Stirling-type pulse-tube refrigerator for 4 K

1. M.A. Etaati, R.M.M. Mattheij, A.S. Tijsseling, A.T.A.M. de WaeleEindhoven University of TechnologyMathematics & Computer Science Dept.May. 09 2006 Stirling-type pulse-tube refrigerator for 4 K

2. Presentation Contents Introduction Project definition and physics of the problem Mathematical model Non-dimensionalization Conclusion and future of the work

3. Stirling-Type Pulse-Tube Refrigerator (S-PTR) Single-Stage PTR

4. Compressor Heat of Compression Q Q Reservoir Regenerator Pulse Tube Q Orifice Pressure-time Temperature-distance Cold Heat Exchanger Hot Heat Exchanger Aftercooler Single-stage Stirling-PTR

5. Gas parcel path in the Pulse-Tube

6. Stirling-Type Pulse-Tube Refrigerator (S-PTR) Three-Stage PTR

7. Reservoir 1 Reservoir 2 Reservoir 3 Compressor Orifice 2 Orifice 1 Orifice 3 Aftercooler Pulse-Tube 1 Reg. 1 Pulse-Tube 2 Pulse-Tube 3 Reg. 2 Reg. 3 Stage 1 Three-Stage Stirling-PTR

8. Compressor Heat of Compression Q Q Reservoir Regenerator Pulse Tube Q Orifice Cold Heat Exchanger Hot Heat Exchanger Aftercooler Single-stage Stirling-PTR • Continuum fluid flow • Reciprocating flow • Newtonian flow • Ideal gas • No external forces act on the gas

9. material derivative: • Conservation of mass • Conservation of momentum Mathematical model • Conservation of energy • Equation of state (ideal gas)

10. The viscous stress tensor ( ) ( is the dynamic viscosity ) ( is the thermal conductivity ) • The heat flux One-dimensional formulation • The viscous dissipation term

11. One-dimensional formulation of Pulse-Tube

12. One-dimensional formulation of Regenerator

13. “ ”: a typical gas density • “ Ta”: room temperature • “ p0”: average pressure • “ ”: the amplitude of the pressure variation • “ ”: the amplitude of the velocity variation • “ ”: the angular frequency of the pressure variation • “ ”: a typical viscosity • “ ”: a typical thermal conductivity of the gas • “ ”: a typical thermal conductivity of the regenerator material • “ ”: a typical heat capacity of the regenerator material Non-dimensionalisation

14. 2 2 Non-dimensionalised model of Pulse-Tube dimensionless parameters:

15. Non-dimensionalised model of Regenerator dimensionless parameters:

16. Momentum equation: Simplified System; Pulse-Tube

17. Simplified System; Regenerator

18. Compressor Heat of Compression Q Q Reservoir Regenerator Pulse Tube Q Orifice Cold Heat Exchanger Hot Heat Exchanger Aftercooler • velocity: Boundary Conditions (Pulse-Tube) • temperature:

19. Compressor Heat of Compression Q Q Reservoir Regenerator Pulse Tube Q Orifice Cold Heat Exchanger Hot Heat Exchanger Aftercooler • velocity: ( known as the interface condition with pulse-tube ) Boundary Conditions (Regenerator) • gas temperature: ( Neumann or Dirichlet Boundary Condition ) • material temperature: • pressure: ( given in the compressor side )

20. Single-stage S-PTR • Three-stage S-PTR • One-dimensional analysis of S-PTR • Consideration of wall interaction effects • Two-dimensional analysis Conclusion and future of the work

21. Thank you for your attention