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A space launch vehicle, during its atmospheric flight, presents a variety of
aerodynamic problems for which solutions are to be obtained through analytical and
Referencetechniques. Generally, the problems are complex and three dimensional in nature
and quite often involve multi body interactions etc. Currently, a large amount of research
work is going on to develop a reusable launch system i.e. a vehicle which is capable of
launching into space more than once. This contrasts with expendable launch systems, where
each launch vehicle is launched once and then discarded. The orbiter, which includes the
main engines, and the two solid rocket boosters, are reused after several months of refitting
work for each launch. The external fuel drop tank is however discarded.
The present work can be carried out by using wind tunnel for conducting experiments
to know the flow past launch vehicles and to know the pressure distribution over the surfaces
or by using the commercial softwareâs for CFD applications. One such software Fluent is
used for this present problem. The benefits involved are the use of computer-based
computational fluid dynamics methods which will accelerate the design process, reduce
preliminary development testing, and help create reliable, high-performance designs of space
launch vehicles and their components. In addition to design verification and optimization,
CFD can be used to simulate anomalies that occur in actual space vehicle tests or flights to
fully understand the anomalies and how to correct them. The result is a more reliable and
trouble-free space vehicle. A booster rocket is either the first stage of a multi-stage launch
vehicle, or else a strap-on rocket used to augment the core launch vehicle's takeoff thrust and
payload capability. Boosters are generally necessary to launch spacecraft into Earth orbit or
beyond. Strap-on boosters are sometimes used to augment the payload or range capability of
jet aircraft.
For thorough understanding of the complex flow field around typical Space launch
vehicles at zero angle flight, axi-symmetric computational simulation of the flow field can be
made useful along with the Referencetesting. This can be done either by developing a code or
by available commercial CFD software. In the present study computation has been attempted
for flow over a typical SLV model with the commercially available software FLUENT 6.3.26
2. COMPUTATIONAL SETUP
2.1 Grid Generation
The grid for the typical SLV model was generated using the GAMBIT software.
Structured and unstructured grid was used for the analysis of the flow field around the model.
2.2 Grid Generation for Space Launch Vehicle Model
A structured grid was generated for 2D simulation of flow around the SLV model.
The grid was made very fine at the geometry surfaces and coarsens away from the body. The
overall domain was selected based on several iterations, boundary conditions and finally a
domain extending 5 times the major length of the SLV model (length L) ahead of the nose
center, 5 times the length to the center line of the geometry and five times length behind the
geometry was chosen. The extents of the domain were evaluated from inviscid simulation of
the problem. A total of 50,000 cells were used in the grid system. The grid system with
boundary conditions, in the vicinity of the geometry and a close up surface grid near main
body and strap-on nose regions respectively. In order to capture the shocks more accurately,
finer mesh cells were created near the surface of the model using appropriate edge mesh
distribution.
3. Journal of Mechanical Engineering and Technology (JMET)
ISSN 2347-3932 (Online), Volume 1, Issue 1, July
Fig. 1
Fig. 2 Grid cell distributions at the nose of the main body
Fig. 3
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Fig. 1 2D unstructured grid for complete body
Grid cell distributions at the nose of the main body
Fig. 3 2D structured grid for complete body
ISSN 2347-3924 (Print),
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Fig. 4 Close view of 2D structured grid for complete body
Firstly 2D unstructured grid was generated, total of 50,000 cells were used in the grid
system. Figures 1, 2, 3 & 4 show the grid system with boundary conditions, in the vicinity of
the geometry and a close up surface grid near main body and strap-on nose regions
respectively. In order to capture the shocks more accurately, finer mesh cells were created
near the surface of the model using appropriate edge mesh distribution. But when it is iterated
for solution in fluent, reverse flow was encountered. This resulted in change of grid.
Structured grid was generated with approximate No. of cells are 64500. This grid was
shown in Figure 4.The smallest size of grid cell chosen is 2.730508e-005. For this grid the
extent of outer domain for the front side is 0.25 times the length of the body and on the rear
side it is 5 times the length of the body, on the top side also it is five times length of the body.
