Earlier Lecture. We studied the effect of the heat exchanger effectiveness ε on the performance of a Linde Hampson system. max

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2 Earlier Lecture We studied the eect o the heat exchanger eectiveness ε on the perormance o a Linde Hampson system. Mathematically, ε = Q act Q max In a Linde Hampson cycle, the heat exchanger eectiveness ε is h or ' hg h3' h2 ε = ε = h h h h g 3 2 Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 2

3 Earlier Lecture The liquid yield y or a Linde Hampson system is given by y = ( h ) ( )( ) h2 ε h hg ( h ) ( )( ) h ε h hg The eectiveness should be more than 85% in order to have a liquid yield in the Linde Hampson cycle. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 3

4 Outline o the Lecture Topic : Gas Liqueaction and Rerigeration Systems (contd) Precooled Linde Hampson system Liquid yield Work requirement Maximum liquid yield Comparison between the Simple and Precooled Linde Hampson systems Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay

5 Introduction We have seen earlier that, as the compression temperature decreases, the yield y increases or a Linde Hampson system. The method o cooling the gas ater the compression or beore the entrance to the heat exchanger is called as precooling. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 5

6 Introduction The Linde Hampson cycle with a precooling arrangement is called as Precooled Linde Hampson cycle. Here ater, we reer these two cycles as Simple Linde Hampson system and Precooled Linde Hampson system respectively. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay

7 r Precooled L H Cycle The Simple Linde Hampson system is as shown in the igure. W c2 W c Q R A 3 luid heat exchanger is used to thermally couple the precooling and the Linde Hampson systems. ( ) g Hence, the temperature is lowered ater compression or beore the entry to the heat exchanger. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 7

8 r Precooled L H Cycle The eatures o the precooling system are as ollows. W c2 LHS It is a closed cycle rerigerator with the cold heat exchanger thermally coupled to the simple Linde Hampson system. In other words, the cooling object or this rerigerator is the Linde Hampson cycle. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 8

9 r W c2 Precooled L H Cycle The heat exchanger o precooling system is cooled by water and J T device is used to attain lower temperature. LHS The process o compression is assumed to be adiabatic. Hence, Q R = 0. R3a, NH 3, CO 2 are the common rerigerants in the precooling systems. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 9

10 r Precooled L H Cycle The salient eatures o a Precooled Linde Hampson system are as ollows. W c2 W c Q R The system consists o a compressor, heat exchangers (2 and 3 luid) and a J T expansion device. ( ) g Compression process is isothermal (adiabatic in precooling system) while the J T expansion is isenthalpic. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 0

11 r W c2 Precooled L H Cycle All the processes are assumed to be ideal in nature and there are no pressure drops in the system. W c Q R ( ) The heat exchangers are assumed to be 00% eective and the processes are isobaric in nature. g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay

12 r Precooled L H Cycle The gas to be liqueied by the liqueaction system is called as Primary Fluid. W c2 Q R Whereas, the rerigerant in the precooling system is called as Secondary Fluid. W c ( ) g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 2

13 a r W c2 b Precooled L H Cycle c 2 3 Precooling Temp. Q R 2 d 3 W c ( ) g 5 h=const g 5 s Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 3

14 Td 3 Precooled L H Cycle 2 Re. BP The precooling limit o the precooling cycle is governed by the boiling point o rerigerant at its suction pressure. 5 h=const s g Boiling point o the common rerigerants at bar are Fluid Boiling Pt. CO 2 2. K NH 3 20 K R3a 27 K Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay

15 a r W c2 b Precooled L H Cycle c Consider a control volume or this system as shown in the igure. Q R 2 d 3 It encloses the 3 luid heat exchanger, J T device and the liquid container. W c ( ) g 5 The st Law is applied to analyse the system. The changes in the velocities and datum levels are assumed to be negligible. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 5

16 a r W c2 b Q R 2 Precooled L H Cycle c d 3 The quantities entering and leaving the control volume are as ollows. IN OUT m d m a 2 m W c ( ) g 5 Applying the st law, we have h dr, 2 ( ) r ar, Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay r + mh = mh + h+ h

17 a r b Precooled L H Cycle c h r + mh dr, 2 ( ) = mh + h+ h r ar, W c2 Q R 2 W c ( ) g 5 d 3 Rearranging the terms, we have h h h 2 r ar, h dr, = + h h h h Denoting the ratio r m = Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay r 7

18 a r W c2 Q R 2 W c b ( ) Precooled L H Cycle g 5 c d 3 We have, y h h h r h 2 ar, dr, = = + h h h h The irst term in the above expression is the yield or a simple Linde Hampson system. The second term is the additional yield occurring due to the precooling o the Simple system. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 8

