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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 affordability 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 devolment 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.

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 invisicd 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 on 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.

Perhaps the most significant advantage of CFD is\ in flow visualisation.
Flow visualisation in the wind tunnel is 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
physical 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.

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. 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$%
%TCIMACRO{\U{b0}}%
%BeginExpansion
{{}^\circ}%
%EndExpansion
$ 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 infinitely 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 simplifing 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 suitability 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 statement is the essence of the motivation for the
thesis; \textit{to gain an in depth understanding of the physics involved in
flow past downwind sails 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
representitive 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. Bailey \cite{Bailey99} developed upon
the work of Jackson and Fiddes \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 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}.

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

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 Migram 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}.

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}. A slightly higher
aspect ratio (3.0) was used, however the influence of three-dimensionalities
can still not be ruled out as a significant source of error. Nevertheless
Wilkinson was the first to paint a detailed description of the behaviour of
the flow past sails with reference a universal description of the pressure
distribution (Figure XXX).

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
behaviour of the models.

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

\bigskip

\end{document}
