 Open Access
 Total Downloads : 467
 Authors : Satyaprakash, S. Senthilkumar, S. Dashlin Jeno
 Paper ID : IJERTV2IS60217
 Volume & Issue : Volume 02, Issue 06 (June 2013)
 Published (First Online): 04062013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Computational Studies Of Flow Field And Associated Aerodynamic Characteristics Of WingBody Configurations
Satyaprakasp , S. Senthilkumar2, S. Dashlin Jeno3
1Sc/Engr F, Aerodynamics & Performance Directorate (ARD&P), Aeronautical Development Agency (ADA), Bangalore
2Department of Aeronautical Engineering, Anna University, Chennai
3Nehru Institute of Engineering and Technology, Coimbatore
ABSTRACT
A Computational study is conducted to investigate flow field around a WingBody configuration. A WingBody model is created using CATIA V5 and Structured Grids were generated by ANSYS ICEM CFD. Numerical Analysis is done using ANSYS FLUENT solver. Different Grids are tested for Grid Independence Test to conclude that the solution is independent of further mesh refinements. Flow field was initialized with freestream values. Calculations were done with the three turbulence models such as Spalart Allmaras model, Realizable model and Stress Transport (SST) model. The three turbulence models were compared with experimental results. The prediction shows that CFD results provide acceptable agreement to experimental observations. Convergence was monitored in terms of Lift, Drag and Moment. Pressure distribution has been studied over the surface of the entire model. Chord wise Cp variation computed is compared with experimental data for 8 sections along the wing span. Adequacy of grid resolution was checked in terms of y+. The resulting y+ values were observed to be less than 1 at all the near body grid points. The surface streamline pattern for wing and different cross section are plotted to study the flow separation at wingbody junction.
NOMENCLATURE
Fluid Density
p Thermodynamic Pressure
Total Energy
H Total Enthalpy Per Unit Mass
, , Cartesian components of the velocity vectoru
Coefficient of Molecular Viscosity
Temperature
Coefficient of Thermal Conductivity
R Gas Constant
Turbulent Prandtl Number
Turbulence Viscosity
Molecular Viscosity
M Mach number
Angle of attack
Re Reynolds Number

INTRODUCTION
In 1980s, the researchers believed that Computational Fluid Dynamics is capable of simulating flow in complex geometries with simple physics or flow with simple geometries with more complex physics. But this is not true anymore, due to the development in computers and algorithms. CFD is widely accepted as a key tool for aerodynamic design. Reynolds Average Navier Stokes (RANS) solutions are a common tool, and methodologies like Large Eddy Simulation (LES) that were once confined to simple canonical flows, are moving to complex engineering applications. Many comparative studies have been carried out for different models to understand the capabilities of numerical solution over experimental solution. In this study, a WingBody model is studied and detailed comparisons are made between the computed and experimental results.

