Solution of KME 064
Que 1
Define Mach Number.
(a)
Ans The Mach number is the ratio of flow velocity after a certain limit of the sound’s speed. In
simple words, it is the ratio of the speed of a body to the speed of sound in the
surrounding medium.
Que 1 What is a stagnation state?
(b)
Ans In thermodynamics and fluid mechanics, stagnation temperature is the temperature at a
stagnation point in a fluid flow. At a stagnation point the speed of the fluid is zero and all
of the kinetic energy has been converted to internal energy and is added to the local static
enthalpy.
Qu Explain Mach cone and Mach Angle.
e1
(c)
Que 1 What is a choked flow in a nozzle?
(d)
Ans Choked flow is a limiting flow that occurs as a result of liquid vaporization when the
internal valve pressure falls below the liquid's vapor pressure. Cavitation has then fully
developed within the valve, and an increase in pressure drop across the valve will not
produce an increase through the valve.
Que 1 Define normal shock.
( e)
Ans If the shock wave is perpendicular to the flow direction it is called a normal shock. A
normal shock occurs in front of a supersonic object if the flow is turned by a large amount
and the shock cannot remain attached to the body. The detached shock occurs for both
wedges and cones
Que 1 What is a Fanno flow?
(f)
Ans Fanno flow is the adiabatic flow through a constant area duct where the effect
of friction is considered. Compressibility effects often come into consideration, although
the Fanno flow model certainly also applies to incompressible flow. For this model, the
duct area remains constant, the flow is assumed to be steady and one-dimensional, and no
mass is added within the duct. The Fanno flow model is considered an irreversible
process due to viscous effects..
Que 1 Define thrust. Write an expression for calculating the thrust in jet engines.
(g)
Ans Thrust is the force which moves an aircraft through the air. Thrust is generated by
the propulsion system of the airplane.
Que 1 Define the propulsive efficiency of a jet engine.
(h)
Ans The efficiency of a propulsor, propulsive efficiency ηp, is the portion of the available
energy that is usefully applied in propelling the aircraft compared to the total energy of
the jet stream.
Que 1 What is a specific impulse?
(i)
Ans Specific impulse (usually abbreviated Isp) is a measure of how efficiently a reaction mass
engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines
whose reaction mass is only the fuel they carry, specific impulse is exactly proportional to
the effective exhaust gas velocity.
A propulsion system with a higher specific impulse uses the mass of the propellant more
efficiently. In the case of a rocket, this means less propellant needed for a given delta-
v, so that the vehicle attached to the engine can more efficiently gain altitude and
velocity.
Que 1 Define a monopropellant. Give examples.
(j)
Ans A monopropellant is a chemical propulsion fuel which does not require a separate
oxidizer. A rocket engine which is based on a monopropellant requires only one fuel line
instead of a fuel and an oxidizer line. The "mono" in monopropellant means singular--a
fuel that can function alone. A chemical propulsion system that combines like hydrogen
and oxygen would be a bipropellant. A monopropellant burns by itself because the
oxidizer is bound into the molecule itself. This makes the rocket engine lighter, less
expensive, and more reliable. Monopropellant designs are typically used in control
thrusters but not in actual propulsion units.
SECTION-B
Que 2 (a) Discuss compressible and incompressible flows. Explain the different regions of
a compressible flow.
Ans The fluids, such as gas, are classified as Incompressible and Compressible fluids.
Incompressible fluids do not undergo significant changes in density as they flow. In
general, liquids are incompressible; water being an excellent example. In contrast
compressible fluids do undergo density changes. Gases are generally compressible; air
being the most common compressible fluid we can find. Compressibility of gases
leads to many interesting features such as shocks, which are absent for incompressible
fluids
A flow is classified as incompressible if the density remains nearly constant.
