FME 322 - Thermodynamics III

8/6/2019 FME 322 - Thermodynamics III

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FME 322:

THERMODYNAMICS3rd Year, 2nd Sem


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GAS POWER CYCLES

The Carnot CycleCarnot cycle: this is a cycle consisting of two isothermal processes and two reversible adiabaticprocesses

A-B: isothermal heat addition

B-C: isentropic expansion

C-D: constant temperature heat rejection

D-A: isentropic compression

From the 1 st law,

Let:

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Thermal efficiency:

Work ratio is the ratio of net work output to the gross

(expansion) work output, given as

Practical Piston-Cylinder construction for Carnot CycleA-B B-C C-D D-A

Practical Problems1. Supplying heat and maintaining constant temperature 2. Insulating the cylinder and removing the insulation as fast as the piston moves3. Ensuring processes and are isentropic

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Air-Standard Cycles for Internal Combustion EnginesAir standard cycles are ideal heat engine cycles that represent the internal combustion engine. In airstandard cycles, the working fluid is assumed to be air and the processes are assumed to be reversibleand the heat source and sink are assumed to be external to the air

Otto CycleThis is the ideal air standard cycle for a petrol engine, using spark ignition

a-1: Working fluid (air) is induced into the cylinder slowly such that the pressure in the cylinder remainsconstant.1-2: Air is compressed isentropically to state 2.2-3: Heat is supplied to the air from an external source at constant volume3-4: Hot air expands to state 4isentropically.4-1: Heat is rejected from the air at constant volume until state 1 is achieved

Heat input into the system Net work input Thermal efficiency:

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is the compression ratio

Therfore, efficieny is a function of and

Work ratio is given as:

Therefore, depends on the cycle temperatures

The Atkinson CycleThermal efficienyis given by:

Where:

Net work is higher than the Otto cycle. Therefore, for the same heat input, the efficiency is higher. Heat

rejection occurs at constant temperature.

Volume displacement is more in the Otto cycle


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The Diesel CycleThe diesel cycle is the air standard cycle for 4-stroke compression ignition (C I) engine. It differs from theOtto cycle in that the last heat addition takes place at constant pressure rather that constant volume.

1-2: isentropic compression2-3: heat supplied at constantpressure3-4: isentropic expansion4-1: heat rejected at constant volume

Efficiency is less than the Otto cycle. Efficiency of diesel cycle approaches efficiency of Otto cycle as

Dual (Mixed) Combustion CycleThis is the air standard cycle for modern diesel engines. Heat addition takes place both at constantvolume and at constant pressure


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Questions:

1. A hot reservoir at and a cold reservoir at are available. Calculate the thermalefficiency and work ratio of a Carnot cycle using air as the working fluid if the maximum andminimum pressures are and respectively.

2. In an air-standard Otto cycle, maximum and minimum temperatures are and . Theheat supplied per kg of air is 800kJ. Calculate the compression ratio and the thermal efficiency.Also determine the ratio of maximum to minimum pressures in the cycle

3. An oil engine takes air at 1.01bar and 20 and the maximum cycle pressure is 69bar. Thecompression ratio is 18:1. Calculate the air-standard thermal efficiency based on the dualcombustion cycle. Assume that heat added at constant volume is equal to hear added atconstant pressure

F urther Examples:

An engine uses air as the working fluid and operates on ideal constant volume cycle. The compressionratio is . The initial pressure and temperature are and respectively and the heattransfer to the air is . Calculate:

1. The net cycle work2. The pressure and temperature at the principle points of the cycle

Solution:

Represent the cycle on an and diagram. Constant volume cycle, therefore the Otto cycle


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Heat transfer at constant volume

Stirling CycleThis consists of two constant volume processes and two isothermal processes


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The heat transfer during process is used to heat the gas during the process 2-3: This is assumed to take place ideally and reversibly in a regenerator. A regenerator is a device whichalternatively stores and rejects heat in a manner which theoretically is thermodynamically reversible:

Mean Effective Pressure:The mean effective pressure is definedas that constant pressure which if acted over the full stroke of thepiston will produce the same work

For a given value of output and various values the volume also varies enginecapacity


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Exercises:

1. A diesel engine has a compression ratio of and operates at a cut-off ratio of . The lowesttemperature and pressure are and . If air is the working fluid, determine:

a. The temperature and pressure at every principle point on the cycle

b. Heat added per kg of airc. Heat rejected per kg of aird. Thermal efficiencye. If the displacement of the engine is , and the engine is operating at ,

obtain the power developed2. Consider an ideal Stirling cycle on which pressure and temperature at the beginning of

isothermal compression process are and . The compression ratio is and themaximum temperature of the cycle is . Calculate:

a. Maximum pressure of the cycleb. Thermal efficiency of the cycle with and without a regenerator

3. A 4-stroke petrol engine has a swept volume of and clearance of volume of eachcylinder is . Calculate the air-standard thermal efficiency if the inlet conditions are ,

and the maximum cycle temperature is . Calculate the mean effective pressurehead based on the air standard cycle.

