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Numerical Analysis on an aerodynamically thrust-vectored Aerospike Nozzle
Conference Paper · September 2014
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NUMERICAL ANALYSIS ON AN AERODYNAMICALLY THRUSTVECTORED AEROSPIKE NOZZLE
M. Propst1, J. Sieder2, C. Bach3 and M. Tajmar4
Institute of Aerospace Engineering TU Dresden, 01069 Dresden, Germany
Abstract
The present study shows results from numerical investigations of aerodynamic thrust vectoring on a small
scale aerospike thruster. The thruster will generate 3 kN of axial thrust at an expansion ratio of ε = 2,941. The
full isentropic spike contour was designed using the open source FORTRAN code by C. C. Lee on pure
external flow expansion plug nozzles. All numerical analyses shown in the study were performed on
two-dimensional spike geometry models using ANSYS FLUENT® to solve the governing flow equations.
Investigations were carried out on flow characteristics for spike truncations from 0 % to 75 %. For secondary
injection analyses an aerospike nozzle, truncated at 75 % of its full theoretical length, was chosen. To
generate thrust vectoring a secondary fluid was injected into the primary flow field normal to the nozzle axis.
Two different injection sites located at 60 % and 90 % of the truncated spike length as well as varying mass
flow rates were applied to examine effects of secondary injection on the thruster main flow. Finally, an
estimation was made regarding the achievable side forces for the investigated configurations due to
aerodynamic thrust vectoring. The thesis shows that secondary fluid injection is a feasible method for active
thrust vectoring on small scale aerospike thrusters and gives an objective for future applications.
and their flow characteristics. In the context of a
parameter study, concerning variable mass flow and
injection sites, flow properties are examined in chapter
five. An estimate of the achievable side forces under the
predetermined conditions completes chapter five.
1. INTRODUCTION
As an alternative to classical
bell nozzle designs,
aerospike or plug nozzle propulsion systems have been
developed and tested since the 1950s [1-12]. They have
been in discussion for the upper stage of Saturn V and
later for the Space Shuttle Main Engine. In form of a linear
plug construction, the nozzles were the single-stage-toorbit propulsion system of choice of the X-33 Mission at
NASA during the 1990s, which is also known as Venture
Star. Today, well known for their altitude adaptive
characteristics up to the designed pressure ratio, the
engines experience a renewed growing interest in recent
years because of further advantageous performance
characteristics towards comparable bell nozzles and the
additional capability of active aerodynamic thrust
vectoring [13, 14].
2. AEROSPIKE CONCEPTS
In general, aerospike nozzles can be devided into linear
and annular plug nozzle designs. Both configurations offer
the possibility to either have only one nozzle or a
clustered arrangement. The advantage of a clustered
configuration is that it already offers an option for
aerodynamic thrust vectoring by applying the method of
differential throttling of single nozzle clusters. Moreover,
there is the possibility to expand the hot exhaust gases
either completely externally or partially internally and
externally, by adding an additional divergent nozzle
structure behind the nozzle throat [3, 4].
In terms of the progression the objective of this paper is to
present a model which provides the possibility to evaluate
flow characteristics of expansion nozzles and
aerodynamic steering in the context of Computational
Fluid Dynamics (CFD) analyses using the commercial
solver ANSYS FLUENT®. Therefore chapter two will give
a brief introduction in aerospike concepts. Section three
shows the modeling of the CFD analyses including the
design of the nozzle contour, the computing strategy and
specific physical models which aim to achieve a realistic
depiction of the fluid flow. In the subsequent chapter four,
a suitable nozzle configuration to investigate aerodynamic
thrust vectoring is selected by comparing different designs
1
2
3
4
Because of the high thermal load at the nozzle exit as well
as aspects of weight optimization and the fact that the
ideal plug is very difficult to manufacture, it is usually
truncated. Truncation itself is always bound to losses
according to the nozzle performance [3].
Furthermore, plug nozzles offer various advantages for
exoatmospheric flight scenarios. Because of their shape,
the nozzles can reach greater expansion ratios by having
the same size of the structures area compared to bell
nozzles as pictured in figure 1.
