1

1: INTRODUCTION

A nozzle is a device designed to manipulate the characteristics of a flow as it passes

through its boundaries often to the effect of increasing or decreasing the velocity of the

fluid. It is usually in the form of a duct of varying cross section and can also be depicted

as an device capable of converting pressure energy into kinetic energy and vice versa.

Nozzles have been implemented in a wide range of applications from spray painting to

laser cutting. Nozzles can either be convergent, divergent or exhibit a converging section

followed by a diverging section. Propulsive nozzles are the type commonly used on high

speed aircraft and launch vehicles. The convergent divergent class first envisioned by

the Swedish engineer Gustav De Laval in 1880 for use in steam turbines and are known

as De-Laval nozzles.

Robert Goddard in his 1917 publication titled “Reaching High Altitudes” discussed how

De-Laval nozzles could be used to accelerate products of combustion. Further

developments in rocket propulsion throughout the years ultimately culminated in the

Saturn V program that was responsible for landing men on the moon.

The expansion of combustion gases through the nozzle generates a force which is known

as Thrust. The thrust chamber and the nozzle are the most important components of a

launch vehicle. Optimal functionality of a Rocket nozzle ensures maximum efficiency

which translates into larger payload capacity and the ability to attain higher orbits. Thus

the design of a nozzle is an important lynchpin in the efficient operation of a launch

Vehicle and the study of its off design performance helps to address issues design

methodology.

Computational Fluid Dynamics has proven to be a valuable tool in the study of flow

phenomenon and has been applied in nozzle design and performance characterization to

the same avail. The availability of commercial CFD packages has enabled relatively fast

analysis and has helped patch the gaps left behind by the simplifying assumptions of

design methods.

2

1.1.1 Literature Survey

The study of Compressible flows is a requisite to the understanding of flow phenomenon

occurring in nozzles. Elementary nozzle flows can be given a one dimensional treatment

but such is an extremely simplifying assumption. The flow through a stream tube is

essentially three dimensional with flow properties being functions of X, Y & Z

coordinates respectively. However, if the variation of stream tube are is moderate the Y

& Z components may be considered negligible when compared with the variation in X

component and thus in such cases, the flow field variables can be assumed to be

functions of X direction. Such flows where the flow parameters such as Pressure,

Density, Velocity etc. are functions of the X co-ordinate such that A=A(x), P=P(x) ,

u=u(x) etc. are termed as Quasi One Dimensional flows and form the basis of nozzle

flow analysis.

For subsonic flows, where the Mach numbers are low, an increase in flow velocity can

only be attributed to a decrease in area of the duct. Similarly for supersonic flows,

velocity increases with an increase in area.

For the case of M=1 i.e. sonic flow, it is observed there exists a flow with a finite velocity

magnitude and corresponds to the minimum area.

A convergent divergent nozzle consists of a convergent section which subsonically

accelerates a gas till it reaches sonic conditions followed by a divergent section which

isentopically expands the gas to supersonic speeds. The basic requirement for a gas to

expand to supersonic speeds is to pass through the region of the duct with minimum area

and furthermore achieve sonic speed at that location, known as the throat of a nozzle.

Due to the multidimensionality of the flow, the region of sonic flow exhibits a slight

curve towards the divergent section.

In conventional nozzle design, the supersonic nozzle is split into two main regions i.e.

convergent section and the divergent section. The convergent or contraction section

plays host to a flow which is entirely in the subsonic regime which is followed by the

throat where the flow reaches sonic conditions. The divergent section consists of an

initial expansion region where the slope of the wall contour reaches its maximum value

3

followed by a straightening or what is otherwise known as a ‘Busemann’ section where

the cross sectional area increases but the wall slope decreases. In case of applications in

supersonic wind tunnels, the ‘Busemann’ section is immediately followed by a test

section where the flow is uniform and parallel to the axis to be used for experimentation.

Practical considerations for use of Convergent Divergent nozzles in Rocket Propulsion

rule out nozzles with considerable length as they incur a considerable weight gain to the

propulsion system. Therefore this has led to the design of Minimum Length Nozzles

which use a centred expansion fan at the throat to achieve the necessary expansion.

Several methods of Nozzle design have been proposed in available literature, from

approximate methods to numerical schemes aimed at ensuring a contour that provides

uniform axial flow of desired Mach number at the exit plane of the nozzle. The Prandtl

Meyer function plays an important role in determining the maximum expansion

possible for a given design Mach number.

This study uses a Method of Characteristics approach to determine the nozzle contour

that corresponds to a uniform flow at exit with a given design Mach number.

This study uses a design altitude of sea level, 6, 12, 20, 30 & 40 km respectively. The

nozzle designed to operate optimally at an altitude of 6 km, has an exit Mach number

of 3.09. For fabrication we have selected an altitude of 5km that has an exit Mach

number of 2.55. Open Jet tests & Schleiren photography have been performed and a

series of pressure readings along the length of the nozzle divergent section have been

taken for validation.

Computational Fluid Dynamics has played an important role in the prediction and

analysis of flow phenomenon. The availability of versatile commercial CFD codes like

ANSYS FLUENT, STAR CCM and CFX etc. have made it possible to obtain initial

design validation. These packages also offer the capability of imparting various

empirical and semi-empirical turbulence models that can be applied to study the

behaviour of different flows. Post processing tools help analyse the generated data in

the form of contour plots, distributions and other representations.

4

1.1.2 Methodology

The domain of interest for the application of Convergent Divergent nozzles in this study

is that of Rocket Propulsion. The efficient design of Rocket Nozzles plays an important

role in the overall efficiency of a rocket or launch vehicle. Rocket Nozzles operate

through a wide range of flow regimes from dense sea level conditions to rarefied

conditions towards and above the 100km.

The vast operating regime of rocket nozzles renders their exhaustive study to be tedious

and time consuming. Thus, a portion of the overall flight regime in terms of altitude is

taken under consideration. These correspond to the different altitudes at which the

Rocket Nozzle will operate. The altitude that has been chosen for the ideal performance

of the nozzle is 6 km and studied for the various off design altitude that is sea level

12km, 20km, 30km and 40km.

1.1.3. Theoretical Background

The Convergent-Divergent nozzle deals with both Subsonic and Supersonic flow

regimes, within this framework, transonic flow is also achieved in the vicinity of the

throat. The ideal expansion of a gas through the divergent section of the nozzle depends

on the relatively simple interplay between the various pressure zones within and outside

the nozzle.

The pressure terms that drive nozzle flows are, stagnation (Total Pressure), Nozzle Exit

Pressure & Back pressure. They may be denoted as P0 , Pe and Pb respectively. To

visualize the concept of backpressure, a setup may be envisioned wherein a convergent

nozzle is connected to an infinite reservoir and is evacuating into an exhaust chamber,

the pressure prevalent in the exhaust chamber is Pb or back pressure whereas the

pressure at the nozzle exit plane is Pe.

The ratio Pe

P0 is termed as the nozzle pressure ratio and

Pb

P0 , can be termed as the back

pressure ratio.

𝐴

𝐴∗=

1

𝑀{

2

𝛾 + 1+

𝛾 − 1

𝛾 + 1𝑀2}

𝛾+12(𝛾−1)

5

The Area-Mach number relation stipulates that as the cross-sectional area decreases,

there occurs an increase in flow velocity. The BPR in the arrangement is allowed to

decrease and the flow is observed. It will be noticed that even after the BPR is decreased

below a certain range, the nozzle exit pressure Pe and the flow adjusts to conditions in

the exhaust chamber through an expansion wave as Pb is still less than Pe. The plot given

below depicts the phenomenon being described.

