Study of Stirling Engine

ME270Zhiyu Gao

IntroductionThe Stirling engine uses the temperature difference between its hot end and cold end to establish a cycle of a fixed mass of gas expanding and contracting within the engine, thus converting thermal energy into mechanical power.

How it works Source: http://www.wikipedia.org

Schematic

Schematic of Stirling Engine

Bond Graph

Differential Equations e1 = SE1 e2 = e5 e3=e5 e4=SE4 e5=Q5/C5+Q6/C5x6+Q8/C5x8+Q10/C5x10 e6=Q5/C6x5+Q6/C6+Q8/C6x8+Q10/C6x10 e7=SE7 e8=Q5/C8x5+Q6/C8x6+Q8/C8+Q10/C8x10 e9=e8 e10=Q5/C10x5+Q6/C10x6+Q8/C10x8+Q10/C10 e11=e10 e12=e11/T11x12 e13=e12 e14=e13/T13x14 e15=e14-e16 e16=f16*R16

Differential Equations f1=e1/R1+e2/R1x2 f2=e1/R2x1+e2/R2 f3=e3/R3+e4/R3x4 f4=e3/R4x3+e4/R4 f5=f2-f3 f6=e6/R6+e7/R6x7+e9/R6x9 f7=e6/R7x6+e7/R7+e9/R7x9 f8=f9 f9=e6/R9x6+e7/R9x7+e9/R9 f10=f11 f11=f12/T11x12 f12=f13 f13=f14/T13x14 f14=f15 f15=P15/I15 f16=f15

State Space Equations dQ5=SE1/R2x1+Q5/C5/R2+Q6/C5x6/R2+Q8/C5x8/R2+Q10/

C5x10/R2-Q5/C5/R3-Q6/C5x6/R3-Q8/C5x8/R3-Q10/C5x10/R3-SE4/R3x4

dQ6=Q5/C6x5/R6+Q6/C6/R6+Q8/C6x8/R6+Q10/C6x10/R6+SE7/R6x7+Q5/C8x5/R6x9+Q6/C8x6/R6x9+Q8/C8/R6x9+Q10/C8x10/R6x9

dQ8=Q5/C6x5/R9x6+Q6/C6/R9x6+Q8/C6x8/R9x6+Q10/C6x10/R9x6+SE7/R9x7+Q5/C8x5/R9+Q6/C8x6/R9+Q8/C8/R9+Q10/C8x10/R9

dQ10=P15/I15/T13x14/T11x12 dP15=Q5/C10x5/T11x12/T13x14+Q6/C10x6/T11x12/

T13x14+Q8/C10x8/T11x12/T13x14+Q10/C10/T11x12/T13x14-P15/I15*R16

Block Diagram Q5

Block Diagram Q6

Block Diagram Q8

Block Diagram Q10

Block Diagram P15

Simplified Bond Graph

Transfer Function Piston to Flywheel 8000000 1 ------- * ------------------------- 19 (100 s + 1) cos(P6)

P6 is the rotated angle of the flywheel

Expected Result

Flywheel speed VS Time