19 a r b Precooled L H Cycle c y h h h h r h h h h 2 ar, dr, = = + W c2 Q R 2 W c ( ) d 3 This increment in the yield is dependent on the The change in enthalpy values rom (h d h a ) o the rerigerant. g 5 Rerigerant low rate (m r ). Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 9

20 a r W c2 Q R 2 W c b ( ) Precooled L H Cycle g 5 c d 3 Since, the 3 luid heat exchanger is assumed to be 00% eective, the ollowing conditions hold true. The minimum value o T 3 would be equal to T d, which is the boiling point o the rerigerant. The maximum value o T would be equal to T d, which is the boiling point o the rerigerant. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 20

21 a r W c2 b Precooled L H Cycle c At this condition, the system produces the maximum yield or a given rerigerant. Q R 2 d 3 Mathematically, y y max or T = T = T = 3 d W c ( ) g 5 Consider a control volume enclosing the heat exchanger, J T device and the liquid container as shown in the igure. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 2

22 a r W c2 b Q R 2 Precooled L H Cycle The quantities entering and c d 3 leaving the control volume are as ollows. IN 3 OUT m W c ( ) g 5 Applying the st law, we have ( ) mh = h + h 3 Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 22

23 a r W c2 b Precooled L H Cycle Rearranging the terms, we c have ( ) = ( ) h h m h h 3 Q R 2 d 3 y max h h h h = = 3 W c ( ) The quantities h 3 and h are evaluated at the boiling point o the rerigerant (T d ). g 5 Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 23

24 a r W c2 b Precooled L H Cycle c Consider a control volume or the compressor in the liqueaction cycle as shown in the igure. Q R 2 W c ( ) g 5 d 3 The quantities entering and leaving this control volume are as given below. IN OUT 2 -W c -Q R Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 2

25 a r W c2 Q R 2 W c b ( ) Precooled L H Cycle g 5 c d 3 Using st Law or the ollowing table, we get IN OUT 2 -W c -Q R Rearranging the terms, we have Q W = h h Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay E in = E out mh W = mh Q c 2 R ( ) R c 2 25

26 a r W c2 b Q R 2 Precooled L H Cycle c d 3 The heat o compression Q R can be obtained by using 2 nd Law or an isothermal compression. It is given by, R ( ) Q W = h h R c 2 ( ) Q = mt s s 2 W c ( ) g 5 Combining the above equations, we have ( ) ( ) W = mt s s m h h c 2 2 Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 2

27 a r W c2 b Precooled L H Cycle Similarly, a control volume c is taken enclosing the rerigerating compressor. Q R 2 W c ( ) g 5 d 3 The quantities entering and leaving this control volume are as given below. IN OUT m a m b -W c2 0 The heat o compression is zero because the process is adiabatic. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 27

28 a r W c2 Q R 2 W c b ( ) Precooled L H Cycle g 5 c d 3 Using st Law or the ollowing table, we get IN OUT m a m b -W c2 0 Rearranging the terms, we have W = h h Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay E in = E out mh W = mh r ar, c2 r br, ( ) c2 r br, ar, 28

29 a r W c2 b Precooled L H Cycle The total work requirement c or this system is W = W + W c c c2 Q R 2 W c ( ) g 5 d 3 Substituting the ollowing values, we have ( ) ( ) W = mt s s m h h c 2 2 ( ) W = h h c2 r br, ar, ( ) ( ) W = mt s s m h h 2 2 ( ) r br, ar, Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay c + h h 29

30 a r W c2 Q R 2 W c b ( ) Precooled L H Cycle c d 3 c ( ) ( ) W = mt s s m h h 2 2 ( ) + h h r br, ar, The work required or a unit mass o primary gas compressed is given as Wc T s s 2 h h 2 ( ) ( ) = r + ( h ) br, h ar, g 5 Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 30

31 a r b Precooled L H Cycle c Denoting the ratio r m = r W c2 Q R 2 d 3 Wc T s s 2 h h 2 ( ) ( ) = r + ( h ) br, h ar, W c ( ) g 5 Wc T s s 2 h h 2 ( ) ( ) = ( h ) + r h br, ar, Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 3

32 Precooled L H Cycle a r W c2 b c Wc T s s 2 h h 2 ( ) ( ) = ( h ) + r h br, ar, Q R 2 W c ( ) g 5 d 3 The irst and second terms are the work requirement in a Simple Linde Hampson system. The third term is the additional work required to precool the system. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 32

33 Tutorial Determine the y, y max, the work/unit mass compressed, work/unit mass liqueied and FOM or the Simple and Precooled Linde Hampson systems with Nitrogen as working luid. The R3A is the rerigerant or the precooling system with ratio r as The liqueaction system is operated between.03 bar ( atm) and 0.3 bar (00 atm) at 300 K. The ollowing is the data or R3a. Comment on the results. a b c p (bar) T (K) h (J/g) Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 33

