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DESIGN AND CFD ANALYSIS OF CONVERGENT AND DIVERGENT NOZZLE

1P.VINOD KUMAR,2B.KISHORE KUMAR 1 PG Scholar, Department ofMECH,NALANDA INSTITUTION OF ENGINEERING AND TECHNOLOGY

KantepudiSattenapalli, GUNTUR,A.P, India, Pin: 522438 2 Assistant Professor, Department of MECH,NALANDA INSTITUTION OF ENGINEERING AND

TECHNOLOGY,Kantepudi,Sattenapalli, GUNTUR,A.P, India, Pin: 522438

Abstract

Nozzle is a device designed to control the

rate of flow, speed, direction, mass, shape, and/or the

pressure of the Fluid that exhaust from them.

Convergent-divergent nozzle is the most commonly

used nozzle since in using it the propellant can be

heated incombustion chamber. In this project we

designed a new Tri-nozzle to increase the velocity of

fluids flowing through it. It is designed based on

basic convergent-Divergent nozzle to have same

throat area, length, convergent angle and divergent

angle as single nozzle. But the design of Tri-nozzle is

optimized to have high expansion co-efficient than

single nozzle without altering the divergent angle. In

the present paper, flow through theTri-nozzle and

convergent divergent nozzle study is carried out by

using SOLID WORKS PREMIUM 2014.The nozzle

geometry modeling and mesh generation has been

done using SOLID WORKS CFD Software.

Computational results are in goodacceptance with the

experimental results taken from the literature.

1. Introduction to nozzle

Swedish engineer of French descent who, in trying to

develop a more efficient steam engine, designed a

turbine that was turned by jets of steam. The critical

component – the one in which heat energy of the hot

high-pressure steam from the boiler was converted

into kinetic energy – was the nozzle from which the

jet blew onto the wheel. De Laval found that the most

efficient conversion occurred when the nozzle first

narrowed, increasing the speed of the jet to the speed

of sound, and then expanded again. Above the speed

of sound (but not below it) this expansion caused a

further increase in the speed of the jet and led to a

very efficient conversion of heat energy to motion.

The theory of air resistance was first proposed by Sir

Isaac Newton in 1726. According to him, an

aerodynamic force depends on the density and

velocity of the fluid, and the shape and the size of the

displacing object. Newton’s theory was soon

followed by other theoretical solution of fluid motion

problems. All these were restricted to flow under

idealized conditions, i.e. air was assumed to posses

constant density and to move in response to pressure

and inertia. Nowadays steam turbines are the

preferredpower source of electric power stations and

large ships, although they usually have a different

design-to make best use of the fast steam jet, de

Laval’s turbine had to run at an impractically high

speed. But for rockets the de Laval nozzle was just

what was needed.

A nozzle is a device designed to control the

direction or characteristics of a fluid flow (especially

to increase velocity) as it exits (or enters) an enclosed

chamber. A nozzle is often a pipe or tube of varying

cross sectional area and it can be used to direct or

modify the flow of a fluid (liquid or gas). Nozzles are

frequently used to control the rate of flow, speed,

direction, mass, shape, and/or the pressure of the

stream that emerges from them. A jet exhaust

produces a net thrust from the energy obtained from

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combusting fuel which is added to the inducted air.

This hot air is passed through a high speed nozzle, a

propelling nozzle which enormously increases its

kinetic energy. The goal of nozzle is to increase the

kinetic energy of the flowing medium at the expense

of its pressure and internal energy. Nozzles can be

described as convergent (narrowing down from a

wide diameter to a smaller diameter in the direction

of the flow) or divergent (expanding from a smaller

diameter to a larger one). A de Laval nozzle has a

convergent section followed by a divergent section

and is often called a convergent-divergent nozzle

("con-di nozzle"). Convergent nozzles accelerate

subsonic fluids. If the nozzle pressure ratio is high

enough the flow will reach sonic velocity at the

narrowest point (i.e. the nozzle throat). In this

situation, the nozzle is said to be choked.

