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Effects of Change in Camber and Location of Maximum Camber on Airfoil Performance in Laminar Flows

Computer Project

ME 431

Autumn 2010

By Scott Schellenberger

December 10, 2010

Introduction and Background

The purpose of this project was to study the effects changes in maximum camber and maximum camber location have on airfoil performance in laminar flows. This study relates to a very important topic in today’s world – aerodynamics. For the last little over a century controlled flight has caused a greater research in this topic than ever before. While this is a simple study of airfoil shape, it gives some important conclusions that can be applied in airfoil design.

Approach

The airfoils used in this project loosely follow the profiles described by the NACA 4-digit airfoil series. The first number in the NACA 4-digit identifier represents the maximum camber in percent of the airfoil chord length, the second number represents the location of maximum camber in tenths of the chord length, and the last two numbers represent the maximum thickness of the airfoil in percent of the chord length. The airfoils were generated using the appropriate equations to obtain coordinate points and were drawn using AutoCAD. Rather than using the 3.75 meter chord length chosen in the initial project proposal, a chord length of 1 meter was used in order to simplify geometry. The fluid was chosen to be air at 20°C and 1 atm. This was also a slight adjustment to the initial project proposal which stated that air at 25°C would be used. Laminar flow was chosen at a Reynold’s number of 100 to avoid turbulent boundary layers. Diagrams of a NACA airfoil and of the model domain are shown below in Figures 1 and 2, respectively.

Figure 1: Diagram of NACA Airfoil

Figure 2: Diagram of Model Domain

This problem was modeled using COMSOL. As shown in the diagram in Figure 2 above, the upper and lower boundaries were given slip boundary conditions. This is to prevent viscous effects near these surfaces. The airfoil was given a no-slip boundary condition. The inlet velocity was specified as 0.0015 m/s to give a Reynold’s number of 100. This was found from the following equation for calculating the Reynold’s number:

ℜ= ρuLμ

=100

Here L equals the airfoil chord length (1m), ρ is the fluid density (1.2 kg/m^3), u is the inlet velocity to be solved for, and μ is the dynamic viscosity (1.8e-5 Pa*s).

The study focused on the lift, total drag, and the form and viscous drag components that describe airfoil performance. Five airfoils were generated with maximum cambers ranging from 0 – 4 % of the chord length in increments of 1%. Location of maximum camber was held constant for these five airfoils at 3/10 of the chord length. The maximum airfoil thickness was held constant throughout the entire project at 9% of the chord length. Six additional airfoils were generated to study the effects of varying the location of maximum camber. These were done for the airfoils with maximum cambers of 2%, 3%, and 4% (NACA numbers beginning with 2, 3, and 4 respectively) to give a set of values of location of maximum camber ranging from 3/10 to 5/10 of the chord in 1/10 increments.

Lift, total drag, and viscous drag were recorded from the simulation of each airfoil studied. These were given in dimensions of force per length as the problem is only 2-dimensional. Form drag was calculated by taking the difference between the total drag and the viscous drag and has the same dimensions as the other three values. The data was studied with regards to the variable parameters to find any trends and relationships. A surface plot of the velocity field and a stream line plot were generated for one of the NACA 3000 series airfoils. These plots aid in visualizing the flow.

Results

The simulation results were tabulated in Tables 1 – 4 below and are grouped in order to clarify the particular parameters studied in each group.

Table 1: Results of Study on Variation of Maximum Camber

Lift [N/m] Total Drag [N/m] Viscous Drag [N/m] Form Drag [N/m]NACA 0009 1.31E-08 5.92E-07 5.12E-07 8.04E-08NACA 1409 3.77E-08 5.93E-07 5.07E-07 8.54E-08NACA 2409 6.25E-09 5.92E-07 5.11E-07 8.10E-08NACA 3409 9.47E-08 5.97E-07 5.02E-07 9.55E-08NACA 4409 1.24E-07 6.01E-07 4.98E-07 1.02E-07

Table 2: Results of Study on Changes in Location of Maximum Camber (Maximum Camber = 2% of Chord)

Lift [N/m] Total Drag [N/m] Viscous Drag [N/m] Form Drag [N/m]NACA 2309 7.73E-08 5.95E-07 5.04E-07 9.05E-08NACA 2409 6.25E-09 5.92E-07 5.11E-07 8.10E-08NACA 2509 5.88E-08 5.94E-07 5.06E-07 8.89E-08





Conclusions

For visualization and ease of study, both the lift and the total drag were plotted against the changing variable for each table. This provides an easy method of establishing patterns in the data. Due to limited space and time, form and viscous drag components were not plotted. Rather, a few conclusions are drawn directly from the data in the tables for these values.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50.00E+002.00E-084.00E-086.00E-088.00E-081.00E-071.20E-071.40E-07

Lift versus Maximum Camber

Location of Max Camber = 3% of Chord

Maximum Camber (% of Chord)

Lift (N

/m)

