CFD Analysis of Eppler 374

ESA 341: GASDYNAMICS

GROUP PROJECT

(Eppler 374)

LECTURER DR. KAMARUL ARIFIN

2008/2009

Analysis of Eppler 374

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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



1 0.7

2 0.8

3 0.76

4 0.6


6.076.08.07.0=

+++

Velocity, v =1

5594.0715.0

4.0 −= ms



1 0.7

2 0.6

3 0.6

4 0.7


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26.027.0=

×+×

Velocity, v =1

6154.065.0

4.0 −= ms



1 0.7

2 0.6

3 0.6

4 0.5


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.

CFD Analysis of Eppler 374

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