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\begin{document}

\title{Application of Computational Fluid Dynamics\ to Downwind Sail Flows}
\author{Stephen Collie}

\chapter{Introduction}

\label{intro}

\section{Motivation}

With the rapid advancement and increasing affordibility of high-end
computers, engineers and designers are increasingly tempted to invest in
computational methods. However unlike many other aspects of yacht and sail
design, downwind sail development is yet to make use of Computational Fluid
Dynamics (CFD) tools. The downwind sail design process is largely
analytical, based around incremental developments and experiences with past
designs. Recently wind tunnel testing has become an integral part of high
performance downwind sail development and with the current rate of increase
of CFD technology and computer power the inclusion of CFD in the sail design
process is inevitable.\FRAME{fhFU}{4.7037in}{4.1528in}{0pt}{\Qcb{Americas
cup yachts sailing downwind under spinnaker.}}{}{themoneyshot.jpg}{\special%
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It is common for sail designers to rely almost entirely on computational
approaches in the design of upwind sails. Wind tunnel tests are inaccurate
for upwind studies due to difficulties in producing a realistic inflow and
trimming the sails accurately. Upwind sails involve predominantly attached
flow for which computational methods are well established. Such aerodynamic
design codes are most commonly based on the vortex lattice method \cite%
{Katz91} and can provide three-dimensional solutions for the flow past
genoa/mainsail configurations in less than a minute on a common desktop PC.
Consequently extensive parametric design studies can be carried out using a
large number of design variables. However inviscid panel methods are only
valid for close-hauled sailing conditions where the flow remains attached.
In fact their inability to predict leading edge and trailing edge separation
makes the application of panel methods for performance prediction
questionable even in close-hauled conditions. Consequently they are seldom
relied upon for aerodynamic input to velocity prediction programs (VPPs).

There are several clear advantages of CFD over wind tunnel testing. Wind
tunnel testing is plagued by inaccuracies in the model construction and in
obtaining the correct sail trim. Also since wind tunnel models are much
smaller than real sails, scaling errors are introduced, both in terms of the
inviscid/viscid behavior (Reynolds number) and in the deformation of the
model under load (density scaling). Difficulties are also found in creating
the flow conditions since the problem is complicated by the twisted apparent
wind profile that is created as the yacht travels within the atmospheric
boundary layer. At present only two wind tunnels in the world have the
facility to reproduce twisted flow for sailing yachts; the twisted flow wind
tunnel (TFWT) \cite{Flay96} at The University of Auckland's Yacht Research
Unit and a similar tunnel in California developed by Oracle BMW\ racing.%
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Perhaps the most significant advantage of CFD is\ in visualisation of the
flow. Flow visualisation techniques in the wind tunnel are time-consuming,
expensive and inaccurate, whereas with a computer model the flow can be
examined in detail with streamlines, velocity vectors and contours plotted
with relative ease. This allows a more comprehensive analysis of design
changes and a better understanding of the physics involved in the flow. By
using CFD designers can learn not just about performances of different sail
shapes, but they can also begin to understand why a sail performs well - or
poorly - and possibly make further improvements based on these findings.%
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\caption{Examples of flow visualisation techniques. a. Streamlines plotted
with CFD. b. Wind tunnel smoke stream visulaisation}\label{flow vis} 
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The prospect of obtaining accurate numerical solutions for the flow past
downwind sails is enticing for a sail designer. However there are also many
downsides to computational modelling and consequently - for downwind sails
at least - CFD is yet to play a significant role in the design process. The
computational demands for a CFD model for a three-dimensional sail are
considerable. Grid accurate analysis requires a computation grid in excess
of 10 million nodes and consequently many gigabytes of computer memory is
required. For downwind sails the angle of attack is large (approximately 30$%
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$ to the chord line) compared to upwind sails and the presence of large and
unsteady separated regions makes the solution process difficult. Simulations
must use a transient solver and time steps small enough to resolve the
transient behavior. Even with state-of-the-art supercomputers simulations of
this flow problem inevitably take days, or even weeks to solve.

