CFD is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. In this thesis, CFD analysis of flow within Convergent-Divergent supersonic nozzle of different cross sections rectangular, square and circular has been performed. The analysis has been performed according to the shape of the supersonic nozzle and keeping the same input conditions. Our objective is to investigate the best suited nozzle which gives high exit velocity among the different cross sections considered. The application of these nozzles is mainly in torpedos. The work is carried out in two stages: 1.Modeling and analysis of flow for supersonic nozzles of different cross sections.2.Prediction of best suited nozzle among the nozzles considered. In this, initially modeling of the nozzles has been done in CATIA and later on mesh generation and analysis have been carried out in ANSYS FLUENT 14.5 and various contours like velocity, pressure, temperature have been taken and their variation according to different nozzles has been studied.

1. IN(Online): 4142-3453 February 2017 Issue
DESIGNANDANALYSISOFCONVERGENTDIVERGENT NOZZLE USINGCFD
Rama Thulasi1
, N. Jashuva 2
1
M.Tech (MECH)., Dept of Mech., Global College Of Engineering and Technology, Kadapa, Andhra Pradesh.
2
Assistant Professor, Dept of Mech, Global College Of Engineering and Technology, Kadapa, Andhra Pradesh.
Abstract- CFD is a branch of fluid mechanics that uses
numerical methods and algorithms to solve and analyze
problems that involve fluid flows. Computers are used to
perform the calculations required to simulate the interaction
of liquids and gases with surfaces defined by boundary
conditions. In this thesis, CFD analysis of flow within
Convergent-Divergent supersonic nozzle of different cross
sections rectangular, square and circular has been performed.
The analysis has been performed according to the shape of the
supersonic nozzle and keeping the same input conditions. Our
objective is to investigate the best suited nozzle which gives
high exit velocity among the different cross sections
considered. The application of these nozzles is mainly in
torpedos. The work is carried out in two stages: 1.Modeling
and analysis of flow for supersonic nozzles of different cross
sections.2.Prediction of best suited nozzle among the nozzles
considered. In this, initially modeling of the nozzles has been
done in CATIA and later on mesh generation and analysis
have been carried out in ANSYS FLUENT 14.5 and various
contours like velocity, pressure, temperature have been taken
and their variation according to different nozzles has been
studied.
1.INTRODUCTION
A nozzle is a device that is used to increase the velocity of a
flowing fluid. It does this by reducing the pressure.
CONVERGENT-DIVERGENT nozzle is designed for
attaining speeds that are greater than speed of sound. the
design of this nozzle came from the area-velocity relation
(dA/dV)=-(A/V)(1-M^2) M is the Mach number ( which
means ratio of local speed of flow to the local speed of
sound) A is area and V is velocity
The following information can be derived from the area-
velocity relation -
1. For incompressible flow limit, i.e. for M tends to zero, AV
= constant. This is the famous volume conservation equation
or continuity equation for incompressible flow.
2. For M < 1, a decrease in area results in increase of
velocity and vice vera. Therefore, the velocity increases in a
convergent duct and decreases in a Divergent duct. This
result for compressible subsonic flows is the same as that for
incompressible flow.
3. For M > 1, an increase in area results in increase of
velocity and vice versa, i.e. the velocity increases in a
divergent duct and decreases in a convergent duct. This is
directly opposite to the behavior of subsonic flow in
divergent and convergent ducts.
4. For M = 1, dA/A = 0, which implies that the location where
the Mach number is unity, the area of the passage is either
minimum or maximum. We can easily show that the
minimum in area is the only physically realistic solution. One
important point is that to attain supersonic speeds we have to
maintain favorable pressure ratios across the nozzle.
Taking the rectangular bent nozzle as reference and keeping
the inlet, throat and exit areas and the axis
length constant, three dimensional rectangular, square and
circular straight nozzles geometries were generated.
1.Square Shape:
2.Circular Shape:

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3.Rectangular Shape
II LITERATURE SURVEY
JET ENGINE
A jet engine is a system for turning fuel into thrust (ahead
motion). The thrust is produced with the aid of action and
reaction a bit of physics additionally known as Newton’s 0.33
law of movement The pressure (movement) of the exhaust
gases pushing backward produces an same and opposite force
(response) known as thrust that powers the automobile ahead.
exactly the same principle pushes a skateboard ahead when you
kick backward along with your foot. In a jet engine, it's the
exhaust gas that gives the "kick".
Jet engine designs are regularly modified for non-aircraft
programs, as business gas turbines. these are utilized in electric
electricity generation, for powering water, natural gasoline, or
oil pumps, and supplying propulsion for ships and locomotives.
industrial gasoline turbines can create as much as 50,000 shaft
horsepower.
