lec 12 gas power cycles - university of jordaneacademic.ju.edu.jo/z.hamamre/material/thermodynamics...

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan

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Dr.-Eng. Zayed Al-Hamamre

Thermodynamics I

Gas Power Cycles


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Content Internal Combustion Engines

o Otto Cycle

o Diesel Cycle

o Dual Cycle

Gas Turbine Cycles

o Brayton Cycle

o Regenerative Gas Turbines

o Regenerative Gas Turbines with Reheat and Intercooling

o Gas Turbines for Aircraft Propulsion

o Ericsson and Stirling Cycles

Compressible flow through Nozzles and Diffusers

Combined Gas-Vapor Cycles


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Many work-producing devices (engines) utilize a working fluid that is always a gas.

The spark-ignition automotive engine is a familiar example, as are the diesel engine and the

conventional gas turbine.

In all these engines there is a change in the composition of the working fluid, because during

combustion it changes from air and fuel to combustion products.

These engines are called internal combustion engines

Because the working fluid does not go through a complete thermodynamic cycle in the engine

(even though the engine operates in a mechanical cycle), the internal combustion engine

operates on the so-called open cycle.

For analyzing internal-combustion engines, the air-standard cycle approach is assumed.

Introduction


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Air Standard Assumption 1. A fixed mass of air is the working fluid throughout

the entire cycle, and the air is always an ideal gas.

The combustion process is replaced by a process

transferring heat (heat-addition process) from an

external source.

2. All the processes that make up the cycle are

internally reversible.

3. The exhaust process is replaced by a heat-rejection

process that restores the working fluid to its initial

state, i.e. the cycle is completed by heat transfer to

the surroundings (in contrast to the exhaust and

intake process of an actual engine).

4. An additional assumption is often made that air has a

constant specific heat, recognizing that this is not the

most accurate model.


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Reciprocating Engines

The piston reciprocates in the cylinder between two

fixed positions called the top dead center (TDC)—the

position of the piston when it forms the smallest volume

in the cylinder—and the bottom dead center (BDC)—

the position of the piston when it forms the largest

volume in the cylinder.

The distance between the TDC and the BDC is the

largest distance that the piston can travel in one

direction, and it is called the stroke of the engine.

The diameter of the piston is called the bore.

The air or air–fuel mixture is drawn into the cylinder

through the intake valve, and the combustion products

are expelled from the cylinder through the exhaust

valve.

Intake valve Exhaust valve


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The minimum volume formed in the cylinder when the piston is

at TDC is called the clearance volume.

The volume displaced by the piston as it moves between TDC

and BDC is called the displacement volume

The ratio of the maximum volume formed in the cylinder to the

minimum (clearance) volume is called the compression ratio r of the engine


Another term frequently used in conjunction with reciprocating engines is the mean effective

pressure (MEP).

It is a fictitious pressure that, if it acted on the piston during the entire power stroke, would

produce the same amount of net work as that produced during the actual cycle


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Reciprocating engines are classified , depending on how the

combustion process in the cylinder is initiated, as

i. Spark-ignition (SI) engines: the combustion of the

air–fuel mixture is initiated by a spark plug

The air–fuel mixture is compressed to a temperature that is

below the autoignition temperature of the fuel, and the

combustion process is initiated by firing a spark plug

The Otto cycle is the ideal cycle for spark-ignition

reciprocating engines.

ii. Compression-ignition (CI) engines: the air–fuel

mixture is self-ignited as a result of compressing the

mixture above its self ignition temperature.

The air is compressed to a temperature that is above the

autoignition temperature of the fuel, and combustion starts

on contact as the fuel is injected into this hot air

The Diesel cycle is the ideal cycle for CI reciprocating

engines



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With the intake valve open, the piston makes an intake stroke to draw a fresh charge into the cylinder.

With both valves closed, the piston undergoes a

compression stroke, raising the temperature and pressure

of the charge. A combustion process is then initiated,

resulting in a high-pressure, high-temperature gas

mixture.

In compression-ignition engines, combustion is initiated

by injecting fuel into the hot compressed air, beginning

near the end of the compression stroke and continuing

through the first part of the expansion.

A power stroke follows the compression stroke, during

which the gas mixture expands and work is done on the

piston as it returns to bottom dead center.

The piston then executes an exhaust stroke in which the

burned gases are purged from the cylinder through the

open exhaust valve.


