1. 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
2. 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, angleof attack and drag force created by the various airfoilconfigurations.
Theory of Airfoils -
A fixed-wing aircraft's wings, horizontal, and vertical stabilizers are built with airfoil-shaped
cross sections, as arehelicopter rotor blades. Airfoils are also found in propellers, fans,
compressors and turbines. Sails arealso 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 downforceon 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 curveobtained 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-surfaceboundary layer, which
separates and greatly thickens over the upper surfaceat 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
pressuredrag, so that the overall drag increases sharply near and past the stall point.
Airfoil design is a major facet of aerodynamics. Various airfoils servedifferentflight
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 increasethe range of
angles of attack to avoid spin–stall. Thus a large range of angles can be used without
3. 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 curvatureis increased beforethe wing achieves maximum thickness to minimize
the chanceof boundary layer separation. This elongates the wing and moves the point of
maximum thickness back fromthe leading edge.
Supersonic airfoils are much more angular in shapeand can have a very sharp leading edge,
which is very sensitive to angle of attack. A supercriticalairfoil 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 havea
low camber to reducedrag divergence. Modern aircraftwings 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 thata negative pressuregradientalong
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, somesurfacecontamination will disruptthe 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 causethe loss of small regions of laminar
flow as well. Before NASA's research in the 1970s and 1980stheaircraftdesign community
understood fromapplication attempts in the WW II era that laminar flow wing designs were
not practical using common manufacturing tolerances and surfaceimperfections. That
belief changed after new manufacturing methods were developed with composite
materials (e.g., graphite fiber) and machined metal methods wereintroduced. 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 aircraftsurfaces,
fromsubsonic general aviation aircraftto transonic large transportaircraft, to supersonic
designs.
Gurney Flaps - The Gurney Flap is a small tab projecting fromthe trailing edge of a wing.
Typically it is set at a right angle to the pressuresidesurfaceof the airfoil, and projects 1%
to 2% of the wing chord. This trailing edge device can improvethe performanceof a simple
airfoil to nearly the samelevel as a complex high-performancedesign.
The device operates by increasing pressureon the pressureside, decreasing pressureon
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,
4. helicopter horizontalstabilizers, and aircraftwhere 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 softwareis written on Parasolid-kernel.
Parameters refer to constraints whosevalues determine the shapeor 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 useof
relations, which allows them to capture design intent.
Design intent is how the creator of the partwants 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
constructthe part. Shape-based features typically begin with a 2D or 3D sketch of shapes
such as bosses, holes, slots, etc. This shapeis then extruded or cut to add or remove
material fromthe part. Operation-based features arenot sketch-based, and include
features such as fillets, chamfers, shells, applying draftto 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). Thesketch consists of geometry such as points, lines, arcs,
conics (except the hyperbola), and splines. Dimensions areadded to the sketch to define
the sizeand 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 drivethe 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
5. additional advanced mating features such as gear and cam follower mates, which allow
modeled gear assemblies to accurately reproducethe rotational movement of an actual
gear train.
Analysis Software – OpenFOAM-
OpenFOAM(for "Open sourceField 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).
OpenFOAMsolvers include:
Simulation of burning Methane.
Basic CFD solvers
Incompressibleflow with RANS and LES capabilities
Compressibleflow 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 conjugateheat transfer
Molecular dynamics solvers
Direct Simulation Monte Carlo solvers
Electromagnetics solvers
Solid dynamics solvers
In addition to the standard solvers, OpenFOAM's syntaxlends itself to the easy
creation of customsolvers.
OpenFOAMutilities aresubdivided into:
Mesh utilities
Mesh generation: they generate computational grids starting either
froman input file (blockMesh), or froma generic geometry specified as
STL file, which is meshed automatically with hex-dominant grids
(snappyHexMesh)
Mesh conversion: they convertgrids generated using other tools to the
OpenFOAMformat
Mesh manipulation: they performspecific operations on the mesh such
as localized refinement, definition of regions, and others
6. Parallel processing utilities: they providetools to decompose,
reconstructand re-distribute the computational caseto perform
parallel calculations
Pre-processing utilities: tools to preparethe simulation cases
Post-processing utilities: tools to process the results of simulation
cases, including a plugin to interface OpenFOAMand ParaView.
Surfaceutilities
Thermophysicalutilities
Advantages-
Friendly syntaxfor partial differential equations.
Fully documented sourcecode.
Unstructured polyhedralgrid capabilities.
Automatic parallelization of applications written using OpenFOAMhigh-level syntax.
Wide range of applications and models ready to use.
Commercial supportand 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
12. Conclusions –
The original airfoil stalls at 17.25 degrees, and Airfoilwith Gurney stalls at 14.5
degree. The cut plots of air velocity vs x- direction, shows thelarge wake of low
velocity air at the bottom surfaceof 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 frontand the lower back surfaceof the airfoil, as the attack
angle increases and the wing reaches full stall, the green wakewidens with blue
areas showing even lower velocities. The wing stalls with a wide blue-green wake,
with the wing suffering frominduced drag.
As seen fromthe History Table, as the angle of attack reaches full stall for the wing,
the lift coefficient drops as a result of large adversepressuregradientin 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 wherethe flow is still
attached. Whereas, the drag forceon the airfoil suddenly increases during stall due
to the aberrantincrease in the induced drag. Dueto decreasein 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.
13. Velocity Vs X-direction vector plots for Stall Angle, Multi-
Element Airfoil Design: with & without Gurney Flap
(OpenFoam Result Images)
17. 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.
