9. 3 33
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810. 24
CHAPTER 2
PROJECT METHODLOGY
The following methodology is adopted for carrying out the proposed area of work.
Literature Review Analysis
Project Concept Note
Solver Simulation
Results and Discussion
Thesis completion
Model Selection
Preprocessor
811. 25
CHAPTER 3
LITERATURE REVIEW
A detailed literature analysis was done on many international journals on
rocket nozzles, gas expansion states, bell nozzle and flow separation. The inferences
from those journals are presented in the following sections.
3.1 Gerald Hagemann, Hans Immich, Thong Van Nguyen,
Gennady E. Dumnov (1998), “Advanced Rocket Nozzles”, Journal
of Propulsion and Power, Vol.14, No.5 (September – October 1998)
INFERENCE:
This paper is concerned with the performance analysis of conventional
nozzles, altitude compensating nozzles.
It is found that the in the conventional nozzles, flow separation at low
altitudes due to high back pressure.
It was also found that by using bell contoured nozzle, a wider range of
altitude compensation can be achieved.
3.2 Z. F. Nasuti, M. Onofri, “Flow Structures and Separation in
Overexpanded Rocket Nozzles”, European Conference for
Aerospace Sciences (EUCASS)
INFERENCE:
The paper analyzes the basic flow structures that may take place inside the
nozzle divergent section during the startup and the low altitude flight, when
nozzles operate in overexpanded regime.
812. 26
The possible generation of the inviscid separation phenomenon, and its role
on the occurrence of the free- and restricted-shock separation regimes are
discussed.
This paper provides to provide indications on the possible generation of a
recirculating flow region behind it that may yield side loads on the nozzle
wall.
3.3 Ralf H. Stark, “Flow Separation in Rocket Nozzles, a Simple
Criteria”, American Institute of Aeronautics and Astronautics
INFERENCE:
Cold and hot flow tests were conducted to investigate the flow separation in
rocket nozzles.
Flow separation is a result of adaptation on ambient conditions. This
adaptation can be divided in two regions (the oblique shock recompresses the
wall pressure to plateau pressure, followed by a system of recompression
waves in the separated backflow region where plateau pressure is adapted to
ambient condition.
3.4 Taro Shimizu, Masatoshi Kodera, Nobuyuki Tsuboi “Internal
and External Flow of Rocket Nozzle”, Journal of the Earth
Simulator, Volume 9, March 2008
INFERENCE:
The transition of the flow structure between free shock separation and
restricted shock separation inside a nozzle, which would sometimes generate
a destructive side-load is studied.
813. 27
The overpressure, which originates in shock wave, imposes high pressure
load on the nozzle or rocket surface and also influences the ignition process,
especially under clustering (more than one) nozzle configurations.
3.5 Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha
Rao “Flow Analysis of Rocket Nozzle Using Computational Fluid
Dynamics (CFD)”, International Journal of Engineering Research
and Applications (IJERA), Vol. 2, Issue 5, September- October
2012, pp.1226-1235
INFERENCE:
Study is carried using software like Gambit 2.4 for designing of the nozzle
and Fluent 6.3.2 for analyzing the flows in the nozzle.
Numerical study has been conducted to understand the air flows in a conical
nozzle at different divergence degrees of angle using two-dimensional
axisymmetric models, which solves the governing equations by a control
volume method.
814. 28
CHAPTER 4
PROJECT CONCEPT NOTE
From the literature review, it is found that theoretical analysis of compressible flow
in rocket nozzle application is complicated and cumbersome. Hence CFD is used to
perform simulation on this type of flow. Earlier CFD simulation has been performed
only on cone nozzles. Therefore it is proposed to design and mesh a rocket nozzle in
three different configurations and to simulate them using ANSYS-FLUENT at four
different altitudes under the same operating conditions. Using the obtained results,
the velocity and total pressure contours will be studied and their specific impulses
will be compared. The ambient pressure or atmospheric pressure will be varied to
simulate the rocket nozzle operating at different altitudes. This will allows us to
study the exhaust gas contours. The different altitudes at which the analysis will be
performed is tabulated below.
Table 4.1: Working Parameters
S. No Altitudes
Ambient Pressure
(in bar)
1. Sea Level 1.01325
2. 5000m 0.540
3. 10000m 0.264
4. 20000m 0.055
874. 32
CHAPTER 6
PREPROCESSOR
Preprocessor module consists of designing, meshing and material selection. The
details of the three different nozzle configurations including their geometric and
mesh attributes are specified below.
