Numerical Simulation Over Flat-Disk Aerospike at Mach 6

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Conference ISBN : ISBN-978-1-5386-4865-0
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i

Numerical Simulation Over Flat-Disk Aerospike at
Mach 6
Rahul S. Pawar
Student, Department of Mechanical Engineering
K. J. Somaiya College of Engineering
Mumbai, India
pawar.rs@somaiya.edu
Dr. N. R. Gilke
Vice-Principal
K. J. Somaiya College of Engineering
Mumbai, India
Mr. Vivek P. Warade
Sr. CAE Engineer
Zeus Numerix Pvt. Ltd.
Pune, India
Abstract— Hypersonic missiles combine the speed of ballistic
missiles along with the accuracy and maneuverability of cruise
missiles. By traveling at hypersonic speed in the atmosphere,
blunt nose of missile experiences great surface heating and a
large amount of drag. This drag force can be minimized by
implementing a structure known as aerospike. This spike is
attached in front of the body that significantly changes the flow
field and manipulates aerodynamic drag at hypersonic speeds. In
the current paper, the effect of implementation a flat-disk
aerospike for various L/D (Length to Diameter) ratios is
investigated by using computational fluid dynamics (CFD)
approach. The CFD analysis is performed to study the effect of
drag, lift and pitching moment coefficient onto the blunt body
with and without implementation of an aerospike. However, the
addition of a flat-disk aerospike in front of the blunt body has an
advantage for the reduction in drag subjected to angle of attack
but increase in pitching moment has to be taken into
consideration.
Keywords—Flat-Disk Aerospike; L/D ratios; angles of attack
I. INTRODUCTION
Hypersonic vehicles are designed to sustain the given
aerodynamic conditions. The vehicles like missiles, space
plane, launch vehicles, etc. typically have blunt nose bodies
normally traveling at higher speeds. Due to this, a large amount
of aerodynamic drag is imposed on these vehicles leading to
malfunctioning of the vehicle due to the presence of strong
bow shock wave in front of the blunt body. This large amount
of aerodynamic drag leads to material damage of blunt body.
So, it is essential to have a low drag vehicle to reduce the
intensity of thrust required from the propulsive system [6]. An
aerospike is more efficient for reduction of drag which
transmutes the strong bow shock wave into weaker shock
waves [8]. This forms a low-pressure region which protects the
blunt body from aerodynamic drag. Various researches are in
process to study the effects of adding aerospike in front of the
blunt nose of body by varying its geometry, dimensions and
blunt nose arrangements.
An oblique shock wave emitted from the front portion of
aerospike continues to move away from the blunt nose of the
body. This mainly occurs due to the geometry of the aerospike,
thus creating a stagnant flow at the tip of aerospike and thereby
generating a recirculation region in between the origin of
aerospike up to the point of reattachment at the shoulder of the
blunt body [7]. If this reattachment point can be shifted
backward or expelled from the shoulder of the blunt body, it
results in the reduction in drag [1].
Various researches are carried out till date to improve the
utility of an aerospike for reduction of drag. Jackson R. Stalder
and Helmer V. Nielsen executed the investigation with the
evolution of conical nosed spikes of semi-apex 100
and L/D
ratio of 0.5 to 2.0. Besides, the effect of heat transfer by
inserting the aerospike with flat disks and blunt cones of semi-
apex angle 400
was studied [1]. Davis H. Crawford explained
the form and nature of the movement of air over a spiked-nose
hemisphere-cylinder which was examined in particular at a
Mach number of 6.8 and at Re range (established on flow
conditions and diameter of the model). He also explained about
pressure circulation in the vicinity of the blunt body which was
associated with the region of separation and the region of
reattachment for shock waves [2]. Lawrence D. Huebner, et al.
performed a sequence of wind tunnel tests on the aerospike at
Mach 6 to gain the recognizable temperature and surface
pressure data. They also performed the wind tunnel tests for
qualitative flow visualization data [4]. Noboru Motoyama et al.
performed the consequences related to the spike length, form
and nose arrangement at various angles of attack for the
decrement of drag, which was studied experimentally with the
employment of a hypersonic wind tunnel situated at the
Department of Aeronautics and Astronautics, University of
Tokyo [5].
