Comparison of Aerodynamic Performance of Aircraft Wing by Changing the Maximum Camber As Percentage of the Chord

Comparison of Aerodynamic Performance of Aircraft Wing by Changing the Maximum Camber As Percentage of the Chord

Mafiz Uddin Ahmed

Cyient Ltd. (Hyderabad)

Abstract In transport aircraft, the wing contributes about 1/3rd of the total aircraft drag. Designers main focus is on the design optimisation of the wing profile so as to reduce the drag and thus obtaining better fuel efficiency and overall performance of the aircraft. The wing profile for most aircraft is of airfoil- shaped. In order to minimize the wing profile drag the figure of merit (FOM) applicable to aircraft should be maximized. FOM is the ratio of the section maximum lift coefficient (CL, max) to the cruise section profile drag coefficient (CD). Here in this paper, we are trying to increase the CL/CD ratio by increasing the percentage of the camber in the NACA airfoil.

We focused our research on a straight wing. The amount of laminar flow can be maximised on a straight wing by using very carefully tailored shapes to move the maximum thickness very far aft on the wing. Here we are going to analyse the impact of increase in the percentage of camber on the ratio of CL/CD. For this purpose, NACA 2412 Airfoil which has a maximum camber of 2% located at 40% (0.4 Chords) from the leading edge with a maximum thickness of 12% of the chord & NACA 3412 which has a maximum camber of 3% located at 40% (0.4 Chords) from the leading edge with a maximum thickness of 12% of the chord are employed. The results obtained from the study shows that by increasing the camber of NACA airfoil, the CL/CD ratio can be increased also the pressure and velocity contours becomes much smoother with NACA 3412 as compared with NACA 2412 airfoils. The simulation results are comparable to the virtual wind tunnel results.

KeywordsDesign optimization of the wing profile; figure of merit; lift coefficient; profile drag coefficient; laminar flow; NACA 2412; NACA 3412

1. INTRODUCTION

   The research on advanced-technology airfoils for general aviation applications started way back in 1900s. The initial emphasis in this research program was on the design and testing of turbulent-flow airfoils with the basic objective of producing a series of airfoils which could achieve higher maximum lift coefficients than the airfoils used on general aviation airplanes during that time. Accordingly, the emphasis in the research program shifted toward natural laminar-flow (NLF) airfoils in an attempt to obtain lower cruise drag coefficients while retaining the high maximum lift coefficients. The wing profiles for most aircraft are of airfoil-shaped, and when this airfoil- shaped wing moves through a fluid, it produces an aerodynamic force. This force has two components, one which is perpendicular to the direction of motion called lift and another which is parallel to the direction of motion is called drag. For most aircraft, the total aircraft drag at cruise condition is mainly occurred by the wing profile drag. It contributes nearly one

   third of the total drag for transport aircraft. As the size of the aircraft decreases, the contribution of the wing profile drag on the total aircraft drag increases. This is because of the increase in relative wing area. [1]

   Figure 1: percentage of Wing profile drag on total aircraft drag for various aircraft type [1]

   The table clearly shows that the percentage of the total aircraft drag due to the wing profile drag for sailplane is the highest among the rest as it has the smallest size relative to others in the given list. Whereas, in transport and business jet aircraft the ratio of Wing profile drag to Total aircraft drag is 1/3 which is the least among rest as its the biggest compared to others. In order to minimize the wing profile drag the figure of merit (FOM) applicable to aircraft should be maximized. FOM is the ratio of the section maximum lift coefficient (cl,max) to the cruise section profile drag coefficient. The FOM can be explained as follows. The reduction in wing area can be reduced if a higher maximum lift coefficient is achieved which will results in lower drag. The reduction in wing profile drag is also possible if a lower section profile drag coefficient is achieved. [1]

   How to increase the extend of laminar flow over Wing:

   1. By carefully adapting the size of the bumps to the depth of the boundary layer (that part of the air flowing next to the skin of the wing), a stable wave can be established in the boundary layer and this allows the flow to remain laminar for long runs (30 to 50 percent of the upper surface) over the wing. [2]

   2. To maximize the amount of laminar flow on a straight wing, designers use very carefully tailored shapes to move the maximum thickness very far aft on the wing. Laminar flow runs of 70 percent on the upper surface and nearly 100 percent on the lower surface are possible if caution is used. The resulting

   drag is very low compared to conventional turbulent airfoils producing the same lift, as much as 70 percent less. So, all this is on the straight wing. [2]

   Here we are going to analyse the impact of increase in the percentage of camber on the ratio of CL/CD. For this purpose, NACA 2412 Airfoil which has a maximum camber of 2% located at 40% (0.4 Chords) from the leading edge with a maximum thickness of 12% of the chord & NACA 3412 which has a maximum camber of 3% located at 40% (0.4 Chords) from the leading edge with a maximum thickness of 12% of the chord are employed.