6.1 Ideal Nozzle
6.1.1 Geometry Creation
The Ideal rocket nozzle takes the shape of the frustum of a cone with a half angle of
15. For matter of convenience, an Area Ratio of 25 is taken as the design parameter
for the nozzle. Such an area ratio ensures that at lower altitudes, the nozzle behaves
over-expanded while at higher altitudes, the nozzle behaves under-expanded. Also a
reservoir is modeled adjoining the outlet which allows the nozzle to exhaust into it.
This simulates the nozzle exhausting into the atmosphere which lets us study the
exhaust jet and the gas flow expansion.
The dimensions of the setup is given below
Throat Diameter – 12.5 cm
Exit Diameter – 63.5 cm
Thrust Chamber Diameter – 25 cm
Length of Nozzle – 116.625 cm
Length of Convergent Section – 23.325 cm
Length of Divergent Section – 93.3 cm
Exit Area Ratio – 25
Convergent Area Ratio – 4
Exit Area – 3067.96 cm2
Throat Area – 122.72 cm2
Inlet Area – 490.87 cm2
875. 33
Width of Reservoir – 92.5 cm
Length of Reservoir – 75 cm
Figure 6.1.1.1: Geometry of Ideal Nozzle
6.1.2 Mesh Attributes
Figure 6.1.2.1: Mesh of Ideal Nozzle
Minimum Size: 1.06e-003m
Maximum Face Size: 0.106066m
Maximum Size: 0.21222m
Minimum Edge Length: 4.84e-002m
876. 34
Element Size: 1e-002m
Nodes: 11319
Elements: 11053
6.2 85% Bell Nozzle
6.2.1 Geometry Creation
A Bell Nozzle has a parabolic contour of the divergent section of the nozzle. This
shortens the length of the nozzle whereas providing the same area ratio. An 85%
Bell Nozzle means that the length of the nozzle is 85% of the length of a similar
ideal nozzle having same throat and exit diameters. This is done to reduce the
weight of the nozzle. A longer reservoir is modeled to accurately study the exhaust
gas flow.
The dimensions of the bell nozzle are the same as that of the ideal nozzle except for
the ones given below:
Length of Divergent Section – 79.305 cm
Length of Nozzle – 102.63 cm
Length of Reservoir – 150 cm
Figure 6.2.1.1: Geometry of 85% Bell Nozzle
877. 35
6.2.2 Mesh Attributes
Figure 6.2.2.1: Mesh of the 85% Bell Nozzle
Minimum Size: 3.9275e-004m
Maximum Face Size: 2.5e-002m
Maximum Size: 5e-002m
Minimum Edge Length: 6.3679e-002m
Nodes: 3017
Elements: 2884
6.3 70% Bell Nozzle
6.3.1 Geometry Creation
A Bell Nozzle has a parabolic contour of the divergent section of the nozzle. This
shortens the length of the nozzle whereas providing the same area ratio. A 70% Bell
Nozzle means that the length of the nozzle is 70% of the length of a similar ideal
nozzle having same throat and exit diameters. This is done to reduce the weight of
the nozzle. A longer reservoir is modeled to accurately study the exhaust gas flow.
878. 36
The dimensions of the bell nozzle are the same as that of the ideal nozzle except for
the ones given below:
Length of Divergent Section – 66.31 cm
Length of Nozzle – 88.635 cm
Length of Reservoir – 150 cm
Figure 6.3.1.1: Geometry of 70% Bell Nozzle
6.3.2 Mesh Attributes
Figure 6.3.2.1: Mesh of 70% Bell Nozzle
879. 37
Minimum Size: 3.9275e-004m
Maximum Face Size: 2.5e-002m
Maximum Size: 5e-002m
Minimum Edge Length: 7.0913e-002m
Nodes: 2931
Elements: 2803
6.4 Material Selection
All the nozzle configurations are run with the same material attributes. The various
parameters are given below:
Fluid – Air
Nozzle Material – Titanium
The reason air is used as the working fluid is because it is a universally accepted
working fluid for cold flow analysis.
Titanium is used as nozzle inner surface material to reduce roughness and hence
friction loss.
880. 38
CHAPTER 7
SOLVER
The analysis simulating software used is ANSYS Fluent version 13.0.0.0.
