2D Flow Visualisation around the Aerofoil at Varying Angles of Attack

Nomenclature

Cp – Pressure coefficient

Cl- Lift coefficient

Cd- Drag coefficient

AOA- Angle of attack

Uinf- Velocity of fluid at inlet

Ux – x component of free stream velocity

Uy - y component of free stream velocity

Cr – root chord

c- Speed of sound

γ – Specific heat ratio

Re- Reynolds number

R- Universal gas constant

T- Temperature

M- Mach number

Ρ – Pressure

ρ- density

Fx/Fy –force in the x axis/yaxis

Introduction

The root aerofoil that was chosen for the aircraft’s wing configuration in the conceptual design stage

of this project was a NACA 38012. It is for this NACA aerofoil that the 2D simulation is performed on.

In this section the Mach number and Pressure contour plots around the aerofoil will be obtained for

varying angles of attack as the aerofoil reaches stall. The Cp will also be obtained in the form of a

plot of Cp against x-position on the aerofoil. The Cd and Cl values for each angle of attack obtained

from the ANSYS simulations will be compared with values from Java-foil and X-foil.

Figure 1 - The co-ordinates of the aerofoil plotted on MS Excel

The co-ordinates obtained by Javafoil is imported into an excel file and plotted, to make sure there are no gaps; points can be modified to close any such gaps. The original co-ordinates of the aerofoil are also multiplied by the root chord length in order to scale the aerofoil into the actual size used in the design. The figure below shows a section of the finalized points, complete set can be found in the appendix page___

Figure 2 - Figure showing modified co-ordinates based on the Cr length

Determining Mesh Quality

Ideally the mesh for the flow domain should have a minimum orthogonal quality of 0.1 or a maximum Skewness of 0.96.

Figure 3 from lecture notes “3 Mesh-Intro_14.0_L-07_Mesh_Quality”

The figure above shows the mesh spectrum that helps to determine the quality of the mesh. Once the initial sizing conditions have been added to the mesh, it is important to change the mesh to further increase the degree of quality.

Creating Geometry and Mesh

Aerofoil was inserted as a 3D curve, and a surface was created from edges. A C-mesh was then created around the aerofoil. Initially the domain dimensions, were R=70m and L=70m.

The figure below details what the previously mentioned R and L parameters are and how they determine domain size.

Figure 4 -Dimensions of the flow domain

The domain is segmented into 4 sections. Mapped face sizing and 2 edge sizing conditions were applied. Each edge sizing having an element size and bias factor of 100.

Quality (to 3 sig. figures): Orthogonal – 0.994 (excellent)

Skewness – 2.34x10-2 (excellent)

Setup

Equations to consider before setup:

Expressions involved that define the boundary conditions:

Uinf = 244.8 [m s^-1] (for cruise Mach no 0.72) AOA = 0[deg] (Initially taken as 0, then varied systematically) Ux = Uinf*cos(AOA) Uy = Uinf*sin(AOA) Static Temperature =229 K (according to cruise conditions) Outlet Relative pressure= 0 [Pa] Operating(absolute) Pressure = Reference P + Relative P = 30166.857[Pa]

Expressions involved in Monitors:

Fy=force_y()@Airfoil Fx=force_x()@Airfoil

c=√γ RT=√1 .4×287×229=303 .3[m /s ]u=M×c=0 .72×303 .3=218 .40 [m /s ]Re=0 .459[ kg /m3 ]fromISA

Table

P=ρRT=0 .459×287×229=30166 .875[Pa ]

Lift =cos(AOA)*Fy-sin(AOA)*Fx Drag =cos(AOA)*Fx +sin(AOA)*Fy Denom=0.5*massFlowAve(Density)@Inlet*Uinf^2*1[m]*0.1[m] cL=Lift/Denom cD=Drag/Denom

Solver control configuration:

Max iterations = 100 Residual target = 1x10-6

Time scale factor = 10

First Run

First run was a failure, there was no convergence observed. This is due to the fluid domain not being big enough to successfully simulate the flow

Figure 5 - no convergence, domain and mesh should be refined to improve the solution

Domain improvement

Initially when the simulation was sun for 0 AOA there was no convergence pattern observed in the CL and CD plots therefore, the domain size was doubles to R=140m and L=140m. This yielded in converging plot lines.

