1. Turbulence Generated By Fractal Square Grids
D. Hurst, R.E. Seoud & J.C. Vassilicos
Imperial College, London

2. 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

7. tmax
tmin
Lmax T

9. Derived quantities and parameters
How do we arrive at Meff ?
Classical Grid
Meff

11. Space-filling Fractal Square Grids

12. Space-filling Fractal Square Grids
tmax
tmin
Lmax T
tr= tmax / tmin

13. Space-filling Fractal Square Grids

14. Larger version fractal square grids
Space-filling Fractal Square Grids
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

15. Space-filling Fractal Square Grids
Df =2.0

16. Measurement Strategy Space-filling Fractal Square Grids Phase 1
T=0.46 m,
tr17 tr13 tr8.5 tr5 tr2.5
Centre line measurements (14 stations)
Off centre line (12 stations) straddle CL
U = 10 m/s
T=0.91m
Centre line measurements(16 stations)
U = 12 m/s
T=0.46m, all stations post xpeak
tr17 (6 stations) 7,10,13,16,19,22 m/s
tr13 (5 stations) 7, ,16, m/s
tr8.5 (4 stations) 7, , m/s
Off centre line stations , one quadrant
(7 stations - every 3 cm)

17. Results Space-filling Fractal Square Grids Homogeneity (H)
Turbulence production / dissipation (p/d)
Isotropy
Large 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?

18. Space-filling Fractal Square Grids Results: H and p/e – Phase 1
Centre Line 10m/s , T=0.46m
Turbulence production by falls
to levels below 10% of dissipation far
Enough from the grid and for high enough tr

19. Space-filling Fractal Square Grids Results: H – Phase 1
x=3.25m
T=0.46 m

20. Space-filling Fractal Square Grids Results: H – Phase 1
xpeak

21. Space-filling Fractal Square Grids
Results: LSI - phase 1

22. Space-filling Fractal Square Grids Results: & IS L11/22 - phase 1

23. Space-filling Fractal Square Grids
Results: TS phase 1

24. Space-filling Fractal Square Grids Results: H - phase 2 s-w map
Grid = tr17
Uinf=10m/s
Uinf=7m/s
Uinf=10m/s
Uinf=13m/s

25. Space-filling Fractal Square Grids Results: Length Scales - phase 2
s-w map
Grid = tr17
Uinf=10m/s
L11

26. Space-filling Fractal Square Grids Results: H - phase 2
x- wire map
Grid = tr17
Grid = tr17
Grid = tr17

27. Space-filling Fractal Square Grids Results: LSI, - phase 2
v x/ cm

28. Space-filling Fractal Square Grids Results: Length Scales - phase 2
x- wire map
Grid = tr13
Grid = tr17,13,8.5
Grid = tr17,13

29. Space-filling Fractal Square Grids
Results: LSI, Length Scales - phase 2
x- wire map
Grid = tr17
Grid = tr17,13

30. Space-filling Fractal Square Grids Results: SSI - phase 2
x- wire map
Grid = tr8.5
Grid = tr13
Grid tr17
Uinf 16.2 m/s
Grid = tr13

31. Space-filling Fractal Square Grids

32. Space-filling Fractal Square Grids

33. Space-filling Fractal Square Grids

34. Space-filling Fractal Square Grids

35. Conclusion Space-filling Fractal Square Grids
-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

36. Thank you for listening
R .E. Seoud