Chapter 10 Rankine Power Cycle

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					Chapter 10: Rankine Power Cycle




                                  1
  Looking at the cycle process

• Put a slide here that shows Carnot
  cycle with cycle inside. Show Qh, Ql,
  and Wnet divided into Win and Wout.
      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.



                                           3
4
5
6
 We’ll simplify the power plant

                3
BOILER
                    TURBINE        wout
          qin

     2                         4

                    CONDENSER

                                    qout
                       1
         win            PUMP
                                           7
 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
                                            8
     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
                                               9
    Vapor-cycle power plants

T

                       3
                qin

                           wout
        2

      win   1   qout   4



                           s      10
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
                                            11
  Start our analysis with the pump

0  Qpump  WPump  m(h1  h 2  KE  PE)

The pump is adiabatic, with no kinetic or
potential energy changes. The work per
unit mass is:

    w pum p  h1  h 2  ( p1  p 2 )
                                         12
             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.

       w Pump  h1  h 2
This gives us a positive value for work.
                                           13
    Boiler is the next component.

              
0  Q boiler  Wboiler  m[h 2  h 3  KE  PE ]
                         

 •Boilers do no work. In boilers, heat
 is added to the working fluid, so the
 heat transfer term is already positive.
 •So
        
        Q boiler
                  q boiler  h 3  h 2
          m
                                                14
       Proceeding to the Turbine

               
0  Q turbine  Wturbine  m[h 3  h 4  KE  PE ]
                           
Turbines are almost always adiabatic. In
addition, we’ll usually ignore kinetic and
potential energy changes:

            
            Wturbine
                      w  h3  h4
              
              m
                                                 15
Last component is the Condenser


            
0  Q cond  Wcond  m[h 4  h1  KE  PE ]
                     
Condensers do no work (they are heat
exchangers),and if there is no KE
and PE,
         
         Q cond
                 q cond  h1  h 4
           
           m
                                            16
          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.
     
     Q cond
             q cond  h1  h 4
       
       m
                                    17
          Ideal Rankine Cycle

• The pump work, because it is reversible
  and adiabatic, is given by

         2
    wP   vdp  h2  h1
         1
 • and


    wP  v( P2  P )
                  1

                                            18
Ideal Rankine Cycle on a p-v
          diagram

P

          p=c
     2            3

    s=c               s=c

     1
            p=c       4




                                19
                            v
              Efficiency


   w out

   q in

   h 3 - h 4 - v(P2 - P1 )

           h3 - h2

                             20
         Example Problem


A Rankine cycle has an exhaust
pressure from the turbine of 10 kPa.
Determine the quality of the steam
leaving the turbine and the thermal
efficiency of the cycle which has
turbine inlet pressure of 15 MPa and
600C.



                                       21
  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!




                                              22
    Draw diagram of cycle

T
                            T3 = 600oC

               P= 15 MPa         3


       2
               P = 10 kPa

           1                 4


                                         23
                                     s
        Put together property data

State     T (C)   P(kPa)   v(m3/kg) h(kJ/kg) s(kJ/kgK)   x


 1                 10


 2                15000


 3        600     15000


 4                 10



                                                             24
Some general characteristics of the
         Rankine cycle
• Low condensing pressure (below
  atmospheric pressure)
• High vapor temperature entering the
  turbine (600 to 1000C)




                                        25
                   Example 10-2




Find (a) thermal efficiency of cycle and (b) net power output of
plan for a mass flow rate of 15 kg/sec.
Put together property data
State   T (C)   P(kPa)   v(m3/kg) h(kJ/kg) s(kJ/kgK)   x


 1


 2


 2s


 3


 4


 5


 6


 6s
                                                           27