vapor and combined power cycles (2) karakteristik beberapa sistem termodinamika

Vapor and Combined Power

Cycles (2)

KARAKTERISTIK BEBERAPA SISTEM TERMODINAMIKA

8.2 The carnot vapor cycles

Feed pump

Boiler

Condenser

Energy reservoir at high temperature, TH

Energy reservoir at low temperature, TL

TurbineW

W

2 3

41

QQININ

QQOUTOUT

WWTURBINETURBINE

WWPUMPPUMP


QQININ

QQOUTOUT

WWTURBINETURBINE

WWPUMPPUMP

High temperature heat addition, TH

High temperature heat addition, TH

Low temperature heat rejection, TL

Low temperature heat rejection, TL

Work input to compress working fluid

Work input to compress working fluid

Turbine to obtain work by expansion of working fluid.

Turbine to obtain work by expansion of working fluid.



Energy reservoir at high temperature, TH

Energy reservoir at low temperature, TL

Wnet=W34-W12

Q1=Q23

Q2=Q41


TH

T

TL

s

2 3

41

Q1=QH

Q2=QL

W1 W4

Process

1-2 Adiabatic compression

(work input to system, W1)

2-3 Isothermal expansion

(heat added, Q1)

3-4 Adiabatic expansion

(work out from system, W4)

4-1 Isothermal compression

(heat rejected, Q2)


H

L

1

2

1

net

11

suppliednet

outwork

cycle,Carnot theof Efficiency

T

T

q

q

q

w


1. Limiting of heat transfer which severely limits the maximum temperature that can be used in the cycle and the thermal efficiency (Higher power requirement)

3. Difficult to control the condensation process at the desired quality.

2. Not practical to design a compressor that handles two phases (Not homogeneous)

4.High quality of steam decrease or high contents of liquid droplets cause erosion and wear at turbine blades

8.2 Rankine cycle : the ideal cycle for vapor power cycles

Elimination of impracticalities of Carnot cycle

Superheating the steam in the boiler and condensing it completely in the condenser

Rankine cycle

8.2.2 Rankine cycle : the ideal cycle for vapor power cycles

Process

1-2 Isentropic compression in a pump

2-3 Isobaric heat addition in a boiler

3-4 Isentropic expansion in a turbine

4-1 Isobaric heat rejection in a condenser

ss

TT

11

22

33

44

3*3*

4*4*


All processes are internally reversible.All processes are internally reversible.

All processes are internally reversible.All processes are internally reversible.

ss

TT

11

22

33

44

3*3*

4*4*

Reversible constant pressure heat rejection (4 1)

Reversible constant pressure heat rejection (4 1)

Reversible constant pressure heat addition (2 3)

Reversible constant pressure heat addition (2 3)

Isentropic compression (1 2)

Isentropic compression (1 2)

Isentropic expansion to produce work (3 4) or (3* 4*)

Isentropic expansion to produce work (3 4) or (3* 4*)


hh

ss

44

33

22Wturb

Qin

Qout11

Wpump


Kinetic energy and potential energy changes are usually small and can be neglected.

For steady flow energy equation per unit mass of steam (From first law of Thermodynamics) reduces to

kJ/kg outinoutin ie hhwwqq


kJ/kg

0)(Boiler For

and where

kJ/kg )(

0)( pump feedFor

23in

1@@1

1212pump

1

hhq

w

vvhh

PPvhhw

q

PfPf


kJ/kg where

1

cycle, Rankine of efficiency Thermal

kJ/kg

0)(condenser For

kJ/kg

0)( eFor turbin

pumpturboutinnet

in

out

in

netth

14out

43turb

wwqqw

q

q

q

w

hhq

w

hhw

q

h

s

44

3*3*

22

WOUT

QH

QC11

WIN

Increased average temperature of heat addition

Increased average temperature of heat addition


2*3

124*3

in

pumpturb

hh

hhhh

q

ww

0*3

h

8.3.3 Deviation of actual vapor power cycles from the idealized ones

ss

TT

11

22

33

44

Pressure drop in boiler

(fluid friction)

Pressure drop in condenser

(fluid friction)

Irreversibility in the pump (heat loss)

Irreversibility in the turbine (fluid friction)

