Unit-1 AIRCRAFT GAS TURBINES Impulse and reaction blading of gas turbines – Velocity triangles and power output – Elementary theory – Vortex theory – Choice of blade profile, pitch and chord – Estimation of stage performance – Limiting factors in gas turbine design- Overall turbine performance – Methods of blade cooling – Matching of turbine and compressor – Numerical problems. Axial and radial flow turbines As with the compressor, there are two basic types of turbine—radial flow and axial flow. The vast majority of gas turbines employ the axial flow turbine. The radial turbine can handle low mass flows more efficiently than the axial flow machine and has been widely used in the cryogenic industry as a turbo-expander, and in turbochargers for reciprocating engines. Although for all but the lowest powers the axial flow turbine is normally the more efficient, when mounted back-to-back with a centrifugal compressor the radial turbine offers the benefit of a very short and rigid rotor. This configuration is eminently suitable for gas turbines where compactness is more important than low fuel consumption. Auxiliary power units for aircraft (APUs), generating sets of up to 3 MW, and mobile power plants are typical applications. Impulse and Reaction Turbine www.Vidyarthiplus.com www.Vidyarthiplus.com
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Unit-1
AIRCRAFT GAS TURBINES
Impulse and reaction blading of gas turbines – Velocity triangles and power output – Elementary
theory – Vortex theory – Choice of blade profile, pitch and chord – Estimation of stage
performance – Limiting factors in gas turbine design- Overall turbine performance – Methods of
blade cooling – Matching of turbine and compressor – Numerical problems.
Axial and radial flow turbines
As with the compressor, there are two basic types of turbine—radial flow and axial flow. The
vast majority of gas turbines employ the axial flow turbine.
The radial turbine can handle low mass flows more efficiently than the axial flow machine and
has been widely used in the cryogenic industry as a turbo-expander, and in turbochargers for
reciprocating engines. Although for all but the lowest powers the axial flow turbine is normally
the more efficient, when mounted back-to-back with a centrifugal compressor the radial turbine
offers the benefit of a very short and rigid rotor. This configuration is eminently suitable for gas
turbines where compactness is more important than low fuel consumption. Auxiliary power units
for aircraft (APUs), generating sets of up to 3 MW, and mobile power plants are typical
applications.
Impulse and Reaction Turbine
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Work can be extracted from a gas at a higher inlet pressure to the lower back pressure by
allowing it to flow through a turbine. In a turbine as the gas passes through, it expands. The work
done by the gas is equivalent to the change of its enthalpy.
It is a well known fact that the turbines operate on the momentum principle. Part of the energy of
the gas during expansion is converted into kinetic energy in the flow nozzles. The gas leaves
these stationary nozzles at a relatively higher velocity. Then it is made to impinge on the blades
over the turbine rotor or wheel. Momentum imparted to the blades turns the wheel. Thus, the two
primary parts of the turbine are,
(i) The stator nozzles, and
(ii) the turbine rotor blades.
Normally a turbine stage is classified as
(i) an impulsion stage, and
(ii) a reaction stage
An impulse stage is characterized by the expansion of the gas which occurs only in the stator
nozzles. The rotor blades act as directional vanes to deflect the direction of the flow. Further,
they convert the kinetic energy of the gas into work by changing the momentum of the gas more
or less at constant pressure.
A reaction stage is one in which expansion of the gas takes place both in the stator and in the
rotor.
The function of the stator is the same as that in the impulse stage, but the function in the
rotor is two fold.
(i) the rotor converts the kinetic energy of the gas into work, and
(ii) contributes a reaction force on the rotor blades.
The reaction force is due to the increase in the velocity of the gas relative to the blades. This
results from the expansion of the gas during its passage through the rotor.
A Single Impulse Stage
Impulse machines are those in which there is no change of static or pressure head of the fluid in
the rotor. The rotor blades cause only energy transfer and there is no energy transformation. The
energy transformation from pressure or static head to kinetic energy or vice versa takes place in
fixed blades only. As can be seen from the below figure that in the rotor blade passage of an
impulse turbine there is no acceleration of the fluid, i.e., there is no energy transformation.
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Hence, the chances are greater for separation due to boundary layer growth on the blade surface.
Due to this, the rotor blade passages of the impulse machine suffer greater losses giving lower
stage efficiencies.
The paddle wheel, Pelton wheel and Curtis stem turbine are some examples of impulse
machines.
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A Single Reaction Stage
The reaction stages are those, in which, changes in static or pressure head occur both in the rotor
and stator blade passages. Here, the energy transformation occurs both in fixed as well as
moving blades. The rotor experiences both energy transfer as well as energy transformation.
Therefore, reaction turbines are considered to be more efficient. This is mainly due to continuous
acceleration of flow with lower losses.
The degree of reaction of a turbomachine stage may be defined as the ratio of the static or
pressure head change occurring in the rotor to the total change across the stage.
Note: Axial-flow turbine with 50% reaction have symmetrical blades in their rotor and stators. It
may be noted that the velocity triangles at the entry and exit of a 50% reaction stage are also
symmetrical.
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Velocity Triangles of a Single Stage Machine
The flow geometry at the entry and exit of a turbomachine stage is described by the velocity
triangles at these stations. The velocity triangles for a turbomachine contain the following three
components.
1. The peripheral / whirl / tangential velocity (u) of a rotor blades
2. The absolute velocity (c ) of the fluid and
3. The relative velocity (w or v) of the fluid
These velocities are related by the following well-known vector equation.
This simple relation is frequently used and is very useful in drawing the velocity triangles
for turbomachines.
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The notation used here to draw velocity triangles correspond to the x-y coordinates; the
suffix (a or α) identifies components in the axial direction and suffix (t) refers to
tangential direction. Air angles in the absolute system are denoted by alpha (α), where as
those in the relative system are represented by beta (β).
Since the stage is axial, the change in the mean diameter between its entry and exit can be
neglected. Therefore, the peripheral or tangential velocity (u) remains constant in the velocity
triangles.
It can be proved from the geometry that
ct2 + ct3 = wt2 + wt3
It is often assumed that the axial velocity component remains constant through the stage. For
such condition,
ca = ca1 = ca2 = ca3
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For constant axial velocity yields a useful relation,
tan α2 + tan α3 = tan β2 + tan β3
Expression for Work Output
Though force and torque are exerted on both stationary and moving blades alike, work can only
be done on the moving rotor blades. Thus the rotor blades transfer energy from the fluid to the
shaft. The stage work in an axial turbine (u3 = u2 = u) can be written as,
W = u2 ct2 – u3ct3
= u{ct2- (-ct3)}
= u(ct2-ct3)
{Note: Usually this equation will be written with a minus sign between ct2 and ct3. Whenever this
is written with a plus sign it is implied that ct3 is negative}
This equation can also be expressed in another form,
+=
u
c
u
cuW tt 322
The first term
u
ct 2 in the bracket depends on the nozzle or fixed angle (α2) and the ratio
2c
u=σ . The contribution of the second term
u
ct3 to the work is generally small. It is also
observed that the kinetic energy of the fluid leaving the stage is greater for larger values of ct3.
The leaving loss from the stage is minimum when ct3 = 0, i.e., when the discharge from the stage
is axial (c3 = ca3). However, this condition gives lesser stage work as can be seen from the above
two equations.
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Blade loading and Flow coefficients
Performance of turbomachines are characterized by various dimensionless parameters. For
example, loading coefficient (ψ) and the flow coefficient (Ф) have been defined as,
u
c
u
W
a=
=Ψ
φ
2
Since the work, W in the above equation is frequently referred to as the blade or stage work, the
coefficient, ψ would also be known as the blade or stage loading coefficient.
For constant axial velocity (ca), it can be shown that
Ψ = Ф(tan α2 + tan α3) = Ф(tan β2 + tan β3)
The Ф – ψ plots are useful in comparing the performances of various stages of different sizes and
geometries.
Blade and Stage efficiencies
Even though the blade and stage work (outputs) are the same, the blade and the stage efficiencies
need not be equal. This is because the energy inputs to the rotor blades and the stage (fixed blade
ring plus the rotor) are different. The blade efficiency is also known as the utilization factor (ε)
which is an index of the energy utilizing capability of the rotor blades. Thus,
ε = ηb
= Rotor blade work / Energy supplied to the rotor blades
= W / Erb
W = u2 ct2 + u3 ct3
( ) ( ) ( )2
2
3
3
2
3
2
2
2
3
2
22
1
2
1
2
1wwuucc −+−+−=
The energy supplied to the rotor blades is the absolute kinetic energy in the jet at the entry plus
the kinetic energy change within the rotor blades.
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( ) ( )2
3
3
2
2
2
2
3
2
22
1
2
1
2
1uuwwcErb −+−+=
For axial machines, u = u2 = u3
( ) ( )( )2
2
2
3
2
2
2
2
2
3
2
3
2
2
wwc
wwccb
−+
−+−== ηε
Maximum utilization factor for a single impulse stage.
2
2
32
2
1
)(
c
ccu tt +=ε
After rearranging the terms, we have
)sin(4 2
2 σασεη −==b
This shows that the utilization factor is a function of the blade-to-gas speed ratio and the nozzle
angle.
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Elementary theory of axial flow turbine
Fig.7.2 Typical representations of velocity triangles
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The above Figures show the velocity triangles for one axial flow turbine stage and the
nomenclature employed. The gas enters the row of nozzle blades (These are also known as 'stator
blades' and 'nozzle guide vanes') with a static pressure and temperature, P1, T1 and a velocity C1
is expanded to P2,T2 and leaves with an increased velocity C2 at an angle α2. The rotor blade inlet
angle will be chosen to suit the direction β2 of the gas velocity V2 relative to the blade at inlet.
β2and V2 are found by vectorial subtraction of the blade speed U from the absolute velocity C2.
After being deflected, and usually further expanded, in the rotor blade passages, the gas leaves at
P3, T3 with relative velocity V3 at angle β3. Vectorial addition of U yields the magnitude and
direction of the gas velocity at exit from the stage, C3 and α3. α3 is known as the swirl angle.
dimensional effects.
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Vortex theory
It was pointed out earlier that the shape of the velocity triangles must vary from root to tip of the blade
because the blade speed U increases with radius. Another reason is that the whirl component in the flow
at outlet from the nozzles causes the static pressure and temperature to vary across the annulus. With a
uniform pressure at inlet, or at least with a much smaller variation because the whirl component is
smaller, it is clear that the pressure drop across the nozzle will vary giving rise to a corresponding
variation in efflux velocity C2. Twisted blading designed to take account of the changing gas angles is
called vortex blading.
