827 research outputs found
The phase-locked mean impulse response of a turbulent channel flow
We describe the first DNS-based measurement of the complete mean response of
a turbulent channel flow to small external disturbances. Space-time impulsive
perturbations are applied at one channel wall, and the linear response
describes their mean effect on the flow field as a function of spatial and
temporal separations. The turbulent response is shown to differ from the
response a laminar flow with the turbulent mean velocity profile as base flow.Comment: Accepted for publication in Physics of Fluid
The laminar generalized Stokes layer and turbulent drag reduction
This paper considers plane channel flow modified by waves of spanwise
velocity applied at the wall and travelling along the streamwise direction.
Laminar and turbulent regimes for the streamwise flow are both studied.
When the streamwise flow is laminar, it is unaffected by the spanwise flow
induced by the waves. This flow is a thin, unsteady and streamwise-modulated
boundary layer that can be expressed in terms of the Airy function of the first
kind. We name it the generalized Stokes layer because it reduces to the
classical oscillating Stokes layer in the limit of infinite wave speed.
When the streamwise flow is turbulent, the laminar generalized Stokes layer
solution describes well the space-averaged turbulent spanwise flow, provided
that the phase speed of the waves is sufficiently different from the turbulent
convection velocity, and that the time scale of the forcing is smaller than the
life time of the near-wall turbulent structures. Under these conditions, the
drag reduction is found to scale with the Stokes layer thickness, which renders
the laminar solution instrumental for the analysis of the turbulent flow.
A classification of the turbulent flow regimes induced by the waves is
presented by comparing parameters related to the forcing conditions with the
space and time scales of the turbulent flow.Comment: Accepted for publication on J. Fluid Mec
Resources and Economic Dynamics, Technology and Rents
The essay investigates non producible (natural) resources and rent from three points of views: stylized facts, quantitative economics and economic theory. Taking the first point of view, the author discusses how economic growth can be represented in terms of never-ending tension between scarcity and technical progress. At least since the onset of modern economic growth, whenever scarcity produced a slowdown of growth, technical progress followed and scarcity was thereby removed. Scarcity, in a long-run perspective, has always been of the «relative» type, while absolute scarcity never set in. This essay consider this problem from many points of view. First of all it considers the point of view of quantitative economics like those of Simon Kuznets and Wassily Leontief who emphasized the relative character of scarcity and the importance of keeping the relationship between scarcity and innovation into account (this is especially true of Kuznets). Secondly the essay considers the contribution of economic theory. In this connection, the author points out that both the macroeconomic and multi-sectoral models developed since the 1930s overlooked the investigation of scarce natural resources and rent, as well as their relationship with technical progress. Only Piero Sraffa examined non producible resources and rent but he has done it in a single-period model. The author of this essay investigated the same issues in a more general analytical set-up starting with a contribution published in 1967 followed by many others. Later on, Quadrio Curzio and Pellizzari, especially in the 1996 volume, analyzed the general relationships among production, prices, income distribution, technical progress and growth when scarce resources play a significant role. Those contributions also investigated the nature of technological rents, which are an important feature of modern economic growth in the presence of technical progress. At the same time Quadrio Curzio, in collaboration with Marco Fortis and Roberto Zoboli, analysed historical, quantitative and qualitative aspects of economic dynamics, and the way in which natural resources and raw materials exert an influence on economic growth and more generally economic dynamics. Those aspects are not fully considered in the present essay, but they represent its fundamental background. Finally in 2008 Quadrio Curzio, Pellizzari and Zoboli outlined in a valuable encyclopaedic dictionary a compact synthesis of the above approach to the economic analysis of raw materials and primary commodities. The essay takes a point of view which is not typical of the «post- Keynesian» approach, yet it belongs to a post-classical perspective that is closely connected to the Italian-Cambridge tradition of political economy as a social discipline. Tradition on which Alberto Quadrio Curzio, especially researching with Roberto Scazzieri, focused his attention in many essays from a methodological point of view.natural resources; technological innovation; relative scarcity; investments; rent;
A perturbative model for predicting the high-Reynolds-number behaviour of the streamwise travelling waves technique in turbulent drag reduction
The background of this work is the problem of reducing the aerodynamic
turbulent friction drag, which is an important source of energy waste in
innumerable technological fields. We develop a theoretical framework aimed at
predicting the behaviour of existing drag reduction techniques when used at the
large values of Re which are typical of applications. We focus on one recently
proposed and very promising technique, which consists in creating at the wall
streamwise-travelling waves of spanwise velocity. A perturbation analysis of
the Navier-Stokes equations that govern the fluid motion is carried out, for
the simplest wall-bounded flow geometry, i.e. the plane channel flow. The
streamwise base flow is perturbed by the spanwise time-varying base flow
induced by the travelling waves. An asymptotic expansion is then carried out
with respect to the velocity amplitude of the travelling wave. The analysis,
although based on several assumptions, leads to predictions of drag reduction
that agree well with the measurements available in literature and mostly
computed through DNS of the full Navier-Stokes equations. New DNS data are
produced on purpose in this work to validate our method further. The method is
then applied to predict the drag-reducing performance of the
streamwise-travelling waves at increasing Re, where comparison data are not
available. The current belief, based on a Re-range of about one decade only
above the transitional value, that drag reduction obtained at low Re is deemed
to decrease as Re is increased is fully confirmed by our results. From a
quantitative standpoint, however, our outlook based on several decades of
increase in Re is much less pessimistic than other existing estimates, and
motivates further, more accurate studies on the present subject
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
Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow
We experimentally assess the capabilities of an active, open-loop technique
for drag reduction in turbulent wall flows recently introduced by Quadrio et
al. [J. Fluid Mech., v.627, 161, (2009)]. The technique consists in generating
streamwise-modulated waves of spanwise velocity at the wall, that travel in the
streamwise direction.
