The accuracy of computational fluid dynamics analysis.pdf

8/10/2019 The accuracy of computational fluid dynamics analysis.pdf

1/19

This article was downloaded by: [150.241.57.132]On: 21 October 2014, At: 04:07Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House37-41 Mortimer Street, London W1T 3JH, UK

Sports BiomechanicsPublication details, including instructions for authors and subscription information:

http://www.tandfonline.com/loi/rspb20

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

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of tContent. Any opinions and views expressed in this publication are the opinions and views of the authors, and

are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon ashould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveor howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
http://dx.doi.org/10.1080/14763140601058581http://www.tandfonline.com/action/showCitFormats?doi=10.1080/14763140601058581http://www.tandfonline.com/page/terms-and-conditionshttp://www.tandfonline.com/page/terms-and-conditionshttp://dx.doi.org/10.1080/14763140601058581http://www.tandfonline.com/action/showCitFormats?doi=10.1080/14763140601058581http://www.tandfonline.com/loi/rspb20


2/19

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


3/19

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.

B. Bixler et al.82


4/19

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.

Computational fluid dynamics and flume passive drag 83


5/19

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.

B. Bixler et al.84


6/19

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.



7/19

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.

B. Bixler et al.86


8/19

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.



9/19

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

B. Bixler et al.88


10/19

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.



11/19

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).

B. Bixler et al.90


12/19

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


13/19

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


14/19


15/19

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


16/19

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


17/19

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


18/19

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.

References

Berger, M., de Groot, G., and Hollander, A. (1995). Hydrodynamic drag and lift forces on human hand/arm

models. Journal of Biomechanics, 28, 125133.

Bixler, B., and Riewald, S. (2002). Analysis of a swimmers hand and arm in steady flow conditions using

computational fluid dynamics. Journal of Biomechanics, 35, 713717.

Bixler, B., and Schloder, M. (1996). Computational fluid dynamics: An analytical tool for the 21st century

swimming scientist. Journal of Swimming Research, 11, 4 22.

Jiskoot, J., and Clarys, J. (1975). Body resistance on and under the water surface. In L. Lewillie, and J. Clarys (Eds.),

International series o n sport sciences: Vol 2, swimming II (pp. 105109). Baltimore: University Park Press.

Kolmogorov, S., and Duplishcheva, O. (1992). Active drag, useful mechanical power output and hydrodynamic

force coefficient in different swimming strokes at maximal velocity. Journal of Biomechanics, 25, 311318.



19/19

Lyttle, A., Blanksby, B., Elliott, B., and Lloyd, D. (1998). The effect of depth and velocity on drag during the

streamlined guide. Journal of Swimming Research, 13, 1522.

Nagamine, H., Yamahata, K., Hagiwara, Y., and Matsubara, R. (2004). Turbulence modification by compliant skin

and strata-corneas desquamation of a swimming dolphin. Journal of Turbulence, 5, 1 25.

Riewald, S., and Bixler, B. (2001). CFD analysis of a swimmers arm and hand acceleration and deceleration.

In J. Blackwell, and R. Sanders (Eds.),XIX international symposium on biomechanics in sports, proceedings of swim

sessions (pp. 117119). San Francisco: University of San Francisco.

Vennell, R., Pease, D. L., and Wilson, B. D. (2006). Wave drag on human swimmers. Journal of Biomechanics,31,

664671.

B. Bixler et al.98

The accuracy of computational fluid dynamics analysis.pdf

Documents

Transcript of The accuracy of computational fluid dynamics analysis.pdf