Intake valve Exhaust valve


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1. Initially, both the intake and the exhaust valves are closed,

and the piston is at its lowest position (BDC).

2. During the compression stroke, the piston moves upward,

compressing the air–fuel mixture. Shortly before the piston

reaches its highest position (TDC), the spark plug fires and

the mixture ignites, increasing the pressure and temperature

of the system.

3. The high-pressure gases force the piston down, which in turn

forces the crankshaft to rotate, producing a useful work

output during the expansion or power stroke.

Otto Engine

At the end of this stroke, the piston is at its lowest position (the

completion of the first mechanical cycle), and the cylinder is

filled with combustion products.

Now the piston moves upward one more time, purging the

exhaust gases through the exhaust valve (the exhaust stroke), and

down a second time, drawing in fresh air–fuel mixture through

the intake valve (the intake stroke).


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Otto Engine


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Otto Engine

i. Process 1–2 is an isentropic compression of the air as the piston moves from bottom dead

center to top dead center.

ii. Process 2–3 is a constant-volume heat transfer to the air from an external source while the

piston is at top dead center. This process is intended to represent the ignition of the fuel–air

mixture and the subsequent rapid burning.

iii. Process 3–4 is an isentropic expansion (power stroke).

iv. Process 4–1 completes the cycle by a constant-volume process in which heat is rejected

from the air while the piston is at bottom dead center.


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Otto Engine


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Otto Engine

Substituting these equations into the thermal efficiency

relation and simplifying,

where


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Otto Engine

For a given compression ratio, an ideal Otto cycle using a monatomic gas (such as argon or

helium, k 1.667) as the working fluid will have the highest thermal efficiency.

The specific heat ratio k, and thus the thermal efficiency of the ideal Otto cycle, decreases as

the molecules of the working fluid get larger

In gasoline engines, a mixture of air and fuel is

compressed during the compression stroke, and

the compression ratios are limited by the onset

of autoignition or engine knock

Remember that for an adiabatic process


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An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air

is at 100 kPa and 17°C, and 800 kJ/kg of heat is transferred to air during the constant-volume

heat-addition process. Accounting for the variation of specific heats of air with temperature,

determine (a) the maximum temperature and pressure that occur during the cycle, (b) the net

work output, (c) the thermal efficiency, and (d ) the mean effective pressure for the cycle.

Example


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Example Cont.


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Example Cont.


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Example Cont.


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Diesel Cycle

In diesel engines, only air is compressed during the compression stroke, eliminating the

possibility of autoignition.

Therefore, diesel engines can be designed to operate at much higher compression ratios,

typically between 12 and 24.

The fuel injection process in diesel engines starts

when the piston approaches TDC and continues

during the first part of the power stroke.

Therefore, the combustion process in these engines

takes place over a longer interval.

Because of this longer duration, the combustion

process in the ideal Diesel cycle is approximated as a

constant-pressure heat-addition process.


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2-3 constant-pressure heat-addition

(includes work and heat)

Diesel Cycle

The Diesel cycle is executed in a piston–cylinder

device, which forms a closed system,

The amount of heat transferred to the working

fluid at constant pressure and rejected from it at

constant volume


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2-3 constant-pressure heat-addition (involves work and heat)

Diesel Cycle

Where cutoff ratio rc, is the ratio of the cylinder volumes after and before the combustion

process:

And


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Diesel Cycle


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Diesel Cycle


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Utilizing this definition and the isentropic ideal-gas relations

Diesel Cycle

Comparing with Otto engine,

=

As rc is the ratio approaching 1


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Diesel and Otto Cycle


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An ideal Diesel cycle with air as the working fluid has a compression ratio of 18 and a cutoff

ratio of 2. At the beginning of the compression process, the working fluid is at 14.7 psia, 80°F,

and 117 in3. Utilizing the cold-airstandard assumptions, determine (a) the temperature and

pressure of air at the end of each process, (b) the net work output and the thermal efficiency, and

(c) the mean effective pressure

Example


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Example Cont.


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Example Cont.


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Example Cont.


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Example Cont.


