157 research outputs found
Inflow/outflow boundary conditions and global dynamics of spatial mixing layers
The numerical simulation of incompressible spatially-developing shear flows poses a special challenge to computational fluid dynamicists. The Navier-Stokes equations are elliptic and boundary equations need to be specified at the inflow and outflow boundaries in order to compute the fluid properties within the region of interest. It is, however, difficult to choose inflow and outflow conditions corresponding to a given experimental situation. Furthermore the effects that changes in the boundary conditions or in the size of the computational domain may induce on the global dynamics of the flow are presently unknown. These issues are examined in light of recent developments in hydrodynamic stability theory. The particular flow considered is the spatial mixing layer but it was expected that similar phenomena were bound to occur in other cases such as channel flow, the boundary layer, etc. A short summary of local/global and absolute/convective instability concepts is given. The results of numerical simulations are presented which strongly suggest that global resonances may be triggered in domains of finite streamwise extent although the evolution of the perturbation vorticity field is everywhere locally convective. A relationship between finite domains and pressure sources which might help in devising a scheme to eliminate these difficulties is discussed
Making superhydrophobic splashes by surface cooling
We study experimentally the enhancement of splashing due to solidification.
Investigating the impact of water drops on dry smooth surfaces, we show that
the transition velocity to splash can be drastically reduced by cooling the
surface below the liquid melting temperature. We find that at very low
temperatures (below ), the splashing behaviour becomes
independent of surface undercooling and presents the same characteristics as on
ambient temperature superhydrophobic surfaces. This resemblance arises from an
increase of the dynamic advancing contact angle of the lamella with surface
undercooling, going from the isothermal hydrophilic to the superhydrophobic
behaviour. We propose that crystal formation can affect the dynamic contact
angle of the lamella, which would explain this surprising transition. Finally,
we show that the transition from hydrophilic to superydrophobic behaviour can
also be characterized quantitatively on the dynamics of the ejecta
Contact Line Catch Up by Growing Ice Crystals
The effect of freezing on contact line motion is a scientific challenge in
the understanding of the solidification of capillary flows. In this letter, we
experimentally investigate the spreading and freezing of a water droplet on a
cold substrate. We demonstrate that solidification stops the spreading because
the ice crystals catch up with the advancing contact line. Indeed, we observe
the formation and growth of ice crystals along the substrate during the drop
spreading, and show that their velocity equals the contact line velocity when
the drop stops. Modelling the growth of the crystals, we predict the shape of
the crystal front and show that the substrate thermal properties play a major
role on the frozen drop radiusComment: Physical Review Letters, 22 juin 202
Inverse lift: a signature of the elasticity of complex fluids?
To understand the mechanics of a complex fluid such as a foam we propose a
model experiment (a bidimensional flow around an obstacle) for which an
external sollicitation is applied, and a local response is measured,
simultaneously. We observe that an asymmetric obstacle (cambered airfoil
profile) experiences a downards lift, opposite to the lift usually known (in a
different context) in aerodynamics. Correlations of velocity, deformations and
pressure fields yield a clear explanation of this inverse lift, involving the
elasticity of the foam. We argue that such an inverse lift is likely common to
complex fluids with elasticity.Comment: 4 pages, 4 figures, revised version, submitted to PR
Influence of through-flow on linear pattern formation properties in binary mixture convection
We investigate how a horizontal plane Poiseuille shear flow changes linear
convection properties in binary fluid layers heated from below. The full linear
field equations are solved with a shooting method for realistic top and bottom
boundary conditions. Through-flow induced changes of the bifurcation thresholds
(stability boundaries) for different types of convective solutions are deter-
mined in the control parameter space spanned by Rayleigh number, Soret coupling
(positive as well as negative), and through-flow Reynolds number. We elucidate
the through-flow induced lifting of the Hopf symmetry degeneracy of left and
right traveling waves in mixtures with negative Soret coupling. Finally we
determine with a saddle point analysis of the complex dispersion relation of
the field equations over the complex wave number plane the borders between
absolute and convective instabilities for different types of perturbations in
