Measurements of the streamwise component of the turbulent fluctuations in fully developed smooth and rough pipe flow are presented over an unprecedented Reynolds number range. For Reynolds numbers $R{e}_{\tau } \gt 20\hspace{0.167em} 000$ , the streamwise Reynolds stress closely follows the scaling of the mean velocity profile, independent of the roughness, and over the same spatial extent. This observation extends the findings of a logarithmic law in the turbulence fluctuations as reported by Hultmark, Vallikivi & Smits (Phys. Rev. Lett., vol. 108, 2012) to include rough flows. The onset of the logarithmic region is found at a location where the wall distance is equal to ∼100 times the Kolmogorov length scale, which then marks sufficient scale separation for inertial scaling. Furthermore, in the logarithmic region the square root of the fourth-order moment also displays logarithmic behaviour, in accordance with the observation that the underlying probability density function is close to Gaussian in this region.
Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from $\mathit{Re}_{{\it\tau}}=2600$ to $\mathit{Re}_{{\it\tau}}=72\,500$ ( $\mathit{Re}_{{\it\theta}}=8400{-}235\,000$ ). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For $\mathit{Re}_{{\it\tau}}\geqslant 20\,000$ , both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.
The imbibition of liquid into a capillary tube is studied both theoretically and experimentally for sufficiently long tubes where viscous resistance from the gas phase ahead of the moving front is significant. At early times, and as the length of the tube is increased, we observe a systematic deviation from classical theory that cannot be attributed to the inertia of the liquid nor entrance effects. Instead, this behaviour is rationalized by considering the viscous resistance from the gas as it is displaced by the liquid. An explicit analytical solution for a one-dimensional description of the flow is given that accounts for viscous resistance from the displaced fluid. Excellent agreement between experiment and theory is obtained.
A new scaling is derived that yields a Reynolds-number-independent profile for all components of the Reynolds stress in the near-wall region of wall-bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behaviour.
Direct numerical simulations of two superposed fluids in a channel with a textured surface on the lower wall have been carried out. A parametric study varying the viscosity ratio between the two fluids has been performed to mimic both idealised super-hydrophobic and liquid-infused surfaces and assess its effect on the frictional, form and total drag for three different textured geometries: longitudinal square bars, transversal square bars and staggered cubes. The interface between the two fluids is assumed to be slippery in the streamwise and spanwise directions and not deformable in the vertical direction, corresponding to the ideal case of infinite surface tension. To identify the role of the fluid–fluid interface, an extra set of simulations with a single fluid has been carried out. Comparison with the cases with two fluids reveals the role of the interface in suppressing turbulent transport between the lubricating layer and the overlying flow decreasing the overall drag. In addition, the drag and the maximum wall-normal velocity fluctuations were found to be highly correlated for all the surface configurations, whether they reduce or increase the drag. This implies that the structure of the near-wall turbulence is dominated by the total shear and not by the local boundary condition of the super-hydrophobic, liquid infused or rough surfaces.
Detailed studies of modern large-scale wind turbines represent a significant challenge. The immense length scales characteristic of these machines, in combination with rotational effects, render numerical simulations and conventional wind tunnel tests unfeasible. Field experiments can give us important insight into the aerodynamics and operation, but they are always accompanied by large amounts of uncertainty, due to the changing nature of the inflow and the lack of accurate control of the test conditions. Here, a series of experiments is presented, using an alternative method that enables us to represent and study much of the physics governing the large-scale wind turbines in small-scale models. A specialized, compressed-air wind tunnel is used to achieve dynamic similarity with the field-scale, but under accurately controlled conditions of the laboratory. Power and thrust coefficients are investigated as a function of the Reynolds number up to , at tip speed ratios representative of those typical in the field. A strong Reynolds number dependence is observed in the power coefficient, even at very high Reynolds numbers (well exceeding those occurring in most laboratory studies). We show that for an untripped rotor, the performance reaches a Reynolds number invariant state at , regardless of the tip speed ratio. The same model was also tested with scaled tripping devices, with a height of only , to study the effect of transition on the rotor performance. In the tripped case, the Reynolds number dependence was eliminated for all tested cases, suggesting that the state of the boundary layer is critical for correct predictions of rotor performance.