Increasing the nozzle pressure ratio further

will not increase the throat Mach number beyond

unity. Downstream (i.e. external to the nozzle) the

flow is free to expand to supersonic velocities. Note

that the Mach 1 can be a very high speed for a hot

gas; since the speed of sound varies as the square root

of absolute temperature. Thus the speed reached at a

nozzle throat can be far higher than the speed of

sound at sea level. This fact is used extensively in

rocketry where hypersonic flows are required, and

where propellant mixtures are deliberately chosen to

further increase the sonic speed. Divergent nozzles

slow fluids, if the flow is subsonic, but accelerate

sonic or supersonic fluids. Convergent-divergent

nozzles can therefore accelerate fluids that have

choked in the convergent section to supersonic

speeds. This CD process is more efficient than

allowing a convergent nozzle to expand

supersonically externally. The shape of the divergent

section also ensures that the direction of the escaping

gases is directly backwards, as any sideways

component would not contribute to thrust.

2. Literature review

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 increases

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. One example is attain just sonic

speeds at the throat, pressure ratio to e maintained is

(Pthroat / P inlet)=0.528.

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Table1: speeds vs mach number

Reg

ime

Ma

ch

Subs

onic

<1.0

Trans

onic

0.8-

1.2

So

nic

1.0

Super

sonic

1.0-

5.0

Hyper

sonic

5.0-

10.0

High-

hyper

sonic

>10.0

From table.1 at transonic speeds, the flow field

around the object includes both sub- and supersonic

parts. The transonic period begins when first zones of

M>1 flow appear around the object. In case of an

airfoil (such as an aircraft's wing), this typically

happens above the wing. Supersonic flow can

decelerate back to subsonic only in a normal shock;

this typically happens before the trailing edge. (Fig.a)

As the speed increases, the zone of M>1 flow

increases towards both leading and trailing edges. As

M=1 is reached and passed, the normal shock reaches

the trailing edge and becomes a weak oblique shock:

the flow decelerates over the shock, but remains

supersonic. A normal shock is created ahead of the

object, and the only subsonic zone in the flow field is

a small area around the object's leading edge

The governing continuity, momentum, and energy

equations for this quasi one-dimensional, steady,

isentropic flow can be expressed, respectively

3. Types of nozzles

Types of nozzles are several types. They could be

based on either speed or shape.

a. Based on speed The basic types of nozzles can

be differentiated as

• Spray nozzles

• Ramjet nozzles

b. Based on shape The basic types of nozzles can

be differentiated as

• Conical

• Bell

• Annular

3.1 Conical Nozzles

Fig3.1 conical nozzles

1. Used in early rocket applications because of

simplicity and ease of construction.

2. Cone gets its name from the fact that the walls

diverge at a constant angle

3. A small angle produces greater thrust, because it

maximizes the axial component of exit velocity and

produces a high specific impulse

4. Penalty is longer and heavier nozzle that is more

complex to build

5. At the other extreme, size and weight are

minimized by a large nozzle wall angle – Large

angles reduce performance at low altitude because

high ambient pressure causes overexpansion and flow

separation

6. Primary Metric of Characterization: Divergence

Loss

3.2 BELL and Dual Bell

Fig3.2 (1): BELL and Dual Bell

This nozzle concept was studied at the Jet Propulsion

Laboratory in 1949. In the late 1960s, Rocket dyne

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patented this nozzle concept, which has received

attention in recent years in the U.S. and Europe. The

design of this nozzle concept with its typical inner

base nozzle, the wall in section, and the outer nozzle

extension can be seen. This nozzle concept offers an

altitude adaptation achieved only by nozzle wall in

section. In flow altitudes, controlled and symmetrical

flow separation occurs at this wall in section, which

results in a lower effective area ratio. For higher

altitudes, the nozzle flow is attached to the wall until

the exit plane, and the full geometrical area ratio is

used. Because of the higher area ratio, an improved

vacuum performance is achieved. However,

additional performance losses are induced in dual-

bell nozzles.

Fig 3.2(2) performance losses are induced in dual-

bell nozzles.