Viren Menezes, et al. discussed the effects of drag onto the
blunt nose of the body for larger angles of incidence due to the
flow pattern around the blunt nose causing separation of shock
waves on the upwind side. The flow fields in the vicinity of the
blunt nose of the body with an aerospike augmented assembly
which travels at high Mach numbers, were also imitated using
a commercial CFD code [6]. R. Kalimuthu, et al. performed the
effects for the spike length, form and nose arrangement at
various angles of attack on account of decrement of drag. This
IEEE International Conference on System,Computation,Automation & Networking 2018
ISBN -978 -1-5386-4865-0 108

was scrutinized experimentally with the use of a Hypersonic
wind-tunnel. The consequences of these parameters onto spike
at various angles of attack onto aerodynamic coefficients were
examined using schlieren pictures and measured the
aerodynamic forces respectively [7].
Roberto Roveda explained the utility of blunt body spikes
known as aerospike that was likely to be produced in a future
class missile design. His study assesses for CFD codes that
may be implemented in an engineering study for future
aerospike configurations [8]. M. Barzegar Gerdroodbary and
S.M. Hosseinalipour explained about different forms and
lengths implemented onto aerospike which was chosen to test
the result of the flow field of the blunt nose cone of the
aerospike. Supplementary adjustments at the tip of the
aerospike were also investigated for obtaining diverse bow
shocks which include a conical aerospike, a flat and
hemispherical aero-disk installed onto the crest of the blunt
body [9]. R. C. Mehta discussed the consequences of
implementing different types of aerospike arrangements for the
reduction of aerodynamic drag and these were computationally
evaluated for various L/D ratios, at Mach 6 and zero angle of
incidence and were in good harmony with the experimental
results [10]. Ramesh Repaka, et al. explained about the effects
related to spike length, form and nose arrangement for the
decrement of drag at zero angle of incidence. The spike
geometry studied by them comprises of the hemispherical
aerospike shaped disk and flat triangular aerospike shaped disk
by varying tip radii and L/D ratios [11]. Divyang Gupta
discussed various efforts dedicated to minimize the drag as
well as the aero heating by adjusting the flow field in the
vicinity of the vehicle’s blunt body. Among all these, using
aerospike is the humblest and the utmost consistent technique
[12].
The primary objectives of the current study are: to visualize
the shock wave structure around the blunt nose body with
aerospike and to study the effect of different L/D ratios as well
as angles of attack for aerospike on account of drag reduction.
All these objectives are discussed in the succeeding sections.
II. GEOMETRIC MODELING AND GRID GENERATION
While implementing any CFD simulation, there are many
constraints which needs to be taken into account. Developing
the model is the first phase to be considered. In the second
phase, the mesh type is to be generated which is either
structured or unstructured mesh type. In the next phase, the
boundary conditions for each surface need to be defined. To
safeguard the accuracy of the solution, an accurate boundary
condition setup is important. The meshing process is completed
by exporting the mesh file into solver software. In solver, the
turbulence model and fluid properties need to be carefully
chosen so as to forecast the fluid behavior in the system.
A. Geometry Details
The diameter of the blunt nose (D) is considered to be
0.04m and length of the body (L0) is considered to be 1.25D
and the Reynolds number is considered as 9.79 × 106
[7].
Details of blunt body geometry and aerospike body geometry
relations are illustrated in Fig. 1 and Fig. 2.
The shape of fluid domain is considered as cylindrical in
shape and length of the domain is 17D & diameter is 10D. The
diameter of the domain is considered long enough for
visualization of shock wave phenomenon in front of the body
and to reduce the backward flow of the velocity.
