(1) Fluid mechanics

sisterpurpleMechanics

Oct 24, 2013 (3 years and 7 months ago)

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5 MARKS


(1)

Fluid mechanics

Fluid mechanics

is the branch of

physics

that studies

fluids

(
liquids
,

gases
, and

plasmas
) and
the

forces

on them. Fluid mechanics can be divided into

fluid statics
, the study of fluids at rest;
fluid

kinematics
, the study of fluids in motion; and

fluid dynamics
, the study of the effect of
forces on fluid motion. It is a branch of

continuum mechanics
, a subject which models matter
without using the information that it is made out of atoms, that is, it models matter from a
macroscopic viewpoint rather than from a microscopic viewp
oint. Fluid mechanics, especially
fluid dynamics, is an active field of research with many unsolved or partly solved problems.
Fluid mechanics can be mathematically complex. Sometimes it can best be solved
by numerical
,
typically using computers. A modern
discipline, called

computational fluid dynamics

(CFD), is
devoted to this approach to solving fluid mechanics problems. Also taking advantage of the

highly visual nature of fluid flow is

particle image velocimetry
, an experimental method for
visualizing and analyzing fluid flow.

(2)

Assumptions

Like

any mathematical model of the real world, fluid mechanics makes some basic assumptions
about the materials being studied. These assumptions are turned into equations that must be
satisfied if the assumptions are to be held true.

For example, consider an f
luid in three dimensions. The assumption that mass is conserved
means that for any fixed

control volume

(for example a sphere)


enclosed by a

control
surface



the

rate of change

of the mass contained is equal to the rate at which mass is pass
ing
from

outside

to

inside
through the surface, minus the rate at which mass is passing the other
way, from

inside

to

outside
. (A special case would be when the mass

inside

and the
mass

outside

remain constant). This can be turned into an

equation in integral form

over the
control volume.
[1]


Fluid mechanics assumes that eve
ry fluid obeys the following:



Conservation of mass



Conservation of en
ergy



Conservation of momentum



The

continuum hypothesis
, detailed below.

Further, it is often useful (at

subsonic

conditions) to assume a fluid is

incompressible



that is,
the density of the fluid does not change.

Similarly, it can sometim
es be assumed that the

viscosity

of the fluid is zero (the fluid
is

inviscid
). Gases can often be assumed to be inviscid. If a fluid is viscous, and its flow
contained in some way (e.g.
in a

pipe
), then the flow at the boundary must have zero velocity.
For a viscous fluid, if the boundary is not porous, the shear forces between the fluid and the
boundary res
ults also in a zero velocity for the fluid at the boundary. This is called the

no
-
slip
condition
. For a porous media otherwise, in the frontier of the containing vessel,
the slip
condition is not zero velocity, and the fluid has a discontinuous velocity field between the free
fluid and the fluid in the porous media (this is related to the

Beavers and Joseph condition
).

[
edit
]
Con
tinuum hypothesis

Main article:

Continuum mechanics

Fluids are composed of

molecules

that collid
e with one another and solid objects. The
continuum assumption, however, considers fluids to be

continuous
. That is, properties such as
density, pressure, temperature
, and velocity are taken to be well
-
defined at "infinitely" small
points, defining a REV (Reference Element of Volume), at the geometric order of the distance
between two adjacent molecules of fluid. Properties are assumed to vary continuously from
one poi
nt to another, and are averaged values in the REV. The fact that the fluid is made up of
discrete molecules is ignored.

The continuum hypothesis is basically an approximation, in the same way planets are
approximated by point particles when dealing with ce
lestial mechanics, and therefore results in
approximate solutions. Consequently, assumption of the continuum hypothesis can lead to
results which are not of desired accuracy. That said, under the right circumstances, the
continuum hypothesis produces extre
mely accurate results.

Those problems for which the continuum hypothesis does not allow solutions of desired
accuracy are solved using

statistical mechanics
. To d
etermine whether or not to use
conventional fluid dynamics or statistical mechanics, the

Knudsen number

is evaluated for the
problem. The Knudsen number is defined as the ratio

of the molecular

mean free path

length to
a certain representative physical length

scale
. This le
ngth scale could be, for example, the
radius of a body in a fluid. (More simply, the Knudsen number is how many times its own
diameter a particle will travel on average before hitting another particle). Problems with
Knudsen numbers at or above

unity

are best evaluated using statistical mechanics for reliable
solutions.