When this grid was initialized for the simulation, this showed a positive trend and all the
residuals converged.
2.3 Solution Methodology Using Fluent
The solution method in FLUENT can be broadly divided into three parts namely: Pre
â processing, Solver and Post processing. Pre â processing of the problem was done in
GAMBIT as discussed in detail in the preceding sections. Once the problem is meshed and
the boundary conditions are specified the meshed geometry is then imported as a âmesh fileâ
into FLUENT.
FLUENT uses a control-volume-based technique to convert the following governing
equations as conservation of mass, conservation of momentum and conservation of energy to
algebraic equations that can be solved numerically. This control volume technique consists of
integrating the governing equations about each control volume, yielding discrete equations
that conserve each quantity on a control volume basis.
FLUENT has two solvers: Segregated solver and Coupled solver. Using either
method, FLUENT will solve the governing integral equations for the conservation of mass
and momentum, and (when appropriate) for energy and other scalars such as turbulence and
chemical species. In both cases a control-volume-based technique is used that consists of:
Division of the domain into discrete control volumes using a computational grid, Integration
of the governing equations on the individual control volumes to construct algebraic equations
for the discrete dependent variables such as velocities, pressure, temperature, and conserved
scalars and Linearization of the discretized equations and solution of the resultant linear
equation system to yield updated values of the dependent variables.
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The segregated solver is the solution algorithm in which, the governing equations are
solved sequentially (i.e., segregated from one another).
The coupled solver solves the governing equations of continuity, momentum, and
(where appropriate) energy and species transport simultaneously (i.e., coupled together).
Governing equations for additional scalars will be solved sequentially (i.e., segregated from
one another and from the coupled set) using the procedure described for the segregated
solver. Because the governing equations are non-linear (and coupled), several iterations of the
solution loop must be performed before a converged solution is obtained. Each iteration
consists of the steps outlined below:
Fluid properties are updated based on the current solution (If the calculation has just
begun the fluid properties will be updated based on the initialized solution).
The continuity, momentum, and energy and species equations are solved simultaneously.
Where appropriate, equations for scalars such as turbulence and radiation are solved
using the previously updated values of the other variables.
A check for convergence of the equation set is made. These steps are continued until
convergence criteria are met.
In both the segregated and coupled solution methods the discrete, non-linear
governing equations are linearized to produce a system of equations for the dependent
variables in every computational cell. The resultant linear system is then solved to yield an
updated flow-field solution. The manner in which the governing equations are linearized may
take an âImplicitâ or âExplicitâ form with respect to the dependent variable (or set of
variables) of interest.
2.4 Solution Methodologies For The Typical SLV Model
The steps of setting up a problem in FLUENT are discussed briefly: defining
geometry, importing and checking the grid, selection of solver formulation and equations to
be solved (laminar/turbulent/inviscid etc.), material properties, specification of operating and
boundary conditions, specification of numerical properties (under-relaxation factors, CFL
etc.) and initialization of variables. The criterion for convergence was in the order of 10-3
for
continuity, x, y and z velocities and 10-5
for energy calculation and turbulence quantities. The
residuals were monitored in the graphics window of FLUENT. In addition the net mass flow
rate was monitored for convergence. For all the cases iterations continued till the
convergence or near convergence were reached.
2.5 Solver Settings
Computations were carried out with double precision 2D models with steady,
coupled, explicit solver scheme. The viscous model chosen for the problem was the standard
Spalart âAllmaras model with turbulent intensity and viscosity ratio as inputs. Standard wall
functions were used for the near wall treatment of the flow.
2.6 Materials Selection
For the present simulations, Ideal gas condition was used. The ideal gas law for
compressible flows was used for air. Since the flow was dependent on temperature, the
Sutherland viscosity model with three coefficients was used. Sutherlandâs viscosity law
resulted from a kinetic theory by Sutherland (1893) using an idealized intermolecular-force
potential.
