Thermodynamics Analysis of Engine Cycles
Summary
Thermodynamics is the science of the relationship between heat, work, and systems that analyze energy
processes. The energy processes that convert heat energy from available sources such as chemical fuels
into mechanical work are the major concern of this science. Thermodynamics consists of a number of
analytical and theoretical methods which may be applied to machines for energy conversion.
First Law of Thermodynamics
The first law of thermodynamics is the application of the conservation of energy principle to heat and
thermodynamic processes:
Change in internal
Heat added to - Work done by
energy =
the system
the system
The first law makes use of the key concepts of internal energy, heat, and system work. It is used
extensively in the discussion of heat engines.
It is typical for chemistry texts to write the first law as ΔU=Q+W. It is the same law, of course - the
thermodynamic expression of the conservation of energy principle. It is just that W is defined as the
work done on the system instead of work done by the system. In the context of physics, the common
scenario is one of adding heat to a volume of gas and using the expansion of that gas to do work, as in
the pushing down of a piston in an internal combustion engine. In the context of chemical reactions and
process, it may be more common to deal with situations where work is done on the system rather than
by it.
Enthalpy
Four quantities called "thermodynamic potentials" are useful in the chemical thermodynamics of
reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy
and the Gibbs free energy. Enthalpy is defined by
H = U + PV
where P and V are the pressure and volume, and U is internal energy. Enthalpy is then a precisely
measurable state variable, since it is defined in terms of three other precisely definable state variables.
It is somewhat parallel to the first law of thermodynamics for a constant pressure system
Q = ΔU + PΔV since in this case Q=ΔH
It is a useful quantity for tracking chemical reactions. If as a result of an exothermic reaction some
energy is released to a system, it has to show up in some measurable form in terms of the state
variables. An increase in the enthalpy H = U + PV might be associated with an increase in internal energy
which could be measured by calorimeter, or with work done by the system, or a combination of the two.
The internal energy U might be thought of as the energy required to create a system in the absence of
changes in temperature or volume. But if the process changes the volume, as in a chemical reaction
which produces a gaseous product, then work must be done to produce the change in volume. For a
constant pressure process the work you must do to produce a volume change ΔV is PΔV. Then the term
PV can be interpreted as the work you must do to "create room" for the system if you presume it
started at zero volume.
System Work
When work is done by a thermodynamic system, it is usually a gas that is doing the work. The work done
by a gas at constant pressure is:
The line from a to b represents an expansion of a gas at constant pressure. The work done is the area
under the curve.
For non-constant pressure, the work can be visualized as the area under the pressure-volume curve
which represents the process taking place. The more general expression for work done is:
The integral gives the exact area under the curve which is equal to the work.
Work done by a system decreases the internal energy of the system, as indicated in the First Law of
Thermodynamics. System work is a major focus in the discussion of heat engines.
Second Law of Thermodynamics
The second law of thermodynamics is a general principle which places constraints upon the direction of
heat transfer and the attainable efficiencies of heat engines. In so doing, it goes beyond the limitations
imposed by the first law of thermodynamics.
The maximum efficiency which can be achieved is the Carnot efficiency.
Second Law: Heat Engines
Second Law of Thermodynamics: It is impossible to extract an amount of heat QH from a hot reservoir
and use it all to do work W. Some amount of heat QC must be exhausted to a cold reservoir. This
precludes a perfect heat engine.
This is sometimes called the "first form" of the second law, and is referred to as the Kelvin-Planck
statement of the second law.
Second Law: Entropy
Second Law of Thermodynamics: In any cyclic process the entropy will either increase or remain the
same:
Entropy: a state variable whose change is defined for a reversible process at T where Q is the heat
absorbed.
Entropy: a measure of the amount of energy which is unavailable to do work.
Entropy: a measure of the disorder of a system.
Entropy: a measure of the multiplicity of a system.
