Thermodynamics Lecture Series

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1 Termodynamics Lecture Series Ideal Ranke Cycle Te Practical Cycle Applied Sciences Education Researc Group (ASERG) Faculty of Applied Sciences Universiti Teknologi MARA ttp://www5.uitm.edu.my/faculties/fsg/drjj1.tml

2 Steam Power Plant Example: A steam power cycle. Combustion Products Fuel Steam Turbe Mecanical Energy to Generator Air Pump Heat Excanger Coolg Water System System Boundary for for Termodynamic Analysis

3 Workg fluid: Water Second Law Hig T Res., T H Furnace q q H Purpose: Produce work, W out, ω out Steam Power Plant ω net,out q out q L Low T Res., T L Water from river An Energy-Flow diagram for a SPP

4 Second Law Dream Enge Wat is te maximum performance of real enges if it can never acieve 100%?? Carnot Cycle P - ν diagram for a Carnot (ideal) power plant P, kpa 1 q 4 desired output η required put 3 η rev q q q ω out net q,out rev q out ν, m 3 /kg

5 Second Law Will a Process Happen Carnot Prciples For eat enges contact wit te same ot and cold reservoir P1: η 1 η η 3 (Equality) P: η real < η rev (Inequality) Consequence q L TL q H TH rev (K) (K) ; η rev 1 q q L H rev ηreal η rev 1 Processes satisfyg Carnot Prciples obeys te Second Law of Termodynamics T T L H (K) (K)

6 Second Law Will a Process Happen Clausius Inequality : Sum of Q/T a cyclic process must be zero for reversible processes and negative for real processes δq kj δq kj 0, 0, T K T kg K δq 0, reversible T δq < 0, real T δq > 0, impossible T

7 Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. Isolated systems FIGURE 6-6 Te entropy cange of an isolated system is te sum of te entropy canges of its components, and is never less tan zero. 6-3

8 S Entropy Quantifyg Disorder Increase of Entropy Prciple closed system isolated Te entropy of an isolated (closed and adiabatic) system undergog any process, will always crease. S eat For pure substance: and Ten S gen + S gen S sys + S S sys m(s s1 ) S surr ( Q Q ) T out surr m( s s1 ) + surr surr 0 ( ) Q T surr net, Surroundg System

9 Entropy Quantifyg Disorder Entropy Balance for any general system For any system undergog any process, Energy must be conserved (E E out E sys ) Mass must be conserved (m m out m sys ) Entropy will always be generated except for reversible processes Entropy balance is (S S out + S gen S sys )

10 Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. Entropy Transfer FIGURE 6-61 Mecanisms of entropy transfer for a general system. 6-18

11 Entropy Quantifyg Disorder Entropy Balance Steady-flow device Q S Q out + W W out S out + S gen Ssys m ϑ 0 out So, m ϑ S gen, kw S out S Ten: S gen S eat + S mass S eat + S mass out Q out Q gen + m s m s Tout exit T S let

12 Turbe: Entropy Quantifyg Disorder Entropy Balance Steady-flow device Q out + W W out m ( ϑexit ϑlet ), kw Q Assume adiabatic, ke mass 0, pe mass 0 Entropy Balance S gen S gen were m m W m( ) out 4 3, kw Q out kw + m 4 s4 m 3 s3, out T K Q T ( s s ) m 4 3, m let kw K exit Out In,3

13 Q Entropy Quantifyg Disorder Entropy Balance Steady-flow device Mixg Camber: Q out + W W out m ϑ exit m ϑ Q Q out + W W out m3 3 m m1 1 Q out Q kw S gen + m 3 s3 m s m1 s1, Tout T K were m let m exit 1 let,, kw kw 3

14 Steam Power Plant Vapor Cycle External combustion Fuel (q H ) from nuclear reactors, natural gas, carcoal Workg fluid is H O Ceap, easily available & ig entalpy of vaporization fg Cycle is closed termodynamic cycle Alternates between liquid and gas pase Can Can Carnot cycle be used for representg real SPP?? Aim: To decrease ratio of T L /T H

15 Vapor Cycle Carnot Cycle Efficiency of a Carnot Cycle SPP TL ηrev 1 1 T H 0.55 TL ηrev 1 1 T H 0.67

16 Vapor Cycle Carnot Cycle Impracticalities of Carnot Cycle T, C T crit T H T L q q H qout ql Isotermal expansion: T H limited to only T crit for H O. Hig moisture at turbe exit Not economical to design pump to work -pase (end of Isotermal compression) No assurance can get same x for every cycle (end of Isotermal compression) s 1 s s 3 s 4 s, kj/kg K

17 Vapor Cycle Alternate Carnot Cycle T H Impracticalities of Alternate Carnot Cycle T, C T crit T L q q H Still Problematic Isotermal expansion but at variable pressure Pump to very ig pressure Can te boiler susta te ig P? s 1 s q out q L s 3 s 4 s, kj/kg K

18 Vapor Cycle Ideal Ranke Cycle Overcomg Impracticalities of Carnot Cycle Supereat Supereat te H O at a constant pressure (isobaric expansion) Can easily acieve desired T H iger tan T crit. reduces moisture content at turbe exit Remove all excess eat at condenser Pase is sat. liquid at condenser exit, ence need only a pump to crease pressure Quality is zero for every cycle at condenser exit (pump let)

19 Vapor Cycle Ideal Ranke Cycle Workg fluid: Water Hig T Res., T H Furnace q q H Boiler ω Pump Turbe ω out q -q out ω out - ω Condenser q out q L Low T Res., T L Water from river q -q out ω net,out A Scematic diagram for a Steam Power Plant

