摘要:

The problem of buoyant-thermocapillary convection in cavities is governed by a relatively large number of nondimensional parameters, and there is consequently a large number of different types of flow that can be found in this system. Previous results give disjoint glimpses of a wide variety of qualitatively and quantitatively different results in widely different parts of parameter space. In this study, we report experiments on the primary and secondary instabilities for acetone as the working fluid with a Prandtl number of 4.44, and in a geometry with equal aspect ratios in the range from 1 to 8 in both the direction along and perpendicular to the applied temperature gradient. We thus complement previous work that mostly involved either fluid layers of large extent in both directions, or consisted of investigations of strictly two-dimensional disturbances. We investigate the qualitative and quantitative features of the fluid velocity field by flow visualization and particle tracking techniques. We observe the primary transition from an essentially two-dimensional flow to steady three-dimensional longitudinal rolls. The critical Marangoni number for this first transition is found to depend on the aspect ratios of the system, and varies from4.6×105at aspect ratio 2.0 to5.5×104at aspect ratio 3.5. The structure of the steady three-dimensional flow far above the transition is found to involve a nonintuitive reverse flow against the temperature driving due to the strongly nonlinear three-dimensional flow associated with the longitudinal rolls. Further, we have investigated the stability of this three-dimensional flow at larger Marangoni numbers, and find a novel oscillatory flow at critical Marangoni numbers of the order of6×105.We suggest possible mechanisms that give rise to the oscillations. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869243

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The transitions from the onset of convection to fully developed turbulence of a Rayleigh–Be´nard flow, in a low-aspect-ratio cell and in mercury, are studied through three-dimensional numerical simulation of the Navier–Stokes equations. The calculation of the growth rate of the azimuthal energy modes permitted the accurate determination of the critical Rayleigh number for the establishment of the convective regime(Rac=3750)which is in good agreement with analytical and other numerical results. Increasing the Rayleigh number, the flow remained steady up toRa≃2.11×104when an oscillatory instability was observed. Further increases in the Rayleigh produced a chaotic state through the period doubling mechanism and finally the turbulent state was achieved. It is shown that forRa⩾Racthe mean flow consists of a large-scale convective cell which persists in the whole range of studied Rayleigh numbers(Ra⩽106). The dependence of the Nusselt number over the Rayleigh number is also analyzed and, forRa⩾3.75×104, when the turbulent state is reached, a power law in quantitative agreement with previous results at higher Ra is observed. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869244

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Thermal Taylor dispersion theory for time-periodic systems was used to study the extent of chaotic laminar heat transfer enhancement and axial thermal dispersion occurring during combined transverse and axial annular flow between two nonconcentric circular cylinders undergoing alternate rotations. A local Newton’s “law of cooling” heat transfer boundary condition was used on the outer cylinder, whereas the inner cylinder was supposed insulated. The effective heat transfer coefficientH¯*describing the global rate of heat loss from the system (differing in general from the true microscale Newton’s law heat transfer coefficienthon the outer cylinder) was calculated as a function of the system parameters, thereby serving to quantify the extent of chaotic heat transfer enhancement. The axial thermal Taylor dispersivity provided an independent measure of the effects of chaotic mixing, as too did the axial thermal velocity. Calculations were performed for three different cases: (i) concentric cylinder rotation (for which case the resulting circular transverse flow has no effect upon the effective transport properties); (ii) nonconcentric counter-rotating circular cylinders, each undergoing a steady rotation, thereby creating a time-independent transverse flow field; (iii) nonconcentric counter- and co-rotating circular cylinders, each undergoing time-periodic alternate rotation while the other remains at rest. A “regular” enhancement of the heat transfer rate over the concentric cylinder case was observed in case (ii), arising from the presence of a secondary-flow recirculation region. Enhancement due to chaotic advection was observed in case (iii) [about 50&percent; more than that of case (ii) and more than double that of case (i), all other things being equal]. Concomitant values of the axial thermal Taylor dispersivity and axial thermal velocity confirmed the existence of enhanced transverse transport due to chaotic advection. It was observed that the functional dependence of the enhanced heat transfer rate upon the system parameters does not consistently display the same trends as are qualitatively suggested by the “degree of chaoticity” of the comparable Poincare´ plots. This observation signals the need for caution in simply assuming that the greater the degree of chaotic “mixing” implicit in the Poincare´ plot the greater will be the corresponding global transport rate. By simple redefinition of the symbols used in the present paper, our energy transport results may be re-interpreted so as to apply to the case of reactive-species transport involving a first-order irreversible chemical reaction occurring on the outer-cylinder surface; explicitly, the Nusselt number quantifying the local heat transfer coefficient rate is simply replaced by a comparable Damko¨hler number quantifying the local kinetics of the surface reaction. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869245