(3)

Altitude

Altitude

or

height

is defined based on the context in which it is used (aviation, geometry,
geographical
survey, sport, and more). As a general definition, altitude is a distance
measurement, usually in the vertical or "up" direction, between a reference

datum

and a point
or objec
t. The reference datum also often varies according to the context. Although the term
altitude is commonly used to mean the height above sea level of a location, in

geography

the
term eleva
tion is often preferred for this usage.

Vertical distance measurements in the "down" direction are commonly referred to as

depth

Altitude in aviation and in spacefligh

Vertical Distance Comparison

In aviation, the term altitude can have several meanings, and is always qualified by either
explicitly
adding a modifier (e.g. "true altitude"), or implicitly through the context of the
communication. Parties exchanging altitude information must be clear which definition is being
used.
1

Aviation altitude is measured using either Mean Sea (MSL) or local ground level (Above Ground
Level, or AGL) as the reference datum.

Pressure altitude

divided by 10
0 feet (30m) as the

flight level
, and is used above the

transition
altitude

(18,000 feet (5,50
0

m) in the US, but may be as low as 3,000 feet (910

m) in other
jurisdictions); so when the altimeter reads 18,000

ft on the standard pressure setting the
aircraft is said to be at "Flight level 180". When flying at a Flight Level, the altimeter is always

set to standard pressure (29.92

inHg

/ 1013.25

mbar
).

On the flight deck, the definitive instr
ument for measuring altitude is the pressure

altimeter
,
which is an

aneroid barometer

with a fro
nt face indicating distance (feet or metres) instead
of

atmospheric pressure
.

There are several types of aviation altitude:



Indicated altitude

is the reading on the a
ltimeter when the altimeter is set to the

local
barometric pressure at Mean Sea Level.



Absolute altitude

is the height of the aircraft above the terrain over which it is flying.
Also referred to feet/
metres

above ground level

(AGL).



True altitude

is the actual elevation above

mean sea level
.

It is Indicated Altitude
corrected for non
-
standard temperature and pressure. In UK aviation radiotelephony
usage,

the vertical distance of a level, a point or an object considered as a point, measured
from mean sea level
; this is referred to over the rad
io as

altitude
.(see

QNH
)
2



Height

is the elevation above a ground reference point, commonly the terrain elevation.
In UK avia
tion radiotelephony usage,

the vertical distance of a level, a point or an object
considered as a point, measured from a specified datum
; this is referred to over the radio
as

height
, where the specified datum is the airfield elevation (see

QFE
)
2



Pressure altitude

is the elevation above a standard datum air
-
pressure plane (typically,
1013
.25 millibars or 29.92" Hg and 15 °C). Pressure altitude and indicated altitude are the
same when the altimeter is set to 29.92" Hg or 1013.25 millibars.



Density altitude

is
the altitude corrected for non
-
ISA

International Standard
Atmosphere

atmospheric conditions. Aircraft performance depends on density altitud
e,
which is affected by barometric pressure, humidity and temperature. On a very hot day,
density altitude at an airport (especially one at a high elevation) may be so high as to
preclude takeoff, particularly for helicopters or a heavily loaded aircraft.


20 MARKS

(1)

Numerical analysis

Babylonian clay tablet YBC 7289 (c. 1800

1600 BC) with annotations. The approximation of
the
square

is four

sexagesimal

figures, which is about six

decimal

figures. 1 + 24/60 + 51/60
2

+
10/60
3

= 1.41421296...
[1]

Numerical analysis

is the study of

algorithms

that use numerical

approximation

(as opposed to
general

symbolic manipulations
) for the problems of

mathematical analysis

(as distinguished
from

discrete mathematics
).

One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian
Collection (
YBC 7289), which gives a sexagesimal numerical approximation of

, the length of
the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being
able to compute square r
oots) is extremely important, for instance, in carpentry and
construction.
[2]

Numerical analysis continues this long tradition of practical mathematical calculations. Much
like

the Babylonian approximation of

, modern numerical analysis does not seek exact
answers, because exact answers are often impo
ssible to obtain in practice. Instead, much of
numerical analysis is concerned with obtaining approximate solutions while maintaining
reasonable bounds on errors.

Numerical analysis naturally finds applications in all fields of engineering and the physical

sciences, but in the 21st

century, the life sciences and even the arts have adopted elements of
scientific computations.

