共查询到20条相似文献,搜索用时 31 毫秒
1.
We explore the effects of fluid films of variable depths on droplets impacting into them. Corresponding to a range of fluid
“film” depths, a non-dimensional parameter—H*, defined as the ratio of the film thickness to the droplet diameter—is varied in the range 0.1≤H*≤10. In general, the effect of the fluid film imposes a dramatic difference on the dynamics of the droplet–surface interaction
when compared to a similar impact on a dry surface. This is illustrated by the size distribution and number of the splash
products. While thin fluid films (H*≈0.1) promote splashing, thicker films (1≤H*≤10) act to inhibit it. The relative roles of surface tension and viscosity are investigated by comparison of a matrix of
fluids with low and high values of these properties. Impingement conditions, as characterized by Reynolds and Weber numbers,
are varied by velocity over a range from 1.34 to 4.22 m/s, maintaining a constant droplet diameter of 2.0 mm. The dependence
of splashing dynamics, characterized by splash product size and number, on the fluid surface tension and viscosity and film
thickness are discussed. 相似文献
2.
Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field
formulation, thus paralleling well-established weak methods of solid mechanics. In this work two different formulations are
developed: a pure displacement formulation and a two-field mixed formulation. With the objective of developing a thorough
understanding of the peculiar features of finite elements in time, the relevant methodologies associated with this approach
for dynamics are extensively discussed. After having laid the theoretical bases, the finite element approximation and the
linearization of the resulting forms are developed, together with a method for the treatment of holonomic and nonholonomic
constraints, thus widening the horizons of applicability over the vast world of multibody system dynamics. With the purpose
of enlightening on the peculiar numerical behavior of the different approaches, simple but meaningful examples are illustrated.
To this aim, significant parallels with elastostatics are emphasized.
Paper presented at the ‘International Technical Specialists' Meeting on Rotorcraft Basic Research’, March 25–27, 1991, Georgia Institute of Technology, Atlanta, Georgia, USA. 相似文献
3.
The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow
to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds
number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to
low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for
Re = 2.0 × 104 and 3.9 × 104 (Dargahi, Exp Fluids 8:1–12, 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared
with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds
number (Re = 1.15 × 105) (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 104 the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than
those observed in the Re = 3.9 × 104 case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced
significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are
dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize
the primary HSV system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing
Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized
by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been
observed in several previous experimental studies. 相似文献
4.
David E. Stewart 《Archive for Rational Mechanics and Analysis》1998,145(3):215-260
This paper gives convergence theory for a new implicit time‐stepping scheme for general rigid‐body dynamics with Coulomb friction
and purely inelastic collisions and shocks. An important consequence of this work is the proof of existence of solutions of
rigid‐body problems which include the famous counterexamples of Painlevé. The mathematical basis for this work is the formulation
of the rigid‐body problem in terms of measure differential inclusions of Moreau and Monteiro Marques. The implicit time‐stepping method is based on complementarity problems, and is essentially
a particular case of the algorithm described in Anitescu & Potra [2], which in turn is based on the formulation in Stewart
& Trinkle [47].
(Accepted January 26, 1998) 相似文献
5.
The Darcy free convection boundary layer flow over a vertical flat plate is considered in the presence of volumetric heat
generation/absorption. In the present first part of the paper it is assumed that the heat generation/absorption takes place
in a self-consistent way, the source term q
′′′≡ S of the energy equation being an analytical function of the local temperature difference T − T
∞. In a forthcoming second part, the case of the externally controlled source terms S = S(x,y ) will be considered. It is shown that due to the presence of S, the physical equivalence of the up- and downflows gets in general broken, in the sense that the free convection flow over
the upward projecting hot plate (“upflow”) and over its downward projecting cold counterpart (“downflow”) in general become
physically distinct. The consequences of this circumstance are examined for different forms of S. Several analytical solutions are given. Some of them describe algebraically decaying boundary layers which can also be recovered as limiting cases of exponentially decayingones. This asymptotic phenomenon is discussed in some detail. 相似文献
6.
7.
