The drag reduction induced by superhydrophobic surfaces is investigated in a turbulent pipe flow. Wetted superhydrophobic surfaces are shown to trap gas bubbles in their asperities. This stops the liquid from coming in direct contact with the wall in that location, allowing the flow to slip over the air bubbles. We consider a well-defined texture with streamwise grooves at the walls in which the gas is expected to be entrapped. This configuration is modeled with alternating no-slip and shear-free boundary conditions at the wall. With respect to the classical turbulent pipe flow, a substantial drag reduction is observed which strongly depends on the grooves’ dimension and on the solid fraction, i.e., the ratio between the solid wall surface and the total surface of the pipe’s circumference. The drag reduction is due to the mean slip velocity at the wall which increases the flow rate at a fixed pressure drop. The enforced boundary conditions also produce peculiar turbulent structures which on the contrary decrease the flow rate. The two concurrent effects provide an overall flow rate increase as demonstrated by means of the mean axial momentum balance. This equation provides the balance between the mean pressure gradient, the Reynolds stress, the mean flow rate, and the mean slip velocity contributions.

Turbulent flow separation induced by a protuberance on one of the walls of an otherwise planar channel is investigated using direct numerical simulations. Different bulge geometries and Reynolds numbers – with the highest friction Reynolds number simulation reaching a peak of $Re_{\unicode[STIX]{x1D70F}}=900$ – are addressed to understand the effect of the wall curvature and of the Reynolds number on the dynamics of the recirculating bubble behind the bump. Global quantities reveal that most of the drag is due to the form contribution, whilst the friction contribution does not change appreciably with respect to an equivalent planar channel flow. The size and position of the separation bubble strongly depends on the bump shape and the Reynolds number. The most bluff geometry has a larger recirculation region, whilst the Reynolds number increase results in a smaller recirculation bubble and a shear layer more attached to the bump. The position of the reattachment point only depends on the Reynolds number, in agreement with experimental data available in the literature. Both the mean and the turbulent kinetic energy equations are addressed in such non-homogeneous conditions revealing a non-trivial behaviour of the energy fluxes. The energy introduced by the pressure drop follows two routes: part of it is transferred towards the walls to be dissipated and part feeds the turbulent production hence the velocity fluctuations in the separating shear layer. Spatial energy fluxes transfer the kinetic energy into the recirculation bubble and downstream near the wall where it is ultimately dissipated. Consistently, anisotropy concentrates at small scales near the walls irrespective of the value of the Reynolds number. In the bulk flow and in the recirculation bubble, isotropy is restored at small scales and the isotropy recovery rate is controlled by the Reynolds number. Anisotropy invariant maps are presented, showing the difficulty in developing suitable turbulence models to predict separated turbulent flow dynamics. Results shed light on the processes of production, transfer and dissipation of energy in this relatively complex turbulent flow where non-homogeneous effects overwhelm the classical picture of wall-bounded turbulent flows which typically exploits streamwise homogeneity.

The exact regularised point particle (ERPP) method is extended to treat the inter-phase momentum coupling between particles and fluid in the presence of walls by accounting for vorticity generation due to particles close to solid boundaries. The ERPP method overcomes the limitations of other methods by allowing the simulation of an extensive parameter space (Stokes number, mass loading, particle-to-fluid density ratio and Reynolds number) and of particle spatial distributions that are uneven (few particles per computational cell). The enhanced ERPP method is explained in detail and validated by considering the global impulse balance. In conditions when particles are located close to the wall, a common scenario in wall-bounded turbulent flows, the main contribution to the total impulse arises from the particle-induced vorticity at the solid boundary. The method is applied to direct numerical simulations of particle-laden turbulent pipe flow in the two-way coupling regime to address turbulence modulation. The effects of the mass loading, the Stokes number and the particle-to-fluid density ratio are investigated. The drag is either unaltered or increased by the particles with respect to the uncoupled case. No drag reduction is found in the parameter space considered. The momentum stress budget, which includes an extra stress contribution by the particles, provides the rationale behind the drag behaviour. The extra stress produces a momentum flux towards the wall that strongly modifies the viscous stress, the culprit of drag at solid boundaries.

The generalised Kolmogorov equation is used to describe the scale-by-scale turbulence dynamics in the shear layer and in the separation bubble generated by a bulge at one of the walls in a turbulent channel flow. The second-order structure function, which is the basis of such an equation, is used as a proxy to define a scale-energy content, that is an interpretation of the energy associated with a given scale. Production and dissipation regions and the flux interchange between them, in both physical and separation space, are identified. Results show how the generalised Kolmogorov equation, a five-dimensional equation in our anisotropic and strongly inhomogeneous flow, can describe the turbulent flow behaviour and related energy mechanisms. Such complex statistical observables are linked to a visual inspection of instantaneous turbulent structures detected by means of the Q-criterion. Part of these turbulent structures are trapped in the recirculation where they undergo a pseudo-cyclic process of disruption and reformation. The rest are convected downstream, grow and tend to larger streamwise scales in an inverse cascade. The classical picture of homogeneous isotropic turbulence in which energy is fed at large scales and transferred to dissipate at small scales does not simply apply to this flow where the energy dynamics strongly depends on position, orientation and length scale.

Suspensions of DNA macromolecules (0.8 wppm, 60 kbp), modeled as finitely extensible nonlinear elastic dumbbells coupled to the Newtonian fluid, show drag reduction up to 27% at friction Reynolds number 180, saturating at the previously unachieved Weissenberg number $\simeq {10}^4$. At a large Weissenberg number, the drag reduction is entirely induced by the fully stretched polymers, as confirmed by the extensional viscosity field. The polymer extension is strongly non-Gaussian, in contrast to the assumptions of classical viscoelastic models.