The terms compressibility and incompressibility describe the ability of molecules in a
fluid to be compacted or compressed (made more dense) and their ability to bounce
back to their original density, in other words, their "springiness." An incompressible
fluid cannot be compressed and has relatively constant density throughout. Liquid is
an incompressible fluid. A gaseous fluid such as air, on the other hand, can be either
compressible or incompressible. Generally, for theoretical and experimental purposes,
gases are assumed to be incompressible when they are moving at low speeds--under
approximately 220 miles per hour. The motion of the object traveling through the air at
such speed does not affect the density of the air. This assumption has been useful in
aerodynamics when studying the behavior of air in relation to airfoils and other objects
moving through the air at slowerspeeds. However, when aircraft began traveling faster
than 220 miles per hour, assumptions regarding the air through which they flew that
were true at slower speeds were no longer valid. At high speeds some of the energy of
the quickly moving aircraft goes into compressing the fluid (the air) and changing its
density. The air at higher altitudes where these aircraft fly also has lower density than
air nearer to the Earth's surface. The airflow is now compressible, and aerodynamic
theories have had to reflect this. Aerodynamic theories relating to compressible airflow
characteristics and behavior are considerably more complex than theories relating to
incompressible airflow. The noted aerodynamicist of the early 20th century, Ludwig
Prandtl, contributed the Prandtl-Glaubert rule for subsonic airflow to describe the
compressibility effects of air at high speeds. At lower altitudes, air has a higher density
and is considered incompressible for theoretical and experimental purposes
➢ Liquid flows are typically incompressible.
➢ Gas flows are often compressible, especially for high speeds.
➢ Mach number, Ma = V/c is a good indicator of whether or not compressibility
effects are important.
➢ Ma < 0.3 : Incompressible
➢ Ma < 1 : Subsonic
➢ Ma = 1 : Sonic
➢ Ma > 1 : Supersonic
➢ Ma >> 1 : Hypersonic
Subsonic flow region :The subsonic flow region is on the right of the
incompressible flow region. In subsonic flow, fluid velocity (c) is less than the
sound velocity (a) and the Mach number in this region is always less than
unity. i.e. M = ca 1. Eg: passenger air craft
Sonic flow region If the fluid velocity (c) is equal to the sound velocity (a),
that type of flow is known as sonic flow. In sonic flow Mach number value is
unity. M = ca = 1 c = a. Eg: Nozzle throat
➢ Transonic flow region : If the fluid velocity close to the speed of sound, that
type of flow is known as transonic flow .In transonic flow, Mach number value is
in between 0.8 and 1.2. i.e.0.8 < M < 1.2.
Supersonic flow region: The supersonic region is in the right of transonic
flow region. In supersonic flow, fluid velocity ( c) is more than the sound
velocity (a) and the mach number in this region is always greater than unity
Hypersonic flow region: In hypersonic flow region, fluid velocity ( c) is
much greater than sound velocity ( a). In this flow mach number is always
greater than unity.
Que 2 Explain the behavior of the flow through a convergent nozzle.
(b)
Ans Convergent nozzles are used almost in all the present subsonic transports. Moreover, in
most cases also these convergent nozzles are choked and incomplete expansion of the
flowing gases to the ambient pressure is encountered. At nozzle outlet, the gases exit at
sonic speed, while the pressure is greater than the ambient pressure. Thus, a pressure
thrust force is developed. On the contrary, C-D nozzle satisfies a full expansion to the
ambient pressure.
Thus, the exit and ambient pressures are equal and the exit velocity is higher than the sonic
speed. C-D nozzle develops higher momentum thrust that is greater than the pressure
thrust of a convergent nozzle operating at the same inlet conditions. Thus, if both types are
examined for the case of subsonic civil transports, C-D nozzle provides
higher thrust. However, it has the penalties of increased weight, length, and diameter,
leading to an increase of aircraft weight, possibly drag
The convergent nozzle is very similar to comvergent part of C-D nozzle. However main
difference is that flow in C-D nozzle is assumed Incentropic while in convergent nozzle
is assumed to be adiabatic.
If the nozzle is chocked then the exit mach number is unity then temperature ratio is then
Que 2 Differentiate between
(C) (a) Fanno flow and Rayleigh flow
(b) Normal and Oblique shocks
Ans Fanno Line:
The line representing the locus of points with the same mass velocity
and stagnation enthalpy is called a Fanno line.
