Aerodynamic Characteristics of a NACA 4412 Airfoil

8/10/2019 Aerodynamic Characteristics of a NACA 4412 Airfoil

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WARSAW UNIVERSITY OF TECHNOLOGY

FACULTY OF POWER AND AERONAUTICAL ENGINEERING

DEPARTMENT OF MACHINE DESIGN

Practical / Internship

Project

Presented By: Emeka Chijioke

St209323

Aerodynamic Characteristics of a NACA 4412

Airfoil

Supervisor: dr in. Sawomir Kubacki

Warsaw, September 2010


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1.IntroductionAirfoil geometry can be characterized by the coordinates of the upper and

lower surface. It is often summarized by a few parameters such as:maximum thickness, leading edge , trailing edge and nose radius as shown

infigure 1. One can generate a reasonable airfoil section given these

parameters.

Figure.1: Outline of an airfoil

2.Objectives

The objectives of this project was to study the pressures

and performances of a NACA 4412 airfoil and compare it

with its real experimental results (a flying hot- wire

measurements).

Determining the characteristics, like pressure coefficient

and distributions along the airfoil.

3.Turbulence modelsTurbulence modelingis the area offluid dynamics modeling where a

simpler mathematical model is used to predict the effects ofturbulence.

There are various mathematical models used in flow modeling to

understand turbulence.
http://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Turbulencehttp://en.wikipedia.org/wiki/Turbulencehttp://en.wikipedia.org/wiki/Fluid_dynamics


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The turbulence model I used was one equation Spalart Allmarasto

predict boundary layer separation on a NACA 4412 airfoil at the position

of maximum lift (= 15) and mach number (= 0.05). Flow conditionsaround the airfoil were built up by finite volume analysis usingFLUENT

12 software by Fluent Inc.

The free stream velocity was set to 18.4 m/sec for the turbulence

models for direct comparison with the flying hot-wire measurements.

4.GeometryThe geometry was done in Gambit software. I copied the airfoil data file

NACA 4412 from the NACA website. The airfoil naca4412.dat file looks like

this below:

Data file

61 20 . 0000000 0 . 0000000 0

0 . 0005000 0 . 0023390 0

0 . 0010000 0 . 0037271 0

0 . 0020000 0 . 0058025 0

0 . 0040000 0 . 0089238 0

0 . 0080000 0 . 0137350 0

0 . 0120000 0 . 0178581 0

0 . 0200000 0 . 0253735 0

0 . 0300000 0 . 0330215 0

0 . 0400000 0 . 0391283 0

0 . 0500000 0 . 0442753 00 . 0600000 0 . 0487571 0

Figure 2below shows the airfoil as it was imported into Gambit software.

How I did it? From Main Menu > File > Import > ICEM Input ...

Form File Name, browse and select the naca4412.dat file. Select both

Verticesand Edgesunder Geometryto Create: since these are the

geometric entities needed, deselect Face. ClickAccept.


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Figure.2: NACA 4412 geometry from Gambit

Coming to the data file above, the first line of the file represents the

number of points on each edge (61) and the number of edges (2). The first

61 set of vertices are connected to form the edge corresponding to the

upper surface; the next 61 are connected to form the edge for the lower

surface.

The chord length, c for the geometry in naca4412.dat file is 1m, so x varies

between 0 and 1.

NOTE:If you are using a different airfoil geometry specification file, note the range of xvalues in the file and determine the chord length c. You will need this later on.


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5.Far field Boundary Conditions

The purpose of far field boundary conditions is to represent the state of

flow at a large distances from the source of disturbance. However, large

outer boundary distances are difficult to model. Either the number of grid

point is too large resulting in an unacceptable increase in computing time

or the grid cells are largely stretched reducing the accuracy of the

computation.

In an external flow such as that over an airfoil, I defined a far field

boundary and meshed the region between the airfoil geometry and the far

field boundary. The far field boundary was well placed away from the

airfoil and ambient conditions was used to define the boundary

conditions at the far field. The farther we are from the airfoil, the less

effect it has on the flow and so more accurate is the far field boundary

condition.

The far field boundary I used is the line ABCDEFA infigure 3below. C is the

chord length.


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Figure.3: Far field boundary geometry

6.Computational MeshI meshed each of the 3 faces separately to get a final mesh. Before the

mesh face, I define the point distribution for each of the edges that form

the face i.e. the edges was first meshed. The mesh stretching parameters

and number of divisions for each edge was selected based on three

criteria:

1. clustering points near the airfoil since this is where the flow is

modified the most; the mesh resolution as we approach the far field

boundaries can become progressively coarser since the flow

gradients approach zero.


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2. Close to the surface, most resolution is needed near the leading and

trailing edges since these are critical areas with the steepest

gradients.

3. Smoothening the transitions in mesh size; large, discontinuous

changes in the mesh size significantly decrease the numerical

accuracy.

The edge mesh parameters I used for controlling the stretching are

successive ratio, first length and last length. The successive ratio R is the

ratio of the length of any two successive divisions in the arrow direction as

shown below. Go to the index of the GAMBIT User Guide and look under

Edge>Meshing for this figure and accompanying explanation.


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F igur e. 4: The final r esul tant mesh of the geometry

Separately I would like to state how I meshed the airfoil in particular:

I split the top and bottom edges of the airfoil into two edges so that

there will be better control of the mesh point distribution. Figure 5 below

shows the splitting edges.

F igure.5: Split edger of the air foil

I did this because a non-uniform grid spacing will be used for x0.3c. To split the top edge into HI and IG, select

Operation Tool pad > Geometry Command Button > Edge Command Button >

Split/Merge Edge

Make sure Point is selected next to Split Within the Split Edge window.


