Earlier Lecture. A Cryocooler is a mechanical device operating in a closed cycle, which generates low temperature.

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2 arlier Lecture A Cryocooler is a mechanical device operating in a closed cycle, which generates low temperature. It eliminates cryogen requirement, offers reliable operation and is also cost effective. Heat exchangers can either be regenerative or recuperative type depending upon heat exchange. Recuperative Type: J T, Brayton, Claude. Regenerative Type: Stirling, GM, Pulse Tube.

3 Outline of the Lecture Topic : Cryocoolers Ideal Stirling cycle Working of Stirling Cryocooler Schmidt's Analysis Conclusions

History A well developed and a most commonly used Cryocooler is the Stirling Cycle Cryocooler. This cycle was first conceived by Robert Stirling in the year 85.

4 History A well developed and a most commonly used Cryocooler is the Stirling Cycle Cryocooler. This cycle was first conceived by Robert Stirling in the year 85. It was an engine cycle and was aimed to produce work (engine). The important events that occurred in the history of cryocoolers are as given in the next slide.

5 Year The Chronology vent 85 Robert Stirling Stirling ngine 8 John Herschel concept of using as a cooler 86 Alexander Kirk The concept into practice 87 Davy Postle Free Piston system 956 Jan Koehler First commercial machine for air liquefaction 965 Jan Koehler Nitrogen Liquefaction 5

6 An Ideal Stirling Cycle Consider a p chart as shown in the figure. Pressure p Q C : Isothermal compression at T C. p p T T TC olume dq dw T R C ln 6

7 Pressure p Q RT An Ideal Stirling Cycle Q C : Constant volume heat rejection. ( ) dq + C T T C : Isothermal expansion. p p Q olume T T T dq dw T R C ln 7

8 An Ideal Stirling Cycle : Constant volume heat absorption. dq C ( T T ) C Q C Pressure p Q RT Q RT Q olume Q COP Q Q C +RT ln RTC ln T ln R 8

9 Pressure p Q RT An Ideal Stirling Cycle Q C Q RT Q +RT ln RTC ln T ln R T COP T T C olume COP (Stirling) COP (Carnot) 9

10 Stirling & Carnot Cycles Stirling Cycle Pressure p Temperature T T C T olume ntropy s 0

11 Stirling & Carnot Cycles Carnot Cycle Stirling Cycle Pressure p 6 5. Temperature T T C T 5 6 olume ntropy s

12 Ideal Stirling Cycle xpander Regenerator Piston Compression T c Q C Pressure p Q RT Q C Q RT Q Regenerative Cooling Q xpansion T olume Regenerative Heating T c

13 Ideal Stirling Cycle,max C 0 C,max xpander Regenerator Piston T c Compression Time Regenerative Cooling xpansion Displacement T Regenerative Heating T c

14 ,max Ideal Stirling Cycle 0 C C,max As mentioned in the earlier lecture, the characteristics of a Stirling cycle are High frequency. Time Regenerative heat exchanger. Displacement Phase difference between the piston and the displacer motions.

15 ,max Time Actual Stirling Cycle 0 C Displacement C,max In actual Stirling cycle the discontinuous motion can not be achieved. In view of this sinusoidal motion may be implemented. This motion is realistic and can be achieved using a Crank or gas spring mechanism. 5

16 Actual Stirling Cycle In reality, the actual working cycle will be different from Ideal Stirling Cycle in following ways. Discontinuous motion, difficult to realize in practice. Presence of void volume or dead space (not swept by piston or displacer), pressure drop. Ineffectiveness in heat transfer or regeneration. Non isothermal compression and expansion. 6

17 Stirling Cryocooler Types Regenerator Compressor α Type xpander Depending upon the relative arrangements of piston and displacer/piston, various types of Stirling Cryocoolers are possible, namely α type Stirling Cryocooler. β type Stirling Cryocooler. γ type Stirling Cryocooler. β Type γ Type 7

18 Stirling Cryocooler Types Regenerator Compressor α Type xpander Two Piston arrangement (α type) whose drive mechanisms may be mounted on same crank shaft. Integral Piston & Displacer arrangement (β type) The piston and displacer are housed inside same cylinder. β Type γ Type 8

19 Stirling Cryocooler Types Regenerator Compressor α Type xpander Split Piston & Displacer arrangement (γ type) The compression space is divided. These systems have variable dead volume in compression space due to the movement of displacer. β Type γ Type 9

20 Regenerator Design Parameters The various design parameters of a Stirling Cryocooler are as follows. T C C R Compressor α Type T xpander vaporator temperature (T ) Condenser temperature (T C ) Compression olume ( C ) xpansion olume ( ) Regenerator olume ( R ) P max, P min, P avg. Phase angle (α) Crank angle (ø) 0

21 Schmidt s Analysis In the year 86, Gustav Schmidt, a German scientist, presented a Stirling Cryocooler analysis. This analysis is based on a realistic cycle and is assumed to provide a first guess of dimensions. The following are the assumptions. Perfect isothermal compression, expansion. Harmonic motion of piston and displacer. Perfect regeneration.

