Energy fluxes in turbulent separated flows

Turbulent separation in channel flow containing a curved wall is studied using a generalised form of Kolmogorov equation. The equation successfully accounts for inhomogeneous effects in both the physical and separation spaces. We investigate the scale-by-scale energy dynamics in turbulent separated flow induced by a curved wall. The scale and spatial fluxes are highly dependent on the shear layer dynamics and the recirculation bubble forming behind the lower curved wall. The intense energy produced in the shear layer is transferred to the recirculation region, sustaining the turbulent velocity fluctuations. The energy dynamics radically changes depending on the physical position inside the domain, resembling planar turbulent channel dynamics downstream

Drag reduction induced by superhydrophobic surfaces in turbulent pipe flow

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 contribution

Transition from shear-dominated to Rayleigh-Taylor turbulence

Turbulent mixing layers in nature are often characterized by the presence of a mean shear and an unstable buoyancy gradient between two streams of different velocity. Depending on the relative strength of shear versus buoyancy, either the former or the latter may dominate the turbulence and mixing between the two streams. In this paper, we present a phenomenological theory that leads to the identification of two distinct turbulent regimes: an early regime, dominated by the mean shear, and a later regime dominated by the buoyancy. The main theoretical result consists of the identification of a cross-over time-scale that discerns between the shear- and the buoyancy-dominated turbulence. This cross-over time depends on three large-scale constants of the flow, namely the buoyancy difference, the velocity difference between the two streams, and the gravitational acceleration. We validate our theory against direct numerical simulations (DNSs) of a temporal turbulent mixing layer compounded with an unstable stratification. We observe that the cross-over time correctly predicts the transition from shear to buoyancy driven turbulence, in terms of turbulent kinetic energy production, energy spectra scaling and mixing layer thickness

Particles in turbulent separated flow over a bump: effect of the Stokes number and lift force

Particle-laden turbulent flow that separates due to a bump inside a channel is simulated to analyse the effects of the Stokes number and the lift force on the particle spatial distribution. The fluid friction Reynolds number is approximately 900 over the bump, the highest achieved for similar computational domains. A range of particle Stokes numbers are considered, each simulated with and without the lift force in the particle dynamic equation. When the lift force is included a significant difference in the particle concentration, in the order of thousands, is observed in comparison with cases where the lift force is omitted. The greatest deviation is in regions of high vorticity, particularly at the walls and in the shear layer but results show that the concentration also changes in the bulk of the flow away from the walls. The particle behaviour changes drastically when the Stokes number is varied. As the Stokes number increases, particles bypass the recirculating region that is formed after the bump and their redistribution is mostly affected by the strong shear layer. Particles segregate at the walls and particularly accumulate in secondary recirculating regions behind the bump. At higher Stokes numbers, the particles create reflection layers of high concentration due to their inertia as they are diverted by the bump. The fluid flow is less influential and this enables the particles to enter the recirculating region by rebounding off walls and create a focus of high particle concentration.Comment: 8 pages, 9 figures, submitted to Physics of Fluid

Effect of geometry and Reynolds number on the turbulent separated flow behind a bulge in a channel

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 Reτ = 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.peer-reviewe

Superhydrophobic surfaces to reduce form drag in turbulent separated flows

The drag force acting on a body moving in a fluid has two components, friction drag due to fluid viscosity and form drag due to flow separation behind the body. When present, form drag is usually the most significant between the two and in many applications, streamlining efficiently reduces or prevents flow separation. As studied here, when the operating fluid is water, a promising technique for form drag reduction is to modify the walls of the body with superhydrophobic surfaces. These surfaces entrap gas bubbles in their asperities, avoiding the direct contact of the liquid with the wall. Superhydrophobic surfaces have been vastly studied for reducing friction drag. We show they are also effective in reducing flow separation in turbulent flow and therefore in reducing the form drag. Their conceptual effectiveness is demonstrated by studying numerical simulations of turbulent flow over a bluff body, represented by a bump inside a channel, which is modified with different superhydrophobic surfaces. The approach shown here contributes to new and powerful techniques for drag reduction on bluff bodies.peer-reviewe

Turbulence dynamics in separated flows : the generalised Kolmogorov equation for inhomogeneous anisotropic conditions

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.peer-reviewe

Particles in turbulent separated flow over a bump : effect of the Stokes number and lift force

Accepted manuscript. Formal publication: Physics of Fluids 31, 103305 (2019); https://doi.org/10.1063/1.5119103Particle-laden turbulent flow that separates due to a bump inside a channel is simulated to analyze the effects of the Stokes number and the lift force on the particle spatial distribution. The fluid friction Reynolds number is approximately 900 over the bump, the highest achieved for similar computational domains. The presence of the bump creates a complex background flow with a recirculating region and a strong shear layer. A range of particle Stokes numbers are considered, each simulated with and without the lift force in the particle dynamic equation. The effect of the lift force on the particle concentration is dominant in regions of high spanwise vorticity, particularly at the walls and in the shear layer. The concentration change is of the order of thousands when compared to cases where the lift force is omitted. At a low Stokes number, the particles segregate at both top and bottom walls and are present in the recirculating region. As the Stokes number increases, particles bypass the recirculating region and their redistribution is mostly affected by the strong shear layer. Particles segregate at the walls and particularly accumulate in secondary recirculating regions behind the bump. At higher Stokes numbers, the particles create reflection layers of high concentration due to their inertia as they are diverted by the bump. The fluid flow is less influential, and this enables the particles to enter the recirculating region by rebounding off walls and create a focused spot of high particle concentration.peer-reviewe

Countergradient turbulent transport in a plume with a crossflow

Direct numerical simulation of a turbulent forced buoyant plume in a crossflow is performed at a source Reynolds number , Richardson number , Prandtl number and source-to-crossflow velocity ratio . The instantaneous and temporally averaged flow fields are assessed in detail, providing an overview of the flow dynamics. The velocity, temperature and pressure fields are used together with enstrophy fields to describe qualitatively the evolution of the plume as it is swept downstream by the crossflow, and the mechanisms involved in its evolution are outlined. The plume trajectory is determined quantitatively in a number of ways, and it is shown that the central streamline and the centre of buoyancy of the plume differ significantly—as with jets in crossflow, the central streamline is seen to follow the top of the plume, whereas the centre of buoyancy, by definition, describes the plume as a whole. We then investigate the turbulence properties inside the plume; in particular the eddy viscosity and diffusivity are presented, which are significant parameters in turbulence modelling. Assessment of turbulence production demonstrates the presence of regions where turbulence kinetic energy is redistributed to the kinetic energy of the mean flow, implying a negative eddy viscosity within certain regions of the domain. Similarly, the observation that the buoyancy flux and buoyancy gradient are anti-parallel in specific regions of the flow implies a negative eddy diffusivity in said regions, which must be realised in models of such flows in order to capture the countergradient transport of thermal properties. A characteristic eddy viscosity and diffusivity are presented, and shown to be approximately constant in the fully developed regime, resulting in a constant characteristic turbulent Prandtl number, in turn signifying self-similarity