A Detailed study on Performance Evaluation of Multiple Co-Axial Nozzles

JoEAM (2015) 1-26 © STM Journals 2015. All Rights Reserved

Journal of Experimental & Applied Mechanics ISSN: 2230-9845(online), ISSN: 2321-516X(print)

Volume 6, Issue 1

www.stmjournals.com

A Detailed study on Performance Evaluation of Multiple

Co-Axial Nozzles

Tridib Kumar Mahata* Department of Mechanical Engineering, Manipal Institute of Technology,

Manipal-576104, Karnataka, India

Abstract A nozzle is a device which converts the PE (Pressure Energy) of flowing jet into KE (Kinetic

Energy). In this paper we tried to determine the performance of various types of nozzles i.e

with varying the inlet cross section dimension (square, circular, hexagon etc.) and keeping the

outlet condition same i.e circular cross section and analysis by using CFD (Computational

fluid dynamics) tools (Gambit, Catia and Ansys Fluent).

Keywords: nozzles, CFD) tools, fluid flow

*Author for Correspondence E-mail: [email protected]

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. The total energy at the end of the pipe

consists of pressure energy and kinectic

energy [1–5].

Fig. 1: Converging-Diverging Nozzle Configuration.

Fig. 2: Showing Flow Velocity Increase from Green to Red.

http://en.wikipedia.org/wiki/Fluid

http://en.wikipedia.org/wiki/Fluid

http://en.wikipedia.org/wiki/Pipe_(material)

http://en.wiktionary.org/wiki/orifice

Performance Evaluation of Multiple Co-Axial Nozzles Mahata Tridib Kumar


In Figure 1 the converging-diverging nozzle is

shown and Figure 2 shows the velocity

increase in the above nozzle.

TYPES OF NOZZLES Aero-spike nozzle; Liquid nozzles; High-

speed gas nozzles; Propelling nozzles;

Magnetic nozzles; Rocket engine.

Fig. 3: Rocket Engine.

A typical rocket engine consists of the nozzle,

the combustion chamber, and the injector

(Figure 3).

Gas velocities from 2 to 4.5 km/s can be

achieved in rocket nozzles. The nozzles which

perform this feat are called DE laval nozzles

and consist of a convergent and divergent

section.

The minimum flow area between the

convergent and divergent section is called the

nozzle throat [4–9]. The flow area at the end of

the divergent section is called the nozzle exit.

The basic equation of thrust used is as follows:

* – *e e a eF V P P AM

where, F=Thrust, M =Propellant mass flow

rate, Ve=Velocity of exhaust gases,

Pe=Pressure at nozzle exit, Pa=Ambient

pressure, Ae=Area of nozzle exit.

Fig. 4: Thrust in Nozzle.

Fig. 5: Action of Exit Pressure and Atmospheric Pressure on Nozzle Surface.

PRINCIPLE OF OPERATION OF

ROCKET ENGINE Rocket engines produce thrust by creating a

high-speed fluid exhaust. This fluid is

generally always a gas which is created by

high pressure (10–200 bars) combustion of

solid or liquid propellants, consisting of fuel

and oxidizer components, within a combustion

chamber. The fluid exhaust is then passed

through a supersonic propelling nozzle which

uses heat energy of the gas to accelerate the

exhaust gases to a very high speed, and from

the Newton’s third law the reaction to this

pushes the engine in the opposite direction [6–

12].

Journal of Experimental & Applied Mechanics

Volume 6, Issue 1

ISSN: 2230-9845(online), ISSN: 2321-516X(print)


CO-AXIAL NOZZLES

Co-axial nozzles are nozzles where pipe and

nozzle are having or being mounted on a

common axis. The pipe supplies at very high

pressure fuel to the nozzle and compressed air

is passed through the nozzle, they react and

combust. The products are water, carbon

dioxide and carbon monoxide.

Fig. 6: Co-axial Flow Gaseous Nuclear Rocket.

Figure 6 shows a NASA-Lewis concept for a

gas core nuclear rocket engine, circa 1960.

Specific impulse was to be 2200 sec, thrust

98,000 pounds, T/W 0.68, reactor diameter

16.6 feet, overall reactor length, 16.6 feet. The

fuel would reach 20,000 degrees R, while the

hydrogen would get to 10,000 degrees R.

