ESA 341: GASDYNAMICS
GROUP PROJECT
(Eppler 374)
LECTURER DR. KAMARUL ARIFIN
2008/2009
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Contents
Page
Project Objective 1
Project Committee 1
CFD Introduction 2
Gambit Methodology 2
Fluent Methodology and Analysis 5
Discussion 13
Water Table Experiment 14
Introduction 15
Observation & Calculation 16
Precaution 19
Comparison 19
Conclusion 20
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Objective
� To study the method of computational fluid dynamic (CFD) in analyzing the flow passing
through a model of certain shape under various circumstances.
� To obtain the shape of the shock wave by using water table method.
� To compare the water table analysis and CFD analysis.
Project Committee
Project Advisor Dr Kamarul Arifin B Ahmad
Project Manager Lim Kui Yuet
92248
Secretary Ng Hong Fai
92261
CFD Analyst Chan Ray Mun
92226
Tan Cheh Chun
92270
Fluid Dynamist Md Shazerin Amri B. Shahatshau
79781
Ng Kok Chian
92262
Shuaidah BT. Hanif
92267
Aerodynamicist Mohd Asmadi R. Fauzi @ Zaharia
92250
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CFD Introduction
Experimental data using closed loop wing tunnel to analyze the flow around an airfoil is costly
and complicated. Therefore, by using CFD (Computational Fluid Dynamics), we can calculated and
obtain similar results with a lower cost. Broadly, the strategy of CFD is to replace the continuous
problem domain with a discrete domain using a grid. Before we start the computations, we need to
create the mesh of the airfoil of our study:
Gambit Methodology
Creating the Mesh by using Gambit Software
First we import the vertex data for Eppler 374 airfoil into the software then we join the points
separately for upper and lower part to form a symmetrical airfoil. Next, we create the vertices for
the boundary according to the coordinates shown in Table A.
Label x-coordinate y-coordinate z-coordinate
A c 12.5c 0
B 21c 12.5c 0
C 21c 0 0
D 21c -12.5c 0
E c -12.5c 0
F -11.5c 0 0
G c 0 0
c=1.0m
Table A
Since the airfoil is in 2D form, so the z-coordinate is zero for all. After that, we join all the vertices to
form edges (AB, BC, CD, DE, EG, GA and CG) and circular arcs (AF and EF) for the boundary. After
creating the edges, we create the faces to be meshed. We created three faces: ABCGA, EDCGE and
GAFEG (subtracting the airfoil). When that is done, we proceed to meshing the edges following Table
B.
Create
vertices
Create
edges
Mesh
edges
Form
faces
Mesh
faces
Create
groups
Specify
Boundary
Types
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Edges Arrow
Direction
Successive
Ratio
Interval Count
AB Right to Left 0.96 100
GC Right to Left 0.96 100
ED Right to Left 0.96 100
AG Downward 0.94 70
BC Downward 0.94 70
EG Upward 0.94 70
DC Upward 0.94 70
Upper Airfoil Right to Left 1 70
Lower Airfoil Right to Left 1 70
AF Upward 0.968 70
EF Downward 0.968 70
Table B
The successive ratio chosen was meant to concentrate more mesh on the area around the airfoil,
which will give a better result of the flow around the airfoil. The successive ratio and interval count
for upper and lower airfoil is same since the Eppler 374 airfoil is symmetric. After that, we mesh the
faces (ABCGA, EDCGE and GAFEG ) since we need to analysis the whole airfoil.
Finally, we group the edges to form 3 groups as stated in Table C. Following by define the
boundary types (Wall for airfoil, Velocity Inlet for arc and Pressure Outlet for level).
Group Name Edges in Group
arc AF , EF
level AB , DE
out BC , CD
airfoil Upper and Lower Surface of
Airfoil
Table C
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This completed mesh was saved and exported into fluent for further analysis.
Completed Mesh
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FLUENT Methodology and Analysis
Following the instructions given to us, first we read the mesh, and then we defined the model as
followed :
Solver : Coupled, implicit, 2D, Steady, Absolute
Energy : By turning on the energy equation (uncheck energy equation for subsonic)
Viscous : Spalart-Allmaras
After that, we define the materials by choosing the default setting which is air and selecting
‘Ideal Gas’ (for supersonic, transonic) or 1.225kg/m3 (for subsonic) for density and ‘Sutherland’ for
Viscosity. For flows with Mach numbers greater than 0.1, an operating pressure of 0 is
recommended. Next we defined the Boundary Condition :
• For supersonic and transonic, “arc” selected under “zone” and “pressure-far-field” was selected
under “type”, the gauge pressure was set to 101325 Pa while Mach number was set to 0.8
(transonic flow), 2.0(supersonic flow). Also, X-component of flow direction was set to 1 and Y-
component of flow direction was set to 0.
• For subsonic, “arc” and “level” selected under “zone” and “Velocity Inlet” was selected under
“type”. Select Components from the Velocity Specification method, using free stream velocity
40m/s since the X-component =1 while Y-component=0
Set up
Grid
Define
Model
Select
appropriate
Material
Set up the
Operating
Condition
Define
Boundary
Condition
Set the
Solution
Control
Choose the
Discretisation
of the Flow
Equations
Define the
Monitor
Run the
Calculation
Analysis
Produce
Output
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The next step is to set the Under-Relaxation Factor for Modified Turbulent Viscosity to 0.9
(Larger under-relaxation factors will generally result in faster convergence. However, instability
can arise that may need to be eliminated by decreasing the under-relaxation factors).After that,
set the Courant Number to 5. The next step is to choose the discretisation of the flow equation.