Ordinary differential e
quations

appear in the

movement of heavenly
bodies (planets, stars and galaxies)
;

optimization

occurs in portfolio management;

numerical
linear algebra

is important for data analysis;

stochastic differential equations

and

Markov
chains

are essential in simulating living cells for me
dicine and biology.

Before the advent of modern computers numerical methods often depended on
hand

interpolation

in large printed tables. Since the mid 20th century, computers ca
lculate the
required functions instead. These same interpolation formulas nevertheless continue to be
used as part of the software

algorithms

for solving

differential equations
.

The overall goal of the field of numerical analysis is the design and analysis of techniques to
give approximate but accurate solutions to hard problems, the variety
of which is suggested by
the following.



Advanced numerical methods are essential in making

numerical weather
prediction

feasible.



Computing the traj
ectory of a spacecraft requires the accurate numerical solution of a
system of

ordinary differential equations
.



Car companies can improve the cr
ash safety of their vehicles by using computer
simulations of car crashes. Such simulations essentially consist of solving

partial
differential equ
ations
numerically.



Hedge funds

(private investment funds) use tools from all fields of numerical analysis to
calculate the value of stocks and derivatives more precisely than other ma
rket
participants.



Airlines use sophisticated optimization algorithms to decide ticket prices, airplane and
crew assignments and fuel needs. This field is also called

operations research
.



Insurance companies use numerical programs for

actuarial

analysis.

The rest of this section outlines several important themes of numerical analysis.



(2)

Differential
equation

Visualization of heat transfer in a pump casing, created by solving the

heat equation
.

Heat

is
being generate
d internally in the casing and being cooled at the boundary, providing a

steady
state

temperature distribution.

A

differential equation

is a

mathematical

equation

for an unknown

function

of one or
s
everal

variables

that relates the values of the function itself and its

derivatives

of v
arious
orders. Differential equations play a prominent role in

engineering
,

physics
,

economics
, and
other disciplines.

Differential equations arise in many areas of science and technology, specifically whenever
a

deterministic

relation involving some continuously varying quantities (modeled by functions)
and their rates of change in space and/or time (expressed as derivatives) is known or
postulated. This is illustrated in
classical mechanics
, where the motion of a body is described by
its position and velocity as the time value varies.

Newton's laws

allow one (given the position,
velocity, acceleration and various forces acting on the body) to express these variables
dynamically as a differential equation for the unknown position of the body as a fun
ction of
time. In some cases, this differential equation (called an

equation of motion
) may be solved
explicitly.

An example of modelling a real world problem using d
ifferential equations is the determination
of the velocity of a ball falling through the air, considering only gravity and air resistance. The
ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration
due to air resis
tance. Gravity is considered constant, and air resistance may be modeled as
proportional to the ball's velocity. This means that the ball's acceleration, which is a derivative
of its velocity, depends on the velocity. Finding the velocity as a function of
time involves
solving a differential equation.

Differential equations are mathematically studied from several different perspectives, mostly
concerned with their solutions

the set of functions that satisfy the equation. Only the
simplest differential equa
tions admit solutions given by explicit formulas; however, some
properties of solutions of a given differential equation may be determined without finding their
exact form. If a self
-
contained formula for the solution is not available, the solution may be
numerically approximated using computers. The theory of

dynamical systems

puts emphasis on
qualitative analysis of systems described by differential equations, while many

numerical
methods

have been developed to determine solutions with a given degree of accuracy.


The study of differential equations is a wide field in

pure

and

applied
mathematics
,

physic
s
,

meteorology
, and

engineering
. All of these disciplines are concerned
with the properties of differential

equations of various types. Pure mathematics focuses on the
existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous
justification of the methods for approximating solutions. Differential equations play an
important role in

modelling virtually every physical, technical, or biological process, from
celestial motion, to bridge design, to interactions between neurons. Differential equations such
as those used to solve real
-
life problems may not necessarily be directly solvable,

i.e. do not
have

closed form

solutions. Instead, solutions can be approximated using

numerical methods
.

Mathematicians also study

weak solutions

(relying on

weak derivatives
), which are types of
solutions that do not have to be

differentiable

everywhere. This extension is often necessary
for solu
tions to exist, and it also results in more physically reasonable properties of solutions,
such as possible presence of shocks for equations of hyperbolic type.

The study of the stability of solutions of differential equations is known as

stability theory


examples

In the first group of examples, let

u

be an unknown function of

x
, and

c

and

ω

are known
constants.

