AERODYNAMICS OF RACING YACHT:APPLICATIONS

A Sail Boat is a complex aerodynamic system immersed in two fluid in relative motion

The interaction between the ‘air part’ and the ‘water part’of the system determines the overall boat performance

DESIGN TOOLS

AERODYNAMIC TOOLS

HULL AND APPENDAGES------------------

Tank TestCFD

SAIL PLAN--------------

Wind TunnelFull scale test

CFD

OVERALL PERFORMANCE

PREDICTION

VELOCITY PREDICTION PROGRAM

VELOCITY PREDICTION PROGRAM

The VPP provides a steady state speed of the Yacht given the wind direction and

magnitude

VPP has a two part structure comprised of the HYDRODYNAMIC FORCE MODELS and AERODYNAMIC FORCE MODELS

The JOB of the Solution Algorithm is to find that combination of Boat Speed and

Heel angle so that aero and hydrodynamic forces are in equilibrium

This is a typical polar plot which shows the boat speed for a specific true wind and heading

VELOCITY PREDICTION PROGRAM

The “cores” of a VPP are the HYDRODYNAMIC and AERODYNAMIC FORCE MODELS

The quality of the solution is dependent on the accuracy of the data of the force models.

The models are usually based on both theory and empiricism

HYDRODYNAMIC MODEL

1. Theoretical relationships2. Systematic Tank Test (e.g. Delft series)3. Computational Fluid Dynamics

AERODYNAMIC MODEL

1. Full scale Test2. Wind Tunnel3. Computational Fluid Dynamics

Usually the total hydrodynamic drag of the yacht is assumed to be the sum of the following components:

HYDRODYNAMIC FORCE MODEL

1. Wave resistance of the canoe body (systematic Tank tests)2. Appendage and canoe body friction and form drag (theoretical

relationships, empiric coefficients)3. Induced drag. Drag associated to the generation of lift (theoretical

relationships)4. Added resistance in waves. Unsteady motion due to the sea waves

(empirical correlations, tank tests)

The model has to provide the total drag as a function of boat speed and leeway (angle of attack)

AERODYNAMIC FORCE MODEL

The model has to provide the DRIVING FORCE and the HEELING FORCE as a function of Apparent Wind Speed (AWS) and Apparent Wind Angle (AWA).

The polar plot of the sail plan is determined making use of Tunnel Wind Test or CFD analysis

VPP

The final results of the VPP analyses are estimates of yacht speeds and sailing times during a regatta, the best true indicator of performance.

This tool is widely used by the naval architects in the early stages of the design process to compare a large number of configurations with different overall parameters (such as displacement, length, sail area, ….)

COMPUTATIONAL FLUID DYNAMICS (CFD)

IMPROVEMENTS IN COMPUTER PERFORMANCE

HAVE MADE THE USE OF Reynolds Averaged Navier-Stokes

(RANS) equations FEASIBLE FOR PRACTICAL DESIGN

APPLICATIONS

LATEST GENERATION OF RACING YACHT HAS

GREATLY BENEFITED OF THESE TOOLS, ORIGINALLY

DEVELOPED FOR AEROSPACE APPLICATIONS

COMPUTAIONAL FLUID DYNAMICS (CFD)

While VPP provides an overall performance prediction, CFD methods allows to reach a refined

aerodynamic optimization

CFD methods allows one to investigate in details the flow fields and to reach a better understanding

of the flow phenomena

1. Panel method, inviscid potential flow equations.2. RANS, Reynolds Averaged Navier-Stokes equations.

Capable of solve viscous effects

PANEL METHODSBased on the inviscid potential flow equation.

Panels are distributed over the model surfaces.Over each panel is distributed a constant sourceand/or doublet singularity, which satisfiesthe governing equations

Low computaional cost

COMPUTAIONAL FLUID DYNAMICS (CFD)

Principal CFD methods:

VISCOUS METHODSRANS equations spatially discretized on a computational grid.

Grid points clustered in regions where viscous effects are important.