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Dual Cycle


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Dual Cycle

During the isentropic compression process 1–2 there is no heat

transfer, and the work is


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Dual Cycle

the constant-volume heat rejection process 5–1 that completes the cycle involves heat transfer but

no work


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Striling and Ericsson Cycles

Stirling cycle

• 1-2 T = constant expansion (heat

addition from the external

source)

• 2-3 v = constant regeneration

(internal heat transfer from the

working fluid to the regenerator)

• 3-4 T = constant compression

(heat rejection to the external

sink)

• 4-1 v = constant regeneration

(internal heat transfer from the

regenerator back to the working

fluid)

Both cycles are totally reversible,


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The execution of the Stirling cycle. A steady-flow Ericsson engine.

The Ericsson cycle is very much like the

Stirling cycle, except that the two

constant-volume processes are replaced

by two constant-pressure processes.

The Stirling and Ericsson cycles give a

message: Regeneration can increase efficiency.

Striling and Ericsson Cycles


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Using an ideal gas as the working fluid, show that the thermal efficiency of an Ericsson cycle is

identical to the efficiency of a Carnot cycle operating between the same temperature limits.

Example

For a reversible isothermal

process, heat transfer is

The entropy change of an ideal gas during

an isothermal process


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Brayton Cycle for Modeling Gas Turbine Power Plants Brayton Cycle is the ideal cycle for modeling gas turbine power plants.

It is used for gas turbines only where both the compression and expansion processes take

place in rotating machinery Constant-pressure

heat-addition

Constant-pressure

heat-removal


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Brayton Cycle for Modeling Gas Turbine Power Plants


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Brayton Cycle for Modeling Gas Turbine Power Plants Assuming the turbine operates adiabatically and with negligible effects of kinetic and potential

energy, the work developed per unit of mass is

compressor work per unit of mass is

The heat added to the cycle per unit of mass is


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For the same pressure rise, a gas turbine compressor would require a much greater work input

per unit of mass flow than the pump of a vapor power plant because the average specific

volume of the gas flowing through the compressor would be many times greater than that of

the liquid passing through the pump



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For fixed values of Tmin and Tmax, the net

work of the Brayton cycle first increases

with the pressure ratio, then reaches a

maximum at rp = (Tmax/Tmin)k/[2(k - 1)], and

finally decreases.


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Brayton Cycle for Modeling Gas Turbine Power Plants The highest temperature in the cycle is limited by the maximum temperature that the turbine

blades can withstand. This also limits the pressure ratios that can be used in the cycle.

The air in gas turbines supplies the necessary oxidant for the combustion of the fuel, and it

serves as a coolant to keep the temperature of various components within safe limits. An air–

fuel ratio of 50 or above is not uncommon.


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Gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas

temperature is 300 K at the compressor inlet and 1300 K at the turbine inlet. Utilizing the air-

standard assumptions, determine (a) the gas temperature at the exits of the compressor and the

turbine, (b) the back work ratio, and (c) the thermal efficiency.

Example


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Example Cont.


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OR

Example Cont.


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Example Cont.


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Development of Gas Turbines

Increasing the turbine inlet (or firing) temperatures

Increasing the efficiencies of turbomachinery components (turbines, compressors):

Adding modifications to the basic cycle (intercooling, regeneration or recuperation, and

reheating).

Deviation of Actual Gas-Turbine

Cycles from Idealized Ones

The deviation of an actual gas-

turbine cycle from the ideal

Brayton cycle as a result of

irreversibilities.

Reasons: Irreversibilities in turbine and

compressors, pressure drops, heat losses

Isentropic efficiencies of the compressor

and turbine


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THE BRAYTON CYCLE WITH REGENERATION

A gas-turbine engine with regenerator. T-s diagram of a Brayton

cycle with regeneration.

In gas-turbine engines, the temperature of the exhaust gas

leaving the turbine is often considerably higher than the

temperature of the air leaving the compressor.

Therefore, the high-pressure air leaving the compressor can

be heated by the hot exhaust gases in a counter-flow heat

exchanger (a regenerator or a recuperator).

The thermal efficiency of the Brayton cycle increases as a

result of regeneration since less fuel is used for the same work

output.

In the limiting (ideal)

case, the air exits the

regenerator at the

inlet temperature of

the exhaust gases


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T-s diagram of a Brayton

cycle with regeneration.

Effectiveness of

regenerator

Effectiveness under cold-air

standard assumptions

Under cold-air standard

assumptions

Thermal efficiency of

the ideal Brayton

cycle with and without

regeneration.

The thermal efficiency depends on the ratio of the minimum to maximum temperatures as well as the pressure ratio.

