Mean velocity proles

The prole of the streamwise component U is shown in gure 21, the velocities

are plottedrelativeto theincomingvelocity. Fromgure21onecansee thatthe

velocityinthewakeexceedsthereferencefreestreamvelocity. Thisindicatesthere

is a speedup eect caused by the cylinder. The average free stream velocity is

9 . 7 m/s

^{whiletheaveragevelocityin the wakeproleis}

9 . 3 m/s

^{. A loweraverage}

velocityin thewakemeansthat thepresenceof thecylindercausesablockageof

theow. Theareaof thecrossection traverseddoeshowevernot covertheentire

crossection. Since thevelocityin thewakeproleishigher closeto thewall, this

means that the average velocity in the wake is higher than

9 . 3 m/s

^{. By simply}

estimating the rest ofthe wake prolefrom the highestmeasuredvelocityin the

wake,the averagevelocityin the wake isfound to be

9 . 66 m/s

^{. This means that}

blockage eects are neglectable, and that areference velocity of

9 . 7 m/s

^{may be}

reasonable. BasedonthereferencevelocitytheReynoldsnumber,

Re _D

^{,iscalculated}

to be30717.

Asthecylinder wakeisanevolvingow,V isnotexpected tobezero,due to

the constraintsof continuity. Fora perfectly symmetrical wake V is expected to

bezeroin thecenter oftheowandnegativeoverthesymmetrylineandpositive

below. TheproleofV isplotted in gure22, alongwith thefreestreamprole.

Ideallythefreestreamconditionsshouldbezero. Duetomisalignmentoftheprobe

anosetfrom zerowouldnotbeunexpected, thevelocitydoeshowevervaryover

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1

−3

−2

−1 0 1 2 3

U/U _r ef [−]

y/D cyl. [−]

U _wake /U _ref U _freestream /U _ref

Figure21: NormalizedproleofUin cylinderwakeforRe=30717,x/D=10

thecrossection. Whetherthis isatruepropertyof theowornotisunclear,the

rangeofvariationinVequals

2 . 4 deg

probepitchrelativetothereferencevelocity.

Ifthevelocityproleiscorrectedbysubtractingthelocalfreestreamvelocity,the

prolewillbeasin gure23. Thiscorrectionassumesthattheowvelocities can

besuperpositioned. The resultlooksmorelikewhatonewouldexpect,but when

comparedtotheresultsofothersi.e. OngandWallace[7]theshapeofthevelocity

proleisnotaperfectmatch.

The velocity component in the z-direction is plotted in gure 24 along with

the freestream measurements. The samevelocity prole correctedfor freestream

conditionsisplottedin gure23.

Thefreestreamvelocityvariationcannotbeexplainedbythenitesizeofthe

probeandit is notaconstantoset asayawangle would give. The variationof

Winfreestreamconditionsishoweverrathersmall,itequalsapproximately

2 ◦

. In

thewakeofthecylinderthevariationofWis sligtlylarger.

Itisnotstraightforwardtounderstandhowthetimevaryingvelocitygradients

in the wakeof cylinder will aect the measurements. If the timeseries could be

conditionallyaveragedoni.e. thepressurevariationonthecylinder,thetimeseries

for dierenty coordinatescould be linked,and thegradientsfound. Evenif that

couldbedoneitisnotstraightforwardto decidewhateect itwould haveonthe

meanowproles. Ifthenitegeometryofthecylinderandthewindtunnelaects

thesheddingprocessthat couldalsocausethreedimensionaleects.

−0.03 −0.02 −0.01 0 0.01

−4

−3

−2

−1 0 1 2 3 4

V/U _r ef [−]

y/D cyl. [−]

V _wake /U _ref V _freestream /U _ref

Figure22: NormalizedproleofVin cylinderwakeforRe=30717,x/D=10

−0.04 −0.02 0 0.02

−3

−2

−1 0 1 2 3

∆ U _i /U _ref [−]

y/D cyl. [−]

∆ V _i /U _ref

∆ W _i /U _ref

Figure23: Normalizedproleof

V − V f reestream

^and

W − W f reestream

^incylinder

wakeforRe=30717,x/D=10

−0.05 −4 −0.04 −0.03 −0.02 −0.01 0 0.01

Figure24: NormalizedproleofWin cylinderwakeforRe=30717,x/D=10

4.3.2 Turbulentshear stresses

Thelargestturbulentshear stressisagainexpectedto be

uv

^{asit hasthelargest}

mean velocitygradientproduction term. Ingure25thenon-dimensionalized

uv

wakeproleisplottedalongwiththefreestreamresult.

