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					11. Power & Refrigeration Systems

11.1 Introduction to Power Systems

Recall the basic formula for the power
cycles:
                   Wout ,net
          η th =
                     QH
The cycles can be categorizes
depending on the working fluid:
• Gas cycles: gaseous phase alone
• Vapor cycles: both liquid and vapor
   phases

The cycles can be also categorized as
• Closed cycles: the working fluid
   returns to the initial state.
• Open cycles: the working fluid is
   renewed.
11.2 The Rankine Cycle
The Rankine cycle is the model for the
simple “steam power plant”. It consists
of four-steady-state processes:
1-2 : Reversible adiabatic pumping
      process
2-3 : Constant-pressure boiling process
3-4 : Reversible adiabatic expansion
4-1 : Constant-pressure condesing
      process
Note:
• State 3 could be saturated vapor or
   superheated vapor.
• If State 3 is saturated vapor, we have
          Wnet area 1 − 2 − 2′ − 3 − 4 − 1
   η th =       =
          Q H area a − 2 − 2′ − 3 − b − a
• The Carnot cycle (1′ − 2′ − 3 − 4 − 1′ )
   is difficult to achieve because the
   two-phase mixture enters the pump.
• The superheated-vapor state is often
   preferable due to the “pure” vapor
   entering the turbine.
11.3 Effect of Pressure and Temperature
on Rankine Cycle
• Effect of the condensing pressure




If P4 decreases, Wnet and ηth increase
(pros), but x4 decreases (cons).

• Effect of the superheating steam
If T3 increases, Wnet and ηth increase
(pros), and x4 increases (pros).

• Effect of the maximum pressure




If P4 decreases, Wnet tends to be the
same, ηth increases (pros), but x4
decreases (cons).

11.4 Reheat Cycle
When the reheat cycle is utilized,
• The boiling pressure can be raised.
• The moisture content in turbine can
  be avoided.
Note:
If the material we use can withstand the
temperature at 3′, there is no need for
the reheat cycle because the simple
Rankine cycle would be more efficient.
11.5 The Regenerative Cycle




Liquid water enters the boiler at
relatively low temperature, causing a
low efficiency.
A practical solution is to use a
regenerator or a feedwater heater,
which has two types:

11.5.1 Open feedwater heater
An open (or direct-contact) feedwater
heater is a mixing chamber between the
extracted stream and the liquid water.
11.5.2 Closed feedwater heater
In a closed feedwater heater, the steam
and the feedwater do not mixed. It can
be used with a drip pump or a trap.
For an actually steam power plant, the
processes are more complex
11.6 Deviation of Actual Cycles from
Ideal Cycles
The most important losses are
• Turbine losses from non-isentropic
  expansion and heat transfer
• Pump losses from non-isentropic
  expansion and heat transfer




• Piping losses from pressure drop and
  heat transfer
• Condensing losses from heat transfer
11.7 Cogeneration
The cogeneration is designed for
supplying a source of both electricity
and the process steam.
11.8 Air-Standard Power Cycles
An air-standard power cycle is an ideal
cycle based on these assumptions:
• Air has a fixed mass (or mass flow).
• Air is an ideal gas.
• Air has a constant CPo.
• The combustion process is replaced
  by a heat-transfer process from a
  source.
• The cycle is completed by heat
  transfer to the surroundings.
• All processes are internally
  reversible.

Examples for air-standard power cycles:
• Gas turbine engines (Brayton cycle)
• Spark-ignition internal combustion
  engines (Otto cycles)
• Compression-ignition internal
  combustion engines (Diesel cycles)
11.9 The Brayton Cycle
The Brayton cycle involves
• two isentropic processes
• one (or two) isobaric process(es).
The working fluid is gas, and the
Brayton cycle is an ideal cycle for a
simple gas turbine engine.

A simple open Brayton cycle
A simple closed Brayton cycle
Note: for an ideal/simple Brayton cycle
          T1     T4             1
η th = 1 − = 1 −    = 1−
          T2     T3      (P2 / P1 )( k −1) / k



P2/P1 is named the pressure ratio of the
Brayton cycle. Thus, as the pressure
ratio increases, ηth is increased as well.
However, P2 is limited by T3 (the
highest temperature in the cycle).
The actual Brayton cycle
Irreversibilities are caused by
• pressure drop in pipes (friction)
• efficiencies of the compressor and
   turbine
                 h 2 s − h 1 T2 s − T1
       ηcomp =              =
                 h 2 − h1     T2 − T1
                h3 − h4       T3 − T4
       η turb =             =
                h 3 − h 4 s T3 − T4 s

Generally, if ηcomp and ηturb is below
60%, all work from the turbine is
required to drive the compressor. Thus,
ηth reduced to zero.


11.10 The Simple Gas Turbine Cycle
with a Regenerator
The efficiency of the cycle is improved
by introducing a regenerator, which is a
counter-flow heat exchanger.
Note: the regenerator is useless if the
pressure ratio is increased from state 2
to state 2′.
It can be shown that for an ideal
regenerative Brayton cycle:
                               ( k −1) / k
                   T1  P2 
         η th = 1 −  
                   T3  P1 
                       
Thus, ηth depends not only on the
pressure ratio, but the ratio of the
maximum to the minimum temperature.
The effectiveness or efficiency of the
regenerator is given by
              hx − h2     h x − h 2 Tx − T2
  η regen   =           =          =
              h x′ − h 2 h 4 − h 2 T4 − T2




11.11 Gas Turbine Power Cycle
Configuration
It is found that the reversible isothermal
compressor or turbine would be
preferable to the isentropic one if the
pressure ratio is the same. Thus, for a
cycle, which has
• two isothermal processes
• two isobaric processes
This is called the Ericsson cycle.
However, the work-related devices are
not practical to transfer heat. The
processes; therefore, become adiabatic.
To modify the Brayton cycle closer to
the Ericsson cycle, we introduce
• multistage compressions with
   intercooling.
• multistage expansion with reheat.
For many stages of compression and
expansion, it approaches the isothermal
process.




