Verma Graduate Project CAD-CAM

Graduate Final Project

CAD/CAM THEORY AND APPLICATIONS

(Design of a Multi-Element Wing)

- Rishabh Verma

PURDUE SCHOOL OF ENGINEERING AND TECHNOLOGY

INDIANA UNIVERSITY PURDUE UNIVERSITY INDIANAPOLIS

Objective-

To model a rear wing for a race car, with modification to a Multi-Element wing profile with

and without a Gurney flap; on a CAD modelling software. Specific analysis on the

downforce, angle of attack and drag force created by the various airfoil configurations.

Theory of Airfoils -

A fixed-wing aircraft's wings, horizontal, and vertical stabilizers are built with airfoil-shaped

cross sections, as are helicopter rotor blades. Airfoils are also found in propellers, fans,

compressors and turbines. Sails are also airfoils, and the underwater surfaces of sailboats,

such as the centerboard and keel, are similar in cross-section and operate on the same

principles as airfoils. Swimming and flying creatures and even many plants and sessile

organisms employ airfoils/hydrofoils: common examples being bird wings, the bodies of

fish, and the shape of sand dollars. An airfoil-shaped wing can create downforce on an

automobile or other motor vehicle, improving traction.

Any object with an angle of attack in a moving fluid, such as a flat plate, a building, or the

deck of a bridge, will generate an aerodynamic force (called lift) perpendicular to the flow.

Airfoils are more efficient lifting shapes, able to generate more lift (up to a point), and to

generate lift with less drag.

A lift and drag curve obtained in wind tunnel testing is shown on the right. The curve

represents an airfoil with a positive camber so some lift is produced at zero angle of attack.

With increased angle of attack, lift increases in a roughly linear relation, called the slope of

the lift curve. At about 18 degrees this airfoil stalls, and lift falls off quickly beyond that. The

drop in lift can be explained by the action of the upper-surface boundary layer, which

separates and greatly thickens over the upper surface at and past the stall angle. The

thickened boundary layer's displacement thickness changes the airfoil's effective shape, in

particular it reduces its effective camber, which modifies the overall flow field so as to

reduce the circulation and the lift. The thicker boundary layer also causes a large increase in

pressure drag, so that the overall drag increases sharply near and past the stall point.

Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight

regimes. Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric

airfoil may better suit frequent inverted flight as in an aerobatic airplane. In the region of

the ailerons and near a wingtip a symmetric airfoil can be used to increase the range of

angles of attack to avoid spin–stall. Thus a large range of angles can be used without

boundary layer separation. Subsonic airfoils have a round leading edge, which is naturally

insensitive to the angle of attack. The cross section is not strictly circular, however: the

radius of curvature is increased before the wing achieves maximum thickness to minimize

the chance of boundary layer separation. This elongates the wing and moves the point of

maximum thickness back from the leading edge.

Supersonic airfoils are much more angular in shape and can have a very sharp leading edge,

which is very sensitive to angle of attack. A supercritical airfoil has its maximum thickness

close to the leading edge to have a lot of length to slowly shock the supersonic flow back to

subsonic speeds. Generally such transonic airfoils and also the supersonic airfoils have a

low camber to reduce drag divergence. Modern aircraft wings may have different airfoil

sections along the wing span, each one optimized for the conditions in each section of the

wing.

Movable high-lift devices, flaps and sometimes slats, are fitted to airfoils on almost every

aircraft. A trailing edge flap acts similarly to an aileron; however, it, as opposed to an

aileron, can be retracted partially into the wing if not used.

A laminar flow wing has a maximum thickness in the middle camber line. Analyzing the

Navier–Stokes equations in the linear regime shows that a negative pressure gradient along

the flow has the same effect as reducing the speed. So with the maximum camber in the

middle, maintaining a laminar flow over a larger percentage of the wing at a higher cruising

speed is possible. However, some surface contamination will disrupt the laminar flow,

making it turbulent. For example, with rain on the wing, the flow will be turbulent. Under

certain conditions, insect debris on the wing will cause the loss of small regions of laminar

flow as well. Before NASA's research in the 1970s and 1980s the aircraft design community

understood from application attempts in the WW II era that laminar flow wing designs were

not practical using common manufacturing tolerances and surface imperfections. That

belief changed after new manufacturing methods were developed with composite

materials (e.g., graphite fiber) and machined metal methods were introduced. NASA's

research in the 1980s revealed the practicality and usefulness of laminar flow wing designs

and opened the way for laminar flow applications on modern practical aircraft surfaces,

from subsonic general aviation aircraft to transonic large transport aircraft, to supersonic

designs.