It has been common steam turbine practice, except in low-pressure blading where the blades are
very long, to design on conditions at the mean diameter, keep the blade angles constant from root to tip,
and assume that no additional loss is incurred by the variation in incidence along the blade caused by the
changing gas angles. Comparative tests have been conducted by the earlier researchers on a single-stage
gas turbine of radius ratio 1-37, using in turn blades of constant angle and vortex blading. The results
showed that any improvement in efficiency obtained with vortex blading was within the margin of
experimental error. This contrasts with similar tests on a 6-stage axial compressor, by another researcher,
which showed a distinct improvement from the use of vortex blading. This was, however, not so
much an improvement in efficiency (of about 1-5 per cent) as in the delay of the onset of surging
which of course does not arise in accelerating flow. It appears, therefore, that steam turbine
designers have been correct in not applying vortex theory except when absolutely necessary at
the LP end. They have to consider the additional cost of twisted blades for the very large number
of rows of blading required, and they know that the Rankine cycle is relatively insensitive to
component losses. Conversely, it is not surprising that the gas turbine designer, struggling to
achieve the highest possible component efficiency, has consistently used some form of
vortex blading which it is felt intuitively must give a better performance however small.
Vortex theory has been outlined earlier by Cohen and others where it was shown that if
the elements of fluid are to be in radial equilibrium, an increase in static pressure from
root to tip is necessary whenever there is a whirl component of velocity. Figure 7.8 shows
(see below) why the gas turbine designer cannot talk of impulse or 50 per cent reaction stages.
The proportion of the stage pressure or temperature drop which occurs in the rotor must increase
from root to tip. Although Fig. 7.8 refers to a single-stage turbine with axial inlet velocity and no
swirl at outlet, the whirl component at inlet and outlet of a repeating stage will be small
compared with CW2- the reaction will therefore still increase from root to tip, if somewhat less
markedly.
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Choice of blade profile, pitch and chord
The next step is to choose stator and rotor blade shapes which will accept the gas incident upon
the leading edge, and deflect the gas through the required angle with the minimum loss. An
overall blade loss coefficient Y (or A) must account for the following sources of friction loss.
(a) Profile loss—associated with boundary layer growth over the blade profile (including
separation loss under adverse conditions of extreme angles of incidence or high inlet
Mach number).
(b) Annulus loss—associated with boundary layer growth on the inner and outer walls of the
annulus.
(c) Secondary flow loss—arising from secondary flows which are always present when a
wall boundary layer is turned through an angle by an adjacent curved surface.
(d) Tip clearance loss—near the rotor blade tip the gas does not follow the intended path,
fails to contribute its quota of work output, and interacts with the outer wall boundary
layer.
The profile loss coefficient Yp is measured directly in cascade tests similar to those described for
compressor blading. Losses (b) and (c) cannot easily be separated, and they are accounted for by
a secondary loss coefficient Ys.
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The tip clearance loss coefficient, which normally arises only for rotor blades, will be denoted by
Yk. Thus the total loss coefficient Y comprises the accurately measured two-dimensional loss Yp,
plus the three-dimensional loss (Ys+Yk) which must be deduced from turbine stage test results.
All that is necessary for our present purpose for finding the choice of blade profile is limited to
the knowledge of the sources of loss.
Figure 7.11 shows a conventional steam turbine blade profile constructed from circular arcs and
straight lines. Gas turbines have until recently used profiles closely resembling this, although
specified by aerofoil terminology.
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Note that the blade profile will be completely determined when (a) the pitch/width ratio (s/w) is
established, and (b) both the camber line angle α' and blade thickness/pitch ratio have been
calculated for various values of x between 0 and 1.
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Turbine Performance
The performance of turbine is limited principally by two factors: compressibility and
stress. Compressibility limits the mass flow that can pass through a given turbine and, stress
limits the wheel speed U. The work per stage depends on the square of the wheel speed.
However, the performance of the engine depends very strongly on the maximum temperature. Of
course, as the maximum temperature increases, the allowable stress level diminishes; hence in
the design of the engine there must be a compromise between maximum temperature and
maximum rotor tip speed U.
For given pressure ratio and adiabatic efficiency, the turbine work per unit mass is proportional
to the inlet stagnation temperature. Since, in addition, the turbine work in a jet or turboshaft
engine is commonly two or three times the useful energy output of the engine, a 1% increase in
turbine inlet temperature can produce a 2% or 3% increase in engine output. This considerable
advantage has supplied the incentive for the adoption of fairly elaborate methods for cooling the
turbine nozzle and rotor blades.
Estimation of stage performance
The last step in the process of arriving at the preliminary design of a turbine stage is to check
that the design is likely to result in values of nozzle loss coefficient and stage efficiency which
were assumed at the outset. If not, the design calculations may be repeated with more probable
values of loss coefficient and efficiency. When satisfactory agreement has been reached, the
final design may be laid out on the drawing board and accurate stressing calculations can be
performed. Before proceeding to describe a method of estimating the design point performance
of a stage, however, the main factors limiting the choice of design, which we have noted during
the course of the worked example, will be summarized. The reason we considered a turbine for a
turbojet engine was simply that we would thereby be working near those limits to keep size and
weight to a minimum. The designer of an industrial gas turbine has a somewhat easier task: he
will be using lower temperatures and stresses to obtain a longer working life, and this means
lower mean blade speeds, more stages, and much less stringentaerodynamic limitations. A power
turbine, not mechanically coupled to the gas generator, is another case where much less difficulty
will be encountered in arriving at a satisfactory solution. The choice of gear ratio between the
power turbine and driven component is normally at the disposal of the turbine designer, and thus
the rotational speed can be varied to suit the turbine, instead of the compressor as we have
assumed here.
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The cooled turbine
Figure 7.29 illustrates the methods of blade cooling that have received serious attention and
research effort. Apart from the use of spray cooling for thrust boosting in turbojet engines, the
liquid systems have not proved to be practicable. There are difficulties associated with
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channelling the liquid to and from the blades—whether as primary coolant for forced convection
or free convection open thermosyphon systems, or as secondary coolant for closed thermosyphon
systems. It is impossible to eliminate corrosion or the formation of deposits in open systems, and
very difficult to provide adequate secondary surface cooling area at the base of the blades for
closed systems. The only method used successfully in production engines has been internal,
forced convection, air cooling. With 1-5-2 per cent of the air mass flow used for cooling per
blade row, the blade temperature can be reduced by between 200 and 300 °C. Using current
alloys, this permits turbine inlet temperatures of more than 1650 К to be used. The blades are
either cast, using cores to form the cooling passages, or forged with holes of any desired shape
produced by electrochemical or laser drilling.
Figure 7.30 shows the type of turbine rotor blade introduced in the 1980s. The next step forward
is likely to be achieved by transpiration cooling, where the cooling air is forced through a porous
blade wall. This method is by far the most economical in cooling air, because not only does it
remove heat from the wall more uniformly, but the effusing layer of air insulates the outer
surface from the hot gas stream and so reduces the rate of heat transfer to the blade. Successful
application awaits further development of suitable porous materials and techniques of blade
manufacture. We are here speaking mainly of rotor blade cooling because this presents the most
difficult problem. Nevertheless it should not be forgotten that, with high gas temperatures,
oxidation becomes as significant a limiting factor as creep, and it is therefore equally important
to cool even relatively unstressed components such as nozzle blades and annulus walls.
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Figure 7.31 (a) illustrates the principal features of nozzle blade cooling. The air is introduced
in such a way as to provide jet impingement cooling of the inside surface of the very hot leading
edge. The spent air leaves through slots or holes in the blade surface (to provide some film
– Selection of liquid propellants – Thrust control in liquid rockets – Cooling in liquid rockets –
Limitations of hybrid rockets – Relative advantages of liquid rockets over solid rockets-
Numerical Problems.
Introduction to Propulsion
Definitions and Basic Relations
• Fluid dynamics of compressible flows is generally referred to as Gas dynamics. This deals with an
unified analysis of dynamics and thermodynamics of compressible flows.
• Convectional fluid mechanics analyses are inadequate for high speed flows of gases and vapours
due to non-compressibility approach.
• Therefore in the application like high speed aerodynamics, rocket and missile propulsion, steam
and gas turbines, and high speed turbocompressors compressible fluid dynamics is used to
obtain solutions of a number of design problems.
• The properties of fluid which are generally considered in compressible flow problems are
temperature, pressure, density, internal energy, enthalpy, entropy and viscosity.
• A major portion covered by the fluid dynamics of compressible flows deals with the relation
between force, mass and velocity.
• The following laws are frequently used in dealing with a variety of compressible flow problems:
• (i) First law of thermodynamics
• (Energy equation).
• (ii) Second law of thermodynamics
• (Entropy relation)
• (iii) Law of conservation of mass
• (Continuity equation)
• (iv) Newton’s second law of motion
• (Momentum equation)
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Goal: Create a Force to Propel a Vehicle
Two options:
1) Take mass stored in a vehicle and throw it backwards (rocket propulsion). Use the
reaction force to propel the vehicle.
Propellant ---> burn ---> expand through nozzle
(chem. energy) (thermal energy) (kinetic energy & momentum)
2) Seize mass from the surroundings and set the mass in motion backwards. Use the reaction
force to propel vehicle (air-breathing propulsion).
• Continuously:
a) Draw in air.
b) Compress it.
c) Add fuel and burn (convert chemical energy to thermal energy).
d) Expand through a turbine to drive compressor (extract work).
e.1) Then expand in a nozzle to convert thermal energy to kinetic energy
& momentum (turbojet).
e.2) Or expand in a second turbine (extract work), use this to drive a
shaft for a fan (turbofan), or a propeller (turboshaft). The fan or propeller
impart k.e. & mom. to the air.
*Remember:
• Overall goal: take at Vo (flight speed), throw it out at Vo + DV
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• Flying model rockets is a relatively safe and inexpensive way for students to learn the basics of
forces and the response of a vehicle to external forces. Like an airplane, a model rocket is
subjected to the forces of weight, thrust, and aerodynamics during its flight.
• On this slide we show the parts of a single stage model rocket. We have laid the rocket on its
side and cut a hole in the body tube so that we can see what is inside. Beginning at the far right,
the body of the rocket is a green cardboard tube with black fins attached at the rear. The fins
can be made of either plastic or balsa wood and are used to provide stability during flight.
Model rockets use small, pre-packaged, solid fuel engines The engine is used only once, and
then is replaced with a new engine for the next flight. Engines come in a variety of sizes and can
be purchased at hobby stores and at some toy stores.
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We live in a world that is defined by three spatial dimensions and one time dimension. Objects move
within this domain in two ways. An object translates, or changes location, from one point to another.
And an object rotates, or changes its attitude. In general, the motion of any object involves both
translation and rotation. The translations are in direct response to external forces. The rotations are in
direct response to external torques or moments (twisting forces).
