162,080 research outputs found
A numerical investigation of horizontal viscous gravity currents
No full textWe study numerically the viscous phase of horizontal gravity currents of immiscible fluids in the lock-exchange configuration. A numerical technique capable of dealing with stiff density gradients is used, allowing us to mimic high-Schmidt-number situations similar to those encountered in most laboratory experiments. Plane two-dimensional computations with no-slip boundary conditions are run so as to compare numerical predictions with the ‘short reservoir’ solution of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43–58), which predicts the front position lf to evolve as t1/5, and the ‘long reservoir’ solution of Gratton & Minotti (J. Fluid Mech., vol. 210, 1990, pp. 155–182) which predicts a diffusive evolution of the distance travelled by the front xf ~ t1/2. In line with dimensional arguments, computations indicate that the self-similar power law governing the front position is selected by the flow Reynolds number and the initial volume of the released heavy fluid. We derive and validate a criterion predicting which type of viscous regime immediately succeeds the slumping phase. The computations also reveal that, under certain conditions, two different viscous regimes may appear successively during the life of a given current. Effects of sidewalls are examined through three-dimensional computations and are found to affect the transition time between the slumping phase and the viscous regime. In the various situations we consider, we make use of a force balance to estimate the transition time at which the viscous regime sets in and show that the corresponding prediction compares well with the computational results
Falling styles of disks
No full textWe numerically investigate the dynamics of thin disks falling under gravity in a viscous fluid medium at rest at infinity. Varying independently the density and thickness of the disk reveals the influence of the disk aspect ratio which, contrary to previous belief, is found to be highly significant as it may completely change the route to non-vertical paths as well as the boundaries between the various path regimes. The transition from the straight vertical path to the planar fluttering regime is found to exhibit complex dynamics: a bistable behaviour of the system is detected within some parameter range and several intermediate regimes are observed in which, although the wake is unstable, the path barely deviates from vertical. By varying independently the body-to-fluid inertia ratio and the relative magnitude of inertial and viscous effects over a significant range, we set up a comprehensive map of the corresponding styles of path followed by an infinitely thin disk. We observe the four types of planar regimes already reported in experiments but also identify two additional fully three-dimensional regimes in which the body experiences a slow horizontal precession superimposed onto zigzagging or tumbling motions
A 'reciprocal' theorem for the prediction of loads on a body moving in an inhomogeneous flow at arbitrary Reynolds number - CORRIGENDUM
No full textSeveral forms of a theorem providing general expressions for the force and torque
acting on a rigid body of arbitrary shape moving in an inhomogeneous incompressible
flow at arbitrary Reynolds number are derived. Inhomogeneity arises because of
the presence of a wall that partially or entirely bounds the fluid domain and/or a
non-uniform carrying flow. This theorem, which stems directly from Navier–Stokes
equations and parallels the well-known Lorentz reciprocal theorem extensively
employed in low-Reynolds-number hydrodynamics, makes use of auxiliary solenoidal
irrotational velocity fields and extends results previously derived by Quartapelle &
Napolitano (AIAA J., vol. 21, 1983, pp. 911–913) and Howe (Q. J. Mech. Appl.
Maths, vol. 48, 1995, pp. 401–426) in the case of an unbounded flow domain and
a fluid at rest at infinity. As the orientation of the auxiliary velocity may be chosen
arbitrarily, any component of the force and torque can be evaluated, irrespective of
its orientation with respect to the relative velocity between the body and fluid. Three
main forms of the theorem are successively derived. The first of these, given in (2.19),
is suitable for a body moving in a fluid at rest in the presence of a wall. The most
general form (3.6) extends it to the general situation of a body moving in an arbitrary
non-uniform flow. Specific attention is then paid to the case of an underlying timedependent
linear flow. Specialized forms of the theorem are provided in this situation
for simplified body shapes and flow conditions, in (3.14) and (3.15), making explicit
the various couplings between the body’s translation and rotation and the strain rate
and vorticity of the carrying flow. The physical meaning of the various contributions
to the force and torque and the way in which the present predictions reduce to
those provided by available approaches, especially in the inviscid limit, are discussed.
Some applications to high-Reynolds-number bubble dynamics, which provide several
apparently new predictions, are also presented
A 'reciprocal' theorem for the prediction of loads on a body moving in an inhomogeneous flow at arbitrary Reynolds number
No full textSeveral forms of a theorem providing general expressions for the force and torque
acting on a rigid body of arbitrary shape moving in an inhomogeneous incompressible
flow at arbitrary Reynolds number are derived. Inhomogeneity arises because of
the presence of a wall that partially or entirely bounds the fluid domain and/or a
non-uniform carrying flow. This theorem, which stems directly from Navier–Stokes
equations and parallels the well-known Lorentz reciprocal theorem extensively
employed in low-Reynolds-number hydrodynamics, makes use of auxiliary solenoidal
irrotational velocity fields and extends results previously derived by Quartapelle &
Napolitano (AIAA J., vol. 21, 1983, pp. 911–913) and Howe (Q. J. Mech. Appl.