It is a one-dimensional model for adiabatic flow in a constant area
duct with friction.
It is a combination of continuity and energy equations.
Fanno line on h-s diagram:
Here, G3>G2>G1
Rayleigh line:
The line representing the locus of points with the same impulse
pressure and mass velocity is called a Rayleigh line.
It is a model for flow in a constant area duct with heat transfer,
but without friction.
It is a combination of continuity and momentum equations.
Rayleigh line on h-s plot:
Here, M is Mach number
Normal and oblique shock
If the shock wave is perpendicular to the flow direction, it is called a normal shock. There
are equations which describe the change in the flow variables. The equations are derived
from the conservation of mass, momentum, and energy. Depending on the shape of the
object and the speed of the flow, the shock wave may be inclined to the flow direction.
When a shock wave is inclined to the flow direction it is called an oblique shock. On this
slide we have listed the equations which describe the change in flow variables for flow
across an oblique shock. The equations presented here were derived by considering the
conservation of mass, momentum, and energy for a compressible gas while ignoring
viscous effects. The equations have been further specialized for a two-dimensional flow
without heat addition. The equations only apply for those combinations of free stream
Mach number and deflection angle for which an oblique shock occurs. If the deflection is
too high, or the Mach too low, a normal shock occurs. For the Mach number change
across an oblique shock there are two possible solutions; one supersonic and one
subsonic. In nature, the supersonic ("weak shock") solution occurs most often. However,
under some conditions the "strong shock", subsonic solution is possible.
Oblique shocks are generated by the nose and by the leading edge of the wing and tail of
a supersonic aircraft. Oblique shocks are also generated at the trailing edges of the aircraft
as the flow is brought back to free stream conditions. Oblique shocks also occur
downstream of a nozzle if the expanded pressure is different from free stream conditions.
In high speed inlets, oblique shocks are used to compress the air going into the engine.
The air pressure is increased without using any rotating machinery.
Que 2 Describe the working of a turboprop engine with the help of a diagram. Write their
(d) advantages and disadvantages
Que 2 Explain the construction and working of
(e) (a)Solid Propellant Rocket Engines and
(b)Liquid Propellant Rocket Engines.
Ans (a) Solid Propellant Rocket Engines
solid-propellant rocket engine (SPRE) is one of the oldest non-air-breathing engines as it
is believed to have been used in China as early as the thirteenth century onward for war
purposes. The solid propellant composition, which was initially black powder, underwent
a series of changes with time. Currently, solid propellants have found a wider application
in various propulsion and gas-generating systems. It has a wide range of thrust levels
ranging from a few N (Newton) to several hundred N. Besides having a solid form, this
propellant can be stored in the combustion chamber ready for use for a longer period of
time, on the order of 10–20 years, provided they are hermitically sealed. Compared to
other types of chemical rocket engines, these are economical, reliable, and simple. Hence,
these engines find a wider range of both civilian and military applications.
Let us consider a simple SPRE as shown in Figure which basically consists of the major
components that are a solid propellant, a combustion chamber, an igniter, and a nozzle.
Note that the propellant, which mainly consists of fuel, oxidizers, and various additives, is
entirely stored within the combustion chamber in the form of blocks of definite shape
called grain and is supported by the walls or by special grids, traps, or retainers. Note that
this grain contributes to around 80%– 95% of the total mass of an SPRE. Hence, the
performance of this kind of engine and its payload capability are dependent on the
optimal design of the grain. The igniter initiates the combustion process on the surface of
the propellant when actuated with the help of an electrical switch. As a result, the
propellant grains will start burning and filling the empty combustion chamber, hence
building up the chamber pressure. Subsequently, the high-temperature and high-pressure
gases are expanded in the supersonic nozzle to produce the requisite thrust. Generally,
these nozzles are made of high-temperature materials, namely, metals with graphite
coating, and are ablative materials that can take a high thermal load with minimal
corrosion. Generally, a fixed nozzle is preferred in SPREs. Hence, a solid rocket engine is
considered to be a non-air-breathing vehicle without any moving parts. But in recent
times, the gimbaled nozzle is being used for controlling the direction of thrust.