Graduate student Martin Propst is a volunteer research assistant at the
Institute of Aerospace Engineering TU Dresden
Dipl.-Ing. Christian Bach is Ph.D. student and administrator of the SMART
Rockets Project (SRP)
Dipl.-Ing. Jan Sieder is Ph.D. student and administrator of the SRP
Prof. Dr. Martin Tajmar is head of Space Systems Chair and leader of the
research group “Space propulsion and new concepts”
1
The greater expansion ratio of the aerospike nozzle
results in a higher generated thrust by having a small form
factor compared to a conventional nozzle.
FIG 1.
predetermined conditions. To reduce the computational
effort of the CFD analysis, the structure of the combustion
chamber is truncated. The resulting line bodies of the fully
isentropic spike and the minimized combustion chamber
are merged as pictured in figure 2.
F1 engine and proposed J-2T-250K aerospike
(left), engine of Altair Lander with proposed plug
nozzle design (right) [13]
3. CFD-MODELLING
FIG 2.
Based on the design principles stated in the previous
section, the center of chapter three is made up by
generating a suitable nozzle geometry, defining the
physical conditions under which the considerations are
made and explaining the simulation process itself.
3.1.
Coordinates of the initial nozzle geometry
All investigations are performed using two-dimensional
CFD analyses. Therefore all line bodies used for the
simulation need to form one structure that encloses the
later flow field. The flow field geometry is depicted in
figure 3.
Geometry
There are different approaches to designing the spike
contour of a plug nozzle. Besides the already mentioned
method lately shown by Kraiko et al [6], there are the
classical approaches by Lee [1] and Angelino [2], which
use the one-dimensional isentropic flow theory. In the
present work, the plug contour was calculated using the
open source FORTRAN code for purely external flow
expansion of ideal gases presented by Lee. The
considerations done by Sieder [15] in a previous thesis
according to an ideal aerospike nozzle, which generates a
total thrust of 3 kN, serve as a basis for the calculation of
the spike geometry. His research provides the required
input data for the FORTRAN program shown in table 1.
Parameter
FIG 3.
Value
Mach number
Geometry of the flow field
2,3
Expansion ratio 
2.941
-1
-1
Specific gas constant RS in [J kg K ]
374.8
Temperature at nozzle exit Te in [K]
2024
Pressure ratio pnozzle exit/pchamber
1/15
Isentropic exponent 
1.4
3.2.
Physical model
The purpose of the present paper is to simulate an onground engine test at sea level under idealized conditions.
In the context of these numerical analyses, the ideal gas
model is used to describe the mixture of 70% Vol. Ethanol
as fuel and liquid Oxygen (LOX) as the oxidizer at an
applied ratio of 1:1. Besides there is no directed fluid flow
imprinted for the surrounding flow field. The boundary
conditions for the combustion chamber defined in table 1
are valid only for the idle state of the fluid. So the actual
conditions given at the truncated end of the combustion
TAB 1. Input data for plug nozzle program
Sieder also developed the MATLAB® program for
calculating the contour of the combustion chamber for the
2
FIG 4.
chamber were calculated
dimensional flow theory.
using
Sequence of performed CDF analyses
isentropic
one-
Furthermore, there are no turbulent models added to the
simulation yet. The idealization is appropriate for flows
with high Reynolds numbers where inertial forces
outweigh those of viscosity. Because of the absence of
molecular diffusion, the conservation equations of
momentum and energy are simplified, whereas the
conservation of mass is identical to laminar behavior.
Future CFD analyses could use the Spalart-Allmaras
model to model turbulence. This approach was especially
conceived for aerospace applications. In correspondence
with the Sutherland model to describe temperature
dependent fluid viscosity, the accuracy of the analysis
could be increased [16].
3.3.
FIG 5.
Simulation Process
Initial mesh (left), adapted final mesh (right)
Gradient adaption based on the gradient of the total
pressure provides a possibility to refine the mesh only in
the region where it is needed. The solution is thereby
significantly refined by a minimum of computational
expense. The procedure of gradient adaption is repeated
until there are only infinitesimal changes in the flow
characteristics of the flow field between the last two
converged solutions. To define a converged solution, an
approach of double monitoring is used. It consists of a
minimization of the residuals while having a converged
and constant primary mass flow.