Figure 1: Variation of pressure along the Nozzle axis (Reference S M YAYA)

Curve ‘c’ depicts the critical pressure achieved in the nozzle. The mass flow rate ceases

to increase beyond its value at this point and the nozzle exit pressure ceases to decrease.

The maximum mass flow occurs at curve c.

A similar illustration can be used to depict flow through the convergent section to the

throat of a convergent divergent nozzle. For a given design pressure ratio, sonic

condition at the throat ensures ideal expansion through the divergent portion of the

nozzle as shown by curve ‘c’ and this demonstrates ideal expansion at the correct

pressure ratio. Any variation in the pressure ratio may cause a normal shock to be

formed within the nozzle which would reduce the flow to subsonic Mach numbers

(Curve‘d’). If the nozzle pressure ratio is decreased below its critical value, the flow

6

expands outside the nozzle whereas, if it is increased, the flow will readjust itself to

ambient conditions outside the nozzle through a series of compression waves (Curves

‘f’ & ‘g’).

Figure 2: Variation of throat pressure ratio in a convergent divergent nozzle (γ = 1.4)

Looking at the isentropic equations, the requisite throat pressure ratios can be

identified by setting M=1 in the following equations.

𝑇𝑜

𝑇= 1 +

𝛾 − 1

2𝑀2

𝑃𝑜

𝑃= {1 +

𝛾 − 1

2𝑀2 }

𝛾𝛾−1

𝜌0

𝜌= {1 +

𝛾 − 1

2 𝑀2}

1(𝛾−1)

7

A superscript ‘*’ is appended to the terms depicting parameters at the throat or any

section exhibiting sonic flow. Thus, substituting γ=1.4 and M=1 in the above relations

and performing the requisite operations, the critical ratios have been determined to

be:

𝑇∗

𝑇=

2

(𝛾 + 1)= 0.833

𝑃∗

𝑃= {

2

𝛾 + 1}

𝛾𝛾−1

= 0.528

𝜌∗

𝜌= {

2

𝛾 + 1}

1𝛾−1

= 0.634

It can be inferred from the above relations that the pressure at the throat needs to be

almost half of the stagnation pressure to ensure sonic flow at the throat. Similar

conclusions can also be drawn for other parameters.

An approach based on the ideal pressure ratio has been followed in order to generate

the necessary inputs to the MOC program. An example has been included for a nozzle

with a design altitude of 6km.

The International Standard Atmosphere (SI Units) was consulted for the appropriate

ambient pressure values at each altitude. In this case the ambient pressure was found

to be, Pa= 47181Pascal (Pa). A chamber pressure of 20bar or 2MPa was stipulated and

the NPR was found to be 0.0235. Isentropic relations were used to determine the

corresponding Mach number, which was then used in association with the Area Mach

number relation to determine the exit area ratio.

Like temperature, pressure, density ratios, area ratio at a given section of passage is

also a useful quantity.

8

Area Ratio is a function of Mach number.

Figure 3: Variation of Area Ratio with Mach No

TABLE 1: Design Conditions for Ideal Performance

Altitude

(km)

Pressure

(Pc)

Pressure

(Pa)

NPR*

Temperature

(k)

Design Mach

number

6 km

2000000

47181

.0235

249.2

3.09

6km

1000000

47181

.047181

249.2

2.63

NPR * nozzle pressure ratio γ= 1.4

9

1.1.4 Methods of characteristics

Method of Characteristics is a numerical method used to solve the host of nonlinear

equations of motion for Inviscid, irrational flow. Most Compressible flow problems

can be solved using linearized flow theory at the expense of accuracy and reliability of

the solution. Improved solution would require the inclusion of the higher order terms

whose neglect serves as the basis of linearized theory. Numerical methods can be used

to great effect in addressing these nonlinear problems.

An important distinction needs to be made between Mach waves and Characteristic

expansion waves. Mach waves are weak isentropic waves across which the flow

experiences an insignificant change in its properties whereas expansion and

characteristic waves are isentropic waves which introduce small but finite property

changes to the flow passing through them. Characteristics only exist in supersonic flow

fields and are coincident along Mach lines. The derivatives of flow properties are

discontinuous but the flow properties themselves are continuous on the characteristics.

On a Characteristic the dependant variables satisfy a relation known as the compatibility

relation.

1.1.5 Supersonic Nozzle Design

The objective is to design a nozzle contour for the appropriate exit Mach number

ensuring uniform parallel flow at nozzle exit. The contour requires a convergent section

to accelerate the flow to sonic condition at the throat followed by a divergent section

that expands the flow isentropically to supersonic condition. As discussed earlier, the

shape and design methodology of the convergent section lends itself to certain

approximations.

Figure 4: Minimum Length Nozzle

10

An improper contour may result in insufficient flow expansion or give rise to

disturbances which may coalesce to form strong shocks within the nozzle. The Method

of Characteristics provides a technique for properly designing the contour of a

supersonic nozzle for shock free isentropic flow, taking into account the

multidimensionality of the flow.

The sonic line which serves as the initial data line for a characteristics solution is slightly

curved in reality owing to multidimensionality of the flow. However for practical

purposes it is considered to be straight. Assume an angle θw to be the angle subtended

by the contour wall with the horizontal at any given point (say P) .The divergent section

features an increase in θw until it reaches a value of θmax at the exit section of the nozzle.

Symmetry of the nozzle about its centre line simplifies the problem to one half. The

point of inflection (say Q) is the point at which θmax is achieved. Downstream of Q, θw

decreases until the wall becomes parallel to the X-Direction at the last point. The

number of Characteristic lines determines the resolution of the contour. A large number

of lines results in a more accurate solution. The Characteristic lines divide the half

nozzle into multiple regions. The right running lines from the throat have a negative

slope and are called waves of family II whereas the waves running to the left are those

of family I and exhibit a positive slope. These waves intersect near the centreline of the

nozzle and the collection of regions thus formed is termed as non-simple regions. The

lines of family II are terminated by the nozzle contour.

This study uses a Method of Characteristics approach to determine the nozzle contour

that corresponds to a uniform flow at exit with a given design Mach number. The

Method of Characteristics Approach is given below.

Figure 5: 1 domain discretization

11

1.1.6 MOC Solution Procedure

Indexing variables i & j are used for regions I & II respectively. The contour angle is

calculated to be exactly half of the Prandtl-Meyer angle i.e. θmax= . The Prandtl

Meyer function is used to calculate νe.

If the number of Characteristic lines is denoted by N then the turning angle of each

characteristic line is given by . The values of i & j are given by:

Similarly,

The Prandtl Meyer angle for each region is given by:

i varies from i to imax

j varies from j to jmax

The Mach angle is given by:

The slopes of characteristic line I & II are given below:

The divergent section of the nozzle is divided into regions by the two families of

characteristic lines. These regions exhibit constant values of flow properties

12

1.1.7. NASA MOC CODE

Once the operating conditions of the nozzle were determined a Method of

Characteristics code was used to generate the required contour of the divergent section.

The NASA Glenn Research Centre has a well maintained online Method of

Characteristics tool which has been used.

With the help of the standard NASA MOC code the contours have been generated by

entering the values of chamber pressure and the pressure ratios.