3.3 Functions of Nozzle

The purpose of the exhaust nozzle is to increase the

velocity of the exhaust gas before discharge from the

nozzle and to collect and straighten the gas flow. For

large values of thrust, the kinetic energy of the

exhaust gas must be high, which implies a high

exhaust velocity. The pressure ratio across the nozzle

controls the expansion process and the maximum

uninstalled thrust for a given engine is obtained when

the exit pressure (Pe) equals the ambient pressure

(P0).The functions of the nozzle may be summarized

by the following list:

1. Accelerate the flow to a high velocity with

minimum total pressure loss.

2. Match exit and atmospheric pressure as closely as

desired.

3. Permit afterburner operation without affecting

main engine operation—requires variable throat

area nozzle.

4. Allow for cooling of walls if necessary.

5. Mix core and bypass streams of turbofan if

necessary.

6. Allow for thrust reversing if desired.

7. Suppress jet noise, radar reflection, and infrared

radiation (IR) if desired.

8. Two-dimensional and axisymmetric nozzles, thrust

vector control if desired.

9. Do all of the above with minimal cost, weight, and

boat tail drag while meeting life and reliability goals. 10.4 Introduction to convergent and divergent

nozzle

A de Laval nozzle (or convergent-divergent

nozzle, CD nozzle or con-di nozzle) is a tube that is

pinched in the middle, making a carefully balanced,

asymmetric hourglass shape. It is used to accelerate a

hot, pressurized gas passing through it to a higher

speed in the axial (thrust) direction, by converting the

heat energy of the flow into kinetic energy. Because

of this, the nozzle is widely used in some types

of steam turbines and rocket engine nozzles. It also

sees use in supersonic jet engines.

Similar flow properties have been applied to jet

streams within astrophysics.

Fig4: convergent and divergent nozzle

5. Conditions for operation

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A de Laval nozzle will only choke at the

throat if the pressure and mass flow through the

nozzle is sufficient to reach sonic speeds, otherwise

no supersonic flow is achieved, and it will act as

a Venturi tube; this requires the entry pressure to the

nozzle to be significantly above ambient at all times

(equivalently, the stagnation pressure of the jet must

be above ambient).

In addition, the pressure of the gas at the exit

of the expansion portion of the exhaust of a nozzle

must not be too low. Because pressure cannot travel

upstream through the supersonic flow, the exit

pressure can be significantly below the ambient

pressure into which it exhausts, but if it is too far

below ambient, then the flow will cease to

be supersonic, or the flow will separate within the

expansion portion of the nozzle, forming an unstable

jet that may "flop" around within the nozzle,

producing a lateral thrust and possibly damaging it.

In practice, ambient pressure must be no

higher than roughly 2–3 times the pressure in the

supersonic gas at the exit for supersonic flow to leave

the nozzle.

Fig5: mach number condition

Its operation relies on the different properties of

gases flowing at subsonic and supersonic speeds.

Thespeed of a subsonic flow of gas will increase if

the pipe carrying it narrows because the mass flow

rate is constant. The gas flowthrough a de Laval

nozzle is isentropic (gas entropy is nearly constant).

In a subsonic flow the gas is compressible,

and sound will propagate through it. At the "throat",

where the cross-sectional area is at its minimum, the

gas velocity locally becomes sonic (Mach number =

1.0), a condition called choked flow. As the nozzle

cross-sectional area increases, the gas begins to

expand, and the gas flow increases to supersonic

velocities, where a sound wave will not propagate

backwards through the gas as viewed in the frame of

reference of the nozzle (Mach number > 1.0).

5.1 Fluid flow inside convergent and divergent

nozzle

A converging-diverging nozzle ('condi'

nozzle, or CD-nozzle) must have a smooth area law,

with a smooth throat, dA/dx=0, for the flow to remain

attached to the walls. The flow starts from rest and

accelerates subsonically to a maximum speed at the

throat, where it may arrive at M<1 or at M=1, as for

converging nozzles. Again, for the entry conditions

we use 'c' (for chamber) or 't' (for total), we use 'e' for

the exit conditions, and '*' for the throat conditions

when it is choked (M*=1).

