Above Research Paper can be downloaded from www.zeusnumerix.com The research paper aims at studying the variation of the geometry of the launch vehicle nose and its effect on heat flux. CFDExpert software is first validated on NASA's hyperballistic model and then used on proposed geometries. Various nose radius and blending shapes are studied for effect on drag and heat flux. Cone ogive shape is found to decrease heat flux with an insignificant increase in drag. Authors Abhishek Jain (Zeus Numerix), Rohan Kedar and Prof V Kalamkar (SPCOE).

1. 1
Proceedings of the National Conference on Advances in Thermophysics and Heat Transfer
April 26-27, 2012, Thiruvananthapuram, Kerala, India
EFFECT OF GEOMETRY ON VARIATION OF HEAT FLUX AND DRAG FOR LAUNCH
VEHICLE
Rohan V. Kedare
Post-Graduate Student, SPCE.
Mumbai, Maharashtra, India
Abhishek Jain
Zeus Numerix Pvt. Ltd.
Mumbai, Maharashtra, India
Dr. Vilas R. Kalamkar
Associate Professor, SPCE.
Mumbai, Maharashtra, India
ABSTRACT
The objective of the project was to numerically simulate
the flow over a launch vehicle without fins and to estimate drag
coefficient and heat flux on surface. Studies have been made to
investigate the effect of different nose radius on heat flux and
drag coefficient at Mach 8 and flight altitude of 20km. A
commercial code CFDExpert™ was used to carry out
simulation. To gain confidence in simulation, validation studies
have been carried out on standard hyper-ballistic model (HB-2).
Results have been tabulated for variation of heat flux and drag
due to change in nose radius and blend surface shape.
Keywords: Hypersonic, Drag, Ogive, Heat Flux.
INTRODUCTION
At hypersonic speed, the vehicle leading edges must be
blunt to some extent in order to reduce the heat transfer rate to
acceptable levels. Use of blunt body finds application in launch
vehicles, missiles, re-entry vehicles, etc. Design of hypersonic
vehicle leading edge involves a tradeoff between making the
leading edge sharp enough to obtain acceptable drag and blunt
enough to reduce the aerodynamic heating in the stagnation
point. A method of designing low heat transfer bodies is
devised on the premise that the rate of heat transfer to the nose
will be low if the local velocity gradient is low, while the rate of
heat transfer to the afterbody will be low if the local density is
low. The typical body that results from these design methods
consists of a spherical nose followed by an ogive curve and a
spherical nose followed by a cone and ogive curve.
Another method of reducing the drag and heat transfer
rates is to introduce spike in front of blunt body. Flow over
blunt body with spike at hypersonic speeds has been studied
extensively in last few decades and reported in Ref. [4-5].
Literature has been demonstrated that use of spike does reduce
the drag and heat transfer and amount of reduction depends on
shape and size of spike. Santos [8] introduced a typical body
with consisting of flat nose followed by a highly curved region
to reduce the heat transfer rates. Ahmed and Quin [6] have
attempted to explain the mechanism of drag reduction using the
results obtained from computations at Mach 6.
However, studies on blunt body with ogive or cone-ogive
as extension to blunt nose are limited. The emphasis of this
work is to compare all the geometries (ogive & cone-ogive) to
determine variation in heat flux with respect to drag. An open
source data was considered for judging the CFD results. As a
validation case, standard hyper-ballistic model (HB-2) was
simulated. Validation of computed results was demonstrated by
very good agreement between the computed aerodynamic
coefficient and those obtained from wind tunnel measurements.
The pressure and heat flux distribution along the model surface
were accurately matched within 5% error of experimental data.