Coaxial jet nozzles are an integral part of

many engineering systems where mixing of

streams of different fluids are required. They

are widely used to mix the fuel and oxidizers

inside the combustors of gas turbine power

plant of aircraft. A properly designed jet will

be desired to mix efficiently, while providing

the best overall combustion efficiencies.

Characteristics of non-circular co-flow jets

have been analyzed for different types of

orifices, i.e. circular, crusi-form, hexagon, and

square [13–20].

Potential Core

In the developing zone of a circular jet

diffusing in a co-flowing stream, the flow

velocity changes from the jet velocity U0 to the

uniform ambient velocity Ua. The thickness of

the potential core gradually diminishes in the

streamwise direction and beyond the potential

core length; no uniform flow region exists

across the jet. The excess velocity within the

shear layer exhibits similarity and the integral

technique is often adopted for prediction of the

length of the potential core. Length of

potential core decreases with increase in

Reynolds number.

Jet Half-Width

The jet half-width is defined as the distance

from the jet centerline to the lateral location

where the local mean velocity has fallen to

one-half its centerline value.

Pressure Far-Field

Pressure far-field conditions are used in fluent

to model a free-stream condition at infinity,

with free-stream mach number and static

conditions being specified. The pressure far-

field boundary condition is often called a

characteristic boundary condition, since it uses

characteristic information to determine the

flow variables at the boundaries [18–26].

Figure 7 is the pictorial representation of far-

field and near field around the aircraft, with

inlet and outlet.



Fig. 7: Far-Field Around The Aircraft.

OBJECTIVE The objective of project is,

To evaluate jet half width and jet decay in

various predefined profiles of nozzle

orifices (viz. circular, hexagon, crusi-form,

and square).

To conduct 3D non-premixed combustion

for co-axial nozzle of different orifices and

compare their thrust with and without

combustion.

METHODOLOGY Design the different orifice types in

CATIA v5 like-circular, hexagon, crusi-

form, and square.

Then export it to Gambit v.2.3.16 where

meshing and cleaning of the model is

done, finally boundary is applied and then

it’s exported to Fluent v2.3.26.

Post processing of the model is done in

Fluent.

The sequence of work undertaken is shown by

means of a flow chart:


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TURBULENCE MODEL Turbulence models are developed based on

time-averaged statistical models. The local

velocities are defined as time-averaged

component and a time dependent fluctuating

component:

U (local velocity)=u (time averaged)+u′

(fluctuating component)

In the present work, standard k–ε models used

for the simulation. This two-equation model is

the most widely used turbulence model for

engineering simulations. Some of the features

of this model are,

It is robust,

Suitable for initial iterations, initial

screening of alternative designs, and

parametric studies.

SUMMARY This chapter reveals the methodology adopted

for the present work. Different types of flow

through pipe or a nozzle and the nozzle

equations. The fundamental governing

equations for flow and even flow passage are

explained for the modeling the turbulence

quantities. Solution flow-chart is shown in

hierarchy. Brief introduction about turbulence

model is explained.

VALIDATION OF THE TOOL Figure 8 shows the nozzle used for getting the

experimental values. It is run by 1 HP and

3000 rpm motor. On the right corner of picture

is the pressure distribution reader throughout

the nozzle. Motor is switched ‘on’ and the

regulator is controlled for different amount of

air supply-(30, 60, 90, and 100%) and the

manometer reading is taken.

Fig 8: Photo of the Experimental Nozzle Setup.

Table 1: Shows the Specification.

Density of water, (ρw) 1000 Kg/m³

Density of air, (ρa) 1.225 Kg/m³

Acceleration due to gravity, (g) 9.81 m/s

Diameter of the supply tube, (de) 25 mm

Area of the thin film of supply pipe is,

ρw=1000 Kg/m³, ρa=1.225 Kg/m³, g=9.81 m/s, A=( d²)/4, d=25 mm, A=4.906e–4 m²



Table 2: Experimental Values of the Nozzle.