7.1 Dimensions
Two dimensional analysis is performed as compressible flow through a nozzle is
similar across any plane perpendicular to the gas flow. By performing 2-D analysis,
number of elements are reduced, thereby reducing computational time as well
design complexity.
7.2 Solver
Pressure-based solver is utilized in this simulation over density-based as there are
sharp pressure gradients which do not reflect in the density and this can cause
divergence in the residuals.
7.3 Time
Steady-state analysis is performed in the simulation as the rocket nozzle undergoes
transient analysis only in a very limited portion of its operating cycle (engine start-
stop). Therefore a steady-state analysis is less time-consuming to perform and less
complex in its simulation.
881. 39
7.4 Turbulence Model
The viscous model used is the Spalart-Allmaras model. Its governing equations
have already been described in the previous chapter. Also the energy equation is
switched on as there are different temperatures across the flow.
7.5 Operating Conditions
Operating Conditions is given as 0 bar. By giving this value, any value entered in
the pressure fields, is the absolute pressure and not gauge pressure. If gauge
pressure is given then divergence is caused in the pressure solver.
7.6 Boundary Conditions
There are two boundary conditions used in the simulation.
7.6.1 Pressure Inlet
Pressure inlet boundary conditions are used to define the fluid pressure at flow
inlets, along with all other scalar properties of the flow. They are suitable for both
incompressible and compressible flow calculations. Pressure inlet boundary
conditions can be used when the inlet pressure is known but the flow rate and/or
velocity is not known. This situation may arise in many practical situations,
including buoyancy-driven flows. Pressure inlet boundary conditions can also be
used to define a “free” boundary in an external or unconfined flow. The pressure
inlet is used to simulate the combustion chamber
Chamber Pressure – 100 psia (or) 7.09275 bar
Temperature – 500 C
882. 40
7.6.2 Pressure Far-Field
Pressure far-field conditions are used in ANSYS FLUENT to model a free-stream
condition at infinity, with free-stream Mach number and static conditions being
specified. The pressure far-field boundary condition is often called a characteristic
boundary condition, since it uses characteristic information (Riemann invariants) to
determine the flow variables at the boundaries. The reservoir walls are simulated
under Pressure Far-Field condition. This allows it to behave as the atmosphere into
which the rocket nozzle is exhausting.
7.7 Solution Methods
Pressure-based Coupled Algorithm is used as the solution method. This pressure-
based coupled algorithm offers an alternative to the density-based and pressure-
based segregated algorithm with SIMPLE-type pressure-velocity coupling. The
coupled algorithm solves the momentum and pressure-based continuity equations
together. The full implicit coupling is achieved through an implicit discretization of
pressure gradient terms in the momentum equations, and an implicit discretization
of the face mass flux, including the Rhie-Chow pressure dissipation terms.
7.8 Solution Controls
Under solution controls, the under-relaxation factors for Pressure, Momentum,
Density and Energy are changed to 0.5 as there are high gradients which will lead to
divergence in the solver if the under-relaxation factors are not reduced.
The solution is initialized with values computed from the inlet.
883. 41
CHAPTER 8
SIMULATION RESULTS
The rocket nozzle configurations have been simulated at various altitudes and the
results are documented.
8.1 At Sea Level
8.1.1 Ideal Nozzle
Figure 8.1.1.1: Residual Graph of Ideal Nozzle operating at Sea Level
Figure 8.1.1.2: Velocity Contour of Ideal Nozzle operating at Sea Level
884. 42
Typically we can see that the nozzle is overexpanded and that flow separation
occurs near to the exit plane. This shows that the nozzle is not working at its
optimum design condition.
Figure 8.1.1.3: Total Pressure Contour of Ideal Nozzle operating at Sea Level
From the total pressure contour we see that the exhaust gas has been allowed to
expand gradually without much loss in stagnation pressure (except at the walls
which is due to viscous flow). However we see a high drop in total pressure outside
the nozzle. This is characteristic of a shock wave occurring.
8.1.2 85% Bell Nozzle
Figure 8.1.2.1: Residual Graph of 85% Bell Nozzle operating at Sea Level
885. 43
Figure 8.1.2.2: Velocity Contour of 85% Bell Nozzle operating at Sea Level
In the case of the bell nozzle operating at sea level, we see similar velocity results to
the ideal nozzle.
Figure 8.1.2.3: Total Pressure Contour of 85% Bell Nozzle operating at Sea Level
But the total pressure contours show a massive loss in stagnation pressure as the gas
moves downstream of the throat. This is due to the irregular shape in which the gas
has been expanded. The parabolic contour causes the total pressure to drop
significantly.