• The motion of a rocket is particularly complex because the rotations and translations are
coupled together; a rotation affects the magnitude and direction of the forces which affect
translations.
• To understand and describe the motion of a rocket, we usually try to break down the complex
problem into a series of easier problems.
• We can, for instance, assume that the rocket translates from one point to another as if all the
mass of the rocket were collected into a single point called the center of gravity.
• We can describe the motion of the center of gravity by using Newton's laws of motion.
• In general, there are four forces acting on the rocket; the weight, thrust, drag and lift.
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• The thrust of the engine is transmitted to the body of the rocket through the engine mount.
• This part is fixed to the rocket and can be made of heavy cardboard or wood.
• There is a hole through the engine mount to allow the ejection charge of the engine to
pressurize the body tube at the end of the coasting phase and eject the nose cone and the
recovery system.
• Recovery wadding is inserted between the engine mount and the recovery system to prevent
the hot gas of the ejection charge from damaging the recovery system.
• The recovery wadding is sold with the engine.
• The recovery system consists of a parachute (or a streamer) and some lines to connect the
parachute to the nose cone.
• Parachutes and streamers are made of thin sheets of plastic.
• The nose cone can be made of balsa wood, or plastic, and may be either solid or hollow. The
nose cone is inserted into the body tube before flight.
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• An elastic shock cord is connected to both the body tube and the nose cone and is used to keep
all the parts of the rocket together during recovery.
• The launch lugs are small tubes (straws) which are attached to the body tube.
• The launch rail is inserted through these tubes to provide stability to the rocket during launch.
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Temperature Variation in the Atmosphere
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SOLID ROCKETS Specific Impulse: 100-400 sec
Thrust: 103-10
7 N
• Solid rockets are the simplest and earliest types of rocket propulsion dating back to the
first rockets used by the Chinese.
• Solid rockets are filled with a solid mixture of a propellant and an oxidizer. Little else is
actually required for these rockets.
• The designs are very simple and therefore very reliable.
• The main drawback of solid rockets is that once ignited, they burn until all of the fuel is
gone. Because of this, they aren't used often in space where propulsion systems are
usually required to be turned on and off many times. However, they are good for getting
things into space. In fact, the space shuttles use solid rocket boosters (SRBs) during
takeoff.
•
Quick Fact : The SRBs are the largest solid-propellant motors ever flown and the first
designed for reuse. Each is 149.16 feet long and 12.17 feet in diameter.
MONOPROPELLANT ROCKETS
Specific Impulse: 100-300 sec
Thrust: 0.1-100 N
• Monopropellant rockets are simple propulsion systems that rely on special chemicals
which, when energized, decompose. This decomposition creates both the fuel and an
oxidizer (which allows the fuel to burn), which then react with each other. Because they
only use a single propellant, monopropellant rockets are quite simple and reliable.
Unfortunately, they are not very efficient. They are mainly used to make small
adjustments such as attitude control. Main propulsion systems usually use some other
technology.
BIPROPELLANT ROCKETS
Specific Impulse: 100-400 sec
Thrust: 0.1-107 N
• Bipropellant rockets separate the fuel and oxidizer and mix them in the chamber where
they burn. Bipropellant rockets are widely used and more efficient than monopropellant
rockets. The reaction given in the lesson on chemistry gives an example of a
fuel(H2)/oxidizer(O2) combination. It's actually a very good combination in that it
releases a large amount of energy. It's the combination used by the space shuttle's main
engines. Unfortunately, large tanks kept at extremely low temperatures are required to
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carry them. In fact, the main purpose of the giant red external tank attached to the space
shuttle on take-off is to carry enough fuel to get the space shuttle into space.
The main drawback of bipropellant rockets is that they are more complex than solid or
monopropellant rockets. The fuel and oxidizer have to be stored separately and fed together in
exactly the right ratios to achieve maximum efficiency. Despite the extra complexity,
bipropellant rockets are still one of the preferred systems for primary propulsion
ROCKET PROPULSION
Isaac Newton stated in his third law of motion that "for every action there is an equal and
opposite reaction." It is upon this principle that a rocket operates. Propellants are combined
in a combustion chamber where they chemically react to form hot gases which are then
accelerated and ejected at high velocity through a nozzle, thereby imparting momentum to
the engine. The thrust force of a rocket motor is the reaction experienced by the motor
structure due to ejection of the high velocity matter. This is the same phenomenon which
pushes a garden hose backward as water flows from the nozzle, or makes a gun recoil when
fired.
Thrust
Thrust is the force that propels a rocket or spacecraft
and is measured in pounds, kilograms or Newtons.
Physically speaking, it is the result of pressure which is exerted on the wall of the combustion chamber.
The figure to the right shows a combustion chamber
with an opening, the nozzle, through which gas can
escape. The pressure distribution within the chamber
is asymmetric; that is, inside the chamber the
pressure varies little, but near the nozzle it decreases
somewhat. The force due to gas pressure on the
bottom of the chamber is not compensated for from
the outside. The resultant force F due to the internal
and external pressure difference, the thrust, is
opposite to the direction of the gas jet. It pushes the
chamber upwards.
To create high speed exhaust gases, the necessary
high temperatures and pressures of combustion are
obtained by using a very energetic fuel and by having
the molecular weight of the exhaust gases as low as
possible. It is also necessary to reduce the pressure
of the gas as much as possible inside the nozzle by
creating a large section ratio. The section ratio, or expansion ratio, is defined as the area of
the exit Ae divided by the area of the throat At.
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The thrust F is the resultant of the forces due to the pressures exerted on the inner and
outer walls by the combustion gases and the surrounding atmosphere, taking the boundary
between the inner and outer surfaces as the cross section of the exit of the nozzle. As we shall see in the next section, applying the principle of the conservation of momentum gives
where q is the rate of the ejected mass flow, Pa the pressure of the ambient atmosphere, Pe
the pressure of the exhaust gases and Ve their ejection speed. Thrust is specified either at sea level or in a vacuum.
Conservation of Momentum
The linear momentum (p), or simply momentum, of a particle is the product of its mass and its velocity. That is,
Newton expressed his second law of motion in terms of momentum, which can be stated as
"the resultant of the forces acting on a particle is equal to the rate of change of the linear momentum of the particle". In symbolic form this becomes
which is equivalent to the expression F=ma.
If we have a system of particles, the total momentum P of the system is the sum of the
momenta of the individual particles. When the resultant external force acting on a system is
zero, the total linear momentum of the system remains constant. This is called the principle
of conservation of linear momentum. Let's now see how this principle is applied to rocket mechanics.
Consider a rocket drifting in gravity free space. The rocket's engine is fired for time t and,
during this period, ejects gases at a constant rate and at a constant speed relative to the
rocket (exhaust velocity). Assume there are no external forces, such as gravity or air resistance.
The figure below-left (a) shows the situation at time t. The rocket and fuel have a total
mass M and the combination is moving with velocity v as seen from a particular frame of
reference. At a time t later the configuration has changed to that shown below-right (b). A
mass M has been ejected from the rocket and is moving with velocity u as seen by the
observer. The rocket is reduced to mass M- M and the velocity v of the rocket is changed to v+ v.
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Because there are no external forces, dP/dt=0. We can write, for the time interval t
where P2 is the final system momentum, figure (b), and P1 is the initial system momentum, figure (a). We write
If we let t approach zero, v/ t approaches dv/dt, the acceleration of the body. The
quantity M is the mass ejected in t; this leads to a decrease in the mass M of the original
body. Since dM/dt, the change in mass of the body with time, is negative in this case, in the
limit the quantity M/ t is replaced by -dM/dt. The quantity u-(v+ v) is Vrel, the relative
velocity of the ejected mass with respect to the rocket. With these changes, equation (1.4) can be written as
The right-hand term depends on the characteristics of the rocket and, like the left-hand
term, has the dimensions of a force. This force is called the thrust, and is the reaction force
exerted on the rocket by the mass that leaves it. The rocket designer can make the thrust
as large as possible by designing the rocket to eject mass as rapidly as possible (dM/dt
large) and with the highest possible relative speed (Vrel large).
In rocketry, the basic thrust equation is written as
where q is the rate of the ejected mass flow, Ve is the exhaust gas ejection speed, Pe is the
pressure of the exhaust gases at the nozzle exit, Pa is the pressure of the ambient
atmosphere, and Ae is the area of the nozzle exit. The product qVe, which we derived above
(Vrel x dM/dt), is called the momentum, or velocity, thrust. The product (Pe-Pa)Ae, called
the pressure thrust, is the result of unbalanced pressure forces at the nozzle exit. As we
shall see latter, maximum thrust occurs when Pe=Pa.
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PROBLEM 1.1
A spacecraft's engine ejects mass at a rate of 30 kg/s with an exhaust
velocity of
3,100 m/s. The pressure at the nozzle exit is 5 kPa and the exit area is 0.7
m2.
What is the thrust of the engine in a vacuum?
SOLUTION,
Given: q = 30 kg/s
Ve = 3,100 m/s
Ae = 0.7 m2
Pe = 5 kPa = 5,000 N/m2
Pa = 0
Equation (1.6),
F = q x Ve + (Pe - Pa) x Ae
F = 30 x 3,100 + (5,000 - 0) x 0.7
F = 96,500 N
Equation (1.6) may be simplified by the definition of an effective exhaust gas velocity, C,
defined as
Equation (1.6) then reduces to
Impulse & Momentum
In the preceding section we saw that Newton's second law may be expressed in the form
Multiplying both sides by dt and integrating from a time t1 to a time t2, we write
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The integral is a vector known as the linear impulse, or simply the impulse, of the force F
during the time interval considered. The equation expresses that, when a particle is acted
upon by a force F during a given time interval, the final momentum p2 of the particle may
be obtained by adding its initial momentum p1 and the impulse of the force F during the interval of time.
When several forces act on a particle, the impulse of each of the forces must be considered.
When a problem involves a system of particles, we may add vectorially the momenta of all
the particles and the impulses of all the forces involved. When can then write
For a time interval t, we may write equation (1.10) in the form
Let us now see how we can apply the principle of impulse and momentum to rocket mechanics.
Consider a rocket of initial mass M which it launched vertically at time t=0. The fuel is
consumed at a constant rate q and is expelled at a constant speed Ve relative to the rocket.
At time t, the mass of the rocket shell and remaining fuel is M-qt, and the velocity is v.
During the time interval t, a mass of fuel q t is expelled. Denoting by u the absolute
velocity of the expelled fuel, we apply the principle of impulse and momentum between time
t and time t+ t. Please note, this derivation neglects the effect of air resistance.