% Manometer

Reading (mm)

(h1-h2)=h

(m) Pressure (Pa) Velocity (m/s)

Mass Flow Rate

(Kg/s)

h1 h2 P=ρaw.g.h V=√(2∆P/ρa) =AVρa

30 11.1 10.4 7e–3 68.67 10.58 6.358e–3

60 12.9 8.6 43e–3 421.83 26.24 1.57e–2

90 17.2 4.4 128e–3 1256.68 45.29 2.72e–2

100 20 1.9 181e–3 1775.61 53.84 3.23e–2

VALIDATION OF 2D-MODEL The nozzle dimension is measured and using

that value model was designed in Catia v5.

Then it was exported to the Gambit where it

was meshed using mapped meshing scheme

and boundary conditions were applied. Then

the model was exported to Fluent where values

were entered for post-processing.

Fig. 9: CATIA Model of the Nozzle. Fig. 10: Nozzle Dimension.

Fig. 11: 2D Model with Mapped Mesh Done in Gambit.


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Fig. 12: Boundary Condition.

Figure 12 displays the boundary condition that

was applied to the 2D model.

Table 3: Boundary Condition for Validation of

Tool.

Working fluid Ideal gas

Material Aluminum

Viscous model K-ε model

Temperature 300 K

In post processing the iteration were

conducted until the convergence was attained.

After the convergence the pressure and

velocity contour plot was taken and values

were taken and graphs were plotted.

Table 4: CFD Values of 2D-Nozzle from

Fluent.

% Pressure

(Pa)

Velocity

(m/s)

Mass Flow

Rate (Kg/s)

30 68.97 10.533 5.98e–3

60 424.73 26.01 1.47e–2

90 1266.69 44.65 2.54e–2

100 1789.75 52.95 3.02e–2

Fig. 13: Pressure Comparison. Fig. 14: Velocity Comparison.

0

500

1000

1500

2000

30 60 90 100

Pre

ssu

re (

in P

a)

Speed at which air passes through the

nozzle (%)

Pressure

Expt

CFD

0

10

20

30

40

50

60

30 60 90 100

Vel

oci

ty (

in m

/s)

Speed at which air passes through the

nozzle (%)

Velocity

Expt

CFD



Fig. 15: Mass Flow Rate Comparison.

Figure 13 is pressure comparison graph for

experimental values and CFD values it depicts

that there is very little difference between the

experimental CFD values, for different amount

of air supply (–30, 60, 90, and 100%).

Similarly Figure 14 and 15 depict the velocity

and mass flow rate comparison where the

values are almost similar.

Fig. 16: Pressure (in Pa) Contour Plot for 2D-Validation Tool.

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

30 60 90 100

Ma

ss f

low

ra

te (

in K

g/s

)

Speed at which air passes through the nozzle (%)

Mass Flow Rate

Expt

CFD


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Fig. 17: Velocity (in m/s) Contour Plot for 2D-Validation Tool.

Figure 17 contour plot of the 2D–model it can be seen that as speed of the air increases from 30 to

100%, the spread of flow is increasing in length and reducing in width.

Fig. 18: Axial Velocity Variation Plot and Pressure Variation Plot in Radial Direction.



Fig. 19: Pressure Variation Plot and Axial Velocity Variation Plot along Center Line.

Fig. 20: Comparison of Jet Half-Width.

Figure 19 shows the potential core along the

axial direction and indicates that 100% air

supply has more potential core than others

(like 30, 60, 90%). And it was even observed

from same plot that 100% air supply has less

jet decay too. The 60% air supply has larger

jet half width than the others as shown in plot

Figure 20.

MODELLING AND MESHING Gambit–CFD preprocessor is powerful design

tool to define CFD simulations which can be

later exported to CFD solvers and

postprocessors like Fluent, Polyflow and Star-

Cd for analysis purpose. This paper includes

detailed modeling descriptions of nozzle

orifice of different configurations. It also


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includes meshing details which is done in

gambit software.

Modeling Process

Modeling the Without Combustion

Specimens.

The different specimens are modeled in Catia

and then exported to Gambit, where the very

large cylinder is constructed connecting to the

nozzle as it is defined as pressure far-field.

Using Fluent the simulation is done.

Methodology of the Literature review [1] was

followed to find jet half-width and potential

core for different profiles of nozzles. All the

orifices shown in the Figure 21 are having

Equivalent diameter [1] (De=26 mm). These

orifices are designed and exported to Gambit.