4. An air standard cycle mixed combustion cycle has a mean effective pressure of . Theminimum pressure and temperature are and respectively. The compression ratio is

. Calculate the maximum cycle temperature when the is and the maximum cyclepressure is .

1.


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Introduction to Reciprocating Internal Combustion EnginesThe term internal combustion engine is applied to all engines in which the combustion of fuel occursinside a cylinder. There are two main types:

(i) Petrol engines which work on the Otto cycle and ignition of fuel-air mixture is by an electricspark (sometimes called SI engines)

(ii) Oil engines (sometimes referred to as diesel engines) which work on either diesel or dualcombustion cycles. Modern oil engines work on the dual cycle. Pure air is compressed in acylinder and fuel is admitted at or near the end of compression. Ignition occurs due to hightemperature of the air. Sometimes called compression ignition (C I) engines. NB. In CI engines, the compression ratio is very high (in order to increase the temperature) while inpetrol engines, a spark is introduced to combust the mixture

4 -Stroke SI Engines


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The piston A is connected by means of rod C and crank-pin E and crank-arm D. The connecting rod Cconverts the reciprocating motion of the piston into rotary motion of the crank shaft.

1 st Stroke (a- 1) (Suction Stroke ) The outlet valve is closed and the inlet valve is opened. The air-fuel mixture is drawn into the cylinder by

the suction effect of the piston. Suction occurs till the piston reaches the end of the cylinder.

2 nd Stroke ( 1 -2 ) (Compression Stroke ) At the end of the suction stroke, the inlet valvecloses and the cylinder contains a charge of volume and pressure . The piston beginsthe compression stroke and the mixture iscompressed as the pressure increases to (apolytrophic process as the compression isaccompanied by heat loss as opposed to

isentropic compression in the air standard cycles). The volume has decreased from to

(approximately ). Compression ratio . When the piston is momentarily at rest as top dead

centre (TDC), both valves remain closed and a spark is introduced by passing across terminals of the plugand ignites the mixture.

3 rd Stroke ( 3 -4 ) (Expansion Stroke ) The post-combustion mixture at high pressure andtemperature forces the piston forward. Expansionproceeds with both valves closed and volume increasesfrom to .

4 th Stroke (4- 1) (Exhaust Stroke ) At the end of expansion stoke at 4, the outlet valve is opened and the gases flow out the cylinder duringthe momentary rest of the piston. During the return stroke, the piston sweeps out the exhaust gases.The crank moves back to the beginning of the cycle.

NB. For every stroke, the pin E moves 180. 1 complete revolution is 2 stokes in the cylinder


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CI EnginesThe events in the C I engines are similar to those of SI engines, save for the following:

1. The suction stroke. Air is induced into the cylinder

2. Compression stroke. The air is compressed to high pressures and temperatures and fuel isignited into the cylinder towards the end of the stroke. At the end of the stroke, the air

temperature is sufficiently high enough for the fuel to vaporise and ignite as they enter thecylinder. Combustion takes place at approximately constant pressure

3. Expansion stroke. There is some rise in pressure during the end stages of combustion but againthe combustion is assumed to be at constant pressure

4. Exhaust stroke. Similar to the SI engine

Internal Combustion Engine PerformanceThermal efficiency:

Indicated thermal efficiency:

Mechanical efficiency:

Specific Fuel Consumption ( SFC):


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Comparisons with the Air-Standard Cycles1. PV diagrams are different from actual indicator diagrams in that the indicator diagrams are

rounded up owing to time taken for valves to open and close. Combustion dies no preciselyoccur at constant volume or constant pressure

2. Temperature changes in actual cycles are large and a variable of specific heat3. The properties of the air-fuel mixture and of exhaust gases are markedly different from those of

air4. Due to cooling of the cylinder, the compression and expansion are not adiabatic and therefore

not isentropic

Exercises:

1. A 4-stroke diesel engine has cylinders, each of diameter by stroke. At, the average brake mean effective pressure is and the fuel consumption is

. The energy released during combustion of of fuel is . Determine:a. The brake powerb. Brake torquec. Brake thermal efficiencyd. Fuel consumption in

Reciprocating CompressorsReciprocating compressors are equipment or machines used to produce high pressure gas. Use of highpressure air includes process industry, pneumatic valves, air blast for workshops, water pumping,compressed air engines, etc.