Precept of jet engine
The gasoline turbine operates on the Brayton cycle in which the
working fluid is a non-stop drift of air ingested into the engine’s
inlet. The air is first compressed by way of a compressor (duct
chamber) to a strain ratio of normally 10 to forty instances the
strain of the inlet airstream.
It then flows into a combustion chamber, where a steady move
of the hydrocarbon gas, in the shape of liquid spray droplets and
vapor or both, is added and burned at approximately consistent
strain.
This offers rise to a continuous stream of high-stress
combustion products whose common temperature is normally
from 980 to at least one,540 °C or higher.
This movement of gases flows via a exhaust nozzle, that is
connected by means of a compressor and combustion chamber
which extracts strength from the gasoline circulation to produce
thrust. due to the fact heat has been brought to the working fluid
at excessive pressure, the gasoline move that exits nozzle is
excessive.
The primary JET ENGINE-quick history OF EARLY JET
ENGINES SIR ISAAC NEWTON within the 18th century
changed into the first to theorize that a rearward-channeled
explosion could propel a gadget forward at a splendid price of
speed. This concept changed into primarily based on his third
law of motion. As the hot air blasts backwards via the nozzle the
aircraft moves forward. HENRI GIFFORD constructed an
airship which turned into powered by way of the primary
aircraft engine, a 3-horse electricity steam engine. It changed
into very heavy, too heavy to fly. In 1874, FELIX DE TEMPLE
built a monoplane that flew only a short hop down a hill with
the
assist of a coal fired steam engine. OTTO DAIMLER, within the
overdue 1800's invented the first fuel engine.
In 1894, American HIRAM MAXIM attempted to strength his
triple biplane with two coal fired steam engines. It best flew for
some seconds. The early steam engines had been powered by
way of heated coal and have been normally an awful lot too
heavy for flight.
American SAMUEL LANGLEY made model airplanes that
have been powered by way of steam engines. In 1896, he was
successful in flying an unmanned plane with a steam-powered
engine, referred to as the Aerodrome. It flew approximately 1
mile earlier than it ran out of steam. He then tried to construct a
full sized plane, the Aerodrome A, with a gasoline powered
engine. In 1903, it crashed at once after being launched from a
residence boat.
STYLES OF JET ENGINES
There are a huge range of different kinds of jet engines, all of
which acquire ahead thrust from the precept of jet propulsion.
reaching a excessive propulsive efficiency for a jet engine is
dependent on designing it in order that the exiting jet pace is not
significantly in excess of the flight speed. at the same time, the
amount of thrust generated is proportional to that very identical
speed extra that have to be minimized. This set of restrictive
requirements has caused the evolution of a big quantity of
specialized variations of the fundamental turbojet engine, every
tailored to reap a balance of suitable gas efficiency, low weight,
and compact size for responsibility in some band of the flight
pace altitude challenge spectrum.
There are two fundamental fashionable features characteristic of
all the one-of-a-kind engine sorts, however. First, so as to obtain
a excessive propulsive performance, the jet pace, or the rate of
the fuel circulate exiting the propulsion, is matched to the flight
pace of the plane slow aircraft have engines with low jet
velocities and fast aircraft have engines with excessive jet
velocities. 2nd, because of designing the jet velocity to match the
flight pace, the size of the propulsion varies inversely with the
flight speed of the aircraft slow plane have very large propulsors,
as, as an instance, the helicopter rotor and the relative length of
the propulsor decreases with growing design flight pace
turboprop propellers are fantastically small and turbofan
enthusiasts even smaller.
The primary idea of the turbojet engine is easy. Air taken in
from a gap within the the front of the engine is compressed to
a few to 12 instances its unique strain in compressor. gasoline
is added to the air and burned in a combustion chamber to
raise the temperature of the fluid aggregate to about 1,a
hundred°F to at least one,three hundred° F. The resulting hot
air is handed via a turbine, which drives the compressor. If the
turbine and compressor are green, the pressure on the turbine
discharge can be nearly two times the atmospheric strain, and
this excess stress is sent to the nozzle to provide a excessive-
pace flow of gas which produces a thrust.
full-size will increase in thrust can be received by way of
employing an afterburner. it's miles a second combustion
chamber placed after the turbine and earlier than the nozzle.
tremendous increases in thrust may be received by way of
using an afterburner. it is a 2nd combustion chamber placed
after the turbine and before the nozzle. The afterburner will
increase the temperature of the gasoline in advance of the
nozzle. The end result of this increase in temperature is an
growth of about 40 percent in thrust at takeoff and a much
larger percent at excessive speeds once the aircraft is inside

3. IN(Online): 4142-3453 February 2017 Issue
the air.