We write
We divide through by t and replace u-(v+ v) with Ve, the velocity of the expelled mass relative to the rocket. As t approaches zero, we obtain
Separating variables and integrating from t=0, v=0 to t=t, v=v, we obtain
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which equals
The term -gt in equation (1.15) is the result of Earth's gravity pulling on the rocket. For a
rocket drifting in space, -gt is not applicable and can be omitted. Furthermore, it is more
appropriate to express the resulting velocity as a change in velocity, or V. Equation (1.15) thus becomes
PROBLEM 1.2
The spacecraft in problem 1.1 has an initial mass of 30,000 kg. What is the
change
in velocity if the spacecraft burns its engine for one minute?
SOLUTION,
Given: M = 30,000 kg
q = 30 kg/s
Ve = 3,100 m/s
t = 60 s
Equation (1.16),
V = Ve x LN[ M / (M - qt) ]
V = 3,100 x LN[ 30,000 / (30,000 - (30 x 60)) ]
V = 192 m/s
Note that M represents the initial mass of the rocket and M-qt the final mass. Therefore,
equation (1.16) is often written as
where mo/mf is called the mass ratio. Equation (1.17) is also known as Tsiolkovsky's rocket
equation, named after Russian rocket pioneer Konstantin E. Tsiolkovsky (1857-1935) who
first derived it.
In practical application, the variable Ve is usually replaced by the effective exhaust gas velocity, C. Equation (1.17) therefore becomes
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Alternatively, we can write
where e is a mathematical constant approximately equal to 2.71828.
PROBLEM 1.3
A spacecraft's dry mass is 75,000 kg and the effective exhaust gas velocity
of its
main engine is 3,100 m/s. How much propellant must be carried if the
propulsion system
is to produce a total v of 700 m/s?
SOLUTION,
Given: Mf = 75,000 kg
C = 3,100 m/s
V = 700 m/s
Equation (1.20),
Mo = Mf x e^( V / C)
Mo = 75,000 x e^(700 / 3,100)
Mo = 94,000 kg
Propellant mass,
Mp = Mo - Mf
Mp = 94,000 - 75,000
Mp = 19,000 kg
For many spacecraft maneuvers it is necessary to calculate the duration of an engine burn
required to achieve a specific change in velocity. Rearranging variables, we have
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PROBLEM 1.4
A 5,000 kg spacecraft is in Earth orbit traveling at a velocity of 7,790 m/s.
Its engine is burned to accelerate it to a velocity of 12,000 m/s placing it
on an escape trajectory. The engine expels mass at a rate of 10 kg/s and an
effective velocity of 3,000 m/s. Calculate the duration of the burn.
SOLUTION,
Given: M = 5,000 kg
q = 10 kg/s
C = 3,000 m/s
V = 12,000 - 7,790 = 4,210 m/s
Equation (1.21),
t = M / q x [ 1 - 1 / e^( V / C) ]
t = 5,000 / 10 x [ 1 - 1 / e^(4,210 / 3,000) ]
t = 377 s
Combustion & Exhaust Velocity
The combustion process involves the oxidation of co
The optimum mixture ratio is typically that which will deliver the highest engine
performance (measured by specific impulse), however in some situations a different O/F
ratio results in a better overall system. For a volume-constrained vehicle with a low-density
fuel such as liquid hydrogen, significant reductions in vehicle size can be achieved by
shifting to a higher O/F ratio. In that case, the losses in performance are more than
compensated for by the reduced fuel tankage requirement. Also consider the example of
bipropellant systems using NTO/MMH, where a mixture ratio of 1.67 results in fuel and
oxidizer tanks of equal size. Equal sizing simplifies tank manufacturing, system packaging, and integration.
As we have seen previously, impulse thrust is equal to the product of the propellant mass flow rate and the exhaust gas ejection speed. The ideal exhaust velocity is given by
where k is the specific heat ratio, R' is the universal gas constant (8,314.51 N-m/kg mol-K
in SI units, or 49,720 ft-lb/slug mol-oR in U.S. units), Tc is the combustion temperature, M
is the average molecular weight of the exhaust gases, Pc is the combustion chamber pressure, and Pe is the pressure at the nozzle exit.
Specific heat ratio(2) varies depending on the composition and temperature of the exhaust
gases, but it is usually about 1.2. The thermodynamics involved in calculating combustion
temperatures are quite complicated, however, flame temperatures generally range from
about 2,500 to 3,600 oC (4,500-6,500 oF). Chamber pressures can range from about about
7 to 250 atmospheres. Pe should be equal to the ambient pressure at which the engine will
operate, more on this later. See below the charts providing optimum mixture ratio,
adiabatic flame temperature, gas molecular weight, and specific heat ratio for some common rocket propellants.
From equation (1.22) we see that high chamber temperature and pressure, and low exhaust
gas molecular weight results in high ejection velocity, thus high thrust. Based on this
criterion, we can see why liquid hydrogen is very desirable as a rocket fuel.
Liquid Oxygen & Liquid Hydrogen
Optimum Mixture Ratio
Unlike other propellants, the optimum mixture ratio for liquid oxygen and liquid hydrogen is
not necessarily that which will produce the maximum specific impulse. Because of the
extremely low density of liquid hydrogen, the propellant volume decreases significantly at
higher mixture ratios. Maximum specific impulse typically occurs at a mixture ratio of
around 3.5, however by increasing the mixture ratio
Optimum Mixture Ratio
Adiabatic Flame Temperature
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Gas Molecular Weight
Specific Heat Ratio
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• Molecular weight equals the sum of the atomic weights of
the atoms in the molecule. For NaCl, the atomic weight of
sodium is 23, of chlorine is 35 and a molecule contains one
sodium and one chlorine, so 23 + 35 = 58, the molecular
weight of NaCl. The formula for glucose ( a very common
sugar) is C6H12O6. The subscripts to the right mean that it
contains 6 atoms of carbon, 12 atoms of hydrogen, and
6 atoms of oxygen. The atomic weight for carbon is 12, for
hydrogen is 1, and for oxygen is 16, so the molecular
Ae = (At / Nm) x [(1 + (k - 1) / 2 x Nm2)/((k + 1) / 2)](k+1)/(2(k-1))
Ae = (0.1756 / 3.185) x [(1 + (1.221 - 1) / 2 x 10.15)/((1.221 + 1) /
2)](1.221+1)/(2(1.221-1))
Ae = 1.426 m2
Section Ratio,
Ae / At = 1.426 / 0.1756 = 8.12
For launch vehicles (particularly first stages) where the ambient pressure varies during the
burn period, trajectory computations are performed to determine the optimum exit
pressure. However, an additional constraint is the maximum allowable diameter for the
nozzle exit cone, which in some cases is the limiting constraint. This is especially true on
stages other than the first, where the nozzle diameter may not be larger than the outer
diameter of the stage below. For space engines, where the ambient pressure is zero, thrust
always increases as nozzle expansion ratio increases. On these engines, the nozzle
expansion ratio is generally increased until the additional weight of the longer nozzle costs
more performance than the extra thrust it generates.
Rocket Nozzle Design:
Optimizing Expansion for Maximum Thrust
A rocket engine is a device in which propellants are burned in a combustion chamber and
the resulting high pressure gases are expanded through a specially shaped nozzle to
produce thrust. The function of the nozzle is to convert the chemical-thermal energy
generated in the combustion chamber into kinetic energy. The nozzle converts the slow
moving, high pressure, high temperature gas in the combustion chamber into high velocity
gas of lower pressure and temperature. Gas velocities from 2 to 4.5 kilometers per second
can be obtained in rocket nozzles. The nozzles which perform this feat are called DeLaval
nozzles (after the inventor) and consist of a convergent and divergent section. The
minimum flow area between the convergent and divergent section is called the nozzle throat. The flow area at the end of the divergent section is called the nozzle exit area.
Hot exhaust gases expand in the diverging section of the nozzle. The pressure of these
gases will decrease as energy is used to accelerate the gas to high velocity. The nozzle is
usually made long enough (or the exit area great enough) such that the pressure in the
combustion chamber is reduced at the nozzle exit to the pressure existing outside the
nozzle. It is under this condition that thrust is maximum and the nozzle is said to be
adapted, also called optimum or correct expansion. To understand this we must examine the basic thrust equation:
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The gas pressure and temperature at the nozzle throat is less than in the combustion
chamber due to the loss of thermal energy in accelerating the gas to the local speed of
sound at the throat. Therefore, we calculate the pressure and temperature at the nozzle throat,
Pt = Pc x [1 + (k - 1) / 2]-k/(k-1)
Pt = 5 x [1 + (1.20 - 1) / 2]
-1.20/(1.20-1)
Pt = 2.82 MPa = 2.82x106 N/m
2
Tt = Tc x [1 / (1 + (k - 1) / 2)] Tt = 3,600 x [1 / (1 + (1.20 - 1) / 2)] Tt = 3,273 K
The area at the nozzle throat is given by
At = (q / Pt) x SQRT[ (R' x Tt) / (M x k) ] At = (100 / 2.82x10
6) x SQRT[ (8,314 x 3,273) / (24 x 1.20) ]
At = 0.0345 m2
The hot gases must now be expanded in the diverging section of the nozzle to obtain
maximum thrust. The Mach number at the nozzle exit is given by
Nm2 = (2 / (k - 1)) x [(Pc / Pa)
(k-1)/k - 1]
Nm2 = (2 / (1.20 - 1)) x [(5 / 0.05)
(1.20-1)/1.20 - 1]
Nm2 = 11.54
Nm = (11.54)1/2 = 3.40
The nozzle exit area corresponding to the exit Mach number is given by
Ae = (At / Nm) x [(1 + (k - 1) / 2 x Nm2)/((k + 1) / 2)]
(k+1)/(2(k-1))
Ae = (0.0345 / 3.40) x [(1 + (1.20 - 1) / 2 x 11.54)/((1.20 + 1) / 2)]
(1.20+1)/(2(1.20-1))
Ae = 0.409 m2
The velocity of the exhaust gases at the nozzle exit is given by
Ve = SQRT[ (2 x k / (k - 1)) x (R' x Tc / M) x (1 - (Pe / Pc)(k-1)/k
) ] Ve = SQRT[ (2 x 1.20 / (1.20 - 1)) x (8,314 x 3,600 / 24) x (1 - (0.05 / 5)
(1.20-1)/1.20) ]
Ve = 2,832 m/s
Finally, we calculate the thrust,
F = q x Ve + (Pe - Pa) x Ae F = 100 x 2,832 + (0.05x10
6 - 0.05x10
6) x 0.409
F = 283,200 N
Let's now consider what happens when the nozzle is under-extended, that is Pe>Pa. If we
assume Pe=Pa x 2, we have
Pe = 0.05 x 2 = 0.10 MPa At = 0.0345 m
2
Nm
2 = (2 / (1.20 - 1)) x [(5 / 0.10)
(1.20-1)/1.20 - 1]
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Nm 2 = 9.19 Nm = (9.19) 1/2 = 3.03 Ae = (0.0345 / 3.03) x [(1 + (1.20 - 1) / 2 x 9. 19)/((1.20 + 1) / 2)] (1.20+1)/(2(1.20-1)) Ae = 0.243 m 2 Ve = SQRT[ (2 x 1.20 / (1.20 - 1)) x (8,314 x 3, 600 / 24) x (1 - (0.10 / 5) (1.20-1)/1.20 ) ] Ve = 2,677 m/s F = 100 x 2,677 + (0.10x10 6 - 0.05x10 6) x 0.243 F = 279,850 N
Pe = 0.05 / 2 = 0.025 MPa At = 0.0345 m 2 Nm 2 = (2 / (1.20 - 1)) x [(5 / 0.025) (1.20-1)/1.20 - 1] Nm 2 = 14.18 Nm = (14.18) 1/2 = 3.77 Ae = (0.0345 / 3.77) x [(1 + (1.20 - 1) / 2 x 14 .18)/((1.20 + 1) / 2)] (1.20+1)/(2(1.20-1)) Ae = 0.696 m 2 Ve = SQRT[ (2 x 1.20 / (1.20 - 1)) x (8,314 x 3, 600 / 24) x (1 - (0.025 / 5) (1.20-1)/1.20 ) ] Ve = 2,963 m/s F = 100 x 2,963 + (0.025x10 6 - 0.05x10 6) x 0.696 F = 278,900 N )��������������������,�"�������������,�"��� ����������������������������������� �������� ����� ��� ��� �� ���� � �� �� �� ���� )���� ��� ��� �� ������ �� ��� ���� ������������� � ���� ������ ��������� ��H��
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As can be easily seen, thrust is maximum when Pa/Pe=1, or when Pe=Pa.
