Abstract
The dragreduction effect of a threedimensional sinusoidal riblet surface is experimentally evaluated in a fully developed turbulent channel flow. The lateral spacing of the adjacent walls of the riblet is varied sinusoidally in the streamwise direction. The obtained maximum total dragreduction rate is approximately 12 % at a bulk Reynolds number of 3,400. The flow structure over the sinusoidal riblet surface is also analyzed in the velocity field by using twodimensional particle image velocimetry. The velocity field is compared with the corresponding flow over a flat surface. It is found through pathlines and Reynolds shear stress analyses that the dragreduction mechanism is similar to those of twodimensional riblets. A different point is that the present riblet respectively induces a downward and upward flows in the expanded and contracted regions, which prevent vortices from hitting the bottom wall with wider lateral spacing of the riblet. In consequence, the wetted area of the present sinusoidal riblet is smaller than those of twodimensional riblets, resulting in the high dragreduction effect.
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Abbreviations
 \(x\) :

Position in the streamwise direction (m)
 \(y\) :

Position in the wallnormal direction (m)
 \(z\) :

Position in the spanwise direction (m)
 \(u\) :

Streamwise velocity (m/s)
 \(v\) :

Wallnormal velocity (m/s)
 \(w\) :

Spanwise velocity (m/s)
 \(\delta\) :

Channel halfwidth (m)
 \({\hbox{d}}p\) :

Differential pressure (Pa)
 \(\nu\) :

Kinematic viscosity (\(\hbox {m}^2/\hbox {s}\))
 \(\rho\) :

Density (\(\hbox {kg/m}^3\))
 \(Q\) :

Mass flow rate (\(\hbox {m}^3/\hbox {s}\))
 \(L_z\) :

Channel spanwise width (m)
 \(C_{\mathrm{T}}\) :

Total drag coefficient
 \(D_{\mathrm{P}}\) :

Pressure drag on the riblet (Pa)
 \(R_{\mathrm{D}}\) :

Dragreduction rate (%)
 \(l_t\) :

Riblet thickness (m)
 \(h\) :

Height of riblet wall (m)
 \(l\) :

Distance between pressure taps (m)
 \(L_p\) :

Distance of the center position between pressure taps from the beginning of the test section (m)
 \(l_{x}\) :

Streamwise length of one cycle of the riblet (m)
 \(l_{z}\) :

Lateral spacing of the riblet (m)
 \(S\) :

Wetted area (\(\hbox {m}^2\))
 \(u_{b}\) :

bulk velocity (m/s) (=\(\frac{1}{2\delta }\int ^{2\delta }_0 \overline{u(y)}{\hbox{d}}y\))
 \(\mu\) :

Viscosity (\(\hbox {Pa}\,\hbox {s}\))
 \(\tau _{w}\) :

Wall shear stress (\(\hbox {N/m}^2\)) (=\(\mu {\hbox{d}}\overline{u}/{\hbox{d}}y_{\mathrm{wall}}\))
 \(u_{\tau }\) :

Friction velocity (\(\hbox {m/s}^2\)) (\(= \sqrt{\tau _{w, \,{\mathrm{flat}}}/\rho }\))
 \(Re_{\tau }\) :

Friction Reynolds number (–) (=\(u_{\tau , \,{\mathrm{flat}}} \delta / \nu\))
 \(Re_{b}\) :

Bulk Reynolds number (–) (=\(u_b 2\delta / \nu\))
 \(B_{i}\) :

Event probability of quadrant
 \(\omega _{z}\) :

Spanwise vorticity (1/s)
 \(t\) :

Time (s)
 \(T\) :

Measurement time (s)
 \(()^{+}\) :

Nondimensionalization by \(u_{\tau , \,{\mathrm{flat}}}\) and \(\nu\) (wallunit)
 \(()^\prime\) :

Fluctuation from the spatiotemporal average
 \(()^{\prime \prime }\) :

Fluctuation from time average (random component)
 \(( ),_{\, {\mathrm{flat}}}\) :

Experimental result for flatflat case (both side walls are flat surface)
 \(( ),_{\, {\mathrm{rib}}}\) :

Experimental result for flatriblet case (riblet boards are installed on a lower wall)
 \(( ),_{\, {\text {2D}}}\) :

Result for a 2D riblet surface
 \(( ),_{\, {\text {3D}}}\) :

Result for a 3D riblet surface
 \(()_{i}\) :

Direction or quadrant
 \(\overline{( )}\) :

Average over time
 \(\langle \rangle\) :

Average over space
 \(\widetilde{( )}\) :

Periodic fluctuation
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Acknowledgments
This research was partially supported by the Ministry of Education, Culture, Sports, Science and Technology through a GrantinAid for Scientific Research (c), 24560186, 2012. The sinusoidal riblet plates in this research were fabricated by using a milling machine in Tokyo University of Agriculture and Technology Center of Design and Manufacturing.
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Sasamori, M., Mamori, H., Iwamoto, K. et al. Experimental study on dragreduction effect due to sinusoidal riblets in turbulent channel flow. Exp Fluids 55, 1828 (2014). https://doi.org/10.1007/s003480141828z
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DOI: https://doi.org/10.1007/s003480141828z
Keywords
 Lateral Spacing
 Streamwise Direction
 Particle Image Velocimetry Measurement
 Lower Wall
 Reynolds Shear Stress