Fig 4: Turbojet engine
A turbofan engine has a big fan on the front, which sucks in
air. most of the air flows around the out of doors of the
engine, making it quieter and giving greater thrust at low
speeds. maximum of state-of-the-art airliners are powered by
means of turbofans. In a turbojet all the air getting into the
intake passes via the gasoline generator, which is composed
of the compressor, combustion chamber, and turbine. In a
turbofan engine simplest a portion of the incoming air goes
into the combustion chamber.
The remainder passes thru a fan, or low-pressure
compressor, and is ejected directly as a "bloodless" jet or
combined with the gas-generator exhaust to produce a "hot"
jet. The objective of this type of bypass system is to boom
thrust without growing gas consumption. It achieves this
with the aid of increasing the entire air-mass drift and
lowering the rate within the identical general strength
deliver.
A turboprop engine is a jet engine connected to a propeller.
The turbine on the again is became by using the new gases,
and this turns a shaft that drives the propeller.
a few small airliners and transport plane are powered by
means of turboprops. like the turbojet, the turboprop engine
includes a compressor, combustion chamber, and turbine, the
air and gasoline pressure is used to run the turbine, which
then creates strength to drive the compressor.
as compared with a turbojet engine, the turboprop has better
propulsion efficiency at flight speeds below approximately
500 miles per hour. current turboprop engines are ready with
propellers that have a smaller diameter but a bigger range of
blades for efficient operation at a great deal better flight
speeds. to house the higher flight speeds, the blades are
scimitar-shaped with swept-returned main edges at the blade
tips. Engines providing such propellers are called prop
fanatics. Max Mueller designed the first turboprop engine
that went into production in 1942.
Fig 5: Turbo prop engine
A ram jet engine is a tool from which beneficial thrust may
be obtained through growing a pace difference between the
atmosphere getting into the ram jet body and the identical
amount of air leaving the ram jet body. This speed distinction
among entrance and go out air is achieved via the addition of
heat to that part of the airstream flowing thru the ram jet
frame. Ramjets can not produce thrust at zero airspeed; they
can not move an aircraft from a standstill. A ramjet powered
car, consequently, calls for an assisted take-off like a rocket
assist to accelerate it to a pace wherein it begins to supply
thrust. Ramjets work most efficiently at supersonic speeds
around Mach 3 (2,284 mph; 3,675 km/h). This sort of engine
can function as much as speeds of Mach 6 (2,041.7 m/s; 7,350
km/h). they have got also been used successfully, although
now not efficiently, as tip jets on the stop of helicopter rotors.
Ramjets haven't any moving elements just like a valve less
pulsejet but they perform with non-stop combustion in place
of the collection of explosions that supply a pulsejet its feature
noise.
Fig 6: Ramjet engine
III. SHOCKWAVES
Whilst some thing reasons a noise, together with a door
lamming or a firecracker popping, it causes a pressure wave to
transport via the air, whilst this wave reaches us our ears
translate the sudden pressure change into the sound we listen.
The stress wave is honestly just air molecules bumping in
opposition to every different. The molecules normally simply
flow around randomly, moving this manner and that. while the
firecracker pops it releases excessive stress gasses that rush
outward, pushing in opposition to the air molecules. these
molecules in flip circulate outward and encounter others,
pushing them along to come upon yet more air molecules.
think of a bunch of balls lined up on a pool table. The cue ball
moves the first, inflicting it to transport and strike the second.
while it does the electricity of motion is transferred to the
second ball and the primary ball stops. Likewise, the second
ball moves the third, transfers power to it, and forestalls. on
this way the electricity passes from one ball to the alternative,
and this energy "wave" flows down the road of balls from the
primary to the closing. despite the fact that the gap from the
primary to closing ball can be high-quality, not one of the
individual balls movements very some distance. This is how
the pressure wave moves through the air, passing from
molecule to molecule. The wave is simply quite a few

4. IN(Online): 4142-3453 February 2017 Issue
molecules that are no longer shifting randomly, but are all
shifting within the identical direction on the identical time
till they stumble upon every other air molecule and pass
electricity to it. After the wave passes the air molecules cross
returned to randomly bumping into every other. As an item
actions via the air it pushes apart the air in its route. The
transferring air forms a stress wave that moves outward at
the velocity of sound. in the image beneath the arrow
categorised "pace of sound" represents the gap sound travels
at some point of the time of flight of the missiles.
