摘要:

The sound radiated by isotropic turbulence is computed using inertial range scaling expressions for the relevant two‐time and two‐point correlations. The result depends on whether the decay of Eulerian time correlations is dominated by large scale sweeping or by local straining: the straining hypothesis leads to an expression for total acoustic power given originally by Proudman, whereas the sweeping hypothesis leads to a more recent result due to Lilley. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868849

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Impact of water droplets on a flat, solid surface was studied using both experiments and numerical simulation. Liquid–solid contact angle was varied in experiments by adding traces of a surfactant to water. Impacting droplets were photographed and liquid–solid contact diameters and contact angles were measured from photographs. A numerical solution of the Navier–Stokes equation using a modified SOLA‐VOF method was used to model droplet deformation. Measured values of dynamic contact angles were used as a boundary condition for the numerical model. Impacting droplets spread on the surface until liquid surface tension and viscosity overcame inertial forces, after which they recoiled off the surface. Adding a surfactant did not affect droplet shape during the initial stages of impact, but did increase maximum spread diameter and reduce recoil height. Comparison of computer generated images of impacting droplets with photographs showed that the numerical model modeled droplet shape evolution correctly. Accurate predictions were obtained for droplet contact diameter during spreading and at equilibrium. The model overpredicted droplet contact diameters during recoil. Assuming that dynamic surface tension of surfactant solutions is constant, equaling that of pure water, gave predicted droplet shapes that best agreed with experimental observations. When the contact angle was assumed constant in the model, equal to the measured equilibrium value, predictions were less accurate. A simple analytical model was developed to predict maximum droplet diameter after impact. Model predictions agreed well with experimental measurements reported in the literature. Capillary effects were shown to be negligible during droplet impact when We≫Re1/2. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868850

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A mesoscopic or coarse‐grained approach is presented to study thermo‐capillary induced flows. An order parameter representation of a two‐phase binary fluid is used in which the interfacial region separating the phases naturally occupies a transition zone of small width. The order parameter satisfies the Cahn–Hilliard equation with advective transport. A modified Navier–Stokes equation that incorporates an explicit coupling to the order parameter field governs fluid flow. It reduces, in the limit of an infinitely thin interface, to the Navier–Stokes equation within the bulk phases and to two interfacial forces: a normal capillary force proportional to the surface tension and the mean curvature of the surface, and a tangential force proportional to the tangential derivative of the surface tension. The method is illustrated in two cases: thermo‐capillary migration of drops and phase separation via spinodal decomposition, both in an externally imposed temperature gradient. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868851

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

When a liquid layer is heated from the side, a monocellular flow develops immediately, no matter how small the temperature difference is. If the temperature gradient between the side walls is increased, this flow becomes unstable. Laser Doppler velocimetry measurements are reported here in an attempt to describe the main features of both the basic flow and the instability modes. It is found that before the appearance of traveling waves (the most dangerous mode as predicted by the theory), stable rolls with their axes perpendicular to the temperature gradient, span over the whole liquid layer, starting from the hot side, even if the aspect ratio (the length of the layer divided by its thickness) is very high. This unexpected situation modifies the basic flow. A further increase of the temperature gradient leads to the appearance of a time periodic motion. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868852

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The annular region between two concentric, confocal ellipses is a new geometry which is particularly effective for either mixing of viscous fluids or heat transfer enhancement in the important limit of a high Pe´clet number. This geometry is in many respects similar to the annular space between two eccentric, rotating cylinders although it possesses two (instead of one) axes of symmetry. The recently obtained analytical solution of the Stokes flow equations in this geometry shows that at steady state and for counter‐rotation of the inner and outer ellipses, two opposite saddle points (connected by two different streamlines) appear in the region of minimum gap. This flow characteristic is also exhibited by the eccentric cylinder system for some cases of co‐rotation. The Poincare´ sections obtained when the inner and outer ellipses are displaced using a discontinuous velocity protocol show that a more effective long term mixing is obtained for the counter‐rotating case, this is confirmed by the experimental data we have obtained. The opposite conclusions (more effective mixing for co‐rotation) have been given in the eccentric cylinder geometry.Photographs of the fluorescent dye after 5 periods are compared with remarkable success to numerical blob deformation experiments. Experimental results also confirm previous results based on an analysis of Poincare´ sections. In particular, better mixing is obtained when the inner ellipse displacement per period increases. Finally, this geometry is shown to be particularly effective as a heat exchanger. For steady, counter‐rotation of the two boundaries, the recirculation zones can lead to a heat transfer rate increase of 80% over that of pure conduction at high Pe´clet numbers, and, by an appropriate sinusoidal modulation of the angular velocity of one boundary, the heat transfer rate can be more than double that of pure conduction. Since an analysis of the experimental data also suggests that the mixing rate for a sinusoidal modulation of the angular velocity of the boundaries is better than for a discontinuous velocity protocol, we propose that the average Nusselt number per period could be one of the several useful tools in the global optimization of the mixing protocol. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868853