Inhomogeneous first
-
order linear constant coefficient ordinary differential equation:


Homogeneous seco
nd
-
order linear ordinary differential equation:


Homogeneous second
-
order linear constant coefficient ordinary differential eq
uation
describing the

harmonic oscillator
:


Inhomogeneous first
-
order nonlinear ordinary differential equation:


Second
-
order nonlinear ordinary differential equa
tion describing the motion of a

pendulum

of
length

L
:


In
the next group of examples, the unknown function

u

depends on two
variables

x

and

t

or

x

and

y
.

Homogeneous first
-
order linear partial differential equation:


Homogeneous second
-
order linear constant coefficient partial differential equation of elliptic
type, the

Laplace equation
:


Third
-
order nonlinear partial differential equation, the

Korteweg

de Vries equation
:



(3)

Bypass ratio

Schematic turbofan engines; the high
-
bypass engine
(middle) has a large fan that routes much
air around the turbine, the low
-
bypass engine (upper) has a smaller fan routing more air into
the turbine; turbojets (bottom) have zero bypass, all air goes through the turbine

The bypass air is shown in pink, whil
st the core gases are shown in red.

The term

bypass ratio (BPR)

relates to the design of

turbofan

engines, commonly used
in

aviation
. It is defined as the ratio between the mass flow rate of air drawn through a fan disk
which bypasses the engine core (un
-
combusted air), to the mass flow rate passing through the
engine core which is involved in

combustion

to produce

mechanical energy
. For example, with a
10:1 bypass ratio, for every 1

kg of air passing through the combus
tion chamber, 10

kg of air
passes

around

the combustion chamber through the ducted fan alone.

In a

high
-
bypass

design, the vast majority of the thrust is derived from the ducted fan, rather
than from combustion gases expanding in a nozzle.
1

A high bypass ratio provides a lower

thrust
specific fuel consumption

(grams/sec

fuel per unit of thrust in kN using

SI units
) for reasons
explained below, especially at zero velocity (at takeoff) and at the cruise speed of most
commercial jet aircraft. They are by fa
r the dominant type for all commercial passenger aircraft
and both civilian and military jet transports. Lower exhaust velocities also figure strongly in
lower noise output which is a decided advantage over earlier low or zero bypass designs.
2

Low bypass

ratios tend to be favored for military combat aircraft as a compromise between
improved fuel economy and the requirements of combat, which values higher

power
-
to
-
weight
ratios
, supersonic performance, and the ability to use
afterburners

which are more compatible
with l
ow bypass engines. A good example of the differences between a pure jet engine and a
low
-
bypass turbofan may be seen in the

Spey turbofan

used in the

F
-
4 Phantom
.

Principles

In a

gas turbine

engine, the

stoichiometry

of the fuel
-
air mixture is limited to a fairly narrow
range, with a tendency to a "leaner" fuel mixture to limit the m
aximum temperatures in the
engine. In a pure (zero
-
bypass) jet engine, the majority of the thrust occurs from the high
temperature and high pressure exhaust gas being accelerated by expansion through
a

propelling nozzle

(the lesser part of the thrust is obtained by accelerating air in the
compressor stage). Note that in a zero
-
bypass engine all the air taken in is involved in
combustion. In a pure jet engine the net mechan
ical energy produced by the compressor
-
turbine system is essentially zero, i.e. all the mechanical energy produced by the turbine is
consumed in the compressor stage. In a design featuring bypass, the gas turbine component (or
engine core) is designed to p
roduce a large net positive power output, i.e. the turbine now
produces far more power than the compressor consumes. This excess power is used to drive
a

ducted fan

to accelerate air f
rom the front of the engine rearwards. Turbofan engines are
closely related to
turbo
-
prop

designs in concept, since both designs de
-
couple the gas turbine
engines' shaft horsepower from

their exhaust velocities. Turbofans represent an intermediate
stage between

turbojets
, which derive almost all their thrust from exhaust gases, and turbo
-
props which derive minimal thrust

from exhaust gases (typically 10% or less). When a gas
turbine engine is optimized for shaft power output, the exhaust pressure and temperature are
minimized for maximum

thermal efficiency
within the limits of a

Brayton cycle

engine. This is in
contrast to pure jet designs where a high pressure and temperature are required features to
allow thr
ust derived by expansion through a nozzle. Note that in a bypass design there are
actually two exhaust velocities, one passing through the core (combustion air) and air passing
through the ducted fan alone (since in reality, most designs pass combustion ai
r through the
ducted fan

first

before passing into the compressor stage). In a high
-
bypass design, the vast
majority of the thrust is derived from the ducted fan, rather than from combustion gases
expanding in a nozzle.
3

