How does the long gap width (2mm, 3mm, 4mm, 5mm) and location (10%, 15%, 20%, 25%) of VGs along a NACA 2412 airfoil affect its stall angle in low speeds (0.84m/s) at a Reynolds number below 2300?

Low-Speed Flow Visualization Wind Tunnel

The wind tunnel used in this study was constructed manually using parts at home (See Figure 3). Detailed step-by-step instructions to build a similar visualization wind tunnel can be found at nasa.gov. The required components for this wind tunnel are as follows: an airflow filter to decrease the Reynolds number and mimic the conditions of low-speed aircraft, a suction fan to mimic air flowing around an airfoil in flight (see Figure 4), a removable back plate to swap airfoils between trials (see Figure 5), an attached protractor to measure the AOA between trials, and a smoke-creating device to visualize airflow inside the wind tunnel.

 

Figure 3. Apparatus diagram

Figure 4. The suction fan inside the testing chamber of the wind tunnel.

The wind tunnel used had a testing chamber that was 7.50cm wide, 34.0cm long, and 12.0cm high. It had a Reynolds number of less than 2300 (Laminar Flow), and an airspeed of 0.84m/s.

 

NACA 2412 Airfoils

The airfoils used in the study were mathematically designed using graphing software before being 3D printed in PLA (see Figure 6). The 2412 airfoil follows the NACA 4-digit airfoil series in the form NACA MPXX. 

M = Max camber that has a value of M100100% as a percentage of the chord

P = Location of max camber where P10100% is its location from the leading edge as a percentage of the chord

XX = Max thickness that has a value of XX100100% as a percentage of the chord

Given this, the NACA 2412 airfoil has a max camber of 2% at 40% chord length while having a max thickness of 12%. Assuming that the size of the chord is 1 unit, the following formulas and steps can be taken to graph a 4-digit airfoil. Note that in these formulas, both x and y refer to the x and y coordinates in a plane and are not variables.

 

Figure 5. Removable backplate with protractor attached.

 

Figure 6. 3D printed PLA airfoil with VGs located at 10% chord length with 4mm spanwise spacing.

 

Formulas to graph mean camber line:

 

f(x)=MP2(2Px – x 2)     0x<P (Eq. 1)        f(x)=M(1-P)2(1 – 2P + 2Px – x2)     Px<1 (Eq. 2)

Formulas to determine the angle of camber:

 

a(x) =arctan(f’(x)) (Eq. 3)

 

Where    f’(x) = 2MP2(P – x)   0x<P            f’(x) = 2M(1-P)2(P – x)   Px<1        

 

Formula to determine thickness distribution across the airfoil:

 

h(x)=XX20(0. 2969x1/2− 0. 1260x2+ 0. 2843x3 − 0. 1036x4 ) (Eq. 4)

 

* Note that these coefficients are constant for an airfoil that has a max thickness of 20%. This formula scales up or down based on these constants.

 

Formula to graph the top and bottom lines on the airfoil:

 

Top Line:                                                                 Bottom Line:

 

xU=x-h(x)sin(a(x))                                          xL=x+h(x)sin(a(x))

yU=f(x)+h(x)cos(a(x)) (Eq. 5)                    yL=f(x)-h(x)cos(a(x)) (Eq. 6)

 

Where xU and yU are the coordinates that form the upper surface, and x and y are the coordinates that form the lower surface, both translated from the original x and y values.

Using these formulas in graphing software will produce a NACA 2412 airfoil which can then be converted to a .stl file to be 3D printed. Eight airfoils scaled to 75mm by 65mm were printed, including one airfoil without vortex generators. The chord of each airfoil was 75mm. Each vortex generator was 3D modeled using TinkerCAD and separately assembled onto the airfoil after the printing.

 

Variables

Controlled:

• VG Height: 2mm¹²
• VG Vane length: 4.38mm (5.8% chord length)¹³
• VG Shape: Triangular¹⁴
• VG Type: Triangular Vane; Counter Rotating¹⁵
• VG Inflow angle: 12°¹⁵
• 0.84m/s airspeed
• Wind tunnel Reynolds number
• Testing chamber volume
• Boundary layer separation point
• Airfoil Type

Manipulated Variables (see Table 1 for each manipulation):

• VG Long gap spacing: 2mm, 3mm, 4mm, 5mm)
• VG Location: 10%, 15%, 20%, 25% of the chord length (75mm)

 

Table 1. Airfoil Specifications for Each Manipulation

 

*4mm @ 10% chord length airfoil is repeated between both manipulated variables.

