design and cfd analysis of convergent and divergent nozzle - ijpres [PDF]

INTERNATIONAL JOURNAL OF PROFESSIONAL ENGINEERING STUDIES

Volume 9 /Issue 2 / SEP 2017

DESIGN AND CFD ANALYSIS OF CONVERGENT AND DIVERGENT NOZZLE 1 1

P.VINOD KUMAR,2B.KISHORE KUMAR

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 narrowed, increasing the speed of the jet to the speed

Abstract Nozzle is a device designed to control the

of sound, and then expanded again. Above the speed

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

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

pressure of the Fluid that exhaust from them.

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

Convergent-divergent nozzle is the most commonly

very efficient conversion of heat energy to motion.

used nozzle since in using it the propellant can be

The theory of air resistance was first proposed by Sir

heated incombustion chamber. In this project we

Isaac Newton in 1726. According to him, an

designed a new Tri-nozzle to increase the velocity of

aerodynamic force depends on the density and

fluids flowing through it. It is designed based on

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

basic convergent-Divergent nozzle to have same

displacing object. Newton’s theory was soon

throat area, length, convergent angle and divergent

followed by other theoretical solution of fluid motion

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

problems. All these were restricted to flow under

optimized to have high expansion co-efficient than

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

single nozzle without altering the divergent angle. In

constant density and to move in response to pressure

the present paper, flow through theTri-nozzle and

and inertia. Nowadays steam turbines are the

convergent divergent nozzle study is carried out by

preferredpower source of electric power stations and

using SOLID WORKS PREMIUM 2014.The nozzle

large ships, although they usually have a different

geometry modeling and mesh generation has been

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

done

Software.

Laval’s turbine had to run at an impractically high

Computational results are in goodacceptance with the

speed. But for rockets the de Laval nozzle was just

experimental results taken from the literature.

what was needed.

1.

using

SOLID

WORKS

CFD

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

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.

gases is directly backwards, as any sideways

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

component would not contribute to thrust.

propelling nozzle which enormously increases its

2. Literature review

kinetic energy. The goal of nozzle is to increase the

CONVERGENT-DIVERGENT nozzle is

kinetic energy of the flowing medium at the expense

designed for attaining speeds that are greater than

of its pressure and internal energy. Nozzles can be

speed of sound. the design of this nozzle came from

described as convergent (narrowing down from a

the area-velocity relation (dA/dV)=-(A/V)(1-M^2) M

wide diameter to a smaller diameter in the direction

is the Mach number ( which means ratio of local

of the flow) or divergent (expanding from a smaller

speed of flow to the local speed of sound) A is area

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

and V is velocity The following information can be

convergent section followed by a divergent section

derived from the area-velocity relation –

and is often called a convergent-divergent nozzle

1. For incompressible flow limit, i.e. for M tends to

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

zero, AV = constant. This is the famous volume

subsonic fluids. If the nozzle pressure ratio is high

conservation equation or continuity equation for

enough the flow will reach sonic velocity at the

incompressible flow.

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

2. For M < 1, a decrease in area results in increase of

situation, the nozzle is said to be choked.

velocity and vice vera. Therefore, the velocity

Increasing the nozzle pressure ratio further

increases in a convergent duct and decreases in a

will not increase the throat Mach number beyond

Divergent duct. This result for compressible subsonic

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

flows is the same as that for incompressible flow.

flow is free to expand to supersonic velocities. Note

3. For M > 1, an increase in area results in increases

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

of velocity and vice versa, i.e. the velocity increases

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

in a divergent duct and decreases in a convergent

of absolute temperature. Thus the speed reached at a

duct. This is directly opposite to the behavior of

nozzle throat can be far higher than the speed of

subsonic flow in divergent and convergent ducts.

sound at sea level. This fact is used extensively in

4. For M = 1, dA/A = 0, which implies that the

rocketry where hypersonic flows are required, and

location where the Mach number is unity, the area of

where propellant mixtures are deliberately chosen to

the passage is either minimum or maximum. We can

further increase the sonic speed. Divergent nozzles

easily show that the minimum in area is the only

slow fluids, if the flow is subsonic, but accelerate

physically realistic solution.

