turbulence generated by fractal square grids d. hurst, r.e. seoud & j.c. vassilicos

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Turbulence Generated By Fractal Square GridsD. Hurst, R.E. Seoud & J.C. Vassilicos

Imperial College, London

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Content- Motivation- Windtunnels used- Fractal grids: three families- Derived Quantities and Parameters- Classical grid – a special case - Space-filling Fractal Square Grids- Measurement Strategy- Results: Homogeneity, turbulence production, large scale Isotropy, small scale isotropy-Conclusions

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tmax

tmin

Lmax

T

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How do we arrive at Meff ?

4

22

2

2

2

2

161

41

14

14

14)(4

2

T

PM

T

MP

M

b

M

T

M

bP

M

T

M

bMP

M

TN

M

bMbM

M

b

M

b

Derived quantities and parameters

14 2

P

TMeff

Classical Grid

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Space-filling Fractal Square Grids

Imperial CollegeSpace-filling Fractal Square Grids

tr= tmax / tmin

tmax tmin

Lmax

T

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Larger version fractal square grids Again , Df=2.0 - best homogeneity T = 0.91m wind tunnel: test section = 5T tr= 17.0 & 28.0 Lmax & Lmin about same for both grids Purpose: Investigate effect of T


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Df =2.0

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Measurement StrategySpace-filling Fractal Square Grids

Phase 1 Phase 2T=0.46m, all stations post xpeak

tr17 (6 stations) 7,10,13,16,19,22 m/str13 (5 stations) 7, 13,16,19 m/str8.5 (4 stations) 7, 13,16 m/sOff centre line stations , one quadrant (7 stations - every 3 cm)

T=0.46 m,tr17 tr13 tr8.5 tr5 tr2.5Centre line measurements (14 stations)Off centre line (12 stations) straddle CL U = 10 m/sT=0.91mCentre line measurements(16 stations)U = 12 m/s

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Homogeneity (H)

Turbulence production / dissipation (p/d)

IsotropyLarge Scale Isotropy (LSI)

Small Scale Isotropy (SSI)

Taylor Reynolds no. Length Scales (L Scales)

Integral Scale (IS) L11,22 , Taylor microscale (TS)

Power/Exponential decay law?

dxdUu /2

dydUuv /

U

xU )(

U

urmsU

vrms

rms

rms

v

u

Coherence

Results

U

yU )(

Re

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Space-filling Fractal Square GridsResults: H and p/e – Phase 1

Turbulence production by falls to levels below 10% of dissipation far Enough from the grid and for high enoughtr

dx

dU

Centre Line data @ 10m/s , T=0.46m

dxdUu /2

U

xU )(

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Profiles @ x=3.25mT=0.46 m

smU /10

U

yU )(

U

urmsU

vrms

Space-filling Fractal Square GridsResults: H – Phase 1

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Space-filling Fractal Square GridsResults: H – Phase 1

smU /10

U

vrms

U

urms

xpeakmin

min75L

Tt

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rms

rms

v

usmU /10

Space-filling Fractal Square GridsResults: LSI - phase 1

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Space-filling Fractal Square GridsResults: & IS L11/22 - phase 1Re

L11 L22

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Space-filling Fractal Square GridsResults: TS - phase 1

smU /10

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Results: H - phase 2

Uinf=7m/s Uinf=13m/s

Uinf=10m/s

U

xU )(

U

yU )(

Uinf=10m/s

s-w mapGrid = tr17

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Results: Length Scales - phase 2

L11

dkkE

dkk

kE

)(11

)(11


Uinf=10m/s

s-w map

Grid = tr17

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Space-filling Fractal Square GridsResults: H - phase 2

U

xU )(

U

yU )(

x- wire map

5.8,/5.13inf trsmU

Grid = tr17 Grid = tr17

smU /2.16inf smU /2.16inf

dydUuv /

Grid = tr17

smU /2.16inf

Imperial CollegeSpace-filling Fractal Square GridsResults: LSI, - phase 2Re

smU /2.16inf

rms

rms

v

u

0

200

400

600

800

100 150 200 250 300 350 400

Re v x/ cm

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x- wire map

Space-filling Fractal Square GridsResults: Length Scales - phase 2

smU /3.7inf

smU /19inf

smU /5.13inf

Grid = tr17,13

Grid = tr13

Grid = tr17,13,8.5

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x- wire mapResults: LSI, Length Scales - phase 2


200 220 240 260 280 300 320 340 360 380

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Integral scale L11

,L22

/ m v x / cm, <Uinf

> = 19 m/s, Grid = tr17,tr13, x-wire

x / cm

L 11/ m

, L 22

/m

tr17 L11tr13 L11tr17 L22tr13 L22

2211 & LL

smU /2.16inf

smU /19inf

Grid = tr17,13

Grid = tr17

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Space-filling Fractal Square GridsResults: SSI - phase 2

smU /3.7inf

Grid = tr8.5

smU /3.7inf

Grid = tr13

x- wire map

smU /19inf

Grid = tr13

Grid tr17Uinf 16.2 m/s

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Conclusion

-Homogeneity is satisfactory and improves with tr

-Turbulence production (Reynolds shear stress) /dissipation for tr17 is less than 10% for x>280cm and 0<y/cm<6cm, tr13 – similar values and range, but for tr8.5 it is quite significant

-Large scale isotropy seems to improve with speed

-Small scale isotropy seem to be very much tied to tr where tr8.5 has a coherence spectrum, which relative to tr17 and tr8.5, that indicates presence of shear

-The turbulence decay zone is governed by an exponential form

-Turbulence intensity is an increasing function of tr-The integral scale and the Taylor micorscale are independent of tr


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Thank you for listening

R .E. Seoud

turbulence generated by fractal square grids d. hurst, r.e. seoud & j.c. vassilicos

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