Simulation of Subsonic Wing of Cessna 182 Skylane
Group Project Report
By:
Group 8
Dwiki Ananda Classirio (13620064)
PramudyaVito Agata (13620076)
Aerospace Engineering Major
Faculty of Mechanical and Aerospace Engineering
Bandung Institute of Technology
2023
Content
Contents
Content ....................................................................................................................................... 2
Chapter 1 .................................................................................................................................... 3
Introduction ............................................................................................................................ 3
1.1 Background .................................................................................................................. 3
1.2 Purpose......................................................................................................................... 3
Chapter 2 .................................................................................................................................... 3
Basic Theory .......................................................................................................................... 3
2.1 Computational Fluid Dynamics (CFD) ........................................................................ 3
Chapter 3 .................................................................................................................................... 5
Subsonic Wing Simulation Procedure.................................................................................... 5
Chapter 4 .................................................................................................................................. 14
Result and Analysis .............................................................................................................. 14
4.1 Result.............................................................................................................................. 14
4.2 Analysis .......................................................................................................................... 19
Chapter 5 .................................................................................................................................. 22
Conclusion and Recommendation ........................................................................................ 22
5.1 Conclusion ................................................................................................................. 22
5.2 Recommendation ....................................................................................................... 22
Chapter 1
Introduction
1.1 Background
The problems regarding fluid dynamics calculations are increasing in complexity over the
years. To be able to solve the ever increasing complexity of the problems, computational fluid
dynamics is required to calculate the present problems. Because of the need to understand the
capabilities and workflow of computational fluid dynamics, the final task will be about
subsonic wing simulation in ANSYS.
1.2 Purpose
The purpose of the creation of this report are:
1. Identify the flight performance and design of Cessna 182 Skylane Aircraft.
2. Conduct a computational fluid dynamics simulation to obtain some aerodynamic
coefficients
3. Compare the result of simulation to the semi-analytic calculation using the software
Xflr 5.
Chapter 2
Basic Theory
2.1 Computational Fluid Dynamics (CFD)
The usage of CFD is expanded to the outside of aeronautics scope. Several cases and design
is solved using it. For example, in automotive design. The awareness of aerodynamic effect
to the vehicle has encouraged the engineers to find the optimization of design in order to
obtain the optimum aerodynamic effect to the model and the design at overall.
CFD use numerical approach in order to analyze the fluid mechanics and solve the problems
which is involved the fluid flow. It uses computer to calculate the simulation of the fluid flow
and its interactions with the surfaces or something like boundary condition. CFD also offer
the advantages which wind tunnel never make it possible before. However, the future
advancement of fluid dynamics will keep balance of theory, experiment, and computational
approach. By this case, CFD helps the engineers to interpret and understand the results of
theory, experiments, and vice versa.
In physics, CFD is based on governing equations of fluid dynamics, which is consist of
continuity, momentum, and energy equations. These equations is referred to these basic of
fluid dynamics: Conservation of mass, Newton’s 2
nd law and conservation of energy.
In this case, the CFD simulation tools use ANSYS ICEM CFD and ANSYS FLUENT. The
software using solver based on Reynolds Average on Navier Stokes (RANS). It is a set of
time-averaged equation in Navier-Stokes Equation as it shown on this formula
Chapter 3
Subsonic Wing Simulation Procedure
The simulation will use the wing of a Cessna 182 Skylane aircraft. The aircraft is a 4 seater,
single engine propeller aircraft, with a high wing configuration and a non-retractable landing
gear.
Figure 3.1 Piper Pa-18 Super Cub
There is given data of the Piper PA-18 Super Cub:
Table 1. Piper PA-18 Super Cub’s Aircraft Data
Wing Geometry
Semi Span Area (m)
7.32
Semi Span (m)
5.46
Chord at Tip (m)
1.63
Chord at Root (m)
1.09
Tapered Wing Span (m)
3.245
Airfoil
NACA 2412
Flight Performance
Maximum Velocity (m/s)
68.33
Cruise Velocity (m/s)
60.278
Cruise Altitude (m)
3100
MTOW (kg)
1.338
Altitude (m)
Pressure (Pa)
Temperature (K)
Density (kg/m3)
Dynamic Viscosity (kg/m.s)
Atmospheric Conditions
3100
69681.7
268.338
0.904637
1.71150 x 10-5
In this case, there is a conduction of simulation of subsonic wing’s aerodynamic of Cessna
182 Skylane using ANSYS FLUENT. This report is aimed for knowing the aerodynamic
forces which occurs on the aircraft’s wing such as lift coefficient, drag coefficient, moment
coefficient, and also the contours for pressure along the chord of the wing.