If the flow is subsonic at the throat, it is

subsonic all along the nozzle, and exit pressure pe

naturally adapts to environmental pressure p0

because pressure-waves travel upstream faster (at the

speed of sound) than the flow (subsonic), so that

pe/p0=1. But now the minimum exit pressure for

subsonic flow is no longer pe=pt(2/(γ+1))γ/(γ−1)

(pe/p0=0.53 for γ=1.4), since the choking does not

take place at the exit but at the throat, i.e. it is the

throat condition that remains valid,

p*=pt(2/(γ+1))γ/(γ−1), e.g. p*/p0=0.53 for γ=1.4; now

the limit for subsonic flow is pe,min,sub>p* because

of the pressure recovery in the diverging part.

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However, if the flow is isentropic all along the

nozzle, be it fully subsonic or supersonic from the

throat, the isentropic equations apply

But if the flow gets sonic at the throat,

several downstream conditions may appear. The

control parameter is discharge pressure, p0. Let

consider a fix-geometry CD-nozzle, discharging a

given gas from a reservoir with constant conditions

(pt,Tt). When lowering the environmental pressure,

p0, from the no flow conditions, p0=pt, we may have

the following flow regimes (a plot of

pressurevariation along the nozzle is sketched in Fig.

2):

• Subsonic throat, implying subsonic flow all along to the exit (evolution a in Fig 2).

Sonic throat (no further increase in mass-flow-rate

whatever low the discharge pressure let be).

Flow becomes supersonic after the throat, but, before

exit, a normal shockwave causes a sudden transition

to subsonic flow (evolution c). It may happen that the

flow detaches from the wall (see the corresponding

sketch).

o Flow becomes supersonic after the throat,

with the normal shockwave just at the exit

section (evolution d).

o Flow becomes supersonic after the throat,

and remains supersonic until de exit, but

there, three cases may be distinguished:

Oblique shock-waves appear at the exit, to

compress the exhaust to the higher back

pressure (evolution e). The types of flow

with shock-waves (c, d and e in Fig. 2) are

named 'over-expanded' because the

supersonic flow in the diverging part of the

nozzle has lowered pressure so much that a

recompression is required to match the

discharge pressure. That is the normal

situation for a nozzle working at low

altitudes (assuming it is adapted at higher

altitudes); it also occurs at short times after

ignition, when chamber pressure is not high

enough.

Adapted nozzle, where exit pressure equals

discharge pressure (evolution f). Notice that,

as exit pressure pe only depends on chamber

conditions for a choked nozzle, a fix-

geometry nozzle can only work adapted at a

certain altitude (such that p0(z)=pe).

Expansion waves appear at the exit, to expand the

exhaust to the lower back pressure (evolution e); this

is the normal situation for nozzles working under

vacuum. This type of flow is named 'under-expanded'

because exit pressure is not low-enough, and

additional expansion takes place after exhaust.

5.2 Choked flow

Chokingisa compressible flow effect that obstructs

the flow, setting a limit to fluid velocity because

theflow becomes supersonic and perturbations cannot

move upstream; in gas flow, choking takes place

when a subsonic flow reaches M=1, whereas in liquid

flow,chokingtakes place when an almost

incompressible flow reaches the vapour pressure (of

the main liquid or of a solute), and bubbles appear,

with the flow suddenly jumping to M>1

Going on with gas flow and leaving liquid

flow aside, we may notice that M=1 can only occur in

a nozzle neck, either in a smooth throat where dA=0,

or in a singular throat with discontinuous area slope

(a kink in nozzle profile, or the end of a nozzle).

Naming with a '*' variables the stage where M=1 (i.e.

the sonic section, which may be a real throat within

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the nozzle or at some extrapolated imaginary throat

downstream of a subsonic nozzle.

5.3 Area ratio

Nozzle area ratio ε (or nozzle expansion

ratio) is defined as nozzle exit area divided by throat

area, ε≡Ae/A*, in converging-diverging nozzles, or

divided by entry area in converging nozzles. Notice

that ε sodefined is ε>1, but sometimes the inverse is

also named 'area ratio' (this contraction area ratio is

bounded between 0 and 1); however, although no

confusion is possible when quoting a value (if it is >1

refers to Ae/A*, and if it is <1 refers to A*/Ae), one

must be explicit when saying 'increasing area ratio'

(we keep toε≡Ae/A*>1). To see the effect of area ratio on Mach

number, (14) is plotted in Fig. 1 for ideal

monoatomic (γ=5/3), diatomic (γ=7/5=1.40), and

low-gamma gases as those of hot rocket exhaust

(γ=1.20); gases like CO2 and H2O have intermediate

values (γ=1.3). Notice that, to get the same high

Mach number, e.g. M=3, the area ratio needed is

A*/A=0.33 for γ=1.67 and A*/A=0.15 for γ=1.20, i.e.

more than double exit area for the same throat area

(that is why supersonic wind tunnels often use a

monoatomic working gas.

