摘要:

Fully developed flow of an incompressible Newtonian fluid through a duct in which the orientation of the cross section is twisted about an axis parallel to an imposed pressure gradient is analyzed here with the aid of the penalty/Galerkin/finite element method. When the axis of twist is located within the duct, flow approaches limits at low and high torsion, the spatial frequency &tgr; by which the duct is twisted. For small torsion, flow is nearly rectilinear and solutions approach previous asymptotic results for an elliptical cross section. For large torsion, flow exhibits an internal layer structure: a rotating circular‐cylinder core with a nearly parabolic axial velocity profile, an internal layer of thickness &tgr;−1along the perimeter of the largest circular cylinder that can be inscribed in the duct, and nearly quiescent flow outside of the circular cylinder. The maximum rate of swirl in the core of a square duct is found to be at moderate torsion. The primary effect of inertia is an increase in pressure with distance from the axis, due to centrifugal acceleration. When the duct is offset from the axis of twist, inertia leads to one, two, or three primary vortices without apparent bifurcation of steady states, although stability of steady flows is lost beyond detected Hopf points.

ISSN:0899-8213    

DOI:10.1063/1.858730

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The dynamic responses of a spherical bubble in an acoustic standing wave field are studied numerically. The equations of motion in the translational and the radial directions are solved simultaneously. It is shown that a bubble which is larger than the resonance size moves to a node of the pressure field and its radial oscillations become small. A sufficiently small bubble is shown to move to an antinode and radially oscillates under the maximum pressure amplitude. It is found using Poincare´ maps and power spectra that a bubble which is slightly smaller than the resonance size oscillates chaotically in both the radial and the translational directions. It is demonstrated that the range of the equilibrium bubble size which shows chaotic motions broadens with the pressure amplitude. Finally, the radial responses of the bubble are shown to be dependent not only on the pressure amplitude but also on the drag force in the translational direction.

ISSN:0899-8213    

DOI:10.1063/1.858731

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Spectral element simulations of the steady, incompressible, parabolized Navier–Stokes equations are used to compare numerically simulated smoke or dye (tracer) patterns with numerically calculated spatially developing flow patterns in the following two geometries: curved channel flow and twisted square duct flow (which consists of three joined 90° square curved ducts with perpendicular planes of curvature). Secondary flows in these two geometries are caused by streamwise‐oriented vortices, which have been visualized in previous experiments by viewing smoke or dye patterns in cross‐sectional planes perpendicular to the streamwise direction. Simulations of tracer patterns (obtained by tracking weightless particles) show that only when there is little streamwise variation of the secondary flow do tracer patterns provide a correct qualitative indication of the secondary flow patterns. For example, tracer patterns misrepresent merging of curved channel vortices and the locations and shapes of the twisted duct vortices. These results highlight the difficulty in obtaining consistent interpretations of tracer patterns in flows with significant streamwise variation, and in obtainingaprioripredictions of the validity of inferring secondary flow patterns from tracer patterns. For the two case studies examined, it is found that unless there is little streamwise variation of the secondary flow structure, inferences of secondary flow patterns from experimental tracer patterns should be made only when well validated by other methods.

ISSN:0899-8213    

DOI:10.1063/1.858732

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The linear stability of unbounded strained vortices in a stably stratified rotating fluid is investigated theoretically. The problem is reduced to a Matrix–Floquet problem, which is solved numerically to determine the stability characteristics. The Coriolis force and the buoyancy force suppress the subharmonic elliptical instability of cyclonic and weak anticyclonic vortices, whereas enhances that of strong anticyclonic vortices. The fundamental and superharmonic instability modes occur, in addition. They are due to higher‐order resonance. The growth rate of each instability shows complicated dependence on the parametersN(the normalized Brunt–Va¨isa¨la¨ frequency) andR0(the Rossby number: defined inversely as usual), if their values are small. It decreases as the background rotation rate becomes larger and as the stratification becomes stronger. The instability mode whose order of resonance is less than Min(N,2‖1+R0‖) is inhibited.

ISSN:0899-8213    

DOI:10.1063/1.858733

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A theoretical study is made of initial algebraic growth for small angular‐dependent disturbances in pipe Poiseuille flow. The analysis is based on the homogeneous equation for the pressure for which the eigenvalue problem is solved numerically. In the limit of small streamwise wave numbers asymptotic results for the eigenvalues are derived. On the basis of the modes of the system, which are all damped, the initial value problem is considered and in particular the largest possible growth of the disturbance energy density is determined following the ideas of Butler and Farrell [Phys. Fluids A4, 1637 (1992)]. The results show that a large amplification of the disturbance energy is possible. The largest amplification is obtained for disturbances with a small streamwise wave number and with an azimuthal wave number of one. The energy growth is then only due to the growth of the streamwise disturbance component. However, for disturbances of shorter wavelength, the energy growth is also substantial and not only concentrated to the streamwise velocity component. The wall shear corresponding to disturbances with the largest energy growth also shows a large amplification and the dependence of wave numbers and the Reynolds number is the same as for the energy. However, the wall pressure of a long wavelength disturbance of the largest growth just decays from its initial value, but for disturbances of shorter wavelength, it is also amplified.

ISSN:0899-8213    

DOI:10.1063/1.858734

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A unified stability curve was generated for impulsively started pipe entrance flows, comprising the variation of critical Reynolds number with a novel dimensionless velocity profile shape parameter. Time dependent regions of stability and instability were obtained, explaining qualitatively the measured almost instantaneous upstream propagation of turbulence in a starting pipe flow. In so doing they provide a formal alternative to the widely held view that the observation of turbulence far downstream under steady‐state conditions is purely from the evolution and washdown of turbulent structures in the unstable entrance region of the pipe, suggesting the possibility that local downstream instabilities and turbulence from an earlier time, play a role.