Before starting the simulation we need to first build the geometry of the wing. The wing uses
the NACA 2412 airfoil, thus we need to obtain the airfoil curves form a source for example
website called Airfoil Tools.
Figure 3.2 Airfoil Coordinate’s Browser
After obtaining the curves coordinates, we need to multiply the coordinates with the length of
the wing chord at root and tip. The chord at root 1630 mm in length while the tip is 1090 mm
in length. To acommodate curve transfer to SOLIDWORKS we need to specify the x,y,z
coordinates of the curve. Because the curve is on the x,z plane and the spanwise direction is on
the y axis the excel will be as follows.
Table 2 Curve Coordinates
Coordinates for Root
x
1630
1548.5
1467
1304
1141
978
815
652
489
407.5
326
244.5
163
122.25
81.5
40.75
20.375
0
20.375
40.75
81.5
122.25
163
244.5
326
407.5
489
652
815
978
1141
1304
1467
1548.5
1630
y
z
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18.582
33.904
61.125
84.434
103.668
118.012
127.14
128.444
125.021
118.338
107.743
91.769
80.848
67.319
48.737
35.045
0
-26.895
-37.001
-49.063
-56.398
-61.125
-66.83
-68.949
-68.786
-67.156
-61.94
-54.442
-44.988
-34.882
-24.45
-13.366
-7.824
0
Coordinates for Tip
After the calculations in excel the we can save the excel file as .txt file in order to transfer the
coordinates into SOLIDWORKS. We can trasnfer the file by usng the Curve Feature and the
click the curve through xyz option.
Figure 3.3 Curve Feature
Figure 3.4 Curve Input in SOLIDWORKS 2021
After transferring the curve we can use the lofted boss/ base feature to fill the volume between
the curve to produce the wing geometry.
Figure 3.5 Solid body of half model of wing of Cessna 182 Skylane
After the model geometry ready, the next step is meshing process. At first, there is a
computational domain which is covered the wing. There will be Inlet (where the flow get into
the fixed control volume (CV), outlet (fluid flow outlet), Farfield (an imaginary boundary
which is not affected by the flow interaction near the surfaces), and symmetry (a part which
represent the other side of the mesh). Before that, the geometry should be downscaled in order
to comply the units of geometry and the software (into meter) by scale at factor 0.001. Then,
the setting of unit will be changed into meters. For the domain geometry of Cessna 182
Skylane, the computational domain will be defined based on following configuration
Table 3 Computational Domain geometry points
X
-10.92
-10.92
21.84
21.84
Z
10.92
-10.92
10.92
-10.92
Using transform geometry feature and translate with Y offset about 16.38 m, the box of
computational domain will appear once these squares is connected using line each other as it
shown in this Figure.
Figure 3.6 Computational Domain
After defining the computational domain, the meshing definition process will be conducted.
The simulation calculation process is depended on computational domain’s size. Bigger
computational domain will increase the mesh element number. It is recommended in order to
get better result as long as it still definitive.
In mesh definition process, the subsonic wing will use 32 of value of “max element” with
maximum global mesh size is 0.05 for all part which is subjected at the wing surface. It is
also be equipped with prism layers. In other hand, there will be 0.5 for inlet, outlet, farfield,
and symmetry. After that, the density at the leading edge and trailing edge of the wing is
defined as 0.02. the mesh model use “prism meshing” using 10 layers.
After define the mesh parameters, compute it using “Tetra/mixed” and mesh method of
Robust (Octree). After computing mesh has done, it gives approximately 1,300,000 million of
mesh elements in the mesh volume.
Figure 3.7, 3.8, and 3.9 Meshing Results
Now, the mesh is ready for simulation. Then, pick ANSYS FLUENT as output solver and
create the boundary condition where the part on the wing surfaces as wall, the farfield, inlet
are acting as velocity inlet, the fluid act as fluid, outlet act as outflow. Then, the data is able
to be inputted with 3D grid dimension.