By applying the preliminary considerations concerning
modeling, the following section describes the simulation
process. Figure 4 elucidates the detailed sequence of the
CFD analyses. All sequencing calculation methods are
oriented towards solution strategies which are
documented in detail in [16, 20, 21].
Once the two-dimensional geometry of the flow field is
established, an initial discretization can be performed on
it. Subsequently, the boundary conditions as well as the
basic solver settings are defined. To give every node of
the mesh a start value regarding its flow characteristics,
the flow field has to be initialized. This is done by using
the full multigrid initialization (FMG). In general, this
method virtually fuses mesh elements and thereby
generates a coarse solution of the flow field. The
initialization completes the pre-processing and the
calculation of the flow can be started. To compensate
potential large non-linearities which may emerge from
compression shocks and other flow characteristics which
are typical for expanding flows at supersonic conditions,
the analysis is performed stepwise by increasing the
accuracy of the solution. This procedure provides a good
numerical stability during calculation. Having reached a
converged solution of the flow field using the most
accurate depicted calculation methods, the solution can
be refined by adapting the mesh as pictured in figure 5.
4. SELECTING THE NOZZLE SETUP
The following section compares three different spike
truncations and the ideal isentropic spike configuration
regarding their fluid flow characteristics. Upon these flow
fields a configuration is selected to investigate
aerodynamic thrust vectoring.
The truncations under consideration range between 0 %
and 75 % in equidistant steps of 25 %, so that we have
setups with 25 % to 100 % of full isentropic spike length.
3
4
FIG 6.
Distribution of the Mach number for varying spike truncations
FIG 7.
Calculated flow characteristics for a spike truncation of 25 %
Figure 6 shows all four setups and the computed flow
fields with increasing spike truncation from a) to d) using
the mentioned equidistant steps. The depicted distribution
functions of the Mach number show that the nozzle flow is
in general slightly over-expanded. The reason for this flow
behavior is the idealized shape of the spike, which is
computed using the theory of one-dimensional isentropic
fluid flow. A fully adapted flow at the design pressure ratio
is described by a free-jet boundary parallel to the spike
axis. The depicted flow field corresponds to an aerospike
nozzle which is designed for a high flight altitude and in
that case tested on ground (sea level). This behavior is
advantageous for the case investigated in our paper,
because the aim of the simulation was to show such a
scenario, which allows to compare the computed data to
real test data. Nevertheless, it is still necessary to find a
design algorithm for the spike contour based on a
predefined pressure ratio that provides the flow-optimized
nozzle structure for the regarded conditions. The method
pointed out by Kraiko et al [6] could be one approach for
that.
4
The displayed fluid flow analyses show that for bigger
spike truncations there are more and especially more
distinct compression shocks. That leads to areas with
higher static pressure downstream of the shock waves.
The aerodynamic spike, which is already fully developed
at a spike truncation of 25 %, widens up for shorter spike
lengths.
At the same time, the size of the region of closed wake
recirculation at the plug base increases. Furthermore, the
shock waves, generated at the lip of the truncated spike,
are getting more pronounced for greater spike truncations.
In general, one can see that shorter spike configurations
lead to more complex flow behavior. The following
investigations require a homogeneous, almost undistorted
flow field, so that the effect of aerodynamic thrust
vectoring can be shown and studied. For that reason the
subsequent considerations are made using a nozzle
configuration with 75 % of the full isentropic spike length.
The flow characteristics for the chosen setup are
determined according to Hagemann et al[3] and are
pictured in figure 7.
5. PARAMETER
VECTORING
STUDY
ON
FIG 8.
Injection site at 60 % (left) and 90 % (rigth) of the
spike legth
For the smaller thrust classes considered here, thrust
vectoring can be performed by injecting a secondary fluid
flow into the expanding primary flow of the thruster along
the spike contour. As pictured in figure 8, the present
study investigates two injection sites: one close to the
base at 90 % of the spike length and one situated nearer
to the nozzle throat at 60 % of the truncated plug.
Furthermore, the injected mass flows are varied for both
setups. In the context of the parameter study injected
mass flows of 0.78 % up to 3.92 % of the primary mass
flow are investigated.