886. 44
Figure 8.1.2.4: Velocity Streamline of 85% Bell Nozzle operating at Sea Level
The Velocity streamline shows a detached shockwave being formed which turns the
gas flow irregularly.
8.1.3 70% Bell Nozzle
Figure 8.1.3.1: Residual Graph of 70% Bell Nozzle operating at Sea Level
We see from the velocity contour that the velocity has decreased significantly due to
the sudden very high expansion of gases in a very short distance. This leads to
reduced thrust and irregular flow direction.
887. 45
Figure 8.1.3.2: Velocity Contour of 70% Bell Nozzle operating at Sea Level
Figure 8.1.3.3: Total Pressure Contour of 70% Bell Nozzle operating at Sea Level
The total pressure has reduced drastically which tells us that there are huge loses
that are taking place in a 70% contoured nozzle.
888. 46
8.2 At 5000m
8.2.1 Ideal Nozzle
Figure 8.2.1.1: Residual Graph of Ideal Nozzle operating at 5000m
Figure 8.2.1.2: Velocity Contour of Ideal Nozzle operating at 5000m
Operating at 5000m, we see that the ideal nozzle is still overexpanded but not as
much as it was when operated at Sea Level. The flow is said to have ‘progressed’
further downstream from the throat of the nozzle and almost to the edge of the
889. 47
nozzle exit plane. Most nozzles are built in such a way that they start working at this
condition only as it is not very dangerous to the nozzle. This is because flow
separation does not occur and hence the gas does not alter its direction of flow
inside the nozzle.
Figure 8.2.1.3: Total Pressure Contour of Ideal Nozzle operating at 5000m
Total pressure does not reduce at the center of the flow even as the exhaust gas
extends away from the nozzle. This shows that the energy loss is much lower and
the shock formation has reduced which on the whole increases thrust.
8.2.2 85% Bell Nozzle
Figure 8.2.2.1: Residual Graph of 85% Bell Nozzle operating at 5000m
890. 48
Figure 8.2.2.2: Velocity Contour of 85% Bell Nozzle operating at 5000m
From the above figure we see that the nozzle is working at or around the optimum
design condition. At the same operating condition and geometric dimensions for the
cone and bell nozzle, we see that the nozzle exit plane pressure is equal to the
ambient pressure for the bell nozzle at a lower altitude than that of the cone nozzle.
This shows that there is a larger pressure drop in the contoured nozzle as compared
to the cone nozzle.
Figure 8.2.2.3: Total Pressure Contour of 85% Bell Nozzle operating at 5000m
As consistent with the contours at Sea Level, after the throat region there is a
significant drop in total pressure, which shows that the contoured nozzle is not very
thermally efficient in the expansion of gases.
891. 49
8.2.3 70% Bell Nozzle
Figure 8.2.3.1: Residual Graph of 70% Bell Nozzle operating at 5000m
Figure 8.2.3.2: Velocity Contour of 70% Bell Nozzle operating at 5000m
Due to the sudden expansion in the divergent section, the velocity very rapidly
decreases downstream of the nozzle and causes combustion instabilities. This
phenomenon is caused by gross overexpansion of the nozzle which makes the
exhaust jet to impinge on the internal surface of the nozzle and produces off-axis
thrust.
892. 50
Figure 8.2.3.3: Total Pressure Contour of 70% Bell Nozzle operating at 5000m
The total pressure contour shows us the irregularity of the exhaust jet at the edges
which cause the exhaust jet axis to move at an angle to the rocket axis. This leads
the thrust being generated in the direction not opposite to the rocket engine
movement.
From the velocity streamlines we can see massive instabilities have caused the flow
to be channeled into a narrow flow path. This leads to a very high decrease in
effective exhaust velocity and hence thrust.
Figure 8.2.3.4: Velocity Streamline of 70% Bell Nozzle operating at 5000m
893. 51
8.3 At 10000m
8.3.1 Ideal Nozzle
Figure 8.3.1.1: Residual Graph of Ideal Nozzle operating at 10000m
Figure 8.3.1.2: Velocity Contour of Ideal Nozzle operating at 10000m
We see that the Ideal nozzle is operating at the optimum design condition at
10000m. The flow has been completely expanded in the nozzle and there are no
shocks in the downstream part of the nozzle. This condition generates the most
optimum thrust.