NOMENCLATURE
Cd = drag coefficient
F = drag force, N
L = Ogive length, mm
M = Mach number,
q = heat flux, W/m²
R = cylinder radius, mm
Ro = ogive radius, mm
rn = nose radius, mm
V = velocity, m/s
ρ = air density, kg/m³
µ = air dynamic viscosity, N-s/m²
C = Sutherlands constant
SA = Spalart-Allmaras
BODY SHAPE DEFINITION
Two types of geometries were used for simulation: (1)
spherical nose followed by ogive blended surface and
cylindrical main body and (2) spherical nose followed by cone,
ogive blended surface and cylindrical main body. An open
source literature was considered for selection of geometry. The
details of the geometry used in present investigation are shown
in figure (1 & 2). In both cases the length (L) was kept constant
as 2600mm. The cylindrical body length and diameter were
taken as 4800mm & 1200mm respectively. The nose radius was
varied as 60mm, 70mm, 80mm, 100mm and 120mm. In second
case the cone angle was kept constant as 14°. The ogive radius
was formulated in such a way that it should be tangent to nose
as well as cylinder. As a validation case, HB-2 geometry was
selected. The model consists of spherical nose of 21mm radius,
a 70mm diameter cylindrical body and a trailing 10° flare.
The geometry and equations to find the tangency location
are as follows:

2. 2
1. Ogive geometry:
‫ݔ‬௢ ൌ ‫ܮ‬ െ ඥሺܴ௢ െ ‫ݎ‬௡ሻଶ െ ሺܴ௢ െ ܴሻଶ
‫ݔ‬௧ ൌ ‫ݔ‬௢ െ ට‫ݎ‬௡
ଶ െ ‫ݕ‬௧
ଶ
‫ݕ‬௧ ൌ
‫ݎ‬௡ሺܴ௢ െ ܴሻ
ሺܴ௢ െ ‫ݎ‬௡ሻ
2. Cone – ogive geometry:
ܴ௢ ൌ
‫ܮ‬ tan ߙ െ ܴ
tan ߙ ൈ tan
ߙ
2
‫ݔ‬ଵ ൌ ‫ݔ‬௢ െ ‫ݎ‬௡ ܿ‫ݏ݋‬ሺ90 െ ߙሻ
‫ݕ‬ଵ ൌ ‫ݎ‬௡ sinሺ90 െ ߙሻ
‫ݔ‬ଶ ൌ ‫ܮ‬ െ ܴ௢ sin ߙ
‫ݕ‬ଶ ൌ ሺ‫ܮ‬ െ ܴ௢ sin ߙሻ tan ߙ
COMPUTATIONAL METHODOLOGY
Three dimensional simulations were performed using
commercial software CFDExpert™ adopting steady, explicit
solver and Spalart-Allmaras(SA) as turbulence model. The use
of turbulence model has been arrived at after necessary grid
independence tests, convergence history, and obtaining good
comparison with the experimental results reported in Ref. [1].
The first step is surface grid generation along the model
surface. Then, is the blocking of the domain and finally, comes
the grid generated inside each block. Since we are not ignoring
viscosity a much finer grid is required near the surfaces. Also, a
finer grid is required in the block, which may contain shock
waves, flow separation, or other high flow gradient region as
shown in figure (3).
The location of block interfaces is also very important. In
this work, the blocks were structured in the stream wise
direction. For blocking of the domain, one needs to first
estimate different flow phenomena and the complexity of the
body geometry, which may be encountered. Then, the block
interfaces are located. On the other hand, for a more accurate
application of the wall boundary conditions and the flow
solutions in each block, it may be required to increase the
number of nodes and the grid lines especially in the direction
perpendicular to the wall. In each block, the boundary
conditions and the information received from the neighboring
blocks affect the flow solution. Thus, any error related to the
transfer of information within the blocks directly affects the
solution in each block, the overall solution and its convergence.
Also, other internal information of each block, such as the
number of nodes and their arrangement, the CFL number and
the artificial viscosity coefficient, etc. has to be known before
the flow solution is performed.
In this work, using a simple and suitable procedure, we
start from the first block at the nose which contains the
upstream inflow information, and pass through the chain of the
blocks until we reach the last one located at the end of the body,
containing the outflow information. The laminar sub-layer also
called the viscous sub-layer is the region of a mainly-turbulent
flow that is near a no-slip boundary and in which the flow is
laminar. The existence of the laminar sub-layer can be
understood in that the flow velocity decreases towards the no-
slip boundary. Because of this, the Reynolds number decreases
until at some point the flow crosses the threshold from
turbulent to laminar. To accurately predict the laminar sub-layer
the first element size close to wall is very important.