THRUST
After having found a suitable nozzle configuration for the
subsequent studies in the previous section, chapter five
presents a parameter study according to aerodynamic
thrust vectoring.
5.2.
5.1.
After having discussed the approach of thrust vectoring on
aerospike nozzles, the following section evaluates the
calculated results from the parameter study.
Aerodynamic thrust vectoring
The main difference between aerodynamic and
mechanical thrust vectoring lies in the absence of heavy
mechanical elements. The thrust vector of conventional
bell nozzles is usually influenced by mechanical structures
such as movable gimbals or flaps. One approach for
mechanical thrust vectoring on an aerospike nozzle could
be a moveable mounted plug, for example. However, it is
obvious that this configuration would lead to an additional,
heavy structure because of the fully gimbaled suspension.
Moreover, possible losses in nozzle performance need to
be taken into account because of the continuously
changing divergent part of the nozzle.
5.2.1.
Evaluation of the parameter study
Injection site at 90 % of the spike length
The distribution functions of the Mach number in figure 9
expose the formation of a bow shock at the position of
injection at 90 % of the spike length. With an increasing
injected fluid flow the intensity of the shockwave increases
as well. From the injection point on the generated
shockwave extends to the free-stream boundary.
Eventually, it gets reflected at this borderline and is being
directed forward to the centralized compression shock
behind the spike. The shockwave interferes with the
already compressed area and is no longer verifiable at the
downstream located region. In total, the entire exhaust
gas flow gets stretched with an increasing secondary
mass flow. Starting from the reflection point of the bow
shock on the free-stream boundary, the necking of the
over-expanded primary flow is unilaterally longitudinally
extending. Considering the strongest secondary flow, the
opposing shear layers of the exhaust gas flow run almost
parallel behind the trailing shock.
The already mentioned method of differential throttling
provides an opportunity for the alternative aerodynamic
thrust vectoring. The approach, being applicable only on
clustered nozzle configurations, could be a suitable
technique for medium or high thrust classes.
5
With an increasing mass injection, the flow pattern
changes only by the intensity of the shape. Thereby a new
expansion region is formed, starting from the specified
necking point, which is caused by the injection bow shock.
This region reaches the high pressure zone behind the
trailing shock and proceeds downstream as a new
shockwave to the opposing boundary of the free-stream.
Here, the shockwave gets reflected again and propagates
within the exhaust gas flow until it is no longer noticeable.
Overall, the flow field at 60 % of the spike length, as it is
depicted in figure 10, gets much more influenced by the
injection compared to the one considered previously.
5.2.3.
FIG 9.
Distribution of Mach number for an injected mass
flow of ca. 2 % (top) and ca. 4 % (bottom) of the
primary mass flow
5.2.2.
Injection site at 60 % of the spike length
Comparison of the results
In direct comparison of the flow patterns, one cannot
identify a visible extension of the free-stream in case of an
injection at 90 % of the spike length. Admittedly, the flow
field shows stronger characteristics of shock- and
expansion waves, but the trail is less affected. However,
both configurations show a visible deflection of the freestream in positive y-direction, when applying great
secondary mass flows. Transferred to an infinitesimal
section of an axisymmetric spike, it is likely that this
reaction has no strong effect on the complete free-stream
because of the surrounding annular flow and thus threedimensional effects. Though having a linear spike
structure, a deflection of the whole exhaust gas flow would
occur. This reaction would definitely affect the direction of
thrust vector.
Originating from an injection site at 60 % of the spike
length, one can observe the same forming of a bow shock
as in the previous case. Because of the injection position,
which is now closer to the narrowest nozzle cross section,
the shockwave now interacts directly with the expanding
primary flow. As a result, a visible unilateral necking is
formed at the position where the bow shock meets the
shear layer of the main flow, even at a minimal secondary
mass flow.
Furthermore, the data shows that the secondary mass
flow has a cooling effect on the spike surface downstream
of the injection point. The cooled flow then propagates
centrally downstream within the free-stream. In direct
vicinity of the exhaust gas flow, the simulation showed
small areas with higher total temperatures. This is caused
by circulation flows. The primary free-stream sucks gas
particles from its surrounding, which get accelerated
towards the exhaust gas stream. When these particles
meet the boundary layer of the primary stream, stagnation
points in the form of localized turbulences can occur.