As mentioned, CFD\ simulations of the three-dimensional flow past downwind
sails require top-of-the-line computer resources and long solution times.
Therefore to perform a comprehensive validation study with suitable grid-
and time step-convergence studies for a three-dimensional model would
require exorbitant computer resources and inappropriate solution times
considering the time frame of the Ph.D. project. Therefore since
three-dimensional solutions are impractical it was decided to study flows
around two-dimensional downwind sail sections, that is, to investigate the
performance of turbulence models for flows around thin highly cambered
airfoils. Two-dimensional simulations require only a fraction of the
computer resources and involve the essence of the physics of
three-dimensional sail flows. Flow separation is the most demanding feature
of the flow physics and simplifying the problem from three- to
two-dimensions does not make the prediction of flow separation any easier.
Further discussion of the differences and similarities between two- and
three-dimensional sail flows is provided in Section \ref{sect intro_sails}.

Perhaps the largest obstacle to the simulation of accurate sail flows is the
phenomenon of turbulence, a phenomenon that cannot be simulated exactly
(without vast computer resources) and must be modelled using a turbulence
model. Turbulence models are notoriously unreliable for flows that involve
flow separation and numerous validation studies have illustrated that
dramatically different results can be achieved depending on the choice of
turbulence model \cite{Menter96}. Consequently it is unwise to embark upon a
computational design program for a flow as complex as a downwind sail
configuration without first performing an in depth investigation into the
relative preformance of the available turbulence models. In order to be
confident of results and understand their limitations it is necessary to
first validate the method carefully and develop a good understanding of the
physics involved. This is the essence of the motivation for the thesis; 
\emph{to gain an in depth understanding of the physics involved downwind
sail flows and to determine the most suitable computation method for
downwind sail analysis.}

\section{Previous related studies}

To the knowledge of the Author there have been no publications to date on
the validation of computational methods for highly cambered foils that are
representative of downwind sail flows. In fact it is difficult to find a
flow case that involves all the typical flow features of downwind sail
flows. Other high-lift foils such as aircraft take-off and landing
configurations and front and rear wings on race cars involve the same design
goal of maximising lift while ignoring the influence of drag, however these
foils are allowed to have slots to sustain attached flow. Downwind sail
flows - with their large unsteady wakes - resemble flows past circular
cylinders more closely than most high-lift devices.

In order to simulate viscous flows involving separation it is necessary to
model the boundary layer of the sail. \emph{Bailey} (1999) \cite{Bailey99}
developed upon the work of \emph{Jackson and Fiddes }(1995) \cite{Jackson95}
using a two-dimensional panel code coupled to integral boundary layer
methods to compute two-dimensional sail flows. Bailey's model was capable of
predicting turbulent transition, leading edge separation and boundary layer
separation. However it was found that the methods used were only applicable
to low camber sails at moderate angles of attack. Unfortunately extension of
such a coupled method to three dimensions is a difficult and as yet
unexplored task.

The work of \emph{Jackson and Fiddes }(1995) highlighted the importance of
accurately representing the leading edge bubble that often forms as air
passes the luff of a sail \cite{Jackson95}. Jackson and Fiddes modelled the
leading edge bubble using a geometric approximation that assumed that the
bubble shape was elliptical. This approximation is inadequate since leading
edge bubbles have complicated shapes that will not necessarily collapse into
a generic function. Jackson and Fiddes also expressed the need for good
experimental data on the problem in order to provide a better understanding
of the bubble shape and dynamics \cite{Jackson95}.

