General Sir John Kotelawala Defence University

COMPUTATIONAL FLUID DYNAMICS

Modelling External Compressible Flow in an Airfoil

by

LLY SRIMAL (ENG/AE/12/0044)

Supervised By

Mr RMPS Bandara

GENERAL SIR JOHN KOTELAWALA DEFENCE UNIVERSITY

RATMALANA, SRI LANKA.

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Contents

List of figures ........................................................................................................................................... ii

List of Tables ........................................................................................................................................... ii

1 Introduction ................................................................................................................................ 1

2 Problem statement ..................................................................................................................... 1

3 Parameters .................................................................................................................................. 1

4 Methodology ............................................................................................................................... 2

4.1 Meshing the airfoil from Gambit ............................................................................................ 2

4.2 Simulating the airfoil using Fluent. ......................................................................................... 5

4.2.1 First Method-Residual Monitoring System ......................................................................... 5

4.2.2 Second Method-Force Monitoring System ......................................................................... 6

5 Results ......................................................................................................................................... 8

5.1 First Method-Residual Monitoring System ............................................................................. 8

5.2 Second Method-Force Monitoring System ........................................................................... 10

6 Interpretation............................................................................................................................ 10

7 Conclusion ................................................................................................................................. 10

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List of figures

Figure 1 airfoil ......................................................................................................................................... 1

Figure 2 Domain ...................................................................................................................................... 2

Figure 3 Mesh is interacted with the Airfoil ........................................................................................... 3

Figure 4 Airfoil after increasing the number of nodges .......................................................................... 3

Figure 5 Smoothen Cells around the surface of the Airfoil ..................................................................... 4

Figure 7 Converged graph after 163 iterations ....................................................................................... 8

Figure 8 Contours of Static Temperature and Static Pressure ................................................................ 8

Figure 9 Contours of Turbulent Viscosity and Velocity Magnitude ........................................................ 9

Figure 10 Convergence Graphs in Force Monitoring System ............................................................... 10

List of Tables

Table 1 Parameters for the Simulation in Fluent .................................................................................... 5

Table 2 Residual Monitor values ............................................................................................................ 6

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1 Introduction

The purpose of this project is to compute the compressible over an airfoil at a 4 degree of

angle of attack. I have used the Spalart-Allmaras turbulence model. In the following chapters

will demonstrate how to process with the methods in developing the model in Gambit and run

the simulation in Fluent and the following are demonstrated.

Model compressible flow using the ideal gas law for density

Set boundary conditions for external aerodynamics.

Use the Spalart-Allmaras turbulence model.

Use force and residual monitors to check solution convergence.

2 Problem statement

The problem to be considered is shown schematically in the following figure. The figure

shows a conventional airfoil which has a 1m chord and 4 angle of attack. This airfoil is in a

free stream Mach number of 0.8. In this problem we will consider how this given airfoil will

act in this given free stream velocity.

3 Parameters

Angle of attack =4

Free stream Mach number M=0.8

Chord Length of the airfoil C=1m

Figure 1 airfoil

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4 Methodology

4.1 Meshing the airfoil from Gambit

First it is needed to draw the above mentioned airfoil. We can draw this in AutoCAD or we

can have coordinates of the points of the airfoil. For this problem we have used coordinated

system of notepad values and imported in it Gambit as an ICEM file.

After importing the airfoil the edges were checked in order to get an acceptable model of the

airfoil. In the following figure it is observed that the edges of the imported are not smooth

and thus created a pointed leading edge which is not acceptable.Because if a mesh is created

with this figure, a fine mesh cannot be created and the flow simulation will have errors.

In order to smoothen the edges we can proceed with the following steps.

Slip the edges by using the split edge command.

Then erase the leading edge.

Now create a new vertex at the leading edge by using the create vertex command. In the

vertex command select the coordinate system as Cartesian and in Global command put these

following values for X=0, Y=0, Z= 0.

To create a new leading edge select the Edge command and select arc command. In arc

command select the Method as Three points and then select the vertices. After applying a

new smoothen leading edge will be created. Label this new edge as Leading edge. After this

create a Face for this airfoil by using the Create Face command.