Davide Catania 《Journal of Mathematical Fluid Mechanics》2012,14(1):95-115
We consider two magnetohydrodynamic-α (MHDα) models with kinematic viscosity and magnetic diffusivity for an incompressible fluid in a three-dimensional periodic box
(torus). More precisely, we consider the Navier–Stokes-α-MHD and the Modified Leray-α-MHD models. Similar models are useful to study the turbulent behavior of fluids in presence of a magnetic field because of
the current impossibility to handle non-regularized systems neither analytically nor via numerical simulations. In both cases,
the global existence of the solution and of a global attractor can be shown. We provide an upper bound for the Hausdorff and
the fractal dimension of the attractor. This bound can be interpreted in terms of degrees of
freedom of the long-time dynamics of the involved system and gives information about the numerical stability of the model.
We get the same bound that holds for the Simplified Bardina-MHD model, considered in a previous paper (this result provides,
in some sense, an intermediate bound between the number of degrees of freedom for the Simplified Bardina model and the Navier–Stokes-α equation in the nonmagnetic case). However, the Navier–Stokes-α-MHD system is preferable since, in the ideal case, it conserves more quadratic invariants derived from the standard MHD model. 相似文献
8.
M. V. D’Angelo B. Semin G. Picard M. E. Poitzsch J. P. Hulin H. Auradou 《Transport in Porous Media》2010,84(2):389-408
The transport of fibers by a fluid flow is investigated in transparent channels modeling rock fractures: the experiments use
flexible polyester thread (mean diameter 280 μm) and water or a water–polymer solution. For a channel with smooth parallel walls and a mean aperture ā = 0.65 mm, both fiber segments of length ℓ = 20–150 mm and “continuous” fibers longer than the channel length have been used: in both the cases, the velocity of the
fibers and its variation with distance could be accounted for while neglecting friction with the walls. For rough self-affine
walls and a continuous gradient of the local mean aperture transverse to the flow, transport of the fibers by a water flow
is only possible in the region of larger aperture (ā ≲ 1.1 mm) and is of “stop and go” type at low velocities. With the polymer solution, the fibers move faster and more continuously
in high aperture regions and their interaction with the walls is reduced; fiber transport becomes also possible in narrower
regions where irreversible pinning occurred for water. In a third rough model with parallel walls and a low mean aperture
ā = 0.65 mm, fiber transport is only possible with the water–polymer solution. The dynamics of fiber deformations and entanglement
during pinning–depinning events and permanent pinning is analyzed. 相似文献
9.
Zhuo Li Xue-Feng Yuan Simon J. Haward Jeffrey A. Odell Stephen Yeates 《Rheologica Acta》2011,50(3):277-290
The non-linear dynamics of a semi-dilute (c/c* = 15) polydisperse polyethylene oxide (PEO) solution in microfluidics are studied experimentally using benchmark contraction–expansion
flow geometries with three contraction–expansion ratios (4:1:4, 8:1:8 and 16:1:16) and two narrow channel lengths (L
c/D
h = 53 and 5.3, where L
c is the length of the narrow channel and D
h is its hydraulic diameter). Complex flows over a range of elasticity numbers (El), Weissenberg numbers (Wi) and Reynolds numbers (Re) are characterized using micro-particle image velocimetry (
\upmu\upmu-PIV) and pressure drop measurements. The evolution of vortex formation and dynamics has been visualized through a step-flow-rate
experiment. Various flow dynamics regimes have been quantified and are presented in a Wi–Re diagram. The experimental results reveal that the contraction ratio can result in qualitatively different vortex dynamics
of semi-dilute polymer solutions in microfluidics, whereas the length of the narrow channel merely affects the dynamics at
a quantitative level. A single elasticity number, if defined by the size of the narrow channel, is not sufficient to account
for the effects of contraction ratio on the non-linear vortex dynamics. 相似文献
10.
A. N. Guz’ 《International Applied Mechanics》2000,36(1):14-39
The article is the first part of a survey of problems in compressible, viscous fluid dynamics as related to the dynamics of
rigid and elastic bodies in a compressible, viscous fluid in the linearized formulation. The formulation of basic problems
is discussed, along with a method of solution based on general solutions of the Navier-Stokes equations in vector and scalar
form in dynamical problems. Forced harmonic vibrations of rigid bodies in rest and moving compressible, viscous fluids are
discussed. Publications relevant to the stated problems are analyzed.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika,
Vol. 36, No. 1, pp. 25–52, January, 2000.
