E220-il airfoil theoretical analysis

7/23/2019 E220-il airfoil theoretical analysis

http://slidepdf.com/reader/full/e220-il-airfoil-theoretical-analysis 1/12

AE311 Aerodynamics

Assignment-1

Shubham Maurya

Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, 695547, India

The aerodynamic characteristics of E220-il were studied and compared with approxi-mately similar NACA series airfoils. For this purpose, NACA 2412 and NACA 25112 werechosen. Cp vs x/c (for selected AOA and Re), Cl vs α, Cd vs α, Cl/Cd vs α, Cm vs α,Clmax vs Re, Cdmin vs Re were computed and plotted using XFoil and XFLR5. In theend applications and specialty of each airfoil were discussed.

Nomenclature

C l Co-efficient of liftC d Co-efficient of dragC m Co-efficient of momentL Lift per unit span, N/mD Drag per unit span, N/mRe Reynolds numberα Angle of attack, degreeD∗ Displacement thickness

I. Aerodynamic characteristics of E220-il

Figure 1: C l vs. angle of attack for Re=50,000(blue); 100,000(yellow); 500,000(red); 1,000,000(green)

From the C l vs α plot, it is inferred that lift co-efficient increases with angle of attack. As Re increases,C l also increases for a given angle of attack (Fig.1). This is because of more fluid velocity and hence low

1 of 12

Aerodynamics Report, IIST



pressure on the curved surface. The flow separation at trailing edge and stall occurs at an angle of attackof 80-120. The C l at stall is higher for high Re which implies the C l would be higher as freestream velocityincreases provided freestream density and dynamic viscosity remains constant.

Figure 2: C d vs. angle of attack

The drag co-efficient increases with angle of attack (Fig.2). This is because of adverse pressure gradientsand subsequent flow separation on the airfoil which are significant at higher angle of attacks. Also, the C dincrease drastically for α > 10o and hence the above reasoning is justified. Moreover, the C d decreases athigher Re because of thin boundary layer and less effect of viscosity.

Figure 3: C m vs. angle of attack

2 of 12




The co-efficient of moment is negative for all range of angle of attacks except 100-170 where it is posi-tive.(Fig. 3) The negative values of moment arise from the fact that lift and drag together exert negative(nose down) torque on the airfoil. The C m hits a maximum around α = 12o− 17o and again shoots down tonegative values. This sharp transitions could be attributed to boundary layer separation and so the lift anddrag co-efficient fluctuate and hence the C m is also varying abruptly.

Figure 4: L/D vs. angle of attack

The L/D plot (Fig.4) are very important in optimizing the performance of an aircraft. In the case of E220-il airfoil, maximum C l

C doccurs at Re=1,000,000 and its value is 123. As explained earlier, C l increases

with Re and C d decreases with Re, resulting in increase of C lC d

ratio with increase in Re. Therefore, the C lC d

is least at Re=50,000. The variation of C l

C d with α results in a maxima at some angle of attack (say criticalα). This critical angle of attack decreases as Re increases, which should mean that an airfoil kept in largerfree stream velocity is more efficient (greater L/D ratio) at smaller angle of attacks compared to the sameairfoil kept at lower freestream velocity of air.

3 of 12






II. Comparison with NACA airfoils

The E220-IL airfoil was compared with NACA 2412 and NACA 25112 as the geometrical aspects of thesewere essentially similar.Why only NACA 2412 and NACA 25112 were chosen for comparison?E220-IL airfoil had maximum thickness of 11.5% at 33.1% chord and maximum camber of 2.2% at 37.7%chord. In contrast to E220-IL, NACA 2412 had maximum thickness 12% at 30% chord and maximumcamber of 2% at 40% chord. Similarly, NACA 25112 had maximum thickness 12% at 29 .5% chord and max-

imum camber of 2% at 27.2% chord. The geometry of the three airfoils are superimposed over each other toget a representative idea for comparing them (Fig.9). Thus, it is clear that all three airfoils are almost similar.

Figure 9: Geometry of E220-IL, NACA 2412 and NACA 25112

Figure 10: C l vs. α for E220-il, NACA 2412 and NACA 25112 at Re = 105

The C l vs. α was compared for all three airfoils at fixed Re of 10 5 (Fig.10). The lift curve slope of allthree airfoils were nearly equivalent as well as the plots were almost coincident for angle of attack varyingfrom 00 to 80. Both NACA 2412 and NACA 25112 airfoils stalled at α = 120 in contrast to E220-IL whichstalled at 80 angle of attack. The NACA 25112 outperformed other airfoils as it had the highest value of C ltill stall. On the other hand, E220-IL airfoil had the least coefficient of lift.

