Thermodynamics Lecture Series Applied Sciences Education Research Group (ASERG) Faculty of Applied Sciences Universiti Teknologi MARA Ideal Rankine Cycle –The Practical Cycle

Example: A steam power cycle. Steam Turbine Mechanical Energy to Generator Heat Exchanger Cooling Water Pump Fuel Air Combustion Products System Boundary for Thermodynamic Analysis System Boundary for Thermodynamic Analysis Steam Power Plant

Second Law Steam Power Plant High T Res., T H Furnace q in = q H  net,out Low T Res., T L Water from river An Energy-Flow diagram for a SPP q out = q L Working fluid: Water Purpose: Produce work, W out,  out

Second Law – Dream Engine Carnot Cycle P - diagram for a Carnot (ideal) power plant P, kPa, m 3 /kg q out q in What is the maximum performance of real engines if it can never achieve 100%??

Carnot Principles For heat engines in contact with the same hot and cold reservoir  P1:  1 =  2 =  3 (Equality)  P2:  real <  rev (Inequality) Second Law – Will a Process Happen Processes satisfying Carnot Principles obeys the Second Law of Thermodynamics Consequence

Clausius Inequality : Sum of Q/T in a cyclic process must be zero for reversible processes and negative for real processes Second Law – Will a Process Happen reversible impossible real

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 6-3 FIGURE 6-6 The entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero. Isolated systems

Increase of Entropy Principle – closed system The entropy of an isolated (closed and adiabatic) system undergoing any process, will always increase. Entropy – Quantifying Disorder Surrounding System For pure substance : and Then

Entropy Balance – for any general system Entropy – Quantifying Disorder  For any system undergoing any process,  Energy must be conserved (E in – E out =  E sys )  Mass must be conserved (m in – m out =  m sys )  Entropy will always be generated except for reversible processes S gen  Entropy balance is (S in – S out + S gen =  S sys )

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display FIGURE 6-61 Mechanisms of entropy transfer for a general system. Entropy Transfer

Entropy Balance –Steady-flow device Entropy – Quantifying Disorder Then:

Entropy Balance –Steady-flow device Entropy – Quantifying Disorder Turbine: Assume adiabatic,  ke mass = 0,  pe mass = 0 where Entropy Balance In,3 Out

Entropy Balance –Steady-flow device Entropy – Quantifying Disorder Mixing Chamber: where 1 3 2

Steam Power Plant Vapor Cycle  External combustion  Fuel (q H ) from nuclear reactors, natural gas, charcoal  Working fluid is H 2 O Cheap, easily available & high enthalpy of vaporization h fg  Cycle is closed thermodynamic cycle  Alternates between liquid and gas phase  Can Carnot cycle be used for representing real SPP??  Aim: To decrease ratio of T L /T H

Efficiency of a Carnot Cycle SPP Vapor Cycle – Carnot Cycle

Impracticalities of Carnot Cycle Vapor Cycle –Carnot Cycle  Isothermal expansion: T H limited to only T crit for H 2 O.  High moisture at turbine exit  Not economical to design pump to work in 2-phase (end of Isothermal compression)  No assurance can get same x for every cycle (end of Isothermal compression) s 3 = s 4 s 1 = s 2 q in = q H T,  C T crit THTH TLTL q out = q L s, kJ/kg  K

Impracticalities of Alternate Carnot Cycle Vapor Cycle – Alternate Carnot Cycle s 3 = s 4 s 1 = s 2 q in = q H T,  C T crit THTH TLTL q out = q L s, kJ/kg  K Still Problematic  Isothermal expansion but at variable pressure  Pump to very high pressure Can the boiler sustain the high P?

Overcoming Impracticalities of Carnot Cycle Vapor Cycle – Ideal Rankine Cycle  Superheat  Superheat the H 2 O at a constant pressure (isobaric expansion) Can easily achieve desired T H higher than T crit. reduces moisture content at turbine exit  Remove all excess heat at condenser Phase is sat. liquid at condenser exit, hence need only a pump to increase pressure Quality is zero for every cycle at condenser exit (pump inlet)

Vapor Cycle – Ideal Rankine Cycle Pump Boiler Turbin e Condenser High T Res., T H Furnace q in = q H  in  out Low T Res., T L Water from river A Schematic diagram for a Steam Power Plant q out = q L Working fluid: Water q in - q out =  out -  in q in - q out =  net,out

T- s diagram for an Ideal Rankine Cycle Vapor Cycle – Ideal Rankine Cycle T,  C s, kJ/kg  K 1 2 T crit THTH T L = T T s 3 = s 4 s 1 = s 2 q in = q H 4 3 PHPH PLPL  in  out pump q out = q L condenser turbine boiler

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-2 FIGURE 9-2 The simple ideal Rankine cycle.