The program takes the ratio of specific heats (γ), desired exit Mach number and the

number of characteristic lines to generate the coordinates of the contour. Similarly the

contours for all the Mach numbers in concern were generated at varying degrees of

resolution. The maximum numbers of characteristic lines used were 100.

Input variables for the MOC program.

The default input panel is the Analysis panel. This panel controls the type of

problem that you will study, and certain parameters associated with the MOC

analysis.

The MOC analysis solves for flow conditions along left running and right

running rays. You can select the number of rays used in the analysis by typing

into the input box.

Nozzle calculation, flow is assumed to be chocked at the nozzle throat and the

flow then expands into the nozzle. Ideally, the throat would be a sharp edged

surface.

The chief input panel is the internal panel. This panel sets the values for most of

the design parameters.

The design Mach number is the desired Mach number at the exit of the nozzle

is entered.

Total pressure in pounds per square inch (psi), and total temperature in degree,

are also used to determine the airflow through the nozzle (Units are as used by

NASA program).

13

The airflow times the exit velocity determines the thrust.

The total temperature affects the flow temperature throughout the nozzle which

in turn affects the value of the specific heat ratio.

The external panel sets the values of flow parameters in the free stream, outside

the nozzle, and along the edge of the plume.

The program can be run in three different modes: internal flow and design,

internal flow plus plume, or internal flow, plume and external (supersonic) flow.

You select the mode by using the drop menu at the top of the panel.

Figure 6: The NASA Glenn Research Centre - Standard NASA MOC

14

Using the standard NASA MOC code the contours for the exit Mach no have been

generated with 100 as number of rays and the exit Mach no 3.09 and 2.63 respectively.

Exit Mach= 3.09 Pressure Ratio= 0.0235 N=100

Figure 7: Contour for exit M=3.09

Exit Mach=2.63 Pressure Ratio=.047181 N=100

Figure 8: Contour for exit M=2.63

15

2. GEOMETRY AND GRID GENERATION

A grid is a small-sized geometrical shape that covers the physical domain, whose

objective is to identify the discrete volumes or elements where conservation laws can

be applied. In computational fluid dynamics, meshing is a discrete representation of the

geometry that is involved in the problem. Essentially, it assigns cells or smaller regions

over which the flow is solved. Several parts of the mesh are grouped into regions where

boundary conditions may be applied to solve the problem Grid generation is the first

process involved in computing numerical solutions to the equations that describe a

physical process. The result of the solution depends upon the quality of grid. A well-

constructed grid can improve the quality of solution whereas, deviations from the

numerical solution can be observed with poorly constructed grid. Techniques for

creating the cell forms the basis of grid generation.

1. Unstructured grids

2. Structured grids

2.1.1 Unstructured Grid Generation

The main importance of this scheme is that it provides a method that will generate the

grid automatically. Using this method, grids are segmented into blocks according to the

surface of the element and a structure is provided to ensure appropriate connectivity.

To interpret the data flow solver is used. When an unstructured scheme is employed,

the main interest is to fulfil the demand of the user and a grid generator is used to

accomplish this task. The domain is divided into polygons, triangles are often used.

Software to generate this type of

Discretization normally require the user to input an initial, very coarse, triangulation.

Perhaps only containing points on the boundary of the domain. Techniques for

automatic refinement is then used.

16

2.1.2 Structured Grid Generation

A structured grid is something which is indexed along coordinate directions. The

generation of structured meshes are descendants of "numerical grid generation"

algorithms, in which a differential equation is solved to determine the nodal placement

of the grid.

2.1.3 Gambit GAMBIT is a software package designed to help analysts and designers build and mesh

models for computational fluid dynamics (CFD) and other scientific applications.

GAMBIT receives user input by means of its graphical user interface (GUI). The

GAMBIT GUI makes the basic steps of building, meshing, and assigning zone types to

a model simple and intuitive, yet it is versatile enough to accommodate a wide range of

modelling applications.

The contours generated using the Method of Characteristics are imported into GAMBIT

(Geometry and Mesh Building Intelligent Toolkit) to build a geometry which is then

meshed. Since the dimensions of the nozzle vary with increase in Mach number a

relative meshing approach has been used to ensure uniformity in the mesh sizing. The

number of nodes and subsequent mesh size have been tabulated below. Furthermore,

the appropriate boundary conditions are imparted onto the meshed geometry.

Half of the nozzle, which can mirrored about the centreline is used as the solution

domain. In order to test grid dependency, two separate meshes have been generated with

exactly double and triple the number of nodes respectively. The total node count is has

been tabulated for each of the nozzles accordingly. The convergent section contour has

no particular requirement other than.

The design methodology used for the convergent contour is quite relaxed and is open

to a suite of approximations, generalizations and rules of thumb. The shape should be

such as to ensure the required pressure ratio at the throat to facilitate supersonic

expansion in the divergent section. To ensure a modest pressure gradient and to prevent

17

unwanted phenomenon that comes with the specification of an arbitrary convergent

section shape, this study specifies the length of the convergent section as being 30%

the length of the divergent section. This falls in line with the general trend observed in

consulted literature. However this method is distinct in its provision of a contoured

convergent section.

2.1.4 Mesh Generated

The contour generated through the standard NASA program is imported in Gambit and

it’s meshed to the suitable requirements.

The contour points are imported for exit Mach 3.09 and 2.63 respectively.

Three types of mesh is generated that is a coarse mesh, a medium mesh and a fine mesh.

The difference between the three types of mesh being the number of nodes, cells and

faces vary for all three types.

Coarse Consist the least number of cells, faces and nodes gives the convergence at lesser

computational time, while fine mesh contains the highest no of cells, faces and nodes

takes time to reach its convergence value as it has almost triple the faces, cells and nodal

points compared to a coarse Mesh.

18

Figure 9: Types of Meshes used

19

2.1.5 Off - Design Conditions (Mesh)

To study the off design performance of the nozzle, we need to analyse the over expanded

and under-expanded condition and how its flow varies outside the exit of the nozzle at

various off design altitude.

To do so a domain is been created such that flow outside can be visualized when

simulated using the computational tools such as Fluent.

The domain is made in such that the flow is not affected by any boundaries, and the

ambient pressure at the domain.

Quadrilateral cell shape is a basic 4 sided one as shown in the figure. It is most common

in structured grid, the accuracy of solution and rate of convergence will be better

compared to the triangular cells.

Triangular cell shape consists of 3 sides and is one of the simplest types of mesh. It is

most common in unstructured grids. It is basically used for better flow capturing at the

exit of the nozzle. Triangular mesh is used with the first length option for creating more

no of cells at the exit plane of the nozzle.

20

Figure 10: Nozzle with the Domain (Mesh)

21

TABLE 2: Mesh Details

Alt(km) Mach

No Type Cells

Length of Length of Nozzle Reservoir

Divergent

Convergent Convergent Divergent

Y x y section Section

(~30%) Nodes Nodes

6

2.63

coarse Quad

7.135 2.1405

30 60 30 NIL NIL

Medium Quad 60 120 60 NIL NIL

Fine Quad 120 240 120 NIL NIL

Reservoir Tri 60 120 60 250 50

First

Length NIL NIL NIL 2 1.81

3.09

coarse Quad

9.872 2.9616

30 60 30 NIL NIL

Medium Quad 60 120 60 NIL NIL

Fine Quad 120 240 120 NIL NIL

Reservoir Tri 60 120 60 250 50

First

Length NIL NIL NIL 2 1.81

Table 2 shows the specification of the Mesh that has been created.

