Lec 23 Brayton cycle regeneration Rankine cycle 1

Lec 23: Brayton cycle regeneration, Rankine cycle 1

• For next time: – Read: § 8 -11 to 8 -13, 9 -1 to 9 -2. – HW 12 due Wednesday, November 19, 2003 • Outline: – Rankine steam power cycle – Cycle analysis – Example problem • Important points: – Know what assumptions you can make about the points along the cycle path – Know how to analyze a pump – Know how all the isentropic efficiencies are defined 2

Improved Brayton Cycle: Add a Heat Exchanger (Regenerator) 3

Ts Diagram for Brayton Cycle with Regeneration 4

Analysis with regeneration Heat input to the cycle: Net work of the cycle: 5

Analysis with regeneration Efficiency of the cycle: For the cold-air assumption: 6

Regenerator in cycle Regenerator heat transfer: Maximum heat transfer in regenerator: 7

Regenerator Effectiveness For the cold-air assumption: 8

Efficiency with regeneration 9

TEAMPLAY Problem 8 -82 10

Vapor Power Cycles • We’ll look specifically at the Rankine cycle, which is a vapor power cycle. • It is the primary electrical producing cycle in the world. • The cycle can use a variety of fuels. 11

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TEAMPLAY How much does it cost to operate a gas fired 120 MW(output) power plant with a 35% efficiency for 24 hours/day for a full year if fuel costs are $6. 00 per 106 Btu? 15

Vapor Power Cycles • The Carnot cycle is still important as a standard of comparison. • However, just as for gas power cycles, it cannot be practically achieved in useful, economical systems. 16

We’ll simplify the power plant 17

Ideal power plant cycle is called the Rankine Cycle • 1 -2 reversible adiabatic (isentropic) compression in the pump • 2 -3 constant pressure heat addition in the boiler. • 3 -4 reversible adiabatic (isentropic) expansion through turbine • 4 -1 constant pressure heat rejection in the condenser 18

Rankine cycle power plant • The steady-state first law applied to open systems will be used to analyze the four major components of a power plant – Pump – Boiler (heat exchanger) – Turbine – Condenser (heat-exchanger) • The second law will be needed to evaluate turbine performance 19

Vapor-cycle power plants 20

What are the main parameters we want to describe the cycle? => Net power or work output Power Work 21

Main parameters…. => Efficiency Or 22

General comments about analysis • Typical assumptions… – Steady flow in all components – Steady state in all components – Usually ignore kinetic and potential energy changes in all components – Pressure losses are considered negligible in boiler and condenser – Power components are isentropic for ideal cycle 23

Start our analysis with the pump The pump is adiabatic, with no kinetic or potential energy changes. The work per unit mass is: 24

Pump Analysis This expression gives us negative value for wp. It is standard practice in dealing with cycles to express works as positive values, then add or subtract depending on whether they’re in or out. This gives us a positive value for work. 25

Boiler is the next component. • Boilers do no work. In boilers, heat is added to the working fluid, so the heat transfer term is already positive. • So 26

Proceeding to the Turbines are almost always adiabatic. In addition, we’ll usually ignore kinetic and potential energy changes: 27

Last component is the Condensers do no work (they are heat exchangers), and if there is no KE and PE, 28

More condenser. . . What is the sign of qcond ? As with work, we’re going to want the sign of all the heat transfer terms positive. 29

Ideal Rankine Cycle • The pump work, because it is reversible and adiabatic, is given by • and 30

Ideal Rankine Cycle on a p-v diagram 31

Efficiency 32

Example Problem A Rankine cycle has an exhaust pressure from the turbine of 10 k. Pa. Determine the quality of the steam leaving the turbine and thermal efficiency of the cycle which has turbine inlet pressure of 15 MPa and 600 C. 33

Start an analysis: Assumptions: · pump and turbine are isentropic · P 2 = P 3 = 15 MPa · T 3 = 600 C · P 4 = P 1 = 10 k. PA · Kinetic and potential energy changes are zero 34

Draw diagram of cycle 35

Some comments about working cycle problems • Get the BIG picture first - where’s the work, where’s the heat transfer, etc. • Tables can useful - they help you put all the data you will need in one place. • You will need to know how to look up properties in the tables! 36

Put together property data 37

Property data • h 1=191. 83 k. J/kg is a table look-up, as is h 3=3582. 3 k. J/kg. 38

Let start with pump work Pump work: 39

More calculations. . . Enthalpy at pump outlet: Plugging in some numbers: 40

Calculate heat input and turbine work. . Boiler heat input: 41

Property data • Because s 3= s 4, we can determine that x 4=0. 803 and thus h 4=2114. 9 k. J/kg 42

Turbine work 43

We’ve got the exit quality, now we need efficiency Cycle efficiency: Substituting for net work: 44

Overall thermal efficiency 45

Some general characteristics of the Rankine cycle • Low condensing pressure (below atmospheric pressure) • High vapor temperature entering the turbine (600 to 1000 C) • Small backwork ratio (bwr) 46

TEAMPLAY Work Problem 8 -102 47