GOVERNING EQUATIONS
Fluent solves the governing equations of conservation of mass, momentum and energy for the flow of viscous, compressible and conducting fluids. For an arbitrary control volume V with differential surface area dS, the equations, in integral form, are written as
V S
V S
+ . = .
Where
= +
= +
=
= +
E
is the vector of conserved variables and
+
(U) = +
where is the coefficient of molecular viscosity.
The heat flux vector for a Newtonian fluid follow the Fouriers law. The components heat conduction flux are expressed as
+
= , = , =
0
+ +
+ +
(U) = + +
+ +
whereis the temperature and is the coefficient of thermal conductivity.
If the fluid is assumed to be thermally perfect ideal
+
+
gas and the closure is provided by the equation of state
are the inviscid and viscous flux vectors, respectively. The terms in energy flux are written as
= .
= .
= .
In these equations, represents the fluid density, p is thermodynamic pressure, is the total energy and H is the total enthalpy per unit mass and , , are the Cartesian components of the velocity vector u.
The viscous effects are represented by the shear stress tensor ( , , , , , , , , ) and the heat conduction vector q (= + +
. Here , , are the basis vectors in , ,
directions, respectively.
The fluid is assumed to be Newtonian. It is also assumed to satisfy Stokes hypothesis. With these assumptions, the components of the Shear Stress tensor may be written as
p = RT
linking the thermodynamic variables, T and p. T is temperature and R is gas constant.
Assuming further that the gas is calorically perfect, then the internal and total energy are given by
= + 2+2 + 2
2
and = +
where = , = , and = .
It is convenient to express the pressure in terms of conservative variables. Using the relations between total enthalpy, total energy and combining with the above definition of equation of state, we finally obtain the following expression relating pressure with the conservative variables
= 1 2+2+ 2
= 2 2 + + 2
3
2
The coefficient of molecular viscosity for a perfect gas is dependent on temperature. The dependent of
= 2 3 + +
= 2 2 + +
3
pressure is however weak.
The molecular viscosity can be obtained by Sutherland law given by
= 1.45×106 T3/2
T+110
Kg/m3
4. GRID GENERATION
Quadrilateral and hexahedral elements have
In the above expression, T is temperature of air in Kelvin (K).
For turbulent flows, and are replaced by + and
+ respectively, where is turbulence viscosity which is calculated using a turbulence model and is obtained from = . The turbulent Prandtl
number, for air flows is taken to be 0.9.

GEOMETRY
The basic planform characteristics of the model are depicted in Figure 1, including the position of the wing. The length of the model is 1192mm, span of the wing is 1171.29mm and the semispan of the wing is 585.645mm. The model is developed using CATIA V5. The half model of the aircraft is utilized for CFD simulation, because the configuration was symmetric, and this procedure could save file size and use less element number. This has the great advantage of faster and more economic processing time of CFD calculation as against CFD simulation employed for the whole aircraft model. Figure 2 shows the WingBody Aircraft model.
Fig 1. WingBody Planform
Fig 2. WingBody CATIA Model
been proved to be useful for finite element and finite volume methods, and for some application triangles or tetrahedral are preferred. Structured Grid is generated by using ANSYS ICEM CFD. ANSYS FLUENT operates on unstructured hybrid grids. Thus, structured grids are converted to unstructured grids and all the calculations in present study were done on grids with hexahedral elements. The grids were refined near the body surfaces to resolve the boundary layers. The initial height of hexahedral is 0.001mm to capture the shear effects. The size of coarse is ~7 million and fine grid is ~12million.
Fig 3.Surface grid of WingBody Configuration
Fig 4.Computational Domain Grid by using Multi Block type

Boundary conditions
Table 1 shows the flow conditions of the WingBody model. Figure 5 shows Boundary conditions applied in computational domain.
M
0.75
Re (based on mean
chord, L=0.1412m)
3×106
T
288.15 K
P
123200.98 N/m2
1.232o
Table 1. Flow conditions
Fig 5. Computational Domain with Boundary Conditions

RESULTS AND DISCUSSION

Grid Independence Tests
A general method for determining the most appropriate mesh configuration is a grid independence test, where different meshes are tested until the solution is independent of further mesh refinements, by matching the numerical results to bench mark tests and/or experimental data. This in itself is a timeconsuming process. Grid independence tests are performed to investigate the influence of grid refinement on the solution and corresponding results are presented here for two of the computational grids used. For this purpose, SpalartAllmaras turbulence model is used and the results are shown in figure 6 and table 2.
Fig 6.Grid convergence usingCpvs x/c at 0.150 of wing span section
Methods
CL
Experimental
1.230
0.5979
Numerical Solution
Coarse grid
1.230
0.36
Fine grid
1.230
0.6
Table 2.Grid convergence using CL vs at 0.150 of wing span section

Convergence Graphs
The convergence was monitored using the scaled residuals of the Lift coefficient and Drag coefficient. For different turbulence model, calculations were computed for 15000 iterations. The solution was converged when the residuals of the conserved variables no longer varied. The convergence history of coefficient of lift is shown in Figure 7 for different turbulence models.
Fig 7.Lift Coefficient versus Number of Iterations for different turbulence model