   NACA AIRFOIL:

   The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). The shape of the NACA airfoils is described using a series of digits following the word "NACA". The parameters in the numerical code can be entered into equations to precisely generate the cross-section of the airfoil and calculate its properties. [3]

   Figure 2: Profile geometry [3]

   FOUR-DIGIT SERIES:

   The NACA four-digit wing sections define the profile by:

   1. First digit describing maximum camber as percentage

      = 5 [0.2969 0.1260 0.35162 + 0.28433 0.10154], [3]

      Where:

      x is the position along the chord from 0 to 1.00 (0 to 100%), y_t is the half thickness at a given value of x (centerline to surface),

      t is the maximum thickness as a fraction of the chord (so t gives the last two digits in the NACA 4-digit denomination divided by 100). [3]

      Note that in this equation, at x = 1 (the trailing edge of the airfoil), the thickness is not quite zero. If a zero-thickness trailing edge is required, for example for computational work, one of the coefficients should be modified such that they sum to zero. Modifying the last coefficient (i.e., to 0.1036) will result in the smallest change to the overall shape of the airfoil. The leading edge approximates a cylinder with a chord- normalized radius of

      = 1.10192 [3]

      Now the coordinates (, ) of the upper airfoil surface and

      (, ) of the lower airfoil surface are

      = = , = +, = – [3]

      Symmetrical 4-digit series airfoils by default have maximum

      thickness at 30% of the chord from the leading edge. [3]

      Figure 3: Plot of a NACA 0015 foil generated from formula [3]

      Equation for a cambered 4-digit NACA airfoil:

      The simplest asymmetric foils are the NACA 4-digit series foils, which use the same formula as that used to generate the 00xx symmetric foils, but with the line of mean camber bent. The formula used to calculate the mean camber line is

      2

      2(2 ), 0, [3]

      of the hord. [3]

      = { 2

   2. Second digit describing the distance of maximum camber from the airfoil leading edge in tenths of the chord. [3]

      where

      (1)2((12)+2 ), 1,

   3. Last two digits describing maximum thickness of the airfoil as percent of the chord. [3]

   For example, the NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with a maximum thickness of 12% of the chord. [3]

   The NACA 0015 airfoil is symmetrical, the 00 indicating that it has no camber. The 15 indicates that the airfoil has a 15% thickness to chord length ratio: it is 15% as thick as it is long. [3]

   Equation for a symmetrical 4-digit NACA airfoil:

   The formula for the shape of a NACA 00xx foil, with "xx" being replaced by the percentage of thickness to chord, is

   m is the maximum camber (100 m is the first of the four

   digits),

   p is the location of maximum camber (10 p is the second digit in the NACA xxxx description).

   For example, a NACA 2412 airfoil uses a 2% camber (first digit) 40% (second digit) along the chord of a 0012 symmetrical airfoil having a thickness 12% (digits 3 and 4) of the chord.

   For this cambered airfoil, because the thickness needs to be applied perpendicular to the camber line, the coordinates

   (, ) and (, ), of respectively the upper and lower

   airfoil surface, become [3]

   = , = + , [3]

   = + , = , [3]

   where

   = arctan ,

   hole in the domain which is of the shape of the thing we are interested in testing and the fluid flows over that gap.

   2

   2 ( ), 0,

   = {

   [3]

   2 (), 1,

   2

   (1)

   Figure 4: Plot of a NACA 2412 foil [3]

2. ANALYSIS OF DESIGN USING CFD: Fluid flow analysis is done in ANSYS fluent.

   The geometry of the NACA 2412 and 3412 airfoils are created in ANSYS fluent software. The co-ordinate points of the airfoils are generated from airfoiltools.com. These data points are then exported to the design modular to generate the airfoil.

   NACA 2412 Airfoil

   Figure 5: NACA 2412 AIRFOIL [4]

   Max. Camber: 2%

   Max. Camber Position: 40% Thickness: 12%

   NACA 3412 Airfoil

   Figure 6: NACA 3412 AIRFOIL [4]

   Max. Camber: 3%

   Max. Camber Position: 40% Thickness: 12%

   A C-style domain i.e., rectangle at the back and a circle in the front is created for the analysis. The airfoil is then subtracted from the domain. In a CFD study, we are essentially making a

   Figure 7: C Style Domain created in ANSYS FLUENT

   1. MATERIAL PROPERTIES:

      Air	Density (kg/m3)	1.225
      	Viscosity (kg/m-s)	1.789 x 10-5
      6061 Aluminium Alloy	Youngs modulus (E)	68.9 GPa
      	Specific heat capacity (c)	897 J/(kgK)
      	Thermal conductivity(k)	151202 W/(mK)
      	Poissons ratio()	0.33

      Table 1: Material properties of Air [5] and 6061 Aluminium Alloy [6]

   2. ELEMENT SELECTION & DOF

      Element Type	Thin Shell Element DOF/Node	No of Nodes	Total DOF
      NACA 2412	6	49518	6×49518=297108
      NACA 3412	6	84098	6×84098=504588

      Table 2: Element selection and Degree of freedom obtained from ANSYS FLUENT after meshing

   3. MESHING (DATA ON ELEMENTS & NODES)

      In order to get better control over the aero foil mesh, we need some edge sizing to our domain. So, we splitted the domain up and created some edges. The final mesh consists of quadrilateral and triangular elements. Overall, it is quadrilateral dominant.

