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The accuracy of computational fluid dynamics analysi
of the passive drag of a male swimmerBarry Bixler
a, David Pease
b& Fiona Fairhurst
c
aHoneywell Aerospace , Arizona, USA
bSchool of Physical Education, University of Otago , Dunedin, New Zealand
cSpeedo International , UK
Published online: 08 May 2007.
To cite this article:Barry Bixler , David Pease & Fiona Fairhurst (2007) The accuracy of computational fluid dynamics analy
of the passive drag of a male swimmer, Sports Biomechanics, 6:1, 81-98, DOI: 10.1080/14763140601058581
To link to this article: http://dx.doi.org/10.1080/14763140601058581
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The accuracy of computational fluid dynamics analysis
of the passive drag of a male swimmer
BARRY BIXLER1, DAVID PEASE2, & FIONA FAIRHURST3
1Honeywell Aerospace, Arizona, USA,
2School of Physical Education, University of Otago, Dunedin,
New Zealand, and 3
Speedo International, UK
AbstractThe aim of this study was to build an accurate computer-based model to study the water flow and dragforce characteristics around and acting upon the human body while in a submerged streamlinedposition. Comparisons of total drag force were performed between an actual swimmer, a virtualcomputational fluid dynamics (CFD) model of the swimmer, and an actual mannequin based on thevirtual model. Drag forces were determined for velocities between 1.5 m/s and 2.25 m/s (representativeof the velocities demonstrated in elite competition). The drag forces calculated from the virtual modelusing CFD were found to be within 4% of the experimentally determined values for the mannequin.The mannequin drag was found to be 18% less than the drag of the swimmer at each velocity examined.This study has determined the accuracy of using CFD for the analysis of the hydrodynamics ofswimming and has allowed for the improved understanding of the relative contributions of variousforms of drag to the total drag force experienced by submerged swimmers.
Keywords: Computational fluid dynamics, flume, passive drag, swimming
Introduction
The passive drag of swimmers moving under water in a streamlined position has been
measured experimentally by, for example, Jiskoot and Clarys (1975), Kolmogorov and
Duplishcheva (1992), and Lyttle, Blanksby, Elliott, and Lloyd (1998). These authors
obtained conflicting results and revealed the difficulties involved in conducting such
experimental research. An alternative approach, previously unused to determine a
swimmers passive drag accurately, is to apply the numerical technique of computational
fluid dynamics (CFD) to calculate the solution.The first application of computational fluid dynamics to swimming was by Bixler and
Schloder (1996), when they used a two-dimensional CFD analysis to evaluate the effects of
accelerating a hand-sized circular plate through the water. Their results suggested that a
three-dimensional CFD analysis of a human form could provide useful information about
swimming. Additional research using CFD techniques was performed by Riewald and Bixler
(2001) and Bixler and Riewald (2002) to evaluate the steady and unsteady propulsive force
of a swimmers hand and arm. However, no accurate CFD analysis of an entire swimmers
body has yet been performed and then verified with testing. The aim of this study was to
ISSN 1476-3141 print/ISSN 1752-6116 online q 2007 Taylor & Francis
DOI: 10.1080/14763140601058581
Correspondence: B. Bixler, Honeywell Aerospace, Phoenix, AZ 85226, USA. E-mail: [email protected]
Sports Biomechanics,
January 2007; 6(1): 8198
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build an accurate computer-based model to study the water flow and drag force
characteristics around and acting upon the human body while in a submerged streamlined
position. The accuracy of the CFD model was checked by comparisons with experimentally
measured drag on a mannequin and a real swimmer of the same shape in a water flume. The
determination of the accuracy of the CFD model is a significant and necessary first step to
take before proceeding to more advanced CFD analyses, such as the evaluation of active drag
with the swimmer kicking or stroking.
Methods
To obtain accurate geometry of a human body, a laser body scan was undertaken of an elite
male swimmer. Both the CFD model and the mannequin were accurately formed to be the
same shape as the scanned swimmer who was later tested in the flume. Before testing,informed consent was obtained from the participant for all activities requiring his
involvement.