Gurney Flaps - The Gurney Flap is a small tab projecting from the trailing edge of a wing.

Typically it is set at a right angle to the pressure side surface of the airfoil, and projects 1%

to 2% of the wing chord. This trailing edge device can improve the performance of a simple

airfoil to nearly the same level as a complex high-performance design.

The device operates by increasing pressure on the pressure side, decreasing pressure on

the suction side, and helping the boundary layer flow stay attached all the way to the

trailing edge on the suction side of the airfoil. Common applications occur in auto racing,

helicopter horizontal stabilizers, and aircraft where high lift is essential, such as banner-

towing airplanes.

Modelling Software Used – SolidWorks –

SolidWorks is a solid modeler, and utilizes a parametric feature-based approach to create

models and assemblies. The software is written on Parasolid-kernel.

Parameters refer to constraints whose values determine the shape or geometry of the

model or assembly. Parameters can be either numeric parameters, such as line lengths or

circle diameters, or geometric parameters, such as tangent, parallel, concentric, horizontal

or vertical, etc. Numeric parameters can be associated with each other through the use of

relations, which allows them to capture design intent.

Design intent is how the creator of the part wants it to respond to changes and updates.

For example, you would want the hole at the top of a beverage can to stay at the top

surface, regardless of the height or size of the can. SolidWorks allows the user to specify

that the hole is a feature on the top surface, and will then honor their design intent no

matter what height they later assign to the can.

Features refer to the building blocks of the part. They are the shapes and operations that

construct the part. Shape-based features typically begin with a 2D or 3D sketch of shapes

such as bosses, holes, slots, etc. This shape is then extruded or cut to add or remove

material from the part. Operation-based features are not sketch-based, and include

features such as fillets, chamfers, shells, applying draft to the faces of a part, etc.

Building a model in SolidWorks usually starts with a 2D sketch (although 3D sketches are

available for power users). The sketch consists of geometry such as points, lines, arcs,

conics (except the hyperbola), and splines. Dimensions are added to the sketch to define

the size and location of the geometry. Relations are used to define attributes such as

tangency, parallelism, perpendicularity, and concentricity. The parametric nature of

SolidWorks means that the dimensions and relations drive the geometry, not the other way

around. The dimensions in the sketch can be controlled independently, or by relationships

to other parameters inside or outside of the sketch.

In an assembly, the analog to sketch relations are mates. Just as sketch relations define

conditions such as tangency, parallelism, and concentricity with respect to sketch

geometry, assembly mates define equivalent relations with respect to the individual parts

or components, allowing the easy construction of assemblies. SolidWorks also includes

additional advanced mating features such as gear and cam follower mates, which allow

modeled gear assemblies to accurately reproduce the rotational movement of an actual

gear train.

Analysis Software – OpenFOAM-

OpenFOAM (for "Open source Field Operation and Manipulation") is a C++ toolbox for the

development of customized numerical solvers, and pre-/post-processing utilities for the

solution of continuum mechanics problems, including computational fluid dynamics (CFD).

OpenFOAM solvers include:

Simulation of burning Methane.

Basic CFD solvers

Incompressible flow with RANS and LES capabilities

Compressible flow solvers with RANS and LES capabilities

Buoyancy-driven flow solvers

DNS and LES

Multiphase flow solvers

Particle-tracking solvers

Solvers for combustion problems

Solvers for conjugate heat transfer

Molecular dynamics solvers

Direct Simulation Monte Carlo solvers

Electromagnetics solvers

Solid dynamics solvers

In addition to the standard solvers, OpenFOAM's syntax lends itself to the easy

creation of custom solvers.

OpenFOAM utilities are subdivided into:

Mesh utilities

Mesh generation: they generate computational grids starting either

from an input file (blockMesh), or from a generic geometry specified as

STL file, which is meshed automatically with hex-dominant grids

(snappyHexMesh)

Mesh conversion: they convert grids generated using other tools to the

OpenFOAM format

Mesh manipulation: they perform specific operations on the mesh such

as localized refinement, definition of regions, and others

Parallel processing utilities: they provide tools to decompose,

reconstruct and re-distribute the computational case to perform

parallel calculations

Pre-processing utilities: tools to prepare the simulation cases

Post-processing utilities: tools to process the results of simulation

cases, including a plugin to interface OpenFOAM and ParaView.