22

3. ANSYS Fluent

ANSYS Fluent software contains the broad physical modelling capabilities needed to

model flow, turbulence, heat transfer, and reactions for industrial applications ranging

from air flow over an aircraft wing to combustion in a furnace, from bubble columns to

oil platforms, from blood flow to semiconductor manufacturing, and from clean room

design to wastewater treatment plants. Special models that give the software the ability

to model in-cylinder combustion, aeroacoustics, turbomachinery, and multiphase

systems have served to broaden its reach.

ANSYS Fluent software as an integral part of the design and optimization phases of

their product development. Advanced solver technology provides fast, accurate CFD

results, flexible moving and deforming meshes, and superior parallel scalability. User-

defined functions allow the implementation of new user models and the extensive

customization of existing ones. The interactive solver setup, solution and post-

processing capabilities of ANSYS Fluent make it easy to pause a calculation, examine

results with integrated post-processing, change any setting, and then continue the

calculation within a single application. Case and data files can be read into ANSYS

CFD-Post for further analysis with advanced post-processing tools and side-by-side

comparison of different cases.

3.1.1 Solution Setup: FLUENT

The mesh generated using GAMBIT is now supplied to FLUENT. Appropriate models

are defined and the associated boundary conditions parameters are specified. The

simulations are conducted using a Coupled or Density based solver available in

FLUENT and the ideal gas model is used for the fluid.

3.1.2 Boundary Conditions

1. Pressure Inlet: The following parameters are supplied at the pressure inlet

boundary condition.

Total(Stagnation) Pressure

Total(Stagnation) Temperature

Flow Direction

23

Static Pressure

Turbulence Parameters (For Turbulent Flow Models)

The ratio of specific heats is taken as 1.4.

FLUENT requires a parameter known as ‘Operating Pressure’ to be stipulated. All

pressure vales are calculated in reference to the specified Operating Pressure’. Thus the

‘Absolute Pressure’ is the sum of specified pressure values and the ‘Operating

Pressure’. The ‘Operating Pressure’ has been set to zero in this case.

P absolute = P gauge + P operating

The Supersonic/Initial Gauge Pressure value is an initial guess which is ignored by

FLUENT when the flow is subsonic, and is calculated from stagnation conditions.

When the solution is initialized using Pressure Inlet conditions, the Supersonic/Initial

Gauge pressure values will be used in conjunction with the specified stagnation (Total

Pressure) to determine the initial values based on isentropic relations in the case of

compressible flow and Bernoulli’s equation for incompressible flow.[FLUENT

Manual]

2. Pressure Outlet:

Static Pressure

The Static pressure at outlet is set according to the optimum pressure ratio for each

nozzle. This parameter is only ever utilised by FLUENT if the flow is subsonic and

when supersonic flow is encountered, the pressure is extrapolated from conditions

upstream.

Interpreted as static pressure of environment into which flow exhausts.

Radial equilibrium pressure distribution option available

Doubles as inlet pressure (total gauge) for cases where backflow occurs

Backflow quantities can occur at pressure outlet either during iterations or

as part of final solution.

24

Backflow Direction Specification Method

Backflow boundary data must be set for all transport variables.

Convergence difficulties can be reduced by providing realistic

backflow quantities.

3. Wall

Thermal Boundary Conditions (For Heat Transfer Calculations)

Wall Roughness

Shear Conditions

4. Axis

The Axis condition is used when the Geometry, Flow Pattern exhibits mirror

symmetry. In this case the centreline of the nozzle has been used as the mirror

axis.

Used at the centre line for axisymmetric problems.

No user inputs required.

Must coincide with the positive x direction.

Fluent Setup

Read

Step 1: Read

Import Mesh

Mesh Check

Step 2: Solver Specifications

Density Based Solver

2-D

25

Ideal Gas

Step 3: Boundary Conditions

Pressure Inlet : Stagnation Pressure & initial Guess Pressure

Pressure Outlet: Exit Pressure

Temperature

Step 4: Solution

Differencing Scheme : First Order Upwind

Courant Number

Convergence Criteria 10e-6

Step 5: Results

Velocity Vectors Coloured by Mach Number

Pressure Contours

Mach Number Contours

Area Weighted Averages of Velocity at Inlet & Outlet

26

3.1.3 Fluent Simulation

The imported mesh is ran at different altitude for varying back pressures.

Altitude Temperature Pressure

0 288.16 101325

6 249.2 47181

12 216.66 19399

20 216.66 5529.3

30 231.24 1185.5

40 260.91 299.77

TABLE 3: Shows the ambient temperature and ambient pressure at the corresponding

altitude.

Altitude vs Pressure

Figure 11: Graphs (Altitude vs Pressure)

0

20000

40000

60000

80000

100000

120000

0 10 20 30 40 50

Pre

ssu

re

Altitude

Altitude Vs pressure

27

Altitude vs Temperature

Figure 12: Graphs (Altitude vs Temperature)

A case is set up in FLUENT using the methods described in previous sections. The

Pressure Inlet & Pressure Outlet boundary conditions are implemented with their

appropriate values. Wall and symmetry have been set and the solution was run. Three

Meshes have been generated and are put through a FLUENT solution in order to rule

out Mesh dependency. They vary in their degree of fineness from coarse to extremely

fine.

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Tem

per

atu

re

Altitude

Altitude vs Temperature

28

TABLE 4: Mesh Quality

Shows the mesh quality of the generated mesh.

3.1.4 Progress of Fluent Solution

A 2 dimensional, steady, inviscid solution has been carried out considering the fluid as

an Ideal Gas. An interesting phenomenon can be identified and recorded during the

progress of the solution. A normal shock is formed inside the nozzle but is forced out

during the course of the solution because of the favourable operating NPR. It can be

seen that the Normal Shock is pushed out of the nozzle and regular flow is established

at the end of the solution. The solution results show a good agreement with design

parameters with insignificant differences near the wall region.

Mach Type Orthogonal Aspect Size

Quality Ratio cells faces nodes partition

2.63Axi

coarse 9.74E-01 3.88E+00 2700 5520 2821 8

Medium 9.74E-01 3.91E+00 10800 21840 11041 6

Fine 9.74E-01 3.90E+00 24300 48960 24661 6

Reservoir 7.00E-01 4.65E+00 82736 135089 52354 7

3.09Axi

coarse 9.45E-01 5.36E+00 2700 5520 2821 4

Medium 9.45E-01 5.43E+00 10800 10800 11041 4

Fine 9.45E-01 5.46E+00 24300 48960 24661 4

Reservoir 6.66E-01 5.45E+00 127122 206898 79777 7

29

Figure 13: Progress of a fluent solution (iterations 0 – 1500)

30

It can be seen that there is more clarity in the formation of expansion waves in fine mesh

when compared to that of coarse and medium mesh. The Details in the view of the fine

mesh is better because of the number of cells present is three times that of the coarse

mesh.