These stagnation points naturally feature a slightly
increased temperature and density. The same
phenomena can be observed directly above and below of
the nozzle exit where the surrounding flow is directed to
the primary one. In this stern region a wake is formed,
which is characterized by a circulation as well. This effect
would get enhanced for the given rear structure, if there
would be an imprinted surrounding flow in positive
x-direction. This simulated flight scenario would be able to
specify the influence of the surrounding stream on the
exhaust gas flow. In any case, the wake generates an
unwanted aerodynamic drag, which decreases the nozzle
performance. In this case a suitable structural design
could provide relief.
5.3.
Estimation of side forces
The recently presented studies by Shannon et al [13, 22]
and Erni et al [14] concerning thrust vectoring on plug
nozzles, give some indication of achievable side forces,
response qualities and amplification factors caused by
FIG 10. Distribution of Mach number for an injected mass
flow of ca. 2 % (top) and ca. 4 % (bottom) of the
primary mass flow
6
FIG 11.
Distribution function of the applied force in y-direction for an injection of ca. 4 % of the primary mass
flow at 60 % of the spike length
FIG 12.
Distribution function of the applied force in y-direction for an injection of ca. 4 % of the primary mass
flow at 90 % of the spike length
superposition of primary and secondary flow. However, as
yet, there does not exist an analytical method that
provides reliable prognoses according to achievable side
forces and amplification factors.
The values for the injected mass flow minj , the averaged
flow velocity at the nozzle exit v e , as well as the averaged
static pressures at the nozzle exit pe and in the ambient
flow field p are provided by the CFD analyses. Together
An early approach introduced by Zukoski and Spaid [23],
considers the injection of gases into a supersonic flow
and supplies an approximation of the generated side force
Fy, applied on an overflowed flat plate by equation (1)
(1)
with the known nozzle exit area A e , the thrust generated
by the injection is computed to 70.88 N for the injection
site at 60 % and to 68.16 N for the injection site at 90 % of
the Spike length. For the second addend of equation (1)
the evaluation of the analysis results could give at least a
qualitative statement. According to Zukoski [23] the
induced side force Find is calculated from the integral of
the pressure distribution over the regarded area. The
CFD analyses provide the applied forces in y-direction
resulting from the pressure distribution. The gained results
are depicted in figure 11 and 12.
Fy  Tinj  Find
where Tinj is the thrust generated by secondary injection
and Find is the additional force induced by superposition of
the two flows. By applying equation (2) agreeable to [24] a
quantitative estimation of Tinj is possible.
(2)
Finj  minj ve  ( pe  p ) Ae
7
The evaluation of the data gives a value range from
-27.88 N to 26.56 N for the injection site at 60 % and from
-28.95 N to 27.35 N for the injection site at 90 % of the
spike. The induced forces over the spike are thus not
symmetrically distributed. Figure 11 shows an almost
homogenous force distribution over the upper and lower
spike area, for the more upstream situated injection site.
Additionally to the fact that the forces induced on the
upper spike area, are of a greater amount than on the
lower one it should be noted that in the trail of the injection
a significant force vector is formed. This vector is caused
by the high pressure region in the trail of the shockwave
resulting from the flow injection. The lower spike surface,
however, experiences a continuously decreasing
pressure, starting with the greatest applied force directly
behind the smallest cross section of the nozzle.
Due to the low technical readiness level, the system
provides a variety of possible research and development
tasks, which should be of interest for student education
and to expedite the technology.
6. OUTLOOK
The gained results serve as a basis for further
calculations and tests. One first approach is to determine
an ideal spike geometry, which provides an adapted
nozzle flow for the considered conditions. The
advancement of the simulation model should be made
with regard to three-dimensional analyses. This would
allow to study thrust vectoring especially for axisymmetric
nozzle configurations in the future, which are affected by
three-dimensional flow effects. For this purpose
considerations should be given to the use of alternative
solver programs. The Viscous Upwind Algorithm for
Complex Flow Analysis (VULCAN) developed by NASA
could offer one option to do so. For further optimization of
the nozzle, structural and thermal numerical analyses
should be considered.