Ratio A*/A (i.e. throat area divided by local area) vs.

Mach number M, for γ=1.20 (beige), γ=1.40 (green),

and γ=1.67] (red).

6. THEORETICAL BACK GROUND

6.1 Flows through Nozzles:

The steam flow through the nozzles may be

assumed as adiabatic flow. Since during the

expansion of steam in nozzle neither heat is supplied

or rejected work. As steam passes through the nozzle

it loses its pressure as well as heat.

The work done is equal to the adiabatic heat

drop which in turn is equal to Rankine area.

6.2 Velocity of Steam:

Steam Enters nozzle with high pressure and

very low velocity (velocity is generally neglected).

Leaves nozzle with high velocity & low pressure

All this is due to the reason that heat energy

at steam is converted into K.E as it passes through

nozzle.

The final or outlet velocity at steam can be found as

follows,

Let

C-Velocity of steam at section considered (m/sec)

h - enthalpy at steam at inlet

h - enthalpy at steam at outlet

h - heat drop during expansion at steam (h − h )

(for 1 kg of steam)

Gain in K.E. = adiabatic heat drop

= h

C=√(2 * 1000*h )

= 44.72√h

In practice there is loss due to friction in the

nozzle and its value from 10-15% at total heat drop.

Due to this the total heat drop is minimized.

Let heat drop after reducing friction loss be kh

Velocity (C) = 44.72 √ kh

6.3 Discharge Through The Nozzle And Condition

For Its Maximum Value:

p - initial pressure at steam

v - initial volume at 1 kg of steam at P (m )

p -steam pressure at throat

v - volume at 1kg steam at P (m )

A-area at cross section at nozzle at throat (m )

C- velocity at steam (m/s)

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Steam passing through nozzle follows adiabatic

process in which

p푣 = constant

n= 1.135 for saturated steam

n= 1.3 for super saturated steam

for wet steam the value at ‘n’ can be calculated by

Dr.Zenner’s equation

n= 1.035 + 0.1x

x- dryness fraction at steam (initial)

workdone per 1 kg at steam during the cycle

(Rankine cycle)

W = (p v - p v )

Already we know

Gain in K.E = adiabatic heat drop

= workdone during Ranlinecycl

Per 1 kg

= (p v - p v )

= p v (1- ) ………….(1)

Also

p 푣 = p 푣

= (vv ) => = (p p ) ………(2)

=>v = v (p p ) ……..(3)

equation 2 in 1

= p v (1- )

= p v [1- (p p ) ]

= p v [1- (pp ) ]

= p v [1- (p p ) ]

푐 = 2 { p v [1- (p p ) ]}

C = √ (2{ 풏풏 ퟏ

퐩ퟏ퐯ퟏ [1- (퐩ퟐ 퐩ퟏ)풏 ퟏ풏 ]}

If m is the mass of steam discharged in kg/sec

m =

by substituting value of c &v we get

m = ( )

√( 2{ p v [1- (p p ) ]})

m = √ (2{ p v [(p p ) - (p p ) ]})

it is obvious form above equation that there is only

one value at the ratio (critical pressure ratio) p p

which will produce max discharge

and this can be obtained by differenciating m with

respect to p p and equating to zero

and other quantities except pp remains here

constant

=> [(p p ) - (p p ) ] = 0

=> [ (pp ) - ( )(p

p ) ]

=>(pp ) = ( ) (p

p )

=>(pp ) = (푛 + 1

2)

pp = (푛 + 1

2)

pp = (2 푛 + 1)

Hence discharge through the nozzle will be

maximum when critical pressure ratio is

= pp = (2 푛 + 1)

By substituting p p value in mass equation we get

the maximum discharge

m = √ (2{ p v [(p p ) - (p p ) ]})

