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

THE FOILING WEEK CFD methods for foil design Mario Caponnetto

• 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

• For example. The flow around a 2-Dimensional foil can be approximated with a vortex of a given intensity (circulation)…


Real flow Mathematical approximation

• …2 adjoining sections of a 3-Dimensional wing release in the wake a vortex filament…


• …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)


• Some noticeable formulas can also be obtained (here for a symmetric profile):

•  𝐶↓𝐿 =2𝜋𝛼 in 2D flow where 𝛼=𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑎𝑡𝑡𝑎𝑐𝑘

•  𝐶↓𝐿 = 2𝜋𝛼/1+ 2/𝐴𝑅   in 3D flow where AR=aspect ratio

•  𝐶↓𝐷𝑖 = 𝐶↓𝐿 ↑2 /𝜋𝐴𝑅  (Lift) induced drag coefficient



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…

• 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.


• 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.


• 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.


•  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.



Real flow Lifting line approximation

Lifting surface approximation Panel method approximation

• 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.



Courtesy of Michael Richelsen

• 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.


• 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.


• Panel codes of marine derivation can handle free surface until a certain complexity of the wave.


Courtesy of Michael Richelsen

• Some kind of cavitation and ventilation can also be modeled with specifically developed panel codes.


Panel method for cavitation analysis of high speed propellers. Comparison with cavitation tunnel experiment. From Brizzolara and Gaggero

• 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 SPRAY

CAVITATION

WAVES

TIP PIERCING




CAD PRE PROCESSING / MESHING

COMPUTATION POST PROCESSING / RESULT ANALYSIS

• 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 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 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).


• 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.


• 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


Design

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