Since entropy gives information about the evolution of an isolated system with time, it is said to give us
the direction of "time's arrow" . If snapshots of a system at two different times shows one state which is
more disordered, then it could be implied that this state came later in time. For an isolated system, the
natural course of events takes the system to a more disordered (higher entropy) state.
Heat Engine Processes
Heat engine processes are shown on a PV diagram. Besides constant pressure, volume and temperature
processes, a useful process is the adiabatic process where no heat enters or leaves the system.
Heat Engine Processes
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatengcon.html#c1
The Diesel Engine
The diesel internal combustion engine differs from the gasoline powered Otto cycle by using a higher
compression of the fuel to ignite the fuel rather than using a spark plug ("compression ignition" rather
than "spark ignition").
In the diesel engine, air is compressed adiabatically with a compression ratio typically between 15 and
20. This compression raises the temperature to the ignition temperature of the fuel mixture which is
formed by injecting fuel once the air is compressed.
The ideal air-standard cycle is modeled as a reversible adiabatic compression followed by a constant
pressure combustion process, then an adiabatic expansion as a power stroke and an iso-volumetric
exhaust. A new air charge is taken in at the end of the exhaust, as indicated by the processes a-e-a on
the diagram.
Since the compression and power strokes of this idealized cycle are adiabatic, the efficiency can be
calculated from the constant pressure and constant volume processes. The input and output energies
and the efficiency can be calculated from the temperatures and specific heats:
It is convenient to express this efficiency in terms of the compression ratio rv = V1/V2 and the expansion
ratio rE = V1/V3. The efficiency can be written
Now using the ideal gas law PV= n R T and g= CP/CV, this can be written
Now using the fact that Va = Vd = V1 and Pc=Pb from the diagram
Dividing the numerator and denominator by V1Pc
Now making use of the adiabatic condition PVg= constant,
the efficiency can be written
The Otto Engine
cv – Specific Heat constant volume γ – Specific Heat Ratio
p – pressure
T – temperature
V – volume
f – fuel/air ratio
Q – Fuel heating value
Cps –cycles per secomd
P – power
Compression stroke:
Work per cycle:
Engine Power:
Combustion:
Power Stroke:
Ideal Otto Cycle
On the figure we show a plot of pressure versus gas volume throughout one cycle. We have broken the
cycle into six numbered stages based on the mechanical operation of the engine. For the ideal four
stroke engine, the intake stroke (1-2) and exhaust stroke (6-1) are done at constant pressure and do not
contribute to the generation of power by the engine. During the compression stroke (2-3), work is done
on the gas by the piston. If we assume that no heat enters the gas during the compression, we know the
relations between the change in volume and the change in pressure and temperature from our solutions
of the entropy equation for a gas. We call the ratio of the volume at the beginning of compression to the
volume at the end of compression the compression ratio, r. Then
where p is the pressure, T is the temperature, and γ is the ratio of specific heats. During the combustion
process (3-4), the volume is held constant and heat is released. The change in temperature is given by
where Q is the heat released per pound of fuel which depends on the fuel, f is the fuel/air ratio for
combustion which depends on several factors associated with the design and temperature in the
combustion chamber, and Cv is the specific heat at constant volume. From the equation of state, we
know that:
During the power stroke (4-5), work is done by the gas on the piston. The expansion ratio is the
reciprocal of the compression ratio and we can use the same relations used during the compression
stroke:
Between stage 5 and stage 6, residual heat is transferred to the surroundings so that the temperature
and pressure return to the initial conditions of stage 1 (or 2).
During the cycle, work is done on the gas by the piston between stages 2 and 3. Work is done by the gas
on the piston between stages 4 and 5. The difference between the work done by the gas and the work
done on the gas is shown in yellow and is the work produced by the cycle. We can calculate the work by
determining the area enclosed by the cycle on the p-V diagram. But since the processes 2-3 and 4-5 are
curves, this is a difficult calculation. We can also evaluate the work W by the difference of the heat into
the gas minus the heat rejected by the gas. Knowing the temperatures, this is an easier calculation.