Description

Turbojet

eng
ines are relatively inefficient as Brayton cycle engines, since it is not their function
to provide mechanical power, but instead to provide direct propulsive thrust through
expanding combustion gases in a nozzle. In fact the conventional units of power me
asurement
for a turbojet engine are in pounds force or kilo Newtons, unlike propeller aircraft (including
turboprops) which are measured in horsepower or kilo
-
watts. Turbojets convert the thermal
energy from combustion directly into kinetic energy in the f
orm of a high
-
velocity reaction jet.
Turbofans, on the other hand, are very efficient Brayton cycle engines. In a turbofan, the gas
turbine is optimized to convert as much of the thermal energy from combustion as possible into
mechanical shaft power. The e
ssential difference between a turbojet and turbofan gas turbine
is that the turbine stage in a turbojet is designed to extract only a

fraction

of the available
thermal energy in the high pressure and temperature exhaust, producing only enough
mechanical en
ergy to run the compressor stage as a net
-
zero mechanical energy system
(ignoring very small mechanical outputs to run auxiliary equipment such as generators) and
leaving a relatively high temperature and

back pressure

exhaust at the turbine exit for
effective

reaction propulsion
. The gas turbine on a turbofan has additional turbine disks and
stators
, sufficient to convert most of the available thermal energy into mechanical work, leaving
an exhaust plume of greatly reduced temperature, pressure, and velocity. The back pressure at
the turbine exit for a high bypass turbofan should be close to

ambient pressure

to allow for
maximum energy extraction, but at the loss of direct jet propulsive efficiency (which is far more
than compensated for by the increased thrust derived

from the ducted fan).

Only the limitations of weight and materials (e.g. the strengths and melting points of materials
in the turbine), prevent the maximum amount of energy being extracted by a turbofan gas
turbine. Note that while the exhaust gases may s
till have available energy to be extracted, there
is a point of

diminishing returns

where each additional stator and turbine disk retrieves
progressively less mechani
cal energy per unit of increased weight added. Alternately, increasing
the

compression ratio

of the system, by adding to the compressor stage, can increase overall
system

efficiency at the cost of higher temperatures at the turbine face (the maximum
operating temperature of the turbine disk being the limiting factor). Stated concisely, a high
bypass turbofan engine may be characterized as a system of two parts: a gas turbi
ne optimized
to convert the maximum amount of thermal energy from combustion into mechanical energy,
and a ducted fan to use the mechanical power to move a large amount of air through a
relatively small change in velocity.

The physics of

propulsive efficiency

may be stated succinctly as follows. For any given amount
of available energy (thermal and mechanical), thrust is optimized by moving the maximum mass
flow at

the minimum difference in inlet and exhaust velocities. This can be explained by the
relationships in an action
-
reaction propulsion system (which an air
-
breathing jet engine is an
example), thrust is calculated by multiplying the mass flow (in kg/s) by th
e difference between
the inlet and exhaust velocities (in m/s), which is a

linear

relationship. Whereas the

kinetic
energy

of the exhaust is the same mass flow (kg/s) multiplie
d by one
-
half the

square

of the
difference in velocities. By mechanically moving a very large volume (and consequently mass) of
air through a relatively small difference in velocity produces a relatively small change in kinetic
energy for a very large chan
ge in momentum and thrust.

Rolls

Royce

came up with a better use of the extra energy in their

Conway

turbofan

engine,
developed in the early 1950s. In the Conway, an otherwise normal

axial
-
flow turbojet

was
equipped with an oversized first compressor stage (the one closest to the front of the engine),
and centered inside a tubular

nacelle

(in effect, a

ducted fan

arrangement). While the inner
portions of the compressor worked "as normal" and provided air into the core of the engine,
the outer portion blew air around the engine to provide extra
thrust. The Conway had a very
small bypass ratio of only 0.3, but the improvement in fuel economy was notable; as a result, it
and its derivatives like the

Spey

became some

of the most popular jet engines in the world.