Detailed information about the author can be found in the journalPrikladnaya Mekhanika, Volume 35, No. 1, pp. 104–108 (1999). 相似文献
11.
Natural convection in a fluid saturated porous medium has been numerically investigated using a generalized non-Darcy approach.
The governing equations are solved by using Finite Volume approach. First order upwind scheme is employed for convective formulation
and SIMPLE algorithm for pressure velocity coupling. Numerical results are presented to study the influence of parameters
such as Rayleigh number (106 ≤Ra ≤108), Darcy number (10−5 ≤ Da ≤ 10−2), porosity (0.4 ≤ ɛ ≤ 0.9) and Prandtl number (0.01 ≤ Pr ≤ 10) on the flow behavior and heat transfer. By combining the method of matched asymptotic expansions with computational
fluid dynamics (CFD), so called asymptotic computational fluid dynamics (ACFD) technique has been employed to generate correlation
for average Nusselt number. The technique is found to be an attractive option for generating correlation and also in the analysis
of natural convection in porous medium over a fairly wide range of parameters with fewer simulations for numerical solutions. 相似文献
12.
We observe aging behavior of neat laponite systems over the course of 1,000 or more days. Under basic conditions, low laponite
concentrations (1 wt%) slowly evolve from a viscoelastic liquid to a glass made of clusters acting as constituent elements
interacting via long-range repulsion. Higher concentrations of laponite (3 wt%) quickly form a glass of individual particles.
Intermediate concentrations of laponite form a glass that is a combination of clusters and individual particles. The aging
rheological response and upturn of the loss modulus at low frequencies are well predicted by models of soft glassy systems
(Fielding et al., J Rheol, 44(2):323–369, 2000; Sollich, Phys Rev E, 58(1):738–759, 1998). If low amounts of high-molecular-weight (M
n ≥ 163 kg/mol) poly(ethylene oxide) (PEO) are added, the aging behavior follows the dynamical response of the clay. Above
a critical ratio, φ, of the free polymer chains in solution to the total laponite surface area, the PEO dynamics dominate at high frequencies.
It appears that the dynamics of these complex laponite-PEO systems are governed by the parameter φ. 相似文献
13.
Luis A. Caffarelli Panagiotis E. Souganidis 《Archive for Rational Mechanics and Analysis》2010,195(1):1-23
In this note we prove that appropriately scaled threshold dynamics-type algorithms corresponding to the fractional Laplacian
of order α ∈ (0, 2) converge to moving fronts. When α ≧ 1 the resulting interface moves by weighted mean curvature, while
for α < 1 the normal velocity is nonlocal of “fractional-type.” The results easily extend to general nonlocal anisotropic
threshold dynamics schemes. 相似文献
14.
Lukas Liechtenstein Fabien S. Godeferd Claude Cambon 《Flow, Turbulence and Combustion》2006,76(4):419-427
Rotating and stably stratified turbulence exhibit not only significant anisotropies but also dynamics, which are qualitatively different from purely rotating or stratified turbulence. Furthermore, the different time scales due to rotation, stratification and the turbulence one open up a wide field of possibilities for the temporal evolution of rotating and stratified turbulence.We analyze results from DNS with different parameters α = f/N by visualizing iso-enstrophy surfaces, the temporal evolution of velocity correlation length scales and angular energy spectra.We retrieve standard results, such as a large anisotropy for small scales in rotating turbulence and a large anisotropy for intermediate scales in the vortex mode of stratified turbulence. Furthermore, at large times we find qualitatively different phenomena for cases α = 10 and α = 0.1 such as modified cascades due to the existence of potential energy or small scale vorticity production respectively. 相似文献
15.