The work times the rate of the cycle (cycles per second cps) is equal to the power P produced by the
engine.
The efficiency is:
Combustion of fossil fuel, Using Thermo Utilities, MS Excel Add-ins
A fossil fuel with the following composition by mass:
C 70%; H 18.5%; O 3%; N 4%; S 1.5%; ash 3%
has been burned in a boiler, when 100% excess air is supplied. Combustion efficiency is 0.75 Calculate:
1. the stoichiometric air-to-fuel (A/F) ratio
2. the A/F ratio
3. analysis of combustion products (dry and wet)
4. temperature of exhaust gases
Air is supplied at atmospheric pressure and 18 C with 0.008 specific humidity. The fuel has an average
temperature of 35 C when enters the boiler. Use Dulong formula to estimate the net calorific value of
the fuel. The specific heat capacity of fuel is 3.2 kJ/kg,K.
Combustion Equations
Combustion equation for coal:
C + O2 => CO2 (12 kg C)+(32 kg O) => (34 kg CO2)
Combustion equation for hydrogen:
2 H2 + O2 => 2 H2O (4 kg H)+(32 kg O) => (36 kg H2O)
Combustion equation for sulphur:
S + O2 => SO2 (32 kg S) + (32 kg O) => (64 kg SO2)
Fuel Analysis
.
Constituent
Mass
fraction
.
.
.
Required
oxygen
Product
mass
. kg/kg fuel
kg/kg fuel
Carbon
0,700
1,867
2,567
Hydrogen
0,185
1,480
1,665
Oxygen
0,030
-0,020
0,010
Nitrogen
0,040
0,000
0,040
Sulphur
0,015
0,015
0,030
Ash
0,030
0,000
0,030
. 1,000
3,342
4,342
Analysis of Supplied Air
.
.
.
Specific Humidity
0,008
.
.
Composition by mass
.
.
.
Constituent
Dry Air
Humid Air
.
N2
0,76280
0,75670
.
O2
0,23290
0,23104
.
CO2
0,00300
0,00298
.
Ar
0,00130
0,00129
.
H2O
0,00000
0,00800
.
SO2
0,00000
0,00000
.
. 1,00000
1,00000
.
Air required per kg of fuel 14,46
Stoichiometric kg/kg
A/F ratio
Excess Air
1
.
.
Actual A/F ratio kg/kg
28,92757
.
.
Exhaust Gases
. Wet Mass
Dry Mass
Constituent
Mass
Composition
Composition
N2
21,92942
0,73373
0,78344
O2
3,34167
0,11181
0,11938
CO2
2,65276
0,08876
0,09477
Ar
0,03730
0,00125
0,00133
H2O
1,89642
0,06345
0,00000
SO2
0,03000
0,00100
0,00107
. 29,88757
1,00000
1,00000
Exhaust Gases
.
. Volume
Constituent
Kg/kmol
Mole Fraction
Composition
N2
28
0,02620
0,74260
O2
32
0,00349
0,09901
CO2
44
0,00202
0,05716
Ar
40
0,00003
0,00088
H2O
18
0,00353
0,09990
SO2
64
0,00002
0,00044
0,03529
1,00000
. .
Mass balance
.
.
.
Fuel
1,00000
.
.
Supplied Air
28,92757
.
.
. 29,92757
.
.
. .
.
.
Exhaust Gases
29,88757
.
.
Ash
0,03000
.
.
. 29,91757
.
.
Dulong suggests the following formula for gross calorific value (GCV) of fossil fuels when oxygen content
is less than 10%
GCV = 337 C +1442 (H - O/8) + 93 S
GCV is in (kJ/kg). C, H, O, S are percentages on weight basis for carbon, hydrogen, oxygen and sulphur.