Spatial Discretization:• Finite element • Finite volume

Steady state solutionUnsteady solution: periodic fluctuations of the main fluidynamic quantities

Unstructured computational grid Structured computational grid

CFD APPLIED TO HULL AND APPENDAGES

HULL

Wave Resistance Prediction

KEEL AND RUDDER

2D Analysis:Laminar foil for low

Reynolds number, capable to shift downstream the

location of transition onset

3D Analysis:--Plan form--Bulb, winglet--Interaction between keel and wave system

CFD APPLIED TO SAILS

UPWIND CONDITIONS

MAINSAIL GENOA AND

MAST CONFIGURATION

DOWNWIND CONDITIONS

MAINSAIL WITH GENNAKER OR

SPINNAKER---------------

Large separationsand unsteadyness

CFD APPLIED TO RACING YACHTS

THE AERODYNAMIC OPTIMIZATION IS A COMPLEX TASK REQUIRING KNOWLEDGE OF AERODYNAMICS AND HOW TO ACT ON THE GEOMETRY IN ORDER TO

IMPROVE THE PERFORMANCE.OPTIMIZATION TECHNIQUES CAN BE USEFUL IN THIS

KIND OF DESIGN PROCESS

Optimization techniques:

• Gradient Based Methods

• Design of Experiments

• Evolutionary algorithms

OPTIMIZATION METHODOLOGIES

Design process as optimization of transfer function:

Pj=Pj(Xi) Pj Performance parameters j=1,M

Xi Geometrical parameters i=1,N

Geometrical parameterization:

• Bezier Curves

• NURBS

Gradient Based Methods

• Exploration of original configuration neibourhood

• Evaluation of the gradient of TF

• Solution moved toward maximum gradient direction

• Time cost depending on initial configuration choice

• Few iterations required

• Widely used for local optimum searching

OPTIMIZATION METHODOLOGIES

Design of Experiments (DOE)• Transfer function approximated with a polynomius:

P= β0+ β1X1+… β11X12+ …β12X1X2 +…β123X1X2X3…

• Evaluation of transfer functions on a set of configurations

• DOE Theory Determination of ß coefficients through least squares

regression

3 Levels - Full Resolution

456153

N. Of runsN. of input parameters

OPTIMIZATION METHODOLOGIES

Genetic Algorithms• Based on Darwin’s evolutionary theory

• Initial set of design configurations (population) randomly selected

• Direct evaluation of TF for each configuration

• Three genetic operators: selection, recombination and mutation

• Sequential generation of improved populations

Time Cost

1506N. Of runsN. of input parameters

OPTIMIZATION METHODOLOGIES

Comparison between different strategies

TF approximationSuitable for simple multipeak TF

Design of Experiments

Suitable for complex multipeak TF

Low computational cost

Advantages

Genetic Algorithms

Gradient Based Methods

High computational cost

Only local optimum

Drawbacks

OPTIMIZATION METHODOLOGIES

ON THE USE OF CFD TO ASSIST WITH SAIL DESIGN INTRODUCTION

TRADITIONALLY THE SAIL DEVELOPMENT IS DELEGATED TO THE SAILMAKERS EXPERIENCE

COMPUTATIONAL FLUID DYNAMICS CAN BE AN

INNOVATIVE TOOL THAT ALLOWS TO TEST AND

COMPARE A LARGE NUMBER OF

CONFIGURATIONS IN A RELATIVELY SHORT

AMOUNT OF TIME

ON THE USE OF CFD TO ASSIST WITH SAIL DESIGN

Aerodynamic design of an IACC sail plan in upwind condition.

Optimal Sails profiles depending on:

•Hull and appendages features

•Wind speed and angle

•Sailing style and trim

Critical for:

•Manufacturing problems

•Sail shapes not fixed, varying with wind pressure

and sail trim

Sails are often compared to aircraft wings.