Regeneration is most effective at lower pressure ratios and low minimum-to-maximum temperature ratios.

THE BRAYTON CYCLE WITH REGENERATION


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THE BRAYTON CYCLE WITH INTERCOOLING, REHEATING, AND

REGENERATION

A gas-turbine engine with two-stage compression with

intercooling, two-stage expansion with reheating, and

regeneration and its T-s diagram.

For minimizing work input to

compressor and maximizing

work output from turbine:


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Comparison of work

inputs to a single-stage

compressor (1AC) and a

two-stage compressor

with intercooling

(1ABD).

Multistage compression with intercooling: The work required to compress a gas between two

specified pressures can be decreased by carrying out the compression process in stages and

cooling the gas in between. This keeps the specific volume as low as possible.

Multistage expansion with reheating keeps the specific volume of the working fluid as high as

possible during an expansion process, thus maximizing work output.

Intercooling and reheating always decreases the thermal efficiency unless they are

accompanied by regeneration. Why?

As the number of compression and expansion

stages increases, the gas-turbine cycle with

intercooling, reheating, and regeneration

approaches the Ericsson cycle.

THE BRAYTON CYCLE WITH INTERCOOLING, REHEATING, AND

REGENERATION


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IDEAL JET-PROPULSION CYCLES

In jet engines, the high-temperature and high-

pressure gases leaving the turbine are

accelerated in a nozzle to provide thrust.

Gas-turbine engines are widely used to power aircraft because they are light and compact and have a high power-to-weight ratio.

Aircraft gas turbines operate on an open cycle called a jet-propulsion cycle.

The ideal jet-propulsion cycle differs from the simple ideal Brayton cycle in that the gases are not expanded to the ambient pressure in the turbine. Instead, they are expanded to a pressure such that the power produced by the turbine is just sufficient to drive the compressor and the auxiliary equipment.

The net work output of a jet-propulsion cycle is zero. The gases that exit the turbine at a relatively high pressure are subsequently accelerated in a nozzle to provide the thrust to propel the aircraft.

Aircraft are propelled by accelerating a fluid in the opposite direction to motion. This is accomplished by either slightly accelerating a large mass of fluid (propeller-driven engine) or greatly accelerating a small mass of fluid (jet or turbojet engine) or both (turboprop engine).


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Propulsive power is the thrust acting on the

aircraft through a distance per unit time.

Propulsive efficiency Propulsive power

Thrust (propulsive force)

IDEAL JET-PROPULSION CYCLES


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A gas power cycle topping a vapor power cycle, which is called the combined gas–vapor

cycle, or just the combined cycle

The combined cycle of greatest interest is the gas-turbine (Brayton) cycle topping a steam

turbine (Rankine) cycle.

The modified cycle has a higher thermal efficiency than either of the cycles executed

individually

Gas-turbine cycles typically operate at considerably higher temperatures than steam cycles.

The maximum fluid temperature at the turbine inlet is about 620°C for modern steam power

plants, but over 1425°C for gas-turbine power plants.

Gas-turbine cycles have a greater potential for higher thermal efficiencies.

However, the gas-turbine cycles have one inherent disadvantage: The gas leaves the gas

turbine at very high temperatures (usually above 500°C), which erases any potential gains in

the thermal efficiency.

Combined Gas-Vapor Cycles


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Combined Gas-Vapor Cycles The efficiency can be modified by using the high temperature exhaust gases as the energy

source for the bottoming cycle such as a steam power cycle.


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Consider the combined gas–steam power cycle

shown. The topping cycle is a gas-turbine cycle

that has a pressure ratio of 8. Air enters the

compressor at 300 K and the turbine at 1300 K.

The isentropic efficiency of the compressor is 80

percent, and that of the gas turbine is 85 percent.

The bottoming cycle is a simple ideal Rankine

cycle operating between the pressure limits of 7

MPa and 5 kPa. Steam is heated in a heat

exchanger by the exhaust gases to a temperature of

500°C. The exhaust gases leave the heat exchanger

at 450 K. Determine (a) the ratio of the mass flow

rates of the steam and the combustion gases and (b)

the thermal efficiency of the combined cycle.

Example


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Example Cont.

Energy balance on the heat exchanger:


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Example Cont.

lec 12 gas power cycles - university of jordaneacademic.ju.edu.jo/z.hamamre/material/thermodynamics...

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