The net calorific value for a constant pressure combustion is:
NCV = GCV - mc * hfg
mc is the mass of condensate per unit quantity of fuel and hfg is the latent heat of steam at 25 degree
Celsius which is 2442 kJ/kg.
Supplied Air Temp.
18
.
.
Fuel Cp
3,2
kJ/(kg.K)
.
Gross Calorific Value, GCV
49866
kJ/kg
.
Net Calorific Value, NCV
49711
kJ/kg
.
Combustion efficiency
0,75
. .
.
.
.
.
. Enthalpy
Mass Flow
m*h
. kJ/kg
kg/s
kJ/s
Supplied Air
38,31
28,93
1108,10
Fuel
64,00
1,00
64,00
Fuel Energy Supplied
49710,80
. .
1,00
37283,10
.
38455,21
Exhaust Gases
1284,94
29,93
38455,21
Exhaust Gases Temp
964,
C
.
Topic group
Topic
Summary
Gasoline fuel system
principles
Gasoline fuel
The properties of gasoline must be balanced to give
satisfactory engine performance over a wide range
of operating conditions including heat, altitude, and
driving patterns. The more effectively liquid gasoline
is changed into vapor, the more efficiently it burns in
the engine.
Gasoline fuel
characteristics
There are several important characteristics of
hydrocarbon based fuels: volatility, octane rating &
energy content. The most important characteristic of
gasoline is its Research Octane Number (RON) or
octane rating, which is a measure of how resistant
gasoline is to premature detonation (knocking). A
range of fuel additives are used to change a fuel's
performance characteristics.
Controlling fuel burn
Detonation is a violent collision of flame fronts in the
cylinder, caused by uncontrolled combustion. The
sudden rise in pressure can cause a knocking sound.
Stoichiometric ratio
Stoichiometric ratio is the air-fuel ratio necessary for
complete combustion.
Air density
The density of air is its mass per unit volume.
Fuel supply system
EFI is a circulation system. A pump draws fuel from
the tank and sends it to solenoid-operated injection
valves, where pressure is maintained by a fuel
pressure regulator. Excess fuel flows back to the tank
through a return line.
Pressure & vacuum
As air pressure is reduced, a vehicle has to reduce
the amount of fuel delivered to the engine to
maintain the correct air-fuel ratio.
Carburetion
A light vehicle under normal conditions needs an airfuel ratio, by mass, of about 15 to 1. By volume,
that's 11000 to 1.
Carburetor system
components
The main components in most carbureted systems
are a float chamber, a venturi, the throttle, idle
circuit, main circuit, a choke and an accelerator
pump.
Carburetor systems
Low speed and idling ports allow the engine to
operate with a low throttle opening before the main
Carburetor operation
system is operating fully.
Carbureted system
components
Metering jets
The main jet size is selected to provide the best
mixture for fuel economy. An extra jet supplies
additional fuel for maximum power.
Accelerating
For acceleration, suddenly depressing the
accelerator delivers extra fuel into the airstream.
Carburetor barrels
A two-stage carburetor has a primary throttle open
only from idle to medium speeds. At higher speeds,
the secondary throttle opens to admit more air-fuel
mixture.
The carburetor
The carburetor atomises the fuel and mixes it with
air, and controls the delivery of the correct mixture
to the engine.
Mechanical fuel pumps
The mechanical fuel pump has a diaphragm
separating two chambers. Moving the diaphragm
down draws fuel into the pumping chamber. A spring
then moves the diaphragm up, forcing fuel from the
pump, into the carburetor.
Electric fuel pumps
An electric fuel pump operates with the ignition
switched on. It can be controlled so that it operates
only if the engine is running.
Tanks & lines
Most fuel tanks are in two parts joined by a weld
around the flanges where the parts fit together.
Baffles make the tank more rigid, prevent surging of
fuel, and ensure fuel is available at the pickup tube.