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Select the top edge of the airfoil by Shift-clicking on it. You should see

something similar to figure 6 below:

F igure 6

I used the point at x=0.3c on the upper surface to split this edge into HI

and IG. To do this, enter 0.3 for x: under Global. If your c is not equal to

one, enter the value of 0.3*c instead of just 0.3.For instance, if c=4, enter

1.2

You should see that the white circle has moved to the correct location on

the edge.


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F igure 7


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Figure 8

Figure 8 above shows the zoomed grid around the airfoil from fluent

software.

7.Results and Discussion:The Meshed geometry was exported from Gambit and was read into the

Fluent solver software. Calculations and observations was made.

Computation was done both for higher and lower mach numbers . It was

computed for in viscid case, and with turbulence Model (Spalart Allmaras).

RESULT FOR LOWER MACH NUMBER

FLUENT:

Run fluent with 2d option and read mesh created in GAMBIT.

Solver settings: density based, implicit ,2D, steady.

DEFINE MODEL VISCOUS, INVISCID.

DEFINE MATERIALS, Ideal gas.

DEFINE OPERATING CONDITIONS, set OPERATING CONDITIONS= 101325 Pa

Boundary Conditions:DEFINE BOUNDARY CONDITIONS


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Set farfield1 , farfield2 and farfield3 to the Pressure far field type.

Pressure far field 1,2,3 : Gauge pressure =0pa,

Mach number = 0.05 constant,

X component of flow direction = 0,9659m/s constant

Y

component of flow direction = 0,2588m/s constantModified turbulent viscosity = 0.001

.

Figure 9 below shows the convergence residuals plot for inviscid case

at design incidence (= 15) and mach number (= 0.05).

18.4 m/s

T = 298K

Spallart allmaras vt= 17.29 m/s

Figure. 9.


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Figure 10 below shows the velocity contour of the airfoil at the leading

edge , the velocity of the upper surface is faster than the velocity on the

lower surface.On the leading edge. The fluid accelerates on the upper

surface as can be seen from the change in colors of the vectors.

Figure. 10: Vector Plot of Velocity Magnitude at the leading edge

Figure 11. shows the velocity contour of the airfoil at the trailing edge . On

the trailing edge, the flow on the upper surface decelerates and converge

with the flow on the lower surface


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Figure. 11: Vector Plot of Velocity Magnitude at the trailing edge

Figure 12 below shows the convergence residuals plot for Spalart Allmaras

case for lower mach number 0.05

Figure. 12


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Figure 13 below shows the velocity magnitude of the airfoil with lower

mach number 0.05 for spalart Allmaras model.

As we can see there is high velocity on the upper surface of the airfoil nearthe leading edge, this includes that there is low pressure at this region.

At the lower surface near the leading edge we see the stagnation point at

low velocity.

At the upper surface of the airfoil near the trailing edge we can see a stall.

A stall is a reduction in the lift coefficient generated by an airfoil as angle

of attack increases. This occurs when the critical angle of attack of the

airfoil is exceeded. The critical angle of attack is typically about 15 degrees

which was used in this computation, but it may vary significantly

depending on the airfoil.

Figure . 13: Contour Plot of Velocity Magnitude


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Figure14 shows the wall pressure distribution (Cp) for NACA 4412, as

computed by the Spalart Allmaras model, inviscid case and compared with

the experimental results. Both case cases gives similar result on pressure

coefficient as in figure 14.In general, the pressure on the surface of an aerofoil is not uniform. From

Figure 14 for = 15 it is seen that at this angle the reduction in the

pressure on the upper surface (suction side), in particular near the leading

edge, is the primary cause of the lift created. From x/c = 0.4 to the trailing

edge the value of Cp varies only slowly. As shown from the flying hot-wire

results (Experimental result), in the rear position of the aerofoil between

x/c = 0.7 to 1 there exists an intermittent low separation near the trailing

edge region. From the foregoing, the following conclusions may be drawn:

(i) At = 15 the lift is principally caused by the pressure reduction on the

front part of

the upper surface and to a smaller extent by a pressure increase on the

lower surface.

(ii) We can see that the S.A model and the inviscid case produces similar

result to that of experiment result.

Figure . 14: Comparison of Pressure coefficients

-6

-5

-4

-3

-2

-1

0

1

2

-0.2 0 0.2 0.4 0.6 0.8 1 1.2pressure coeff. For

Spalart-Allmaras

invincid case

Pressure coeff. For Exp.


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8. RESULT FOR THE CASE OF HIGER MACH NUMBER(1.5)

Here the grid around the wall of the airfoil was redefined. The data,properties and boundary conditions added is the same as in the case of

lower mach number(0.05), the only change is the input of the value of the

high mach number which is 1.5. This was inserted in fluent solver.

By increasing the grid numbers and changing the type of arranging mesh,

refining the mesh, around the wall of the airfoil a proper y+ value is

obtained, and the following results was obtained for higher mach 1.5

with Spalart Allmaras model : The range of y+ if from 2 20 as seen in

figure .15.

Figure. 15: y+ range from 2 - 20


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Figure.16: Redefined grid around the wall of the airfoil


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Figure.19: Pressure distribution around the airfoil

9.Conclusion

Compressible flow past NACA 4412 has been studied in detail using

a turbulence model computation(Spalart Allmaras). Computational

results are found to agree reasonably well with available

experimental data.

Conclusion can be drawn from the convergence of both inviscid

case and S.A model, for lower mach number 0.05 as shown in

figures 9 and 12 respectively. It is observed that we have better

convergence in the case of S.A model than that of inviscid case. The

reason is that there is unsteady flow around the airfoil for inviscid

case, whereby causing slow and bad convergence history.

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Aerodynamic Characteristics of a NACA 4412 Airfoil