Fig. 1 Blunt body geometry relations [7]
Fig. 2 Aerospike Body geometry relations [7]
B. Mesh Generation
As there are complexities in the geometry, unstructured
mesh is selected. But to capture the behavior of fluid near the
wall, prism layered mesh is used. Prism layered mesh has been
employed for generating the boundary layer elements around
the whole body. Its primary function is for capturing the key
variables such as pressure, velocity or temperature which
experiences rapid change in the flow field. Hence the mesh
type generated is hybrid mesh. The y+
value for generating of
prism layer is considered as 1 (as required by the turbulence
model [9]), along with growth ratio of 1.2 and number of layers
as 18. Tetrahedral and Pyramid meshes are usually used for
generating nodes and components in the fluid domain. The
surface mesh and volume mesh for the blunt body are as shown
in Fig. 3 and Fig. 4.
Fig. 3 Surface Mesh of Blunt body
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Fig. 4 Prism layer over the Blunt body
C. Flow field conditions
The computational results are purely dependent upon the
boundary conditions. The flow of velocity is taking place in
positive X-direction and is flowing through the inlet face of the
domain, then impinged onto the blunt body or aerospike body
and finally coming out of the outlet face. The boundary
conditions imposed onto the inlet face is velocity inlet, then on
the cylindrical face as well as on the outlet face are pressure
far-field and body along with spike are given as no-slip wall
boundary condition. The solver parameters used for numerical
simulations are presented in Table I.
Table I. Solver parameters of the body
Solver Density based
Analysis Type 3D
Turbulence Model Spalart-Allmaras
Fluid Type Air
Time Steady State
III. GRID INDEPENDENCE TEST AND VALIDATION
After simulations, the solutions obtained are having
residuals of order three for mass, momentum and energy
equations. Likewise, the pressure and friction forces acting on
the models were monitored and converged. The coefficient of
drag, lift and pitching moment are calculated using these
equations [3]:
Fx = 0.5 Cx A V2
(1)
Fy = 0.5 Cy A V2
(2)
Cd = Cx cos + Cy sin (3)
Cl = Cy cos - Cx sin (4)
Fm = 0.5 Cm A V2
l (5)
where, Fx and Fy are forces acting in X and Y direction (N),
Fm is pitching moment (Nm), , A and V are density (kg/m3),
area of cross-section (m2) and velocity of an object (m/s), l is
the reference length of model (m), Cx and Cy are co-efficient
of forces along X and Y direction, Cd, Cl and Cm are co-
efficient of drag, lift and pitching moment, is angle of attack
or incidence (in degrees).
A. Grid Independence Test
The grid independence test is performed to examine the
consequences of mesh size over the computational results
obtained. The grid independence test is implemented on the
same body, same domain, and same boundary conditions.
Generally, three different kinds of mesh are used for studying
the grid independence, i.e. coarse, medium and fine mesh. The
usual CFD practices start with the coarse mesh and gradually
refines it till the fine mesh by changing the element sizing. The
size of the mesh is refined until the results for coefficient of
drag are approaching the literature experimental value [7] for
coefficient of drag. This computational study is carried out
using CFD Expert-LiteTM
solver (Developed by M/s Zeus
Numerix Pvt. Ltd.) The CFD simulation results of the three
types of mesh are shown in Table II. It can be observed that
obtained value for coefficient of drag for the medium and fine
mesh is nearly similar. So medium mesh is chosen for further
analysis. If the fine mesh is chosen, the number of elements
will be increased, resulting in an increase of the computational
time.
Table II. CFD results of Grid Independence Test
Mesh
type
Number of
Elements
CFD
Simulation
Cd
Literature
Experimental
Cd
%
|Error|
Coarse 1528373 0.8690 0.89 2.35
Medium 3242393 0.8907 0.89 0.07
Fine 6395146 0.8904 0.89 0.04
B. Validation
The validation is done by comparing the present
computational result with the literature experimental result for
the blunt body at different angles of attack. It is observed that
the coefficient of drag (Cd) of the computed result and
experimental result [7] for different angles of attack are near to
each other as shown in Fig. 5.
Fig. 5 Validation of CFD result with Experimental result
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IV. RESULTS AND DISCUSSION
A. Flow field visualization
In this section, the numerical results are validated with the
experimental results. In flat-disk aerospike case, a bow shock
wave is generated far in front of the blunt nose of the body.
