Power Cycles

Chapter 7 & 8

Outline of Power Cycles

Heat engines

Steam power plants

1. Carnot cycle

2. Rankine cycle

Turbines/compressors – Chap 7

Internal combustion engines

1. Otto engine

2. Diesel engine

3. Gas turbine engines

Regenerative cycle

Heat into work

Most present day methods based on the evolution of heat and subsequent conversion of part of the heat into useful work.

Fossil fuel steam power plants (Efficiency: 35%) Combined cycle plants (Efficiency: 50%) – advanced

technology gas turbines Conversion of chemical energy directly into electrical

energy Eg.: Electrochemical cell (battery), fuel cell (Efficiency: 50%

and more)

Heat engines

Internal combustion energy Conversion of chemical energy of fuel directly into internal

energy Eg: Otto engine, Diesel engine, gas turbines Power plants Working fluid such as steam is separated from heat source and

heat is transferred across a physical boundary

Heat Engine Cycle

Heat engines operate in a cyclic manner, adding energy in the form of heat in one part of the cycle and using that

energy to do useful work in another part of the cycle.

Revision

Specific volumes at constant temperature and states within the vapor dome in a liquid-vapor system

Boiler – part of heat from fuel oil converts water to steam at high T and P QH

Turbine – shaft work by a turbine Ws

Condenser – condenses exhaust steam at low T QC Pump – pumps water back to boiler. Ws

Simple steam power plant

Carnot engine

The most efficient heat engine cycle is the Carnot cycle, consisting of two isothermal processes and two adiabatic processes.

When the second law of thermodynamics sets the limiting value on the fraction of the heat which can be so used.

Carnot efficiency

H

C

T

T1

Issues in Carnot cycle

Turbines (Expanders - gas)

• The expansion of a gas in a nozzle to produce a high velocity stream • Converts internal energy into kinetic energy and finally shaft work • Consists of alternate sets of nozzles and rotating blade through which vapour flows in an expansion process

Conversion of a high pressure stream into shaft work

Shaft work, Ws

In open systems, DH = Q + Ws

For turbines, Ws = DH = H2 – H1

If the fluid in turbine expands reversibly and adiabatically isentropic process

Isentropic: S2 = S1

Ws (isentropic) = (DH)s

Ws (isentropic) is the maximum that can be obtained

Adiabatic expansion process in turbine

Turbine efficiency

Values of range from 0.7 – 0.8

Adiabatic expansion process in turbine

Compressors

Expansion process (turbines): pressure reduction in a flowing fluid

Compression process (compressor): pressure increases (by reducing volume)

Compressors are similar to pumps: both increase the pressure on a fluid and both can transport the fluid through a pipe

Adiabatic compression

P1

P2

W

Compressor efficiency

A steam turbine with rated capacity of 56400kW operates with steam at

inlet conditions at 8600 kPa and 500oC, and discharges into a condenser at

a pressure of 10kPa. Assuming the turbine efficiency at 0.75, determine the

state of the steam at discharge and the mass flow rate of the steam.

1) Determine quality, x2’

2) Find (DH)s

M=Ml +xvDMlv

3) Find H2 actual using efficiency and determine new quality, x2

4) Find S2 actual and actual shaft work, Ws

H=Hl +xvDHlv

What if the fluid is not steam?

How can the isentropic shaft work be calculated?

Where will you obtain data from?

Let’s say the stream going through the turbine is a gas eg. ethylene – you have two options:

1. Ideal gas assumption

)( 12 TTCHH

ig

P D

D2

11

2

1

2 lnlnT

T

ig

PP

PR

T

TCS

For isentropic conditions, DS=0

)()()( 12 TTCsHisentropicWsH

ig

P D

Alternatively…

2. Choose an appropriate generalised equation

),,(

10

OMEGAPRTRHRBRT

H

RT

H

RT

H

c

R

c

R

c

R

),,(

10

OMEGAPRTRSRBR

S

R

S

R

S RRR

RR

H

ig

P HHTTCH 1212 )( D

RRT

T

ig

P SSP

PR

T

dTCS 12

1

22

1

ln D

RR

H

ig

P HHTTCsHisentropicWs 1212 )()()( D

Refer to Example 7.7

Simple steam power plant

Turbine and pump work Work output of the cycle (Steam turbine), Wturbine and work

input to the cycle (Pump), Wpump are:

Wturbine = m (h2-h1) (negative value) Wpump = m (h4-h3)

where m is the mass flow of the cycle. Heat supplied to the cycle (boiler), QH and heat rejected from the cycle (condenser), QC are:

QH = m (h4-h1) QC = m (h3-h2) (negative value)

The net work of the cycle is:

W = Wturbine + Wpump

Rankine Cycle

Practical power cycle - Rankine

Rankine Cycle

Carnot Cycle

Rankine Cycle

1. Saturated or superheated steam enters the turbine at state 1, where it expands isentropically to the exit pressure

2. The steam is then condensed at constant pressure and temperature to a saturated liquid.

3. The heat removed from the steam in the condenser is typically transferred to the cooling water. The saturated liquid then flows through the pump

4. The pump increases the pressure to the boiler pressure where the water is heated to the saturation temperature, boiled and typically superheated to state 1.