sonic or supersonic fluids. Convergent-divergent

One important point is that to attain supersonic

nozzles can therefore accelerate fluids that have

speeds we have to maintain favorable pressure ratios

choked in the convergent section to supersonic

across the nozzle. One example is attain just sonic

speeds. This CD process is more efficient than

speeds at the throat, pressure ratio to e maintained is

allowing

(Pthroat / P inlet)=0.528.

a

convergent

nozzle

to

expand

supersonically externally. The shape of the divergent section also ensures that the direction of the escaping

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Table1: speeds vs mach number

3.1 Conical Nozzles

Reg

Subs

Trans

So

Super

Hyper

High-

ime

onic

onic

nic

sonic

sonic

hyper

Ma

10.0

ch

1.2

From table.1 at transonic speeds, the flow field around the object includes both sub- and supersonic

Fig3.1 conical nozzles

parts. The transonic period begins when first zones of

1. Used in early rocket applications because of

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

simplicity and ease of construction.

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

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

happens above the wing. Supersonic flow can

diverge at a constant angle

decelerate back to subsonic only in a normal shock;

3. A small angle produces greater thrust, because it

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

maximizes the axial component of exit velocity and

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

produces a high specific impulse

increases towards both leading and trailing edges. As

4. Penalty is longer and heavier nozzle that is more

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

complex to build

the trailing edge and becomes a weak oblique shock:

5. At the other extreme, size and weight are

the flow decelerates over the shock, but remains

minimized by a large nozzle wall angle – Large

supersonic. A normal shock is created ahead of the

angles reduce performance at low altitude because

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

high ambient pressure causes overexpansion and flow

a small area around the object's leading edge

separation

The governing continuity, momentum, and energy

6. Primary Metric of Characterization: Divergence

equations for this quasi one-dimensional, steady,

Loss

isentropic flow can be expressed, respectively

3.2 BELL and Dual Bell

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

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

• Annular IJPRES

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patented this nozzle concept, which has received

2. Match exit and atmospheric pressure as closely as

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

desired.

design of this nozzle concept with its typical inner

3. Permit afterburner operation without affecting

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

main engine operation—requires variable

extension can be seen. This nozzle concept offers an

area nozzle.

altitude adaptation achieved only by nozzle wall in

4. Allow for cooling of walls if necessary.

section. In flow altitudes, controlled and symmetrical

5. Mix core and bypass streams of turbofan if

flow separation occurs at this wall in section, which

necessary.

results in a lower effective area ratio. For higher

6. Allow for thrust reversing if desired.

altitudes, the nozzle flow is attached to the wall until

7. Suppress jet noise, radar reflection, and infrared

the exit plane, and the full geometrical area ratio is

radiation (IR) if desired.

used. Because of the higher area ratio, an improved

8. Two-dimensional and axisymmetric nozzles, thrust

vacuum

vector control if desired.

performance

is

achieved.

However,

throat

additional performance losses are induced in dual-

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

bell nozzles.

boat tail drag while meeting life and reliability goals. 10.4Introduction 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 Fig 3.2(2) performance losses are induced in dual-

hot, pressurized gas passing through it to a higher

bell nozzles.

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

3.3 Functions of Nozzle

heat energy of the flow into kinetic energy. Because

The purpose of the exhaust nozzle is to increase the

of this, the nozzle is widely used in some types

velocity of the exhaust gas before discharge from the

of steam turbines and rocket engine nozzles. It also

nozzle and to collect and straighten the gas flow. For

sees use in supersonic jet engines.

large values of thrust, the kinetic energy of the

Similar flow properties have been applied to jet

exhaust gas must be high, which implies a high

streams within astrophysics.

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

Fig4: convergent and divergent nozzle 5. Conditions for operation

minimum total pressure loss.