894. 52
Figure 8.3.1.3: Total Pressure Contour of Ideal Nozzle operating at 10000m
From studying the total pressure, we see that there are no shocks present in the
exhaust gas flow as shocks reduce the total pressure in the flow.
Figure 8.3.1.4: Velocity Streamline of Ideal Nozzle operating at 10000m
The velocity streamline show that there are no irregularities in the gas flow and flow
out in a straight line from the nozzle exit plane. This confirms that the nozzle is
operating at its design operating conditions.
895. 53
8.3.2 85% Bell Nozzle
Figure 8.3.2.1: Residual Graph of 85% Bell Nozzle operating at 10000m
Figure 8.3.2.2: Velocity Contour of 85% Bell Nozzle operating at 10000m
At 10000m we see that the irregular expansion of the parabolic contour has caused
the flow to stick around the nozzle lip. This is typical of low area ratio nozzles
operating at high altitudes. This is caused by the boundary layer sticking to the lip
even after exiting the nozzle. Overall this causes a small loss (about 2%) in the
nozzle thrust.
896. 54
Figure 8.3.2.3: Total Pressure Contour of 85% Bell Nozzle operating at 10000m
The total pressure contour shows us the extent of how much the flow sticks around
the nozzle lip. At this altitude, it is not very apparent as the ambient pressure is just
a little lower than the nozzle exit pressure.
The velocity streamlines do not give an accurate reading of the exhaust flow around
the lip as there are not enough streamlines in the boundary layer. The same applies
for the velocity contour. However from both the figures, we see that the exhaust gas
flow is almost similar to the bell nozzle operating at 5000m. This shows us that by
using an appropriate bell contoured nozzle, the nozzle can attain design conditions
over a wider range of altitudes. This has led to the widespread use of the bell
nozzles in almost all nozzle applications.
Figure 8.3.2.4: Velocity Streamline of 85% Bell Nozzle operating at 10000m
897. 55
Figure 8.3.2.5: Velocity Vector of 85% Bell Nozzle operating at 10000m
8.3.3 70% Bell Nozzle
Figure 8.3.3.1: Residual Graph of 70% Bell Nozzle operating at 10000m
898. 56
Figure 8.3.3.2: Velocity Contour of 70% Bell Nozzle operating at 10000m
By studying the velocity contour, we see that there is a minor boundary layer
interaction with the nozzle lip. However this results in greater loss when compared
to the 85% bell nozzle as the gases have not been allowed to expand gradually. This
causes much more loss in nozzle thrust.
This is apparent in the loss of stagnation pressure.
Figure 8.3.3.3: Total Pressure Contour of 70% Bell Nozzle operating at 10000m
899. 57
8.4 At 20000m
8.4.1 Ideal Nozzle
Figure 8.4.1.1: Residual Graph of Ideal Nozzle operating at 20000m
Figure 8.4.1.2: Velocity Contour of Ideal Nozzle operating at 20000m
At 20000m, the pressure is very low and can be assumed to be non-existent (i.e.
vacuum). Hence there is no ambient back pressure to restrict the nozzle gas in its
expansion. The nozzle operates in an underexpanded state. From the velocity
contour we can see a huge shock wave being formed at the edge of the nozzle exit.
900. 58
Figure 8.4.1.3: Total Pressure Contour of Ideal Nozzle operating at 20000m
The total pressure contour shows us how the gas is still underexpanded when it
leaves the nozzle. Theoretically at ambient pressure much lower that off the nozzle
exit pressure, the thrust will be maximum. By examining the total pressure, there is
a huge drop in the exhaust flow which shows that there are friction losses.
Figure 8.4.1.4: Velocity Streamline of Ideal Nozzle operating at 20000m
The velocity streamline gives us a better idea of how the gas flows in an outward
direction after exiting the nozzle. This is typical of low area ratio nozzles operating
901. 59
at very high altitudes. Therefore in multistage rockets, we see that nozzles operating
primarily in vacuum have very high area ratios (up to 400) which allows the gas to
expand completely inside the nozzle.
Figure 8.4.1.5: Velocity Vector of Ideal Nozzle operating at 20000m
8.4.2 85% Bell Nozzle
Figure 8.4.2.1: Residual Graph of 85% Bell Nozzle operating at 20000m
902. 60
Figure 8.4.2.2: Velocity Contour of 85% Bell Nozzle operating at 20000m
Similar to the Ideal nozzle, the velocity contour is not very different when the
nozzle operates in near vacuum.