Next refer to the following figure to create a domain. Here all the dimensions are in meters.

Figure 2 Domain

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To create the mesh for this airfoil we need to subtract the domain form the airfoil by using the

Subtract real faces in the real faces in the Face command. When meshing the airfoil select the

Domain in the Face command, select elements as Quad, select the Type as Pave and give the

Interval Size as 0.02. After completing the meshing process we will get the following figure.

In this figure it is clear that the mesh is interfering with the wall of the airfoil. That is we

cannot get a smooth and a fine mesh to run the simulation. This is due to the lack of nodges

on the wall of the airfoil. So it is essential to increase the number of nodges as higher as

possible. The higher number of nodges will give cells which are smaller. In order to reduce

this problem we will use a second method to mesh.

Figure 3 Mesh is interacted with the Airfoil

Figure 4 Airfoil after increasing the number of nodges

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In this method initially, we will mesh the edges. To do that selects the Mesh Edge command.

Then select the upper surface edge, lower surface edge and the leading edge respectively and

apply following values.

Successive Ratio 1 Leading edge interval count 20 Upper surface interval count 100 Lower surface interval count 100.

Then again proceed with the Face mesh. Then the following figure will appear. Here we can

that there is a fine smoothen mesh around the wall of the airfoil and we can that the cells are

not interfere with the surfaces of the airfoil. After that we need to assign Boundary

Conditions for this mesh. In order to do those select the Specify Boundary Types command.

Here assign the Domain as the Pressure-Far-Field and the airfoil as Wall. Then export this

file as a mesh file.

Figure 5 Smoothen Cells around the surface of the Airfoil

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4.2 Simulating the airfoil using Fluent.

4.2.1 First Method-Residual Monitoring System

After completing the above procedure accurately till the importing command, then we need to

open this mesh file in Fluent. This mesh file will be read as a case file in fluent (Fluent will

read in the grid geometry and mesh that was previously created by Gambit). If all is read

well, it should give no errors and the word Done should appear. After reading the mesh file

in Fluent we need to check the validity of the Grid by using Grid-Check command. From this

command we can observe the following parameters of the Grid such as Domain Extents,

Volume Statistics Face area statistics. Then I have selected the Grid-Reorder-Domain

command to rearrange the domain. This is to rearrange the domain to avoid convergence

problems. If the grid was not created in given scale we need to rescale the grid to meters.

Here I have left the scale as it is. Then I have use the Display-Grid-Display command to look

at the grid to make sure it is correct.

According to the following table I have defined the parameters to be assigned for this

simulation.

Table 1 Parameters for the Simulation in Fluent

Define Models Solver Solver-Pressure Based

Space-2D

Velocity Formulation-Absolute

Gradient Option-Green-Gauss Node

Based

Energy Select the Energy Equation Check Box

Viscous Model-Spalart Allmaras

Spalart Allmaras Options-

Strain/Vorticity Based Production

Materials

Fluent Fluid

Materials Air

Density Ideal-gas

Viscosity

Sutherland-> Sutherland Law-> three

Coefficient Method

Operating

Conditions No changes

Boundary

Conditions Airfoil-Wall No Change

Domain-Pressure

far field Mach Number-0.8

x-Component of Flow

Direction=0.8Cos=0.9976

Y-Component of Flow

Direction=0.8Sin=0.0698

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Turbulence->Specification Method-

>Turbulent Viscosity Ratio

Turbulent Viscosity Ratio=10

Solve Controls Solution Discretization-Pressure->Second Order

Density,Momentum,Modified turbulent

Viscosity, Energy-> Second Order

Upwind

Pressure Velocity Coupling-Coupled

Courant Number=200

explicit Relaxation Factors-

Momentum=0.5/Pressure=0.5

Under Relaxation Factors-

Density=0.5/Body Forces=1/Modified

Turbulent Viscosity=09/Turbulent

Viscosity=1

Monitors

Residual-Check the Print and Plot

Boxes

Convergence Criterion-Absolute

Absolute Criteria for

continuity=0.0001

Only check convergence for the

continuity

Initialize Compute From-Domain

Iterate Number of Iterations=1000

After 193 iterations the Fluent display has indicated that the solution is converged. After the

convergence of the solution we can refer to the DisplayGrid/Contours/Vectors commands to observe the effects to the airfoil by velocity, temperature, pressure etc