The laser scan created a cloud of points that represented the swimmers shape. The
surfaces of the swimmer were then created from these points using Gambit, a geometry
modelling program developed by Fluent, Inc. (Hanover, NH, USA), which provides
sophisticated computational fluid dynamics software. These surfaces were then meshed
using Tgrid, a meshing program also developed by Fluent Inc. Tgrid was also used to create
the volume mesh just before importing the whole mesh into the Fluent Computational Fluid
Dynamics (CFD) program for analysis.
CFD model
The swimmer was modelled as if he were underwater in a streamlined position, the shape
normally achieved after pushing off from the wall after each turn. In the analyses reported
here, the CFD model swimmer was not wearing a swimsuit. The swimmer used for the CFD
and mannequin models was 1.86 m tall, with a finger to toe length of 2.34 m, and had head,
chest, waist, and hip circumferences of 0.59 m, 1.02 m, 0.84 m, and 0.98 m respectively. The
frontal projected area was 0.0934 m2, the total surface area was 1.859 m2, and the chest
depth was 0.25 m.
Figure1. CFDmodel geometry of swimmer and flume. The water surface andflume left wall have been removed for
clarity. The flume water depth is 1.5 m. The width is 2.5 m. The mannequin is 2.34m long from fingertips to toes,
and the length of the model is 6.0 m.
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The CFD model was built to represent the geometry and flow conditions in the water
flume where the testing of the mannequin and swimmer took place. The boundaries of the
CFD model were created to match the water depth (1.5 m) and channel width (2.5 m) of the
flume (Figure 1). The length of the CFD model of the flume was 6.0 m, of which 2.4 m was
behind the swimmer so as to adequately capture the trailing water flow characteristics. The
swimmer portion of the model was placed at a water depth of 0.75 m, equidistant from the
top and bottom surfaces. The water surface was modelled as a plane of symmetry. This made
the solution of the problem easier than if it had been modelled as a free surface. This
assumption was proven to be correct in a separate experimental study (using the same
mannequin) by Vennell and colleagues (Vennell, Pease, and Wilson, 2006), in which the
mannequin was moved incrementally closer to the water surface at various velocities. It was
found that the original mannequin position, 0.75 m below the water surface, was below the
location where surface effects begin to influence significantly the drag force on themannequin. Specifically, the measurements showed that, to avoid significant wave drag, a
swimmer must be deeper than 1.8 chest depths and 2.8 chest depths below the surface for
velocities of 0.9m/s and 2.0m/s respectively. Since the mannequin and swimmer have a chest
depth of 0.25 m, this corresponds to depths of 0.45 m and 0.70 m respectively. These results
agree with research conducted by Lyttle et al. (1998), who concluded that there is no
significant wave drag when a typical adult swimmer is at least 0.6m under the waters
surface.
The boundary inlet of the computational domain had uniform velocities applied to it,
while the outlet surface had no prescribed values (classical outflow boundary). The sides and
bottom of the flume were modelled as walls. The CFD swimmers body surface (Figures 2 5)
Figure2. Front,side andback views of theswimmer CFDgeometry. These surfaces were created from thelaserbody
scans.
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had roughness parameters of zero (no swimsuit). Non-equilibrium wall functions, designed
to bridge the viscosity-affected region between the wall and the fully turbulent region, were
used on the swimmer surface to capture better the flow separation and reattachment from
the body, and to improve the accuracy of the skin friction calculations.
The initial number of cells in the model was about 1.3 million. The grid was a hybrid mesh
composed of prisms and pyramids. Significant efforts were made to ensure that the modelwould provide accurate results. Five prism cell layers were developed within the boundary
layer of the swimmer to provide values valid for the log-law used in fluid dynamics
applications. In addition, adaptive meshing was performed in areas of high velocity and
pressure gradients (adaptive meshing is a process whereby, after the initial analysis, the mesh
Figure3. Mesh detail of thehead with goggles. Themesh aroundthe head is critical for theaccurateprediction of the
boundary layer separation that takes place there.
Figure 4. Mesh detail of the hands. The modeling of the hands is also critical, for they are the first thing that the
water sees. As such, they significantly impact the flow along the rest of the body.
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is refined in selective volumes based upon the initial solution). The analyses were then re-
run, and the results compared with previous findings. This was repeated several times until
the total drag results, as well as the local drag results in high gradient areas, stopped changing
with additional refinement, indicating that the mesh size was optimum. This increased the
mesh size to around 2.6 million cells. This is a standard technique to ensure that meshrefinement is sufficient to achieve accurate results.