Surface utilities

Thermophysical utilities

Advantages-

Friendly syntax for partial differential equations.

Fully documented source code.

Unstructured polyhedral grid capabilities.

Automatic parallelization of applications written using OpenFOAM high-level syntax.

Wide range of applications and models ready to use.

Commercial support and training provided by the developers.

No license costs.

Modelling – (SolidWorks Coordinates for Basic Airfoil modelling)

-Attached STL Files

Coordinates for Airfoil

No. X - Y- Z-

1 203.2736 0 -0.24526 2 202.9728 0 -0.3812

3 202.0718 0 -0.78638 4 200.5747 0 -1.45288

5 198.4882 0 -2.36789 6 195.8222 0 -3.51373

7 192.5891 0 -4.86847 8 188.8047 0 -6.40669 9 184.4877 0 -8.09935

10 179.6597 0 -9.91575 11 174.3456 0 -11.8226

12 168.5739 0 -13.7857 13 162.3755 0 -15.7704

14 155.7847 0 -17.7422 15 148.8389 0 -19.6669

16 141.5784 0 -21.5118 17 134.0458 0 -23.2453

18 126.2864 0 -24.8386 19 118.3484 0 -26.2648 20 110.2813 0 -27.5001

21 102.1373 0 -28.524 22 93.96943 0 -29.3201

23 85.8327 0 -29.8757 24 77.65796 0 -30.1634

25 69.4629 0 -30.0313 26 61.47308 0 -29.4624

27 53.75453 0 -28.4836 28 46.37085 0 -27.1307

29 39.38158 0 -25.449 30 32.84139 0 -23.4905 31 26.79924 0 -21.3124

32 21.29719 0 -18.9754 33 16.37142 0 -16.5417

34 12.05118 0 -14.0722 35 8.359648 0 -11.6261

36 5.313883 0 -9.25779 37 2.925064 0 -7.01609

38 1.199693 0 -4.94162 39 0.139395 0 -3.0673

40 -0.25847 0 -1.41569 41 0 0 0 42 0.884733 0 1.134466

43 2.362403 0 1.95011 44 4.414723 0 2.45872

45 7.020357 0 2.677566

No. X - Y- Z- 46 10.1539 0 2.628595

47 13.78773 0 2.338629 48 17.89217 0 1.838554

49 22.43633 0 1.16271 50 27.38831 0 0.347675

51 32.71683 0 -0.56693 52 38.39058 0 -1.54087

53 44.3803 0 -2.53289 54 50.65735 0 -3.50134

55 57.1945 0 -4.40578 56 63.96573 0 -5.20619

57 70.94484 0 -5.86557 58 78.10602 0 -6.34878 59 85.57971 0 -6.65216

60 93.2877 0 -6.88076 61 101.0627 0 -7.036

62 108.8616 0 -7.10651 63 116.6392 0 -7.08437

64 124.3497 0 -6.96529 65 131.9465 0 -6.74949

66 139.383 0 -6.44042 67 146.6118 0 -6.0454

68 153.5871 0 -5.575 69 160.2626 0 -5.04221 70 166.5939 0 -4.46268

71 172.5383 0 -3.85328 72 178.0548 0 -3.2319

73 183.1045 0 -2.6164 74 187.6517 0 -2.02489

75 191.6633 0 -1.47401 76 195.1102 0 -0.97942

77 197.9664 0 -0.55474 78 200.2109 0 -0.21194

79 201.8266 0 0.039624 80 202.8009 0 0.193446 81 203.1264 0 0.245262

Velocity Vs X-direction vector plots for Stall Angle, Basic Airfoil

Design: with & without Gurney Flap

(OpenFoam Result Images)