Unfortunately classic aeronautical design criteria are only

partially useful:

• Contrary to wings, sails must work in a wide operative range

(i.e. angle of attack)

• The goal in the aeronautical design is to minimize the losses

(drag). In sail design the goal is to maximize the driving force,

without taking into account losses.

• The classic Lift-Force projection must replaced with the sailing

aerodynamics terms “Driving-force Heeling-Force”

• The flow is often separated (depending on the angle of attack)

DESIGN CRITERIA

Design Operating Conditions:

•True Wind Speed

•Apparent Wind Angle

DESIGN CRITERIA

Under fundamental hypothesis of a constrained Heeling Moment,

the GOAL is to find a maximum driving force configuration.

Input data:

•Initial configuration recovered

from pictures (deformed shape)

•Righting Moment available

GEOMETRY DATA ACQUISITION

Superimposition of Bezier curves.

Principal parameters used to describe the profile:

• CAMBER

• DRAFT

• Entry Angle

• Exit Angle

• Twist Angle

NAVIER-STOKES Solver “Hydro”

• 3D, fully viscous, multi-grid, multi-block code developed by the

University of Florence

• Acceleration techniques employed:

1. Local time-stepping

2. Residual smoothing

3. Multi-grid Full Approximation Storage (FAS)

• Boundary Conditions:

1. Solid walls: no-slip condition

2. Inlet: total pressure and flow angles

3. Outlet: static pressure

The Earth’s boundary layer can be taken into account imposing

spanwise variable inlet conditions.

GRID GENERATION

The size (number of points) of the computational grid has to fulfill three main requirements:

1. To solve the flow phenomena of interest (e.g. boundary layer)

2. To compute solutions sufficiently grid-independent

3. To match computational times to design needs

Mainsail

Genoa

The first step is to generate a computational grid around the sail plan.

The computational grid represents the domain where the solver computes the solution.

GRID GENERATION

The boundaries have

to be defined far

enough from the

sails, where the

flow is

indisturbed.

GRID GENERATION

Mainsail

Genoa

HORIZONTAL SECTION OF THE GRIDThe Grid consists of three

block.

Structured H-type grids

were employed in

computations.

The grid generation is based

on an elliptic procedure

on 2D grids which are

subsequently stacked in

the vertical direction.

GRID GENERATION

Details of the viscous grid around the mast

2 200 000 grid point was judged to

be a good compromise (memory

requirements of about 650MB) for

mainsail-genoa configuration

For a complete mast model, a viscous

grid with 285 x 129 x 93 grid points in

the chordwise, chordwise-orthogonal,

and spanwise directions, was used

(3 400 000 grid point,

1000 MB memory requirements)

Grid points clustered near the solid walls in

order to solve the boundary layer

VISCOUS SOLUTION

The RANS codes allow to take into

account the viscous effect such as

boundary layer, separation bubble.

Compared to other design tools, the

RANS solution allows to investigate in

detail the flow structures

PARAMETRIC ANALYSIS

The first analysis presented is

obtained through a parametric

variation of the Genoa Camber on the

whole span from the initial value 11%

up to 21%. The design Apparent Wind

Angle (AWA) is 16 deg.

PARAMETRIC ANALYSIS

The results of the

computations, for

incompressible flow,

are the velocity vectors

and the static pressure

field (one value for

each grid point)

Static pressure distribution on the genoa profile

LEA

DIN

G E

DG

E

TRA

ILIN

G E

DG

E

PARAMETRIC ANALYSIS

Obviously the Camber variations from its initial value involve both driving force

and heeling moment changes.

PARAMETRIC ANALYSIS

Which is the Optimal Genoa Camber value?

-- The optimal Camber is a comprime solution between heeling-moment and driving

force.