The simulation is conducted using ANSYS FLUENT 2019 R3 in 3D. At first, launch ANSYS
FLUENT. Then, read the mesh from previous steps. The solver type is pressure-based and
steady.the viscous model is Spalart-Allmaras, one-equation model that solves a modelled
transport equation from kinematic eddy turbulent viscosity. The fluid is defined as same as
the air condition during cruise. The boundary condition is defined based on reference values
on previous table.the inlet and farfield will be defined with desired air velocity based on
reference values.
In reference values, the area use half of Cessna 182 Skylane. Then, the density, pressure,
temperature, and viscosity is set up for the properties on cruise altitude of the aircraft
(3100 m) based on ISA calculator. Since there is not any heattransfer, the enthalpy must be
zero. Then, use the chord length to be the same in length column. Fill the velocity column
with the aircraft cruise speed.
Then, set the initialization using standard method, compute from inlet, with reference frame
to cell zones. Then, prepare the report plots to get the aerodynamic coefficient of lift, drag,
and moment.
Because we need to include angle of attack into the simulation, we need to include the velocity
on the x axis and the z axis. The table below shows the velocity value with different of attack.
Angle of Attack
-8
-4
0
4
8
12
16
Table 4 Computational Domain geometry points
Velocity Vectors
Velocity (X) in m/s
Velocity (Z) in m/s
59.69118
-8.38905
60.13097
-4.20477
60.2778
0
60.13097
4.20477
59.69118
8.38905
58.96059
12.5325
57.94274
16.6115
The values on the table will be inserted into the boundary conditions for velocity and farfield to
replicate the effect of angle of attack on the wing.
Figure 3.10 Reference Value Setup
Figure 3.11 Iteration Process has converged
At converged point, the calculation is nearly stable. The stability criteria for turbulence model
of Spalart-Allmaras is 10 -7 for nut and 10^-3 for the continuity. The stability of data results
imply that the method is applicable for this case. It also capable for post-processing data. The
post-processing will show the results of simulation, where in this report: static pressure
contour in xz-plane, and how does the wing obtain lift, drag, and moment coefficient. The
tools for post processing result will be shown in graphic contour and reports forces.
Chapter 4
Result and Analysis
4.1 Result
For result, these are figures of graphic contour of the post-processing. In this report, the postprocessing result shows the contour of Piper PA-18 Super Cub’s wing during angle of attack
(AoA) on zero degree and at 12 degrees. The values for aerodyamics coefficient is listed as
below.
Table 5 Aerodynamic Coefficient From Simulation
AoA
CL
CD
CM
-8
0.0348891
0.012811834
-0.02310574
-4
0.1497782
0.014529526
-0.03003469
0
0.3395564
0.015567217
-0.03696364
4
0.5840564
0.031347217
-0.04381111
8
0.8015564
0.045927217
-0.05062341
12
1.0126564
0.062711217
-0.05741412
16
1.1260564
0.081527000
-0.06421412
The contour below shows the static pressure, total pressure, and velocity magnitude.
Figure 4.1 static pressure (α=0°)
Figure 4.2 Absolute pressure (α=0°)
Figure 4.3 Velocity Magnitude (α=0°)
Figure 4.4 velocity vector at wing surface (α=0°)
Figure 4.5 Static Pressure (α=16°)
Figure 4.6 Total Pressure (α=16°)
Figure 4.7 Velocity magnitude (α=16°)
Figure 4.8 Velocity Vector (α=16°)
4.2 Analysis
After get calculated projection of value of CL and CD, there is comparison between CFD
simulation and the data on XFLR5 on figure . The Analysis method which is used in XFLR5
is Vortex Lattice Method (VLM). Due to its limitation on detect the separation flow on high
angle of attack, VLM can not display the maximum value of CL before the wing experience
stall.