Steady-state CFD analyses were performed using the Fluent CFD code, and drag forces
were calculated for velocities ranging between 1.50 and 2.25 m/s in increments of 0.25 m/s.
The Fluent code solves flow problems by replacing the complex Navier-Stokes fluid flow
equations with discretized algebraic expressions that can be solved by iterative computerized
calculations. Fluent uses the finite volume method of solution, where the equations are
integrated over each control volume. The following paragraphs detail the parameters chosen
to be used in the Fluent solution. Readers not familiar with CFD terminology are referred to
Bixler and Riewald (2002), where an online appendix defines many of these parameters
discussed below.
There are various choices within the Fluent code for solution techniques, turbulence
models, and computation schemes. A proper choice for these parameters is critical for
achieving accurate results and the choices are usually based upon the experience of the user.
We chose the segregated solver with the standard turbulence model for most of the analyses
because this turbulence model was shown to be accurate in previous research for predicting
the drag on a swimmers arm and hand (Bixler and Riewald, 2002). In addition, to assess the
sensitivity of drag predictions to the choice of turbulence model, analyses using three other
turbulence models were also done for a single velocity of 2.0 m/s. The use of these models
implies that the flow, when attached to the swimmer, is turbulent. Turbulent flow means that
the flow does not move along in smooth layers, but that it twitches up, down, and side to
side in small amounts as it moves forward. Turbulent flow does not necessarily imply that the
fluid is detached from the swimmers surface. Turbulent flow can, and often is, still attached
to the surface.
Figure 5. Mesh detail of the feet. On the feet, it is the heels that are most important, as they stick out into the flow
steam, picking up a lot of drag.
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All numerical computation schemes were second-order, which provides a more accurate
solution than first-order schemes. The water properties used in the analysis were those
measured in the flume, including a turbulence intensity of 1.0% and a turbulence scale of
0.093 m. Turbulence intensity can be viewed as a measure of the fluid velocity fluctuation
over time relative to the steady-state velocity. Mathematically it is defined as the ratio of the
root-mean-square of the velocity fluctuations to the mean flow velocity. Turbulence scale is
best thought of as the size of turbulence pockets in the flow. Both of these parameters are a
function of the flume geometry and structural grid within the flume. Incompressible flow,
appropriate for water, was assumed. The water temperature, based upon flume measurements,
was 298C, with a density of 996.0 kg/m3 and a viscosity of 8.1 1024 kg/(ms).
The initial CFD analyses were done with the swimmer in the same horizontal position
(angle of attack 08) as the mannequin and human swimmer would be when tested in the
flume. We wanted, however, to determine what effect small changes in the angle of attackhad on drag. Therefore, two additional models were created and analysed, where the angles
of attack were 3.08 and 24.58 respectively from the horizontal orientation. The angle of
attack was defined as the angle between a horizontal line and a line drawn from the tip of the
leading middle finger to the ankle bone.
Interference drag occurs when an object is tested in a flume or wind tunnel. If the true drag
of object A is known and the true drag of object B is known, when they are put close together
in a flume or wind tunnel, their total drag when measured is not equal to the sum of their
individual drags. This is because each object can interfere with the flow around the other
object. Although experimentalists are aware of interference drag, they do not have the means
Figure 6. CFD model with supports included. The extended CFD model, which includes the flume supports, is
8.5 m long. The support strut is 2.81m upstream from the fingertips. The small strut has a frictionless sleeve on its
end through which the support rod moves. The velocity meter is 0.115 m above the support rod and is 1.07 m
forward of the fingertips.
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to determine it, and the drag on a test specimen is usually simply taken as the drag of the test
specimen with its supporting structure minus the drag of the supporting structure alone.
However, CFD analysis techniques allow us to calculate interference drag through the
creation and use of a second CFD model that includes all the support structures (Figure 6) in
front of the swimmer. The interference drag was calculated by subtracting the drag force on
the CFD swimmer from the larger model that includes the supports from the drag force on
the CFD model of the swimmer only, without supports. This calculated interference drag
shows that the support structures partially shield the swimmer from the water flow, reducing
the drag from what it would be if the support structures had not been there. Therefore,
calculated interference drag was added to the measured drag on the mannequin and
swimmer to account for the support interference during the flume testing.
