摘要:

The stochastic collisions of drops of two intersecting streams were investigated experimentally. The drop streams were produced by Rayleigh breakup of two laminar jets of propanol-2 and were arranged spatially so that they lie in one plane and intersect at an angle which was varied in the experiments. The collisional interactions of the drops were visualized using video equipment. In the zone between the drop streams downstream of the intersection point new drops occur which are formed by the collisions. The visualization showed that these new drops may be produced either by the merging of two colliding drops or by the breakup of liquid bridges formed between drops after off-center collisions. Measurements of velocity and size of the drops in the flow field were carried out using a phase-Doppler anemometer (PDA). These data and the frequency of drop arrival in the measurement control volume of the PDA give insight into the drop formation processes caused by the collisions and enable the computation of the collision frequency. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869236

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The first flow regimes which have been observed experimentally for a circular Couette flow with a stable, axial stratification in density are investigated through direct numerical simulations of the three-dimensional Navier-Stokes equations for a Boussinesq fluid. The setup of two concentric cylinders has a nondimensional gap width of&egr;=(b−a)/a=0.289;the outer cylinder is fixed and the stratification in density in the axial direction is linear. The main effect of an axial density stratification is to reduce the height of the Taylor vortices and to cause the formation of density layers of small aspect ratio. For large enough Prandtl number, the primary bifurcation from circular Couette flow is found to be axisymmetric and of Hopf-type in the direct numerical simulations. An analytical solution for onset of instability and slightly different boundary conditions from the experimental ones agrees within 0.6&percent; with numerical simulations at a Prandtl number of 700. The experimental flow regimes with well-defined density layers are well reproduced by the numerical simulations in the appropriate range of relative Reynolds numberRe/Rec1,whereRec1denotes the critical Reynolds number for the primary bifurcation from circular Couette flow. However, the increase of axial scale withRe/Rec1is found to be continuous, whereas it is quantized in the laboratory experiments. Numerical results reveal that the first two transitions between the flow regimes are primarily due to the temporal behavior of the axially symmetric part of the flow. Onset of nonaxisymmetric motions appears at the sameRe/Rec1≈1.18as in the homogeneous fluid case at the same&eegr;=a/b.Stratification precludes large axial displacements and the azimuthal modes patterns have a quite distinct appearance from the homogeneous wavy modes. At large enough Re, a destabilization of the jet-like outflow between pairs of vortices causes the suppression of the density front which is located at the same axial height. This nonaxisymmetric flow regime presents common features with the wavy outflow boundary (WOB) pattern, which is commonly observed in the homogeneous Couette-Taylor case. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869237

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Advective nonsolenoidal (&bnabla;⋅v≠0) flow driven by diffusion-induced density changes in strictly zero gravity is studied in a two-dimensional rectangular box. Our model, which is more general than the Oberbeck–Boussinesq model, is a precursor for the study of fluid flow that occurs due to density changes during isothermal interdiffusion in a binary liquid under the influence of stochastic microgravity (g-jitter). We consider perturbation expansions of mass fraction(w)of the second chemical component of a binary solution, pressure(p), velocity(v), and chemical flux(j)with respect to a small parameter &agr; [=&rgr;0∂(1/&rgr;)/∂w], where &rgr; is the density and &rgr;0is its value for some average composition. The total barycentric velocity field is given by the sum of an average flow, having a nonzero divergence, and a solenoidal flow derived from a pseudo-stream-function. At first order in &agr;, we obtain a fourth order partial differential equation for this pseudo-stream-function. We solve this equation analytically in a quasi-steady-state approximation for an infinitely long diffusion couple by using transform techniques. We also solve it numerically for the full time-dependent problem for a finite domain. We conclude that such nonsolenoidal flows will dominate for sufficiently small gravity, for which the Oberbeck–Boussinesq approximation will certainly not be valid. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869238

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

In nature, in many technological applications and in some laboratory experiments, the basic state of shear flows can be time-varying. The effects of such variations on the stability characteristics of these flows are not well understood. In previous work, Miksad &etal; [J. Fluid Mech.123, 1 (1982)] and Hajj &etal; [J. Fluid Mech.256, 385 (1992)], it has been shown that low-frequency components, generated by nonlinear difference interactions, play an important role in the redistribution of energy among spectral components. In particular, phase modulation was found to be the most effective mechanism in energy transfer to the sidebands of unstable modes. In this work, the effects of small-amplitude low-frequency mean flow unsteadiness on the stability of a plane mixing layer are determined. By extending earlier analytical arguments, it is shown that periodicity in the mean flow causes modulations of the most unstable modes. The analysis is then verified experimentally by comparing levels of amplitude and phase modulations in mixing layers with steady and unsteady basic flows. The results show that small-amplitude low-frequency unsteadiness results in enhanced modulations of the fundamental mode. These modulations cause variations in the growth rates of the unstable modes and energy redistribution among them. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869239

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The electrohydrodynamic instabilities of plane Poiseuille flow when subjected to an orthogonal arbitrary unipolar injection of charge has been studied. Appropriate boundary conditions for the perturbed charge density in the space charge limited current regime in the presence of forced flows has been derived. The effect of the injection level on the stability of the flow is analyzed, as well as the role played by the ratio of the hydrodynamic to the true ionic mobility. It is shown that in the low Reynolds number region traverse rolls are destabilized more strongly as the ratio of mobilities decreases. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869477