With the injection site closer to the base, a clearly
enlarged area with an applied force in negative y-direction
can be noticed on the upper spike surface, directly behind
the nozzle throat. The lower surface again experiences a
continuously decreasing pressure towards the base.
Qualitatively, it is noticeable that the injection at 90 % plug
length has a greater influence regarding the generated
force distribution over the upper spike surface compared
to the second configuration.
To validate the CFD analyses, several experiments are
suitable. Besides a full scale test setup of an aerospike
nozzle including a combustion chamber, some more
easily realizable tests could be performed. Shallow water
analyses and cold gas engine tests, for example, offer
such opportunities.
Overall, the evaluation of the CFD analyses verifies an
induced force according to secondary fluid injection. The
force reaches a maximum, when the injection site is close
to the base. Admittedly, the generated thrust is slightly
smaller for the injection at 90 % of the plug length, but it
should be noted that the procreated steering moment is
directly dependent on the distance between the force
transmission point and the center of gravity of the
launcher system. Since the differences in generated thrust
are marginal for the studied setups and a maximum of the
induced force is verifiable for the injection at 90 % of the
spike length, it can be concluded that this injection
configuration generates the largest side force under the
regarded conditions. Further tests and analyses have to
show to what extent the injected secondary mass flows
could be optimized.
5.4.
We will start our validation experiments with a shallow
water test bench at the Institute of Fluid Mechanics (ISM).
The needed nozzle model is shown in figure 13 and
currently manufactured. First results are expected within
the next quarter. Utilizing the analogy of shallow water
and one-dimensional gas flows, the flow patterns of the
water test can be compared directly to the simulation
results. A gas flow analysis using Schlieren photography
will be realised in a second step, which also can be
conducted in cooperation with the ISM.
Possible Applications
The presented propulsion system with aerodynamic thrust
vectoring is especially suitable for applications in the field
of small and medium thrust classes. In Erni et al [14] the
capability of a CubeSat propulsion system using an
aerospike engine is discussed. The advantage of higher
expansion ratios by having the same size of area of the
system compared to conventional bell nozzles results in a
more compact structure. At the same time the specific
impulse increases and the fuel consumption is reduced.
Furthermore, the secondary injection could be used as a
stand-alone attitude control system which is not possible
for bell nozzles [13]. In summary, thrust vectored
aerospike engines offer the possibility to release a swarm
of small satellites by only one launcher system. Each
satellite is then able to reach its own individual orbit and to
perform attitude control, everything done by one system
[14]. Of course the engines are also conceivable for
deorbiting maneuvers. Last but not least, the described
propulsion system appears to be an attractive scope for
the student rockets project conducted at the TU Dresden.
FIG 13. Shallow water test model
While the above mentioned methods are for optical
validation and analyses of the flow behaviour for linear
aero spike nozzles or two dimensional models, a cold gas
engine setup can be used for three dimensional analyses
of forces and turning moments. Furthermore, we intend to
build a test bench with a variable nozzle setup for various
parameter studies, such as spike lengths, injection sites,
mass flow rates etc. With these experiments and
8
numerical analyses we want to contribute to the
establishment of a larger database for aerospike nozzles
using secondary fluid injection for thrust vectoring, so that
an analytical description might be derived.
H. Immich, P. Sacher, and P. Reijasse, Plug
nozzles: Summary of flow features and engine
performance, AIAA, no. 2002-0584, 2002.
[9]
7. CONCLUSION
[10] M. Nazarinia, A. Naghib-Lahouti, and E. Tolouei,
Design and numerical analysis of aerospike nozzles
with different plug shapes to compare their
performance with a conventional nozzle, vol. 11. ,
AIAC, 2005.
In the context of the presented paper a CFD model was
developed which enables the determination of fluid
dynamic characteristics of nozzle flows using numerical
flow analyses. By applying the one-dimensional isentropic
flow theory, an initial aerospike nozzle geometry for
further studies has successfully been generated. In the
course of subsequent CFD analyses, a nozzle
configuration was determined which allows the optimal
investigation of aerodynamic thrust vectoring. The plug
nozzle was then submitted to a parameter study regarding
different injection sites and secondary mass flow rates.