 

The AOA of each airfoil was increased until the separation point reached 30% of the chord length from the leading edge (see Figure 7 for an example). This was observed qualitatively, and the corresponding AOA was then recorded as quantitative value. Stalling usually occurs when the separation point reaches the point of max thickness, which is located at 30% chord length on a NACA 2412.¹⁶ Furthermore, vortex generators mitigate boundary layer separation in general, and therefore choosing the separation point to record the AOA is arbitrary.

Procedure

Begin by gathering the airfoils and wind tunnel, along with all the other required materials. This includes 5-10 incense sticks, an incense stand, 8 10cm wooden dowels, a hot glue gun, a lighter, a sharpie, and a flashlight. Using the sharpie, mark out the 30% chord length point on each airfoil from the leading edge. Then, attach the wooden dowel to the marked point using the hot glue gun. Once this has been completed, insert the airfoil into the wind tunnel using the backplate and turn on the wind tunnel. It is crucial to ensure that the airfoil is initially at 0° AOA to avoid any random error. Insert the incense sticks into the stand and ignite them using the lighter before quickly blowing out the sticks to produce visible smoke. Using the flashlight to increase smoke visibility, slowly increase the angle of attack until the airflow is visibly separated from the airfoil at the marked point. You will know that the boundary layer has separated correctly when the recirculation region flows up until the marked point (see Figure 7). Once this has been achieved, record the AOA using the protractor on the backplate and then reset the airfoil to an AOA of 0°. Slowly increase the AOA again, only viewing the AOA once separation has occurred to remove unconscious bias between trials. Repeat and record the AOA for 3 trials per airfoil. Finally, repeat this entire process for all 8 airfoils, before unplugging the wind tunnel and cleaning the experiment space.

 

Raw Data

Table 2. Boundary layer separation AOA at 10%, 15%, 20%, and 25% VG location as a percentage of the chord. The table shows that the highest AOA before boundary layer separation occurs at 20% chord length while the lowest AOA occurs at 20%.

 

Table 3. Boundary layer separation AOA at a VG long gap spacing of 2mm, 3mm, 4mm, and 5mm. The table shows that the highest AOA before boundary layer separation occurs at 4mm spacing while the lowest AOA occurs at 2mm.

 

Average Angle Sample Calculation

For control:

avg=Trial #1 + Trial #2 + Trial #33 (Eq. 7)        avg=8.0°+6.5°+5.5°3          avg=6.6°=6.7°

 

Figure 7. Boundary layer separation at 30% for airfoil #2 with θ outlined.

Processed Data

Table 4. Average AOA for boundary layer separation at 10%, 15%, 20%, and 25% VG location as a percentage of the chord. Table 4 confirms the main findings from Table 2.

 

Table 5. Boundary layer separation AOA at a VG long gap spacing of 2mm, 3mm, 4mm, and 5mm. Table 5 confirms the main findings from Table 3.

 

Graphs

Figure 8. Average boundary layer separation angle as a function of VG location. The graph shows that the optimal location for VGs is located between 15% and 20% as indicated by the maxima. This produces an AOA just below 12.0 degrees.

Figure 9. Average boundary layer separation angle as a function of VG long gap spacing. The graph shows that the optimal long gap spacing for VGs is between 3 and 4 mm as indicated by the maxima. This produces an AOA of between 6.0 and 8.0 degrees.

 

Maximum Curve Calculations

For Figure 8:

f'(x)=2(-0.082)x+2.82

f'(x)=-0.164x+2.82

0=-0.164x+2.82

0.164x=2.82

x=17.19512=17.2%

y=(-0.082)(17.19512)2+(2.82)(17.19512)-12.4=11.845...

y=11.8°

For Figure 9:

g'(x)=2(-0.9)x+6.54

g'(x)=-1.8x+6.54

0=-1.8x+6.54

1.8x=6.54

x=3.63=3.6mm

y=(-0.9)(3.63)2+(6.54)(3.63)-4.39=7.491

y=7.5°

The experiment was intended to optimize the placement and long gap spacing of vortex generators on the NACA 2412 airfoil, aiming to mitigate boundary layer separation, which would increase aerodynamic efficiency and postpone stalls. Eight airfoils with varying VG configurations concerning long gap spacing and location on the chord were 3D-printed. The AOA on each airfoil was increased until the boundary layer separation reached 30% of the chord length from the leading edge. 

