Turbulent boundary layer over 2D Transverse Rod-Roughened Walls



-      A series of DNSs of the spatially developing TBLs over 2D rod-roughened walls were performed to investigate the statistics and structures of the TBL with various streamwise spacing (px/k).


-      The Reynolds stress profiles over the rough walls showed that the effects of px/k extended to the outer layer for px/k = 8 and 16.

-       The inner peak values decreased from px/k = 8 to px/k = 32 and then increased near the wall for px/k >32.

-      The larger values of the Reynolds stresses in the inner region for px/k = 16 were attributed to the reattachment of the TBL near the wall.

-      For px/k >= 32, the profiles of the Reynolds stresses showed good agreement with the smooth wall data.


-      Two-point amplitude modulation (AM) covariance showed that modulation effect of large-scale motions on near-wall small-scale motions was strongly disturbed over the rough wall for px/k = 8 and 16.

-      For the flows over the rough walls, the positions of the inner and outer peaks on the two-point AM covariance were shown to be changed.

-      Shifting of the on-diagonal peak location indicates that near-wall turbulence cycle was shifted around the crest of roughness element.

-       The second peak located at y1+ = 80 and y2+ =7~8 indicates that the large-scale motions existing at y1+ = 80 had modulating effects on the small-scales motions present at y2+ = 7~8 and the small magnitude showed the weak interaction.

(Nadeem et al., International Journal of Heat and Fluid Flow, Vol. 56, pp.16-27, 2015)

Direct numerical simulation of a 30R long turbulent pipe flow at Re=3008

Numerical scheme

-       Navier-Stokes and continuity equations in cylindrical coordinates

-       Fully implicit fractional step method (Kim et al. 2002)

-       Centerline condition for the radial velocity - 
averaging the corresponding values across the centerline (Akselvoll & Moin 1996)

-       Streamwise domain length (Lx): 30R

       Raw data size of velocities and pressure for each step is O(1TB)
(# of grid points > 30 billion).

-       Hybrid parallelization: OpenMP + MPI

       4096 cores (Intel Xeon X5570 2.93GHz) from KISTI Supercomputing center



(Nx, Nr, Nz)








(12289, 901, 3073)






Streamwise mean velocity

-       The present streamwise mean velocity well followed the power law in the overlap region rather than the log law.

       `The plateau of the power law indicator function supported the power-law behavior, whereas the log law indicator function did not show a flat region.

       The coefficients of each law were obtained by the indicator functions.



Pre-multiplied streamwise energy spectra of streamwise velocity fluctuations

-       Short- and long wavelength spectral peaks were observed, which was called bimodal distribution.

-       The kx-1 region was observed at y+ = 90 – 300 with x/R = 2 – 5, which supported the attached eddy hypothesis.

-       In the 2D contour spectra, two energy sites were found.

       Inner site: y+ = 13 & x+ = 800; self-sustaining near-wall cycle.

       Outer site: y/R = 0.087 & x/R= 10; very-large-scale motions, formed by streamwise alignment of large-scale motions.