5 of 12




Figure 11: C d vs. α for E220-il, NACA 2412 and NACA 25112 at Re = 10 5

The C d vs. α plots are shown in Fig.11. Coefficient of drag increases with angle of attack due to flowseparation resulting in high pressure drag. All three airfoils exhibited similar behaviour in C d with angle of attack.

Figure 12: C m vs. α for E220-il, NACA 2412 and NACA 25112 at Re = 105

From the C m vs. α plot (Fig.12), the pitching moment coefficient becomes less negative as angle of attack increases, which implies longitudinal stability decreases with angle of attack(upto 100). In short, dC m

dα

is positive, hence the airfoil gets more tendency to dive downwards upon increasing angle of attack. But,this trend is reversed at higher values of angle of attack as evident from the graph.

6 of 12




Figure 13: L/D vs. α for E220-il, NACA 2412 and NACA 25112 at Re = 10

5

The C l/C d vs. α plot for Re = 105 is illustrated in Fig.13. The highest lift to drag ratio is observed tobe of E220-IL that is around 53. Now, here the practical application of E220-IL is realized. We found earlierthat C l for E220-IL was the least among the three airfoils. But this smaller lift is compensated by smallerdrag which in a way gives a higher lift co-efficient per unit drag. Thus the efficiency and performance of aplane is improved because the lift that has to be generated requires less propulsive power to counter the drag.

Figure 14: C p vs x

c

for α = 30 and Re=105 Figure 15: C p vs x

c

for α = 30 & Re=105

The C p vs. xc

graph is plotted at α = 30 and Re = 105 for each of the three airfoils (Fig.14,15,16)

7 of 12




Figure 16: C p vs xc

for α = 30 & Re=105

Clearly the boundary layer appears to be similar for all the three airfoils. However, the NACA 25112airfoil due to location of maximum camber near to leading edge exhibits early transition from laminar toturbulent.

The C lmax and C dmin vs. Re were tabulated and plotted (Fig.17, 18)

Airfoil ↓ Re → C lmax

50000 100000 500000 1000000

E220-IL 1.072258 1.043403 1.141882 1.181957

NACA 2412 1.125334 1.202066 1.338982 1.491072

NACA 25112 0.8355122 1.229343 1.356918 1.473096

Table 1: Comparison of C lmax

with Re for E220-IL, NACA 2412 and NACA 25112 airfoils

Airfoil ↓ Re → C dmin

50000 100000 500000 1000000

E220-IL 0.02540813 0.0182169 0.007364166 0.005360507

NACA 2412 0.02136979 0.01576447 0.006297085 0.005464215

NACA 25112 0.02286631 0.01456981 0.007588354 0.005995777

Table 2: Comparison of C dmin with Re for E220-IL, NACA 2412 and NACA 25112 airfoils

8 of 12




Figure 17: C lmax vs. Re for E220-IL, NACA 2412 and NACA 25112 airfoils

Figure 18: C dmin vs. Re for E220-IL, NACA 2412 and NACA 25112 airfoils

The airfoils tend to follow a general trend; C lmax for all the airfoils effectively increases with Re andC dmin decreases as Re is increased. The increase in C lmax with Re can be attributed to higher flow ve-

locity and hence more negative C p over upper surface. The decrease in C dmin with Re is due to sufficientpressure recovery by inertial effects causing thinner wake region. This causes less pressure drag on the airfoil.

9 of 12




Figure 19: C p vs. xc

for E220-IL airfoil at α = 50 and Re = 106

The location of laminar to turbulent transition is also plotted for E220-il at 50 angle of attack andRe = 106 (Fig.19). The transition of flow to turbulent helps in reducing the drag at higher Re compared tothat at lower Re. As α is increased, transition region moves towards leading edge and the adverse pressuregradient causes the C d to increase.

III. Specialty and applications

A. E220-il (11.48%)

The Eppler E 22x series airfoils have reflex camber lines. The reflexed camberlines bend upwards or straightto the chord line at the trailing edge. The reflexed and cambered airfoils have special importance in 5 digitNACA airfoil series nomenclature, where 3rd digit denotes simple cambered by 0 and reflex camber by 1.The reflex camber lines concentrate or shift resultant lift towards leading edge. This helps in stabilizing someplane or gliders while pitching. The Eppler E 22x series airfoils are extensively used in sailplanes, glidersand as spoilers in racing cars.

B. NACA 2412

NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with amaximum thickness of 12% of the chord. Four-digit series airfoils by default have maximum thickness at30% of the chord (0.3 chords) from the leading edge. NACA 2412 is a low speed airfoil; this airfoil is usedin single engine Cessna 152, 172 and 182 airplanes.