Fuel lines
The fuel tank is connected to the engine by fuel lines.
A return line may carry excess fuel back to the tank,
to keep fuel system components cool.
Charcoal canister
Charcoal canisters are used in some emission
systems as a means of preventing pollution to the
atmosphere.
Carburetor filters
Carburetor filters are used to prevent particles from
entering the fuel carburetion/injection components.
EFI fuel supply system - EFI principles
principles
Basic EFI principles
EFI systems employ injectors to spray the fuel into
the intake system. An electronic control unit
processes data received from various sensors to
optimize the air fuel mixture at any given moment by
adjusting the amount of fuel injected.
EFI is a pressurised, indirect-injection system with
solenoid-operated injectors. In multi-point injection,
one injector is in each intake manifold runner.
Single-point injection uses one or two injectors in a
carburetor-like throttle-body.
Air supply
The design of the intake system determines how
much air can be drawn into a cylinder at any given
engine RPM. EFI can achieve uniform distribution of
the air delivered to the cylinders.
Air volume
The amount of air entering the engine must be
measured, so that the amount of fuel injected into it
forms a mixture to suit the engine operating
conditions at that time.
Multi-point injection
systems
For any injection duration, if fuel is held at constant
pressure, then, as manifold pressure varies, so does
the amount of fuel delivered. That means fuel
pressure must be held constant above manifold
pressure.
Simultaneous injection
In multi-point injection, the injectors can all be
triggered simultaneously, twice per cycle. In a
throttle-body system, the central injector is normally
triggered on each ignition pulse. With two injectors,
alternate triggering may be used.
Efficient combustion
Adaptive learning is a form of feedback that lets fuel
settings change as components age. The ECU
memorizes its fuel settings for different operating
conditions, and stores them for future use.
EFI fuel supply system - Fuel pumps
components
EFI fuel pumps operate electrically to provide fuel
under pressure to the fuel rail and the injectors.
Fuel filters
EFI fuel filters remove contaminants from the fuel, so
that clean fuel can be supplied to the injectors.
Tanks & lines
Most fuel tanks are in two parts joined by a weld
around the flanges where the parts fit together.
Baffles make the tank more rigid, prevent surging of
fuel, and ensure fuel is available at the pickup tube.
Fuel lines
The fuel tank is connected to the engine by fuel lines.
A return line may carry excess fuel back to the tank,
to keep fuel system components cool.
Fuel rail
The fuel rail supplies fuel to the injectors under
constant pressure.
Fuel pressure regulator
The fuel pressure regulator controls the return of
fuel to the fuel tank, to maintain the pressure in the
fuel rail at a constant value above intake manifold
pressure.
Injectors
Injectors are solenoid-operated valves which deliver
fuel in the form of an atomised spray, into the intake
manifold, or the intake ports.
Tachometric relay
The tachometer indicates engine RPM.
Thermotime switch
The thermotime switch senses engine coolant
temperature, to control the operation of the cold
start injector, during cranking conditions.
EFI sensors
EFI sensors include: wide band oxygen sensors, twin
oxygen sensors, knock sensors, oil deterioration
sensor, exhaust gas recirculation sensors and
switches.
Potentiometer
A potentiometer is a mechanically variable resistor.
Auxiliary air valves
Auxiliary air valves allow additional air to bypass the
throttle plate during cold start, and warm-up
conditions.
Idle speed control devices Idle speed control devices allow the preset idling
speed to be maintained automatically when
additional loads are placed on the engine, during
idling conditions.
Fuel system procedure
Inertia sensors
Inertia sensors shut off the fuel pump in the event of
an accident, to minimize the danger of fuel spillage
from a leak in the system.
Replacing a fuel filter
There are two types of fuel filter: carbureted system
filter and EFI system filter. It is important to follow
the correct procedure for the type of vehicle you are
servicing. The objective of this procedure is to show
you how to remove and replace a fuel filter.