Flat Endplate Versus Airfoils

The first simulations were done with two geometries. A flat endplate (the usual design) and an endplate with curvature. To add the curvature to the endplates, the airfoils of the NACA 4-Digit Series were used due to their simplicity and overall good general applicability. Their nomenclature is as follows:

the first digit is the camber of the airfoil, the second the position of maximum camber, and the last two its thickness. So for example, the 2412 airfoil has the following characteristics:

1. the first digit is the camber of the airfoil, 2% (0.02c);

2. the second digit 4 means that the maximum camber occurs at 40% (0.4c) of the chord from the leading edge;

3. the last two digits 12 represent the thickness of the airfoil in percentage (t= 0.12c).

The first simulations were done with a flat endplate and the 2412 aifoil with the following dimensions:

top = 0mm∨bottom= 50mmandtop =bottom= 50mm, the results of which are given in Table 4.1.

In the case oftop= 0mm∨bottom= 50mm, theCLis larger and theCD smaller for the flat endplate, resulting in a higherCL/CDthan that of the 2412 endplate . Withtop=bottom= 50mm, theCLof the flat endplate was still larger, but theCDwas higher too. The consequence is that the 2412 endplate now has an efficiency only 1.65% smaller than that of the flat endplate. Despite the increase inCL/CD and lowerCD, theCLof the 2412 endplate falls short of that of the flat endplate by 8.3%. A factor could have been the decrease in span of the main element due to the airfoil thickness, since the wing’s overall span has to stay the same due to the rules constraint mentioned in subsection 1.4.2. Therefore, the same two variants of the endplate were simulated with a thinner airfoil, the 2402, whose results are also in Table 4.1. Concerning thetop= 0mm∨bottom= 50mmcombination, the thinner 2402 airfoil compares favorably against the flat endplate: higherCL, identicalCDand a higherCL/CD. When increasing the top dimension, though, both theCLandCDare smaller than those of the flat endplate, with theCL/CD

still larger owing to a bigger decrease in theCD.

Endplate Bottom [mm] Top [mm] Lift [N] Drag [N] CL CD CL/CD

Flat 50 00 24.911 3.507 1.056 0.149 7.102

50 26.575 3.567 1.127 0.151 7.450

2412 50 00 24.470 3.570 1.037 0.151 6.854

50 24.376 3.327 1.033 0.141 7.327

2402 50 00 25.224 3.518 1.069 0.149 7.170

50 25.787 3.430 1.093 0.145 7.519

Table 4.1: Results of the first simulations.

Upon seeing the airflow of the 2402 and flat endplates, it was noted that the vortices generated by the 2402 endplate were at an identical distance from the chord line, as illustrated in Figure 4.2. Consequently their combined effect vanished, and thus only slight to no improvements in the performance of the wing were observed. To test this hypothesis, two sets of simulations were done, using both the flat and 2402 endplates:

Figure 4.2: Orientation of the vortices generated by the main plane and endplate. Wing in front view.

• Fixing the top coordinate totop= 50mm, the bottom coordinate was incremented in 50mm steps untilbottom= 200mm;

• The same procedure was done but in the opposite direction:bottom= 50mmandtop= 100mm, top= 150mm, top= 200m.

The forces’ and coefficients’ values are in Tables 4.2 and 4.4; further, the components of the drag are shown in Tables 4.3 and 4.5.

Endplate Top [mm] Lift [N] Drag [N] CL CD CL/CD

Flat

100 25.801 3.449 1.094 0.146 7.481 150 26.221 3.460 1.112 0.147 7.578 200 26.532 3.468 1.125 0.147 7.651 2402

100 26.138 3.404 1.108 0.144 7.679 150 26.487 3.404 1.123 0.144 7.781 200 26.610 3.361 1.128 0.142 7.917 Table 4.2: Results for fixed dimensionbottom= 50mm.