4.2.2 Second Method-Force Monitoring System

In the second method we do know whether the solution is converged. So that we use force

monitoring system. Here the convergence criteria is same as the above mentioned fist

method. But in the Residual Monitors command I have changed the Convergence Criteria as

None. In this command select the Plot and Write boxes and the use the below table to assign

the values.

Table 2 Residual Monitor values

Solve Force

Monitors Coefficient-Drag

Force Vector-

X=0.9976/Y=0.06976

Plot Window=1

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Coefficient-Lift

Force Vector-x=-

0.06976/Y=0.9976

Plot Window=2

Coefficient-Moment

Moment Center-

X(m)=0.25/Y(m)=0

Plot Window=3

After completing assigning the values I have initialize this simulation. Same as the above fist

method I have selected these commands. SolveInitializeCompute from Domain. After initializing I have started the simulation for 10000 iterations.

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5 Results

5.1 First Method-Residual Monitoring System

Figure 6 Converged graph after 163 iterations

In the above figure it is clear that the solution is converged at 163 iterations. In these graph

residuals of continuity, X velocity component, Y velocity component, energy can be

observed.

Figure 7 Contours of Static Temperature and Static Pressure

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These figures show the compressibility effects when this airfoil meets with the free stream

Mach number of 0.8. In the top left corner figure is the turbulent viscosity variation of the

flow at the trailing edge of this airfoil. And we can see how the magnitudes of this viscosity

will vary throughout the upper surface of the trailing edge of this airfoil and the turbulent will

increase when the flow is leaving the trailing edge.

In the bottom left corner figure we can see that the static temperature variation. At the leading

edge and the trailing edges of this airfoil we can see the maximum values of the static

temperature the blue marked region indicating the lesser values of the static temperature at

the upper surface of the airfoil.

In the top right corner figure we can see that variation of the static pressure. In this figure we

can observe at the stagnation point static pressure is maximum. And throughout the leading

edge to the trailing edge static pressure will vary to a minimum.

At last as we referring to the right bottom figure we can see the variation of velocity

magnitude. As above mentioned this airfoil is simulated in a transonic velocity. So when the

velocity magnitude increases to the leading to the trailing edge, we can observe the formation

of a shock wave. As the flow leaves the trailing edge it will adopt the free stream velocity

magnitude which indicated in light blue region.

Figure 8 Contours of Turbulent Viscosity and Velocity Magnitude

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5.2 Second Method-Force Monitoring System

From this force monitoring system we can obtain contours for pressure, velocity, density,

turbulence etcAs above figures we can clearly observe variations of aforementioned

parameters. But in this method we do not the where the convergence occur. To recognize that

we can observe the convergence point to our naked eye. Above four figures shows the

coefficients of lift, drag and momentum for given angle of attack and for given free stream

Mach number.

6 Interpretation

By proceeding with this exercise which is modelling and simulating this airfoil through

external compressible flow which leads us to reach an initial solution. We may be able to

obtain a more accurate solution by using an appropriate higher order discretization scheme

and by adapting the grid. By using the mesh adaptation we can modify the existing mesh so

as to accurately capture the flow features. So that these modification will improve resolution

of flow features without excessive increase in computational effort.

7 Conclusion

This exercise demonstrated how to set up and solve external aerodynamics problem using the

Spalart-Allmaras turbulence model and it showed how to monitor convergence using force

monitors and residual monitors. After obtaining convergence to the above problem we can

see how the compressible flow will interact with the airfoil. We could observe important

phenomena such as the shock wave, turbulent flow, flow separation, flow reversal etcBy

plotting the graphs we could observe how the lift, drag, moment coefficients are varying in

this transonic free stream Mach number.

Figure 9 Convergence Graphs in Force Monitoring System

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