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A de Laval nozzle will only choke at the

rate is constant. The gas flowthrough a de Laval

throat if the pressure and mass flow through the

nozzle is isentropic (gas entropy is nearly constant).

nozzle is sufficient to reach sonic speeds, otherwise

In a subsonic flow the gas is compressible,

no supersonic flow is achieved, and it will act as

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

a Venturi tube; this requires the entry pressure to the

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

nozzle to be significantly above ambient at all times

gas velocity locally becomes sonic (Mach number =

(equivalently, the stagnation pressure of the jet must

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

be above ambient).

cross-sectional area increases, the gas begins to

In addition, the pressure of the gas at the exit

expand, and the gas flow increases to supersonic

of the expansion portion of the exhaust of a nozzle

velocities, where a sound wave will not propagate

must not be too low. Because pressure cannot travel

backwards through the gas as viewed in the frame of

upstream through the supersonic flow, the exit

reference of the nozzle (Mach number > 1.0).

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

5.1 Fluid flow inside convergent and divergent nozzle A

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

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 Mp* because of the pressure recovery in the diverging part.

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However, if the flow is isentropic all along the

discharge pressure. That is the normal

nozzle, be it fully subsonic or supersonic from the

situation for a nozzle working at low

throat, the isentropic equations apply

altitudes (assuming it is adapted at higher

But if the flow gets sonic at the throat,

altitudes); it also occurs at short times after

several downstream conditions may appear. The

ignition, when chamber pressure is not high

control parameter is discharge pressure, p0. Let

enough.

consider a fix-geometry CD-nozzle, discharging a



Adapted nozzle, where exit pressure equals

given gas from a reservoir with constant conditions

discharge pressure (evolution f). Notice that,

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

as exit pressure pe only depends on chamber

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

conditions for a choked nozzle, a fix-

the

geometry nozzle can only work adapted at a

following

flow

regimes

(a

plot

of

pressurevariation along the nozzle is sketched in Fig. 2):

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

•

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

is the normal situation for nozzles working under vacuum. This type of flow is named 'under-expanded'

Sonic throat (no further increase in mass-flow-rate whatever low the discharge pressure let be).

because exit pressure is not low-enough, and additional expansion takes place after exhaust.

Flow becomes supersonic after the throat, but, before

5.2 Choked flow

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

Flow becomes supersonic after the throat, with the normal shockwave just at the exit

Flow becomes supersonic after the throat, and remains supersonic until de exit, but

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'

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

because

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

there, three cases may be distinguished: 

move upstream; in gas flow, choking takes place

flow,chokingtakes

section (evolution d). o

the flow, setting a limit to fluid velocity because theflow becomes supersonic and perturbations cannot

sketch). o

Chokingisa compressible flow effect that obstructs

the

supersonic flow in the diverging part of the nozzle has lowered pressure so much that a

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

recompression is required to match the IJPRES

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the nozzle or at some extrapolated imaginary throat

expansion of steam in nozzle neither heat is supplied

downstream of a subsonic nozzle.

or rejected work. As steam passes through the nozzle

5.3 Area ratio

it loses its pressure as well as heat.

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

The work done is equal to the adiabatic heat drop which in turn is equal to Rankine area. 6.2 Velocity of Steam:

divided by entry area in converging nozzles. Notice

Steam Enters nozzle with high pressure and

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

very low velocity (velocity is generally neglected).

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

Leaves nozzle with high velocity & low pressure

bounded between 0 and 1); however, although no

All this is due to the reason that heat energy

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

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

*

*

refers to Ae/A , and if it is 1).

follows,

To see the effect of area ratio on Mach

Let

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

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

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

h - enthalpy at steam at inlet

low-gamma gases as those of hot rocket exhaust

h - enthalpy at steam at outlet

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

h - heat drop during expansion at steam (h

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

(for 1 kg of steam)

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

Gain in K.E. = adiabatic heat drop

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.

−h )

=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

*

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

6.3 Discharge Through The Nozzle And Condition

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

For Its Maximum Value:

and γ=1.67] (red).

p - initial pressure at steam

6. THEORETICAL BACK GROUND 6.1 Flows through Nozzles: The steam flow through the nozzles may be assumed as adiabatic flow. Since during the

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

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

p

m=

= constant

n= 1.135 for saturated steam

by substituting value of c &v we get

n= 1.3 for super saturated steam for wet steam the value at ‘n’ can be calculated by (

)

n= 1.035 + 0.1x m=

x- dryness fraction at steam (initial)

p p v [1- ( p )

√( 2{

m=

Dr.Zenner’s equation

]})

p p p v [( p ) - ( p )