The bow shock wave produced from aerospike is mainly
reliant on the angle of incidence. The blunt body is completely
confined inside the zone of recirculation. The phenomena for
the shaping of the shock wave is due to the geometry of the
aerospike, which produces a stagnant flow at the tip of
aerospike and thereby generating a recirculation region in
between the origin of aerospike up to the point of reattachment
at the shoulder of the nose of blunt body. Hence, if this
reattachment point can be shifted backward or expelled from
the shoulder of the blunt body, it results in decrement in drag.
Fig. 6 Comparison between CFD and Experimental Mach plot
The contour plots describe the reduction in drag due to rise
in the separation region in front of the flat-disk aerospike. The
normal shock wave which is generated in front of the flat-disk
aerospike will reduce the drag. Motoyama et al. [4] also
experimentally witnessed that a bow shock wave is created
due to flat-disk aerospike and a large recirculation zone is
developed at the origin of aerospike. The comparison between
the CFD and Experimental Mach plot for flat-disk aerospike at
an L/D ratio of 1.5 and angle of incidence 00
is illustrated in
Fig. 6.
Surface flow contours for Pressure and Mach number over
blunt body and flat-disk aerospike are obtained for the L/D
ratios of 1, 1.5 and 2, at zero angle of attack and Mach 6, as
illustrated in Fig. 7 and Fig. 8. Fig. 7 represents pressure
distribution over blunt body and flat-disk aerospike at midplane
of body. For blunt body, there is a sudden increase in pressure
at stagnant point thereby affecting the velocity of the body.
This indicates, there is development of bow shock wave in
front of the blunt body. In flat-disk aerospike case, the bow
shock wave is generated due to the configuration of the
aerospike. The pressure acting onto tip of nose of body for flat-
disk aerospike is lower as compared to the pressure acting
directly on blunt body due to the presence of larger bow shock
wave and the recirculation region formed due to the
configuration of aerospike.
Fig. 7 Pressure contour for Blunt body and Flat-Disk aerospike at angle of
attack = 00
Fig. 8 represents Mach contour over blunt body and flat-
disk aerospike at midplane of body. For blunt body, there is
formation of bow shock wave due to the presence of stagnant
point in front of the blunt body. Whereas in case of flat-disk
aerospike, the bow shock wave generated due to the
configuration of aerospike which shields the nose of body and
as L/D ratio increases, the reattachment point is shifted away
from the shoulder of the nose body, thereby reducing drag.
Fig. 8 Mach contour for Blunt body and Flat-Disk aerospike at angle of
attack = 00
B. Effect of Flat-disk aerospike on angle of attack
A comparative study of drag onto the blunt body and
aerospike implemented body configurations for the angle of
ISBN -978 -1-5386-4865-0 111

incidence ranging from 00
to 80
can be observed in Fig. 9. An
important inference can be drawn that the implementation of
aerospike is beneficial for the decrease in drag when the body
is subjected to an angle of incidence. It is observed that the
implementation of aerospike has a smaller coefficient of drag
as compared to the blunt body. This mainly occurs due to the
existence of a recirculation region in between the origin of
aerospike up to the point of reattachment at the shoulder of the
blunt body. As the angle of attack increases, the flow over the
aerospike becomes uneven and therefore changes the intensity
of recirculation region.
Fig. 9 Comparison between the coefficient of drag vs angles of attack
The coefficient of lift tends to increase as the angle of
attack increases, as illustrated in Fig. 10. Besides, a
comparative study is performed on pitching moment
coefficient on the blunt body and aerospike implemented body
configurations for angles of incidence ranging from 00
to 80
. It
can be observed from Fig. 11 that when the blunt body with
flat-disk aerospike is at an angle of attacks, it is subjected to
large pitching moment raised from the aerospike. Hence, as the
angle of incidence increases the pitching moment coefficient
further increases. It is a vital point to be considered for counter-
balancing the added pitching moment for utilization of the
aerospike as the angle of incidence increases [7].