3.1.6 Results

TABLE 5: Tabulation of result without reservoir

Fluent Simulation Pictures (refer appendix 1)

Alt

(Km)

Quality

of Mesh

Diameter Design Inlet Outlet Mach

No Iterations

Time

Inlet Throat Exit Mach Pressure Pressure (min)

6km

Coarse

3.25 1 4.755 3.09 2000000 47217

3.19 2107 56.1866667

Medium 3.29 4608 122.88

Fine 3.32 7686 204.96

6km

Coarse

2.76 1 6.314 2.63 1000000 47181

2.77 1955 52.1333333

Medium 2.83 2405 64.1333333

Fine 2.85 3634 96.9066667

31

4. Off- Design

Bell nozzle combustion gases flow through a constriction (throat) and then the

expansion away from the centreline is contained by the diverging walls of the nozzle

up to the exit plane. Bells nozzles are a point design with optimum performance at one

specific ambient pressure (i.e., altitude).

When it’s operated at off design parameters that is at different altitudes the nozzle

exhibits Over Expanded and under expanded phenomenon.

4.1.1 Operation of a C-D Nozzle

32

Figure 14: Operation of a C-D Nozzle

• Figure (a) shows the flow through the nozzle when it is completely subsonic (i.e.

nozzle isn't choked). The flow accelerates out of the chamber through the

converging section, reaching its maximum (subsonic) speed at the throat. The

flow then decelerates through the diverging section and exhausts into the ambient

as a subsonic jet. Lowering the back pressure in this state increases the flow

speed everywhere in the nozzle.

• Further lowering pb results in figure (b). The flow pattern is exactly the same as

in subsonic flow, except that the flow speed at the throat has just reached Mach

1. Flow through the nozzle is now choked since further reductions in the back

pressure can't move the point of M=1 away from the throat. However, the flow

33

pattern in the diverging section does change as the back pressure is lowered

further.

• As pb is lowered below that needed to just choke the flow a region of supersonic

flow forms just downstream of the throat. Unlike a subsonic flow, the supersonic

flow accelerates as the area gets bigger. This region of supersonic acceleration

is terminated by a normal shock wave. The shock wave produces a near-

instantaneous deceleration of the flow to subsonic speed. This subsonic flow then

decelerates through the remainder of the diverging section and exhausts as a

subsonic jet. In this regime if the back pressure is lowered or raised the length of

supersonic flow in the diverging section before the shock wave increases or

decreases, respectively.

• If pb is lowered enough the supersonic region may be extended all the way down

the nozzle until the shock is sitting at the nozzle exit, figure (d). Because of the

very long region of acceleration (the entire nozzle length) the flow speed just

before the shock will be very large. However, after the shock the flow in the jet

will still be subsonic.

• Lowering the back pressure further causes the shock to bend out into the jet,

figure (e), and a complex pattern of shocks and reflections is set up in the jet

which will now involve a mixture of subsonic and supersonic flow, or (if the

back pressure is low enough) just supersonic flow. Because the shock is no

longer perpendicular to the flow near the nozzle walls, it deflects it inward as it

leaves the exit producing an initially contracting jet. We refer to this as over-

expanded flow because in this case the pressure at the nozzle exit is lower than

that in the ambient (the back pressure) i.e. the flow has been expanded by the

nozzle too much.

• A further lowering of the back pressure changes and weakens the wave pattern

in the jet. Eventually, the back pressure will be lowered enough so that it is now

equal to the pressure at the nozzle exit. In this case, the waves in the jet disappear

34

altogether, figure (f), and the jet will be uniformly supersonic. This situation,

since it is often desirable, is referred to as the 'design condition‘, Pe=Pa.

• Finally, if the back pressure is lowered even further we will create a new

imbalance between the exit and back pressures (exit pressure greater than back

pressure), figure (g). In this situation, called under-expanded, expansion waves

that produce gradual turning and acceleration in the jet form at the nozzle exit,

initially turning the flow at the jet edges outward in a plume and setting up a

different type of complex wave pattern.

4.1.2 Over Expansion

The rocket's nozzle is designed to be efficient at altitudes above sea level, and,

at engine start, the flow is over-expanded, that is, the exhaust gas pressure, pe, is

higher than the supersonic isentropic exit pressure but lower than the ambient

pressure, pa. This causes an oblique shock to form at the exit plane of the nozzle.

To reach ambient pressure, the gases undergo compression as they move away

from the nozzle exit and pass through the oblique shock wave standing at the exit

plane. The flow that has passed through the shock wave will be turned towards

the center line. At the same time, the oblique shock wave, directed toward the

center line of the nozzle, cannot penetrate the center plane since the center plane

acts like a streamline. This causes the oblique shock wave to be reflected

outward from the center plane. The gas flow goes through this reflected shock

and is further compressed but the flow is now turned parallel to the centerline.

This causes the pressure of the exhaust gases to increase above the ambient

pressure. The reflected shock wave (see diagram below) now hits the free jet

boundary called a contact discontinuity (or the boundary where the outer edge of

the gas flow meets the free stream air). Pressure is the same across this boundary

and so is the direction of the flow. Since the flow is at a higher pressure than

ambient pressure, the pressure must reduce. Thus, at the reflected shock wave-

contact discontinuity intersection, expansion waves of the Prandtl-Meyer (P-M)

type are set up to reduce the pressure to pa. These expansion waves are directed

35

towards the centerline of the nozzle. The gas flow passing through the Prandtl-

Meyer expansion waves turn away from the centerline. The Prandtl-Meyer

expansion waves in turn reflect from the center plane towards the contact

discontinuity. The gas flow passing through the reflected Prandtl-Meyer waves

is now turned back parallel to the centerline but undergoes a further reduction of

pressure. The reflected Prandtl-Meyer waves now meet the contact discontinuity

and reflect from the contact discontinuity towards the centerline as Prandtl-

Meyer compression waves. This allows the gas flow to pass through the Prandtl-

Meyer compression waves and increase its pressure to ambient pressure, but

passage through the compression waves turns the flow back towards the

centerline. The Prandtl-Meyer compression waves now reflect from the center

plane as compression waves further increasing the pressure above ambient, but

turning the flow parallel to the nozzle centerline. The flow process is now back

to when the flow had just passed through the reflected shock wave, i.e., the flow

pressure is above ambient and the flow is parallel to the centerline. This process

of expansion-compression wave formation begins again.

Figure 15: Over Expansion

36

4.1.3 Under Expansion

At very high altitudes where the ambient pressure is less than the exhaust

pressure of the gases, the flow is under expanded, the exhaust gases are exiting

the nozzle at pressures below the supersonic isentropic exit pressure which is

also the ambient pressure. To reach ambient pressure, the exhaust gases expand

via Prandtl-Meyer expansion waves. This expansion occurs by the gases turning

away from the centerline of the rocket engine. The Prandtl-Meyer expansion

waves in turn reflect from the center plane towards the contact discontinuity. The

gas flow passing through the reflected Prandtl-Meyer waves is now turned back

parallel to the centerline but undergoes a further reduction of pressure. The

reflected Prandtl-Meyer waves now meet the contact discontinuity and reflect

from the contact discontinuity towards the centerline as Prandtl-Meyer

compression waves. This allows the gas flow to pass through the Prandtl-Meyer

compression waves and increase its pressure to ambient pressure, but passage

through the compression waves turns the flow back towards the centerline. The

Prandtl-Meyer compression waves now reflect from the center plane as

compression waves further increasing the pressure above ambient, but turning

the flow parallel to the nozzle centerline. The flow process is now back to when

the flow had just passed through the reflected shock wave, i.e., the flow pressure

is above ambient and the flow is parallel to the centerline.