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Complementary flow visualization photographs and numerical calculations are presented for the transitional state between the laminar and turbulent flow regimes in a helically coiled pipe. The flow visualization covers a Reynolds number range from 3800 to 8650 (890<De<2030, where De is the Dean number). Estimates of the wavelength and wave speed of a traveling wave instability are made from photographs and video recordings at Re=5060 and 5480 (De=1190 and 1280). The unsteady three-dimensional finite difference approximations of the Navier–Stokes equations formulated for the toroidal coordinate system are solved numerically. The calculations are performed in a curved pipe with a radius of curvature to pipe radius ratio equal to 18.2 and Re=5480 (De=1280). These test conditions match the flow visualization and previously reported laser Doppler velocimetry measurements. The calculations reveal a complex interaction between the centrifugal force and the cross-stream velocity, hence explaining the mechanism for maintaining the traveling wave. An analogy is made with known centrifugal instabilities to explain the character of the motion observed in the inner half of the pipe along planes defined by the radial and streamwise coordinate directions. Simple considerations show that the cross-stream flow has the potential for a centrifugal instability. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869139

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

This study deals with the instabilities that arise in the flow generated in a rotating tank by the evolution of a two-layer density stratified fluid. Numerical investigations have been performed by direct simulation of the Navier-Stokes equations for axisymmetric and fully three-dimensional flows. In the former case results have shown the attainment, in a very short time, of an equilibrium position and the formation of an anticyclonic structure in the upper light layer and a cyclonic one in the lower layer, consistently with the observation of Griffiths and Linden. In the long term, however, the Ekman layer at the bottom damps out the cyclone and a steady state with only an anticyclone in the upper layer is reached. In three-dimensions the flow is unstable to azimuthal disturbances and the steady state is no longer achieved. In particular a ring of cyclonic vorticity, surrounding the anticyclone, by the combined effects of baroclinic and barotropic processes, breaks, entrains vorticity from the anticyclone and eventually forms vortex pairs. As observed by Griffiths and Linden the azimuthal wave number(n*)of the instability depends on the Richardson number(Ri)and the ratio between the depth of the light fluid and the total depth(&dgr;). However, since several modes, in addition to the most unstable, are amplified an initial perturbation whose energy is not equidistributed among the modes can lead to an instability with wave number different from the expectedn*. Finally, the analysis of the equation for the energy of the instability has shown that the instability is initially driven by baroclinic effects, even for low values of&dgr;. The barotropic source, in contrast, sets in only in the large-amplitude phase of the instability and its effect is larger when&dgr;is small. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869136

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Low-dimensional models for the turbulent wall layer display an intermittent phenomenon with an ejection phase and a sweep phase that strongly resembles the bursting phenomenon observed in experimental flows. The probability distribution of inter-burst times has the observed shape [E. Stone and P. J. Holmes, Physica D37, 20 (1989); SIAM J. Appl. Math.50, 726 (1990); Phys. Lett. A5, 29 (1991); P. J. Holmes and E. Stone, inStudies in Turbulence, edited by T. B. Gatski, S. Sarkar, and C. G. Speziale (Springer, Heidelberg, 1992)]. However, the time scales both for bursts and interburst durations are unrealistically long, a fact that was not appreciated until recently. We believe that the long time scales are due to the model’s inclusion of only a single coherent structure, when in fact a succession of quasi-independent structures are being swept past the sensor in an experiment. A simple statistical model of this situation restores the magnitude of the observed bursting period, although there is a great deal of flexibility in the various parameters involved. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869137

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Mass transfer through the solid boundary of a turbulent channel flow is analyzed by means of large-eddy simulation (LES) for Schmidt numbers Sc=1, 100, and 200. For that purpose the subgrid stresses and fluxes are closed using the Dynamic Mixed Model proposed by Zang &etal; [Phys. Fluids A5, 3186 (1993)]. At each Schmidt number the mass transfer coefficient given by the LES is found to be in very good quantitative agreement with that measured in the experiments. At high Schmidt number this coefficient behaves like Sc−2/3, as predicted by standard theory and observed in most experiments. The main statistical characteristics of the fluctuating concentration field are analyzed in connection with the well-documented statistics of the turbulent motions. It is observed that concentration fluctuations have a significant intensity throughout the channel at Sc=1 while they are negligible out of the wall region at Sc=200. The maximum intensity of these fluctuations depends on both the Schmidt and Reynolds numbers and is especially influenced by the intensity of the velocity fluctuations present in the buffer layer of the concentration field. At Sc=1, strong similarities are observed between the various terms contributing to the turbulent kinetic energy budget and their counterpart in the budget of the variance of concentration fluctuations. At high Schmidt number, the latter budget is much more influenced by the small turbulent structures subsisting in the viscous sublayer. The instantaneous correlation between the spatial characteristics of the concentration field and those of the velocity field is clearly demonstrated by the presence of low- and high-concentration streaks close to the wall. The geometrical characteristics of these structures are found to be highly Sc dependent. In particular their spanwise wavelength is identical to that of the streamwise velocity streaks at Sc=1 while it is reduced by half at Sc=200. Analysis of the co-spectra between concentration and normal velocity fluctuations emphasizes the fact that the large-scale structures play an essential role in the turbulent mass transfer process at high Schmidt number. Overall the picture that emerges from this investigation fully confirms the conclusions of Campbell and Hanratty [AIChE J.29, 221 (1983)]: high-Schmidt-number mass transfer at a solid wall is governed by the low-frequency part of the normal velocity fluctuation gradient at the wall, i.e., by the large-scale structures observed in planes parallel to the wall in the viscous sublayer. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869138

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck &etal; [P W. Duck, D. G. Lasseigne, and M. Y. Hussaini, “On the interaction between the shock wave attached to a wedge and freestream disturbances,” Theor. Comput. Fluid Dyn.7, 119 (1995) (also ICASE Report No. 93-61)] through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e., time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869140

出版商:AIP    

年代:1997

数据来源: AIP