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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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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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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
Space-filling Fractal Square Grids
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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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Space-filling Fractal Square Grids
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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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
Space-filling Fractal Square Grids
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
Space-filling Fractal Square Grids
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
Space-filling Fractal Square Grids