COMPUTATIONAL ANALYSIS OF FLUID FLOW THROUGH ROTATING VANELESS DIFFUSER
report
1. 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. 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. 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.
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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 + 1
𝑀2
}
𝛾+1
2(𝛾−1)
5. 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. 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
2
𝑀2
𝑃𝑜
𝑃
= {1 +
𝛾 − 1
2
𝑀2
}
𝛾
𝛾−1
𝜌0
𝜌
= {1 +
𝛾 − 1
2
𝑀2
}
1
(𝛾−1)
7. 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
}
𝛾
𝛾−1
= 0.528
𝜌∗
𝜌
= {
2
𝛾 + 1
}
1
𝛾−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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.
19. 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.
21. 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. 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. 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. 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. 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. 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
Pressure
Altitude
Altitude Vs pressure
27. 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
Temperature
Altitude
Altitude vs Temperature
28. 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
30. 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. 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. 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. 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. 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. 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. 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. 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. 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 = 𝑚̇ 𝑣𝑒 + ( 𝑃𝑒 − 𝑃𝑎) 𝐴 𝑒
During operation at design condition, the above equation reduces to:
𝑇 = 𝑚̇ 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
2
𝐴 𝑒
𝑝0 𝐴𝑡 𝑉2
Substituting for v2 and
𝐴 𝑒
𝐴 𝑡
, where v2 is the nozzle exit velocity:
𝐶𝑓 = √2𝛾2
γ−1
(
2
γ+1
)
(γ+1)
(γ−1)
[1 − (
𝑝 𝑒
𝑝0
)
γ−1
γ
]
39. 39
Appending the pressure thrust component
𝑃𝑒−𝑃 𝑎
𝑃 𝑡
𝐴
𝐴 𝑡
We obtain: 𝐶𝑓 = √2𝛾2
γ−1
(
2
γ+1
)
(γ+1)
(γ−1)
[1 − (
𝑝 𝑒
𝑝0
)
γ−1
γ
] −
𝑃𝑒−𝑃 𝑎
𝑃 𝑡
𝐴
𝐴 𝑡
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.
42. 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. 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. 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. 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. 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. 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 o
C 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. 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. 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. 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.
52. 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. 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. 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
56. 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. 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. 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