20 Vapor Cycle Ideal Ranke Cycle T- s diagram for an Ideal Ranke Cycle T H T crit T, C q q H boiler P H 3 turbe P L T sat@p ω out T L T sat@p4 ω pump 1 s 1 s q out q L condenser 4 s 3 s 4 s, kj/kg K

21 Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 9- Te simple ideal Ranke cycle. 9-

22 Vapor Cycle Ideal Ranke Cycle Energy Analysis In, q q H Out,3 Boiler Assume ke 0, pe 0 for te movg mass, kj/kg q q out + ω ω out θ out θ, kj/kg q exit let, kj/kg q 3, kj/kg Q m( 3 ), kj Q m ( ), kw 3

23 Vapor Cycle Ideal Ranke Cycle Energy Analysis Assume ke 0, pe 0 for te movg mass, kj/kg q q out + ω ω out θ out θ, kj/kg 0 q out exit let -q out 1 4, Out,1 Condenser In,4 So, q out 4 1, kj/kg Q out m( 4 1), kj q out q L ( ) kw Q out m 4 1,

24 Vapor Cycle Ideal Ranke Cycle Energy Analysis In,3 q q out + ω ω out θ out θ, kj/kg Turbe ω out ω out exit let, kj/kg - ω out 4 3, kj/kg So, ω out 3 4, kj/kg Out,4 W out m( 3 4), kj W out m ( ), kw 3 4 Assume ke 0, pe 0 for te movg mass, kj/kg

25 Vapor Cycle Ideal Ranke Cycle Energy Analysis Out, q q out + ω ω out θ out θ, kj/kg ω 0 exit let, kj/kg ω 1, kj/kg For reversible pumps were ω ω pump pump,, ν ω Pdν + νdp ν ν 1 ν f So, W m( 1), kj 1 ( P ) P1 P 1 W m ν 1 Pump dp In,1 ( ), kw 1

26 Vapor Cycle Ideal Ranke Cycle Energy Analysis Efficiency η η ω ω net q net q,out,out q ω η q out 3 q q out ω ( ) 4 1 ( ) 1

27 Vapor Cycle Ideal Ranke Cycle T- s diagram for an Ideal Ranke Cycle T H T crit T, C q q H Note tat P 1 P 4 boiler P H 3 turbe P L s 1 s f@p1 1 f@p1 s 3 T sat@p L T sat@p4 pump ω 1 s 1 s q out q L condenser 4 s 3 s 4 ω out s 4 [s f +xs fg s 3 x s 3 s 4 [ f +x fg s, kj/kg K s f P P 4 1 +ν (P P 1 ); were ν ν 1 ν P 1

28 Vapor Cycle Ideal Ranke Cycle Energy Analysis Increasg Efficiency Must crease ω net,out q q out Increase area under process cycle Decrease condenser pressure; P 1 P 4 P m > P sat@tcoolg+10 deg C Supereat T 3 limited to metullargical strengt of boiler Increase boiler pressure; P P 3 Will decrease quality (an crease moisture). Mimum x is 89.6%.

29 Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 9-6 Te effect of lowerg te condenser pressure on te ideal Ranke cycle. Lowerg Condenser Pressure 9-4

30 Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 9-7 Te effect of supereatg te steam to iger temperatures on te ideal Ranke cycle. Supereatg Steam 9-5

31 Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. Increasg Boiler Pressure FIGURE 9-8 Te effect of creasg te boiler pressure on te ideal Ranke cycle. 9-6

32 FIGURE 9-10 T-s diagrams of te tree cycles discussed Example 9 3. Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-8

33 Vapor Cycle Reeat Ranke Cycle Hig T Reservoir, T H ω Pump 1 q q H Boiler q reeat Hig P turbi ne Low P turbi ne ω out,1 ω out, Condenser 6 q out q L Low T Reservoir, T L

34 FIGURE 9-11 Te ideal reeat Ranke cycle. Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-9

35 Vapor Cycle Reeat Ranke Cycle Reeatg creases η and reduces moisture turbe T, C q reeat 5-4 T 3 5 H T q primary 3 - crit P 3 P 4 P ω 5 out T sat@p3 T ω sat@p4 out, II P 6 P 1 4 T L T sat@p1 1 ω q out s, kj/kg K s 1 s s 3 s 4 s 5 s 6

36 Vapor Cycle Reeat Ranke Cycle Energy Analysis q q primary +q reeat q out 6-1 ω net,out ω out,1 + ω out, - ω η ω net,out q q q q out ( ) η ω net, out q ω out1 + ω q out ω

37 Vapor Cycle Reeat Ranke Cycle Energy Analysis were s 6 [s f +xs fg Use x and s 5 s 6 6 [ f +x fg Knowg s 5 and T 5, P 5 needs to be estimated (usually approximately a quarter of P 3 to ensure x is around 89%. On te property table, coose P 5 so tat te entropy is lower tan s 5 above. Ten can fd

38 Vapor Cycle Reeat Ranke Cycle Energy Analysis were s 1 s f@p1 1 f@p1 s 3 s ν (P P 1 ); were ν ν 1 ν P 1 P 5 P 4. From P 4 and s 4, lookup for 4 te table. If not found, ten do terpolation.

39 Copyrigt Te McGraw-Hill Companies, Inc. Permission required for reproduction or display. Supercritical Ranke Cycle FIGURE 9-9 A supercritical Ranke cycle. 9-7

Thermodynamics Lecture Series

Thermodynamics Lecture Series Second Law uality of Energy Applied Sciences Education Research Group (ASERG) Faculty of Applied Sciences Universiti Teknologi MARA email: drjjlanita@hotmail.com http://www.uitm.edu.my/faculties/fsg/drjj.html