Select Second Order Upwind for Modified Turbulent Viscosity The second-order scheme will
resolve the boundary layer and shock more accurately than the first-order scheme. Then, we
initialize the solution by selecting “arc” and pressing “Init”. Also, before running the calculations,
in order to see how the residuals vary with time step, we tick the check box for “Print” and
“Plot” for the residual and all the ticks for the item list under “Check Convergence” are removed.
After all are done, request 100 iterations and continuing until 1000 (for transonic, supersonic)
or request 100 iterations and continuing until 200 (for subsonic). Next, increase the Courant
Number to 20. The iteration ended until 1500 (transonic, supersonic) or 300 (for subsonic).
Mach number 0.115(subsonic)
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Mach number 0.8(transonic)
Mach number 2.0(supersonic)
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After calculation was done, we proceeded to plot the contours of static pressure, Mach number,
Velocity Magnitude and Velocity Vector.
Mach number 0.115(subsonic)
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Mach number 0.8(transonic)
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Mach number 2.0(supersonic)
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Discussion
The residual for supersonic would not converge below 1e-03. We could only get it to
fluctuate between the 1e-03 regions. The residual for transonic condition is even worse as it
fluctuates at the 1e-02 region. The residual plot for subsonic condition is the best. However, the
iterations give us a constant Cd, Cl, and Cm value for all flow cases.
As noticed in the velocity vector plot of transonic flow (M 0.8), the flow reversal is clearly
visible behind the shock near to the airfoil. Also, if noticed closely, the velocity is lower at the wall of
the airfoil. This is due to skin friction of the airfoil.
As expected, Eppler 374 is a chambered airfoil as it produces lift (from the positive Cl) even
at zero angle of attack.
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Water Table Experiment
The following flow chart represents the algorithm and steps used in the water table experiment.
Start
Pour water into the water table tank
Motor was turned on to 4.5Hz for 30s to allow
steady water flow established.
A small piece of paper was put on the water surface near
the starting edge of the tank.
Once the small piece of paper was released,
stopwatch was started.
When the small piece of paper reached the ending edge of the
tank, stopwatch was stopped.
The duration of travel of the small piece of
paper was recorded.
The distance between the starting edge and ending edge
of the tank was measured.
Airfoil was carefully placed on the centre of water
flowing region in the tank.
Photo was taken from the top of the airfoil.
The shape of the wave was observed.
End
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Introduction
1. The primary objective of the water table is to reveal the concept of lift, drag, and
streamlines of certain fluids.
2. To illustrate this, different shape of model will be put inside a closed channel with steady
water flow in it.
3. The model can be put in any orientation in the middle front of the tank so that the waved
generated will not be disturbed by reflected tank wall water wave.
4. A graph paper was put on the bottom of the transparent water tank in order to ease the
observation of the wave generated and also help to calculate shock wave angle.
Water
Pump Rotor
Sluice Gate
The water table
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Observation & Calculation
� Distance travelled by small piece of paper, d = 0.4m
1. Motor frequency = 4.5Hz
Number of data Time (s)
1 0.8
2 0.8
3 0.7
4 0.8
Time average: s775.04
7.038.0=
+×
Velocity, v =1
5161.0775.0
4.0 −= ms
2. Motor frequency = 6.52Hz
Number of data Time (s)
1 0.7
2 0.8
3 0.76
4 0.6
Time average: s715.04
6.076.08.07.0=
+++
Velocity, v =1
5594.0715.0
4.0 −= ms
3. Motor frequency = 11.49Hz
Number of data Time (s)
1 0.7
2 0.6
3 0.6
4 0.7
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Time average: s65.04
26.027.0=
×+×
Velocity, v =1
6154.065.0
4.0 −= ms
4. Motor frequency = 16.50Hz
Number of data Time (s)
1 0.7
2 0.6
3 0.6
4 0.5
Time average: s60.04
5.026.07.0=
+×+
Velocity, v =1
6667.060.0
4.0 −= ms
The following photos correspond to the four different motor frequencies shown above.
1. 4.5Hz
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2. 6.52Hz
3. 11.49Hz
4. 16.50Hz
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Precaution
1. To avoid wave generated is being disturb by the reflected wave that generated through the
wall, the test object have to be placed at the middle front section of the tank.
2. Motor frequency should not adjust such that the bubble appears in the water tank.
3. In order to get a sharp photo of the flow, the focal plane of the camera should be the water
surface and not the airfoil upper surface.
4. Do not use pieces of paper to measure the velocity because paper absorbs water thus
changing its mass and affecting the accuracy of the measurement of velocity. We suggest
using bits of polystyrene as it is able to float on the water surface.
Comparison
The photo above is the overlapping of the CFD Mach Number diagram (M=2.0) with
the photo of the water table experiment (motor frequency = 4.5 Hz). It can be observed that the
shock wave simulated in the CFD has very similar properties with the water table experiment in
term of shock wave shape. However, slight difference is observed. This phenomena is believed
to be due to the disturbance wave generated from side wall of the water tank, as shown in the
following photo.
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Conclusion
1. It is evident through this experiment that the shock wave shape can be demonstrated
through a simple water table experiment.
2. The water wave generated by flowing water passing through an airfoil is similar with the
shock wave simulated in CFD with supersonic air flow through the same airfoil.
3. From these facts, it can be deduced that the water table equipment provide an alternative
method to observe the shock wave shape. This method is far cheaper and easier than the
real supersonic wind tunnel experiment.
4. However, the constraint in the water table experiment (for instance, the disturbance wave
generated from the side wall of the tank) has limited the accuracy of this experiment. If
more accurate analysis is desired, CFD and real supersonic wind tunnel experiment are
preferable.