22 Schmidt s Analysis The non dimensional parameters in the Schmidt s analysis are Swept volume ratio : k C Temperature ratio : τ T T C Dead volume ratio : X D

23 Schmidt s Analysis xpansion volume variation : e ( + cosφ ) Compression volume variation : c C + φ α ( cos( )) c k + φ α ( cos( )) k C olume α C Angle ø

24 M T Schmidt s Analysis p p p + + RT RT RT e e c c d d e c d K RT C Let the instantaneous pressure in the system be same throughout the system, p. Also, T e and T c are assumed to be constants as T and T C respectively. Let M T be given as shown. M T K RT C

25 Schmidt s Analysis ( + cosφ) T k( + cos( φ α) ) p C T K + + RT T T RT D C D C τ T T C X D T d T + T C S Xτ τ + K p ( ) k( ) τ + cosφ + + cos( φ α) + S ( τ + cos α) + ( sin α) τ + + A k k k sinα tanθ τ + k cosα B k S δ A B 5

26 p p min p ratio K B δ θ φ Schmidt s Analysis Substituting, A, B, θ and δ in the mass equation and rearranging, we get p max [ cos( ) + ] B B K [ + δ ] K [ δ ] [ + δ ] [ δ φ φ θ π 6

27 Schmidt s Analysis Mean pressure pm π π 0 pd( θ φ) pm p max δ + δ Q π p δ sinθ + δ Q π pδ sin( θ α) k pd + δ m m pde 0.5 C c 0.5 COP Q W T COP Q Q Q C T C T T 7

28 Losses In the earlier slide, we saw the cooling effect based on Schmidt's analysis. But, in an actual system, there are many losses. Few of them are as listed below. Ineffectiveness of regenerator. Pressure drop in system. Solid conduction losses. Shuttle conduction losses. Losses in power input. 8

Losses Considering the above mentioned losses, the net cooling effect and gross power required is given by the following correlations. Q net Q Σ(losses).

29 Losses Considering the above mentioned losses, the net cooling effect and gross power required is given by the following correlations. Q net Q Σ(losses). W total W T + Σ(losses). In general, Q calculated from Schmidt's analysis, in which 60 70% are considered as losses, while losses in power input is due to mechanical efficiency. 9

30 Summary A Stirling Cycle was first conceived by Robert Stirling in the year 85. COP (Stirling) COP (Carnot). In reality, the actual working cycle has discontinuous motion, pressure drop, ineffectiveness and non isothermal processes. Depending upon the relative arrangements of piston and displacer/piston, α, β, γ are the different types of Stirling cryocooler. 0

31 Summary Gustav Schmidt presented a Stirling Cryocooler analysis in the year 86, it is assumed to provide a first guess of dimensions. The net cooling effect and gross power required is given by the following correlations. Q net Q Σ(losses). W total W T + Σ(losses).

32 A self assessment exercise is given after this slide. Kindly asses yourself for this lecture.

33 Self Assessment. A Stirling cycle consist of two processes.. In an isothermal process, dq is given by.. In a constant volume process, du is given by.. COP Carnot and COP Stirling are. 5. COP of Stirling cycle is. 6. In an actual Stirling cycle, the discontinuous motion is approximated to motion. 7. The volume not swept by piston/displacer is. 8. In a type unit, the piston and displacer are housed inside same cylinder. 9. In Schmidt's analysis, instantaneous pressure is assumed to be.

34 Answers. Isothermal and Constant volume. mdq dw RTC ln /. RdU + C T T. qual. ( ) 5. MT / T T C 6. Sinusoidal 7. oid volume 8. Beta 9. Constant ( ) C [ ]

35 Thank You! 5

Performance Evaluation of 0.5 W at 80 K Stirling Cryocooler

Performance Evaluation of 0.5 W at 80 K Stirling Cryocooler International Journal of urrent ngineering and Technology -ISSN 2277 4106, P-ISSN 2347 5161 2016 INPRSSO, All Rights Reserved Available at http://inpressco.com/category/ijcet Research Article Performance