Theproleshowsthesamedistinctshapefoundbyi.e. WissinkandRodi [13].

Atthecenterwhere

∂U

∂y

^iszero,

uv

^{shouldbezero,theresultsshowthat}

uv

^validate

this. Themaximum/minimumvaluesfor

uv

^{isexpectedwherethesecondgradient}

ofUiszero. Thisoccursat

y/D ≈ ± 1

andmatchesthemeanvelocityprolefairly well.

Thesignof

uv

^{canbefoundfromasimple}considerationofthemeanprole. If anair-particleattheupperhalfofthewakeweretobegivenanegativeturbulent

velocitycomponent,

v ⁰

^{,itwouldexperienceapositivestreamwiseturbulentvelocity,}

u ⁰

^{. Theproductofthese twowould benegative,hence}

uv

^{should benegativefor}

theupperhalf ofthevelocityprole. Iftheparticleismovedupinsteadtheresult

isthesame. Thesamelineofreasoningwillgiveapositivevalueof

uv

^inthelower

half ofthewake.

Ong and Wallace found that the largest magnitude of

uv/U _ref ²

^{was about}

± 0 . 004

at

x/D = 10

. From gure 25one cansee that the corresponding largest shear stress measuredranged from -0.005 to0.008. The rangeof the variationis

of thesameorder of magnitude,but it wasexpected that thevariationwould be

symmetricabout0. Thetwoothershearstressesareexpectedtobesmallfora2D

ow. Figure26showstheshearstresses,normalizedbythereferencevelocity.

uw

^and

vw

^{are not negligiblysmall asexpected, rather they are of the same}

orderofmagnitudeas

uv

^{. Thiscannotbe}interpretedasaphysicallyvalidresult,

−6 −4 −2 0 2 4 6 8 x 10 ⁻³

−3

−2

−1 0 1 2 3

uv/U _ref ² [−]

y/D cyl. [−]

wake freestream

Figure 25: Proleofnormalizedturbulentshearstress

uv

^{incylinderwakeforRe}

=30717,x/D=10

−8 −7 −6 −5 −4 −3 −2 −1 0 1

x 10 ⁻³

−4

−3

−2

−1 0 1 2 3 4

[−]

y/D cyl. [−]

uw/U _ref ² vw/U _ref ²

Figure 26: Prole of normalized turbulent shear stresses

uw

^and

vw

^{in cylinder}

wakeforRe=30717,x/D=10

in themeasurementsetuporprocessing.

4.3.3 Turbulentnormal stresses

The largest normalstress measuredin the turbulent wake is not the streamwise

component but the crossow normal stress

v ²

^{. This in accordance with the}

re-sults reportedby i.e. OngandWallace[7]. Thecentrelinestreamwiseturbulence

intensityat

x/D = 10

measured byOng and Wallaceis approximately

17%

and atinthecentreregionwithasmallreductioninturbulenceintensityonthe

cen-treline. From gure 27 one can nd that the centreline turbulence intensity is

approximately

17 . 5%

, which matchesthe result of Ongand Wallacebut there is noreductiononthecentreline. OnthecentrelineOngandWallacefound

v ^{2 /} U _ref ²

to be 0.083,from gure27acorrespondingvalueof 0.06isfound, which givesa

28%

deviation.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

−3

−2

−1 0 1 2 3

[−]

y/D cyl. [−]

u ² /U _ref ² v ² /U _ref ² w ² /U _ref ² u ² /U _ref ² , freestream

Figure27: Proleofnormalizedturbulentnormalstressesin cylinderwakeforRe

=30717,x/D=10

Ongand Wallacedoes notreport themagnitude of

w ²

^{relativeto the others.}

w ²

^{exhibitsavery}characteristicplatouinthecentreregion.

In document Three-dimensional wake measurements (sider 40-45)