Table 6 Simulation Results
AoA
-8
-4
0
4
8
12
16
Simulation
CD
0.012811834
0.014529526
0.015567217
0.031347217
0.045927217
0.062711217
0.081527000
CL
0.0348891
0.1497782
0.3395564
0.5840564
0.8015564
1.0126564
1.1260564
CM
-0.0231057
-0.0300347
-0.0369636
-0.0438111
-0.0506234
-0.0574141
-0.0642141
Table 7 XFLR 5 Results
AoA
-8
-4
0
4
8
12
16
CL
0.038057462
0.162895635
0.368970427
0.634405178
0.870551439
1.099755243
1.222978102
XFLR5
CD
0.018989103
0.015516993
0.016730125
0.03343911
0.048886757
0.06665106
0.08655100
CM
-0.0242396
-0.031409
-0.0385783
-0.0456617
-0.058599
-0.063729
-0.069139
Figure 4.10 Coefficient of Lift (CL) vs Alpha
CL vs AoA
1.4
1.2
1
CL
0.8
0.6
Simulations
0.4
XFLR5
0.2
0
-10
-5
0
5
10
15
20
AoA
Figure 4.11 Coefficient of Drag(CL) vs Alpha
CD vs AoA
0.1
0.09
0.08
0.07
CD
0.06
0.05
XFLR5
0.04
Simulation
0.03
0.02
0.01
0
-10
-5
0
5
10
15
20
AoA
Figure 4.12 Coefficient of Moment (CM) vs Alpha
CM vs AoA
0
-10
-5
0
5
10
15
20
-0.01
-0.02
CM
-0.03
-0.04
SIMULATION
-0.05
XFLR5
-0.06
-0.07
-0.08
AoA
For error analysis, the error for each angle of attack will be calculated and will be averaged in
the tables below.
Table 7 CL Error
AoA
-8
-4
0
4
8
12
16
Simulation
0.0348891
0.1497782
0.3395564
0.5840564
0.8015564
1.0126564
1.1260564
CL
XFLR5
0.038057462
0.162895635
0.368970427
0.634405178
0.870551439
1.099755243
1.222978102
Total Error (%)
Error
-0.0832521
-0.0805266
-0.0797192
-0.0793638
-0.0792544
-0.0791984
-0.0792506
-8.0080713
Table 8 CD Error
CD
AoA
-8
-4
0
4
8
12
16
Simulations
0.012811834
0.014529526
0.015567217
0.031347217
0.045927217
0.062711217
0.081527
XFLR5
0.018989103
0.015516993
0.016730125
0.03343911
0.048886757
0.06665106
0.086551
Total Error (%)
Error
-0.32531
-0.06364
-0.06951
-0.06256
-0.06054
-0.05911
-0.05805
-9.98155
Table 9 CM Error
CM
A0A
-8
-4
0
4
8
12
16
Simulations
-0.02310574
-0.03003469
-0.03696364
-0.04381111
-0.05062341
-0.05741412
-0.06421412
XFLR5
-0.024239628
-0.031408981
-0.038578334
-0.045661703
-0.058598962
-0.063728962
-0.069138962
Total Error (%)
Error
-0.04678
-0.04375
-0.04185
-0.04053
-0.1361
-0.09909
-0.07123
-6.84772
According to the comparison data, the simulation result still has some error although
realtively small. This small error however is not within acceptable range and is
relatively not reliable to be used to calculate aerodynamic coefficient.
Chapter 5
Conclusion and Recommendation
5.1 Conclusion
After conduct the simulation using computational fluid dynamics, there are some conclusion
which is obtained on the writing of this report:
1. The flight performance of Cessna 182 Skylane has be mentioned in the chapter 3
2. The aerodynamic coefficient analysis is conducted on computational fluid dynamics
simulation with its following post-processing results on chapter 4.
3. The comparison results between simulation and semi-analytic software like XFLR5
gives realtively not accurate results due to realtively high error percentage.
5.2 Recommendation
In order to get better experience on simulation of subsonic wing, there is a recommendation
1. Conduct mesh convergence test to ensure how does the result of calculation is
convergence around an amount of mesh element
2. Find the most optimum mesh element to get better analysis result.
Reference
[1] Amalia, E. , Agoes M., "AE4015 Computational Aerodynamics: Structure Grid
Generation (TFI and Smoothing)" Bandung, 2022.
[2]Amalia, E. , Agoes M., "AE4015 Computational Aerodynamics: Week 11 UCAV
Simulation by Using Fluent" Bandung, 2022.
[3] Ansys Inc., ANSYS FLUENT Manual Version 16.1, 2015
[3] Airfoiltools.com Accessed April 28th 2022.