Vapor Cycle – Ideal Rankine Cycle Boiler In,2 Out,3 q in = q H Energy Analysis q in – q out +  in –  out =  out –  in, kJ/kg q in – – 0 = h exit – h inlet, kJ/kg q in = h 3 – h 2, kJ/kg Assume  ke =0,  pe =0 for the moving mass, kJ/kg Q in = m(h 3 – h 2), kJ

Vapor Cycle – Ideal Rankine Cycle Condenser Out,1 In,4 q out = q L Energy Analysis q in – q out +  in –  out =  out –  in, kJ/kg 0 – q out + 0 – 0 = h exit – h inlet - q out = h 1 – h 4, So, q out = h 4 – h 1, kJ/kg Assume  ke =0,  pe =0 for the moving mass, kJ/kg Q out = m(h 4 – h 1), kJ

Vapor Cycle – Ideal Rankine Cycle Energy Analysis q in – q out +  in –  out =  out –  in, kJ/kg 0 – 0 +  –  out = h exit – h inlet, kJ/kg -  out = h 4 – h 3, kJ/kg So,  out = h 3 – h 4, kJ/kg  out In,3 Out,4 Turbin e Assume  ke =0,  pe =0 for the moving mass, kJ/kg W out = m(h 3 – h 4), kJ

Vapor Cycle – Ideal Rankine Cycle Energy Analysis q in – q out +  in –  out =  out –  in, kJ/kg 0 – 0 +  in –  = h exit – h inlet, kJ/kg  in = h 2 – h 1, kJ/kg Pump  in Out,2 In,1 For reversibl e pumps where So, W in = m(h 2 – h 1), kJ

Vapor Cycle – Ideal Rankine Cycle Energy Analysis Efficiency

T- s diagram for an Ideal Rankine Cycle Vapor Cycle – Ideal Rankine Cycle T,  C s, kJ/kg  K 1 2 T crit THTH T L = T T s 3 = s 4 s 1 = s 2 q in = q H 4 3 PHPH PLPL  in  out pump q out = q L condenser turbine boiler s 1 = s h 1 = h s 3 = s 4 = [s f +xs fg = s 3 h 3 = h 4 = [h f +xh fg h 2 = h (P 2 – P 1 ); where Note that P 1 = P 4

Vapor Cycle – Ideal Rankine Cycle Energy Analysis Increasing Efficiency  Must increase  net,out = q in – q out Increase area under process cycle  Decrease condenser pressure; P 1 =P 4 P min > P deg C  Superheat T 3 limited to metullargical strength of boiler  Increase boiler pressure; P 2 =P 3 Will decrease quality (an increase in moisture). Minimum x is 89.6%.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-4 FIGURE 9-6 The effect of lowering the condenser pressure on the ideal Rankine cycle. Lowering Condenser Pressure

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-5 FIGURE 9-7 The effect of superheating the steam to higher temperatures on the ideal Rankine cycle. Superheating Steam

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-6 FIGURE 9-8 The effect of increasing the boiler pressure on the ideal Rankine cycle. Increasing Boiler Pressure

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-8 FIGURE 9-10 T-s diagrams of the three cycles discussed in Example 9–3.

Vapor Cycle – Reheat Rankine Cycle Pump Boiler Hig h P turb ine Condenser High T Reservoir, T H q in = q H  in  out,1 q out = q L Low T Reservoir, T L Lo w P turb ine  out, q reheat

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 9-11 The ideal reheat Rankine cycle. 9-9

Reheating increases  and reduces moisture in turbine Vapor Cycle – Reheat Rankine Cycle T L = T  in s 5 = s 6 s 1 = s 2 T crit THTH T T s 3 = s 4 q out = h 6 -h 1  out, II P 4 = P 5 P 6 = P q reheat = h 5 -h 4 q primary = h 3 -h 2  out P3P3 3 2 T,  C s, kJ/kg  K

Energy Analysis Vapor Cycle – Reheat Rankine Cycle q in = q primary + q reheat = h 3 - h 2 + h 5 - h 4 q out = h 6 -h 1  net,out =  out,1 +  out,2 -  in = h 3 - h 4 + h 5 - h 6 – h 2 + h 1

Energy Analysis Vapor Cycle – Reheat Rankine Cycle where s 6 = [s f +xs fg Use x = and s 5 = s 6 Knowing 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 the property table, choose P 5 so that the entropy is lower than s 5 above. Then can find h 5 = h 6 = [h f +xh fg

Energy Analysis Vapor Cycle – Reheat Rankine Cycle s 1 = s where s 3 = = s 4. h 1 = h h 3 = h 2 = h (P 2 – P 1 ); where From P 4 and s 4, lookup for h 4 in the table. If not found, then do interpolation. P 5 = P 4.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-7 FIGURE 9-9 A supercritical Rankine cycle. Supercritical Rankine Cycle