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

We report experiments on the instability of the sidewall Stewartson layer that arises in the fluid next to the vertical boundary of a cylinder that is rotating about its axis at rate &OHgr;, and is driven by slow differential rotation of a contact lid. There are three primary instabilities that come in sequentially as the driving is increased: vertically traveling axisymmetric rolls, quasistationary diagonal rolls inclined backward (retrograde, or opposite to the direction of the basic rotation &OHgr;) with height, and prograde‐traveling waves that tilt forward with height. These instabilities are markedly different from those observed in laboratory studies or computational simulations of pressure‐driven flow down a rotating channel. The instability mechanisms appear to be related to our particular method of driving these flows. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868854

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A special procedure is applied to remove the non‐physical distortion that always appears when numerically calculating velocity and related quantities in the close vicinity of a discretized vortex sheet. The procedure is used in conjunction with a semi‐Lagrangian boundary integral method to study the flowfield beneath free surface standing water waves. Pressure, velocity and acceleration are calculated below the wave and some aspects of crest formation are investigated. At large depths results confirm the existence of an unattenuated oscillatory pressure component, giving behavior consistent with previously known theory. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868855

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

At high Reynolds numbers, the process leading to dynamic stall on airfoils initiates in the leading‐edge region. For thin airfoils, the local motion near rounded leading edges can be represented as flow past a parabola and when the mainstream flow is at an angle of attack to the airfoil, a portion of the boundary layer will be exposed to an adverse pressure gradient. Once the angle of attack exceeds a certain critical value, it is demonstrated that unsteady boundary‐layer separation will occur in the leading‐edge region in the form of an abrupt focused boundary‐layer eruption. This process is believed to initiate the formation of the dynamic stall vortex. For impulsively‐started incompressible flow past a parabola, a generic behavior is found to occur over a range of angles of attack, and a limit solution corresponding to relatively large angles is found. The separation in the leading‐edge region develops in a zone of relatively limited streamwise extent over a wide range of angles of attack. This suggests that localized control measures (such as suction) may possibly be effective at inhibiting separation. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868856

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The dynamics of small, heavy, spherical particles are investigated in an analytical model of the stretched counterrotating streamwise braid vortices commonly found in three‐dimensionally evolving mixing layers. The flow field consists of two superimposed rows of Stuart vortices of opposite sign, with an additional two‐dimensional strain field. The particle dynamics are determined by a balance of inertial, gravitational, and viscous drag forces, i.e., the dimensionless Stokes and Froude numbers,StandFr, as well as by the dimensionless strain rate, and the Stuart vortex family parameter. Equilibrium points for the particles, as well as their stability criteria, are determined analytically, both in the absence and in the presence of gravity, and for different orientations of the gravity vector. In the absence of gravity, accumulation of lowStparticles can occur at the center of the braid vortices. An analytical expression for the critical particle diameter, below which accumulation is possible, is derived. The presence of gravity can lead to the emergence of multiple equilibrium points, whose stability properties depend on their locations. For a horizontal mixing layer flow and strong gravity effects, unconditional accumulation can occur midway between the streamwise braid vortices in the upwelling regions. Conditionally stable accumulation regions exist a short horizontal distance away from the centers of the braid vortices. If the gravity vector lies within the plane of the mixing layer, accumulation points exist only for moderate strengths of gravity. Under these circumstances, conditional accumulation is possible near the streamwise vortex centers. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868857

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A computational investigation of the nonlinear dynamics of heavy particles in a row of counterrotating strained vortices is presented. By tracking the particles numerically in the quasi‐two‐dimensional fluid velocity field, information is obtained on the nature of their trajectories, as well as on probability distribution functions and potential accumulation regions. The particle behavior is discussed as a function of the dimensionless strain rate, the particle Stokes numberSt, and the dimensionless gravity parameterFr. Only for very low values of theStcan the particles accumulate at the vortex centers. For moderate values ofSt, they remain trapped on closed trajectories around the vortex centers. IncreasingStleads to periodic open trajectories that allow for spanwise transport of the particles. Further bifurcations lead to the generation of multiple trajectories, as well as to subharmonic solutions. Eventually, intermittent and chaotic particle dynamics are observed. In the chaotic regime, a simplified flow model is employed in order to derive various scaling laws for the particle concentration field. For strong levels of gravity, the accumulation of large numbers of particles is observed in the upwelling regions predicted in part I of the present investigation [B. Marcu and E. Meiburg, Phys. Fluids8, 715 (1996)]. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868858

出版商:AIP    

年代:1996

数据来源: AIP