The results show the emergence of a significant force
vector by injecting a secondary fluid flow. A final
estimation showed that the maximum steering force is
generated for a nozzle configuration with an injection site
at 90 % of the spike length.
[11] A. Naghib-Lahouti and E. Tolouei, Investigation of
the effect of base bleed on thrust performance of a
truncated aerospike nozzle in off-design conditions. ,
ECCOMAS CFD, 2006.
[12] T. Zebbiche and Z. Youbi, Supersonic twodimensional plug nozzle conception at high
temperature, Emirates Journal for Engineering
Research, vol. 11, no. 2, 2006.
[13] S. D. Eilers, M. D. Wilson, D. S. A. Whitmore, and
Z. W. Perterson, Analytical and experimental
evaluation of aerodynamic thrust vectoring on an
aerospike nozzle, AIAA, no. 2010-6964, Juli 2010.
[14] N. M. Erni, S. A. Whitemore, and D. J. Baker,
Closed-loop attitude control using fluid dynamic
vectoring on an aerospike nozzle, IREASE, vol. 5,
no. 1, Februar 2012.
ACKNOWLEDGEMENTS
We appreciate the assistance and support by:
[15] J. Sieder, AUSLEGUNG EINES 3 KN-TRIEBWERKS MIT
HÖHENANPASSBARER DÜSE, Großer Beleg, Juni 2011,
technische Universität Dresden.
Prof. Tajmar, who finances the shallow water model and
Dr. Rüdiger from the Institute of Fluid Mechanics, for his
time, advice and support during the development of the
shallow water model.
[16] ANSYS Inc. (2009, April) Ansys fluent 12.0 theory
guide. Available: http://orange.engr.ucdavis.edu/Documentation12.1/121/FLUENT/flth.pdf
[17] ANSYS Inc. (2009, October) Ansys fluent 12.1
workbench user’s guide. Available: http://orange.engr.ucdavis.edu/Documentation12.1/121/FLUENT/flwb.pdf
REFERENCES
[1]
E. Besnard and J. Garvey, Aerospike engine for
nanosat and small launch vehicles (nlv/slv), Space
2004 Conference Exhibit. AIAA 2004-6005,
September 2004.
C. C. Lee, Technical note - fortran programs for plug
nozzle design, Tech. Rep., März 1963.
[2]
G. Angelino, Performance methode for plug nozzle
design, AIAA, vol. 2, no. 10, 1964.
[18] ANSYS Inc. (2009, April) Ansys fluent 12.0 udf
manual. Available: http://orange.engr.ucdavis.edu/Documentation12.1/121/FLUENT/fludf.pdf
[3]
G. Hagemann, H. Immich, and M. Terhardt, Flow
phenomena in advanced rocket nozzles - the plug
nozzle, vol. 34. , AIAA/ASME/SAE/ASEE Joint
Propulsion Conference And Exhibit, Juli 1998.
[19] ANSYS Inc. (2009, April) Ansys fluent 12.0 text
command list. Available: http://orange.engr.ucdavis.edu/Documentation12.1/121/FLUENT/fltui.pdf
[4]
G. Hagemann, H. Immich, T. V. Nguyen, and G. E.
Dumnov, Advanced rocket nozzles, Journal of
Propulsion and Power, vol. 14, no. 5, SeptemberOktober 1998.
[5]
J. J. Korte, Parametric model of an aerospike rocket
engine, AIAA, no. 2000-1044, 2000.
[6]
A. N. Kraiko and N. I. Tillyayeva, Optimal profiling
of the supersonic part of a plug nozzle contour, Fluid
Dynamics, vol. 35, no. 6, pp. 945–955, 2000.
[7]
E. Besnard, H. H. Chen, and T. Mueller, Design,
manufacturing and test of a plug nozzle rocket
engine, AIAA, no. 02-4038, 2002.