Results

Run no. Date File Name Airspeed Drag Force Lift Force A A AR Rho Alpha Cd CL L/D

f/s in sq sq ft lb-sec2 / ft 4deg

1 First Run 0 Degree 45 5.25 -197.76 454.15 3.153 5.91 2.38E-03 0.0 0.016 -0.604 37.669

2 AOA -3 degree 45 6.97 -293.23 454.15 3.153 5.91 2.38E-03 -3.0 0.021 -0.895 42.070

3 AOA -5 degree 45 7.72 -340.36 454.15 3.153 5.91 2.38E-03 -5.0 0.024 -1.039 44.088

4 AOA -6 degree 45 10.97 -339.88 454.15 3.153 5.91 2.38E-03 -6.0 0.033 -1.038 30.983

5 AOA -10 degree 45 18.31 -403.05 454.15 3.153 5.91 2.38E-03 -10.0 0.056 -1.230 22.013

6 AOA -11 degree 45 23.60 -370.72 454.15 3.153 5.91 2.38E-03 -11.0 0.072 -1.132 15.708

7 AOA -12 degree 45 23.05 -417.76 454.15 3.153 5.91 2.38E-03 -12.0 0.070 -1.275 18.124

8 AOA -14 degree 45 27.44 -451.47 454.15 3.153 5.91 2.38E-03 -14.0 0.084 -1.378 16.453

9 AOA -15 degree 45 31.56 -398.03 454.15 3.153 5.91 2.38E-03 -15.0 0.096 -1.215 12.612

10 AOA -16 degree 45 33.58 -435.41 454.15 3.153 5.91 2.38E-03 -16.0 0.103 -1.329 12.966

11 AOA -17 degree 45 41.64 -464.96 454.15 3.153 5.91 2.38E-03 -17.0 0.127 -1.419 11.166

12 AOA -17.10 45 38.8 -437.21 454.15 3.153 5.91 2.38E-03 -17.1 0.118 -1.335 11.268

13 AOA -17.25 45 48.51 -392.22 454.15 3.153 5.91 2.38E-03 -17.3 0.148 -1.197 8.085

14 AOA -18 degree 45 47.43 -389.01 454.15 3.153 5.91 2.38E-03 -18.0 0.145 -1.188 8.202

15 AOA -19 degree 45 44.85 -441.67 454.15 3.153 5.91 2.38E-03 -19.0 0.137 -1.348 9.848

16 AOA -21 degree 45 77.20 -336.04 454.15 3.153 5.91 2.38E-03 -21.0 0.236 -1.026 4.353

17 AOA with Gurney -0 45 11.47 -411.6 454.15 3.153 5.91 2.38E-03 0.0 0.035 -1.256 35.885

18 AOA with Gurney -5 45 21.78 -497.17 454.15 3.153 5.91 2.38E-03 -5.0 0.066 -1.518 22.827

19 AOA with Gurney-8 45 32.49 -519.27 454.15 3.153 5.91 2.38E-03 -8.0 0.099 -1.585 15.982

20 AOA with Gurney -10 45 35.02 -553.30 454.15 3.153 5.91 2.38E-03 -10.0 0.107 -1.689 15.800

21 AOA with Gurney -11 45 44.48 -470.28 454.15 3.153 5.91 2.38E-03 -11.0 0.136 -1.436 10.573

22 AOA with Gurney -12 45 44.30 -551.07 454.15 3.153 5.91 2.38E-03 -12.0 0.135 -1.682 12.440

23 AOA with Gurney -13 45 51.0 -571.7 454.15 3.153 5.91 2.38E-03 -13.0 0.156 -1.745 11.207

24 AOA with Gurney -14 45 52.5 -577.3 454.15 3.153 5.91 2.38E-03 -14.0 0.160 -1.762 10.998

25 AOA with Gurney -14.5 45 54.48 -538.57 454.15 3.153 5.91 2.38E-03 -14.5 0.166 -1.644 9.886

26 AOA with Gurney -15.1 45 59.2 -530.9 454.15 3.153 5.91 2.38E-03 -15.1 0.181 -1.621 8.969

27 AOA with Gurney -16 45 62.8 -534.0 454.15 3.153 5.91 2.38E-03 -16 0.192 -1.630 8.508

28 AOA with Gurney -17 45 62.9 -565.4 454.15 3.153 5.91 2.38E-03 -17 0.192 -1.726 8.991

29 AOA with Gurney -18 45 88.5 -450.1 454.15 3.153 5.91 2.38E-03 -18 0.270 -1.374 5.089

30 AOA with Gurney -19 45 82.8 -490.3 454.15 3.153 5.91 2.38E-03 -19 0.253 -1.497 5.924

31 AOA with Gurney -21 45 116.9 -379.6 454.15 3.153 5.91 2.38E-03 -21 0.357 -1.159 3.247

32 AOA with Gurney -23 45 138.0 -419.5 454.15 3.153 5.91 2.38E-03 -23 0.421 -1.281 3.040

Conclusions –

The original airfoil stalls at 17.25 degrees, and Airfoil with Gurney stalls at 14.5