Figure 16: Under Expansion

37

4.1.4 Results

TABLE 6: Tabulation of Fluent Result M= 2.63

Fluent pictures refer appendix 2

TABLE 7: Tabulation of Fluent Result M= 3.09

Fluent Pictures refer appendix 2

Mach No Altitude(km) Pc (Pa) Po (pa) Iterations Time

2.63

Sea level 1000000 101325 17155 343

6 1000000 47181 27478 550

12 1000000 19399 10634 213

20 1000000 5529.3 9850 197

30 1000000 1185.5 10845 217

40 1000000 299.77 3641 73

Mach

No Altitude(km) Pc (Pa) Po (pa) Iterations Time

3.09

Sea level 2000000 101325 18561 371

6 2000000 47181 12366 247

12 2000000 19399 13388 268

20 2000000 5529.3 12134 243

30 2000000 1185.5 24921 498

40 2000000 299.77 4390 88

38

4.1.5 Thrust Calculations

The efflux of gases or the momentum flux out of the nozzle causes a force to act upon

the rocket structure. This is termed as thrust or thrust force. Since the gases exiting

the nozzle are supersonic, the pressure at the exit plane of the nozzle is quite different

from that which is prevalent outside. This difference in pressure causes a pressure

thrust to act on the nozzle. At lower altitudes, specifically at altitudes where the

ambient pressure is greater than the nozzle exit pressure, pressure thrust provides a

negative contribution to the overall thrust. Therefore the difference between nozzle

exit pressure and ambient pressure is an important factor in the operation of rocket

nozzles.

Thrust can be computed using the following relation:

𝑇 = �̇�𝑣𝑒 + (𝑃𝑒 − 𝑃𝑎)𝐴𝑒

During operation at design condition, the above equation reduces to:

𝑇 = �̇�𝑣𝑒

A factor called Thrust Coefficient is introduced here, it is defined as the thrust divided

by the chamber pressure.

The Thrust Coefficient gives a good measure of the amplification of thrust due to

supersonic expansion of exhaust gases through the nozzle. It has values ranging from

0.8 to 1.9 and is dependent on the chamber pressure and throat area. It is a useful

parameter by which the thrust off an Ideal rocket can be computed. It is given by

𝐶𝑓 =𝑣2

2𝐴𝑒

𝑝0𝐴𝑡𝑉2

Substituting for v2 and𝐴𝑒

𝐴𝑡, where v2 is the nozzle exit velocity:

𝐶𝑓 = √2𝛾2

γ−1(

2

γ+1)

(γ+1)

(γ−1)[1 − (

𝑝𝑒

𝑝0)

γ−1

γ]

39

Appending the pressure thrust component𝑃𝑒−𝑃𝑎

𝑃𝑡

𝐴

𝐴𝑡

We obtain: 𝐶𝑓 = √2𝛾2

γ−1(

2

γ+1)

(γ+1)

(γ−1)[1 − (

𝑝𝑒

𝑝0)

γ−1

γ] −

𝑃𝑒−𝑃𝑎

𝑃𝑡

𝐴

𝐴𝑡

The force coefficient in conjunction with the chamber pressure P0 and throat area At can

be used to determine the ideal thrust of the nozzle by:

T=CfAtP0

The thrust coefficient is a convenient factor to assess the performance of rocket nozzles.

From the above relations, it is clear that the thrust coefficient is proportional to the

chamber pressure however it also depends on the throat area. The Thrust Coefficient

therefore can be thought of as representing the amplification of thrust due to the

geometry of the throat. When the ambient pressure becomes sufficiently low (e.g.

Vacuum Conditions) the Thrust coefficient reaches an asymptotic maximum. An

assessment of a rocket nozzles based on the theory of thrust coefficient is presented

below.

The solution is run for nozzles and compared with the design parameters. Variation of

flow properties are depicted in the data plots generated during post processing. The

velocity at nozzle outlet is extracted for all the nozzles and is used in the following

relations to determine the corresponding thrust.

40

Thrust Calculated for M= 3.09 at design and off-design conditions

TABLE 8: Theoretical Thrust Calculation M=3.09

TABLE 9: Fluent Thrust Validation M=3.09

Mach

No Altitude(km) Po (pa)

Pe

(pa) A* (m2) A/A* Ae (m2) m(Kg/s) Ve(m/s) Cf

Ideal

Thrust(N) Thrust(N)

3.09

Sea level 101325 47181 0.000314

4.613246

0.00274 1.463 629.35 1.34 844.24 772.717

6 47181 47181 0.000314 0.00274 1.463 629.35 1.46 922.72 921.179

12 19399 47181 0.000314 0.00274 1.463 629.35 1.53 962.99 997.358

20 5529.3 47181 0.000314 0.00274 1.463 629.35 1.56 983.10 1035.38

30 1185.5 47181 0.000314 0.00274 1.463 629.35 1.57 989.38 1047.3

40 299.77 47181 0.000314 0.00274 1.463 629.35 1.57 990.70 1049.72

Ve (m/s) Pe (pa) Po (pa) m(Kg/s) Ae Thrust (N)

634 41338.09 101325 1.435382 0.00159 814.6532

634 40235.148 47181 1.434949 0.00159 898.7134

634 40462.395 19399 1.435362 0.00159 943.5105

634 47181 5529.3 1.463709 0.00159 994.2177

634 40038.867 1185.5 1.435064 0.00159 971.6076

634 39839.637 299.77 1.43561 0.00159 973.0454

41

Thrust Calculated for M= 2.63 at design and off-design conditions

TABLE 10: Theoretical Thrust Calculation M=2.63

TABLE 11: Fluent Thrust Validation M=2.63

Mach

No Altitude(km) Po (pa)

Pe

(pa) A* (m2) A/A*

Ae

(m2) m(Kg/s) Ve(m/s) Cf

Ideal

Thrust(N) Thrust(N)

2.63

Sea level 101325 47181 0.000314

2.979068

0.0009 0.7318 592.30 1.220 383.36 382.912

6 47181 47181 0.000314 0.0009 0.7318 592.30 1.382 434.01

433.483

12 19399 47181 0.000314 0.0009 0.7318 592.30 1.464 459.97

459.431

20 5529.3 47181 0.000314 0.0009 0.7318 592.30 1.506 472.97 472.386

30 1185.5 47181 0.000314 0.0009 0.7318 592.30 1.519 477.02 476.443

40 299.77 47181 0.000314 0.0009 0.7318 592.30 1.521 477.84

477.270

Ve (m/s) Pe (pa) Po (pa) m(Kg/s) Ae(m2) Thrust(N)

600.0652 40485.57 101325 0.725503 0.001041 372.0398

600.0784 40475.13 47181 0.725503 0.001041 428.3807

600.0784 40469 19399 0.725503 0.001041 457.2843

600.07 40431.2 5529.3 0.725503 0.001041 471.6717

600.0864 40471.22 1185.5 0.725503 0.001041 476.2454

600.0928 40466.77 299.77 0.725503 0.001041 477.1672

42

5. DESIGN AND FABRICATION OF CONVERGENT DIVERGENT

NOZZLE

The design of the CAD model of the nozzle is done using the SOLID WORKS and its

fabricated using the CNC machine.