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= √ (2{ p v [[ (2푛 + 1) ] –

[(2 푛 + 1) ] ]})

= √ (2{ p v [[ (2푛 + 1) –

[(2 푛 + 1) ]})

= √ (2{ p v [[ (2푛 + 1) –

[(2 푛 + 1) − 1]})

= √ (2{ p v [[ (2푛 + 1) –

[(2 푛 + 1) − 1]]})

= √ (2{ p v [ (2푛 + 1) –

[( − 1)] })

= √ (2{ p v [ (2푛 + 1) –

( )]})

푚 = A √ n ( ) [(2푛 + 1)

By substituting p p = (2푛 + 1) in equation c

we get 퐶

퐶 = √ 2( ) p v [1- ((2푛 + 1) )

= √ 2( ) p v [1- ]

= √ 2( ) p v ( )

퐶 = √ 2( ) p v

From maximum equation, it is evident that the

maximum mass flow depends only on the inlet

conditions ( p v ) and the throat area.and it is

independent at final pressure at steam i.e., exit at the

nozzle

Note: p푣 = constant

= constant

= constant

pp = ( ) = ( )

Specific volume v = v (p p )

Apparent temperature 푇 = 푇 (p p )

Nozzle efficiency:

When the steam flows through a nozzle the final

velocity of steam for a given pressure drop is reduced

due to following reasons

I. The friction between the nozzle surface and

steam

II. Internal friction of steam itself and

III. The shock losses

Most of these frictional losses occur between the

throat and exit in convergent divergent nozzle. These

frictional losses entail the following effects.

1. The expansion is no more isentropic and

enthalpy drop is reduced.

2. The final dryness fraction at steam is

increased as the kinetic energy gets

converted into heat due to friction and is

observed by steam.

3. The specific volume of steam is increased as

the steam becomes more dry due to this

frictional reheating 1

K =

= = 3 2

1-2-2 - actual

1-2-3 -3 isentropic

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Nozzle efficiency is the ratio of actual enthalpy drp to

the isentropyenthalpy drop between the same

pressure.

Nozzle efficiency =

If actual velocity at exit from the nozzle is 푐 and the

velocity at exit when the flow is isentropic is 푐 then

using steady flow energy equation. In each case we

have

ℎ + = ℎ + =>ℎ - ℎ =

ℎ + = ℎ + =>ℎ - ℎ =

Nozzle efficiency =

Inlet velocity 푐 is negligibly small

Nozzle efficiency =

Sometimes velocity coefficient is defined as the ratio

of actual exit velocity to the exit velocity when the

flow is isentropic between the same pressures.

i.e., velocity coefficient =

Velocity coefficient is the square root of the nozzle

efficiency when the inlet velocity is assumed to be

negligible.

Enthalpy drop = (( ) p v [1- (pp ) ])

= (pp )

푐 = √ {2( ) p v [1- (pp ) ]}

v = v (p p )

푇 = 푇 (p p )

퐴 =

m =

7. SOLID WORKS

Solid Works is mechanical design

automation software that takes advantage of the

familiar Microsoft Windows graphical user interface.

It is an easy-to-learn tool which makes it

possible for mechanical designers to quickly sketch

ideas, experiment with features and dimensions, and

produce models and detailed drawings.

A Solid Works model consists of parts, assemblies,

and drawings.

Typically, we begin with a sketch, create a

base feature, and then add more features to

the model. (One can also begin with an

imported surface or solid geometry).

We are free to refine our design by adding,

changing, or reordering features.

Associatively between parts, assemblies,

and drawings assures that changes made to

one view are automatically made to all

other views.

We can generate drawings or assemblies at

any time in the design process.

The Solid works software lets us customize

functionality to suit our needs.

8. Modeling of convergent divergent nozzle

First select a new file and front plane

Draw sketch as follows

Then go to features and make revolve

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3d model of c & d nozzle

9. FLOW SIMULATION

SolidWorks Flow Simulation 2010 is a fluid flow

analysis add-in package that is available

forSolidWorks in order to obtain solutions to the full

Navier-Stokes equations that govem the motion of

fluids. Other packages that can be added to

SolidWorks include SolidWorks Motion and

SolidWorks Simulation. A fluid flow analysis using

Flow Simulation involves a number of basic steps

that are shown in the following flowchart in figure.