Figure 3: Comparison of Lift and Maximum Camber

0 0.5 1 1.5 2 2.5 3 3.5 4 4.55.86E-075.88E-075.90E-075.92E-075.94E-075.96E-075.98E-076.00E-076.02E-07

Drag versus Maximum Camber

Location of Max Camber = 3% of Chord

Maximum Camber (% of Chord)

Drag

(N/m

)

Figure 4: Comparison of Total Drag and Maximum Camber

From Figures 3 and 4 above, it is evident that lift tends to increase as maximum camber increases. This relationship appears to be linear, at least over the range of data studied. Furthermore, it is apparent that total drag increases with increasing camber as well. However, lift increases at a greater rate than total drag. This means that an increase in camber gives a larger increase in lift than in the total drag. This relationship likely has limitations at some point outside the range of the data studied, as change in lift divided by change in total drag cannot be greater than 1 indefinitely. At some point, drag would most likely increase at a much steeper rate than lift. This would then become an optimization problem and would be interesting to study, but is beyond the scope of this project.

While the total drag increases with increasing camber, it appears from Table 1, above, that this behavior is mainly attributed to an increase in the form drag. Viscous drag actually decreases very slightly with increasing maximum camber. This behavior would need to be studied more in depth before strong conclusions could be made however.

The data for the NACA 2409 airfoil appears to be an outlier in the data set as it does not follow the trend of the rest of the data. The problem likely lies in the geometry of the CAD file from where the airfoil was imported, but this is not clear. Based on the results shown above, as well as later ones, the data for this airfoil should be disregarded.

Lift and total drag are plotted against location of maximum camber in Figures 5 – 10 below.

2.5 3 3.5 4 4.5 5 5.50.00E+001.00E-082.00E-083.00E-084.00E-085.00E-086.00E-087.00E-088.00E-089.00E-08

Lift versus Location of Maximum Camber

Maximum Camber = 2% of Chord

Location of Max Camber (% of Chord)

Lift (N

/m)

Figure 5: Comparison of Lift and Location of Maximum Camber for NACA 2000 Series Airfoils

2.5 3 3.5 4 4.5 5 5.55.90E-07

5.91E-07

5.92E-07

5.93E-07

5.94E-07

5.95E-07

Total Drag versus Location of Maximum Camber


Location of Maximum Camber (% of Chord)

Drag

(N/m

)

Figure 6: Comparison of Total Drag and Location of Maximum Camber for NACA 2000 Series Airfoils

2.5 3 3.5 4 4.5 5 5.50.00E+00

2.00E-08

4.00E-08

6.00E-08

8.00E-08

1.00E-07

1.20E-07




Lift (N

/m)


2.5 3 3.5 4 4.5 5 5.55.97E-07

5.97E-07

5.98E-07

Total Drag versus Location of Maximum Camber



Drag

(N/m

)


2.5 3 3.5 4 4.5 5 5.50.00E+002.00E-084.00E-086.00E-088.00E-081.00E-071.20E-071.40E-071.60E-07




Lift (N

/m)


2.5 3 3.5 4 4.5 5 5.56.00E-07

6.01E-07

6.02E-07

Total Drag versus Location of Max-imum Camber



Drag

(N/m

)


From the preceding plots, it is clear that lift tends to increase as the location of maximum camber is moved toward the front of the airfoil. As with the relationship between lift and maximum camber, this tendency likely has limitations - for example when the location of maximum camber becomes very close to the front of the airfoil and significant distortion of the airfoil occurs. Once again, these limitations were beyond the scope of this project and were not studied. Total drag also increases as the location of maximum camber moves toward the front of the airfoil, however not to as great an extent as the lift increases. This is similar to the conclusions of the study of the effect of maximum camber.

Interestingly enough, in contrast to the study of the effect of maximum camber, form drag decreased as the location of the maximum camber moved toward the front of the airfoil while viscous drag increased. The overall net effect was still an increase in the total drag.

Here, once again, we see that the data for the NACA 2409 airfoil is not consistent with the trend observed in the other airfoils (see Figures 5 and 6). It should be noted that this airfoil was redrawn and re-simulated, however the results were the same.

Below in Figures 11 and 12 are shown a surface plot of the velocity field and the streamlines of the flow for one of the airfoils studied. Because differences between these plots for the various airfoils were not easily distinguished, the rest were left out of this paper. A stagnation point is clearly seen at the front and back of the airfoil in the velocity field surface plot. A laminar boundary layer is also present as evidenced by the low magnitude velocity fluid surrounding the airfoil (red indicates higher velocity while blue indicates lower velocity).

Figure 11: Velocity Field Surface Plot for NACA 3409 Airfoil

Figure 12: Streamline Plot for NACA 3409 Airfoil

References

Scott, Jeff. “NACA Airfoil Series.” Aerospaceweb.org. 26 Aug. 2001. <http://www.aerospaceweb.org/question/airfoils/q0041.shtml>

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