Investigated in this paper is the quasi-one-dimensional Gross–Pitaevskii equation, which describes the dynamics of the Bose–Einstein
condensates with the harmonic trapping potential and time-varying interatomic interaction. Via the Horita method and symbolic
computation, analytic bright N-soliton solution is obtained. One-, two- and three-soliton solutions are analyzed graphically. Based on the limit analysis
on the one- and two-soliton solutions, the modulation on the speed of the matter-wave bright solitons is realized. Via the
parameters, the interaction between the matter-wave solitons are adjustable. Furthermore, an approach to construct the interference
between the matter-wave solitons has been proposed. Finally, investigation on the three-soliton solution verifies our conclusions
drawn from the one and two solitons. Our conclusions might be useful in the fields of the control on the matter-wave solitons,
atom lasers, and atomic accelerators. 相似文献
16.
Robert McKibbin 《Transport in Porous Media》1986,1(3):271-292
The theory describing the onset of convection in a homogeneous porous layer bounded above and below by isothermal surfaces
is extended to consider an upper boundary which is partly permeable. The general boundary condition p + λ ∂p/∂n = constant is applied at the top surface and the flow is investigated for various λ in the range 0 ⩽ λ < ∞. Estimates of the magnitude and horizontal distribution of the vertical mass and heat fluxes at the surface, the horizontally-averaged
heat flux (Nusselt number) and the fraction of the fluid which recirculates within the layer are found for slightly supercritical
conditions. Comparisons are made with the two limiting cases λ → ∞, where the surface is completely impermeable, and λ = 0, where the surface is at constant pressure. Also studied are the effects of anisotropy in permeability, ξ = K
H
/K
V
, and anisotropy is thermal conductivity, η = k
H
/k
V
, both parameters being ratios of horizontal to vertical quantities. Quantitative results are given for a wide variety of
the parameters λ, ξ and η. In the limit ξ/η → 0 there is no recirculation, all fluid being converted out of the top surface, while in the limit ξ/η → ∞ there is full recirculation. 相似文献
17.
We study the Euler equations for slightly compressible fluids, that is, after rescaling, the limits of the Euler equations
of fluid dynamics as the Mach number tends to zero. In this paper, we consider the general non-isentropic equations and general
data. We first prove the existence of classical solutions for a time independent of the small parameter. Then, on the whole
space ℝ
d
, we prove that the solution converges to the solution of the incompressible Euler equations.
Accepted December 1, 2000?Published online April 23, 2001 相似文献
18.
In this paper, the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized
Maxwell fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. Initially,
the fluid is at rest, and the motion is produced by the rotation of the cylinder about its axis with a unsteady angular velocity.
The solutions that have been obtained are presented under series form in terms of the generalized G
a,b,c
(, t)-functions. The similar solutions for the ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained
as special cases, when β → 1, respectively β → 1 and λ → 0, from general solutions. Finally, the solutions that have been obtained are compared by graphical illustrations,
and the influence of the pertinent parameters on the fluid motion is also underlined by graphical illustrations. 相似文献
19.
The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due
to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations,
where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed
transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium,
found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled
this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, τ, scales according to an inverse square-root power law, τ∼(μ−μ
c
)−1/2, as the bifurcation parameter μ, is driven further away from its critical value, μ
c
. In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional
maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species
ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising
due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement
with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling
laws of one-dimensional discrete dynamical systems with saddle-node bifurcations. 相似文献
20.
c ). To begin with, we assume that the flux-function f(u) is piecewise genuinely nonlinear, in the sense that it exhibits finitely many (at most p, say) points of lack of genuine nonlinearity along each wave curve. Importantly, our analysis applies to arbitrary large p, in the sense that the constant c restricting the total variation is independent of p. Second, by an approximation argument, we prove that the existence theory above extends to general flux-functions f(u) that can be approached by a sequence of piecewise genuinely nonlinear flux-functions f
ε(u).
The main contribution in this paper is the derivation of uniform estimates for the wave curves and wave interactions (which are entirely independent of the properties of the flux-function) together
with a new wave interaction potential which is decreasing in time and is a fully local functional depending upon the angle
made by any two propagating discontinuities. Our existence theory applies, for instance, to the p-system of gas dynamics for general pressure-laws p=p(v) satisfying solely the hyperbolicity condition p′(v)<0 but no convexity assumption.
(Accepted December 30, 2002)
Published online April 23, 2003
Communicated by C. M. Dafermos 相似文献