Multi-stage Analysis And Optimization Model For Stirling Cycles

Solar energy is a kind of renewable energy with large amout of resource and wide range of applications.Concentrating solar power(CSP)is the main application of solar energy,which can be classified into tower-type,trough-type,dish-type and linear Fresnel-type.The dish-type CSP system has the advantages of high concentrating ratio,high efficiency,low water consumption and being applicable on distributed generation.A Stirling engine is the essential heat engine in a dish-type CSP system.This is a closed regenerative cycle piston engine which is heated externally.It has the merits of higher theoretical efficiency,lower emission,quieter operation,wider range of heat sources,etc.The analysis models for Stirling cycle include first-order,second-order,third-order and fourth-order models.A second-order one has relatively reliable accuracy without detailed cyclic information,while a third-order one provides relatively comprehensive operational information with uncertainty.In this study,a 100 W ?-type Stirling engine is experimented under the condition of 440?1396 r/min rotary speed and 1.523?2.848 MPa pressure.Then,a second-order model and a third-order model are developed by the Improved Simple Analytical Model(ISAM)and the Sage model,respectively.It is indicated that ISAM has errors less than 20%for indicated power output and errors less than 30%for thermal efficiency,respectively.However,errors of Sage are over 50%and 30%,respectively,and the p-V diagrams have deviation in the aspects of area,pressure ratio and volume ratio,comparing with the experimental ones.In order to improve Sage,the gap of piston seal and the empirical multiplier for heat transfer of cooler is adjusted,as suggested by ISAM,to consider the effects of seal leakage loss,gas spring hysteresis loss,and piston friction loss in an improved Sage.The improved Sage indicates that the errors of indicated power output and thermal efficiency are reduced by an average of 32 percentage points and an average of 28 percentage points,respectively,and the similarities of p-V diagrams are increased by an average of 3 percentage points.The improved Sage also reveals that regenerator is the part with the maximum amount of heat transfer and pressure drop,whose heat capacity is-6 and 7?times higher than those of heater and cooler and?59 times higher than the indicated power output,and the flow resistance resulted from the pressure drop of regenerator is 99%of that in the whole engine.The maximum exergy loss is caused by regenerator as well,which takes up 75.96%of the whole engine.The design parameters of regenerator,heater and cooler,including the lengths,diameters and woven wire screens,are optimized based on the improved Sage in order for the maximum indicated power output,and the results show that the power could be increased by 65%.If the pressure and rotary speed are improved further,the power could be increased up to be 3.3 times higher than the original one.