Internal
Solutions Manual
to Accompany
Combustion Engine
Fundamentals
Second Edition
JOHN B. HEYWOOD
Sun Jae Professor of Mechanical Engineering, Emeritus
Massachusetts Institute of Technology
McGraw-Hill Education
TABLE OF CONTENTS
SOLUTIONS MANUAL
PAGE
NOTES AND ACKNOWLEDGMENT ........................................................................... iv
CHAPTER 1 - ENGINE TYPES AND THEIR OPERATION ....................................... 1
CHAPTER 2 - ENGINE DESIGN AND OPERATING PARAMETERS ..................... 6
CHAPTER 3 - THERMOCHEMISTRY OF FUEL-AIR MIXTURES ....................... 21
CHAPTER 4 - PROPERTIES OF WORKING FLUIDS .............................................. 38
CHAPTER 5 - IDEAL MODELS OF ENGINE CYCLES ........................................... 54
CHAPTER 6 - GAS EXCHANGE PROCESSES ......................................................... 80
CHAPTER 7 - MIXTURE PREPARATION IN SI ENGINES..................................... 93
CHAPTER 8 - CHARGE MOTION WITHIN THE CYLINDER .............................. 104
CHAPTER 9 - COMBUSTION IN SPARK-IGNITION ENGINES .......................... 113
CHAPTER 10 - COMBUSTION IN COMPRESSION-IGNITION ENGINES ........... 135
CHAPTER 11 - POLLUTANT FORMATION AND CONTROL ............................... 144
CHAPTER 12 - ENGINE HEAT TRANSFER ............................................................. 155
CHAPTER 13 - ENGINE FRICTION AND LUBRICATION ..................................... 163
CHAPTER 14 - MODELING REAL ENGINE FLOW AND COMBUSTION
PROCESSES (NO PROBLEMS INCLUDED IN THIS CHAPTER)
CHAPTER 15 - ENGINE OPERATING CHARACTERISTICS ................................. 169
iii
Notes
1. The problems in this text vary widely in complexity and time required for solution.
Some are easy, some are much more difficult; most fall in between these extremes.
Some of the problems involve substantial calculations; others do not. Check the
solutions of any problems to be assigned to ensure that the difficulty level and time
requirements are appropriate.
2. Many of the problems in the text require information beyond that given in the
problem statement. This approach is a deliberate choice. In a field such as internal
combustion engines which draws on many disciplines as well as extensive practical
experience, students should be taught that engineering “problems” often need further
definition. Making the appropriate additional assumptions and finding the necessary
additional information is part of the learning process. The answers to these problems
will of course depend to some extent on the additional assumptions and data used.
3. A number of the problems are design problems. These have “better” or “worse”
solutions, but not necessarily a unique or correct solution.
4. A number of the problems ask for estimates of typical or characteristic quantities
which define one or more aspects of engine operation. Use of an appropriate logic and
set of assumptions to obtain the answer, and the approximate magnitude of that
answer are what matters. Alternatives to the solutions given here may be just as
satisfactory.
Acknowledgment
Many of the Sloan Automotive Laboratory’s graduate students assisted in preparing these
problems and solutions. Their valuable assistance is gratefully acknowledged.
iv
Chapter 1
ENGINE TYPES AND THEIR OPERATION
1.1
Piston: Transmit the gas pressure force to the connecting rod; seal the cylinder (with piston
rings); compress the fuel-air mixture prior to combustion; draw in fresh mixture, expel
burned gases (4-stroke cycle).
Connecting rod: Transform the rotating motion of crank to reciprocating motion of piston;
transmit forces from crank to piston and piston to crank.
Crankshaft: Transmit the usable mechanical power; crank throws with connecting rods
convert reciprocating motion of piston to rotating motion.
Cams and camshaft: Open and close the valves (inlet and exhaust) at appropriate times in the
cycle, via the lifters and rocker arms. Camshaft driven off crankshaft.
Valves: Control the flow of gas into and out of the cylinder.
Intake manifold: Direct approximately equal masses of air (and in some cases fuel) to each
cylinder; in SI engines acts as a sub-atmospheric pressure plenum to reduce engine load
below WOT levels.
Exhaust manifold: Collect exhaust gases from individual cylinders and feed to common pipe
which contains muffler (and sometimes catalytic converter).
1.2 Note: piston accelerating towards crankshaft axis.
1
1.3
Spark-ignition Diesel
1. Air enters cylinder; fuel Air drawn in; fuel injection into
injected in intake port, or cylinder just before combustion.
cylinder.
2. Spark-ignition of fuel-air Spontaneous ignition of fuel-air
mixture. mixture in fuel sprays.
3. Load reduced by throttling air Load reduced by reducing fuel
and fuel. injected per cycle: no throttling.