In Gambit a flow region is defined as pressure

far-field for knowing the flow characteristics

of the nozzle outlet. The pressure far-field is

the cylindrical as in Figure 23, it is meshed in

tetrahedral scheme mesh and boundary

condition is applied. Fluid and solid region is

defined for identifying the fluid flow region.

Then it is exported to fluent for further

analysis. The models shown in the Figure 22

are the nozzle configuration used. And were

designed in Catia v5.

Fig. 21: Co-Axial Jet Flow Configuration.

Fig. 22: Different Orifices are Constructed in Catia.



Fig. 23: 3D-Model with Far-Field.

Fig. 24: 3D-Model After Meshing With Tetrahedral Mesh.

Fig. 25: 3D-Model Showing The Boundary Conditions.


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Table 5: Brief Information of Model with

Boundary Condition.

Air inlet Diameter (Da) 94 mm

The width of cylindrical object(wc) 1600 mm

The radius of cylindrical object (rc) 300 mm

No. cells for different configuration 2000000 cells

Meshing Tet/hybrid mesh

Type T-grid

The spacing for nozzle .6


Fluid Ideal gas

Density of ideal gas (air) 1.225 Kg/m

3

(remains constant )

Material Aluminum

An ideal gas is one that follows the gas laws at

all conditions of pressure and temperature. An

ideal gas is a substance that does not really

exist. Kinetic theory presumes that the

particles of an ideal gas have no volume and

that the particles are not attracted to each

other. There is no gas for which this is true.

Never the less, under many conditions, the

behavior of a real gas is similar to that of an

ideal gas [27–33].

Modeling with Combustion Specimens

A simple pipe is designed and placed in centre

exactly on the centre axis of different orifice

configurations. The pipe has 18 holes the

spray the fuel all around the nozzle.

Fig. 26: Different Specimens with Fuel Inlet Pipe Supply.



Fig. 27: Co-Axial Nozzle with Far-Field Region to Find the Flow Characteristics.

The liquid petroleum gas (LPG) is passed

through the pipe which has equal parts of

butane (C4H10) and propane (C3H8), the nozzle

will be supplied with compressed air. The

combustion takes place when the compressed

air meets the high speed fuel same as in diesel

engines. The fuel inlet and air inlets entry

being different it is known as non-premixed

combustion. The pdf table for non-premixed

combustion model is generated by entering the

chemical contents of (CH4, C2H6, C3H8, C4H10,

N2, and CO2). Many of nozzles used are made

from refractory metal such as Tungsten alloys

or Niobium alloys. These alloys can withstand

high temperature and wear.

Fig. 28: Meshed Using Tet/Hybrid Mesh. Fig. 29: Boundary Condition is Applied.

Table 6: Boundary Condition.

Fuel inlet diameter (Df) 13 mm [1]

Length of fuel tube (Lf) 60 mm [1]

Material Nickel


Fluid PDF mixture (CH4, C2H6, C3H8, C4H10, N2, and CO2) [19, 28]

Air inlet pressure 2 bar [33]

Air inlet temperature 312 K [19, 28]

Fuel inlet temperature 308 K [19, 28]

Fuel inlet pressure 6.06 bar [32]

Fuel inlet temperature 308 [19, 28]

Species model Non-premixed combustion [19, 28]

Radiation model P1 [19, 28]


Volume 6, Issue 1



SUMMARY In this paper we discussed about designing and

meshing of the different configuration of

nozzles using Catia V5 and Gambit software.

Also, boundary conditions are applied.

RESULT AND ANALYSIS This paper discusses about results which are

obtained for various nozzle configuration with

and without fuel supply pipe. The jet half-

width for without combustion nozzle

configuration is determined from the graph.

And with fuel supply pipe co-axial nozzle

configuration the combustion product graph is

plotted.

Figures 30, 31, and 32 show the comparison

between experimental and different types of

nozzle configuration (circular, hexagon, crusi-

form, and square) for different amount of air

supply (in %). There is very less difference

between the experimental and other non-

circular nozzle orifices and thus, tool

validation is done for all the specimens.

Fig. 30: Pressure Comparison for 3D. Fig. 31: Velocity Comparison for 3D.

