EMI will contribute to solving environmental problems to maintain clean and sustainable energy as one of the energy harvesting technologies.
基金Supported by the National Natural Science Foundation of China (Grant No. 11061020)the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 20080404MS010)
文摘In this paper,we give several identities of finite sums and some infinite series involving powers and inverse of binomial coefficients,which extends the results of T.Trif.
文摘We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.
基金supported by the Ministry of Science and Technology of China(Grant No.2022YFE0209000)the Shanghai Rising-Star Program(Grant No.21QB1403900)Shanghai Municipal Commission of Science and Technology(Grant No.22170712600)。
文摘Thermochemical recuperation heat recovery is an advanced waste heat utilization technology that can effectively recover exhaust waste heat from oxy-fuel Stirling engines.The novel combustor of a Stirling engine with thermochemical recuperation heat recovery system is expected to utilize both reformed gas and diesel fuels as sources of combustion.In this research,the effects of various factors,including the H_(2)O addition,fuel distribution ratio(FDR),excess oxygen coefficient,and cyclone structure on the temperature distribution in the combustor,combustion emissions,and external combustion system efficiency of the Stirling engine were experimentally investigated.With the increase of steam-to-carbon ratio(S/C),the temperature difference between the upper and lower heating tubes reduces and the circumferential temperature fluctuation decreases,and the combustion of diesel and reformed gas remains close to complete combustion.At S/C=2,the external combustion efficiency is 80.6%,indicating a 1.6%decrease compared to conventional combustion.With the increase of FDR,the temperature uniformity of the heater tube is improved,and the CO and HC emissions decrease.However,the impact of the FDR on the maximum temperature difference and temperature fluctuation across the heater is insignificant.When the FDR rises from 21%to 38%,the external combustion efficiency increases from 87.4%to92.3%.The excess oxygen coefficient plays a secondary role in influencing temperature uniformity and temperature difference,and the reformed gas and diesel fuel can be burned efficiently at a low excess oxygen coefficient of 1.04.With an increase in the cyclone angle,the heater tube temperature increases,while the maximum temperature difference at the lower part decreases,and the temperature fluctuation increases.Simultaneously,the CO and HC emissions increase,and the external combustion efficiency experiences a decrease.A cyclone angle of 30°is found to be an appropriate value for achieving optimal mixing between reformed gas and diesel fuel.Th
基金supported by the National Natural Science Foundation of China(Grant No.51736004).
文摘Regenerators play a vital role in enhancing the overall performance of Stirling engines.Hence,this paper performed an energy and exergy analysis to elucidate the significance of regenerator characteristics concerning system performance,contributing to the optimal regenerator’s design and selection.The relationship between regenerator structure,regenerator exergy destruction,and output power,thermal efficiency,and exergy efficiency for Stirling engines was established by integrating the thermal model of Stirling engines with a mathematical model of regenerators.In contrast to cross-flow and parallel-flow regenerators,a novel concept of inclined-flow regenerators,featuring a matrix surface inclined in the direction of gas flow,was developed to achieve higher and more balanced engine output power and energy utilization efficiency.A comprehensive investigation was conducted into the effects of matrix structure types and regenerator geometries on the performance of both regenerators and engines.The results reveal that,following structural optimization,Stirling engines equipped with the inclined-flow regenerator demonstrate a substantial 16.6%,38.3%,and 37.2%increase in power output,thermal efficiency,and exergy efficiency,respectively,compared to those equipped with cross-flow regenerators.In contrast,when compared to engines fitted with parallel-flow regenerators,they experience a 13.5%reduction in power output but achieve remarkable enhancements of 45.4%and 36.7%in thermal and exergy efficiency,respectively.This study introduces new insights into selecting regenerator structures for enhancing the output performance of Stirling engines.
基金the Natural Science Foundation of Jiangsu Province(No.BK20220588)the Initial Scientific Research Fund of Yangzhou University(No.137012553)and the Public Welfare Technology Research Program of Zhejiang Province(Nos.LGG19E060001 and LGG 21E090001)。
文摘The reduction of oxygen consumption is a key factor to improve the energy density of underwater Stirling engine.A series of fundamental experiments are carried out to elucidate the spray characteristics of soybean oil/2,5-dimethylfuran(DMF)blended fuel in an underwater Stirling engine.Spray characteristics such as spray penetration,spray angle,spray area,and light intensity level under low injection and ambient pressures are obtained using image post-processing method.The results show that the effects of injection pressure,ambient pressure,and nozzle diameter on the transient spray characteristics of underwater Stirling engine are similar to those of diesel engine.However,in the steady spray process,the injection pressure has little effect on spray near angle,and the spray far angle increases with the increase of the injection pressure.Compared with the spray far angle at injection pressure of 3 MPa,the spray far angle at 5 MPa and 7 MPa increased by 11.38%and 18.14%respectively.The addition of DMF can obviously improve the atomization of soybean oil/DMF blended fuel.The spray angle of blended fuel in transient process increases with the increase of the DMF concentration.The spray near angle has exceeded that of diesel(46.21°)when the DMF volume fraction exceeds 25%.The spray far angle is equivalent to that of diesel when the DMF volume fraction reaches 75%.Moreover,the spray with gas ejection no longer keeps conical,the droplet diameter distribution is more dispersed,and the droplet diameter is smaller.
基金Supported by the National Natural Science Foundation of China (51675509)Wenzhou Public Welfare Industrial Technology Project (G20170026).
文摘In order to improve the performance and service life of the Leningrader seal of the Stirling engine piston rod,interference,pre-load and friction coefficient were taken as influencing factors,and the curved surface response method was adopted to reduce the contact stress of sealing surface and von Mises stress of the sealing sleeve as the response index,with the optimization goal of reducing wear and extending life.The above three key parameters are analyzed and optimized,the influence of each parameter on the sealing performance and service life is obtained,and the best combination scheme of the three is determined.The results show that the interaction between pre-tightening force and interference fit has the greatest impact on contact stress.The interaction between interference fit and friction coeffi-cient has the most significant effect on von Mises stress.The optimized parameters can reduce the maximum contact stress and maximum von Mises stress of the sealing sleeve by 26.3%and 20.6%,respectively,under a media pressure of 5-9 MPa.Test bench verification shows that the leakage of the optimized sealing device in 12 h is reduced by 0.44 cc·min^(-1)(1 cc=1 cm^(3)).The wear rate of the sealing sleeve is 1.08%before optimization and 0.45%after optimization,indicating that the optimized parameters in this paper are effective.