Geometry Part Drag Component CDComponents

Dpressure[N] Dviscous[N] Dtotal[N] CDpressure CDviscous CDtotal

Flat

Endplate 0.362 0.111 0.474 0.015 0.005 0.020

Main 2.885 0.110 2.994 0.122 0.005 0.127

Total 3.247 0.221 3.468 0.138 0.009 0.147

2402

Endplate 0.167 0.093 0.260 0.007 0.004 0.011

Main 3.002 0.099 3.101 0.127 0.004 0.131

Total 3.169 0.192 3.361 0.134 0.008 0.142

Table 4.3: Drag components of the Flat and 2402 endplates withtop= 200mmandbottom= 50mm.

The changes in the dimensions brought significant differences between the two endplate designs, with the 2402 endplate generally displaying identical or betterCL,CDandCL/CDvalues. Changing the top dimension resulted in slightly largerCLand smallerCD values of the 2402 endplate in comparison with the flat endplate, leading to slightly higher CL/CD values. This trend is more pronounced when

Endplate Bottom [mm] Lift [N] Drag [N] CL CD CL/CD

Flat

100 26.295 3.466 1.115 0.147 7.587

150 27.177 3.512 1.152 0.149 7.738

200 27.826 3.548 1.180 0.150 7.843

2402

100 27.072 3.420 1.148 0.145 7.916

150 28.115 3.389 1.192 0.144 8.296

200 28.981 3.348 1.229 0.142 8.656

Table 4.4: Results of the fixed dimensiontop= 50mm.

Geometry Part Drag Component CDComponents

Dpressure[N] Dviscous[N] Dtotal[N] CDpressure CDviscous CDtotal

Flat

Endplate 0.398 0.133 0.531 0.017 0.006 0.023

Main 2.906 0.112 3.017 0.123 0.005 0.128

Total 3.304 0.245 3.548 0.140 0.010 0.150

2402

Endplate 0.076 0.104 0.180 0.003 0.004 0.008

Main 3.054 0.114 3.168 0.129 0.005 0.134

Total 3.130 0.218 3.348 0.133 0.009 0.142

Table 4.5: Drag components of the Flat and 2402 endplates withtop= 50mmandbottom= 200mm.

increasing the bottom dimension. The CD values are similar to those of increasing top dimension, but the increase inCL is more noticeable, with the gains in term ofCL/CD evident, reaching a maximum increase of 10.4% for thetop= 50mm∨bottom= 200mm.

The placement of the endplate relative to the main plane affects the strength of the tip vortices of the wing assembly, as can be seen in the vorticity countour of Figure 4.3. Moving the endplate upward leads to a stronger lower vortex and a weaker top vortex, while the opposite happens when the endplate is moved downward. Since the strengthening of one of the vortices comes with a decrease in the intensity of the other, the two configurations have similarCD.

Looking at the different drag components, the introduction of the airfoil to the endplate reduces the wing’s overall drag by reducing the endplate’s pressure and viscous drag. This is again intensified in the case of thetop= 50mm∨bottom = 200mm. The viscous and pressure drag values of the main wing increase somewhat with the 2402 endplate, however, resulting in a larger main wing total drag. Still, this increase is not enough to offset the drag reduction of the endplate.

The difference in lift coefficient seems to come from the different pressure distribution of the low- pressure side of the wing Figure 4.4. The isobaric lines of the top = 50mmconfiguration are closer to being parallel than those of the bottom= 50mmdesign. Not only that, but the magnitude of theCp

values on the underside of the wing are higher in the first configuration, especially near the tip of the wing. This will inevitably result in a higher lift coefficient.

(a) Top=50, bottom=200. (b) Top=200, bottom=50.

Figure 4.3: Vorticity countour atx= 400mmof the 2402 endplate.

(a) Top=50, bottom=200. (b) Top=200, bottom=50.

Figure 4.4: Pressure coefficient contour on the underside of the wing.