Fig. 10 Comparison between the coefficient of lift vs angles of attack
Fig. 11 Comparison between the pitching moment coefficient vs angles of
attack
V. CONCLUSION
The study shows that there is a formation of the
recirculation zone immediately behind the flat-disk aerospike
and if the reattachment point is shifted backward or expelled
from the shoulder of the blunt body, there are chances for the
reduction in drag. Hence, the aerodynamic drag acting on the
blunt body is greatly affected by choosing the optimal
aerospike length. From CFD results, it is observed that the
aerospike produces 67.5%, 68% and 73.6% reduction in drag
for the L/D ratios of 1, 1.5 and 2 respectively (which is
maximum at 00
angle of attack.) Also, studying the effects of
drag reduction and lift increment without taking into
consideration the aerodynamic stability, the flat-disk aerospike
with an L/D ratio of 2 is more effective as compared to L/D
ratios of 1 and 1.5 respectively. But, increase in pitching
moment due to aerospike attached needs to be taken into
account for study.
ACKNOWLEDGMENT
The author, R. S. P. has completed this project during his
project internship at Zeus Numerix Pvt. Ltd., Pune. He is
grateful to his internal guide Dr. N. R. Gilke and company
guide Mr. Vivek P. Warade for guiding him and being a part of
this project.
REFERENCES
[1] Jackson R. Stalder and Helmer V. Nielsen, “Heat transfer from a
hemisphere-cylinder equipped with flow-separation spikes”, National
Advisory Committee for Aeronautics, Technical Note 3287, September
1954.
[2] Davis H. Crawford, “Investigation of the flow over a spiked nose
hemisphere cylinder at M=6.8”, National Aeronautics and Space
Administration, Washington, NASA TN-118, December 1959.
[3] John D. Anderson Jr., “Computational Fluid Dynamics – The basics
with Applications”, McGraw-Hill Inc., 1995.
[4] Lawrence D. Huebner, Anthony M. Mitchell, Ellis J. Boudreaux,
“Experimental Results on the Feasibility of an Aerospike for Hypersonic
Missiles”, 33rd Aerospace Sciences Meeting and Exhibit, Reno, NV,
AIAA 95-0737, January 1995.
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[5] Noboru Motoyama, Ken Mihara, Ryo Miyajima, Tadaharu Watanuki
and Hirotoshi Kubota, “Thermal protection and drag reduction with use
of spike in hypersonic flow”, American Institute of Aeronautics &
Astronautics, Kyoto, Japan, AIAA 2001-1828, April 2001.
[6] Viren Menezes, S. Saravanan and K.P.J. Reddy, “Shock tunnel study of
spiked aerodynamic bodies flying at hypersonic Mach numbers”,
Symposium on Shock Waves at Fort Worth, Texas, Shock Waves 12:
197–204, October 2002.
[7] R. Kalimuthu, R. C. Mehta, E. Rathakrishnan, “Experimental
investigation on spiked body in hypersonic flow”, The Aeronautical
Journal, Vol. 112, No. 1136, October 2008.
[8] Roberto Roveda, “Benchmark CFD Study of Spiked Blunt Body
Configurations”, 47th AIAA Aerospace Sciences Meeting Including the
New Horizons Forum and Aerospace Exposition, Orlando, Florida,
AIAA 2009-367, January 2009.
[9] M. Barzegar Gerdroodbary, S.M. Hosseinalipour, “Numerical simulation
of hypersonic flow over highly blunted cones with spike”, ACTA
Astronautica 67, pp. 425-449, 2010.
[10] R. C. Mehta, “Numerical heat transfer study around a spiked blunt-nose
body at Mach 6”, Heat and Mass Transfer, ISSN 0947-7411, Springer-
Verlag, Berlin, Heidelberg, 2012.
[11] Ramesh Repaka, Sudhir Joshi, Rajesh Yadav, Adarsh Baboo Gupta,
Prakash S. Kulkarni and Ugur Guven, “Flow Field Computations over
Hemispherical, Flat Triangular Disk Spiked Blunt Body at Mach
Number 6”, 17th Annual CFD Symposium, Bangalore, 2015.
[12] Divyang Gupta, “Drag Reduction of Hypersonic Vehicles using
Aerospike”, International Journal of Research in Aeronautical and
Mechanical Engineering, Vol. 5, Issue No. 1, ISSN 2321-3051, 2017.
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Numerical Simulation Over Flat-Disk Aerospike at Mach 6

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