 

Table 4 summarizes the AOA values for different VG locations across the chord, given a fixed long gap spacing at 4mm. Table 4 was derived from the raw data in Table 2 using Equation 7. The highest AOA of 11.5° was observed at placement at 20% of the chord, and the lowest value, 6.8°, occurred at 25%. This indicated that placing VGs too close to the trailing edge reduced effectiveness in delaying boundary layer separation, likely because of insufficient interaction between the boundary layer and free-stream air at higher chord lengths. Oppositely, the 20% chord position gave the most efficient boundary layer and free-stream air combination, allowing for better flow attachment at higher AOAs. Long gap spacing and its effects are explored in Table 5. Table 5 was derived from the raw data in Table 3 using Equation 7. 2mm, the smallest gap spacing resulted in the lowest average AOA (5.2°). A gap spacing of 4mm produced the highest average AOA. We interpret this as meaning that having more vortices isn’t always better, as the reduced gap spacing might actually reduce their strength. This would, in turn, lead to a less effective mixing of boundary layer and free-stream air. The vortices generated by the 2mm VGs may begin to interfere destructively with the ones generated destructively, leading to less effective vortices overall. Furthermore, the increase in VGs could lead to an increased parasitic drag. Adding VGs increases the amount of drag created due to form resistance, which also increases the tendency for airflow to separate. This effect is generally outweighed by the positive effects of properly optimized VGs (at 3mm and 4mm). Still, it tends to stick out in poorly optimized VGs with negligible positive effects.

 

A parabolic regression line was used to model both tables of values, each with an R² value of above 0.936. Finding the maximum value of both these equations gives the maximum angle possible for each manipulation and the exact value for this max. In Figure 8, the maximum value reached is 11.8° at a VG location of 17.2% from the airfoil’s leading edge. This value represents a 76% increase in angle from the controlled airfoil. In Figure 9, the maximum value reached is 7.5° at a VG long gap spacing of 3.6mm. This value represents a 12% increase in angle from the controlled airfoil. Given this, it is evident that the location of the VGs plays a much greater role in postponing stalls in aircraft than the long gap spacing of the VGs. This could indicate that positioning the vortices along the chord is more effective in mitigating boundary layer separation than the size of the vortices generated.

 

Conclusion

Modern airfoil designs have reached their maximum potential in aerodynamic performance to keep up with the constant need for increased fuel efficiency. Given this, innovative and modern solutions are required to improve aircraft performance further. Of these, passive flow control systems such as vortex generators show great potential as a solution to aerodynamic performance, significantly postponing stalls and boundary layer separation. The effectiveness of these generators is defined by 11 factors that need to be specifically optimized for each airfoil and flying condition.

 

Our study optimizes two of these 11 factors on a NACA 2412 airfoil, targeting beginner aircraft flying at low Reynolds numbers and airspeeds to help reduce the costs of entry. These factors include the long gap spacing between VG sets and their location on the chord. These factors were optimized experimentally in a low-speed visualization wind tunnel based on observations of flow separation at 30% of the chord. The results from this study indicate that a long gap spacing of 3.6mm at 17.2% chord length is optimal for the NACA 2412, showing a significant increase in AOA before flow separation.

 

Experimentation results show that on a blank airfoil, the separation point reaches 30% chord length at an AOA of 6.7°, whereas optimized VGs delay the AOA up to 11.8°. Furthermore, the results of this study indicate that the location along the airfoil plays a much greater role in delaying flow separation than the long gap spacing, as the long gap spacing alone only delayed the AOA to 7.5° before the separation point reached 30%. Something else to consider is that improper implementation of VGs can increase flow separation and decrease the AOA for stalls compared to a blank airfoil. This is seen in VGs with 2mm and 5mm spacings, as their AOA for separation is recorded as 5.2° and 5.7°, respectively. This performance is significantly worse than the blank airfoil at 6.7° and is most likely the result of parasitic drag.

 

Further improvements and research include measuring each airfoil’s lift and drag forces and determining the ratio of their coefficients. Determining how the lift and drag coefficients are affected by the location of VGs on a NACA 2412 airfoil would provide valuable information and insight into their effects on parasitic drag as well. Another area of further research could be optimizing other factors, including intake angle or size.

 

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We would like to thank Nathan's parents, William Xia and May Hu, for their support and allowance of experimenting at their home. Further, we would like to thank Mr. Alex Watt at Henry Wise High School’s Physics department for guiding us along our research processes.