The first element size close to the wall is equal to 6
microns chosen to give y+ value of about 2.0. The hypersonic
shock wave presence makes it difficult to establish the y+ with
Figure 1
Figure 2
Figure 3: Mesh of Launch vehicle with 21 blocks & 6.5 lakh cells

3. 3
the same value over the entire model. It may be important to
remember that the y+ parameter is calculated like Reynolds
number at the first cell near the wall. This value is normally
calculated by the code. This equation includes density ૉ‫ܟ‬,
Velocity ࢜࢝, height of first cell ࢎ࢝ and viscosity ࣆ࢝.
‫ܡ‬൅ ൌ
࣋࢝࢜࢝ࢎ࢝
ࣆ࢝
GOVERNING EQUATION
The governing equations for steady compressible viscous
flow are as follows:
1. Mass Conservation:
݀
݀‫ݐ‬
ශ ߩܸ݀ ൅ ඾ ߩ݊ሬԦ݀‫ݏ‬ ൌ 0
2. Momentum Conservation:
݀
݀‫ݐ‬
ශ ߩ‫ݑ‬ሬԦܸ݀ ൅ ඾ ߩ‫ݑ‬ሬԦ݊ሬԦ݀‫ݏ‬ െ ශ ߩ݂Ԧ݀‫ݒ‬ െ ඾ ܲሬԦ݀‫ݏ‬ ൌ 0
3. Energy Conservation:
݀
݀‫ݐ‬
ශ ߩ݁௧ܸ݀ ൅ ඾ ߩ݁௧݊ሬԦ݀‫ݏ‬ െ ශ ‫ݑ‬ሬԦ. ݂Ԧ݀‫ݒ‬ െ ඾ ‫ݑ‬ሬԦ. ܲሬԦ݀‫ݏ‬
൅ ඾ ‫ݍ‬Ԧ . ݊ሬԦ݀‫ݏ‬ ൌ 0
The formula integrated into solver to calculate heat flux is as
follows:
‫ݍ‬௧௢௧௔௟
ᇱᇱ
ൌ ሺ‫ݍ‬௟௔௠௜௡௔௥
ᇱᇱ
൅ ‫ݍ‬௧௨௥௕௨௟௘௡௧
ᇱᇱ
ሻ. ݊ො
Where,
‫ݍ‬௟௔௠௜௡௔௥
ᇱᇱ
ൌ െሺ‫ܭ‬௔௜௥. ‫ܶ׏‬ሻ௪௔௟௟
‫ݍ‬௧௨௥௕௨௟௘௡௧
ᇱᇱ
ൌ ሺ
െߤ௧ܿ௣
ܲ‫ݎ‬௧
ሻ‫ܶ׏‬௪௔௟௟
Where,
‫ܭ‬௔௜௥,௪௔௟௟ ൌ ‫ܭ‬௢ ൬
ܶ
273
൰
ଷ
ଶൗ
൬
273 ൅ ‫ܥ‬
ܶ ൅ ‫ܥ‬
൰
T – Nearest cell – centre temperature
C - Sutherlands Constant = 110.3
‫׏‬T୵ୟ୪୪ - Temperature gradient
TURBULENCE MODELING: SPALART-ALLMARAS
To overcome limitations of algebraic models, an eddy
viscosity transport equation model has been implemented.
Baldwin and Barth discovered this class of one equation
models, proposed originally by Nee and Kovasznayin in the
sixties. The SA model has been chosen due to the satisfactory
results obtained over a wide range of flows and due to its
numerical properties. In this model a step by step procedure is
used to develop the transport equation for flows with increasing
complexity. Moreover this one-equation model naturally takes
history effects into account. Generally any transportable scalar
quantity, like eddy viscosity, subject to the conversion laws is
transported according to the following equation, which is the
basic equation for SA model:
஽ி
஽௧
ൌ
డி
డ௧
൅ ሺ‫.ݑ‬ ‫׏‬ሻ‫ܨ‬ ൌ ‫݊݋݅ݏݏݑ݂݂݅ܦ‬ ൅ ܲ‫݊݋݅ݐܿݑ݀݋ݎ‬ െ
‫݊݋݅ݐܿݑݎݐݏ݁ܦ‬
BOUNDARY CONDITIONS
Once a discrete computational domain has been obtained,
the boundary conditions must be specified before applying the
solution algorithm. The boundaries are those domain meshes
that serve to close the computational domain, thereby making it
finite. For the model these are the farfield (sides of the box)
domains and the surface mesh representing the model surface.