Mannequin flume test set-up
The flume used for the testing is located at the University of Otago, Dunedin, New Zealand.
It was chosen for its low turbulence and its large size, which limits the effect of the flume
boundaries on drag force determination. The mannequin was designed such that it could be
made neutrally buoyant and centrally balanced and its surface was very smooth. The balance
and buoyancy of the mannequin were controlled by selective purging or filling of multiple
ballast tanks distributed within the body of the mannequin. To minimize free surface or
Figure 7. Mannequin with briefs in the flume, showing strut, rod, and load cell positions. The bottom photo is taken
through an underwater viewing window.
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bottom effects, the mannequin was positioned in the flume at a depth of 0.75 m, an equal
distance between the water surface and the flume bottom, and also halfway between the
two wall surfaces (Figure 7). It was supported by a rod 0.015 m in diameter that
extended from a single fingertip to a support strut 2.81 m upstream from the mannequin
(Figure 6).
Preliminary testing of the mannequin was done for both face-up and face-down positions;
the mean drag results were the same. However, because of the location of the mannequins
internal ballast tanks, it was most stable when submerged face-up in the water; therefore,
that was the way it was oriented once final testing began.
An AMTI model MC3-6-1000 load cell interfaced with an AD Instruments Maclab 8e
was attached to the support strut (Figure 7) to measure drag force. A smaller thin strut of
width 0.015 m was placed 1.07 m in front of the mannequin to act as a frictionless guide
through which the rod was fed. Attached to this strut 0.115 m above the horizontal rod was avelocity meter (Marsh McBinney Flow Mate 2000; Figure 6), which measured the free
stream velocity. Data sampling of both force and velocity was made at 100 Hz. Each test
lasted 30 s, and five tests were performed at each velocity (1.50, 1.75, 2.00, and 2.25 m/s).
The mannequin was tested both with and without a Speedo brief. After the mannequin
testing was complete, the mannequin was detached from the support structures, and the
drag of the support structures alone was measured. This tare drag was subtracted from the
mannequin support structure total drag to determine just the drag on the mannequin.
Then, the adjustment for interference drag was added, as described in the previous section,
and shown in the following equation:
Total Mannequin Drag TableII Drag SSm 2Drag SDrag I
where Drag SSm measured flume drag of mannequin with supports, Drag
S measured flume drag of support only, and Drag I calculated interference drag
from CFD modelling.
Swimmer flume test set-up
The participating swimmer, who had been scanned to create the CFD and mannequin
model, was also tested in the flume, wearing a Speedo brief. The support configuration
was the same as for the mannequin, with two exceptions: a small handle was attached to
the end of the rod for the swimmer to grasp, and the swimmer was tested face-down in
the water but still at a depth of 0.75 m. The swimmer was tested face-down because
preliminary testing showed he was better able to maintain a more consistent streamline
while face-down. During testing, the swimmer successfully held an overall shape equal to
the shape he was in while scanned, but small increases in angle of attack of less than 3 8
were noted as the velocity was increased. Data sampling of both force and velocity was
made at 100 Hz. Each test lasted 15s, after swimmer stabilization, and five tests were
performed at each velocity (1.50, 1.75, 2.00, and 2.25 m/s).
We wanted to determine the drag of the swimmer without a swimsuit for comparison with the
CFDmodelling. Since theswimmer could notbe easilytested without a suit, he wastested with a
Speedo brief and drag forces were measured. Then, after corrections for support and
interference drag, the ratio of the mannequin drag without a suit to mannequin drag with a suit
was determined as an adjustment factor. The drag forces of the human swimmer with suit were
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multiplied by this factor to approximate the drag forces of the human swimmer without a suit.
The following equation represents how the final drag on the human swimmer without swimsuit
was calculated:
Human Drag no suit Table III Drag SSh 2Drag S Drag I Ratio
where Drag SSh measured drag of swimmer with suit and supports, Drag S measured
flume drag of support only, Drag I calculated interference drag from CFD modelling, and
Ratio the ratio of mannequin drag without suit to mannequin drag with suit
Drag coefficients were also calculated from the final results using Cd Fd/(1/2 rV2A),
where Cd is the drag coefficient,Fd is the drag force, r is the water density, Vis the steady free
stream relative velocity of the swimmer to the water, andAis the frontal maximum projected
area of the body.
