The Foiling Week, July 8th 2014 - Presentation by Mario Caponnetto: "CFD method for foil design"

1. THE FOILING WEEK
CFD methods for foil design
Mario Caponnetto

2. • Wing theory is well established since almost one
century. We can use most of this know-how
initially developed for airplane also for foil design.
• Despite the complexity of the real flow, some
very smart simplification can be done to
mathematically capture the salient features of
aerodynamic wing behavior.
CFD methods for foil design

3. • For example. The flow around a 2-Dimensional
foil can be approximated with a vortex of a given
intensity (circulation)…
CFD methods for foil design
Real flow Mathematical approximation

4. • …2 adjoining sections of a 3-Dimensional wing
release in the wake a vortex filament…
CFD methods for foil design

5. • …this is enough to build a simple mathematical
model that can gives us probably 90% of the
basic aerodynamic information to make an
airplane to fly.
• The methods is called Lifting Line and can be
still used in a preliminary phase of the wing (or
foil) design. (Lanchester and Prandtl about 1910)
CFD methods for foil design

6. • Some noticeable formulas can also be obtained
(here for a symmetric profile):
• ​ 𝐶↓𝐿 =2 𝜋𝛼 in 2D flow where 𝛼= 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑎𝑡𝑡𝑎𝑐𝑘
• ​ 𝐶↓𝐿 =​2 𝜋𝛼/1+​2/𝐴𝑅 in 3D flow where
AR=aspect ratio
• ​ 𝐶↓𝐷𝑖 =​​​ 𝐶↓𝐿 ↑2 /𝜋𝐴𝑅 (Lift) induced drag
coefficient
CFD methods for foil design

7. CFD methods for foil design
Span
Area
AR=Span^2/Area
AOA
Cl
𝐿𝑖𝑓𝑡=​​1/2 * 𝐷𝑒𝑛𝑠𝑖𝑡𝑦∗Area∗Cl∗velocity^2
𝐷𝑟𝑎𝑔=​​1/2 * 𝐷𝑒𝑛𝑠𝑖𝑡𝑦∗Area∗(Cd+Cdi)∗velocity^2
Section Cd from tables…

8. • Nevertheless, important additional information are
required to properly approach the wing/foil
design.
• To get them the mathematical complexity of
the problem growths exponentially.
• Most of these information could only be achieved
in the past with experiments, mainly testing
models in a wind tunnel.
CFD methods for foil design

9. • Computer power has also grown exponentially in
the last decades. What was once impossible to
solve analytically can now be solved
numerically with computer “muscles”.
• One difference is that numerically we can’t get
simple, general and meaningful formula as the
ones shown before.
• But we can virtually replicate wind tunnel tests
(and now much more) obtaining numbers.
CFD methods for foil design

10. • There are 2 principal numerical approaches
possible: using potential flow or viscous
solvers.
• With potential flow solvers the effect of viscosity
is neglected in the mathematical formulation
(except for localized phenomenon).
• Viscous solvers embed viscosity with different
level of complexity depending on the method.
CFD methods for foil design

11. • In principle also the Lifting Line is a basic
potential flow solver. The wing/foil is represented
as a line (and a section as a point).
• If we stretch the point chord wise we can
approximate the wing with a thin surface. This
approach goes under the name of Lifting
Surface.
• If we also consider the thickness of the section
we have the Panel Method formulation.
CFD methods for foil design

12. CFD methods for foil design
Real flow
Lifting line approximation
Lifting surface approximation Panel method approximation

13. • Lifting surface and panel methods have been
successfully used in the last 30 years and more.
• Although viscosity is not directly incorporated in
the solver, some viscous effect can be added.
• Thin boundary layer methods can be coupled
with panel methods to deal with viscous drag
computation and viscous effects on generated lift.
CFD methods for foil design

14. CFD methods for foil design
Courtesy of Michael Richelsen

15. • Panel methods are very useful in a preliminary
design phase. They are fast and cheap (laptop).
• We only have to “represent” (mesh) the boundary
surface of the flow (body/hull/foil surface, wake,
free surface). Once we know what happens at the
boundary we can know all about the fluid.
• If the effect of viscosity is important (flow
separation, stall…) panel codes become less
accurate or un-useful.
CFD methods for foil design

16. • Marine foils must face some phenomenon that
airplane wings don’t experience.
• Free surface. Foils operate at the interface between 2
fluids, water and air. Wave, spray and ventilation
occur and we must be able to compute them.
• At high speed water pressure can go below
saturation pressure. In this case we have cavitation ,
and a cavity filled with water vapor is formed.
CFD methods for foil design

17. • Panel codes of marine derivation can handle free
surface until a certain complexity of the wave.
CFD methods for foil design
Courtesy of Michael Richelsen

18. • Some kind of cavitation and ventilation can also
be modeled with specifically developed panel
codes.
CFD methods for foil design
Panel method for cavitation analysis
of high speed propellers. Comparison
with cavitation tunnel experiment.
From Brizzolara and Gaggero

19. • To properly capture these phenomenon all
together became possible after Volume of Fluid
solvers (VOF) or equivalent methods where
developed.
• VOF methods can handle extremely complex free
surface features as spray, overturning waves,
cavitation and ventilation.
CFD methods for foil design

20. CFD methods for foil design
SPRAY
CAVITATION
WAVES
TIP PIERCING

21. CFD methods for foil design

22. CFD methods for foil design

23. CFD methods for foil design
CAD PRE PROCESSING / MESHING
COMPUTATION POST PROCESSING / RESULT ANALYSIS

24. • There is an almost general consensus (at least
between CFD users…:-) that the best CFD
solvers can give results equivalent in precision
with wind tunnel and towing tank for most of the
standard computations we normally need (naval
architects).
• In reality there are pros and cons with both
methods.
CFD methods for foil design

25. • CFD pros. Faster, cheaper, allow easy flow
visualization, better flow insight (pressure,
velocity map…), better control of the boundary
and ambient conditions, can be used in a
automatic optimization loop, multi physics...
• CFD cons. Need for expert users, physics still not
perfectly reproduced (turbulence, transition…)…
CFD methods for foil design

26. • CFD was normally used to virtually replicate an
experiment (and experimental limitations…).
• Steady state, model constrained in some way,
model un-deformable…
• Example: in the past we used to test sails in the
wind tunnel, foil/hulls in towing tank, cavitation in
cavitation tunnels. All the data obtained were later
assembled together (VPP).
CFD methods for foil design

27. • We do the same replacing experiments with CFD,
but nowadays we can do a single global CFD
computation simultaneously accounting for all
these aspect simultaneously.
• We can also couple CFD with FEM to analyze
the fluid-structure interaction…
• This would be extremely complicated and
expensive to do with experimental facilities.
CFD methods for foil design

28. • We moved from a phase when CFD and
computer were not mature enough, to now when
CFD are almost indispensable for design.
• There are still limits but also a lot of merits in
using CFD.
• The development never stops…
• THANK YOU
CFD methods for foil design