international journal of engineering, management ...decreased. after that, the pressure will slidely...

International Journal of Engineering, Management & Sciences (IJEMS)

ISSN-2348 –3733, Volume-3, Issue-5, May 2016

1 www.alliedjournals.com

Abstract--This paper presents the results obtained from

numerical and experimental studies of supersonic freejets

coming out from conical nozzles. In the numerical calculations,

the two-stage Runge-Kutta time-stepping scheme is applied

assumed flow is inviscid and the nozzle is axially symmetric. The

Conical Nozzle is designed by using CATIA. Meshes are

generated by using GAMBIT. We choose 0.40mm as the conical

nozzle’s diameter. By using isentropic relation we found the

mass flow rate of the conical nozzle which is corresponding to

the diameter 0.40mm. Freejet is analyzed by using Fluent. Here,

how the shockwave will be Occur when the freejet is mixed into

the atmosphere region. This shock wave will obtain in various

conditions. Conditions are obtained by changing the mach

number and exit ambient pressure. These are investigated with

the aid of schlieren pictures and time relationship between

velocity and pressure contour plots.

Index Terms--- Conical nozzle, Freejet, Isentropic relation,

Mach number

I. INTRODUCTION

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

or pipe via an orifice. It 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). They are frequently used to control

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

pressure of the stream that emerges from them.

The Aim of a 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. 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.

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. Manuscript received May 08, 2016.

J.C.Sophia Florance, PG-Aeronautical Engineering ,Nehru institute of

Engineering and Technology, Coimbatore

Fig.1. Conical nozzle design with a rounded throat

II. GEOMETRICAL CONFIGURATION

A. Dimensions

Length of the Nozzle is 24mm

Length of the nozzle inlet is 8mm

Length of the nozzle outlet is 5.19mm

Length of the Throttle is 4.003mm

Length of the Pressure farfield at region 1&2 is 53.528mm

(5D)

Length of the Axis is 507.91mm (48D)

B. Commands:

Line, Constrain, Angle.

Using above commands and dimensions our CATIA Design

Obtained.

C. Conical Nozzle Design

Fig.2. Nozzle design

Computational Study of Supersonic Free Jet

J.C.Sophia Florance



III. MESH GENERATION

"GAMBIT" is geometry and mesh generation software

for computational fluid dynamics (CFD) analysis. GAMBIT

has a single interface for geometry creation and meshing that

brings together several preprocessing technologies in one

environment. Advanced tools for journaling let you edit and

conveniently replay model building sessions for parametric

studies. GAMBIT can import geometry from virtually any

CAD/CAE software in Para solid, ACIS, STEP, IGES, or

native CATIA V4/V5 formats.

Import CATIA design into GAMBIT.

Generate Grid to the Conical Nozzle.

Apply Boundary Conditions.

A. Boundary Conditions

Inlet - Mass Flow Inlet

Outlet Boundary - Pressure Outlet

Axis - Axis

Wall - Wall

Farefield 1 - Wall

Farefield 2 – Wall

Fig.3. Meshed nozzle

Export this file in Mesh Format.

This Mesh File is used to Import the GAMBIT file

into Fluent.

IV. ANALYSIS

"Fluent" is the general name for the collection of

computational fluid dynamics(CFD) programs sold by

Fluent, Inc. of Lebanon, NH. The Mechanical Engineering

Department at Penn State has a site license for Fluent, along

with its family of programs. Up to 20 users can run Fluent

simultaneously in the Graduate Computing Lab.

Fluent is the CFD solver which can handle both

structured grids, i.e. rectangular grids with clearly

defined node indices, and unstructured grids.

Unstructured grids are generally of triangular nature,

but can also be rectangular. In 3-D problems,

unstructured grids can consist of tetrahedrals

(pyramid shape), rectangular boxes, prisms, etc.

Note: Since version 5.0, Fluent can solve both

incompressible and compressible flows.

The normal procedure in any CFD problem is to first

generate the grid (with Gambit), and then to run

Fluent.

Import the Mesh File into Fluent.

Apply the conditions.

A. The Mass Flow Rate of the nozzle

etiAVM ,,

* (1)

Equation for Nozzle Exit:

eeee VAM *

(2)

eM =Mass flow rate at exit of the nozzle

e =Density of Jet at exit (1.225 3mkg

)

eA =Area at exit of the nozzle

eV =Velocity at the exit of the nozzle

24 e

eD

A

(3)

eD =Diameter at the exit of the nozzle (0.05mm)

eA = 205.4

eA =1.96*10-3m3

aV

M ee

(4)

a =Speed of Sound 2/1

eee TR

2/1

eee

ee

TR

VM

(5)

e =Density of the gas at exit of the nozzle (1.4)

R =Gas Constant (287)

B. Boundary Conditions

Operation Condition - 0

Scale - mm

In SOLVER:

Type - Density Based

Velocity Formulation - Absolute

2D Space - Axisymmetric

Time - Steady

In MODELS:

Energy - On

Viscous - In Viscous

In MATERIAL:

Fluid




In CELL ZONE CONDITION:

Fluid - Air

In BOUNDARY CONDITION:

Inlet: Mass Flow Inlet ( eM *=1.6335kg/m3)

Outlet: 3 Conditions are there

Under Expansion eP =121590m/s

Over Expansion eP =81060m/s

Correctly Expansion eP =101325m/s

In SOLUTION METHOD: Implicit

In SOLUTION CONTROL:

Courant Number = 0.1 to 0.001

In SOLUTION INITALIZATION:

Standard Initialization

RUN CALCULATION: Iterations Saved.