-- It is necessary to evaluate the trade-off between heeling moment and driving force.-- To this aim the initial Heeling Moment (constrained) has to be re-

established through the Mainsail Twist Distribution

-- This is a well-known practice for reducing the heeling moment used by

every yachtsmenHeeling force

PARAMETRIC ANALYSIS

--Three parametric curve for three

separate mainsail twist

--To re-establish the initial Heeling

Moment (which is the

optimization process constraint)

the mainsail twist is varied

Heeling Moment Coefficient definition:

dmSAAWSChmHm 2

21

Where:Hm: Heeling MomentChm: Heeling Moment CoefficientSA: Sail Areadm: Distance between CLR and mast-head

Chm TWS

PARAMETRIC ANALYSIS

IT SHOULD BE NOTED THAT THE HEELING MOMENT COEFFICIENT IS

CORRELATED TO THE WIND SPEED

SINCE Hm IS UPPER BOUNDED BY THE BOAT STABILITY, THE GREATER

THE WIND SPEED (AWS), THE LOWER THE HEELING MOMENT

COEFFICIENT (Chm) MUST BE

PARAMETRIC ANALYSIS

Which is the Optimal Genoa Camber value?

-- Points A,B and C represent the optimal camber values for three

separate wind magnitude

Light Wind

Moderate Wind

Heavy Wind

GENOA CAMBER PARAMETRIC ANALYSIS

PLOTTING THE DRIVING FORCE

IN A THIRD DIMENSION WITH THE

AID OF THE CONTOUR LINES

(lines at constant driving force)

GIVEN THE RESULT OF THE

ANALYSIS,

THE ESSENTIAL FEATURES OF

SAILS IS ITS ABILITY TO BE

ADJUSTED TO MATCH THE

WIND SPEED CHANGES

GENOA CAMBER PARAMETRIC ANALYSIS

NEED FOR MANY SAILS FOR EACH WIND SPEED

SAIL REQUIREMENTS:

ABILITY TO BE ADJUSTED TO MATCH

THE WIND SPEED CHANGES

In upwind conditions, an America’s Cup Class has 2/3

different mainsail and 5/6 different genoa:

• Genoa code 1: <6 kn TWS

• Genoa code 2: 8 kn TWS

• Genoa code 3: 12 kn TWS

• Genoa code 4: 16 kn TWS

• Genoa code 5: 20 kn TWS

MAINSAIL CAMBER PARAMETRIC ANALYSIS

THE ANALYSIS HAS BEEN

REPEATED FOR THE

MAINSAIL CAMBER

(AWA 16 deg)

True Wind Speed Optimal camber

8 kn 9.8%

13 kn 6%

MAINSAIL CAMBER PARAMETRIC ANALYSIS

GIVEN THE RESULT OF THE

ANALYSIS, MAINSAIL SHOULD BE

FLATTER THAN GENOA.

TWS 8 kn Optimal camber

Mainsail 9.8%Genoa 16%

Genoa Base

Genoa Head

Main Head

Main Base

Mainsail Genoa

This fact can be explained by taking into

account the load distribution:

The aerodynamic load on the Genoa is

greater than the load on the mainsail

OPTIMUM SPANWISE CAMBER DISTRIBUTION

To go further in the analysis is it possible to consider the optimum spanwise

distribution of the Genoa camber

LIGHT WIND CONDITION

CAMBER

should

increase

with

increasing

height

OPTIMUM SPANWISE CAMBER DISTRIBUTION

To go further in the analysis is it possible to consider the optimum spanwise

distribution of the Genoa camber

MODERATE WIND CONDITION

CAMBER

should

decrease

with

increasing

height

OPTIMUM SPANWISE CAMBER DISTRIBUTION

SPANWISE LOAD

DISTRIBUTION

--Light Wind: increasing load with

increasing height

--Moderate Wind: decreasing load with

increasing height

Genoa Twist distribution fixed

Load on the Genoa is induced by

the Mainsail twist distribution

CONCLUSION

From the 1983 turning point in the America’s Cup hystory to

today, the use of CFD in the yacht design process has quickly

increased

While no CFD methos should claim to replace other design tools

(wind tunnel, tank test…), CFD play an important role in a

modern design process

Improvements in computer performance have made the use of

RANS the main CFD tool for practical design applications,

opening new frontiers in racing yacht design