Actual cycle

Ideal cycle


12

12P hh

hh

w

w

a

s

a

s

s

a

s

a

hh

hh

w

w

43

43T

Isentropic efficiency for pump

Isentropic efficiency for turbine

Example


Steam is the working fluid in an Ideal Rankine cycle. Saturated vapor enter the turbine at 80 bar and saturated liquid exits the condenser at a pressure of 0.08 bar. The turbine and the pump each have an isentropic efficiency 85%. Determine

a. Thermal efficiencyb. Mass flow rate of steam in kg/hr for a net power output 100 kWc. Rate of heat transfer into working fluid as it passes through the

boiler (MW)d. Rate of heat transfer from condensing steam as it passes

through the condenser (MW)e. Mass flow rate of the condenser cooling water in kg/hr if

cooling water enter the condenser at 15oC and exits as 35oC

Solution


Example


Superheated steam at 30 bar and 360oC enter the turbine of steam power plant operating at steady state and expands to a condenser pressure 1.0 bar. Assume the isentropic efficiencies of the turbine and pump 85% and 80% respectively. Determine

a. The thermal efficiencyb. The heat ratec. The steam supply to deliver 1000kWd. The corresponding Rankine efficiency

Solution


8.2.4 How can we increase the efficiency of the Rankine cycle

Usage of steam power plants :

production of most electric power in the world

Basic idea of increasing the thermal efficiency of the steam power plants :

1.Increase the average temperature in the boiler

2.Decrease the average temperature in the condenser

3.4 How can we increase the efficiency of the Rankine cycle

Lowering the condenser pressure (Lower Tlow,avg)

Steam in saturated mixture during condensation

rejected isheat theof re temperatuthus

,mean TP

Increase in net work output

And also the heat input requirements (2 to 2’) but small compare to Wnet

Condenser operating pressure is limited by the temperature of the cooling medium

Could cause air leakage to condenser and moisture content of the steam in the

turbine


Superheating the steam to high temperatures (Increases Thigh,avg)

Steam is superheated at P constant (3 to 3’) which increase the net work output.

Decreases the moisture content of the steam at the turbine exit.

Steam superheated temperature is limited by metallurgical

considerations and material limitation


Increasing the boiler pressure (Increases Thigh,avg)

Pboiler increase which will automatically raises the boiling temperature

Instead of increase the net work output, it also increase the moisture content in

the turbine


Example

Consider a steam power plant operating on the ideal Rankine cycle. Steam enters the turbine at 3MPa and 350oC and is condensed in the condenser at a pressure of 75kPa. Determine

a. The thermal efficiency of this power plantb. The thermal efficiency of this power plant if the condenser

pressure decrease to 10kPa.c. The thermal efficiency if steam is superheated to 600oC

instead of 350oCd. The thermal efficiency if the boiler pressure is raised to

15MPa while the turbine inlet temperature is maintained at 600oC


Solution

8.2.5 The ideal reheat Rankine cycle

Objective of reheat the Rankine cycle :

Increase the net work output and thus the thermal efficiency without the problem of excessive moisture at the final stage of the turbine

Two possible solutions :

1. Superheat the steam to very high temperature before it enters the turbine (limited by metallurgical consideration)

2. Expand the steam in the turbine in two stages, and reheat it in between.


primaryq

reheatq

II turbwI turbw 1-2 Isentropic compression

in pump

2-3 Isobaric heat addition in

boiler

3-4 Isentropic expansion in

high pressure turbine


boiler (reheat)


low pressure turbine

6-1 Isobaric heat rejection in

condenser

12pump

16out

6543II turbI turbout turb

4523reheatprimaryin

hhw

hhq

hhhhwww

hhhhqqq


primaryq

reheatq

II turbw

I turbw

1-2 Isentropic compression

in pump


boiler


high pressure turbine


boiler (reheat)


low pressure turbine

6-1 Isobaric heat rejection in

condenser

primaryq

reheatq

II turbw

I turbw

reheatprimary

pumpII turbI turbth qq

www

in pumpw


Increase the number of expansion and reheat stage is limited by :

Superheated exhaust which increase the temperature for the heat rejection process (decrease the thermal efficiency)


Example

Steams are the working fluid in an ideal Rankine cycle with superheat and reheat. Steam enters the first stage turbine at 80 bar 480oC and expands to 7 bar. It is then reheated to 440oC before entering the second stage turbine where it expand to the condenser pressure of 0.08 bar. The net power output is 100 MW. Determine

a. The thermal efficiency of the cycleb. The mass flow rate of steam in kg/hrc. The rate of heat transfer Qout from the condensing steam as

it passes through the condenser in MW.


Solution

3.6 The ideal regenerative Rankine cycle

Feed water : liquid that living the pump

Regeneration : heat transfer from the expanding steam in a counterflow heat exchanger built in the turbine

Regenerator : or a feedwater heater (FWH) is a device where heat transfer occur

Usage of regeneration : improves cycle efficiency

Type of FWH : Open type and Closed type

Regeneration

8.2.6 The ideal regenerative Rankine cycle

Open Feedwater Heaters a mixing chamber of steam and feedwater

1-2 Isentropic compression to saturation temperature in pump I.