Following Jacskon and Fiddes' request for experimental data on leading edge
bubble \emph{Crompton }(2001) performed wind tunnel tests on a flat plate a
shallow angle so of incidence \cite{Crompton01}. Surface pressures were
recorded using pressure tappings and laser doppler anemometry (LDA) was used
to measure velocities and normal turbulent stresses in the leading edge
bubble and in the developing turbulent boundary layer downstream of the
point where the leading edge bubble reattaches. This study answers many
questions with regard to the shape and structure of the leading edge bubble,
but unfortunately it provides little insight into the behavior of trailing
edge separation of the type that occurs in downwind sail flows.

Whilst a wealth of experimental data exists for two-dimensional airfoil
sections - including airfoils past stall - there is little data available
for sections representative of two-dimensional sails shapes. There have been
just two significant investigations into the behavior of the flow past
two-dimensional sail sections, \emph{Milgram }(1971, 1978) and \emph{%
Wilkinson} (1984, 1989, 1990).

\emph{Milgram }(1971) performed water tunnel tests for thin cambered plates
shaped according to the NACA 65 and $a=0.8$ mean lines \cite{Milgram71}. The
data is presented is in the form of lift, drag and pitching moment, all
measured using the force balance. The experiments used Reynolds numbers of $%
6,9$ and $12\times 10^{5}$ and camber ratios of 0.120, 0.129, 0.150 and
0.180. Large chord lengths were used relative to the width of the tunnel so
that high Reynolds numbers could be achieved, consequently the aspect ratio
of the models was just 2.2. For such low aspect ratio sections and large
camber ratios spanwise three-dimensionalities are likely and Milgram was
unable to assess the extent of their influence \cite{Milgram71}. In 1978
Milgram tested the NACA $a=0.8$ mean line at camber ratios of 0.12 and 0.15
in the same fashion as the 1971 tests, however this time he also measured
the forces for the sections with circular and elliptical masts of different
diameters \cite{Milgram78}.

\emph{Wilkinson }(1984) tested the NACA 63 and $a=0.8$ mean lines with a
circular mast attached in the same manner as Milgram, however unlike Milgram
he also measured the surface pressure distributions and boundary layer
profiles (1990) \cite{Wilkinson84, Wilkinson89, Wilkinson90}. Wilkinson was
the first to paint a detailed description of the behavior of the flow past
sails with reference a universal description of the pressure distribution
(Figure XXX). Neither Milgram or Wilkinson reported witnessing vortex
shedding in their experiments. Regular vortex shedding from a IACC\ mainsail
has been witnessed by the Author using smoke flow visualisation in the
University of Auckland's Twisted Flow wind tunnel. Smoke flow visualisation
for spinnakers and gennakers does not show clear vortex shedding, but rather
a chaotic and unsteady wake region. The lack of regular shedding for these
sails is thought to be due to the very low aspect ratios of these sails.
Initial CFD\ investigations carried out in 2000 were unsteady with periodic
vortex shedding, therefore it is expected that model tests of
two-dimensional downwind sail sections will also exhibit vortex shedding 
\cite{Collie00}. The largest camber values tested by Wilkinson and Milgram
were 20\% and 18\% respectively and at these high cambers it is surprising
that vortex shedding was not present. However since the chord lengths were
small the frequency of vortex shedding would be in the order of 5-20Hz for a
Strohal numbers of 0.1-0.4 and hence it is possible that vortex shedding was
present but that it's effect was lost due to low sample rates.\FRAME{ftbpFU}{%
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Unfortunately, due to errors associated with three-dimensional effects, the
available experimental data for two-dimensional sail sections is
insufficient both in terms of quality and detail if one's goal is to
reliably validate a computation method. In order to discern differences in
the performance of different turbulence models it is necessary to have data
that is firstly accurate enough so that the differences between the
different turbulence models is more significant than the error in the data
itself and secondly it is important to have a range of different flow
variables to examine in order to enable better understanding of the behavior
of the models.