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2.7 Operating Conditions
The input of the operating pressure is of great importance when density with the ideal
gas law is being computed. The criteria for choosing a suitable operating pressure are based
on the Mach-number regime of the flow and the relationship used to determine density. For
the present case where ideal gas law is used and the flow Mach number is greater than 0.1 the
operating pressure is set to 101325.
2.8 Boundary Conditions
Pressure far field boundary condition was set for the inflow (surface facing the flow),
where it is need to specify the free stream static pressure and Mach number. Pressure outlet
boundary condition was set to the out flow (surface from which the flow leaves), where the
variable will be extrapolated from the interior cells. Wall boundary condition is assigned for
the model surfaces and domain boundary extents other than inflow and outflow.
2.9 Post processing
The simulation setup can be stored as case and data file. The auto save option can be
used to save the results of the iterations from step to step. The case file includes the
information for the grid, the boundary conditions and the solver settings. The data file stores
information about the data in each node of the cells. The contour plots, vector plots and the
surface data plots etc. of pressure, velocity and density etc. can be checked during the
solution process and at convergence. These plots can be saved as image files and the data
from the surface plots can be written on to a file and plotted. Points, lines, rakes and planes
can be created in the flow domain to analyze the properties at the desired locations. FLUENT
offers a very good range of post processing options which can be used to analyze the
computational data, compare computational results with the Referenceresults as desired.
For the present analysis points, lines and planes were used to analyze the properties at
the desired locations in the flow domain. Multigrid option was also used to reduce the
computational time.
Computations were performed to understand the flow field around a scaled down
model of a typical space launch vehicle with strapons. Computations using the commercially
available software FLUENT 6.3.26 were carried out for two dimensional and three
dimensional fully developed flows. A validation test was performed by referring to the same
type of model for the same Mach number.
3. RESULT AND DISCUSSION
Two dimensional computational simulations were carried out for studying the flow
field around typical space launch vehicle geometry at supersonic Mach number. The results
for the computations performed are discussed in detail in the following sections. The
computations were performed on a work station Core 2 Duo processor with a bus speed of
2.0GHz and a RAM of 2GB. Typical times taken for inviscid problem were 250 iterations per
hour and for viscous three dimensional problems were 150 iterations per hour. For all the
cases, an average 3000 iterations were performed until the desired convergences are obtained.
The inviscid analysis was performed for comparing the results obtained for viscous flows.
3.1 Validation of Computational Procedure
Verification and validation are the primary means to assess accuracy and reliability in
computational simulations. Several computational tests were performed on a typical space
7. Journal of Mechanical Engineering and Technology (JMET), ISSN 2347-3924 (Print),
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60
launch vehicle at a Mach number of 2 for verifying and validating the computational grid and
turbulence model that are going to be adopted for the present work.
Inviscid, laminar, S-A, standard k-Δ and standard k-Ï models were tested for
verifying the most suitable turbulence model for present case of a typical launch vehicle
configuration. The solver settings operational conditions, material properties, and boundary
conditions were set according to the present typical space launch vehicle problem. The
problem was iterated till the residuals of continuity, momentum, and energy converged to a
value of 10-3
and the scalars nut (SA) residuals converged to a value of 10-5
.
After importing this grid to Fluent, all the residuals show a converging trend and
matches with the Referenceresults. Hence this grid was tried for the selection of suitable
turbulent model. Trials were made for Inviscid, Laminar, K Epsilon, K Omega and SA
models.
For K Epsilon case Cp Vs X/L plot, as shown in Figure 6a, Cp distribution varies
from the Referenceresults of Reference and does not follow the trend. Density contours
captured are plotted in Figure 6b. The main body region density distribution is higher near the
nose and the shock formation near the nose of the booster is invisible.
For K Omega case Cp Vs X/L plot, as shown in Figure 7a, Cp trend near the main
body region is good when compared to the Referenceresults. But the Cp distribution near the
location of the booster is much higher when compared with Referencevalue as well as
numerical value. When density contours are observed, as given in Figure 7b, it can be clearly
visualized that near the booster shock wave in front of the booster is standing at a distance.