Fig 7: Object moves through the air
The missile at the left is moving at 1/2 the rate of sound
(Mach zero.five). The stress waves created as it movements
via the ecosystem are transferring twice as rapid as the
missile and use up in all instructions. In all cases the stress
waves race in advance of the missile. every semicircle
suggests how some distance the sound wave has traveled
since the missile surpassed the numbered positions. notice
that the space between waves is shorter in front of the
missile than off to the aspect of the missile - the waves are
compressed ahead of the missile. but, they do not overlap to
generate a shock wave. in the center photograph the missile
is moving at the speed of sound. The pressure waves make
bigger outward at the speed of sound however they can not
pass beforehand of the missile. on the main tip of the missile
all waves are compressed so that they overlap, however they
use up commonly some other place so a surprise wave is not
propagated. within the proper hand image the missile is
moving quicker than the speed of sound. The strain wave
can't move as speedy as the missile so the missile races
beforehand of the strain waves. consequently all waves
moving outward from the missile's course combine to create
a excessive pressure conical "surprise wave" emanating from
the nose of the missile, moving outward thru the air at the
velocity of sound, like the wake of a ship moving thru water.
whilst this surprise wave reaches our ears we hear a "sonic
increase."
Simple Ramjets
It’s far this supersonic surprise wave that is essential to
ramjet air consumption functioning, and it turned into the
purpose of main complications within the layout of ramjets
that could work reliably. it's miles critical to understand that
the air molecules in this wave are shifting at the speed of
sound, and no faster.
The handiest air consumption design is only a hole tube with
a circular starting - a pipe. consider a pipe fixed to a
supersonic plane or rocket. whilst the pipe is propelled via
the air at supersonic speeds the threshold of the opening
pushes air molecules out of the manner, forming a shock
wave. at the out of doors fringe of the pipe the surprise wave
actions outwardly similar to it does around the nose of a
supersonic bullet. but, at the inside of the tube the surprise
waves from all around the starting converge, as proven by
way of the dashed strains. The air molecules moving far from
the internal fringe of the outlet run into different molecules
moving inward and the stress wave can move no farther.
pressure builds up at the back of the shock wave, compressing
the air within the tube and slowing the fee at which it flows
thru the tube.
Fig 8: Shock waves in simple ramjet
Now we want to reconsider the relative motions of the tube
and the atmosphere. it's far the tube that is shifting faster than
the speed of sound, and the air is standing nonetheless.
however, the idea of relativity permits us to consider the
situation as if the tube become status still and the air was
rushing by using at supersonic speeds.
As stress rises in the tube air temperature also rises. for the
reason that inner walls of the tube save you outward growth of
the air in the tube, and the air speeding in the the front
prevents get away that way, the hot high pressure gasses can
break out most effective from the rear wherein they extend
unexpectedly and return to the temperature and pressure of the
encircling air. however, this occurs handiest while the tube is
shifting through the air very unexpectedly.
whilst the new gasses get away at the rear of the tube they
may be accelerated as the stress drops. you see the same
component whilst water escapes via the quit of your garden
hose. The better the water stress inside the hose the faster the
water flows from the hose.
The higher the stress in the ramjet tube, the quicker the gasses
break out on the rear. because the gasses are heated as they
may be compressed into the tube, the stress increases even
more and that they get away the rear even quicker.

5. IN(Online): 4142-3453 February 2017 Issue
IV. RESULTS
Fig 21: High pressure in combustion chamber
Fig 37: Meshed model of rectangular shaped convergent-
divergent nozzle
Fig 38: Pressure distribution on rectangular shaped
convergent-divergent nozzle
Fig 39: Velocity distribution on rectangular shaped
convergent-divergent nozzle
V.CONCLUSION
After successfully completing this simulation of a layout
created, the decisions have been subsequently restricted into
the following factors.
 FLUENT evaluation has been done on Convergent-
Divergent nozzles of different pass sections like
square, square and rectangle for Ram Jet Engine by
way of using ANSYS 14.5.
 In parent 31, 35 and 39 speed distribution of round,
square and rectangular formed nozzles are shown
respectively.
 As the speed and mass go with the flow fee of air
will increase earlier than the diffuser the speed of the
jet also will increase
 It's miles sincerely visible the rate is increasing along
with the duration of the nozzle. Because of stunning
within the nozzle, the speed reduced for some time
however later started out to growth because the fluid
accelerated via the divergent component.
 Stress gradually reduced along the duration of the
nozzle except a moderate upward thrust for the
duration of the stunning. however, the rise changed
into now not huge comparing to the total fall in
strain. consistent with Bernoulli’s equation, pressure
lower as pace boom alongside growth sector.
 In discern 32, 36 and 40 represents temperature
distribution in C-D nozzle of Ram Jet engine. Right
here, the most temperature acquired at the quit of the
nozzle and at the throat phase we are able to examine
the variation of temperature.
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AUTHORS PROFILE
RAMA THULASI he is pursuing M.Tech
(Mechnical) at Global College Of Engineering
and Technology, Kadapa, Andhra Pradesh..
Mr. N. Jashuva,M.Tech. Assistant Professor at
Global College Of Engineering and Technology,
Kadapa, Andhra Pradesh.