A reciprocating compressor consists of a basic piston, a cylinder, a connecting rod and a crank. Thecylinder is fitted with two valves that permit the gas to flow in and out of the cylinder

a-b : inlet valve is opened and a mass of gas at state enters the cylinder without change of state. It

mixes with mass already present in the clearance volume.

b-c : both valves are closed and total mass ( ) change state during compression to


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H eat transfer:

Effect of Compression

isothermal compression

adiabatic compression

polytrophic compression We need to compress such that the value of is as close to unitas possible. Typically, is between and

Isothermal EfficiencyMinimum compression work occurs when the process is isothermal. Hence:

Overall isothermal efficiency:

Isothermal work between and

Mechanical efficiency:

V olumetric EfficiencyVolumetric efficiency is the ratio of actual volume induced per cycle to the swept volume:


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clearance ratio (a function of design and manufacture)

Clearance ratio should be as low as possible for a high volumetric efficiency. Increasing compressionratio decreases efficiency

Exercises

1. A single stage reciprocating compressor takes in of air at and anddelivers it at . Assuming that the law of compression is , and clearance isnegligible, calculate the i.p.2. A single stage air compressor is required to deliver of air per minute at and

. Delivered pressure is and speed is . Take of with a compressionindex of . calculate the swept volume if the cylinder, the delivered temperature and theindicated power

3. A low pressure cylinder for an air compressor for an air compressor has a stroke of and a clearance volume of . The pressure at the end of suction is and thetemperature is . The delivered pressure is . The index of compression,

.

Determine:a. The temperature and volume of air at the end of compressionb. Mass of air left in the clearing space at the end of delivery

Solution:

End of compression is at :


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Mass

Multi-Stage CompressionMinimum compression work occurs when the process is isothermal. The delivery temperature increases

with pressure ratio . For near isothermal compression, the pressure ratio should be as low as

possible. If the delivery pressure is high, then the required work would be reduced if compression isdone in stages of small ratios. The volumetric efficiency decreases with increase in pressure ratio. Forhigh pressure ratio, the volumetric efficiency can be increased by carrying out the compression in two ormore stages. For pressure greater than , use two stagesTwo-Stage Compressors if the gas is not cooled at stage . if cooled

Air is compressed to an intermediate pressure, in the low pressurecylinder and then transferred to a high pressure cylinder andcompressed to . The air would be delivered at the end of this stagebut can be delivered to a third stage.

Compression work between and intermediate pressure in stage1:

For stage 2:

Total work . If intercooling between the stages is complete, For minimum work,


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The pressure ratio, is the same for each stage, known as geometric progression

G etting maximum work for 3 stage processes:

The pressure ratio should be the same between the stages

Work done for each stage is the same:

For 2 stages: For 3 stages: For stages:

Questions:

In a 2 stage single acting sir compressor, the suction pressure is and final delivery is .The temperature at the end of suction is . in compression and expansion. Clearancevolume of the low pressure cylinder is if its stroke volume and that of the high pressure cylinder is

of the stroke volume. The compressor is required to deliver of air per minute when runningat . Determine:


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(i) Stroke volume of each cylinder(ii) Power of the compressor(iii) Heat transfer in the intercooler

Assume the stage pressures to be in geometric progression

A 2 stage single acting compressor is required to compress of fluid air per hour from to. Prove that with complete cooling, the stage pressure ratio should be equal to for the required power to be minimum. If , calculate the powerrequired. If the mean piston speed is , calculate the piston areas, neglecting clearance

Constant Pressure Brayton Cycle

This is the air standard cycle for jet engines. It consists of two constant pressure process and twoisentropic processes

Heat is added at constant pressure, and rejected at constant pressure :


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P rocesses:

compression heat addition expansion

heat rejection

Thermal efficiency:

is a function of and pressure ratio

Work Ratio:

is a function of as well as lowest and highest temperatures


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Example:

A Brayton cycle with air as the working fluid operates between temperatures of and andhas lower pressure of and a pressure ratio of .