Fig.4. Fluent Diagram

V. EXPANSION PROCESS

Expansion is the process that converts the thermal

energy of combustion into kinetic energy to move an object

forward. In other words, the hot jet created by burning fuel

inside combustion chamber or rocket engine are exhausted

through a nozzle to produce thrust. It is the shape of this

nozzle that is key to the expansion process. As that high

temperature flow is exhausted, it expands against the walls of

the nozzle to create a force that pushes the vehicle forward.

Flow passing though a rocket nozzle

The behavior of this expansion process is largely

dictated by pressure--both the pressure of the exhaust itself as

well as the pressure of the external environment into which it

exhausts. Of greatest concern is to design the shape and

length of the nozzle so that it converts as much of that thermal

energy into thrust as possible. In an ideal nozzle that

optimizes performance, the exit pressure ( exitP ) will be equal

to the ambient pressure of the external atmosphere. The flow

in this case is perfectly expanded inside the nozzle and

maximizes thrust.

Unfortunately, this situation can only occur at one

specific atmospheric pressure on a fixed-geometry nozzle. As

we have seen previously, pressure decreases as altitude

increases. Nozzle designers typically must select a shape that

is optimum at only one altitude but minimizes the losses that

occur at lower or higher altitudes. These losses result from the

fact that the atmospheric pressure will either be higher than

the exit pressure of the exhaust gases, i.e. at low altitudes, or

lower than the exit pressure, i.e. at high altitudes.

There are 3 conditions

Under expanded nozzle

Over expanded nozzle

Correctly expanded nozzle

A. Under Expanded Nozzle

The opposite situation, in which the atmospheric

pressure is lower than the exit pressure, is called under

expanded. In this case, the flow continues to expand outward

after it has exited the nozzle. This behavior also reduces

efficiency because that external expansion does not exert any

force on the nozzle wall. This energy can therefore not be

converted into thrust and is lost. Ideally, the nozzle should

have been longer to capture this expansion and convert it into

thrust.

Calculation For Under Expanded Nozzle:

a

e

PP =1.2

ae PP 2.1

eP =Pressure at exit

aP =Ambient Pressure (101325m/s)

eP =1.2*101325

eP =121590m/s

Fig.5. Pressure & Time for Mach 2 under expansion

Fig.6. Velocity & Time for Mach 2 under Expansion



This Figure represents the relationship between the

pressure and velocity with respect to time. This Graph Clearly

Shows that, when the jet i.e. High pressurized gas mixed into

the atmospheric region at the condition of under expansion,

jet will suddenly expand into the atmospheric region.

Because, at the condition of under expansion pressure at exit

of the nozzle is greater than the atmospheric pressure. So, the

high pressurized jet will be trying to get neutralized with the

atmospheric pressure. At that time Shock wave will be

created. In this Shock Wave Region Pressure will suddenly

Decreased. After that, the Pressure will slidely accelerated

(increase and decrease) in the Shock wave region. And then it

will get neutralized.

Pressure is inversely proportional to the Velocity.

By this condition when the value of pressure will increased at

the same time value of velocity will be get decreased.

B. Over Expanded Nozzle

The external pressure is higher than the exit pressure, is

referred to as over expanded. When an over expanded flow

passes through a nozzle, the higher atmospheric pressure

causes it to squeeze back inward and separate from the walls

of the nozzle. This "pinching" of the flow reduces efficiency

because that extra nozzle wall is wasted and does nothing to

generate any additional thrust. Ideally, the nozzle should have

been shorter to eliminate this unnecessary wall.

Calculation For Over Expanded Nozzle:

ae P

P=0.8

eP =0.8 aP



eP =0.8*101325

eP =81060m/s

Fig.7. Pressure& Time for Mach 2 over Expansion

Fig.8. Velocity & Time for Mach 2 over Expansion

This Figure represents the relationship between the

pressure and velocity with respect to time. This Graph Clearly

Shows that, When the jet i.e pressurized gas mixed into the

atmospheric region at the condition of Over expansion, jet

will suddenly compressed into the atmospheric region.

Because, at the condition of under expansion pressure at exit

of the nozzle is less than the atmospheric pressure. So, the

low pressurized jet will be trying to get neutralized with the

atmospheric pressure. At that time Shock wave will be

created. In this Shock Wave Region Pressure will suddenly

Decreased. After that, the Pressure will slidely accelerated

(increase and decrease) in the Shock wave region. And then it

will get neutralized.

Pressure is inversely proposional to the Velocity. By

this condition when the value of pressure will increased at the

same time value of velocity will be get decreased.