Specifying the conditions at these boundaries provides the
solver (the computer code that executes the solution algorithm)
with information about the possible fluxes across the
boundaries. For this model there are four different types of
boundary conditions: farfield, viscous isothermal wall, inflow
(flux across a boundary into the computational domain), and
outflow (flux across a boundary leaving the computational
domain). A farfield boundary condition establishes the flow
field parameters for the problem. It provides information about
the flow (velocity, Reynolds number, etc) in the form of net
system fluxes across its boundaries. A wall boundary condition
indicates that there is a no slip (zero velocity) condition
enforced on fluid particles immediately adjacent to the surface.
RESULT AND DISCUSSION
We considered Mach number 8 and flight altitude of 20 km
for simulations and a uniform 300K wall temperature was
specified. Grid independence study was done for optimizing the
solution accuracy and solution run time. Several trial runs were
carried out to find the first cell distance close to the wall. Once
the grid was finalized, all meshes were run with same boundary
conditions to determine variation in flow structure and other
parameters.
VALIDATION
Before simulating the flow around launch vehicle, it is
necessary to evaluate performance of solver. The fluid flow
patterns and characteristics obtained from our simulations are
in good agreement with available literatures. We compared our
numerical results with results of Robinson and Hannemann[13]
for validating results of HB-2 model. Figure (4) shows
comparison of present results with Robinson and
Hannemann[14] for pressure & heat flux distribution. Drag
coefficient obtained from present numerical simulation were
within 5% error of experimental results given in Robinson and
Hannemann[14].

4. 4
EFFECT OF VARIATION IN GEOMETRY
As shown in the figure (5), a strong bow shock is formed
in front of the nose. Downstream of the bow shock a thin zone
is formed where magnitudes of the velocity component are still
characterized by their magnitude in the uniform upstream
region, but the temperature, pressure & density are
considerably greater than they are in the free stream. This
increase in pressure & temperature leads to large drag &
heating rates. As the nose radius was increased, there was
considerable decrease in pressure, temperature, heat flux on the
model surface. Also the expansion waves formed at the leeside
were clearly seen in figure. An open source data was
considered for comparison with computational results. The heat
flux distribution contour of the body is as shown in figure (6). It
can be seen that the high heat flux not formed at centre of nose.
It can be concluded from figure (7) that high heat flux region is
formed only at the nose section of body & very less heat flux is
observed on the cylindrical portion. So as far as design part is
concerned much care is to taken of nose region. The pressure
and heat flux distribution along the surface is as shown in
figure (8), (9), (10) & (11). The variation in maximum heat flux
and drag coefficient observed in different geometries is shown
in figure (12).
Figure 4: Comparison of Pressure & Heat flux distribution along
the surface of HB-2 model
Figure 5: Bow shock formation in front of nose of ogive & cone-
ogive body
Figure 6: Heat Flux distribution contour on the surface of
ogive & cone-ogive body
Figure 7: Heat Flux distribution on model surface
Figure 8: Pressure distribution plot along the surface of
ogive body (Nose section)
Figure 9: Heat Flux distribution plot along the surface of
ogive body (Nose section)
Figure 10: Pressure distribution plot along the surface of
Cone-ogive body (Nose section)

5. Figure 11: Heat Flux distribution plot along the surface of
Cone-ogive body (Nose section)
CONCLUSION
The objective was to determine the drag coefficient and
heat flux on model surface. In this analysis, nose & ogive
radius were varied keeping the length constant. It is observed
from results that
1. Heat flux considerably decreased with increase in nose
radius in both the cases ogive as well as cone
be said that character of heat transfer is a manifestation of
two characteristics. The increase in stand-off distance and
Figure 12: Comparison of Drag coefficient and Maximum
Heat Flux of Ogive & Cone-Ogive bodies
5
along the surface of
The objective was to determine the drag coefficient and
heat flux on model surface. In this analysis, nose & ogive
radius were varied keeping the length constant. It is observed
creased with increase in nose
radius in both the cases ogive as well as cone-ogive. It can
be said that character of heat transfer is a manifestation of
off distance and
corresponding reduction in thermal gradient
leads to significant reduction in the stagnation point heat
transfer.