Power Cycles
Liquid bipropellant rocket engines can be categorized according to their power cycles, that
is, how power is derived to feed propellants to the main combustion chamber. Described below are some of the more common types.
Gas-generator cycle: The gas-generator cycle, also called open cycle, taps off a small
amount of fuel and oxidizer from the main flow (typically 3 to 7 percent) to feed a burner
called a gas generator. The hot gas from this generator passes through a turbine to
generate power for the pumps that send propellants to the combustion chamber. The hot
gas is then either dumped overboard or sent into the main nozzle downstream. Increasing
the flow of propellants into the gas generator increases the speed of the turbine, which
increases the flow of propellants into the main combustion chamber, and hence, the amount
of thrust produced. The gas generator must burn propellants at a less-than-optimal mixture
ratio to keep the temperature low for the turbine blades. Thus, the cycle is appropriate for
moderate power requirements but not high-power systems, which would have to divert a large portion of the main flow to the less efficient gas-generator flow.
As in most rocket engines, some of the propellant in a gas generator cycle is used to cool
the nozzle and combustion chamber, increasing efficiency and allowing higher engine
temperature.
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Regenerative cooling is the most widely used
method of cooling a thrust chamber and is
accomplished by flowing high-velocity coolant over
the back side of the chamber hot gas wall to
convectively cool the hot gas liner. The coolant
with the heat input from cooling the liner is then
discharged into the injector and utilized as a propellant.
Earlier thrust chamber designs, such as the V-2
and Redstone, had low chamber pressure, low
heat flux and low coolant pressure requirements,
which could be satisfied by a simplified "double
wall chamber" design with regenerative and film
cooling. For subsequent rocket engine
applications, however, chamber pressures were
increased and the cooling requirements became
more difficult to satisfy. It became necessary to
design new coolant configurations that were more
efficient structurally and had improved heat transfer characteristics.
This led to the design of "tubular wall" thrust chambers, by far the most widely used design
approach for the vast majority of large rocket engine applications. These chamber designs
have been successfully used for the Thor, Jupiter, Atlas, H-1, J-2, F-1, RS-27 and several
other Air Force and NASA rocket engine applications. The primary advantage of the design
is its light weight and the large experience base that has accrued. But as chamber pressures
and hot gas wall heat fluxes have continued to increase (>100 atm), still more effective
methods have been needed.
One solution has been "channel wall" thrust chambers, so named because the hot gas wall
cooling is accomplished by flowing coolant through rectangular channels, which are
machined or formed into a hot gas liner fabricated from a high-conductivity material, such
as copper or a copper alloy. A prime example of a channel wall combustion chamber is the
SSME, which operates at 204 atmospheres nominal chamber pressure at 3,600 K for a duration of 520 seconds. Heat transfer and structural characteristics are excellent.
In addition to the regeneratively cooled designs mentioned above, other thrust chamber
designs have been fabricated for rocket engines using dump cooling, film cooling,
transpiration cooling, ablative liners and radiation cooling. Although regeneratively cooled
combustion chambers have proven to be the best approach for cooling large liquid rocket
engines, other methods of cooling have also been successfully used for cooling thrust chamber assemblies. Examples include:
Dump cooling, which is similar to regenerative cooling because the coolant flows through
small passages over the back side of the thrust chamber wall. The difference, however, is
that after cooling the thrust chamber, the coolant is discharged overboard through openings
at the aft end of the divergent nozzle. This method has limited application because of the
performance loss resulting from dumping the coolant overboard. To date, dump cooling has
not been used in an actual application.
Film cooling provides protection from excessive heat by introducing a thin film of coolant
or propellant through orifices around the injector periphery or through manifolded orifices in
the chamber wall near the injector or chamber throat region. This method is typically used in high heat flux regions and in combination with regenerative cooling.
Transpiration cooling provides coolant (either gaseous or liquid propellant) through a
porous chamber wall at a rate sufficient to maintain the chamber hot gas wall to the desired temperature. The technique is really a special case of film cooling.
With ablative cooling, combustion gas-side wall material is sacrificed by melting,
vaporization and chemical changes to dissipate heat. As a result, relatively cool gases flow
over the wall surface, thus lowering the boundary-layer temperature and assisting the cooling process.
With radiation cooling, heat is radiated from the outer surface of the combustion chamber
or nozzle extension wall. Radiation cooling is typically used for small thrust chambers with a
high-temperature wall material (refractory) and in low-heat flux regions, such as a nozzle extension.
Solid Rocket Motors
Solid rockets motors store propellants in solid form. The fuel is typically powdered
aluminum and the oxidizer is ammonium perchlorate. A synthetic rubber binder such as
polybutadiene holds the fuel and oxidizer powders together. Though lower performing than
liquid propellant rockets, the operational simplicity of a solid rocket motor often makes it the propulsion system of choice.
Solid Fuel Geometry
A solid fuel's geometry determines the area and contours of its exposed surfaces, and thus
its burn pattern. There are two main types of solid fuel blocks used in the space industry.
These are cylindrical blocks, with combustion at a front, or surface, and cylindrical blocks
with internal combustion. In the first case, the front of the flame travels in layers from the
nozzle end of the block towards the top of the casing. This so-called end burner produces
constant thrust throughout the burn. In the second, more usual case, the combustion
surface develops along the length of a central channel. Sometimes the channel has a star shaped, or other, geometry to moderate the growth of this surface.
The shape of the fuel block for a rocket is chosen for the particular type of mission it will
perform. Since the combustion of the block progresses from its free surface, as this surface
grows, geometrical considerations determine whether the thrust increases, decreases or stays constant.
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Burn Rate
The burning surface of a rocket propellant grain recedes in a direction perpendicular to this
burning surface. The rate of regression, typically measured in millimeters per second (or
inches per second), is termed burn rate. This rate can differ significantly for different
propellants, or for one particular propellant, depending on various operating conditions as
well as formulation. Knowing quantitatively the burning rate of a propellant, and how it
changes under various conditions, is of fundamental importance in the successful design of
a solid rocket motor.
Propellant burning rate is influenced by certain factors, the most significant being:
combustion chamber pressure, initial temperature of the propellant grain, velocity of the
combustion gases flowing parallel to the burning surface, local static pressure, and motor acceleration and spin. These factors are discussed below.
• Burn rate is profoundly affected by chamber pressure. The usual representation of
the pressure dependence on burn rate is the Saint-R
a grain L/D ratio of 6. A greater Aport/At ratio should be used for grains with larger L/D ratios.
• In an operating rocket motor, there is a pressure drop along the axis of the
combustion chamber, a drop that is physically necessary to accelerate the increasing
mass flow of combustion products toward the nozzle. The static pressure is greatest
where gas flow is zero, that is, at the front of the motor. Since burn rate is
dependant upon the local pressure, the rate should be greatest at this location.
However, this effect is relatively minor and is usually offset by the counter-effect of
erosive burning.
• Burning rate is enhanced by acceleration of the motor. Whether the acceleration is a
result of longitudinal force (e.g. thrust) or spin, burning surfaces that form an angle
of about 60-90o with the acceleration vector are prone to increased burn rate.
It is sometimes desirable to modify the burning rate such that it is more suitable to a
certain grain configuration. For example, if one wished to design an end burner grain, which
has a relatively small burning area, it is necessary to have a fast burning propellant. In
other circumstances, a reduced burning rate may be sought after. For example, a motor
may have a large L/D ratio to generate sufficiently high thrust, or it may be necessary for a
particular design to restrict the diameter of the motor. The web would be consequently thin, resulting in short burn duration. Reducing the burning rate would be beneficial.
There are a number of ways of modifying the burning rate: decrease the oxidizer particle
size, increase or reduce the percentage of oxidizer, adding a burn rate catalyst or
suppressant, and operate the motor at a lower or higher chamber pressure. These factors are discussed below.
• The effect of the oxidizer particle size on burn rate seems to be influenced by the
type of oxidizer. Propellants that use ammonium perchlorate (AP) as the oxidizer
have a burn rate that is significantly affected by AP particle size. This most likely
results from the decomposition of AP being the rate-determining step in the
combustion process.
• The burn rate of most propellants is strongly influenced by the oxidizer/fuel ratio.
Unfortunately, modifying the burn rate by this means is quite restrictive, as the
performance of the propellant, as well as mechanical properties, are also greatly
affected by the O/F ratio.
• Certainly the best and most effective means of increasing the burn rate is the
addition of a catalyst to the propellant mixture. A catalyst is a chemical compound
that is added in small quantities for the sole purpose of tailoring the burning rate. A
burn rate suppressant is an additive that has the opposite effect to that of a catalyst
-- it is used to decrease the burn rate.
• For a propellant that follows the Saint-Robert's burn rate law, designing a rocket
motor to operate at a lower chamber pressure will provide for a lower burning rate.
Due to the nonlinearity of the pressure-burn rate relationship, it may be necessary to
significantly reduce the operating pressure to get the desired burning rate. The
obvious drawback is reduced motor performance, as specific impulse similarly decays with reducing chamber pressure.