Statistical analysis
A statistical analysis of the experimental results provides some useful insight into the
accuracy of the testing. The mannequin was tested five times for each test condition, and the
test duration was 30 s per test, after the water velocity reached steady state. The swimmer
was also tested five times, but the test duration was limited to 15 s per test, after the swimmer
achieved as stable a streamline as was possible. Force and velocity were both sampled at
100 Hz. The drag force and velocity means and standard deviations (s) were calculated for
each individual test. Then the data of the five tests for each condition were combined and
new means and standard deviations for the pooled data were determined.
Figure 8. CFD oil-film plot shows the direction of water flow around the body.
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Results
CFD results
The path of the water moving near the swimmers surface is revealed by a CFD oil-film plot
(Figure 8). The drag coefficients for the CFD model (Table I) were calculated as detailed in
the Methods section. They changed slightly from 0.302 at 1.5 m/s to 0.297 at 2.25 m/s. A
similar slight decline in drag coefficients was seen by Bixler and Riewald (2002) in their CFD
study of propulsive arm and hand drag, and also by Berger and colleagues (Berger, de Groot,
and Hollander, 1995) in their experimental study of hand and arm drag.
The calculated drag forces (Figure 9) show that, although pressure drag was dominant,
skin friction drag was by no means insignificant. The percentage of total drag due to skin
friction varied from 27% at 1.50 m/s to 25% at 2.25 m/s. However, these percentages are
based upon the swimmers surface having a zero roughness. If the surface roughness were
increased in the model, the friction drag would be even higher. On the other hand, if the
swimmer were on the waters surface, these percentages would be reduced owing to the
reduction in wetted area and the generation of wave drag. Also, increased roughness couldlead to earlier boundary layer separation, thus increasing pressure drag.
In addition to the chosen standard turbulence model used in the analyses, three other
turbulence models were tried to establish whether the percentage of total drag attributable to
skin friction (26%) changed. There were small changes in the friction contribution to total
drag, but all were within 2.7% of the original 26%, providing additional confidence that the
distribution of total drag between skin friction and pressure was determined with sufficient
accuracy.
Table I. Results of CFD analysis.
Velocity
(m/s)
Pressure force
(N)
Skin friction
(N)
Total force
(N)
% Skin friction Total drag coefficient
1.50 22.99 8.59 31.58 27.20 0.302
1.75 31.46 11.28 42.74 26.39 0.300
2.00 41.26 14.32 55.57 25.77 0.298
2.25 52.40 17.68 70.08 25.23 0.297
Figure 9. Model drag force versus velocity. The skin friction drag is approximately 26% of the total drag when the
swimmer is streamlined under the surface (as after each turn).