Fig. 32: Mass Flow Rate Comparison for 3D.

Grid Independent Test

Grid independent test has been performed for

the model. The Tet/Hybrid grid is used for

meshing. The plot in Figure 33 shows the

different types of grid spacing (0.5, 0.6, and

0.7), the plot is in terms of total pressure

variation in the axial direction. There isn’t

much difference in different types of grid

spacing used but for optimum use 0.6 spacing

is adopted for simulation.



Fig. 33: Grid Sensitivity Study.

Results of Without Fuel Supply Pipe Nozzle

Configuration

Simulation for without fuel was carried out for

different specimens: circular, crusi-form,

hexagon, and square in commercial software

Fluent 6.3.26. The velocity and pressure

contour was taken, from which the graph of jet

half-width along the centerline plotted.

Graph

The Figures 34, 35, 36, and 37 depict the jet

half-width in X-Y and X-Z direction, these

profiles represents the radial velocity

component of different configurations. And

comparison is done for circular, crusi-form,

hexagon, and square profiles. The Figure 38

gives the pressure and velocity plot along the

centerline axis.

Fig. 34: Dispersion Plot 30% Air Supply in X-Y and X-Z Direction for Different Nozzle Orifices.



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Table 7: Effect of Jet Shapes in the Spreading

Rate Along the Radial Direction.

Name of profiles (R/De)

Circular 2.9

Hexagon 2.4

Crusi-form 2.96

Square 2.55

The effect of jet shapes in the spreading rate

along the radial direction was shown in

Table 7. From the Table 7 it can be easily

noted that the single crusi-form and circular jet

has larger spreading rate when compare to the

other two profiles. In case of non-circular

profiles, the hexagonal jet have less spreading

rate than the other configurations due to the

concave corners attached.

Fig. 38: Pressure and Velocity Plot Alon Centerline for Different Orifices.



Table 8: The Potential Core Length of All the

Profiles.

Profiles Z/De

Circular 1.96

Square 4.04

Hexagon 4.76

Crusi-Form 5.11

Briefing for the Without Combustion Nozzle

Configurations

The Figures 34, 35, 36, and 37 due to the

different surface of the nozzle exit there is

change is dispersion of the fluid flow for

the different air supply (30, 60, 90 and

100%). The crusi-form has more half

width than other specimens in X-Y

direction. But in the X-Z direction the

circular jet half-width is more.

As the jet progresses the circular and

square orifices are having equal jet half-

width in X-Y direction. Due to

complicated shape of the cruciform orifice

the jet drops after certain distance as seen

in X-Y plot in Figure 37. As there is

maximum velocity obtained in square

orifice the jet gradually increases after

certain distance.

The Figure 38 the velocity along the

centerline from the nozzle exit has no

variation of velocity up to the distance of

Z/De=9 where the circular nozzle shows a

drop in velocity. The potential core and

velocity decay of the circular specimen is

lesser compared to other specimens.

Single circular nozzle has very less

potential core.

RESULTS OF WITH COMBUSTION,

CO-AXIAL NOZZLE

CONFIGURATIONS The fuel supply pipe is introduced, it has 18

fuel holes and each hole is of 1.5 mm diameter

[26]. The contour plot as well as graph is

plotted to know the characteristics of the fuel

combustion in nozzles.

Contour Plots

The contour plot of different specimen taken.

For 3D models even the cros-sectional view

was also taken. Figure 39 represents velocity

plot along the x-axis, Figure 40 shows cross-

sectional view for different nozzle

configuration.

Fig. 39: Velocity (in m/s) Contour Plot for All Co-Axial Nozzle Configuration.


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Fig. 40: Cross-Sectional Velocity(in m/s) Plot for Different Co-Axial Nozzle Configuration.

Fig. 41: Temperature(in K) Contour Plot for All Co-Axial Nozzle Configuration.

Figure 41 represents axial contour plot of temperature, Figure 42 shows cross-sectional contour plot

of temperature at nozzle exit.



Fig. 42: Cross-Sectional Temperature (in K) Plot for Different Co-Axial Nozzle Configuration.

Fig. 43: Mass Fraction O2 Contour Plot for All Co-Axial Nozzle Configuration.