For SA method, Cp Vs X/L plot, as shown in Figure 8a, Cp trend near the main body
region is good when compared to the Referenceresults. Near the booster location, Cp
distribution is lesser than the Referenceresults but the nature of the curve is good. The
variation of the Cp distribution near the booster location peak with the Density contours are
given in Figure 8b, this contours gives the appropriate reasons for choosing it as the turbulent
model. One can clearly observe the shock wave near the nose cone of the main body, high
density region and near the booster also a shock wave can be visualized.
After the solution was obtained from the different models, the pressure coefficients on
the main body of the space launch vehicle were plotted and compared with the
Referenceresults from reference Scalabrin et al. It is observed that standard SA model with
appropriate turbulence specification method, turbulent intensity and turbulent viscosity ratio
is most suitable model producing approximate results as of the Referenceresults.
Figure 9 shows the comparison for Cp distributions obtained from the different
models. From this plot we can see SA model results match well with Referenceresults.
Spalart Allarmas method is chosen for the detail study, because of its simplicity.
. High density is attained at the nose of the main body, shock wave is observed near
the nose. Low density region near the boat tail. Circulation is observed near the booster nose.
Shock wave formation at the nose of the booster can be seen. The entire flow phenomenon is
visualized in these contours. Though flow behavior is captured through 2D simulations, Cp
distribution is not following the Referenceresults trend.
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ISSN 2347-3932 (Online), Volume 1, Issue 1, July -December (2013)
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Fig. 5 Pressure coefficient distributions on a vehicle core in a plane between two boosters for
Mach 2 and zero angle of attack Ref. Scalabrin et al
Fig. 6a Cp Vs X/L for K Epsilon case
Fig. 6b Density contours for K Epsilon case
-1
-0.5
0
0.5
1
1.5
0 0.5 1 1.5
Cp
X/L
Cp Vs X/L
K Epsilon Cp
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Fig. 7a Cp Vs X/L for K Omega case
Fig. 7b Density contours for K Omega case
Fig. 8a Cp Vs X/L for SA method
-1
-0.5
0
0.5
1
1.5
2
0 0.5 1 1.5
Cp
X/L
Cp Vs X/L
k Omega Cp
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5
Cp
X/L
Cp Vs X/L
SA Cp
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Fig. 8b Density contours for SA method
Fig. 9 Cp comparisons with the reference plot
4. CONCLUSION
Computational studies were carried out to get an understanding of the flow field
around typical space launch vehicle with strapons at Mach 2. Two dimensional simulations of
the flow field using FLUENT 6.3.26 were performed. SA turbulent model was adopted to
capture the flow field. Computations were validated through a simulation of flow field around
the similar geometry at a Mach number 2 by earlier investigators. After a good agreement
with reported results, simulation of the present case was carried out and compared with
available experiments.
The following important observations were made from the results obtained through
computations and experiments:
1. The basic flow structure around a typical launch vehicle with strapons was
captured through 2D computations.
-1
-0.5
0
0.5
1
1.5
2
0 0.5 1 1.5
Cp
X/L
Cp vs X/L
Ref plot
K Epsilon
K Omega
SA
Laminar
Inviscid
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2. Mach and density contours showed the bow shock wave structure, near the nose
cone of the main body and near the booster nose. Shock and boundary layer
interferences were observed near the booster nose.
3. Comparison of SA, k-Δ and k-Ï turbulence modeled viscous simulations around
the typical space launch vehicle showed that the SA model predicts well for the
flow field features of wall bounded shear flows.
4. A good comparison of computations and available Referenceresults were
achieved.
ACKNOWLEDGMENT
We first thank our âGODâ, the supreme power for giving us a good knowledge and
our parents for making us study in a renowned college we owe a great many thanks to my
colleagues and friends for their help and encouragement.
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