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Table II. Mannequin test data (mean ^ s).
Mean velocity
(m/s)
Mean force
(N)
Mean velocity
(m/s)
Mean force
(N)
Mean velocity
(m/s)
Mean force
(N)
Mean velocity
(m/s)
Support-only test number160 1.50 ^ 0.01 6.95 ^ 0.42 1.75 ^ 0.01 9.36 ^ 0.53 2.02 ^ 0.01 12.14 ^ 0.54 2.26 ^ 0.01
161 1.50 ^ 0.01 7.25 ^ 0.49 1.75 ^ 0.01 9.71 ^ 0.50 2.02 ^ 0.01 12.23 ^ 0.56 2.25 ^ 0.01
163 1.49 ^ 0.01 7.55 ^ 0.43 1.74 ^ 0.01 10.13 ^ 0.55 2.01 ^ 0.01 12.70 ^ 0.56 2.25 ^ 0.01
164 1.50 ^ 0.01 7.10 ^ 0.40 1.75 ^ 0.01 9.58 ^ 0.47 2.02 ^ 0.01 12.28 ^ 0.56 2.24 ^ 0.01
171 1.49 ^ 0.01 7.00 ^ 0.45 1.74 ^ 0.02 9.58 ^ 0.47 2.02 ^ 0.01 12.29 ^ 0.54 2.25 ^ 0.02
All (n 15,000) 1.50 ^ 0.01 7.17 ^ 0.49 1.75 ^ 0.01 9.67 ^ 0.56 2.02 ^ 0.01 12.33 ^ 0.59 2.25 ^ 0.01
All (n 5) 1.50 ^ 0.01 7.17 ^ 0.24 1.75 ^ 0.01 9.67 ^ 0.28 2.02 ^ 0.01 12.33 ^ 0.22 2.25 ^ 0.01
No suit test number
210 1.50 ^ 0.02 34.44 ^ 1.07 1.72 ^ 0.01 47.62 ^ 1.38 2.02 ^ 0.01 63.87 ^ 2.36 2.25 ^ 0.01
211 1.49 ^ 0.01 33.91 ^ 1.11 1.74 ^ 0.00 47.44 ^ 1.60 2.01 ^ 0.01 63.90 ^ 1.91 2.25 ^ 0.01
212 1.49 ^ 0.01 33.73 ^ 1.13 1.73 ^ 0.01 47.65 ^ 1.56 2.01 ^ 0.01 64.89 ^ 2.45 2.24 ^ 0.01
213 1.49 ^ 0.00 34.45 ^ 1.16 1.75 ^ 0.01 48.39 ^ 1.55 1.99 ^ 0.01 64.62 ^ 2.46 2.24 ^ 0.01
214 1.50 ^ 0.01 33.65 ^ 0.96 1.73 ^ 0.01 46.93 ^ 1.55 2.03 ^ 0.01 64.28 ^ 2.55 2.25 ^ 0.01
All (n 15,000) 1.49 ^ 0.01 34.03 ^ 1.14 1.74 ^ 0.01 47.61 ^ 1.60 2.01 ^ 0.02 64.31 ^ 2.39 2.25 ^ 0.01
All (n 5) 1.49 ^ 0.01 34.03 ^ 0.39 1.74 ^ 0.01 47.61 ^ 0.52 2.01 ^ 0.01 64.31 ^ 0.45 2.25 ^ 0.01
Briefs test number
368 1.49 ^ 0.01 35.59 ^ 1.63 1.76 ^ 0.02 51.07 ^ 2.25 2.01 ^ 0.01 68.23 ^ 2.82 2.24 ^ 0.01
369 1.50 ^ 0.01 36.33 ^ 1.45 1.75 ^ 0.01 51.09 ^ 1.80 2.03 ^ 0.01 70.29 ^ 2.69 2.25 ^ 0.01
370 1.49 ^ 0.01 35.75 ^ 1.53 1.74 ^ 0.01 50.86 ^ 1.87 2.03 ^ 0.01 68.85 ^ 2.41 2.25 ^ 1.01
371 1.49 ^ 0.01 35.67 ^ 1.02 1.75 ^ 0.01 51.20 ^ 1.95 2.01 ^ 0.01 69.09 ^ 2.75 2.25 ^ 0.01
372 1.50 ^ 0.01 36.08 ^ 1.17 1.74 ^ 0.01 51.36 ^ 2.06 2.03 ^ 0.01 69.97 ^ 2.47 2.25 ^ 0.02
All (n 15,000) 1.49 ^ 0.01 35.89 ^ 1.41 1.75 ^ 0.01 51.12 ^ 2.00 2.02 ^ 0.01 69.25 ^ 2.74 2.25 ^ 0.01
All (n 5) 1.49 ^ 0.01 35.89 ^ 0.31 1.75 ^ 0.01 51.12 ^ 0.19 2.02 ^ 0.01 69.25 ^ 0.87 2.25 ^ 0.00
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Table III. Summary of mannequin test results (mean ^ s).
Mannequin with support Support only Interference drag Mannequi
n Mean velocity (m/s) Mean force (N) n Mean velocity (m/s) Mean force (N) Force (N) Mean forc
No Swimsuit
5 1.49 34.03 ^ 0.39 5 1.50 7.17 ^ 0.24 3.38 30.24^ 0.2
5 1.74 47.61 ^ 0.52 5 1.75 9.67 ^ 0.28 4.53 42.46^ 0.2
5 2.01 64.32 ^ 0.45 5 2.02 12.33 ^ 0.22 5.85 57.84^ 0.2
5 2.25 81.61 ^ 0.98 5 2.25 16.25 ^ 0.31 7.41 72.76^ 0.4
With briefs Mean force (N)
[Drag ratio: no swim
5 1.49 35.89 ^ 0.31 5 1.50 7.17 ^ 0.24 3.38 32.10^ 0.2
5 1.75 51.12 ^ 0.19 5 1.75 9.67 ^ 0.28 4.53 45.97^ 0.15 2.02 69.25 ^ 0.88 5 2.02 12.33 ^ 0.22 5.85 62.77^ 0.4
5 2.25 89.96 ^ 0.46 5 2.25 16.25 ^ 0.31 7.41 78.11^ 0.2
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Table IV. Swimmer test data (mean ^ s).