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Product Generation Rate
The rate at which combustion products are generated is expressed in terms of the
regression speed of the grain. The product generation rate integrated over the port surface area is
where q is the combustion product generation rate at the propellant surface, p is the solid propellant density, Ab is the area of the burning surface, and r is the propellant burn rate.
It is important to note that the combustion products may consist of both gaseous and
condensed-phase mass. The condensed-phase, which manifests itself as smoke, may be
either solid or liquid particles. Only the gaseous products contribute to pressure
development. The condensed-phase certainly does, however, contribute to the thrust of the rocket motor, due to its mass and velocity.
PROBLEM 1.9
A solid rocket motor burns along the face of a central cylindrical channel 10
meters long and 1 meter in diameter. The propellant has a burn rate
coefficient of 5.5, a pressure exponent of 0.4, and a density of 1.77 g/ml.
Calculate the burn rate and the product generation rate when the chamber
pressure is 5.0 MPa.
SOLUTION,
Given: a = 5.5
n = 0.4
Pc = 5.0 MPa
p = 1.77 g/ml
Ab = x 1 x 10 = 31.416 m2
Equation (1.30),
r = a x Pcn
r = 5.5 x 5.00.4 = 10.47 mm/s
Equation (1.31),
q = p x Ab x r
with associated burn rate variation. Other factors may play a role, however, such as nozzle throat erosion and erosive burn rate augmentation.
Monopropellant Engines
By far the most widely used type of propulsion for spacecraft attitude and velocity control is
monopropellant hydrazine. Its excellent handling characteristics, relative stability under
normal storage conditions, and clean decomposition products have made it the standard. The general sequence of operations in a hydrazine thruster is:
• When the attitude control system signals for thruster operation, an electric solenoid
valve opens allowing hydrazine to flow. The action may be pulsed (as short as 5 ms)
or long duration (steady state).
• The pressure in the propellant tank forces liquid hydrazine into the injector. It enters
as a spray into the thrust chamber and contacts the catalyst beds.
• The catalyst bed consists of alumina pellets impregnated with iridium. Incoming
hydrazine heats to its vaporizing point by contact with the catalyst bed and with the
hot gases leaving the catalyst particles. The temperature of the hydrazine rises to a
point where the rate of its decomposition becomes so high that the chemical
reactions are self-sustaining.
• By controlling the flow variables and the geometry of the catalyst chamber, a
designer can tailor the proportion of chemical products, the exhaust temperature,
the molecular weight, and thus the enthalpy for a given application. For a thruster
application where specific impulse is paramount, the designer attempts to provide
30-40% ammonia dissociation, which is about the lowest percentage that can be
maintained reliably. For gas-generator application, where lower temperature gases
are usually desired, the designer provides for higher levels of ammonia dissociation.
• Finally, in a space thruster, the hydrazine decomposition products leave the catalyst
bed and exit from the chamber through a high expansion ratio exhaust nozzle to
produce thrust.
Monopropellant hydrazine thrusters typically produce a specific impulse of about 230 to 240 seconds.
Other suitable propellants for catalytic decomposition engines are hydrogen peroxide and
nitrous oxide, however the performance is considerably lower than that obtained with hydrazine - specific impulse of about 150 s with H2O2 and about 170 s with N2O.
Monopropellant systems have successfully provided orbit maintenance and attitude control
functions, but lack the performance to provide weight-efficient large V maneuvers required
for orbit insertion. Bipropellant systems are attractive because they can provide all three
functions with one higher performance system, but they are more complex than the
common solid rocket and monopropellant combined systems. A third alternative are dual
mode systems. These systems are hybrid designs that use hydrazine both as a fuel for high
performance bipropellant engines and as a monopropellant with conventional low-thrust
catalytic thrusters. The hydrazine is fed to both the bipropellant engines and the
monopropellant thrusters from a common fuel tank.
Cold gas propulsion is just a controlled, pressurized gas source and a nozzle. It represents
the simplest form of rocket engine. Cold gas has many applications where simplicity and/or
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the need to avoid hot gases are more important than high performance. The Manned Maneuvering Unit used by astronauts is an example of such a system.
Staging
Multistage rockets allow improved payload capability for vehicles with a high V
requirement such as launch vehicles or interplanetary spacecraft. In a multistage rocket,
propellant is stored in smaller, separate tanks rather than a larger single tank as in a single-
stage rocket. Since each tank is discarded when empty, energy is not expended to
accelerate the empty tanks, so a higher total V is obtained. Alternatively, a larger payload
mass can be accelerated to the same total V. For convenience, the separate tanks are usually bundled with their own engines, with each discardable unit called a stage.
Multistage rocket performance is described by the same rocket equation as single-stage
rockets, but must be determined on a stage-by-stage basis. The velocity increment, Vi, for each stage is calculated as before,
where moi represents the total vehicle mass when stage i is ignited, and mfi is the total
vehicle mass when stage i is burned out but not yet discarded. It is important to realize that
the payload mass for any stage consists of the mass of all subsequent stages plus the
ultimate payload itself. The velocity increment for the vehicle is then the sum of those for the individual stages where n is the total number of stages.
PROBLEM 1.10
A two-stage rocket has the following masses: 1st-stage propellant mass
120,000 kg,
1st-stage dry mass 9,000 kg, 2nd-stage propellant mass 30,000 kg, 2nd-stage
dry mass
3,000 kg, and payload mass 3,000 kg. The specific impulses of the 1st and
2nd stages
are 260 s and 320 s respectively. Calculate the rocket's total V.
We define the payload fraction as the ratio of payload mass to initial mass, or mpl/mo.
For a multistage vehicle with dissimilar stages, the overall vehicle payload fraction depends
on how the V requirement is partitioned among stages. Payload fractions will be reduced if
the V is partitioned suboptimally. The optimal distribution may be determined by trial and
error. A V distribution is postulated and the resulting payload fraction calculated. The V
distribution is varied until the payload fraction is maximized. Once the V distribution is
selected, vehicle sizing is accomplished by starting with the uppermost or final stage (whose
payload is the actual deliverable payload) and calculating the initial mass of this assembly.
This assembly then forms the payload for the previous stage and the process repeats until
all stages are sized. Results reveal that to maximize payload fraction for a given V requirement:
1. Stages with higher Isp should be above stages with lower Isp.
2. More V should be provided by the stages with the higher Isp.
3. Each succeeding stage should be smaller than its predecessor. 4. Similar stages should provide the same V.
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Solid Rocket Components
The key inert components of solid propellant rocket motors are the motor case, nozzle, and
igniter case. Thrust vector control (TVC) mechanism also a component of many rocket motors.
Motor Case:
The case not only contains the propellant grain, but also serves as a highly loaded pressure
vessel. Case design is usually governed by a combination of motor and vehicle requirements.
Besides constituting the structural body of the rocket motor with its nozzle, propellant grain, and
so on, the case frequently serves also as the primary structure of the missile or launch vehicle.
Different types of loads and their sources must be considered at the beginning of a case design.
In addition, the environmental conditions peculiar to a specific motor and its usage must be
carefully considered. Typically, these conditions include the following; (1) temperature (internal
heating, temperature cycling during storage, or thermal stress and strains); (2) corrosion
(moisture/chemical, galvanic, stress corrosion etc.); (3) space conditions: vacuum or radiation.
Three classes of materials have been used: high-strength metals (such as steel, aluminum, or
titanium alloys), wound-filament reinforced plastics, and a combination of these.
Rocket Motor Case Loads
(Ref: G.P.Sutton)
Origin of Load Type of Load/Stress Internal pressure Tension biaxial, vibration
Axial thrust Axial, vibration
Motor nozzle Axial, bending, shear
Thrust vector control actuators Axial, bending, shear
Thrust termination equipment Biaxial, bending
Aerodynamic control surface or wings
mounted to case
Tension, compression, bending, shear, torsion
Staging Bending, shear
Flight maneuvering Axial, bending, shear, torsion
Vehicle mass and wind forces on launch pad Axial, bending, shear
Dynamic loads from vehicle oscillations Axial, bending, shear
Ground transport, Ground handling, including
lifting
Tension, compression, bending, shear, torsion,
vibration
Earthquakes (large motors) Axial, bending, shear
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Nozzles
Nozzles for solid propellant rockets can be classified into five categories.
1. Fixed nozzle; simple and used in small missiles
2. Movable nozzle : provide thrust vector control for the flight.
3. Submerged nozzle: it reduces the overall motor length by inserting the significant portion
of the nozzle structure into the combustion chamber.
4. Extendible nozzle: it improves specific impulse. Nozzle area ratio is enlarged by
mechanically adding a nozzle cone extension piece.
5. Blast-Tube-Mounted nozzle: Used in missiles. The blast tube allows the rocket motor’s
center of gravity (CG) to be close to or ahead of the vehicle CG. This limits the CG travel
during motor burn and makes flight stabilization much easier.
Design and Construction
Almost all solid rocket nozzles are ablatively cooled. The general construction of a solid
rocket nozzle features steel or aluminium shells (housings) that are designed to carry
structural loads (motor operating pressure and nozzle TVC actuator load are the biggest), and
composite ablative liners which are bonded to the housings. Solid rocket nozzles are
designed to ensure that the thickness of ablative liners is sufficient to maintain the liner-to-
housing adhesive bond line below the temperature that would degrade the adhesive structural
properties during the motor operation.
The construction of nozzle ranges from simple single-piece non-movable graphite nozzles
to complex multipiece nozzles capable of moving to control the direction of the thrust vector.
Igniter hardware
There are generally two types:
• Pyrotechnic igniters and
• pyrogen igniters.
In industrial practice, pyrotechnic igniters are defined as igniters using solid explosives or
energetic propellant-likw chemical formulations (usually small pellets of propellant which
give a large burning surface and a short burning time) as the heat-producing material.
Pyrogen igniter is basically a small rocket motor that is used to ignite a large rocket
motor. The pyrogen is not designed to produce thrust. All use one or more nozzle orifices,
both sonic and supersonic types, and most use conventional rocket motor gra8 0 Td[(a)3.15789(t)-2.53658( )-2156(o)-0.9564(a)3.15789(.4973(a)3.15789(( )-80.6325(m)-3.4916033( )-100.671(o)-0. )-80.6325(r)2.3678(o)-0.956418(y)-000.67143.15544( )-80.6325(l)-2(5.957028(f)2.36842( )-0.478208(t)-2.53536(h)-56417(a13(s)-1.746s)-1.7465(t)-2.535789(d(c)3.15789( )-)9.06272( )-0.479(d)-10.9756( )-80.6313(t)-2.5353s)389]TJ/R11 12 T)-0.956417(r)2.3.0831(p)-10.9756 o
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ROCKET PROPELLANTS
Propellant is the chemical mixture burned to produce thrust in rockets and consists of a fuel
and an oxidizer. A fuel is a substance which burns when combined with oxygen producing
gas for propulsion. An oxidizer is an agent that releases oxygen for combination with a fuel.
