Abstract
The flow development in a groove-modified channel consisting of flat and grooved walls was investigated by direct numerical simulations based on the Navier–Stokes equations at a Reynolds number of $5\times 10^{3}$ based on the full channel height and the bulk velocity. Simulations were performed for highly disturbed initial flow conditions leading to the almost instantaneous appearance of turbulence in channels with flat walls. The surface morphology was designed in the form of profiled grooves aligned with the flow direction and embedded in the wall. Such grooves are presumed to allow development of only the statistically axisymmetric disturbances. In contrast to the rapid production of turbulence along a flat wall, it was found that such development was suppressed over a grooved wall for a remarkably long period of time. Owing to the difference in the flow structure, friction drag over the grooved wall was more than 60 % lower than that over the flat wall. Anisotropy-invariant mapping supports the conclusion, emerging from analytic considerations, that persistence of the laminar regime is due to statistical axisymmetry in the velocity fluctuations. Complementary investigations of turbulent drag reduction in grooved channels demonstrated that promotion of such a state across the entire wetted surface is required to stabilize flow and prevent transition and breakdown to turbulence. To support the results of numerical investigations, measurements in groove-modified channel flow were performed. Comparisons of the pressure differentials measured along flat and groove-modified channels reveal a skin-friction reduction as large as $\text{DR}\approx 50\,\%$ owing to the extended persistence of the laminar flow compared with flow development in a flat channel. These experiments demonstrate that early stabilization of the laminar boundary layer development with a grooved surface promotes drag reduction in a fully turbulent flow with a preserving magnitude as the Reynolds number increases.
Highlights
Understanding viscous drag reduction is a major challenge in engineering, since any achievement can potentially result in technological advances which affect the comfort of everyday life
This negative trend can be minimized by restricting the groove dimensions to a few viscous length scales, which implies that successful applications of simple square grooves are possible for weakly turbulent flows characterized by low turbulent Reynolds numbers, Rλ, and situations corresponding to marginal deviations of uiuj from the axisymmetric state
The anisotropy-invariant mapping presented in figure 8(a) exhibits a trajectory common for turbulence developing in wall-bounded flows at low Reynolds numbers
Summary
Understanding viscous drag reduction is a major challenge in engineering, since any achievement can potentially result in technological advances which affect the comfort of everyday life. Results of direct numerical simulations (Pashtrapanska et al 2006) suggest that rotation reduces anisotropy and promotes turbulence in the viscous sublayer by increasing at the wall Following this trend, it is expected that at sufficiently high rotation, turbulence will reach the state of minimum anisotropy, which coincides with the left boundary of the anisotropy-invariant map (Lumley & Newman 1977) and axisymmetric stress configuration uiuj = Aδij + Bkikj with (IIa)wall = 1/6, leading to unexpected laminarization denoted the rotation anomaly in the turbulence community (Jakirlic 1997). In the region between grooves, inflectional profiles might induce the production of turbulence since statistical axisymmetry cannot be a priori guaranteed This negative trend can be minimized by restricting the groove dimensions to a few viscous length scales, which implies that successful applications of simple square grooves are possible for weakly turbulent flows characterized by low turbulent Reynolds numbers, Rλ, and situations corresponding to marginal deviations of uiuj from the axisymmetric state. Of special interest are: (i) a wall morphology capable of creating axisymmetry in turbulence fluctuations over the entire wetted surface; (ii) parameterization the geometry of the antiturbulence surface; and (iii) development of turbulence anisotropy and deviations in uiuj from the statistically axisymmetric state
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