comparison with the appropriate Ginzburg-Landau amplitude equation
approximation. PACS:47.20.-k,47.20.Bp, 47.15.-x,47.54.+rComment: 19 pages, 15 Postscript figure
Numerical analysis of the linear and nonlinear vortex-sound interaction in a T-junction
T-junctions correspond to a classical academic configuration employed to unravel the vortexsound interaction leading to self-sustained oscillations. It is composed of a closed deep cavity exposed to a low-Mach grazing flow, in which an unstable shear layer can develop. Many studies usually consider this hydrodynamic instability either as a “flapping shear layer", or as a “discrete vortex shedding", which then couples with the acoustic field. This paper follows the idea that these two descriptions are related to the linear and non-linear regimes of the shear layer response to acoustic waves, and thus intends to further analyze these regimes and their transition. To do so, a typical T-junction turbulent flow is computed by forced Large Eddy Simulation (LES) where acoustic waves are injected at several amplitudes. The flow response is extracted, and exhibits a linear regime as well as two distinct non-linear regimes where a partial saturation of the response occurs. The post-processing of the flow field in the three situations reveals that a flapping mechanism exists at low wave amplitudes, whereas a vortex shedding appears for highest acoustic levels. For moderate wave amplitudes, the behavior of the shear layer lies between these two classical views. This suggests that during self-sustained oscillations, a transition between these scenarios occurs, starting from a flapping motion followed by a vortex shedding
Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow
A unique pattern selection in the absolutely unstable regime of a driven,
nonlinear, open-flow system is analyzed: The spatiotemporal structures of
rotationally symmetric vortices that propagate downstream in the annulus of the
rotating Taylor-Couette system due to an externally imposed axial through-flow
are investigated for two different axial boundary conditions at the in- and
outlet. Unlike the stationary patterns in systems without through-flow the
spatiotemporal structures of propagating vortices are independent of parameter
history, initial conditions, and system's length. They do, however, depend on
the axial boundary conditions, the driving rate of the inner cylinder and the
through-flow rate. Our analysis of the amplitude equation shows that the
pattern selection can be described by a nonlinear eigenvalue problem with the
frequency being the eigenvalue. Approaching the border between absolute and
convective instability the eigenvalue problem becomes effectively linear and
the selection mechanism approaches that one of linear front propagation.
PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript
Pattern selection as a nonlinear eigenvalue problem
A unique pattern selection in the absolutely unstable regime of driven,
nonlinear, open-flow systems is reviewed. It has recently been found in
numerical simulations of propagating vortex structures occuring in
Taylor-Couette and Rayleigh-Benard systems subject to an externally imposed
through-flow. Unlike the stationary patterns in systems without through-flow
the spatiotemporal structures of propagating vortices are independent of
parameter history, initial conditions, and system length. They do, however,
depend on the boundary conditions in addition to the driving rate and the
through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation
elucidates how the pattern selection can be described by a nonlinear eigenvalue
problem with the frequency being the eigenvalue. Approaching the border between
absolute and convective instability the eigenvalue problem becomes effectively
linear and the selection mechanism approaches that of linear front propagation.
PACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 18 pages in Postsript format including 5 figures, to appear in:
Lecture Notes in Physics, "Nonlinear Physics of Complex Sytems -- Current
Status and Future Trends", Eds. J. Parisi, S. C. Mueller, and W. Zimmermann
(Springer, Berlin, 1996
Multiple Front Propagation Into Unstable States
The dynamics of transient patterns formed by front propagation in extended
nonequilibrium systems is considered. Under certain circumstances, the state
left behind a front propagating into an unstable homogeneous state can be an
unstable periodic pattern. It is found by a numerical solution of a model of
the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of
decay of such periodic unstable states is the propagation of a second front
which replaces the unstable pattern by a another unstable periodic state with
larger wavelength. The speed of this second front and the periodicity of the
new state are analytically calculated with a generalization of the marginal
stability formalism suited to the study of front propagation into periodic
unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page
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