C. Correctly Expanded Nozzle

The external pressure is equal to the exit pressure, is referred

to as correctly expanded

Calculation for Correctly Expanded Nozzle:

ae PP 1



eP =1*101325

eP =101325m/s

Fig.9. Pressure& Time for Mach 2 Correctly Expansion

Fig.10. Velocity& Time for Mach 2 Correctly Expansion




VI. RESULTS AND DISCUSSIONS

A. Mach Number 1.8 (0.8 Over Expansion)

Fig.11. Velocity & Time for Mach 1.8 over expansion

Fig.12. Pressure & Time for Mach 1.8 over expansion

B. Mach Number 2 (0.8 Over Expansion)

Fig.13. Velocity & Time for Mach 2 over expansion

Fig.14. Pressure & Time for Mach 2 over Expansion



C. Mach Number 1.8 (1 Correctly Expansion)

Fig.15. Velocity & Time for Mach 1.8 correctly expansion

Fig.16. Velocity & Time for Mach 1.8 Correctly Expansion

D. Mach Number 2 (1 Correctly Expansion)

Fig.17. Velocity & Time for Mach 2 Correctly Expansion

Fig.18. Pressure & Time for Mach 2 Correctly Expansion




E. Mach Number 2 (1.2 under expansion)

Fig.19. Velocity & Time for Mach 2 under expansion

Fig20. Pressure & Time for Mach 2 under expansion

F. Mach Number 1.8 (1.2 under expansion)

0

50000

100000

150000

200000

250000

300000

350000

0 2 4 6

(title "Static Pressure")

pre 1.8 1.2

Fig.21. Pressure & Time for Mach 1.8 under expansion

0

100

200

300

400

500

600

700

0 2 4 6

(title "Velocity Magnitude"

)

velocity

Fig.22. Velocity & Time for Mach 1.8 under expansion



VII. RESULT

The fears of boundary layer skewing the smooth

flow through nozzle were laid to rest The CFD analysis for

the C‐D nozzle gave required flow parameters viz. Mach

number, Temperature, Pressure and Velocity. Since CFD is

cheaper than experimental prototype testing the study has

reduced number of wind tunnel tests that would be required.

This project helped us CFD skills and 2D mesh generation

capabilities were improved. All drawings made in CATIA

while graphs were plotted in Tecplot/MatLAB increasing

experience using this software.

VIII. CONCLUSION

Computational study of supersonic free jet flow

from conical nozzle with a design Mach number of 1.8 & 2

has been carried out. Jet conditions with various total

pressure ratios from over expanded to under expanded cases

have been investigated. Spacing of the shock cells and the

length of the potential core increase as the total pressure ratio

increases. A Mach disk is observed for over, under expanded

free jet conditions. Computational study of supersonic freejet

and measurements can play complementary roles in the

investigation of the noise generation from supersonic freejet

flows.

ACKNOWLEDGEMENT

Anna university support for the work of the authors is greatly

acknowledged. It has provided extensive resources and

materials for the completion of this research work

successfully.

REFERENCES

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[2] Bogey, C., and Bailly, C., ―Effects of Inflow Conditions and Forcing on

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1000–1007.

[3] Norum, T. D., and Seiner, J. M., ―Broadband Shock Noise from

Supersonic Jets‖, AIAA Journal, Vol. 20, No.1, 1982, pp.68–73.

[4] Panda, J., ―Identification of Noise Sources in High Speed Jets via

Correlation Measurements—A Review‖, AIAA, 2005-2844,2005.

[5] Raman, G., ―Advances in Understanding Supersonic JetScreech: Review

and Perspective‖, Progress in Aerospace Sciences, Vol. 34, Nos. 1–2, 1998,

pp. 45–106.

[6] Seiner, J. M., ―Advances in High Speed Jet Aeroacoustics‖, AIAA,

84-2275, 1984.

[7] Tam, C. K. W., and Tanna, H. K., ―Shock-Associated Noise of

Supersonic Jets from Convergent-Divergent Nozzles‖, Journal of Sound and

Vibration, Vol. 81, No. 3, 1982, pp. 337-358.

[8] W. ―Jet Noise Generated by large Scale Coherent Motion, Aero acoustics

of Flight Vehicles: Theory and Practice‖, Vol. 1, NASA, RP-1258, 1991, pp.

311–390.

[9] Tam, C. K. W., ―Supersonic Jet Noise‖, Annual Review of Fluid

Mechanics, Vol. 27, 1995, pp. 17–43.

[10] Umeda, Y., and Ishii, R., ―On the Sound Sources of Screech Tones

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A Brief Author Biography

J.C.Sophia Florance –Pursuing PG-Aeronautical Engineering in Nehru

institute of Engineering and Technology, Coimbatore. Completed

UG-Aeronautical Engineering in 2014 at PSN College of Engineering and

Technology, Tirunelveli. Paper presented in ICONMERIT conference under

the title of ‗Fatigue Analysis of Lug Joint in the Main Landing Gear‘, Paper

Published in IJRAME under the title of ‗Fatigue Analysis of Lug Joint in the

Nose Landing Gear‘ and IJERT under the title of ‗Fatigue Analysis of Lug

Joint in the Main Landing Gear‘.

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