Turbulent boundary layer over 2D Transverse RodRoughened Walls

A series of
DNSs of the spatially developing TBLs over 2D rodroughened 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.

Twopoint
amplitude modulation (AM) covariance showed that modulation effect of
largescale motions on nearwall smallscale 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 twopoint AM covariance were shown to be
changed.
 Shifting of the ondiagonal peak location
indicates that nearwall turbulence cycle was shifted around the crest of
roughness element.
 The second peak located at y1+ = 80 and y2+ =7~8
indicates that the largescale motions existing at y1+ = 80 had modulating
effects on the smallscales 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.1627, 2015)
Direct numerical simulation of a 30R long turbulent pipe flow at Re_{¥ó=3008}
_{}
Numerical scheme

NavierStokes
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
Re_{D}

Re_{¥ó}

(N_{x},
N_{r}, N_{z})

¥Äx^{+}

¥Är^{+}_{min}

¥Är^{+}_{max}

¥Ä(R¥è)^{+}

¥ÄtU_{CL}/R

133000

3008

(12289, 901,
3073)

7.34

0.36

9.91

6.15

0.003

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 powerlaw behavior,
whereas the log law indicator function did not show a flat region.
¡¤
The
coefficients of each law were obtained by the indicator functions.
Premultiplied streamwise energy spectra
of streamwise velocity fluctuations

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

The k_{x}^{1}
region was observed at y^{+} = 90 – 300 with ¥ë_{x}/R = 2 – 5, which supported the attached eddy
hypothesis.

In the
2D contour spectra, two energy sites were found.
¡¤
Inner
site: y^{+} = 13 & ¥ë_{x}^{+} = 800; selfsustaining nearwall cycle.
¡¤
Outer
site: y/R = 0.087 & ¥ë_{x}/R= 10;
verylargescale motions, formed by streamwise alignment of largescale
motions.