Liquid Propellant Rocket Engines.
An American professor, Robert Goddard, had designed and developed an LPRE, which
had flown only 46 m. Subsequently, the Germans took this technology to a mature level
that culminated in the famous V2 rocket engine. Currently, the LPRE has found a wider
application in various propulsion and gas-generating systems. It has a wide range of thrust
levels ranging from a few N (Newton) to several hundred N. In addition to having a liquid
form, this propellant can be stored in a separate tank and can be controlled easily, and
hence thrust can be varied easily unlike in an SPRE. As LPREs are stored in separate
tanks unlike SPRE, one can achieve a higher level of thrust and is thus considered to be
more powerful than an SPRE. Therefore, it is preferred for large spacecraft and ballistic
missiles. However, the design of an LPRE is quite complex and requires specialized
nozzles. Compared to other types of chemical rocket engines, LPREs are compact, light,
economical, and highly reliable. Hence, they have a wider range of both civilian and
military applications.
Let us consider a simple LPRE as shown in Figure 1.5b, which basically consists of major
components, namely, a propellant feed system, a combustion chamber, an igniter system,
and a nozzle. Note that both fuel and oxidizer propellants are stored separately in special
tanks at high pressure. Of course the propellant feed system along with the propellant
mass contributes significantly to the mass of the engine but it is significantly less
compared to the total mass of an SPRE. In fact, sometimes, the mass of the nozzle for
deep-space applications is comparable to the propellant mass and its feed system in the
case of an LPRE. The pressurized liquid propellants are converted into spray consisting of
arrays of droplets with the help of atomizers as shown in Figure 1.5b. Of course, an
igniter is used to initiate the combustion process on the surface of the propellant. As a
result, the propellant will start burning and fill up the empty thrust chamber, thereby
building up pressure in the chamber similar to that of other chemical rocket engines.
Subsequently, these high-temperature and high-pressure gases are expanded in a CD
nozzle to produce the requisite thrust. As mentioned earlier, these nozzles are made of
high-temperature materials, namely, metals with graphite coating and ablative materials
that can take a high thermal load with minimal corrosion. It may be noted that propellant
feed lines have several precision valves with whose help the operations of such kinds of
rocket engine can be started and shut off at will, and hence repetitive operation is possible
for this engine unlike the SPRE.
Section-C
Qu
e3
(a)
Ans
Ans
Que 3 Air (γ = 1.4, R = 0.287 kJ/kg K) enters a straight axisymmetric duct at 300 K, 3.45 bar,
(b) 150 m/s and leaves it at 277 K, 2.058 bar, and 260 m/s. The area of the cross- section at
the entry is 500 cm2. Assuming adiabatic flow, calculate:
(a) Stagnation temperature
(b) Maximum velocity
(c) Mass flow rate
(d) Area of the cross-section at the exit
Qu Explain the variation of the flow parameters with Mach number in case of an isentropic
e4 flow of gas through a nozzle and a diffuser.
(a)
Que A conical diffuser has entry and exit diameters of 15 cm and 30 cm, respectively.
4 (b) The pressure, temperature, and velocity of air at entry are 0.69 bar, 340 K, and 180 m/s,
respectively. Calculate:
(a) Exit pressure and (b) Exit velocity and (c) force exerted on diffuser
walls.
Qu State and prove the Prandtl-Meyer relation for a normal shock.
e5
(a)
Que a. The state of a gas (γ =1.3, R =0.469 KJ/kg K) upstream of the normal shock
5 (b) wave is given by the following data: M x =2.5, Px =2 bar and Tx =275 K.
Calculate the following downstream of the shock:
(a) Mach number, (b) Pressure, and (c) Temperature
Qu Compare the construction and working of a turbojet and turbofan engine with the
e6 help of a neat sketch.