Figure 8.4.2.3: Total Pressure Contour of 85% Bell Nozzle operating at 20000m
The total pressure contour also does not show much difference. The boundary layer
going around the nozzle lip can be seen clearly which leads to viscous heating and
higher heat transfer to the wall of the nozzle.
903. 61
8.4.3 70% Bell Nozzle
Figure 8.4.3.1: Residual Graph of 70% Bell Nozzle operating at 20000m
Figure 8.4.3.2: Velocity Contour of 70% Bell Nozzle operating at 20000m
The velocity contour is similar to the one for 85% Bell Nozzle, but the oblique
shocks are more exaggerated due to the abrupt expansion of exhaust gas.
904. 62
Figure 8.4.3.3: Total Pressure Contour of 70% Bell Nozzle operating at 20000m
Here we see massive drop in stagnation pressure at the plume boundary due to
viscous forces acting on it.
8.5 Specific Impulse
The thrust is calculated using ANSYS’s own in-built CFX-Post calculator. The
function calculates the thrust at the nozzle exit plane and also the mass flow rate.
From Section 4.3.2, we have found that when the thrust is divided by the propellant
mass flow rate, the specific impulse (in sec) is obtained.
905. 63
The thrust for various conditions are given below:
1. At Sea Level:
Ideal Nozzle - 12703.68 N
85% Bell Nozzle - 12892.8 N
70% Bell Nozzle - 12729.6 N
2. At 5000m:
Ideal Nozzle - 12791.68 N
85% Bell Nozzle - 13044.48 N
70% Bell Nozzle - 12842.7 N
3. At 10000m:
Ideal Nozzle - 12745.92 N
85% Bell Nozzle - 13142.4 N
70% Bell Nozzle - 12932.4 N
4. At 20000m:
Ideal Nozzle - 12774.08 N
85% Bell Nozzle - 13228.88 N
70% Bell Nozzle - 13035.75 N
The mass flow rates for various conditions are given below:
1. Ideal Nozzle - 176 kg/s
2. 85% Bell Nozzle - 192 kg/s
3. 70% Bell Nozzle - 195 kg/s
Therefore using the above obtained data, the specific impulse Isp, of the nozzle
operating at various operating conditions is presented in a tabular form.
910. 66
REFERENCES
1. Dieter K. Huzel, David H. Huang, (1992) “Modern Engineering for
Design of Liquid-Propellant Rocket Engines”, Progress in Astronautics
and Aeronautics, Vol. 147
2. Gerald Hagemann, Hans Immich, Thong Van Nguyen, Gennady E.
Dumnov, (1998) “Advanced Rocket Nozzles”, Journal of Propulsion and
Power, Vol.14, No.5
3. George P. Sutton, Oscar Biblarz, (2001) “Rocket Propulsion Elements,
7th Edition” John Wiley Sons
4. H. Versteeg W. Malalasekra, (2007) “Introduction to Computational
Fluid Dynamics” Pearson Publications
5. Joel H. Ferziger, Milovan Peric, (2002) “Computational Methods for
Fluid Dynamics” Springer Publications
6. Pardhasaradhi Natta, V. Ranjith Kumar, Dr. Y. V. Hanumantha Rao,
(2012) “Flow Analysis of Rocket Nozzle Using Computational Fluid
Dynamics (CFD)”, International Journal of Engineering Research and
Applications (IJERA), Vol. 2, Issue 5, pp.1226-1235
7. Ralf H. Stark, “Flow Separation in Rocket Nozzles, a Simple Criteria”,
American Institute of Aeronautics and Astronautics
8. Robert E. Biggs, (1889) “Space Shuttle Main Engine, the First Ten
Years” History of Liquid Rocket Engine Development in the United
States, 1955-1980
911. 67
9. Robert Zucker, O. Biblarz, (2002) “Fundamentals of Gas Dynamics” John
Wiley Sons
10. S. M. Yahya, (2011) “Fundamentals of Compressible Flow”, New Age
Publishers
11. Taro Shimizu, Masatoshi Kodera, Nobuyuki Tsuboi, (2008) “Internal
and External Flow of Rocket Nozzle”, Journal of the Earth Simulator,
Volume 9
12. Z. F. Nasuti, M. Onofri, “Flow Structures and Separation in
Overexpanded Rocket Nozzles”, European Conference for Aerospace
Sciences (EUCASS)