The ratio of oxidizer to fuel is called the mixture ratio. Propellants are classified according to
their state - liquid, solid, or hybrid.
The gauge for rating the efficiency of rocket propellants is specific impulse, stated in
seconds. Specific impulse indicates how many pounds (or kilograms) of thrust are obtained
by the consumption of one pound (or kilogram) of propellant in one second. Specific impulse
is characteristic of the type of propellant, however, its exact value will vary to some extent with the operating conditions and design of the rocket engine.
Liquid Propellants
In a liquid propellant rocket, the fuel and oxidizer are stored in separate tanks, and are fed
through a system of pipes, valves, and turbopumps to a combustion chamber where they
are combined and burned to produce thrust. Liquid propellant engines are more complex
than their solid propellant counterparts, however, they offer several advantages. By
controlling the flow of propellant to the combustion chamber, the engine can be throttled, stopped, or restarted.
A good liquid propellant is one with a high specific impulse or, stated another way, one with
a high speed of exhaust gas ejection. This implies a high combustion temperature and
exhaust gases with small molecular weights. However, there is another important factor
which must be taken into consideration: the density of the propellant. Using low density
propellants means that larger storage tanks will be required, thus increasing the mass of
the launch vehicle. Storage temperature is also important. A propellant with a low storage
temperature, i.e. a cryogenic, will require thermal insulation, thus further increasing the
mass of the launcher. The toxicity of the propellant is likewise important. Safety hazards
exist when handling, transporting, and storing highly toxic compounds. Also, some
propellants are very corrosive, however, materials that are resistant to certain propellants have been identified for use in rocket construction.
Liquid propellants used in rocketry can be classified into three types: petroleum, cryogens, and hypergols.
Petroleum fuels are those refined from crude oil and are a mixture of complex
hydrocarbons, i.e. organic compounds containing only carbon and hydrogen. The petroleum
used as rocket fuel is a type of highly refined kerosene, called RP-1 in the United States.
Petroleum fuels are usually used in combination with liquid oxygen as the oxidizer. Kerosene
delivers a specific impulse considerably less than cryogenic fuels, but it is generally better than hypergolic propellants.
Specifications for RP-1 where first issued in the United States in 1957 when the need for a
clean burning petroleum rocket fuel was recognized. Prior experimentation with jet fuels
produced tarry residue in the engine cooling passages and excessive soot, coke and other
deposits in the gas generator. Even with the new specifications, kerosene-burning engines still produce enough residues that their operational lifetimes are limited.
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Liquid oxygen and RP-1 are used as the propellant in the first-stage boosters of the Atlas
and Delta II launch vehicles. It also powered the first-stages of the Saturn 1B and Saturn V
rockets.
Cryogenic propellants are liquefied gases stored at very low temperatures, most frequently
liquid hydrogen (LH2) as the fuel and liquid oxygen (LO2 or LOX) as the oxidizer. Hydrogen
remains liquid at temperatures of -253 oC (-423 oF) and oxygen remains in a liquid state at temperatures of -183 oC (-297 oF) .
Because of the low temperatures of cryogenic propellants, they are difficult to store over
long periods of time. For this reason, they are less desirable for use in military rockets that
must be kept launch ready for months at a time. Furthermore, liquid hydrogen has a very
low density (0.071 g/ml) and, therefore, requires a storage volume many times greater
than other fuels. Despite these drawbacks, the high efficiency of liquid oxygen/liquid
hydrogen makes these problems worth coping with when reaction time and storability are
not too critical. Liquid hydrogen delivers a specific impulse about 30%-40% higher than most other rocket fuels.
Liquid oxygen and liquid hydrogen are used as the propellant in the high efficiency main
engines of the Space Shuttle. LOX/LH2 also powered the upper stages of the Saturn V and
Saturn 1B rockets, as well as the Centaur upper stage, the United States' first LOX/LH2 rocket (1962).
Another cryogenic fuel with desirable properties for space propulsion systems is liquid
methane (-162 oC). When burned with liquid oxygen, methane is higher performing than
state-of-the-art storable propellants but without the volume increase common with LOX/LH2
systems, which results in an overall lower vehicle mass as compared to common hypergolic
propellants. LOX/methane is also clean burning and non-toxic. Future missions to Mars will
likely use methane fuel because it can be manufactured partly from Martian in-situ
resources. LOX/methane has no flight history and very limited ground-test history.
Liquid fluorine (-188 oC) burning engines have also been developed and fired successfully.
Fluorine is not only extremely toxic; it is a super-oxidizer that reacts, usually violently, with
almost everything except nitrogen, the lighter noble gases, and substances that have
already been fluorinated. Despite these drawbacks, fluorine produces very impressive
engine performance. It can also be mixed with liquid oxygen to improve the performance of
LOX-burning engines; the resulting mixture is called FLOX. Because of fluorine's high toxicity, it has been largely abandoned by most space-faring nations.
Some fluorine containing compounds, such as chlorine pentafluoride, have also been considered for use as an 'oxidizer' in deep-space applications.
Hypergolic propellants are fuels and oxidizers which ignite spontaneously on contact with
each other and require no ignition source. The easy start and restart capability of hypergols
make them ideal for spacecraft maneuvering systems. Also, since hypergols remain liquid at
normal temperatures, they do not pose the storage problems of cryogenic propellants. hypergols are highly toxic and must be handled with extreme care.
Hypergolic fuels commonly include hydrazine, monomethyl hydrazine (MMH) and
unsymmetrical dimethyl hydrazine (UDMH). Hydrazine gives the best performance as a
rocket fuel, but it has a high freezing point and is too unstable for use as a coolant. MMH is
more stable and gives the best performance when freezing point is an issue, such as
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spacecraft propulsion applications. UDMH has the lowest freezing point and has enough
thermal stability to be used in large regeneratively cooled engines. Consequently, UDMH is
often used in launch vehicle applications even thou
Solid Propellants
Solid propellant motors are the simplest of all rocket designs. They consist of a casing,
usually steel, filled with a mixture of solid compounds (fuel and oxidizer) which burn at a
rapid rate, expelling hot gases from a nozzle to produce thrust. When ignited, a solid
propellant burns from the center out towards the sides of the casing. The shape of the
center channel determines the rate and pattern of the burn, thus providing a means to
control thrust. Unlike liquid propellant engines, solid propellant motors can not be shut down. Once ignited, they will burn until all the propellant is exhausted.
There are two families of solids propellants: homogeneous and composite. Both types are dense, stable at ordinary temperatures, and easily storable.
Homogeneous propellants are either simple base or double base. A simple base propellant
consists of a single compound, usually nitrocellulose, which has both an oxidation capacity
and a reduction capacity. Double base propellants usually consist of nitrocellulose and
nitroglycerine, to which a plasticiser is added. Homogeneous propellants do not usually
have specific impulses greater than about 210 seconds under normal conditions. Their main
asset is that they do not produce traceable fumes and are, therefore, commonly used in
tactical weapons. They are also often used to perform subsidiary functions such as jettisoning spent parts or separating one stage from another.
Modern composite propellants are heterogeneous powders (mixtures) which use a
crystallized or finely ground mineral salt as an oxidizer, often ammonium perchlorate, which
constitutes between 60% and 90% of the mass of the propellant. The fuel itself is
generally aluminum. The propellant is held together by a polymeric binder, usually
polyurethane or polybutadienes, which is also consumed as fuel. Additional compounds
are sometimes included, such as a catalyst to help increase the burning rate, or other
agents to make the powder easier to manufacture. The final product is rubberlike substance with the consistency of a hard rubber eraser.
Composite propellants are often identified by the type of polymeric binder used. The two
most common binders are polybutadiene acrylic acid acrylonitrile (PBAN) and hydroxy-
terminator polybutadiene (HTPB). PBAN formulations give a slightly higher specific impulse,
density, and burn rate than equivalent formulations using HTPB. However, PBAN propellant
is the more difficult to mix and process and requires an elevated curing temperature. HTPB
binder is stronger and more flexible than PBAN binder. Both PBAN and HTPB formulations
result in propellants that deliver excellent performance, have good mechanical properties, and offer potentially long burn times.
Solid propellant motors have a variety of uses. Small solids often power the final stage of a
launch vehicle, or attach to payloads to boost them to higher orbits. Medium solids such as
the Payload Assist Module (PAM) and the Inertial Upper Stage (IUS) provide the added
boost to place satellites into geosynchronous orbit or on planetary trajectories.
The Titan, Delta, and Space Shuttle launch vehicles use strap-on solid propellant rockets to
provide added thrust at liftoff. The Space Shuttle uses the largest solid rocket motors ever
built and flown. Each booster contains 500,000 kg (1,100,000 pounds) of propellant and can produce up to 14,680,000 Newtons (3,300,000 pounds) of thrust.
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Hybrid Propellants
Hybrid propellant engines represent an intermediate group between solid and liquid
propellant engines. One of the substances is solid, usually the fuel, while the other, usually
the oxidizer, is liquid. The liquid is injected into the solid, whose fuel reservoir also serves as
the combustion chamber. The main advantage of such engines is that they have high
performance, similar to that of solid propellants, but the combustion can be moderated,
stopped, or even restarted. It is difficult to make use of this concept for vary large thrusts,
ROCKET PROPELLANT PERFORMANCE
Combustion chamber pressure, Pc = 68 atm (1000 PSI) ... Nozzle exit pressure, Pe = 1 atm
Oxidizer Fuel
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An Introduction to Hybrid Rockets
Hybrid Rocket Engines are those which use liquid oxidizer and a solid fuel. Below figure shows
typical elements of an Hybrid Rocket Engine.
The liquid oxidizer is atomized and sprayed over the fuel block. In hypergolic systems, only gas
phase reactions occur. The oxidizer content of the hot product gases decreases along the port and
the length of the grain.
• Two of the issues in this combustion process are
• (i) mixing of the oxidizer rich and fuel rich gases across the diffusion flame occurs much
later than the length of the fuel grain and
• (ii) fuel regression rate is small.
The first issue is resolved by adding mixing devices and second issue is solved by adding a
certain amount of oxidizer into the fuel.
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• Hybrid rocket engines retain the advantage of controllability like liquid rockets. The
added safety is an attraction for use of hybrid rockets in situations calling for safety
similar to civil aircraft operations. There may be possibilities for their use in single stage-
to-orbit vehicles providing low cost access to space.
When considering different methods of propelling an aerospace vehicle, it must be realized that
there is an overall hierarchy of engines that produce a desired thrust. There are air-breathing
engines, which include most sub-orbital vehicles such as airplanes and jets, and then there are
spacecraft engines.