Figure 6 - Doubling the domain size

Other changes:

Mesh No of elements- 150

Bias Factor- 150

Figure 7 - Edge sizing features of the final mesh setup used to run the simulation

Mesh quality (to 3sf) for the finalised configuration:

Orthogonal – 0.994 (excellent)

Skewness – 2.33x10-2 (excellent)

Figure 8 - Mesh Quality features of the final mesh setup used to run the simulation

Since the qualities on both settings (orthogonal and skewness) are excellent it can be accepted without further mesh refinement.

Setup Residual target – 1x10-4

The figure below shows what the 2D setup configuration looks like once the stup step of ANSYS CFX has been completed.

Figure 9 - Setup configuration

Results

8 th Run (the results of simulations done from run no 1 to 7, were discarded due to domain inadequacies, changing the mesh technique, error messages that prevented the solution to complete, setup errors, university ANSYS licence expiration error messages, etc)

For reasons of clarity and to avoid repetition, detailed results will be presented for one case: when angle of attack is zero. The rest of the results will be compared with each other in the commentary part of this section.

The figure below shows the user defined plots for Cp and Cl for the case where angle of attack ( AOA) is zero

Figure 10 - Convergence seen for Cd and Cl plot lines

Cd = 2.977x10-6

Cp = 3.8927x10-6

Comparing the Cp and Cl obtained from ANSYS with varying angles of attack.

Discussion

ANSYS resultsAOA CL CD

0 3.89E-06 2.98E-064 2.25E-05 4.65E-058 3.55E-05 8.56E-06

12 4.81E-05 1.41E-0516 5.77E-05 2.10E-05

Table – shows the values of Cp and Cl at which the respective plot lines converge at varying angles of attack.

ANSYS resultsAOA Pressure Plot

0

4

8

12

16

From Table it is observed that:

Pressure plots al indicate a reddish-yellow region of positive pressure propagating around the lower front regions (close to the leading edge) of the aerofoil, the blue-green regions of the pressure plots that are located on the upper surface closer to the trailing edge are areas of negative pressure. This

difference in pressure, negative on the upper surface and positive on the lower surface is how the lift is generated on the wing.

As the angle of attack increases, the regions of opposing pressure increase in area as well. The region with the negative pressure on top grows and moves towards the leading edge. Simultaneously the positive region increases in area as well, this increases eventually causes the ‘boundary layer separation’ (as seen on the 16 AOA pressure plot) effect on the top surface. This eventually leads to a sudden decrease in lift at a certain point; this

is where the aircraft stalls.

In the case of average transporter jet aircraft carrying passengers, these types will have aerofoil characteristics where stall conditions are achieved when an angle of attack

of about 15 degrees is reached. The aerofoil used in this design is proven

to follow the similar characteristics of a transporter jet.

AOA

Mach no Plot

0

4

8

12

16

From Table it is observed that:

The red-yellow regions are areas of high Mach number and the areas that are blue have low Mach numbers and the air flows slower in these regions. These regions of high Mach number make more prominent layers of ‘supersonic air pockets’ as the angle of attack is increased.

The regions of fast airflow (the red-yellow regions) around the aerofoil are more prominent on the upper surface than the lower surface of the aerofoil. The reason for this cannot be limited to the geometrical features of the aerofoil alone.

The point at the leading edge where flow separates to either surface of the aerofoil is called the flow separation point. This point at the leading edge is closer to the bottom surface than the top surface.

So there is a slightly greater surface on the aerofoil wall above this point in comparison to below this point. We know that fluid particles that are about the same distance from the aerofoil (air in this case) take approximately the same amount of time to pass around it. So if there is a greater area on the top surface to cover in the same amount of time, the flow on the upper surface will have greater speed that that of the lower surface.

As the angle of attack increases, the point of separation falls further to the direction of the lower surface, thus amplifying the above described effect. This is why the general trend with increasing AOA is for the Mach speed above the surface to intensify on comparison to the bottom.

References

JAVAFOIL – the Applet [Online] Available at: <http://www.mh-aerotools.de/airfoils/jf_applet.htm> [Accessed on 18th March 2013].

CFD Online. Y+ Estimation Tool. [Online] Available at < http://www.cfd-online.com/Tools/yplus.php>[Accessed on 23thMarch 2013]

Bibliography

Department of Environmental Engineering, U. o. G., 2013. FLOW AROUND AN AIRFOIL. [Online] Available at: http://www.diam.unige.it/~irro/profilo_e.html [Accessed 22 05 2013].