[8]
[20] ANSYS Inc. (2009, April) Ansys fluent 12.0 users‘s
guide. Available: http://orange.engr.ucdavis.edu/Documentation12.1/121/FLUENT/flug.pdf
[21] ANSYS Inc. (2009, April) Ansys fluent 12.0 tutorial
guide. Available: http://orange.engr.ucdavis.edu/Documentation12.1/121/FLUENT/fltg.pdf
[22] S. D. Eilers, M. D. Wilson, D. S. A. Whitmore, and
Z. W. Perterson, Side-force amplification on an
aerodynamic thrust vectored aerospike nozzle,
Journal of Propulsion and Power, vol. 28, no. 4,
Juli-August 2012.
[23] E. E. Zukoski and F. W. Spaid, Secondary injection
of gases into a supersonic flow, AIAA, vol. 2, no. 10,
Oktober 1964.
M. Onofri, F. Nasuti, M. Calabro, G. Hagemann,
9
[24] E. Messerschmid and S. Fasoulas
Raumfahrtssysteme - Eine Einführung mit Übungen
und Lösungen. Springer, 2004.
[39] M. S. Shamnas, S. R. Balakrishnan, and S. Balaji,
Effects of secondary injection in rocket nozzle at
various conditions, IJERT, vol. 2, no. 6, Juni 2013.
[25] J. E. Broadwell, Analysis of the fluid mechanics of
secondary injection for thrust vector control, AIAA,
vol. 1, no. 5, Mai 1963.
[40] B. T. Maia, L. M. Nascimento, and J. E. Mautone,
Mathematical simulation of blow through supersonic
nozzles, Universidade Federal de Minas Gerais &
Lumar Metals, Tech. Rep., Dezember 2013.
[26] H. F. R. Schöyer, Thrust vector control for (clustered
modules) plug nozzles: Some considerations,
Journal of Propulsion and Power, vol. 16, no. 2,
März- April 2000.
[41] Rohanverse. (Dezember 2013) Aerospike engine.
Available: http://rohanverse.webnode.com/aerospike-engine/
[27] J. Östlund, Flow processes in rocket engine nozzles
with focus on flow separation and side-loads, Royal
Institute of Technology Department of Mechanics
Stockholm, Tech. Rep. 2002:09, Mai 2002.
[28] E. Erdem, Thrust vector control by secondary
injection, Master’s thesis, Graduate School Of
Natural And Applied Sciences Of Middle East
Technical University, September 2006.
[29] C. G. S. Jr., G. J. Callis, and R. K. Masse, Thrust
vector control system for a plug nozzle rocket
engine, Amerika Patent 7155898, Januar, 2007.
[30] N. Zeoli and S. Gu, Computational validation of an
insentropic plug nozzle design for gas atomisation,
Computational Materials Science, vol. 42, no. 2, April
2008.
[31] B. J. Olson. (2009, Januar) 2-d nozzle design.
Available: http://www.mathworks.com/matlabcentral/fileexchange/14682-2-d-nozzle-design/content/nozzle.m
[32] W. S. Case, Aerospike thrust vectoring slot-type
compound nozzle; Master’s thesis, Faculty of
California Polytechnic State University, San Luis
Obispo, Juni 2010.
[33] ANSYS Inc. Introduction To ANSYS FLUENT
Lectures & Workshops, iMechanica Std., Dezember
2010. Available: http://imechanica.org/node/15400
[34] S. L. Kulhanek, Design, analysis and simulation of
rocket propulsion system, Master’s thesis, University
of Kansas, Juni 2012.
[35] K. O. Mon and C. Lee, Optimal design of supersonic
nozzle contour for altitude test facility, Journal of
Mechanical Science and Technology, no. 26
(8)(2012) 2589 2594, März 2012.
[36] B. Ray, R. Bhaskaran, and L. R. Collins,
Introduction To CFD Basics, Februar 2012.
Available: http://www.erac.ntut.edu.tw/ezfiles/39/1039/img/832/3-1-00001-intro-FiniteDifference.pdf
[37] K. M. Khan and S. Khushnood, Numerical
simulation of aerospike nozzle inviscid isentropic
flowfield, Life Sciences Journal, vol. 10, no. 3,
September 2013.
[38] J.-B. M. Mbuyamba, Calculation and design of
supersonic nozzles for cold gas dynamic spraying
using matlab and ansys fluent, Master’s thesis,
University of the Witwatersrand Johannesburg,
Mai 2013.
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