4. Fuel: gasoline. Volatile, does Fuel: distillate oil. Must ignite
not spontaneously ignite easily. easily at high temperatures.
5. Lower compression ratio (~10) Higher compression ratio (15 to
due to knock limits. 22); not knock limited.
6. Lighter construction since Heavier construction; higher
pressure forces lower and less forces and durability more
durability required. important.
1.4
2
1.5
1. Differences between spark-ignition (SI) engines and diesel engines
Standard automobile SI engine Truck diesel engine
(a) Where the fuel is Liquid gasoline is injected into the Fuel is injected directly into the cylinder
injected and why intake port. Fuel then vaporizes off (or into a prechamber which is connected
the port and valve walls flowing to the cylinder for indirect injection
into the cylinder largely as vapor engines), just before (some 5 CAD) the
when the engine is warmed-up. A desired start of combustion. High
homogeneous charge (air, fuel and pressure injection produces small, high
burned residual) in the cylinder velocity fuel droplets which vaporize
results. rapidly in the sprays.
(b) How the load is varied The air-fuel ratio (AFR) is held The air flow is held constant (no throttle)
at fixed speed constant at close to the in a naturally aspirated engine, and only
stoichiometric value. Thus both air the fuel flow is varied to vary torque. In
and fuel flows are varied (air flow TC engines, boost level varies with load.
is regulated by a throttle and fuel
flow by injector pulse width).
(c) How the combustion The charge is ignited by a spark- Spontaneous ignition occurs shortly after
process starts, develops, discharge-created hot gas kernel. A start of injection, as the injected fuel
and ends premixed flame forms around this, atomizes, vaporizes and mixes with high
propagates across the chamber as a temperature air. Rapid chemical energy
turbulent flame, and extinguishes release then occurs in fuel already mixed
at the cylinder walls. with air. A diffusion flame then develops
around each fuel spray as fuel continues
to mix with air, until all fuel is consumed.
(d) How the fuels are Gasoline: sufficiently volatile to Distilled oil: less volatile than gasoline.
different and why vaporize in the intake port. Resists Needs rapid spontaneous ignition
spontaneous ignition (onset of characteristics (to auto-ignite at high
knock) well. pressures and temperatures in the absence
of a spark).
(e) How the in-cylinder See diagram See diagram
pressure varies as a
function of crank angle
3
1.6 Intake and exhaust strokes of four-stroke cycle are much more effective at removing
the burned gases from the cylinder and filling the cylinder volume with fresh fuel-air mixture
than is two-stroke cycle scavenging process. Hence, full load four-stroke cycle cylinder
pressures are substantially higher than two-stroke cycle pressures. Also, power is required to
boost scavenging air (mixture) pressure prior to entry to cylinder.
1.7 (1) With multicylinder engine, more firing strokes per crank revolution hence
smoother output torque versus time.
(2) Forces on each piston, connecting rod, etc. reduced with multicylinder engine.
(3) Inertia forces that result from the acceleration and deceleration of piston (and
connecting rod) reduced and with suitable arrangement of crank throws can be balanced so
there is no (or only small) net inertia force. Reduces engine vibration, problems substantially.
(4) For a given displacement, the more cylinders the higher the engine’s maximum
power. Smaller size cylinders have higher maximum engine speed before intake flow choking
occurs: so engine maximum power is increased.
(5) Packaging the engine into a vehicle is easier with multicylinder engines with
more, but smaller cylinders.
4
1.8 (a) Currently, competing “prime movers” are the diesel compression-ignition engine,
the gasoline-electric hybrid and the battery-powered all-electric vehicle. Variations in the
fuels used exist such as alcohol (ethanol, methanol) in SI engines and biodiesel, often blended
with gasoline and diesel fuel, respectively. Other alternative fuels options are: natural gas,
LPG, and hydrogen, in SI engines.
(b) Diesel engines are normally more robust and achieve a better fuel economy due to
their higher efficiency. Their current problem is their air pollutant emissions: due to the
complexity of the NOx and particulates after-treatment emission reduction technologies,
these as yet have not been sufficiently developed. All-electric vehicles don’t have this vehicle
emissions problem, but due to their power source (batteries), they are range limited and have
long recharging times. They are currently more expensive. Gasoline – electric hybrids have
been growing in popularity, and for a reason. They combine the best of both worlds,
achieving lower emissions and higher fuel economy. They are still more expensive. Fuels
such as ethanol or biodiesel are good supplements to traditional fuels; they are starting to be
used in the U.S., and elsewhere. Price, availability, and sources for their production, are all
factors currently affecting the scale of their use.
(c) The most important factors for me “would be price of the fuel, fuel economy,
price of the car, and performance. “I definitely like smooth driving, high performance cars,
and I would be willing to pay for that.” Remember size scales with weight, so bigger vehicles
have worse fuel consumption. “A gasoline-electric hybrid would be my choice.”