(a)
Turbojet Engine
The turbojet is an airbreathing jet engine, typically used in aircraft. It consists of a gas
turbine with a propelling nozzle. The gas turbine has an air inlet, a compressor, a combustion
chamber, and a turbine (that drives the compressor). The compressed air from the compressor
is heated by burning fuel in the combustion chamber and then allowed to expand through the
turbine. The turbine exhaust is then expanded in the propelling nozzle where it is accelerated
to high speed to provide thrust.Two engineers, Frank Whittle in the United Kingdom and
Hans von Ohain in Germany, developed the concept independently into practical engines
during the late 1930s.
While the turbojet was the first form of gas turbine powerplant for aviation, it has largely
been replaced in use by other developments of the original concept. In operation, turbojets
typically generate thrust by accelerating a relatively small amount of air to very high
supersonic speeds, whereas turbofans accelerate a larger amount of air to lower transonic
speeds. Turbojets have been replaced in slower aircraft by turboprops because they have
better specific fuel consumption. At medium speeds, where the propeller is no longer
efficient, turboprops have been replaced by turbofans. The turbofan is quieter and has better
range-specific fuel consumption than the turbojet. Turbojets can be highly efficient for
supersonic aircraft.
Turbojets have poor efficiency at low vehicle speeds, which limits their usefulness in
vehicles other than aircraft. Turbojet engines have been used in isolated cases to power
vehicles other than aircraft, typically for attempts on land speed records. Where vehicles are
"turbine-powered", this is more commonly by use of a turboshaft engine, a development of
the gas turbine engine where an additional turbine is used to drive a rotating output shaft.
These are common in helicopters and hovercraft. Turbojets were used on Concorde and the
longer-range versions of the TU-144 which were required to spend a long period travelling
supersonically. Turbojets are still common in medium range cruise missiles, due to their high
exhaust speed, small frontal area, and relative simplicity. They are also still used on some
supersonic fighters such as the MiG-25, but most spend little time travelling supersonically,
and so employ turbofans and use afterburners to raise exhaust speed for supersonic sprints.
Turbojets are the oldest kind of general-purpose jet engines.Turbojets are rotary engines that
extracts energy from a flow of combustion gasThey produce thrust by increasing the velocity
of the air flowing through the engine and operate on Newton’s third law of motion " For
every action there is an equal and opposite reaction”. Newton’s 2nd Law on motion F= Mass
* Acceleration. Here Large acceleration with small mass of air
a-1 Isentropic increase in pressure (diffuser)
1-2 Isentropic compression (compressor)
2-3 Isobaric heat addition (combustion chamber)
3-4 Isentropic expansion (turbine)
4-5 Isentropic decrease in pressure with an increase in fluid velocity (nozzle)
The operation of a turbojet is modelled approximately by the Brayton cycle. The efficiency
of a gas turbine is increased by raising the overall pressure ratio, requiring higher-
temperature compressor materials, and raising the turbine entry temperature, requiring better
turbine materials and/or improved vane/blade cooling. It is also increased by reducing the
losses as the flow progresses from the intake to the propelling nozzle. These losses are
quantified by compressor and turbine efficiencies and ducting pressure losses. When used in
a turbojet application, where the output from the gas turbine is used in a propelling nozzle,
raising the turbine temperature increases the jet velocity. At normal subsonic speeds this
reduces the propulsive efficiency, giving an overall loss, as reflected by the higher fuel
consumption, or SFC. However, for supersonic aircraft this can be beneficial, and is part of
the reason why the Concorde employed turbojets. Turbojet systems are complex systems
therefore to secure optimal function of such system, there is a call for the newer models
being developed to advance its control systems to implement the newest knowledge from the
areas of automation, so increase its safety and effectiveness
Turbo-Fan Engine
Propulsion efficiency is a function of the exhaust velocity to flight speed ratio. This can be
increased by reducing the effective exhaust velocity. In a turbofan engine, a fan of a larger
diameter than the compressor is used to generate a mass flow higher than the core mass flow.
This ratio is called the bypass ratio.Turbofan engines have a higher propulsion efficiency as
compared with turbojet engines operating in the same speed range. A turbofan engine is the
most modern variation of the basic gas turbine engine. As with other gas turbines, there is a
core engine, whose parts and operation are discussed on a separate page. In the turbofan
engine, the core engine is surrounded by a fan in the front and an additional turbine at the
rear.
