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

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

tmax tmin Lmax T

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

Space-filling Fractal Square Grids

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

Space-filling Fractal Square Grids

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

Space-filling Fractal Square Grids Df =2.0

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, 13,16,19 m/s tr8.5 (4 stations) 7, 13,16 m/s Off centre line stations , one quadrant (7 stations - every 3 cm)

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?

Space-filling Fractal Square Grids Results: H and p/e – Phase 1 Centre Line data @ 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

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

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

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

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

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

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

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

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

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

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

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

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

Space-filling Fractal Square Grids

Space-filling Fractal Square Grids

Space-filling Fractal Square Grids

Space-filling Fractal Square Grids

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

Thank you for listening R .E. Seoud