A proof-of-principle experiment has been devised to measure the reduction of
turbulent friction in a pipe flow, in which the wall is subdivided into thin
slabs that rotate independently in the azimuthal direction. Different speeds of
nearby slabs provide, although in a discrete setting, the desired streamwise
variation of transverse velocity.
Our experiment confirms the available DNS results, and in particular
demonstrates the possibility of achieving large reductions of friction in the
turbulent regime. Reductions up to 33% are obtained for slowly
forward-traveling waves; backward-traveling waves invariably yield drag
reduction, whereas a substantial drop of drag reduction occurs for waves
traveling forward with a phase speed comparable to the convection speed of
near-wall turbulent structures.
A Fourier analysis is employed to show that the first harmonics introduced by
the discrete spatial waveform that approximates the sinusoidal wave are
responsible for significant effects that are indeed observed in the
experimental measurements. Practical issues related to the physical
implementation of this control scheme and its energetic efficiency are briefly
discussed.Comment: Article accepted by Phys. Fluids. After it is published, it will be
found at http://pof.aip.or
A low-cost parallel implementation of direct numerical simulation of wall turbulence
A numerical method for the direct numerical simulation of incompressible wall
turbulence in rectangular and cylindrical geometries is presented. The
distinctive feature resides in its design being targeted towards an efficient
distributed-memory parallel computing on commodity hardware. The adopted
discretization is spectral in the two homogeneous directions; fourth-order
accurate, compact finite-difference schemes over a variable-spacing mesh in the
wall-normal direction are key to our parallel implementation. The parallel
algorithm is designed in such a way as to minimize data exchange among the
computing machines, and in particular to avoid taking a global transpose of the
data during the pseudo-spectral evaluation of the non-linear terms. The
computing machines can then be connected to each other through low-cost network
devices. The code is optimized for memory requirements, which can moreover be
subdivided among the computing nodes. The layout of a simple, dedicated and
optimized computing system based on commodity hardware is described. The
performance of the numerical method on this computing system is evaluated and
compared with that of other codes described in the literature, as well as with
that of the same code implementing a commonly employed strategy for the
pseudo-spectral calculation.Comment: To be published in J. Comp. Physic
Numerical simulation of turbulent duct flows with constant power input
The numerical simulation of a flow through a duct requires an externally
specified forcing that makes the fluid flow against viscous friction. To this
aim, it is customary to enforce a constant value for either the flow rate (CFR)
or the pressure gradient (CPG). When comparing a laminar duct flow before and
after a geometrical modification that induces a change of the viscous drag,
both approaches (CFR and CPG) lead to a change of the power input across the
comparison. Similarly, when carrying out the (DNS and LES) numerical simulation
of unsteady turbulent flows, the power input is not constant over time.
Carrying out a simulation at constant power input (CPI) is thus a further
physically sound option, that becomes particularly appealing in the context of
flow control, where a comparison between control-on and control-off conditions
has to be made.
We describe how to carry out a CPI simulation, and start with defining a new
power-related Reynolds number, whose velocity scale is the bulk flow that can
be attained with a given pumping power in the laminar regime. Under the CPI
condition, we derive a relation that is equivalent to the
Fukagata--Iwamoto--Kasagi relation valid for CFR (and to its extension valid
for CPG), that presents the additional advantage of natively including the
required control power. The implementation of the CPI approach is then
exemplified in the standard case of a plane turbulent channel flow, and then
further applied to a flow control case, where the spanwise-oscillating wall is
used for skin friction drag reduction. For this low-Reynolds number flow, using
90% of the available power for the pumping system and the remaining 10% for the
control system is found to be the optimum share that yields the largest
increase of the flow rate above the reference case, where 100% of the power
goes to the pump.Comment: Accepted for publication in J. Fluid Mec
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