2-3 Mixing of Feedwater from pump

6-3 with steam from turbine.

3-4 Isentropic compression to the boiler pressure in pump II.

4-5 Isobaric heat addition in boiler.

5-6 Isentropic expansion to intermediate pressure (y portion to FWH).

5-7 Isentropic expansion to the condenser pressure.

7-1 Isobaric heat rejection in condenser.


Open Feedwater Heaters


Closed Feedwater Heaters Heat transfer without mixing taking place

1-2 Isentropic compression in pump I.

2-9 Regeneration (only heat transfer)

3-4 Isentropic compression in pump II

9/4-5 Mixing of feed water and steam

5-6 Isobaric heat addition in boiler.

6-7 Isentropic expansion to intermediate pressure (y portion to FWH).

6-8 Isentropic expansion to the condenser pressure.

7-3 Regeneration (only heat transfer)

8-1 Isobaric heat rejection in condenser.


Closed Feedwater Heaters


26

23

3226

326

1

hh

hhy

hyhhyh

hhyyh

45in hhq

7665turb

776turb5

76turb5

1

1

hhyhhw

yhhyhwh

hyyhwh

17out 1 hhyq

4321pump

II pumpI pumppump

1 hhhhyw

www


Example

A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at 6MPa and 450oC and is condensed in the condenser at 20kPa. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s diagram, and determine

a. The net work output per kilogram of steam flowing through the boiler

b. The thermal efficiency of the cycle


Solution


Example

A regenerative vapor power cycle with one open feedwater heater. Steam enters the turbine at 80 bar 480oC and expands to 7 bar, where some of the steam is extracted and diverted to the open feedwater heater operating at 7 bar. The remaining steam expands through the second stage turbine to the condenser pressure 0.08 bar. Saturated liquid exits the open feedwater heater at 7 bar. The isentropic efficiency of each turbine stage is 85% and each pump operates isentropically. If the net power output of the cycle is 100 MW. Determine

1. The thermal efficiency2. The mass flow rate of steam entering the first turbine stage in kg/hr


Solution


Example

A steam power plant operates on an ideal reheat-regenerative Rankine cycle and has a net power of 80MW. Steam enters the high pressure turbine at 10MPa and 550oC and leaves at 0.8MPa. Some steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to 500oC and is expanded in the low pressure turbine to the condenser pressure of 10kPa. Show the cycle on a T-s diagram with respect to saturation lines, and determine

1. The mass flow rate of steam through the boiler2. The thermal efficiency of the cycle


Solution

8.2.7 combined gas-vapor cycles

Purpose of combination :

To achieve higher thermal efficiency

Combined cycle of Brayton gas power cycle and Rankine vapor power cycle

Gas turbine engine(Temperature limit 1500oC)

Steam turbine engine(Temperature limit 620oC)

Regeneration, 500oC


Example

The gas turbine portion of a combined gas-steam power plant has a pressure ratio of 16. air enters the compressor at 300K at a rate of 14kg/s and is heated to 1500K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400oC at 10MPa in a heat exchanger. The combustion gases leave the heat exchanger at 420K. The steam leaving the turbine is condensed at 15kPa. Assuming all the compression and expansion processes to be isentropic, determine

a. The mass flow rate of the steamb. The net power outputc. The thermal efficiency of the combined cycle

For air, assume constant specific heats at room temperature.


Solution


Example

Consider a combined gas-steam power cycle. The topping cycle is a simple Brayton cycle that has a pressure ratio of 7. Air enters the compressor at 15oC at a rate of 10kg/s and the gas turbine at 950oC. The bottoming cycle is a reheat Rankine cycle between the pressure limits of 6MPa and 10kPa. Steam is heated in a heat exchanger at a rate if 1.15 kg/s by the exhaust gases leaving the gas turbine and the exhaust gases leave the heat exchanger at 200oC. Steam leaves the high-pressure turbine at 1.0MPa and is reheated to 400oC in the heat exchanger before it expands in the low pressure turbine. Assuming 80% isentropic efficiency for all pumps and turbine, determine

a. The moisture content at the exit of the low pressure turbineb. The steam temperature at the inlet of high pressure turbinec. The net power output and the thermal efficiency of the combined

plant


Solution

vapor and combined power cycles (2) karakteristik beberapa sistem termodinamika

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