      Figure 8: Meshing created in ANSYS FLUENT

      Figure 9: Enlarge view of the meshing around the Airfoil created in ANSYS FLUENT

      Model	Element	Nodes
      NACA 2412	50895	49518
      NACA 3412	85126	84098

      Table 3: Nodes and elements for NACA 2412 & NACA 3412 Airfoil generated from Meshing in ANSYS FLUENT

      • Method: Quadrilateral Dominant

      • The final mesh consists of quad and tri elements

   4. BOUNDARY CONDITION

   We use pressure based steady state solver because pressure based is generally for sub-sonic incompressible flow and the steady state assumes that the flow wont be varying with time. We use the K-omega SST turbulence model. It is good model for attach flows, its robust and deals well with separated flows. The working fluid is air. We are assuming that the velocity at the airfoil wall is zero i.e., there is no slipping on the airfoil wall. Velocity magnitude is taken as 30m/s because its close to wind tunnel type of airspeed. Angle of attack is assumed to be zero. [7]

   Boundary conditions Gauge pressure (Pascal) = 0 X Velocity = 30 m/s

   Y Velocity = 0 Turbulence intensity: 5%

   Turbulent Viscosity Ratio: 10

   Turbulent Kinetic Energy = 3.375 m2/s2 Specific Dissipation Rate = 23104.81 1/s Shear condition: no slip [7]

3. RESULTS AND DISCUSSIONS

   Coupled scheme solution method is used. In this scheme pressure and velocity solves simultaneously, it converges lot quicker.

   1. PRESSURE CONTOUR

      Figure 10: Pressure contours of NACA 2412 & NACA 3412 generated in ANSYS FLUENT

      At the leading edge of the airfoil a high-pressure region is generated as the flow directly hits this portion. The pressure at the top of the airfoil is lower than the atmospheric pressure. The pressure at the bottom of the airfoil is a little bigger than atmospheric pressure. So, the lift generated depends on the difference between the pressure at the bottom and the pressure at the top. We can see from pressure contour that the flow with NACA 3412 is much smoother than with NACA 2412.

   2. VELOCITY CONTOUR

      Figure 11: Velocity contours of NACA 2412 & NACA 3412 generated in ANSYS FLUENT

      At the leading edge of the airfoil the velocity is almost at stagnation point. Velocity increases above the airfoil and then the flow kinds of losses a bit of momentum and slows down a little bit. The velocity at the bottom of the airfoil keeps on decreasing. We can see from velocity contour that the flow with NACA 3412 is much smoother than with NACA 2412.

   3. SIMULATION RESULTS

   	NACA 2412	NACA 3412
   Drag Co-eff. (C ) d	1.378e-2	7.374e-3
   Lift Co-eff. (C ) l	2.26e-1	3.225e-1
   C / C l d	16.40	44.73

   Figure 12: Simulation Results of NACA 2412 & NACA 3412

   Table 4: Table comparing the values of Drag co-eff., Lift co-eff., Cd/Cl ratio of NACA 2412 & NACA 3412 obtained from simulation results done in ANSYS FLUENT

4. CONCLUSION

So, by increasing the camber i.e., moving the maximum thickness very far aft on the wing it can be seen that the figure of merit (FOM) applicable to aircraft can be maximized obtaining an increased CL/CD ratio thus achieving better fuel efficiency and overall performance of the aircraft. From the pressure and velocity contours it can be seen that the flow with Naca 3412 is much smoother than Naca 2412. Thus, it can be concluded that NACA 3412 gives a better CL/CD ratioand smoother pressure and velocity contours than NACA 2412. But in order to give structural support and space for accommodating the fuel tanks, the Aircraft wings cant be curved beyond some extend.

REFERENCES

[1] D. M. Somers, "Design of a Slotted, Natural-Laminar-Flow Airfoil for Business-Jet Applications," NASA/CR2012-217559 , pp. 60-70, 2012.

[2] "NASA Blogs home," Armstrong Flight Research Center, 11 February 2011.

https://blogs.nasa.gov/armstrong/2011/02/11/post_1296777084480/#:~: text=To%20maximize%20the%20amount%20of,possible%20if%20cau tion%20is%20used.

[3] https://en.wikipedia.org/wiki/NACA_airfoil

[4] http://airfoiltools.com/airfoil/naca4digit

[5] Viscosity of Air, Dynamic and Kinematic Engineers Edge:https://www.engineersedge.com/physics/viscosity_of_air_dynami c_and_kinematic_14483.htm

[6] https://www.engineeringclicks.com/6061-aluminum-properties/

[7] T Aero NACA 0012 CFD analysis Ansys Fluent Part 3: CFD Analysis https://youtu.be/iyIQPASVXKk.