Isentropic conditions

1 to 2: Isentropic expansion (Steam turbine)

2 to 3: Isobaric heat rejection (Condenser)

3 to 4: Isentropic compression (Pump)

4 to 1: Isobaric heat supply (Boiler)

Rankine efficiency

The efficiency of the Rankine cycle is not as high as Carnot cycle but the cycle has less practical difficulties

Internal Combustion Engines

Does not require heat transfer areas such as in steam power plant

Internal combustion engines burn fuel within the engine

Does not happen in cyclic process for the working medium such as steam in power plants, therefore the cyclic process is imagined with air as the working fluid

First presented in qualitative description than quantitative using air as an ideal gas

The Otto Engine

Stage 1: Beginning of the intake stroke of the engine. The pressure is near atmospheric pressure and the gas volume is at a minimum. The pressure remains constant, and the gas volume increases as fuel/air mixture is drawn into the cylinder through the intake valve. Stage 2: Compression stroke of the engine with the closing of the intake valve. Between Stage 2 and Stage 3, the piston moves back into the cylinder, the gas volume decreases, and the pressure increases because work is done on the gas by the piston. Stage 3: Combustion of the fuel/air mixture. The combustion occurs very quickly and the volume remains constant. Heat is released during combustion which increases both the temperature and the pressure, according to the equation of state.

Internal –Combustion Engines

- The Otto Engine

Stage 4: Power stroke of the engine. Between Stage 4 and Stage 5, the piston is driven towards the crankshaft, the volume in increased, and the pressure falls as work is done by the gas on the piston. Stage 5: Exhaust valve is opened and the residual heat in the gas is exchanged with the surroundings. The volume remains constant and the pressure adjusts back to atmospheric conditions. Stage 6: Exhaust stroke of the engine during which the piston moves back into the cylinder, the volume decreases and the pressure remains constant. At the end of the exhaust stroke, conditions have returned to Stage 1 and the process repeats itself.

Internal –Combustion Engines

- The Otto Engine

Idealised Air Standard Cycle

•Heat is transferred at

constant volume during 1-2.

•The gas expands

reversibly and adiabatically

during 2-3, where work is

done.

•Heat is rejected at

constant volume at low

temperature during 3-4.

•The gas is compressed

reversibly and adiabatically

in 4-1.

The thermal efficiency of an Otto cycle with a perfect gas as working fluid is: It can be shown that: where, r = V1/V2= Compression ratio g = constant depending on specific heat capacity

The Otto Engine efficiency

Ideal Otto cycle thermal efficiency

Diesel engine

Diesel Cycle

1 to 2: Isentropic compression 2 to 3: Reversible constant pressure heating 3 to 4: Isentropic expansion 4 to 1: Reversible constant volume cooling

•Heat is supplied reversibly at constant pressure in 1-2.

•Reversible adiabatic expansion during which work is done in 2-3.

•Heat is rejected reversibly at constant volume in 3-4.

•Gas is compressed reversibly and

adiabatically in 4-1.

Diesel Cycle

- Advantages of internal combustion and those of the

steam turbine are combined in the gas-turbine engine.

- Driven by high temperature gases from combustion chamber, compressed to several bars

Gas Turbine Engine

PA

PB

Ideal cycle: Brayton cycle Working fluid is air as ideal gas

Idealisation of gas turbine is known as the Brayton cycle

Comparison of efficiency

g = 1.4 for ideal cycle conditions

Both k and g may be used. However they represent the same constant

Example 8.1 from textbook

Turbine – as done previously

For condenser and boiler,

Thermal efficiency

When turbine efficiency = 0.75,

If rating of power cycle = 80000kW,

what is the steam rate, QB and QC

Regenerative cycle

The incremental steps of heat transfer to the feedwater increases the cycle efficiency over having all of the heat transfer taking place within the boiler. The steam from the turbine releases its heat to the feedwater, reducing the amount of heat rejected in the condenser.

After emerging from the condenser as a subcooled liquid the working fluid is heated by steam tapped from the hot portion of the cycle. On the diagram shown, the fluid at 2 is mixed with the fluid at 4 (both at the same pressure) to end up with the saturated liquid at 7.

Tutorial Questions

Attempt the following from textbook (7th Edition):

Chapter 7: 10, 18, 23

Chapter 8: 1, 4, 6, 7