Through the 1960s the bypass ratios grew, making

jetliners

competitive in fuel terms with
piston
-
powered planes for the first time. M
ost of the very
-
large engines in this class were
pioneered in the United

by both

Pratt & Whitney

and

General Electric
, which for the first time
was out
-
competing the

United Kingdom

in engine design.

Rolls
-
Royce

also started the
development of the high
-
bypass turbofan, and although it caused considerable trouble at the
time, the

RB.211

would

go on to become one of their most successful products.

Today, almost all jet engines include some amount of bypass. For lower speed operations, such
as airliners, modern engines use bypass ratios up to 17, while for higher speed operations such
as

fighter aircraft

the ratios are much lower, around 1.5; and around 0
-
0.5 for speeds up to
Mach 2 and somewhat above. For flights consisting mostly of extended supersonic cruise at

Mach 2, having no bypass at all was found to be optimal on both

Concorde

and

Tu
-
144

due to
reduction in inlet drag.

(4)

Com
bustion

"Burning" redirects here. For combustion without external ignition, see

spontaneous
combustion
. For the vehicle engine, see

internal combustion engine
. For other uses,
see

Burning (disambiguation)

and

Combustion (disambiguation)
.

The

flames

caused as a result of a
fuel

undergoing combustion (burning)

Combustion

(

/
k
ə
m
ˈ
b
ʌ
s
.
t
ʃ
ə
n
/
) or

burning

is the sequence of

exothermic

chemical reactions
between a

fuel

and an

oxidant

accompanied by the production of

heat

and conversion of
chemical species. The release of heat can result in the production of

light

in the form of
either

glowing

or a

flame
. Fuels of interest often include organic compounds
(especially

hydrocarb
ons
) in the gas,

liquid

or solid phase.

In a complete combustion reaction, a compound reacts with an oxidizing element, such
as

oxygen

or

fluorine
, and the products are compounds of each element in the fuel with the
oxidizing element. For example:

CH
4

+ 2

O
2



CO
2

+ 2 H
2
O + energy

A simple example can be seen in t
he combustion of

hydrogen

and

oxygen
, which is a commonly
used reaction in

rocket engines
:

2

H
2

+

O
2

→ 2 H
2
O(g) + heat

The result is

water

vapor.

Complete combustion is almost impossible to achieve. In reality, as actual combustion reactions
come to

equilibrium
, a wide variety of major and minor species will be present such as

carbon
monoxide

and pure

carbon

(
soot

or ash). Additionally, any combustion in

atmospheric

air
,
which is 78%

nitrogen
, will also create several forms of

nitr
ogen oxides
.

Types

Complete vs. incomplete

In complete combustion, the reactant burns in oxygen, producing a limited number of products.
When a

hydrocarbon

burns in oxygen, the reaction w
ill only yield carbon dioxide and water.
When elements are burned, the products are primarily the most common oxides. Carbon will
yield

carbon dioxide
, nitrogen will yield

nitrogen dioxide
, sulfur will yield

sulfur dioxide
, and iron
will yield
iron(III) oxide
.

Combustion is not necessarily favorable to the maximum degree of oxidation and it can be
temperature
-
dependent. For example,

sulfur trioxide

is not produced quantitatively in
combustion of sulfur. Nitrogen oxides start to form above

2,800 °F

(1,540

°C)

and more nitrogen
oxides are produced at higher temperatures. Below this temperature, molecular nitroge
n (N
2
) is
favored. It is also a function of oxygen excess.
1

In most industrial applications and in

fires
,

air

is the source of oxygen (O
2
). In air, each mole of
oxygen is mixed with approximately 3.76

mole of

nitrogen
. Nitrogen does not take part in
com
bustion, but at high temperatures, some nitrogen will be converted to

NO
x
, usually
between 1% and 0.002% (2 ppm).
2

Furthermore, when there is any incomplete combustion,
some of carbon is converted to

carbon monoxide
. A more complete set of equations for
combustion of methane in air is
therefore:

CH
4

+ 2

O
2



CO
2

+ 2 H
2
O

2

CH
4

+ 3

O
2

→ 2

CO

+ 4 H
2
O

N
2

+

O
2

→ 2

NO

N
2

+ 2

O
2

→ 2

NO
2

Incomplete

Incomplete combustion will only occur when there
is not enough oxygen to allow the fuel to
react completely to produce carbon dioxide and water. It also happens when the combustion is
quenched by a heat sink such as a solid surface or flame trap.