5.1.1 Solid Works

SOLIDWORKS is a solid modeller, and utilizes a parametric feature-based approach to

create models and assemblies. Parameters refer to constraints whose values determine

the shape or geometry of the model or assembly. Parameters can be either numeric

parameters, such as line lengths or circle diameters, or geometric parameters, such as

tangent, parallel, concentric, horizontal or vertical, etc. Numeric parameters can be

associated with each other through the use of relations, which allows them to capture

design intent.

5.1.2 Design of a CAD model

Computer-aided design (CAD) is the use of computer systems to assist in the creation,

modification, analysis, or optimization of a design. CAD software for mechanical

design uses either vector-based graphics to depict the objects of traditional drafting, or

may also produce raster showing the overall appearance of designed objects. However,

it involves more than just shapes. As in the manual drafting of technical and engineering

drawings, the output of CAD must convey information, such as materials,

processes, dimensions, and tolerances, according to application-specific conventions.

Design of a Nozzle-CAD model

Design is done using various comments available in solid works. Few of the comments

used are

Curve through XYZ points

Revolve Boss/ Base

43

Extruded Boss/ Base

Sketch

Dimensions

Sketch

The sketch is the basis for a 3D model. We can create a sketch on any of the default

planes (Front Plane, Top Plane, and Right Plane), or a created plane. We can start by

selecting:

Sketch entity tools (line, circle, and so on)

Sketch tool

Planes

Revolve Boss/ Base

Revolves add or remove material by revolving one or more profiles around a centreline.

You can create revolved boss/bases, revolved cuts, or revolved surfaces. The revolve

feature can be a solid, a thin feature, or a surface.

Extruded Boss/ Base

The Extrude Property Manager defines the characteristics of extruded features. You can

create

Thin / Solid

Bose / Base

Cut

Surface

Curve through XYZ points

Create new sets of coordinates by double-clicking cells in the X, Y, and Z columns and

entering a point coordinate in each one. (Created outside of a sketch, the X, Y, and Z

coordinates are interpreted with respect to the Front plane coordinate system.)

44

Steps Followed

Solid works is started

A new part drawing is selected

Points are imported using the option curve through XYZ

The curve is revolved

The part is made according to the requirement of the experimental setup

45

5.1.3 CAD Model

Figure 17: 3D solid Model (Nozzle) Figure 18: 2D model

(Nozzle)

All Dimensions are in mm

Figure 19: Fabricated Nozzle

46

6. EXPERIMENTAL SETUP

6.1.1 THE OPEN JET TEST FACILITY

The open jet test facility allows experimentation of the scaled down models at high

velocity. It can be used to study the flow phenomenon that is the formation of shocks

and boundary layer at the Nozzle exit.

It is used to validate the Nozzle’s design exit Mach no, Pressure at the throat etc. using

the pressure scanners.

The different parts of open jet test facility are

Compressor- Reciprocating air compressor

Air Dryer

Pressure Reservoir

Piping

Settling Chamber

Nozzle

Compressor- Reciprocating Air Compressor

An air compressor is a device that converts power (usually from an electric motor, a

diesel engine or a gasoline engine) into kinetic energy by compressing and

pressurizing air, which, on command, can be released in quick bursts. There are two

types of reciprocating air compressors

Positive-displacement

Negative-displacement

The Compressor used in the setup is a Positive-displacement air compressors, work by

forcing air into a chamber whose volume is decreased to compress the air. Piston-type

air compressors use this principle by pumping air into an air chamber through the use

of the constant motion of pistons. They use one-way valves to guide air into a

chamber, where the air is compressed.

This Air compressor is also incorporated with an air cooler.

47

Specifications:

1. High Pressure 2 Stage

2. Air cooled, Splash lubricated

3. Displacement – 92.18 m3/h

4. Free air delivery – 67.92 m3/h

5. Working pressure – 30 kgf/cm2 or 29.42 bar

6. Compressor speed – 1150 rpm

7. Outlet air Temperature – 15 oC above ambient

Air dryer

A compressed air dryer is a device for removing water vapour from compressed air.

The process of air compression concentrates atmospheric contaminants, including

water vapour. This raises the dew point of the compressed air relative to free

atmospheric air and leads to condensation within pipes as the compressed air cools

downstream of the compressor.

Excessive water in compressed air, in either the liquid or vapour phase, can cause a

variety of operational problems for users of compressed air. These include freezing of

outdoor air lines, corrosion in piping and equipment.

The principle is of operation is the removal of moisture by cooling air to a certain

present temperature.

The air entering the system enters into the pre-cooler. A pre-cooler is a heat exchanger

where the incoming air is being cooled by the outgoing cold air so as to reduce the

heat load for the evaporator and thereby the refrigeration system. The air from the pre-

cooler enters into the evaporator. In evaporator the cooling, heat removal is done by

the boiling refrigerant. The air with condensate, enters into moisture separator, where

the moisture is removed by centrifugal action of air. The air free from moisture enters

pre-cooler to cool the incoming air and thereby some heat is added.

48

Specifications:

1. Desiccant type

2. Inlet condition:

Flow rate – 127.42 m3/h

Pressure – 6.86 to 12.3 bar

Temperature – 42 0C

3. Outlet Condition:

Flow rate – 114.68 m3/h

Pressure – 6.67 to 12.1 bar

Temperature – 40 0C

4. Pressure drop through dryer – 0.2 bar

Pressure Vessel

A Pressure vessel is a closed container designed to hold gases or liquids at a pressure

substantially different from the ambient pressure.

The pressure vessel is used to store compressed dry air for various operations to be

executed in the supersonic wind tunnel, the open jet facility and in the high altitude

test facility. Pressure vessels are used in a variety of applications in both industry and

the private sector. They appear in these sectors as industrial compressed air receivers

and domestic hot water storage tanks. Other examples of pressure vessels are diving

cylinders, recompression chambers, distillation towers, pressure reactors, autoclaves,

and many other vessels in mining operations, oil refineries and petrochemical plants.

Pressure vessels can theoretically be almost any shape, but shapes made of sections of

spheres, cylinders, and cones are usually employed. A common design is a cylinder

with end caps called heads. Head shapes are frequently either hemispherical or dished

(tori spherical). More complicated shapes have historically been much harder to

analyse for safe operation and are usually far more difficult to construct.

49

Specifications:

1. Length – 8 m

2. Diameter – 1m

3. Volume – 6.28 m3

4. Max. safe operating pressure – 20 bar

Piping

Piping system is a network of pipes used to transfer gases from one location to another

location. It is an effective method of transferring fluids without considerable losses.

Settling Chamber

The "settling chamber" or "stilling section" is the largest cross section, and contains a

honeycomb. A honeycomb with its cells aligned in the flow direction will reduce

mean or fluctuating variations in transverse velocity (flow direction), with little effect

on stream wise velocity because the pressure drop through a honeycomb is small.

6.1.2 Schlieren System

Figure 20: Schileren reference NASA

50

Schlieren flow visualization is based on the deflection of light by a refractive

index gradient. The index gradient is directly related to flow density gradient. The

deflected light is compared to un-deflected light at a viewing screen. The undisturbed

light is partially blocked by a knife edge. The light that is deflected toward or away

from the knife edge produces a shadow pattern depending upon whether it was

previously blocked or unblocked. This shadow pattern is a light-intensity

representation of the expansions (low density regions) and compressions (high density

regions) which characterize the flow.

Schlieren photography is a visual process that is used to photograph the flow of fluids

of varying density.

