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DIRECT NUMERICAL SIMULATIONS OF TURBULENT BOUNDARY LAYERS OVER SQUARE-EDGED 2-D AND 3-D ROUGH WALLS

Jae Hwa Lee
Dept. of Mechanical and Nuclear Engineering, UNIST, Ulsan 689-798, Korea; Sch. for Engr. of Matter, Transport & Energy Arizona State University Tempe, AZ 85287-6106, USA

Hyung Jin Sung
Department of Mechanical Engineering, KAIST 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea

Sinopsis

Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over two-dimensional (2-D) rod- and three-dimensional (3-D) cube-roughened walls were performed to see the roughness effects on the properties of TBL. The 2-D and 3-D roughness were periodically arranged in the downstream direction with pitches of px/k = 2, 3, 4, 6, 8 and 10 and, for the cube the spanwise spacing is fixed at pz/k = 2 with staggered array, where px and pz are the streamwise and spanwise spacings of the roughness and k is the roughness height. Inspection of the Reynolds stresses showed that except for px/k = 2 and 3 over the 2-D rough walls, the effects of the surface roughness extend to the outer layer over the 2-D and 3-D rough walls and the magnitude of the Reynolds stresses in the outer layer is increased in proportion to px/k. The consistent results were observed in the behavior of wall-normal fluctuations ( νw+ ) on the crest of the roughness suggested by Orlandi & Leonardi (2008), indicating that νw+ might be a suitable parameter to predict the influence of the surface roughness in the outer layer over the square-edged rough walls. However, such results are contrary to the trends of the form drag, roughness function and roughness length against px/k, which showed the maximum values at px/k = 8 and 4 over the 2-D and 3-D rough walls respectively.