For most fuels, such as diesel oil, coal or wood,

pyrolysis

occurs before combustion. In
incomplete combustion, products of pyrolysis remain unburnt and contaminate the smoke with
noxious particulate matter and gases. Partially oxidized compoun
ds are also a concern; partial
oxidation of ethanol can produce harmful

acetaldehyde
, and carbon can produce toxic

carbon
monoxide
.

The quality of combustion can be improved by design of combustion devices, such
as

burners

and

internal combustion engines
. Further improvements are achievable
by

catalytic

after
-
burning devices (such as

catalytic converters
) or by the simple partial return of
the

exhaust gases

into the combustion process. Such devic
es are required by

environmental
legislation

for cars in most countries, and may be necessary in large combustion devices, such
as

thermal power plants
, to reach legal

emission standards
.

The degree of combustion can be measured a
nd analyzed, with test
equipment.

HVAC

contractors,

firemen

and

engineers

use combustion analyzers to test
the

efficiency

of a burner during the combustion process. In addition, the efficiency of an
internal combustion engine
can be measured in this way, and some states and local
municipalities are using combustion analysis to define and rate the efficiency of vehicles on the
road today.

Smoldering

Smoldering

is the slow, low
-
temperature, flameless form of combustion, sustained by the heat
evolved when oxygen directly attacks the surface o
f a condensed
-
phase fuel. It is a typically
incomplete combustion reaction. Solid materials that can sustain a smoldering reaction include
coal, cellulose, wood, cotton, tobacco, peat, duff, humus, synthetic foams, charring polymers
including polyurethane
foam, and dust. Common examples of smoldering phenomena are the
initiation of residential fires on upholstered furniture by weak heat sources (e.g., a cigarette, a
short
-
circuited wire), and the persistent combustion of biomass behind the flaming front of
wildfires

Rapid

Container of ethanol vapour mixed with air, undergoing rapid combustion

Rapid combustion is a form of combustion, otherwise
known as a

fire
, in which large amounts
of heat and

light

energy are released, which often results in a

flame
. This is used in a form of
machinery such as

internal combustion engines

and in

thermobaric weapons
. Sometimes, a
large volume of gas is liberated in combustion besides the production of heat and light. The
sudden evolution of large quantities of gas creates excessive pressure that

produces a loud
noise. Such a combustion is known as an

explosion
. Combustion need not involve oxygen; e.g.,
hydrogen burns in chlorine to form hydrogen chloride with the liberation of
heat and light
characteristic of combustion.

Turbulent

Combustion resulting in a turbulent flame is the most used for industrial applica
tion (e.g. gas
turbines, gasoline engines, etc.) because the turbulence helps the mixing process between the
fuel and oxidizer.

Micro
gravity

Colourized gray
-
scale composite image of the individual frames from a video of a backlit fuel
droplet burning in microgravity.

Combustion processes behave differently in a

microgravity environment

than in Earth
-
gravity
conditions due to the lack of

buoyancy
. For example, a candle's flame takes the shape of a
sphere.
3

Microgravity combustion research contributes to understanding of spacecraft fire
safety and diverse aspects of combustion physics.

Micro combustion

Combustion processes which happen in very small volume are considered as

micro
combustion
.

Quenching

distance plays a vital role in stabilizing the flame in such combustion
chambers.

Chemical equation

Generally, the

chemical equation

for

stoichiome
tric

burning of

hydrocarbon

in oxygen is


For examp
le, the burning of

propane

is


Generally, the

chemical equation

for

stoichiometric

incomplete combustion of

hydrocarbon

in
oxygen is as follows:


For example, th
e incomplete combustion of

propane

is:


The simple word equa
tion for the combustion of a hydrocarbon in oxygen is:


If the combustion takes place using air as the oxygen source, the nitr
ogen can be added to the
equation,as and although it does not react, to show the composition of the flue gas:


For example, th
e burning of

propane

is:


The simple word equation for this
type of combustion is hydrocarbon in air:


Nitrogen may also oxidize when there is an excess of oxygen. The reaction is
thermo
dynamically favored only at high temperatures.

Diesel engines

are run with an excess of
oxygen to combust small particles that tend to form with only a stoichiometric amount of

oxygen, necessarily producing nitrogen oxide emissions. Both the United States and European
Union are planning to impose limits to nitrogen oxide emissions, which necessitate the use of a
special

catalytic converter

or treatment of the exhaust with

urea
.