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Linear stability of two-dimensional flows in a frame rotating with angular velocity vector&OHgr;=&OHgr;ezperpendicular to their plane is considered. Sufficient conditions for instability have been derived for simple inviscid flows, namely parallel shear flows (characterized by the “Pedley” or “Bradshaw-Richardson” number), circular vortices (by the “generalized Rayleigh” discriminant) and unbounded flows having a quadratic streamfunction (with elliptical, rectilinear or hyperbolic streamlines). These exact criteria are reviewed and contrasted using stability analysis for both three-dimensional disturbances and oversimplified “pressureless” versions of the linear theory. These suggest that one defines a general inviscid criterion for rotation and curvature, based on the sign of the second invariant of the “inertial tensor,” and stating that, in a Cartesian coordinate frame:a sufficient condition for instability is that&Fgr;(x,y)=−12S:S+14Wt⋅Wt<0somewhere in the flow domain.It involves the “tilting vorticity”Wt=W+4&OHgr;[Cambon &etal;, J. Fluid Mech.278,175 (1994)] and the symmetric partSof the velocity gradient of the basic flow. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869273

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

In this paper we are concerned with the theoretical behavior of the laminar von Ka´rma´n boundary-layer flow, extending the work presented by Lingwood [J. Fluid Mech.299, 17 (1995);314, 373 (1996)] to the flow with mass transfer at the surface of the disk. It is known that, within specific regions of the parameter space, the flow is absolutely unstable in the radial direction, i.e. disturbances grow in time at every radial location within these regions. Uniform suction through the disk is shown to delay the onset of absolute instability, while uniform injection promotes the onset. By comparing suction and injection velocities of the same magnitude, it is shown that suction has a greater stabilizing effect on the absolute instability than the destabilizing effect of injection. Suction is also strongly stabilizing to both stationary and travelling inviscidly unstable branch-1 modes; injection is destabilizing. Stationary viscously unstable branch-2 modes are strongly stabilized and destabilized by suction and injection, respectively, but travelling branch-2 modes are shown to be much less sensitive to mass transfer through the disk. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869246

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

It is shown that the kinetic equation proposed by Enskog for a dense hard sphere gas can be solved numerically by a particle simulation method. The technique can be considered an extension of the well known DSMC method used to solve the Boltzmann equation. Unlike a recently proposed Nanbu-like particle scheme, the present method exactly preserves momentum and energy. The calculation of the density profile in a dense gas in equilibrium near a hard wall is presented as an example. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869247

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869259

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Impact pressure probes may be used to measure the stagnation pressure of a spacecraft vehicle during reentry into the atmosphere. We model the flow in an impact pressure probe in the collision-free and transition regime using a kinetic simulation scheme of the Boltzmann equation. It is shown that, depending on the gasdynamic properties density, velocity, temperature of the inflow into the impact pressure probe, the measured pressure may deviate by almost a factor 2 from the stagnation pressure. Furthermore, we study the dependence of the flow in the impact pressure probe on the gas–wall interaction. The models by Maxwell, Cercignani and Lampis, and by Lord are implemented. The influence of the gas–wall interaction is sensible for small accommodation coefficients; it is more pronounced, however, for temperature and density than for the pressure. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869248

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We study numerically a model of random advection of a passive scalar by an incompressible velocity field of different prescribed statistics. Our focus is on the conditional statistics of the passive scalar and specifically on two conditional averages: the averages of the time derivative squared and the second time derivative of the scalar when its fluctuation is at a given value. We find that these two conditional averages can be quite well approximated by polynomials whose coefficients can be expressed in terms of scalar moments and correlations of the scalar with its time derivatives. With the fitted polynomials for the conditional averages, analytical forms for the probability density function (pdf) of the scalar are obtained. The variation of the coefficients with the parameters of the model result in a change in the pdf. Three different kinds of velocity statistics, (i) Gaussian, (ii) exponential, and (iii) triangular, are studied, and the same qualitative results are found demonstrating that the one-point statistics of the velocity field do not affect the statistical properties of the passive scalar. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869249

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The statistics of solutions to a family of one-dimensional random-force-driven advection-diffusion equations is studied using high resolution numerical simulations. The equation differs from the usual Burgers equation by the non-local form of the nonlinear interaction term mimicking the non-locality of the Navier–Stokes equation. It is shown that under an appropriate choice of random forcing the statistical properties of the solution (energy spectrum and scaling exponents of structure functions) coincide with those of Kolmogorov turbulence. Also, a generalization is proposed which allows intermittency effects to be modeled. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869250

出版商:AIP    

年代:1997

数据来源: AIP