(i) Determine the temperature and pressure at each principle point in the cycle(ii) What is the net work done per cycle per unit mass(iii) What is the thermal efficiency(iv) What is the maximum efficiency of a cycle operating between the same temperatures and

low pressure

Solution

Net work:

Thermal efficiency:

Maximum efficiency:

Optimum Pressure Ratio


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1st Law for a Thermodynamic Cycle:

Consider cycle

Net work output is given by the area enclosed by the cycle. If the pressure ratio is increased to the

cycle becomes . Thermal efficiency increases but the net work decreases. Theefficiency approaches carnot efficiency since and . No work is done. Similarly, whenpressure ratio is decreased the net work decreases and approaches zero. and

and are fixed. for maximum net work

In the above example, optimum pressure ratio:

Gas Turbine Unit The basic turbine unit operates on the open Brayton cycle. In the open cycle, the compressor (rotary) ismounted on the shaft as is the turbine. Air is drawn into the compressor then passes to combustionchamber where fuel is continually injected and the resulting hot gases expand through the turbine andexhaust to the atmosphere


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Ideal cycle is . Practical cycle is For net work output, the turbine must develop more work than required to turn the compressor.Compressor isentropic efficiency:

Compressor work:

Heat supplied:

Turbine isentropic efficiency:

Turbine work:

Net work:

Cycle efficiency:

Modifications to the Open Cycle to Improve Efficiency and Work Cycle

1. Multi-stage compression and intercooling.Net work input into the compressor can be reduced if the compression is done in stages (geometric progression) and complete intercooling betweenstages

2. Reheating between turbine expansions. Due to divergence of isobars on diagram, theturbine work is high at high values of entropy. Hence, expansion in stages together withreheating between the stages increases the overall turbine work and therefore efficiency andwork ratio

3. Incorporating a heat exchanger (regenerator) between gases leaving at (exhaust gases) andair into the combustion chamber. This reduces the between and . Heat input is then . Heat balance on the heat exchanger:


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diagram of modifications and

Modifications and


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Examples:

An a gas turbine plant, compression and expansion are isentropic, heat transfer takes place at constantpressure. Pressure of air at inlet to compressor is and compressor delivery is . The tempof inlet to turbine is and turbine expands to pressure. Determine, per of air:

(i) Compressor work(ii) Turbine work(iii) Hear transfer to air(iv) Heat transfer from air(v) Thermal efficiency of air

In a marine gas turbine unit, a H P stage turbine drives the compressor, and a L P stage turbine drives thepropeller through s uitable gearings. The overall pres sure ratio is 4/ 1. The mass flow rate is . The

maximum temperature is and the air intake conditions are and . The isentropicefficiencies of the compressor, H P turbine, and LP turbine, are , , and respectively, and themechani cal efficiency of both shafts is 98% . Neglecting kinetic energy changes, and the pressure loss incombustion, calculate:

(i) The pressure between turbine stages [ ] (ii) The cycle efficiency [ ] (iii) The shaft power [ ]

H eat Balance

Effectiveness of the heat exchanger (regenerator) is defined as ratio of heat received by air to themaximum possible transferrable heat from the gases. This is also called thermal ratio

Thermal efficiency with regenerator:

Example:

An industrial gas turbine plant combines low pressure and high pressure compressors, intercooler, highpressure, intermediate pressure and low pressure turbines. It has 3 combustion chambers and anexhaust heat exchanger. The high pressure turbine drives both the L P and H P compressors, and theintermediate and low pressure turbines supply the power output. From the data below, determine:


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(i) Power output(ii) Fuel consumption(iii) Thermal efficiency- Pressure at inlet to L P compressor and exhaust low pressure turbine = 1.035bar- Temperature at inlet to each compressor = 15C- Temperature to each turbine = 650C- Pressure ratio to each compressor = 3:1- Isentropic efficiency to each compressor = 0.85- Thermal ratio of heat exchanger = 0.7- Thermal ratio of turbine = 0.8- CV of fuel = 44200kJ/kg- Mass flow rate of gas/air = 45.4kg/s- Assume properties of gas and air are the same

Compressor work Turbine work

Heat transfer to air Heat transfer from air

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FME 322 - Thermodynamics III

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