ISSN:0899-8213    

DOI:10.1063/1.858735

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Using linear stability analysis, the instability characteristics are examined of both planar wakes and mixing layers subjected to rigid‐body rotation with axis of rotation perpendicular to the plane of the ambient flow. In particular, the tendency of rotation to stabilize or destabilize three‐dimensional motions is addressed. In the inviscid limit the results are consistent with the criterion established by Pedley [J. Fluid Mech.35, 97 (1969)] and Bradshaw [J. Fluid Mech.36, 177 (1969)]. Cyclonic rotation and strong anticyclonic rotation tend to stabilize three‐dimensional motions, whereas weaker anticyclonic rotation (Ro≳1) acts to destabilize these motions. This latter instability is in the form of streamwise rolls, similar to previous results obtained for boundary layer and channel flows. It is found that this instability is stronger than the coexisting Kelvin–Helmholtz instability for roughly the range 1.5<Ro<8, and its effect is maximum for Ro&bartil;2. For the case of constant ambient shear, exact solutions are obtained which give further insight into the nature of the instability.

ISSN:0899-8213    

DOI:10.1063/1.858736

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Sideband instabilities following the onset of traveling interfacial waves in two‐layer Couette–Poiseuille flow are considered. The usual Ginzburg–Landau equation does not apply to this problem due to the presence of a long‐wave mode for which the decay rate tends to zero in the limit of infinite wavelength. Instead of the Ginzburg–Landau equation, a coupled set of equations for three amplitude factors is derived. The first corresponds to an amplitude of a traveling wave, the second to a long‐wave modulation of the interface height, and the third results from the pressure. The criteria which determine the stability of the primary traveling wave to sideband perturbations are presented. This scenario raises the possibility that as a result of sideband instability of a primary traveling wave, the flow may eventually be dominated by a long‐wave mode. Experimental data on a gas–liquid flow are analyzed and models for air–water waves are discussed. Finally, it is noted that the amplitude equations allow for possibilities other than periodically modulated waves. In the concluding section, the presence of homoclinic and heteroclinic orbits is investigated. These correspond to solutions which approach either a flat interface or periodic waves at infinity.  

ISSN:0899-8213    

DOI:10.1063/1.858737

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

This is an experimental study of the flattening and breakup of liquid drops in a single‐axis acoustic levitation field, and is an extension of the authors’ previous work [C. P. Leeetal., Phys. Fluids A3, 2497 (1991); Proceedings of the 30th Aerospace Sciences Meeting and Exibit, Reno, NV (1992)], on the static shape and stability of acoustically levitated drops. Two aspects, namely (i) the variation of drop equilibrium shape with sound pressure level and, (ii) the mechanism of disintegration of small drops in intense sound fields, have been studied mainly with water drops. The drop‐shape study reveals that the critical acoustic Bond numberBa,cr [Ba=A2Rs/(&sgr;&rgr;c2);A: acoustic amplitude;Rs: spherical radius of the drop; &sgr; : surface tension of the drop liquid; &rgr;: density of air and;c: sound speed in air], at which a downturn in acoustic intensity occurs for the larger drops, or loss of stability occurs for the smaller drops, varies from about 2.6 (forkRs∼0.74;k: acoustic wave number) to about 3.6 (forkRs∼0.25). The corresponding nondimensional critical equatorial radiusR*cr(R*=R/Rs,R: equatorial radius of the drop) varies between 1.5 and 1.4. The study also reveals that, for deformationR* greater than about 1.3, the drop assumes the shape of a disk. The study of the dynamics of disintegration of small drops reveals that, following loss of stability, the drop expands horizontally with the liquid close to the edge drawn into a sheet by acoustic suction. The sheet continuously thins during expansion and two types of waves, one in the azimuthal direction, and the other in the radial direction, are parametrically excited on it. The ensuing violent vibration shatters the drop; with the whole process having a time scale of the order of 0.5 msec. These results partially confirm the mechanism of drop disintegration postulated by Danilov and Mironov [J. Acoust. Soc. Am.92, 2747 (1992)]. The parametric instability of the thin sheet differs from that of the well established Faraday instability of a liquid half‐space, where the parametric oscillations are excited at half the frequency of the external field.

ISSN:0899-8213    

DOI:10.1063/1.858738

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Kolmogorov‐type cascade processes have long been postulated to explain power‐law falloff of the spectrum of gravity wave autocorrelations. In an effort to understand these processes more deeply, simplified models of the nonlinear Hasselmann resonant four‐wave interaction have been introduced. These models respect the fundamental structural aspects of that interaction, but are otherwise chosen for computational simplicity. In this paper the concept of quasilocality within the context of such models is extended to its logical limit in one spatial dimension. This results in differential rather than integral equations for the wave fields. One scaling solution to the new equations has a spectral exponent independent of the details of the model interaction, and is stable to small perturbations. In addition, under weak restrictions on the first and second derivatives of the model interactions, a further pair of two‐parameter families of scaling solutions exist. The spectral exponents in this case depend on the details of the model, but unstable as well as stable perturbations to these solutions are supported.

ISSN:0899-8213    

DOI:10.1063/1.858739

出版商:AIP    

年代:1993

数据来源: AIP