Mean velocity
(m/s)
Mean force
(N)
Mean velocity
(m/s)
Mean force
(N)
Mean velocity
(m/s)
Mean force
(N)
Mean velocity
(m/s)
Support-only (with handle) test number
6 1.49 ^ 0.01 9.17 ^ 0.98 1.74 ^ 0.01 13.22 ^ 1.13 2.00 ^ 0.01 17.28 ^ 1.57 2.28 ^ 0.01
32 1.55 ^ 0.04 9.04 ^ 1.15 1.77 ^ 0.02 12.36 ^ 1.96 2.02 ^ 0.02 16.46 ^ 1.76 2.26 ^ 0.01
63 1.50 ^ 0.02 8.49 ^ 0.91 1.75 ^ 0.01 11.99 ^ 1.95 2.01 ^ 0.01 15.83 ^ 1.13 2.26 ^ 0.01
94 1.48 ^ 0.01 8.98 ^ 0.88 1.76 ^ 0.01 12.83 ^ 1.04 2.02 ^ 0.01 16.55 ^ 1.60 2.25 ^ 0.01
125 1.50 ^ 0.01 8.36 ^ 0.97 1.76 ^ 0.01 12.28 ^ 1.06 2.03 ^ 0.02 16.12 ^ 1.59 2.26 ^ 0.01
All (n 15,000) 1.50 ^ 0.03 8.81 ^ 1.03 1.76 ^ 0.02 12.54 ^ 1.55 2.02 ^ 0.02 16.45 ^ 1.62 2.26 ^ 0.01
All (n 5) 1.50 ^ 0.03 8.81 ^ 0.36 1.76 ^ 0.01 12.54 ^ 0.49 2.02 ^ 0.01 16.45 ^ 0.55 2.26 ^ 0.01
Briefs test number
1 1.45 ^ 0.01 45.01 ^ 1.74 1.75 ^ 0.01 61.45 ^ 1.96 2.01 ^ 0.01 84.30 ^ 3.14 2.23 ^ 0.01
2 1.48 ^ 0.01 43.20 ^ 1.66 1.75 ^ 0.01 61.43 ^ 2.29 2.03 ^ 0.00 83.95 ^ 3.11 2.25 ^ 0.01
3 1.50 ^ 0.00 44.72 ^ 2.00 1.76 ^ 0.01 61.94 ^ 2.23 2.06 ^ 0.01 88.05 ^ 3.61 2.25 ^ 0.01 4 1.52 ^ 0.01 45.22 ^ 1.46 1.77 ^ 0.01 66.27 ^ 1.84 2.06 ^ 0.01 84.79 ^ 2.05 2.27 ^ 0.01
5 1.55 ^ 0.02 46.35 ^ 1.34 1.78 ^ 0.01 68.58 ^ 1.98 2.06 ^ 0.01 91.97 ^ 2.07 2.30 ^ 0.01
All (n 15,000) 1.50 ^ 0.04 44.90 ^ 1.94 1.76 ^ 0.01 63.94 ^ 3.60 2.04 ^ 0.02 86.61 ^ 4.18 2.26 ^ 0.02
All (n 5) 1.50 ^ 0.04 44.90 ^ 1.13 1.76 ^ 0.01 63.94 ^ 3.30 2.04 ^ 0.03 86.61 ^ 3.41 2.26 ^ 0.03
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Table V. Summary of swimmer test results (mean ^ s).
Swimmer with briefs and support Support only Interference drag Adjustment ratio
n Mean velocity (m/s) Mean Force (N) n Mean velocity (m/s) Mean Force (N) Force (N) Force (N)
5 1.501 44.90^ 1.94 5 1.50 8.81 ^ 0.36 3.38 0.94
5 1.761 63.94^ 3.60 5 1.76 12.54 ^ 0.49 4.53 0.92
5 2.045 86.61^ 4.18 5 2.02 16.45 ^ 0.55 5.85 0.92
5 2.260 108.1^ 3.53 5 2.26 20.98 ^ 0.38 7.41 0.93
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approximately 18% less than the drag of the swimmer at all velocities. This comparison is less
satisfying, and will be evaluated further in the Discussion.