\section{Present contributions}

The overall purpose of the current work is to gain an in depth understanding
of the physics involved in downwind sail flows and to determine the most
suitable computation method for downwind sail analysis. In order to achieve
this goal the research pursues three specific aims: The first one was to
assess the performance of different turbulence models for leading edge
bubbles of the type found in downwind sail flows. This was achieved by
comparing CFD\ simulations with the wind thunnel results of Crompton \cite%
{Crompton01}. The second aim was to perform wind tunnel experiments for
several two-dimensional downwind sail sections in order to develop further
understanding of the flow features and to provide a database of results
suitable for turbulence model validation. The final aim was to assess the
performance of different turbulence models for our downwind sail test suite
from the wind tunnel experiments.

The present research began in 2000 with a study of the current downwind sail
design methodology and proceedures of North Sails New Zealand Ltd and Team
New Zealand Ltd. This involved investigation into the design parameters and
goals, wind tunnel testing, the computational tools - both aerodynamics and
structural FEA - and the manufacturing process itself. The result of the
study was a list of specifications for the basic input and output parameters
for a CFD program and details as to how such a tool would fit into the
design process. Following on from this study work was carried out
investigating the suitability of different computational methods for
downwind sail analysis and design. Initial a\ wide range of different
methods were investigated from panel codes to advanced turbulence
simulations (LES, DES) and it became apparent that CFD\ codes based on the
Reynolds Averaged Navier-Stokes (RANS) equations were the most applicable. A
literature review was then carried out investigating a wide range of RANS\
based turbulence models considering the suitability of the models based both
on accuracy and simulation efficiency. The review focused on validation
studies that have been carried out for flows involving features that are
relevant to sail flows, e.g., airfoils near maximum lift, flows involving
adverse pressure gradients and boundary layer separation, flows with high
streamline curvature, unsteady vortex shedding and three-dimensional effects
such as tip vortices. This literature review is documented in \emph{Collie
et al.} (2001) \cite{Collie01}, the key aspects of this study are also
presented in Chapter \ref{Chapter turbulence}.

Subsequent work specifically addressed the three aims listed above, the
validation of CFD methods for the leading edge bubble for flat plates, wind
tunnel testing of downwind sail sections, and comparison of CFD results with
the wind tunnel results. As a final extension to the project a parametric
design study was carried out looking at a range of downwind section designs.
This study was used to illustrate how CFD can be employed in the downwind
sail design process and to gain a better understanding of the influence of
different design paramenters.

\section{Thesis outline}

A description of the basic principles of yachts sailing downwind and the
physics involved with downwind sails is presented in Chapter \ref{Chapter
intro sails}. This chapter is intended to provide the reader with insight
into the design goals and obstacles related to downwind sails and to provide
familiarity to the flow problem. Chapter \ref{Chapter turbulence} describes
issues related to turbulence and turbulence models and presents the results
from a review of literature related to turbulence model validation. Chapter %
\ref{Chapter numerical method} describes the numerical method used in the
CFD\ simulations and the key aspects of the solver. The validation study for
the flat plate at shallow incidence is presented in Chapter \ref{Chapter
plate}. A preliminary\ wind tunnel and CFD study of the flow past a
two-dimensional downwind sail section is presented in Chapter \ref{Chapter
preliminary study}. This study details initial efforts to guage the
performance of different turbulence models for downwind sail flows and to
determine the nature of complications that are inevitable whenever wind
tunnel experiments are carried out. Chapter \ref{Chapter validation}
presents the validation study for two-dimensional downwind sail sections.
This chapter presents the results from wind tunnel tests carried out at NASA
ames in conjunction with Stanford Yacht Research. It then goes on to compare
CFD results with the wind tunnel data and to assess the strengths and
weaknesses of the different turbulence models. The most suitable turbulence
model is then selected and used to perform a parametic analysis of downwind
sail designs. This study is presented in Chapter \ref{Chapter design study}.
The final chapter summarises the thesis, draws conclusions and suggests
opportunities for further research.

\bibliographystyle{ieee}
\bibliography{INTRODUCTION,PLATE,turbulence}

\bigskip

\end{document}