degree. The cut plots of air velocity vs x- direction, shows the large wake of low

velocity air at the bottom surface of the wing. Also, Drag numbers suddenly increase,

whereas the lift numbers plummet for the specific attack angles.

Velocity Vs X-direction plots for the two wing setup shows the velocity of air around

the airfoil, depicted with different colors. As the wing reaches initial stall, there is a

small green patch at the front and the lower back surface of the airfoil, as the attack

angle increases and the wing reaches full stall, the green wake widens with blue

areas showing even lower velocities. The wing stalls with a wide blue-green wake,

with the wing suffering from induced drag.

As seen from the History Table, as the angle of attack reaches full stall for the wing,

the lift coefficient drops as a result of large adverse pressure gradient in the lower

back part, which in-turn creates a positive Cp at the top surface; the magnitude of lift

seen during stall, is mostly due to the front edge of the wing where the flow is still

attached. Whereas, the drag force on the airfoil suddenly increases during stall due

to the aberrant increase in the induced drag. Due to decrease in the wind velocity

and the sudden change in its direction, a region of suction is formed, which coupled

with friction drag results into a high drag coefficient.

Velocity Vs X-direction vector plots for Stall Angle, Multi-

Element Airfoil Design: with & without Gurney Flap

(OpenFoam Result Images)

Results-

Run no. File Name Airspeed Drag Force Drag Lift Force Lift A A AR Rho Alpha Cd CL L/D

f/s N Lbs N Lbs in sq sq ft lb-sec2 / ft 4 deg

1 AOA 2-Element 0 degree 146.65 9.38 2.10112 -503.08 -112.69 490.98 3.409 4.54 0.002377 0 0.024114 -1.29329 -53.6333

2 AOA 2-Element -5 degree 146.65 16.35 3.6624 -640.25 -143.416 490.98 3.409 4.54 0.002377 -5 0.042032 -1.64591 -39.159

3 AOA 2-Element -9 degree 146.65 39.86 8.92864 -677.62 -151.787 490.98 3.409 4.54 0.002377 -9 0.10247 -1.74198 -17









12 AOA 2-Element with Gurney 0Deg 146.65 16.23 3.63552 -683.01 -152.994 490.98 3.409 4.54 0.002377 0 0.041723 -1.75584 -42.0832

13 AOA 2-Element with Gurney -2 146.65 21.28 4.76672 -718.13 -160.861 490.98 3.409 4.54 0.002377 -2 0.054705 -1.84612 -33.7467






19 AOA 2-Element with Gurney -9.8 146.65 70 15.68 -761.62 -170.603 490.98 3.409 4.54 0.002377 -9.8 0.179952 -1.95792 -10.8803


21 AOA 2-Element with Gurney-10.5 146.65 77.74 17.41376 -742.12 -166.235 490.98 3.409 4.54 0.002377 -10.5 0.199849 -1.9078 -9.54618


23 AOA 2-Element with Gurney-15 146.65 124.09 27.79616 -574.79 -128.753 490.98 3.409 4.54 0.002377 -15 0.319003 -1.47763 -4.63204

24 AOA 2-Element with Gurney-20 146.65 219.54 49.17696 -548.22 -122.801 490.98 3.409 4.54 0.002377 -20 0.56438 -1.40933 -2.49713

Conclusion-

The Most Effective Angle of attack for the 2-element airfoil with

downforce of 156.538lbs is -12deg; and a gurney flap modification gives a

downforce of 176.88lbs at -9deg. All the airfoils have a Span of 1.2meters.

There is a significant increase in the downforce numbers from the basic

airfoil to a 2-element wing with a gurney flap.

The drag numbers doesn’t increase significantly, to diminish downforce

improvement. Hence, a two element wing with a gurney flap has been

designed.

Results could be extrapolated according to the specific Aspect Ratio.

Verma Graduate Project CAD-CAM

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