C. NACA 25112

NACA 25112 is a reflex camber airfoil. Intended applications of this airfoil are yet to be worked out.

References

1E220 (11.48%) (e220-il), www.airfoiltools.com/airfoil/details?airfoil=e220-il

10 of 12




IV. Appendix on Displacement thickness

Data of displacement thickness (D∗) for NACA 2412 airfoil at 60 angle of attack and Re = 106 is tabulatedalong with U e

V ∞, momentum thickness and skin friction coefficient (C f ). The displacement thickness at all

the co-ordinates of airfoil section were obtained by XFoil.(TABLE 3)The displacement thickness is more near trailing edge of upper surface which clearly imply presence of slightly thick boundary layer compared to that at point of maximum curvature. The displacement thicknessincreases as we move from leading edge to trailing edge which mean that boundary layer grows and its

maximum thickness occurs at the trailing edge.

11 of 12




Table 3: NACA 2412 airfoil datasheet generated by XFoil at 60 angle of attack and Re = 106

x y Ue/Vinf

Displacement

thickness

Dstar

Momentum

thickness

Theta

Skin friction

coefficientCf

Shape

factor

H1.00008 0.00126 0.90856 0.011567 0.005728 0.00075 2.019

0.95654 0.01006 0.96093 0.008095 0.004585 0.001371 1.766

0.89344 0.02189 1.02698 0.005694 0.003538 0.002165 1.609

0.81142 0.03571 1.09159 0.004229 0.00276 0.002942 1.532

0.72897 0.0479 1.14358 0.003364 0.002243 0.00357 1.5

0.64638 0.0584 1.19003 0.002735 0.001842 0.004145 1.485

0.56383 0.06708 1.23508 0.00222 0.001501 0.004734 1.479

0.48154 0.07373 1.28152 0.001768 0.001196 0.0054 1.478

0.39989 0.07803 1.33422 0.001341 0.00091 0.006337 1.473

0.32014 0.07913 1.38694 0.000955 0.000655 0.007679 1.46

0.24188 0.07618 1.43277 0.000645 0.000429 0.008663 1.5040.16626 0.0685 1.50379 0.000871 0.000284 0.000987 3.069

0.09707 0.05559 1.56827 0.000658 0.000214 0.001367 3.069

0.04637 0.03989 1.6589 0.000433 0.000145 0.00255 2.977

0.01988 0.02682 1.75307 0.000263 0.000094 0.005828 2.787

0.0067 0.01625 1.80753 0.000148 0.000058 0.014595 2.526

0.00071 0.00652 1.64174 0.000084 0.000036 0.02919 2.305

0.00052 -0.0027 0.97691 0.000069 0.000031 0.022922 2.217

0.00632 -0.01177 0.14792 0.000088 0.00004 0.002708 2.22

0.01913 -0.02014 -0.35644 0.00014 0.000062 0.003923 2.271

0.04364 -0.02854 -0.63737 0.000223 0.000096 0.004209 2.32

0.09206 -0.03677 -0.80126 0.000355 0.000149 0.003146 2.3760.16381 -0.04154 -0.87572 0.00052 0.000214 0.002222 2.431

0.24391 -0.04227 -0.90484 0.000682 0.000275 0.001673 2.475

0.32706 -0.04054 -0.91742 0.00083 0.000332 0.001356 2.501

0.41166 -0.03758 -0.92733 0.000937 0.000378 0.001243 2.478

0.49606 -0.03367 -0.93339 0.001064 0.000423 0.001059 2.516

0.58104 -0.02892 -0.93473 0.001192 0.000468 0.000912 2.549

0.66643 -0.02368 -0.93453 0.001311 0.00051 0.000811 2.569

0.75205 -0.01817 -0.9336 0.001423 0.000551 0.000735 2.584

0.83772 -0.01251 -0.93127 0.001546 0.000592 0.000651 2.614

0.92272 -0.00672 -0.92434 0.001756 0.000642 0.000491 2.736

0.99362 -0.00171 -0.90936 0.002344 0.000711 0.000142 3.2971.02244 -0.00117 0.90398 0.013705 0.0066 0 2.076

1.09412 -0.00307 0.93345 0.009288 0.005843 0 1.59

1.25321 -0.00303 0.96383 0.00668 0.005235 0 1.276

1.60602 0.00679 0.98345 0.005426 0.004909 0 1.105

1.9995 0.02583 0.99075 0.005073 0.004799 0 1.057

12 of 12

A d i R t IIST

Documents

E220-il airfoil theoretical analysis