Discussion and implications
The excellent comparisons between the CFD test results and the mannequin test results
validate both the chosen CFD techniques and the mannequin experimental set-up and
procedure. In particular, the assumption in the CFD modelling that the flow is turbulent,rather than laminar, around the body appears to be confirmed by the close agreement with
the mannequin test results. It should be noted, however, that although the forces from the
mannequin tests and CFD models were within 4% of each other for this streamlined
position, there may be other postures encountered during actual swimming where CFD
models, as presently built, would not adequately predict the drag forces, without changing
internal CFD modelling parameters. Future research should include creation of moving
CFD models to evaluate active drag and assess this potential limitation.
The comparisons between the mannequin drag and the real swimmer drag are less
satisfying, with the difference being about 18%. This is not surprising, as it was difficult for
the swimmer to hold consistently an optimal streamlined position throughout the tests.
Indeed, a slight increase in angle of attack was noted as the water test velocity was increased.
It is also certain that the position of the hands while holding the handle, as well as the handle
itself, would have slightly increased the drag force of the swimmer above that of the
mannequin, whose hands were streamlined with no handle present. One other difference
between the mannequin and the swimmer is that the swimmers skin is flexible while the
mannequins skin is rigid. However, recent research on the effect of a dolphins compliant
skin on drag (Nagamine, Yamahata, Hagiwara, and Matsubara, 2004) indicates that
compliant skin reduces drag, rather than increases it. Thus, human skin, which is quite
flexible compared with dolphin skin, is an unlikely contributor to the increased drag of the
swimmer over the mannequin. Finally, both the mannequin and CFD model have smooth
surfaces relative to the human swimmer whose skin has some roughness. This smoothness is
also partially responsible for the drag of the CFD model and the mannequin being lower
than the drag of the actual swimmer.
Figure11. Drag force versus velocity for theswimmer,mannequin, andCFD model.The CFDand mannequindrag
results arevery similar, butboth of them areapproximately 18%less than theswimmer results. This is most probably
due to the hand position and variable streamline position of the swimmer.
B. Bixler et al.96
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The principal implication of this study is that it demonstrates the validity of CFD analysis
as a tool to examine the water flow around a submerged swimmers body. This form of
analysis has opened a new avenue of research into the hydrodynamics of swimming and has
been shown to hold promise as a way to assess the flow characteristics and associated drag
forces experienced by swimmers. This study, although limited to passive drag, has been a
novel and well-advised first step towards the ultimate goal of evaluating active drag. In
addition to predicting total drag, CFD methods have provided a way to estimate the relative
contributions of each drag component to the total drag.
Future research can build upon these CFD and experimental results by analysing the
passive drag of a swimmer on the waters surface, and including wave drag in the
calculations. But the most obvious next step would be to evaluate underwater active drag
while the swimmer is kicking. After that, kicking on the surface and then, finally, arm motion
could be added. In addition, the development of roughness parameters for human skinwould allow a more accurate CFD model to be built. As CFD methods continue to develop,
it will be possible to evaluate the effects of different techniques, body positions, and
swimwear on performance, thereby optimizing athletes performance.
Conclusion
Based on the results, we succeeded in achieving our aim of establishing a CFD model of a
submerged human body subject to passive drag. In addition, we have demonstrated the
accuracy of this model by comparing model results with real-world test results. Although
the limitations of this study are recognized (no more than 15% of a swimmers race occurs in
a passive drag position underwater), it represents a necessary first step towards more
complicated analyses in which active drag is evaluated using CFD techniques, and where
long-standing questions about swimming propulsion can be answered. In addition, the CFD
technique was able to show how passive drag is affected by small changes in the angle of
attack of a swimmer. Future passive drag work could evaluate the effects of posture changes
on drag and determine the optimum streamlined position.
Acknowledgements
This research was supported by Speedo International and Fluent, Inc. The authors would
like to thank Eve Davies of Speedo for her encouragement and helpful suggestions and also
Dr. Keith Hanna of Fluent for his continuous support. Special thanks go to Neil George for
some very creative laboratory and underwater improvisations.
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