2. Less heat flux values were observed in case of cone
case as compared to ogive case.
3. Drag coefficient observed in cone
compared to ogive case, though not much effect was
observed with variation in geometry
ACKNOWLEDGMENTS
The authors wish to acknowledge guidance of Prof
Shevare, IIT Bombay during the study and CEO Zeus Numerix
for providing the resources for carrying out the study.
REFERENCES
1. Mattew, Robinson, and Klaus, Hanemann, “Short Duration
Force Measurements in Impulse Facilities,” German Aerospace
Centre (DLR), Bunsenstrasse 10, Gottingen, 37073, Germany,
2004.
2. Don Gray, J., Earl Lindsay, E., “Force Tests of Standard
Hypervelocity Ballistic Models HB
10”, NTIS, AD412651.
3. Birch, T.J., Prince, S.A., Ludlow, D.K., Qin,N., “The
application of parabolised Navier
hypersonic flow problems”, AIAA2001
4. Meneses, V., Saravanan, S., and
tunnel study of spiked aerodynamic bodies flying at hypersonic
Mach numbers,” Shock Waves 12,2004, pp. 197
5. Mehta, R. C., “Numerical investigation of viscous flow over
a hemisphere cylinder,” Acta Mechanica, Vol. 128, 1998,
49-58.
6. Ahmed, M. Y. M., and Qin, N., “D
aerodisks for hypersonic hemispherical bodies,” Jr. of space
craft and Rockets, Vol.47, No.1, pp. 62
7. A. Fiala, R. Hiller, S. G. Mallinson and H. S. Wijesinghe,
“Heat transfer measurement of turbulent spots in a hypersonic
blunt-body boundary layer,” Jr. of Fluid Mechanics, 2006, Vol.
555, PP. 81-111.
8. Wilson F. N. Santos, “A Numerical study of Drag and Heat
Transfer to Blunt nose shapes in Rarefied Hypersonic flo
24th International Congress of the Aeronautical S
Comparison of Drag coefficient and Maximum
Ogive bodies
corresponding reduction in thermal gradient in this region
leads to significant reduction in the stagnation point heat
Less heat flux values were observed in case of cone-ogive
case as compared to ogive case.
Drag coefficient observed in cone-ogive case was less as
though not much effect was
observed with variation in geometry.
s wish to acknowledge guidance of Prof G. R.
IIT Bombay during the study and CEO Zeus Numerix
for providing the resources for carrying out the study.
Mattew, Robinson, and Klaus, Hanemann, “Short Duration
Force Measurements in Impulse Facilities,” German Aerospace
Centre (DLR), Bunsenstrasse 10, Gottingen, 37073, Germany,
Don Gray, J., Earl Lindsay, E., “Force Tests of Standard
ocity Ballistic Models HB-1 and HB-2 at Mach 1.5 to
Birch, T.J., Prince, S.A., Ludlow, D.K., Qin,N., “The
Navier-Stokes solver to some
hypersonic flow problems”, AIAA2001-1753.
Meneses, V., Saravanan, S., and Reddy, K. P. J., “Shock
tunnel study of spiked aerodynamic bodies flying at hypersonic
Mach numbers,” Shock Waves 12,2004, pp. 197-204.
Mehta, R. C., “Numerical investigation of viscous flow over
a hemisphere cylinder,” Acta Mechanica, Vol. 128, 1998, PP.
Ahmed, M. Y. M., and Qin, N., “Drag reduction using
aerodisks for hypersonic hemispherical bodies,” Jr. of space
craft and Rockets, Vol.47, No.1, pp. 62-80, 2010.
A. Fiala, R. Hiller, S. G. Mallinson and H. S. Wijesinghe,
ment of turbulent spots in a hypersonic
,” Jr. of Fluid Mechanics, 2006, Vol.
Wilson F. N. Santos, “A Numerical study of Drag and Heat
Transfer to Blunt nose shapes in Rarefied Hypersonic flow”,
24th International Congress of the Aeronautical Sciences, 2004.