Some arrangements of components in
the gas turbine cycle.
11.13 Reciprocating Engine Power
Cycles
                 Define Compression
                 ratio (rv) [-],
                            Vmax
                       rv =
                            Vmin
                 Mean effective
                 pressure (Pmeff) [Pa],
                 Wnett = Pmeff (Vmax − Vmin )
11.14 The Otto Cycle
The air-standard Otto cycle is an ideal
cycle to approximate a spark-ignition
internal combustion engine.
The four processes are composed of
• two isentropic processes
• two isochoric processes




Recall that rv is the compression ratio:
            Vmax V1 v1 v 4
       rv =     =  =   =
            Vmin V2 v 2 v 3
From the derivation,
             T1     T4        1
   η th = 1 − = 1 −    = 1 − k −1
             T2     T3      rv
Thus, increasing rv leads to a higher
thermal efficiency of the Otto cycle.




11.15 The Diesel Cycle
The air-standard Diesel cycle is an ideal
cycle to approximate a compression-
ignition internal combustion engine.
The four processes are composed of
• two isentropic processes
• one isobaric process
• one isochoric process
The compression ratio is
            Vmax V1 v1
       rv =     =  =
            Vmin V2 v 2
Define the cutoff ratio (rc) [-]
           V3 v 3
      rc =    =
           V2 v 2
From the derivation,
                 T1 (T4 / T1 − 1)
    η th = 1 −
                kT2 (T3 / T2 − 1)
We can rewrite in terms of rv and rc:
                    1  rc − 1 
                              k

      η th               k (r − 1) 
             = 1 − k −1            
                  rv  c            
The term in the brackets is always
greater than unity. We conclude that
η th ,otto > η th ,diesel if both engines have
the same rv.
Note:
• ηth,diesel increases with decreasing rc.
• At rc = 1, ηth,diesel = ηth,otto.
• However, Diesel cycles operated at
   much higher rv, resulting in the
   typical higher value of ηth.

11.16 The Stirling Cycle
The Stirling cycle is composed of
• two isothermal processes
• two isochoric processes
This engine has been developed as an
external combustion engine with
regeneration.

11.17 Introduction to Refrigeration
Systems
For the basic ideal refrigeration system,
the cycle is the same as the Rankine
power system:
• two isentropic processes
• two isobaric processes
except that the processes are reversed.
11.18 The Vapor-Compression
Refrigeration Cycle
Consider the reversed Rankine cycle:




However, the isentropic expansion from
state 3 to state 4′ (mostly liquid)
provides only little work. Thus it is not
worth to place a turbine here. As a
result, we replace the isentropic
expansion with the throttling process
(state 3 to state 4). Note that the two-
phase mixture entering the compressor
(state 1′ to state 2′) should be avoided.
Thus the vapor-compression
refrigeration cycle becomes




Note:
• For the throttling process across the
   expansion valve, h = constant.
• The analysis of a refrigerator and a
   heat pump is the same.
• Recall the COP of a refrigerator and
   a heat pump:
               QL
        β =
              Wcomp
                QH
        β′ =
               Wcomp
11.19 Working Fluids for Vapor-
Compression Refrigeration Systems
There are many different working fluids
(refrigerants) for the vapor-compression
refrigeration systems:
• Ammonia was used in the early days
    and is still used in industrial
    refrigeration. It is toxic, but cheap.
    It has favorable transport properties
    to get higher COP. No effect on O3.
• CFCs, such as R11, R12, or R22, are
    good for many applications. R11 is
    for water chillers. R12 is for house-
    hold refrigerators. R22 is for air
    conditioners. All of them cause
    ozone crisis.
• R134a, which has no effect on the
    ozone layer, is presently replacing
    R12.
11.20 Deviation of the Actual Vapor-
Compression Refrigeration Cycle from
the Ideal Cycle
• Non-quasi-equilibrium compression
  and heat transfer in the compressor
• Pressure drop in pipes, condenser,
  and evaporator
• Heat transfer through pipes
11.21 The Absorption Refrigeration
Cycle
In this type of refrigerator, the refrigerant
is transported by a “transport” medium.
Ammonia-Water is the most favorite one
where Ammonia is the refrigerant, and
water is the transport medium.




                   QL
Note:   β =
                Wpump + Q′H
Advantage (compared with the vapor-
compression refrigeration system)
• a liquid is compressed rather than a
   vapor. Thus, it requires less work.
• good for inexpensive heat source
   such as geothermal or solar energy.
Disadvantage
• more expensive
• more complexity and require more
   space
• less COP (COP < 1)

11.22 The Air-Standard Refrigeration
Cycle
This refrigeration system uses a gas as a
working fluid. The cycle is the reversed
Brayton cycle. Its applications are
• liquefaction of air and other gases.
• aircraft cooling (lighter components).
Closed cycle
Open cycle




The analysis of the air-standard
refrigeration cycle is similar to the
Brayton cycle.
11.23 Combined-Cycle Power and
Refrigeration Systems

				
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posted:1/8/2010
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