Among spacecraft engines there are two general types, those being electric propulsion and
chemical propulsion. Electric motors are very efficient and make excellent use of fuel, but
provide very little thrust. Chemical rockets, however, are powerful enough to launch payloads
from the ground into orbit.
In chemical rockets, the idea is to combine two substances, a fuel and an oxidizer, in some
mixing region. The chemical energy associated with combining these two substances is
transferred to the total flow as thermal (kinetic) energy. This high-energy flow can then be
expanded out a nozzle to provide thrust for the attached vehicle.
One major issue involved is apparent, for we need to what substance are best usable as oxidizer
and fuel. However, the even larger question is : what is the best way to mix the fuel and
oxidizer? The two long-standing answers to this question involve liquid and solid rockets.
However, a third response to this question seems to be feasible these days, and that answer
involves hybrid rockets.
To review, liquid rockets utilize liquid fuel and liquid oxidizer stored in tanks. By either pressure
feeding or by mechanically pumping the propellants from their tanks, they are forced into a
mixing chamber where chemical combustion occurs. These types of systems generally provide
good thrust and can be thrust-controlled (throttled). In addition, they tend to be the most efficient
of high-thrust engines. However, the complexity of these systems is also high. There are stop-
valves, pressure regulators, injectors, turbopump machinery and all sorts of “plumbing”. When
considering that there needs to be redundancies on all of these systems in order to make a
reliable motor, it easy to see that the overall cost and weight of liquid rockets will be excessive.
In addition, due to the liquid nature of the propellants involved, there can also be storage
problems.
Solid rockets are somewhat different in nature, but also have a specific set of advantages and
drawbacks. In solid rocket motors, the fuel and oxidizer are chemically premixed to form a solid
fuel grain. By simply igniting this substance, the oxidizer and fuel in the solid react and produce
the high-energy combustion gases desired. A variety of designs for the central burning port of the
solid fuel can be created so as to produce the desired thrust performance. Solid rockets provide
good thrust and are the most simple systems available. On the down side, they also are fairly
inefficient fuel burners and cannot be throttled. In some cases there may also be explosion
dangers since the oxidizer and fuel are not separated.
It appears necessary to obtain some "optimal" solution to this dilemma. On the one hand, we
have a high-thrust rocket engine with good performance but high complexity and cost, while on
the other hand to get low complexity we must accept lower performance as well. It is at this
point where hybrid rockets become an attractive alternative. Hybrid rockets combine elements
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from both types of rockets. In a hybrid rocket, a gaseous or liquid oxidizer is stored in a tank
separate from a solid fuel grain. The fuel grain is placed inside a pressure chamber which lies
between an oxidizer injector and the exit nozzle. The solid grain is hollowed out in the same
fashion to produce a combustion port, very similar to that of a solid rocket motor type system.
Unless the fuel is hypergolic (spontaneously combustible in the presence of an oxidizer), the fuel
must be initially ignited in order to vaporize some of the fuel into a region just above the solid
surface. Then, by injecting the oxidizer at a high mass flow rate and pressure into the pressure
chamber / combustion port area, the oxidizer and fuel are free to react in a thin boundary layer
just above the surface of the fuel grain. The high energy released and the high temperature
attained both increase the energy in the flow and sustain the solid fuel vaporization. The
combustion gases pass down the remainder of the combustion port and are expanded via nozzle.
By changing the flow rate of the oxidizer, the total production of combustion gases and the
energy going into them will be changed in a like fashion (increasing or decreasing). This fact
demonstrates that hybrid rockets can be throttled. Given a simple ignition system that would
Coasting Flight
Coasting is defined as the free flight of a space vehicle during which the thrust acting on it is
zero.
The thrust is zero after the “burn out” and the rocket coasts. During this flight the rocket
ascends to the maximum altitude and decelerates to zero velocity. Therefore,
u = up - gtc = 0
The coasting time is given by, tc = up / g
The gain in altitude during coasting is given by,
2
2
1ccpc gttuZ −=
Thrust vectoring
• Thrust vectoring is the ability of an aircraft or rocket or other vehicle to deflect the angle
of its thrust away from the vehicles longitudinal axis.
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• The advantages of thrust vectoring systems on aircraft include improved post stall
performance, the ability (ability to change the body's position, and requires a
combination of balance, coordination, speed, strength, endurance etc.) to operate on
damaged airfields due to reduced takeoff distances and overall enhanced agility.
• These factors can provide substantial benefits for military aircraft, which are primarily
concerned with manoeuvrability and control.
• The concept of thrust vectoring is not a new one. The Germans used graphite control
vanes in the exhaust stream of their V-2 ballistic missile in World War II for some
directional control.
• Thrust vectoring in aircraft though is a relatively new practice and the concept came
under widespread consideration during the cold war.
• There are several methods employed to produce thrust vectoring.
• Most current production aircraft with thrust vectoring use turbofan engines with
rotating nozzles or turning vanes to deflect the exhaust stream. This method can deflect
thrust to as much as 90 degrees providing a vertical take off and landing capability.
However for vertical thrust the engine has to be more powerful to overcome the weight
of the aircraft, this means the aircraft requires a bigger heavier engine. As a result of the
increased overall weight of the aircraft the manoeuvrability and agility are reduced in
normal horizontal flight.
• Another method to produce thrust vectoring is through fluidic thrust vector control. This
is achieved using a static nozzle and a secondary flow between the primary jet and the
nozzle. This method is desirable for its lower weight, mechanical simplicity and lower
radar cross section.
Advantages and Disadvantages of Thrust Vector Control
• Thrust-vectoring research to date has successfully identified and demonstrated many
potential benefits to high-performance aircraft.
• These include enhanced aircraft manoeuvrability, performance, survivability, and
stealth.
• The full extent of these benefits, however, has yet to be realized even with new
generation aircraft because current mechanical thrust-vectoring configurations are
heavy, complex, and expensive.
Countercurrent shear layer enhancement for fluidic thrust vector control
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Photo courtesy Pratt & Whitney, A United Technologies Company
F119 engine for F/A-22 Raptor showing the 2 extreme vectoring cases
• Thrust Vector Control or Thrust Vectoring is a technology that deflects the mean flow of
an engine jet from the centerline in order to transfer some force to the aimed axis. By
that imbalance, a momentum is created and used to control the change of attitude of
the aircraft.
• Among other things, thrust vectoring greatly improves maneuverability, even at high
angles of attack or low speeds where conventional aerodynamic control surfaces lose all
effectiveness.
• Thrust Vector Control is currently achieved by complex arrays of mechanical actuators
capable of modifying the geometry of the nozzle and thus defect the flow.
• This variable geometry greatly increases weight and maintenance to the engine, and
therefore limits the benefits from vectoring the thrust.
• Fluidic Thrust Vector Control is a technology aiming at the above listed benefits by the
use of fluidic means, implying less complexity and faster dynamic responses.
• Different concepts have been developed in the last decade to redirect the thrust
without mechanical actuators.
• Induction to flow separation, countercurrent shear layer, synthetic pulses or skewing of
the sonic line are some of the proven concepts.
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• Countercurrent shear flow control has been established as an effective method for
fluidic thrust vector control.
• However, hardware integration issues exist and must be overcome in order to make a
viable technology for future aircraft.
• Recent developments in fluidic thrust vector control have focused on nozzle interior
methods that skew the throat of the nozzle using multiple transverse jets.
Rockets
• The thrust vector control history first came from rocket. The evolution of the rocket
has made it an indispensable tool in the exploration of space.
• For centuries, rockets have provided ceremonial and warfare uses starting with the
ancient Chinese, the first to create rockets. But for centuries rockets were in the main
rather small, and their use was confined principally to weaponry, the projection of
lifelines in sea rescue, signalling, and fireworks displays.
• Not until the 20th century did a clear understanding of the principles of rockets emerge,
and only then did the technology of large rockets begin to evolve. Thus, as far as
spaceflight and space science are concerned, the story of rockets up to the beginning of
the 20th century was largely prologue.
•
• Early in the 20th century, an American scientist, Robert H. Goddard (1882-1945), he
began to try various types of solid fuels and to measure the exhaust velocities of the
burning gases.
• Since the earliest days of discovery and experimentation, rockets have evolved from
simple gunpowder devices into giant vehicles capable of travelling into outer space.
• Rockets have opened the universe to direct exploration by humankind.
• A third great space pioneer, Hermann Oberth (1894-1989) of Germany, published a
book in 1923 about travel into outer space has led to the development of the V-2
rocket. The V-2 rocket (in Germany called the A-4) was small by comparison to today's
designs.
• It achieved its great thrust by burning a mixture of liquid oxygen and alcohol at a rate of
about one ton every seven seconds.
• Once launched, the V-2 was a formidable weapon that could devastate whole city
blocks. Other than that, the V-2 rocket use graphite vanes in the exhaust to achieve the
thrust vector control.
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• The concept of thrust vectoring is not a new one. The Germans used graphite control
vanes in the exhaust stream of their V-2 ballistic missile in World War II for some
directional control. Thrust vectoring in aircraft though is a relatively new practice and
the concept came under widespread consideration during the cold war.
• There are several methods employed to produce thrust vectoring. Most current
production aircraft with thrust vectoring use turbofan engines with rotating nozzles or
turning vanes to deflect the exhaust stream.
• This method can deflect thrust to as much as 90 degrees providing a vertical take off
and landing capability. However for vertical thrust the engine has to be more powerful
to overcome the weight of the aircraft, this means the aircraft requires a bigger heavier
engine. As a result of the increased overall weight of the aircraft the manoeuvrability
and agility are reduced in normal horizontal flight.
Thrust vector control in rockets
• All chemical propulsion systems can be provided with one of several types of thrust
vector control (TVC) mechanisms.
• Some of these apply either to solid, hybrid, or to liquid propellant rocket propulsion
systems, but most are specific to only one of these propulsion categories.
• Thrust vector control is effective only while the propulsion system is operating and
creating an exhaust jet. For the flight period, when a rocket propulsion system is not
firing and therefore its TVC is inoperative, a separate mechanism needs to be provided
to the flying vehicle for achieving control over its attitude or flight path.
Hence, there are two types of thrust vector control concept:
(1) for an engine or a motor with a single nozzle; and
(2) for those that have two or more nozzles.
TVC Mechanisms with a single nozzle
• Mechanical deflection of the nozzle or thrust chamber.
• Insertion of heat-resistant movable bodies into the exhaust jet; these experience
aerodynamic forces and cause a deflection of a part of the exhaust gas flow.
• Injection of fluid into the side of the diverging nozzle section, causing an asymmetrical
distortion of the supersonic exhaust flow.
• Separate thrust-producing devices that are not part of the main flow through nozzle.