Fan
The fan is responsible for producing the majority of the thrust generated by a turbofan
engine and is easily visible when looking at the front of the engine.The fan is directly
connected to the low pressure compressor (LPC) and the low pressure turbine (LPT) by way
of a shaft known as the low pressure shaft. Turbofans were invented to circumvent the
undesirable characteristic of turbojets being inefficient for subsonic flight. To raise the
efficiency of a turbojet, the obvious approach would be to increase the burner temperature, to
give better Carnot efficiency and fit larger compressors and nozzles. However, while that
does increase thrust somewhat, the exhaust jet leaves the engine with even higher velocity,
which at subsonic flight speeds, takes most of the extra energy with it, wasting fuel.Instead, a
turbofan can be thought of as a turbojet being used to drive a ducted fan, with both of those
contributing to the thrust. Whereas all the air taken in by a turbojet passes through the turbine
(through the combustion chamber), in a turbofan some of that air bypasses the
turbine.Because the turbine has to additionally drive the fan, the turbine is larger and has
larger pressure and temperature drops, and so the nozzles are smaller. This means that the
exhaust velocity of the core is reduced. The fan also has lower exhaust velocity, giving much
more thrust per unit energy (lower specific thrust). The overall effective exhaust velocity of
the two exhaust jets can be made closer to a normal subsonic aircraft's flight speed. In effect,
a turbofan emits a large amount of air more slowly, whereas a turbojet emits a smaller
amount of air quickly, which is a far less efficient way to generate the same thrustThe ratio of
the mass-flow of air bypassing the engine core compared to the mass-flow of air passing
through the core is referred to as the bypass ratio. The engine produces thrust through a
combination of these two portions working together; engines that use more jet thrust relative
to fan thrust are known as low-bypass turbofans, conversely those that have considerably
more fan thrust than jet thrust are known as high-bypass. Most commercial aviation jet
engines in use today are of the highbypass type and most modern military fighter engines are
low-bypass. Afterburners are not used on high-bypass turbofan engines but may be used on
either low-bypass turbofan or turbojet engines
Compressor
The purpose of compression is to prepare the air for combustion by adding energy in the
form of pressure and heat.The compressor is divided into two portions: the low pressure
compressor, mentioned above, and the high pressure compressor however, they interact with
different parts of the turbofan engine.
Combustion Chamber
Combustion occurs within the combustor, a stationary chamber within the core of the engine
The combustor is directly downstream of the HPC and directly upstream of the high pressure
. The purpose of the combustor is to add even more energy to the air flow by way of heat
addition. Within the combustor, fuel is injected and mixed with the air. This fuel-air mixture
is then ignited, creating a dramatic increase in temperature and energizing the flow,
propelling it rearward towards the high pressure turbine.
Turbine
Expansion occurs within the high pressure and low pressure turbines. Similar in appearance
to the compressors, the turbines have rows of blades which spin . The purpose of the turbines
is to extract energy from the flow which is then used to spin the compressors and the fan. The
spinning fan draws more air through the core of the engine which continues the entire
process, and it pulls more bypass air around the engine, generating continuous thrust.
Nozzle
The exhaust nozzle is located directly downstream of the LPT and it is the last component
that the air flow touches before exiting the engine. The purpose of the exhaust nozzle is to
propel the core flow out of the engine, providing additional thrust. This is accomplished by
way of its geometry or shape. The nozzle also helps regulate pressures within the engine to
keep the other components functioning properly and efficiently.
Qu a. An aircraft fly at 960 kmph. One of its turbojet engines takes in 40 kg/s of air and
e expands the gases to ambient pressure. The air-fuel ratio is 50 and the lower
6 calorific value of the fuel is 43 MJ/kg. For maximum thrust power, calculate the
(b) following:
(c) Jet Velocity, (b) Thrust, (c) Specific Thrust, (d) Thrust Power, and (e)
Propulsive, thermal, and overall efficiencies
An (a) Jet Velocity:
s
(b) Thrust: (c) Specific thrust
(d)Thrust Power:
( e) Propulsive, thermal, and overall efficiencies