The basic optical schlieren system uses light from a single collimated source shining

on, or from behind, a target object. Variations in refractive index caused by density

gradients in the fluid distort the collimated light beam. This distortion creates a spatial

variation in the intensity of the light, which can be visualised directly with

a shadowgraph system.

In schlieren photography, the collimated light is focused with a lens, and a knife-edge

is placed at the focal point, positioned to block about half the light. In flow of uniform

density this will simply make the photograph half as bright. However in flow with

density variations the distorted beam focuses imperfectly, and parts which have been

focused in an area covered by the knife-edge are blocked. The result is a set of lighter

and darker patches corresponding to positive and negative fluid density gradients in

the direction normal to the knife-edge. When a knife-edge is used, the system is

generally referred to as a schlieren system.

51

Figure 21: Schileren System Used

6.1.3 Pressure Scanners

Figure 22: Pressure Scanners

52

Pressure scanners are used to measure the differential pressure at various pressure

ports of the nozzle. There are two modes of operation through which the scanners

work.

Wind Off Mode

Wind On Mode

Before the valves are open for the flow to pass through the nozzle the wind off mode

is selected and the logging is started so that the scanner measure the atmospheric

pressure available at the ports.

Once the flow is started wind on mode is selected and the data is logged in.

The scanners give the differential readings between the wind off and wind on mode in

PSI.

Specification

16 port pressure scanner

Port 1 = 150 PSI

Port 2-4 = 100 PSI

Port 5-6 = 30 PSI

Port 7-16 = 15 PSI

53

7. Results

7.1.1 Validation of Fluent and Schileren Imaging

Inlet Pressure: 10 bar Outlet Pressure: 101325

Figure 23: Fluent Simulation of the fabricated nozzle at sea level

Figure 24: Schileren Imaging of the fabricated nozzle

54

The fluent results shows the Under Expanded flow when run at sea level as the

back pressure is higher than the exit pressure of the nozzle.

Similar flow pattern is seen at the exit of the nozzle when the nozzle is run a 10 bar

inlet pressure and the flow at the exit is captured from the schlieren imaging.

This shows that nozzle is under expanded when back pressure is higher than the

exit pressure.

7.1.2 Experimental Pressure Thrust

Ambient Pressure = 13.8656 psi Ambient Pressure = .956 bar

TABLE 12: Differential Pressure Recoded by Pressure Scanners

Differential pressure

Time chamber throat exit ambient

00:01 18.188 -1.181 -1.055 -0.058

00:02 21.319 0.118 -1.114 0

00:03 24.33 1.358 -1.231 -0.116

00:04 27.104 2.539 -1.173 -0.058

00:05 29.997 3.779 -1.231 -0.058

00:06 32.256 4.605 -1.29 -0.058

00:07 34.396 5.609 -1.348 0

00:08 36.417 6.554 -1.407 -0.058

00:09 38.557 7.499 -1.466 -0.058

00:10 40.538 8.267 -1.524 -0.058

00:11 43.034 9.329 -1.583 -0.116

00:12 45.848 10.747 -1.818 -0.058

00:13 48.582 12.223 -1.818 -0.058

00:14 30.592 13.64 -1.7 0

55

TABLE 13: Pressure Recoded (PSI)

TABLE 14: Recorded Pressure (Bar)

Pressure (bar)

Time chamber throat exit ambient

00:01 2.209632 0.874573 0.88326 0.952001

00:02 2.425507 0.964136 0.879192 0.956

00:03 2.633108 1.049631 0.871125 0.948002

00:04 2.824369 1.131058 0.875124 0.952001

00:05 3.023834 1.216553 0.871125 0.952001

00:06 3.179587 1.273503 0.867057 0.952001

00:07 3.327135 1.342727 0.863058 0.956

00:08 3.466478 1.407882 0.85899 0.952001

00:09 3.614026 1.473038 0.854923 0.952001

00:10 3.750611 1.525989 0.850924 0.952001

00:11 3.922704 1.599212 0.846856 0.948002

00:12 4.116723 1.696979 0.830653 0.952001

00:13 4.305225 1.798746 0.830653 0.952001

00:14 3.064858 1.896445 0.838789 0.956

Pressure (psi)

Time chamber throat exit ambient

00:01 32.048 12.6846 12.8106 13.8076

00:02 35.179 13.9836 12.7516 13.8656

00:03 38.19 15.2236 12.6346 13.7496

00:04 40.964 16.4046 12.6926 13.8076

00:05 43.857 17.6446 12.6346 13.8076

00:06 46.116 18.4706 12.5756 13.8076

00:07 48.256 19.4746 12.5176 13.8656

00:08 50.277 20.4196 12.4586 13.8076

00:09 52.417 21.3646 12.3996 13.8076

00:10 54.398 22.1326 12.3416 13.8076

00:11 56.894 23.1946 12.2826 13.7496

00:12 59.708 24.6126 12.0476 13.8076

00:13 62.442 26.0886 12.0476 13.8076

00:14 44.452 27.5056 12.1656 13.8656

56

The results obtained were not been useful in validation of the thrust and the design

exit Mach as there were instrumentation error with the pressure scanners as it failed to

record pressure more than 4bar as well as there were inconsistency in the results being

recorded.

The instrumentation error was cross verified by connecting a T joint near the valves

and checking the values of pressure using a digital pressure transducer and a pressure

scanner.

The digital pressure transducer showed a reading of 10 bar while the pressure scanners

failed to do so.

57

8. CONCLUSION

The contoured bell nozzle is designed for Exit Mach no 2.63, 3.09 using standard

NASA MOC code and it’s validated using computational dynamics tool Fluent.

Its design and off design performance that is the over and under expanded conditions

at different altitudes are studied using computational Fluid dynamics tool Fluent.

Further the nozzle is fabricated using CNC. The fabricated nozzle is tested in open jet

facility and the flow pattern is studied and validated using schileren system

58

REFERENCES

• H. C. Man et.al, Design and Characteristic Analysis of Supersonic Nozzles for

High Gas Pressure Laser Cutting, Journal of Materials Processing Technology,

Hong Kong, 63 (1997) 217-222

• Radhakrishnan.E, Gas Dynamics, PHI Learning,4th Edition(2002),New Delhi

• Young.R, Automated Nozzle Design through Axis-Symmetric Method of

Characteristics Coupled with Chemical Kinetics, Auburn

University(2012),Auburn, Alabama

• Turner.M,Rocket & Spacecraft Propulsion,Second Edition,Springer

Publishing,UK,2001

• Sutton.G, Biblarz.O, Rocket Propulsion Elements, 7th Edition, John Wiley &

Sons, p64, 2001,New York, Singapore, Toronto

• Anderson.J.D, Fundamentals of Aerodynamics,3rd Edition, McGraw

Hill(2001),Boston, New York

• McCabe.A,Design of a Supersonic Nozzle, Aeronautical Research Council

Reports & Memoranda Ministry of Aviation,p2,London,1967

• Crown.J.C, Heybey.H.W, Supersonic Nozzle Design, U.S.Naval Ordinance

Laboratory, Maryland,1950

• Foelsch, Kuno. A New Method of Designing Two-Dimensional Laval Nozzles for

a Parallel and Uniform Jet. North American Aviation Report No. NA-46-235

(Mar. 1946).

• Vanco.M, Goldman.L, Computer Program for Design of Two Dimensional

Supersonic Nozzle with Sharp Edged Throat, NASA Technical Memorandum,TM

X-1502,Washington,1968