34 Tutorial Given Cycle : Simple and Precooled L H System Working Fluid : Nitrogen Pressure : atm 00 atm Temperature : 300 K Rerigerant : R3a, atm 0 atm Mass ratio(r) : 0.08 For above cycles, Calculate and comment Liquid Yield y, y max 2 Work/unit mass o gas compressed 3 Work/unit mass o gas liqueied FOM Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 3

35 a r W c2 Q R 2 W c b ( ) g 5 Tutorial c d 3 2 p (bar) T (K) h (J/g) s (J/gK) a b c p (bar) T (K) h (J/g) s (J/gK) R3a h d = h c, since the expansion is isenthalpic. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 35

36 Tutorial Ideal Work Requirement = Wi T s s h h ( ) ( ) T 2 p (bar) T (K) h (J/g) s (J/gK) s g W c ( ) ( ) = = 77 J / g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 3

37 Liquid yield y h h h h 2 = Tutorial 2 p (bar) T (K) h (J/g) s (J/gK) T=const h=const s g y h h h h 2 = 2 5 = = 33 = 0.0 Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 37

38 Tutorial Work/unit mass o gas compressed Wc = T ( s s 2) ( h h 2) 2 p (bar) T (K) h (J/g) s (J/gK) T=const h=const s g W c ( ) ( ) = = 379 J / g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 38

39 Tutorial Work/unit mass o gas liqueied T=const W c = 379 y = h=const W c = Wc y 379 = = 975 J / 0.0 g s g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 39

40 Tutorial Figure o Merit (FOM) T=const W c = 975 W i = 77 3 h=const FOM W m = Wc i 77 = = s g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 0

41 Tutorial The T s diagram or a Precooled Linde Hampson system is as shown Prec. Temp The state properties are as tabulated below. 2 p (bar) T (K) h (J/g) s (J/gK) h=const s g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay

42 Liquid yield Tutorial y h h h h r h h h h 2 ar, dr, = = + r = a b c p (bar) T (K) h (J/g) s (J/gK) R3a y ( ) ( ) ( ) ( ) = ( ) ( ) ( ) ( ) 7 30 = = Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 2

43 Tutorial Work/unit mass o N 2 compressed Wc T s s 2 h h 2 ( ) ( ) = ( h ) + r h br, ar, r = a b c p (bar) T (K) h (J/g) s (J/gK) R3a W c ( ) ( ) ( ) = = 38.3 J / g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 3

44 Tutorial Work/unit mass o N 2 liqueied Prec. Temp W c = W c = 38.3 Wc y y = = = 3.7 J / 0.03 g 5 h=const s g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay

45 Tutorial Figure o Merit (FOM) Prec. Temp W c = FOM 3.7 W m = Wc i W i = = = h=const s g Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 5

46 Tutorial Maximum Liquid yield y = y max T3 = T = T = 27 K d Re BP y max = h h h h r = p (bar) T (K) h (J/g) h=const s g y max = ( ) ( 08 29) ( 28) ( 379) = = 0.07 Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay

47 y W c m Wc m FOM Tutorial Simple Precooled Max Tabulating the results, we have the above comparison or Simple and Precooled Linde Hampson System. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 7

48 Assignment. Compare and comment on the ollowing or both Simple and Precooled Linde Hampson systems with Air as working luid when the system is operated between.03 bar ( atm) and 202. bar (200 atm) at 300 K. The eectiveness o HX is 00% and r=0.. Ideal Work requirement Liquid yield Work/unit mass compressed Work/unit mass liqueied FOM Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 8

49 Summary The method o cooling the gas ater the compression or beore the entrance to the heat exchanger is called as precooling. The Linde Hampson cycle with a precooling arrangement is called as Precooled Linde Hampson cycle. In a Precooled Linde Hampson system, a closed cycle rerigerator is thermally coupled to a simple Linde Hampson system through a 3 luid heat exchanger. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 9

50 Summary Compression process is isothermal in Liqueaction cycle but it is adiabatic in precooling system o a Precooled Linde Hampson system. The precooling limit o the precooling cycle is governed by the boiling point o rerigerant at its suction pressure. The yield or a Precooled Linde Hampson system is h h h 2 ar, h dr, y = = + r r h h h h m = r Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 50

51 Summary y max h h h h = = 3 The maximum liquid yield is given by the above expression. The enthalpy values are evaluated at the boiling point o the rerigerant. The work requirement or the unit mass o primary luid compressed is Wc = T ( ) ( ) ( ) s s 2 h h 2 + r h br, h ar, From the tutorial, the yield o the precooled system is more than that o a simple system. Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 5

52 Thank You! Pro. M D Atrey, Department o Mechanical Engineering, IIT Bombay 52