Figure: Flowchart for fluid flow analysis using

Solidworks Flow Simulation

General setting

Table2: List of different general settings in

SolidWorks Flow Simulation

Now flow simulation Wizard

Set units

Flow type- internal in x-axis direction

Next gases add air as fluid

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Computational domain

9.1 For 5 bar inlet pressure

Boundary conditions

Inlet mass flow rate 50 kg/sec, pressure 5 bar (select

inside faces)

Result

Pressure

Velocity

Mach number

Goals result table

9.2 For pressure 10bars

Boundary conditions

Give mass flow rate 50kg/s and pressure 10bars

Pressure

Velocity

INTERNATIONAL JOURNAL OF PROFESSIONAL ENGINEERING STUDIES Volume 9 /Issue 2 / SEP 2017

IJPRES

Mach number

Goals tables

10. Graphs

10.1 5bar

Pressure

Velocity

Mach number

10.2 10 bar

Pressure

Velocity

Mach number

Table: Results

Given Pressure

Pressure Velocity Mach number

5bars 22.14 661.617 4.57 10bars 22.42 740.168 3.28

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11. Conclusion:

Modeling and analysis of Convergent and

divergent nozzle is done in Solidworks 2016

Modeling of single nozzle is done by using

various commands in solid works and

analyzed at various pressures i.e., at 5bars

and 10bars respectively.

Analysis is done on single nozzle at 5 bars

and 10 bars and values are noted.

Velocity of nozzle at 5 bar and 10 bar

pressure are tabulated in results table.

Thus variations in velocities at certain given

pressures of convergent and divergent

nozzle are analyzed in this project.

12. References:

A.A.Khan and T.R.Shembharkar, “Viscous

flow analysis in a Convergent-Divergent

nozzle”. Proceedings of the international

conferece on Aero Space Science and

Technology, Bangalore, India, June 26-28,

2008.

H.K.Versteeg and W.MalalaSekhara, “An

introduction to Computational fluid

Dynamics”, British Library cataloguing pub,

4th edition, 1996.

David C.Wil Cox, “Turbulence modeling for

CFD” Second Edition 1998.

S.Majumdar and B.N.Rajani, “Grid

generation for Arbitrary 3-D configuration

using a Differential Algebraic Hybrid

Method, CTFD Division, NAL, Bangalore,

April 1995.

Layton, W.Sahin and Volker.J, “A problem

solving approach using Les for a backward

facing-step” 2002.

M.M.Atha vale and H.Q. Yang, “Coupled

field thermal structural simulations in Micro

Valves and Micro channels” CFD Research

Corporation.

Lars Davidson, “An introduction to

turbulence Models”, Department of thermo

and fluid dynamics, Chalmers university of

technology, Goteborg, Sweden, November,

2003.

Kazuhiro Nakahashi, “Navier-Stokes

Computations of two and three dimensional

cascade flow fields”, Vol.5, No.3, May-June

1989.

Adamson, T.C., Jr., and Nicholls., J.A., “On

the structure of jets from Highly

underexpanded Nozzles into Still Air,”

Journal of the Aerospace Sciences, Vol.26,

No.1, Jan 1959, pp. 16-24.

Lewis, C. H., Jr., and Carlson, D. J.,

“Normal Shock Location in underexpanded

Gas and Gas Particle Jets,” AIAA Journal,

Vol 2, No.4, April 1964, pp. 776-777.

Romine, G. L., “Nozzle Flow separation,”

AIAA Journal, Vol. 36, No.9, Sep. 1998. Pp

1618- 1625.

Anderson Jr, J. D., “Computational Fluid

Dynamics the basic with Applications,”

McGrawHill, revised edition 1995.

Dutton, J.C., “Swirling Supersonic Nozzle

Flow,” Journal of Propulsion and Power,

vol.3, July 1987, pp. 342-349.

Elements of Propulsion: Gas Turbines and

Rockets ---- Jack D. Mattingly

Introduction to CFD---- H K VERSTEEG

&W MALALASEKERA