26 research outputs found
Reynolds-dependence of turbulent skin-friction drag reduction induced by spanwise forcing
This paper examines how increasing the value of the Reynolds number
affects the ability of spanwise-forcing techniques to yield turbulent
skin-friction drag reduction. The considered forcing is based on the
streamwise-travelling waves of spanwise wall velocity (Quadrio {\em et al. J.
Fluid Mech.}, vol. 627, 2009, pp. 161--178). The study builds upon an extensive
drag-reduction database created with Direct Numerical Simulation of a turbulent
channel flow for two, 5-fold separated values of , namely and
. The sheer size of the database, which for the first time
systematically addresses the amplitude of the forcing, allows a comprehensive
view of the drag-reducing characteristics of the travelling waves, and enables
a detailed description of the changes occurring when increases. The effect
of using a viscous scaling based on the friction velocity of either the
non-controlled flow or the drag-reduced flow is described. In analogy with
other wall-based drag reduction techniques, like for example riblets, the
performance of the travelling waves is well described by a vertical shift of
the logarithmic portion of the mean streamwise velocity profile. Except when
is very low, this shift remains constant with , at odds with the
percentage reduction of the friction coefficient, which is known to present a
mild, logarithmic decline. Our new data agree with the available literature,
which is however mostly based on low- information and hence predicts a
quick drop of maximum drag reduction with . The present study supports a
more optimistic scenario, where for an airplane at flight Reynolds numbers a
drag reduction of nearly 30\% would still be possible thanks to the travelling
waves
Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number
A fundamental problem in the field of turbulent skin-friction drag reduction
is to determine the performance of the available control techniques at high
values of the Reynolds number . We consider active, predetermined
strategies based on spanwise forcing (oscillating wall and streamwise-traveling
waves applied to a plane channel flow), and explore via Direct Numerical
Simulations (DNS) up to the rate at which their performance
deteriorates as is increased. To be able to carry out a comprehensive
parameter study, we limit the computational cost of the simulations by
adjusting the size of the computational domain in the homogeneous directions,
compromising between faster computations and the increased need of
time-averaging the fluctuating space-mean wall shear-stress.
Our results, corroborated by a few full-scale DNS, suggest a scenario where
drag reduction degrades with at a rate that varies according to the
parameters of the wall forcing. In agreement with already available
information, keeping them at their low- optimal value produces a relatively
quick decrease of drag reduction. However, at higher the optimal
parameters shift towards other regions of the parameter space, and these
regions turn out to be much less sensitive to . Once this shift is
accounted for, drag reduction decreases with at a markedly slower rate. If
the slightly favorable trend of the energy required to create the forcing is
considered, a chance emerges for positive net energy savings also at large
values of the Reynolds number.Comment: Revised version: change of title, revised intro, small improvements
to figures and tex
Curvature effects on the structure of near-wall turbulence
The interaction between near-wall turbulence and wall curvature is described
for the incompressible flow in a plane channel with a small
concave-convex-concave bump on the bottom wall, with height comparable to the
wall-normal location of the main turbulent structures. The analysis starts from
a database generated by a direct numerical simulation and hinges upon the
anisotropic generalised Kolmogorov equations, i.e. the exact budget equations
for the second-order structure function tensor. The influence of the bump on
the wall cycle and on the energy production, redistribution and transfers is
described in the physical and scale spaces. Over the upstream side of the bump,
the energy drained from the mean flow to sustain the streamwise fluctuations
decreases, and the streaks of high and low streamwise velocity weaken and are
stretched spanwise. After the bump tip, instead, the production of streamwise
fluctuations grows and the streaks intensify, progressively recovering their
characteristic spanwise scale. The wall-normal fluctuations, and thus the
quasi-streamwise vortices, are sustained by the mean flow over the upstream
side of the bump, while energy flows from the vertical fluctuations to the mean
field over the downstream side. On the concave portion of the upstream side,
the near-wall fluctuations form structures of spanwise velocity which are
consistent with Taylor-G\"ortler vortices at an early stage of development.
Their evolution is described by analysing the scale-space pressure-strain term.
A schematic description of the bump flow is presented, in which various regions
are identified according to the signs of curvature and streamwise pressure
gradient.Comment: Under consideration by Journal of Fluid Mechanic
Global energy budgets in turbulent Couette and Poiseuille flows
Turbulent plane Poiseuille and Couette flows share the same geometry, but produce their flow rate owing to different external drivers: pressure gradient and shear, respectively. By looking at integral energy fluxes, we pose and answer the question as to which flow performs better at creating flow rate. We define a flow efficiency, which quantifies the fraction of power used to produce flow rate instead of being wasted as a turbulent overhead; effectiveness, instead, describes the amount of flow rate produced by a given power. The work by Gatti et al. (J. Fluid Mech., vol. 857, 2018, pp. 345–373), where the constant power input concept was developed to compare turbulent Poiseuille flows with drag reduction, is here extended to compare different flows. By decomposing the mean velocity field into a laminar contribution and a deviation, analytical expressions are derived which are the energy-flux equivalents of the FIK identity. These concepts are applied to literature data supplemented by a new set of direct numerical simulations, to find that Couette flows are less efficient but more effective than Poiseuille flows. The reason is traced to the more effective laminar component of Couette flows, which compensates for their higher turbulent activity. It is also observed that, when the fluctuating fields of the two flows are fed with the same total power fraction, Couette flows dissipate a smaller percentage of it via turbulent dissipation. A decomposition of the fluctuating field into large and small scales explains this feature: Couette flows develop stronger large-scale structures, which alter the mean flow while contributing less significantly to dissipation
Structure function tensor equations in inhomogeneous turbulence
Exact budget equations for the second-order structure function tensor ⟨uu⟩, where u is the difference of the i th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure–strain term and contain also budget equations for the off-diagonal components of ⟨uu⟩. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of Re = 200 is considered. The off-diagonal component ⟨-uυ⟩, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at Re = 500 and 1000. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time
Direct Numerical Simulation of turbulent Taylor-Couette flow
The direct numerical simulation (DNS) of the Taylor--Couette flow in the
fully turbulent regime is described. The numerical method extends the work by
Quadrio & Luchini (Eur. J. Mech. B / Fluids, v.21, pp.413--427, 2002), and is
based on a parallel computer code which uses mixed spatial discretization
(spectral schemes in the homogeneous directions, and fourth-order, compact
explicit finite-difference schemes in the radial direction). A DNS is carried
out to simulate for the first time the turbulent Taylor--Couette flow in the
turbulent regime. Statistical quantities are computed to complement the
existing experimental information, with a view to compare it to planar,
pressure-driven turbulent flow at the same value of the Reynolds number. The
main source for differences in flow statistics between plane and curved-wall
flows is attributed to the presence of large-scale rotating structures
generated by curvature effects.Comment: To appear in European Journal of Mechanics B / Fluid