Fig. 44: Mass Fraction of O2 in Cross-Sectional Contour Plot for All Co-Axial Nozzle Configuration.


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Fig. 45: CO2 Contour Plot for All Co-Axial Nozzle Configuration.

Fig. 46: Mass Fraction of CO2 in Cross-Sectional Contour Plot for All Co-Axial Nozzle

Configuration.

Figures 39, 41, 43, and 45 show the axial

contour plot for velocity, temperature, O2, and

CO2. The cross-sectional view in Figures 40,

42, 44, and 46 show the exit of different co-

axial nozzle profiles.

Graphs

When the fuel and air is entering in the

combustion chamber according to the x and y

plot, its burn due to high velocity and

temperature and then temperature increase

rapidly in combustion chamber. The velocity,

temperature, O2, CH4 and CO2 plot are plotted

in graph, Figure 47–52.



Fig. 47: Velocity Plot for Different Co-Axial Configuration At Nozzle Exit.

Fig. 48: Temperature Plot for Different Co-Axial Nozzle Configuration.

Fig. 49: Mass Fraction of CH4 for Different Co-Axial Nozzle Configuration.


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Fig. 50: Mass Fraction of CO2 for Different Co-Axial Nozzle Configuration.

Fig. 51: Mass Fraction of O2 for Different Co-Axial Nozzle Configuration.

Fig. 52: Total Pressure Plot for Different Co-Axial Nozzle Configuration.



Briefing for the With Combustion, Co-Axial

Nozzle Configurations

From Figure 50 we can see that square co-

axial nozzle produces more CO2 than other

co-axial nozzles.

Crusi-form and circular co-axial nozzles

have maximum temperature.

The cruciform has maximum velocity as

seen in graph.

Combustion of oxygen is very good in the

nozzle, Figure 50 shows crusi-form has a

good O2 consumption, and so, complete

combustion takes place when the fuel

reaches the exit of the nozzle.

For the same value of air and fuel if

increase the fuel inlet the amount of air is

decrease compared to fuel amount.

When the air enters the combustion

chamber and burned with fuel, then mass

fraction is high of value 2.33e–01 in the

combustion chamber and minimum value

2.10e–02, and goes on decreasing in part

of the nozzle, while near to the nozzle wall

mass fraction of oxygen is zero.

But in case of square profile O2

consumption was not complete.

Mass fraction of CO2 goes on decreasing

in part of the nozzle, while near to the

nozzle wall mass fraction CO2 is zero.

Thrust Comparison

The Figure 51 shows that square co-axial

nozzle has maximum thrust as its area is more

and thus the thrust is maximum for it. The

Table 9 gives the basic formula to calculate

thrust. The crusi-form and square profiles are

giving maximum thrust. 2D and 3D-Circular

co-axial nozzles are having almost similar

thrust. Hexagon produces least thrust due to its

concave edges shape the there is no expansion

freely and annular flow moves to the centre of

the jet, thus, the thrust is less. There is

complete combustion of oxygen in crusi-form

co-axial nozzle, which gives out maximum

velocity.

Table 9: The Important Formulas.

Thrust e e a eF= *V + P –Pm *A

Area of circle 2 2A= r /4=530.6e–6 mm r=13 mmπ

Area of square A=a*a=576e–6 mm a=24 mm

Area of crusi-form A= b*x*4 + x*x =507e–6 mm x=13 mm, b=6.5 mm

Area of hexagon 2A= =475.87e–6 mm t=13 3

t2

5 mm

Fig. 53: Thrust for Different Configuration with Fuel Co-Axial Nozzle and Without Fuel.


Volume 6, Issue 1



SUMMARY The graph and contour plot were plotted, the

without fuel nozzle configuration were

compared with each other. With fuel co-axial

nozzles were compared with each other and

finally the thrust for both with and with

combustion were compared.

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Cite this Article

Tridib Kumar Mahata. A Detailed Study

on Performance Evaluation of a Multiple

Co-Axial Nozzles. Journal of

Experimental & Applied Mechanics.

2015; 6(1):

http://www.engineeringtoolbox.com/propane-butane-mix-d_1043.html

http://www.engineeringtoolbox.com/propane-butane-mix-d_1043.html

A Detailed study on Performance Evaluation of Multiple Co-Axial Nozzles

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