Stirling Cycle. Ab Hashemi

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1 Stirling Cycle Ab Hashemi

2 Stirling Cycle T-s and P-v Diagrams 3 Tmax =constant T min =constant Ab Hashemi 2

3 Stirling Cycle Stirling cycle is made up of four totally reversible processes: 1-2 Isothermal compression (heat transfer from the working fluid at T min to the external sink) 2-3 Constant volume regeneration (heat transfer to the working fluid from the regenerative matrix) 3-4 Isothermal expansion (heat transfer to the working fluid at T max from an external source) 4-1 constant volume regeneration (heat transfer from the working fluid to the regenerative matrix) Ab Hashemi 3

4 Initial Condition Assume that the compression-space piston is at the outer dead point and the expansion-space piston is at the inner dead point, close to the face of the regenerator Expansion Space Compression Space T min Regenerator Ab Hashemi 4

5 Process 1-2 The compression piston moves toward the inner dead point, and the expansion-space piston remains stationary The working fluid is compressed in the compression space and the pressure increases The temperature is maintained constant because of heat is rejected from the compression-space to the surroundings (sink) Expansion Space Compression Space T min Regenerator Heat rejection Ab Hashemi 5

6 Process 2-3 Both pistons move simultaneously, the compression piston towards and the expansion piston away from the regenerator, so that the volume between them remains constant. The working fluid from the compression space moves through the porous metallic matrix and in this process is heated from T min to T max (heat transfer from the regenerator to the working fluid) The gradual increase in temperature in passage through the matrix, at constant volume, causes an increase in pressure Expansion Space Compression Space T max Regenerator Heat rejection Ab Hashemi 6

7 Process 3-4 The expansion piston continues to move away from the regenerator towards the outer dead point and the compression piston remains stationary at the inner dead point adjacent to the regenerator. As the expansion proceeds, the pressure decreases as the volume increases. The temperature remains constant because heat is added to the system from an external source. Expansion Space Compression Space T max Regenerator Heat addition Ab Hashemi 7

8 Process 4-1 Both pistons move simultaneously to transfer the working fluid (at constant volume) back, through the regenerative matrix from the expansion space to the compression space. In the passage through the matrix, heat is transferred from the working fluid to the matrix, so that the working fluid decreases in temperature and emerges at T min into the compression space. Heat transferred in the process is contained in the matrix for transfer to the gas in process 2-3 of the subsequent cycle. Expansion Space Compression Space T min Regenerator Ab Hashemi 8

9 Pistons Displacement (1) (2) time (3) (4) (1) Ab Hashemi 9

10 Comparison of Stirling & Carnot Cycles (for the same T max & T min ) Additional heat transfer of the Stirling Cycle Additional work output in Stirling Cycle Ab Hashemi 10

11 Stirling Cycle Efficiency In an Stirling Cycle: Heat is supplied at T max Heat is rejected at T min This heat supply and heat rejection at constant temperature satisfies the second Law of Thermodynamics for maximum thermal efficiency, so that the efficiency of the Stirling cycle is the same as the Carnot cycle, i.e.: η th = T max T T max min = 1 The principle advantage of the Stirling cycle over the Carnot cycle lies in the replacement of two isentropic processes by two constant volume processes which greatly increases the area of the P-V diagram. Therefore, to obtain a reasonable amount of work from the Stirling cycle, it is not necessary to resort to very high pressures and swept volumes. T T min max Ab Hashemi 11

12 Ideal Stirling Engine (isothermaal compression and expansion processes) 3 3 T H 4 2 T H Heat in T 2 P T C 1 Heat Out T C 1 v s Expansion space Compression space Heat in T H Regenerator T C Heat Out Ab Hashemi 12

13 Efficiency and specific power as a function of regenerator effectiveness i.m.e.p./p 1 Ab Hashemi 13

Lecture 40: Air standard cycle, internal combustion engines, Otto cycle

ME 200 Thermodynamics I Spring 206 Lecture 40: Air standard cycle, internal combustion engines, Otto cycle Yong Li Shanghai Jiao Tong University Institute of Refrigeration and Cryogenics 800 Dong Chuan