√ (2{

]})

workdone per 1 kg at steam during the cycle it is obvious form above equation that there is only p one value at the ratio (critical pressure ratio) p

(Rankine cycle) (p v - p v )

W=

which will produce max discharge Already we know Gain in K.E = adiabatic heat drop = workdone during Ranlinecycl Per 1 kg =

constant

(p v - p v )

p v (1-

=

p p [( p ) - ( p )

=>

p => [ ( p )

) ………….(1)

p =>( p )

Also p

and this can be obtained by differenciating m with p respect to p and equating to zero p and other quantities except p remains here

v = ( v ) => =>v = v (

p

p = ( p )

p )

………(2) ……..(3)

p )( p ) ]

- (

p ) ( p )

= (

p =>( p )

= p

] =0

= ( + 1 2)

p

+1 ) p = ( 2

p

2 p = (

+ 1)

equation 2 in 1 Hence discharge through the nozzle will be =

p v (1-

=

p v [1-

maximum when critical pressure ratio is

) p ( p ) ]

=

p v [1-

=

p p v [1- ( p )

=2{

(

p

=

By substituting

]

+ 1)

p

p value in mass equation we get

the maximum discharge

p p v [1- ( p ) [1- (

2 p = (

p ) ]

]} m=

C = √ (2{

p

)

√ (2{

p p p v [( p ) - ( p )

]})

]}

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√ (2{

= [(2

+ 1)

]

p v

[[ (2

Volume 9 /Issue 2 / SEP 2017

+ 1)

]

–

p

p =( ) =( )

p Specific volume v = v ( p )

]})

Apparent temperature

[(2

+ 1)

–

due to following reasons I.

p v [[ (2

+ 1)

–

II. III.

− 1]]}) p v [ (2

√ (2{

+ 1)

Internal friction of steam itself and The shock losses

Most of these frictional losses occur between the –

− 1)] })

throat and exit in convergent divergent nozzle. These frictional losses entail the following effects.

p v [ (2

√ (2{

+ 1)

1.

–

2. A √ n ( ) [(2

By substituting

p

The expansion is no more isentropic and enthalpy drop is reduced.

)]}) =

The friction between the nozzle surface and steam

= (

+ 1)

− 1]})

= [(

p v [[ (2

√ (2{

+ 1)

Nozzle efficiency:

velocity of steam for a given pressure drop is reduced

= [(2

–

p ( p )

When the steam flows through a nozzle the final √ (2{

+ 1)

+ 1)

]})

= [(2

p v [[ (2

√ (2{

=

=

The final dryness fraction at steam is increased as

+ 1)

the

kinetic

energy gets

converted into heat due to friction and is observed by steam.

2 p = (

+ 1)

in equation c

3.

we get

The specific volume of steam is increased as the steam becomes more dry due to this

= √ 2(

) p v [1- ((2

= √ 2(

) p v [1-

= √ 2(

)p v (

= √ 2(

)p v

+ 1)

frictional reheating

)

] )

From maximum equation, it is evident that the

1

K= =

=

3 2

1-2-2 - actual 1-2-3 -3 isentropic

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: p

= constant

= constant = constant

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Nozzle efficiency is the ratio of actual enthalpy drp to

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

the isentropyenthalpy drop between the same

possible for mechanical designers to quickly sketch

pressure.

ideas, experiment with features and dimensions, and

Nozzle efficiency =

produce models and detailed drawings. A Solid Works model consists of parts, assemblies,

If actual velocity at exit from the nozzle is

and the

velocity at exit when the flow is isentropic is

then

and drawings. 

using steady flow energy equation. In each case we

Typically, we begin with a sketch, create a base feature, and then add more features to

have

the model. (One can also begin with an

ℎ +

= ℎ +

ℎ +

= ℎ

=>ℎ - ℎ =

+

=>ℎ - ℎ

imported surface or solid geometry). 

=

We are free to refine our design by adding, changing, or reordering features.

Nozzle efficiency = Inlet velocity



Associatively between parts, assemblies, and drawings assures that changes made to

is negligibly small

one view are automatically made to all

Nozzle efficiency =

other views. 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.

any time in the design process. 

i.e., velocity coefficient =

We can generate drawings or assemblies at

The Solid works software lets us customize functionality to suit our needs.