Maths, vol. 48, 1995, pp. 401–426) in the case of an unbounded flow domain and
a fluid at rest at infinity. As the orientation of the auxiliary velocity may be chosen
arbitrarily, any component of the force and torque can be evaluated, irrespective of
its orientation with respect to the relative velocity between the body and fluid. Three
main forms of the theorem are successively derived. The first of these, given in (2.19),
is suitable for a body moving in a fluid at rest in the presence of a wall. The most
general form (3.6) extends it to the general situation of a body moving in an arbitrary
non-uniform flow. Specific attention is then paid to the case of an underlying timedependent
linear flow. Specialized forms of the theorem are provided in this situation
for simplified body shapes and flow conditions, in (3.14) and (3.15), making explicit
the various couplings between the body’s translation and rotation and the strain rate
and vorticity of the carrying flow. The physical meaning of the various contributions
to the force and torque and the way in which the present predictions reduce to
those provided by available approaches, especially in the inviscid limit, are discussed.
Some applications to high-Reynolds-number bubble dynamics, which provide several
apparently new predictions, are also presented
[Report to Chief J. E. Curry, by an unknown author #1]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
[Report to Chief J. E. Curry, by an unknown author #2]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
Interaction between two spherical bubbles rising in a viscous liquid
No full textThe three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier-Stokes equations. The study considers the interaction between two bubbles for moderate Reynolds numbers (50 ≤ Re ≤ 500, Re being based on the bubble diameter) and for positions described by the separation S (2.5 ≤ S ≤ 10, S being the distance between the bubble centres normalized by the bubble radius) and the angle θ (0o ≤ θ ≤ 90o ) formed between the line of centre and the direction perpendicular to the direction of the motion. We provide a general description of the interaction extending the results obtained for two bubbles moving side by side (θ = 0o ) by Legendre, Magnaudet & Mougin 2003 (J. Fluid Mech., 497,133-166) and for two bubbles moving in line (θ = 90o ) by Yuan & Prosperetti 1994 (J. Fluid Mech., 278, 325-349). Simple models based on physical arguments are given for the drag and lift forces experienced by each bubble. The interaction is the combination of three effects: a potential effect, a viscous correction (Moore correction) and a significant wake effect observed on both the drag and the transverse force of the second bubble when located in the wake of the first one
Reversal of the lift force on an oblate bubble in a weakly viscous linear shear flow
No full textWe compute the flow about an oblate spheroidal bubble of prescribed shape set fixed in a viscous linear shear flow in the range of moderate to high Reynolds numbers. In contrast to predictions based on inviscid theory, the numerical results reveal that for weak enough shear rates, the lift force and torque change sign in an intermediate range of Reynolds numbers when the bubble oblateness exceeds a critical value that depends on the relative shear rate. This effect is found to be due to the vorticity generated at the bubble surface which, combined with the velocity gradient associated with the upstream shear, results in a system of two counter-rotating streamwise vortices whose sign is opposite to that induced by the classical inviscid tilting of the upstream vorticity around the bubble. We show that this lift reversal mechanism is closely related to the wake instability mechanism experienced by a spheroidal bubble rising in a stagnant liquid
Dynamics of a gas bubble in a straining flow: Deformation, oscillations, self-propulsion
No full textWe revisit from a dynamical point of view the classical problem of the deformation of a gas bubble suspended in an axisymmetric uniaxial straining flow. Thanks to a recently developed Linearized Arbitrary Lagrangian-Eulerian approach, we compute the steady equilibrium states and associated bubble shapes. Considering perturbations that respect the symmetries of the imposed carrying flow, we show that the bifurcation diagram is made of a stable and an unstable branch of steady states separated by a saddle-node bifurcation, the location of which is tracked throughout the parameter space. We characterize the most relevant global mode along each branch, namely, an oscillatory mode that becomes neutrally stable in the inviscid limit along the stable branch, and an unstable nonoscillating mode eventually leading to the breakup of the bubble along the unstable branch. Next, considering perturbations that break the symmetries of the carrying flow, we identify two additional unstable nonoscillating modes associated with the possible drift of the bubble centroid away from the stagnation point of the undisturbed flow. One of them corresponds merely to a translation of the bubble along the elongational direction of the flow. The other is counterintuitive, as it corresponds to a drift of the bubble in the symmetry plane of the undisturbed flow, where this flow is compressional. We confirm the existence and characteristics of this mode by computing analytically the corresponding leading-order disturbance in the inviscid limit, and show that the observed dynamics are made possible by a specific self-propulsion mechanism that we explain qualitatively
Path oscillations and enhanced drag of light rising spheres
No full textThe dynamics of light spheres rising freely under buoyancy in a large expanse of viscous fluid at rest at infinity is investigated numerically. For this purpose, the computational approach developed by Mougin \& Magnaudet (Int. J. Multiphase Flow, 28:1837-1851, 2002) is improved to account for the instantaneous viscous loads induced by the translational and rotational sphere accelerations, which play a crucial role in the dynamics of very light spheres. A comprehensive map of the rise regimes encountered up to Reynolds numbers (based on the sphere diameter and mean rise velocity) of the order of is set up by varying independently the body-to-fluid density ratio and the relative magnitude of inertial and viscous effects in about distinct combinations. These computations confirm or reveal the presence of several distinct periodic regions on the route to chaos, most of which only exist within a finite range of the sphere relative density and Reynolds number. The wake structure is analyzed in these various regimes, evidencing the existence of markedly different shedding modes according to the style of path. The variations of the drag force with the flow parameters is also examined, revealing that only one of the styles of path specific to very light spheres yields a non-standard drag behaviour, with drag coefficients significantly larger than those measured on a fixed sphere under equivalent conditions. The outcomes of this investigation are compared with available experimental and numerical results, evidencing points of consensus and disagreement
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