Wall Y+ Approach
Turbulence flows are significantly affected by the presence of walls due to the noslip condition resulting in large gradients in the solution variables in this viscosity affected region. y+< 5 is in the viscous sublayer, 5 < y+< 30 is in buffer region, 30 < y+< 300, which is fully turbulent portion.
Fig 8.Grid resolution (Near wall Y+) contours at M=0.75, =1.230
Figure 8 shows near wall Y+ contour of WingBody configuration. The Y+ values for the fine grid configuration is 1.09 corresponding to resolution in the viscous sublayer(y+<5), indicates adequate grid resolution.

Pressure Distribution
Pressure contour of WingBody configuration is shown in figure 9 at Mach Number
0.75 and Alpha 0.232 using Tecplot 360.
Fig 9.Pressure Contour at M=0.75, =1.230 using Tecplot 360 (SpalartAllmaras)

Pressure Coefficient vs Chord Ratio
Pressure coefficient variation with respect to chord ratio is calculated for various crosssections and compared with wind tunnel data. Experimental Results were compared with different turbulence models for 8 wing crosssections and is shown in figure 10(ah). Turbulence models include Spalart Allmaras, Realizable and Stress Transport (SST) Turbulence model.
Fig 10(a). Wing span section, y/b=0.150
Fig 10(b). Wing span section, y/b=0.239
Fig 10(c). Wing span section, y/b=0.331
Fig 10(d). Wing span section, y/b=0.377
Fig 10(e). Wing span section, y/b=0.411
Fig 10(f). Wing span section, y/b=0.514
Fig 10(g). Wing span section, y/b=0.638
Fig 10(h). Wing span section, y/b=0.847 Fig 10(ah).Comparison of computed Cp with
experimental data for different wing span sections
The computed Cp shows that three turbulence models gives reasonable good agreement with the experimental data. The results are plotted using Tecplot 360.

Lift Coefficient vs Alpha
Lift coefficient versus Angle of Attack () is compared between Experimental and numerical results. Table 3 shows the comparison of CL vs. for different turbulence models. SpalartAllmaras models, shows good match with experimental value, when compared to others.
Methods
CL
Experimental
1.230
0.5979
Numerical Solution Turbulence Model
Spalart Allmaras
1.230
0.6
kepsilon
1.230
0.568
komega SST
model
1.230
0.554
Table 3. Comparing CL versus with different turbulence model

Flow Separation
Flow separation study has been carried out for the model. Flow separations are visualised at Fuselage wing junction at low Angle of Attack (=1.230). Fig 11(ab) shows streamline pattern of the model. Fig 12(ac) shows the streamline pattern of different turbulent model at0.150 of wing span section. Flow separation are clearly captured in SpalartAllmaras and SST , when comparing Realizable
model. Results shows that flow separation can be minimized by providing fairing at Fuselagewing junction.
Fig 11(a). SpalartAllmaras model
Fig 11(b). Realizable model
Fig 11(ab).Streamline pattern comparison for different model at M=0.75, =1.230
Fig 12(a).SpalartAllmaras model
Fig 12(b). Realizable model
Fig 12(c). SST model
Fig 12(ac).Streamline pattern comparison for different model at 0.150 of wing span section



CONCLUSION
Flow field around a wingbody configuration is investigated by carrying out Reynolds Averaged NavierStokes (RANS) flow simulation. Results of calculation are presented for moderate angle of attack. The steady RANS turbulence provides acceptable agreement to experimental observations. SST clearly predicts the separation region near fuselagewing junction, when compared to realizable k. It is noted that the accuracy of the computed results are dependent on a number of solver variables such as mesh configuration, numerical schemes, convergence criteria, under relaxation factors and turbulence models employed.It is observed that for fluid problems with complex turbulent flow structures, e.g. separations, most steadyflow RANS turbulence models are able to predict the flow broadly to an agreeable extent. However, different flow regions have different best models for their flow prediction.
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