Examination of the wall law based on determining virtual origins over riblets in a turbulent boundary layer

Abstract

Experimental investigations in a wind tunnel facility have been made over riblets and smooth surfaces at moderate Reynolds numbers under zero pressure gradient. The local wall shear stress was obtained by using the newly designed direct measurement device, and mean velocity and turbulence intensity profiles near the wall were obtained by using the aid of constant temperature anemometer and a single hot-wire probe. In the smooth surface boundary layer as canonical flow, Kármán constant κ and the coefficients of the log-law C and the velocity deficit law D were determined as κ = 0.387，C = 3.79，D = −0.515 at Rθ = 4505 and κ = 0.384，C = 3.94，D = −0.562 at Rθ = 6824. The coefficient F in the Fernholz-Finley equation is reduced due to variation in C and D at low Reynolds numbers. Trapezoidal groove riblets of 8.7 < s+ < 19.4 reduce the local wall shear stress by 4.4% to 7.2% compared to the smooth surface. The downward shift from the riblet top to the virtual origin of the wall shear stress hpτw to the surface for uniform shear stress coincides with the downward shift from the riblet top to the virtual origin of the longitudinal mean velocity hpl for similarity requirement. The estimated distance from riblet top to the virtual origin of cross flow hpc is slightly smaller than hpl. The maximum value of the turbulence intensity nondimensionalized by the friction velocity of the smooth surface is certainly decreased over riblets, but the maximum value nondimensionalized by each friction velocity is almost same over smooth and riblets surfaces.

Keywords

• riblets
• wall shear stress
• kármán constant
• drag reduction
• direct measurement
• turbulent boundary layer
• log-low
• wall defect low
• virtual origin