Velocity coefficient is the square root of the nozzle

8. Modeling of convergent divergent nozzle

efficiency when the inlet velocity is assumed to be

First select a new file and front plane

negligible.

Draw sketch as follows

Enthalpy drop = (( = (

p

])

p )

= √ {2( v =v ( =

p ) p v [1- ( p )

(

p

p

p ) p v [1- ( p )

]}

p ) p )

Then go to features and make revolve

= m = 7. SOLID WORKS Solid

Works

is

mechanical

design

automation software that takes advantage of the familiar Microsoft Windows graphical user interface.

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Table2: List of different general settings in SolidWorks Flow Simulation Now flow simulation Wizard

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

Set units

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.

Flow type- internal in x-axis direction

Figure: Flowchart for fluid flow analysis using Solidworks Flow Simulation

General setting Next gases add air as fluid

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Computational domain

Mach number

9.1 For 5 bar inlet pressure

Goals result table

Boundary conditions Inlet mass flow rate 50 kg/sec, pressure 5 bar (select inside faces)

9.2 For pressure 10bars Boundary conditions Give mass flow rate 50kg/s and pressure 10bars Result

Pressure

Pressure

Velocity

Velocity

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Mach number

Goals tables

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Mach number

10.2 10 bar Pressure

Velocity

10. Graphs 10.1 5bar Pressure

Mach number

Velocity

Table: Results Given Pressure 5bars 10bars

Pressure

Velocity

22.14 22.42

661.617 740.168

Mach number 4.57 3.28

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11. Conclusion: 



field thermal structural simulations in Micro

Modeling and analysis of Convergent and

Valves and Micro channels” CFD Research

divergent nozzle is done in Solidworks 2016 

Corporation.

Modeling of single nozzle is done by using various commands in solid works and



Velocity of nozzle at 5 bar and 10 bar





“Navier-Stokes

structure

of

jets

from

Highly

underexpanded Nozzles into Still Air,” Journal of the Aerospace Sciences, Vol.26,

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

nozzle”. Proceedings of the international

No.1, Jan 1959, pp. 16-24. 

Lewis, C. H., Jr., and Carlson, D. J., “Normal Shock Location in underexpanded

conferece on Aero Space Science and

Gas and Gas Particle Jets,” AIAA Journal,

Technology, Bangalore, India, June 26-28,

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

2008. H.K.Versteeg and W.MalalaSekhara, “An introduction

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

flow analysis in a Convergent-Divergent

to

Computational



1618- 1625. 

4th edition, 1996.

Romine, G. L., “Nozzle Flow separation,” AIAA Journal, Vol. 36, No.9, Sep. 1998. Pp

fluid

Dynamics”, British Library cataloguing pub,

Anderson Jr, J. D., “Computational Fluid

David C.Wil Cox, “Turbulence modeling for

Dynamics the basic with Applications,”

CFD” Second Edition 1998.

McGrawHill, revised edition 1995.

S.Majumdar

and

B.N.Rajani,

“Grid



Dutton, J.C., “Swirling Supersonic Nozzle

generation for Arbitrary 3-D configuration

Flow,” Journal of Propulsion and Power,

using a Differential Algebraic Hybrid

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

Method, CTFD Division, NAL, Bangalore,



Layton, W.Sahin and Volker.J, “A problem solving approach using Les for a backward

Elements of Propulsion: Gas Turbines and Rockets ---- Jack D. Mattingly

April 1995. 

Nakahashi,

1989.

12. References:



Kazuhiro

cascade flow fields”, Vol.5, No.3, May-June Thus variations in velocities at certain given

nozzle are analyzed in this project.



to

Computations of two and three dimensional

pressures of convergent and divergent



introduction

2003.

pressure are tabulated in results table.



“An

technology, Goteborg, Sweden, November,

Analysis is done on single nozzle at 5 bars and 10 bars and values are noted.



Davidson,

and fluid dynamics, Chalmers university of

and 10bars respectively.



Lars

turbulence Models”, Department of thermo

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



M.M.Atha vale and H.Q. Yang, “Coupled



Introduction to CFD---- H K VERSTEEG &W MALALASEKERA

facing-step” 2002.

IJPRES

163