摘要:

A direct numerical simulation of thermal convection between horizontal plane boundaries has been performed, at a Rayleigh number Ra=9800 Rac, where Racis the critical Rayleigh number for the onset of convection (Pr=0.72). The flow is found to be fully turbulent and analysis of the probability distributions for temperature fluctuations indicates that this is within the ‘‘hard turbulence’’ regime, as defined by the Chicago group. Good agreement is shown to exist between their experiments and the present simulation.

ISSN:0899-8213    

DOI:10.1063/1.857516

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

A rigorous analytical framework is presented for the computation of the effective viscosity of a neutrally buoyantnondiluteemulsion of two immiscible Newtonian Stokes fluids. The capillary number, which is a relative measure of viscous forces that tend to distort the drop and of the interfacial tension that favors sphericity, is assumed to be small. Thus drop distortion is ignored to first order and sphericity is preserved under small shear rates. The so‐called ‘‘direct method,’’ which does not involve any energy concepts, is used and also is shown to be equivalent to the traditional approach based on the dissipation function. The micromechanics model is based on the ‘‘generalized self‐consistent model’’ commonly used in composite media. At low concentrations the present theoretical prediction reduces to Taylor’s formula [Proc. R. Soc. London Ser. A138, 41 (1932)] and is also compared against other approximate theories and experimental data for the nondilute case. The agreement is in general surprisingly good. The present model is also shown to fall between some existing bounds, which result from the application of various variational principles. A critical comparison between these bounds is also given.

ISSN:0899-8213    

DOI:10.1063/1.857517

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

A cylindrical interface containing a viscous liquid set into axial motion is subject to a capillary and to a surface‐wave instability. Clues from previous studies suggest that, even though both mechanisms separately are destabilizing, under certain circumstances their mutual interaction can lead to a stable interface; shear can stabilize capillary breakup. These clues lead the authors to consider an axial flow through an annular cross section bounded on the inside by a rigid rod and on the outside by a deformable interface. The competition between the two mechanisms is studied through the temporal growth of infinitesimal axisymmetric and nonaxisymmetric disturbances. This examination of temporal stability shows that, indeed, for geometries corresponding to thin annular layers both instabilities can be completely suppressed—disturbances of all wavelengths decay.

ISSN:0899-8213    

DOI:10.1063/1.857518

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

A few‐mode Galerkin truncation is used to set up Lorenz models for convection in rotating binary mixtures. Idealized as well as realistic boundary conditions are treated. An extended model to handle Ku¨ppers–Lortz instability is studied. For idealized boundary conditions the nonlinear terms cause the Hopf bifurcation to the traveling wave state to be backward. Finite amplitude traveling waves are expected for negative values of the separation parameter. For Prandtl numbers less than unity, a codimension three‐point should be seen. The amplitude equation near the codimension three‐point is discussed. Realistic boundary conditions, however, make the possibility of observing the codimension three‐point remote, even in3He–4He mixtures.

ISSN:0899-8213    

DOI:10.1063/1.857519

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Thin film formation using the process of spin coating is investigated. The liquid film and surrounding gas phase two‐dimensional (2‐D) full governing equations with applicable boundary conditions are formulated. The heat and mass transfer that occurs in the gas and liquid phase and across the free surface, including the evaporation of solvent, are taken into account. The governing equations and boundary conditions are then reduced to a 1‐D case based on the variables radial dependency. The detailed film formation process that commences at the start of the spinning and ends with the dry‐up of the coated film is numerically simulated by utilizing the 1‐D governing equations. The complex effects of various process parameters, e.g., spinning speed, initial solute concentration, and disk heating, are clarified by the present numerical analysis. It was found that the final film thickness is mainly determined at the time when the film thinning rate resulting from radial convection has the same order as the film thinning rate resulting from solvent evaporation.

ISSN:0899-8213    

DOI:10.1063/1.857520

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The effect of streamwise vorticity on the three‐dimensional breakdown of two‐dimensional Tollmien–Schlichting waves in a plane‐channel flow is studied via direct numerical simulation. Streamwise vortices of the strength inherent to most transition experiments are shown to alter the relative importance of the subharmonic and fundamental modes and to explain discrepancies observed between theory, previous computations, and experiments in both the plane channel and in the flat‐plate boundary layer. It is shown that without the inclusion of the vortices, the computations support the theory; with inclusion of the vortices, the computations support the experiments. This work demonstrates the importance of combining theory, experiments, and computations in the study of transition in both internal and external applications.

ISSN:0899-8213    

DOI:10.1063/1.857521

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Measurements on the onset of turbulence in oscillating flow of water in small diameter tubes are presented. Observations, based upon the streaming birefringence method, show that the heretofore observed radius independent onset criterion for turbulence fails to hold as the tube radius and oscillation frequency become small. In particular, it is found that with decreasing values of Womersley number, oscillating flows become increasingly stable.

ISSN:0899-8213    

DOI:10.1063/1.857469

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

A numerical study of the two‐dimensional flow of linearly stratified Boussinesq fluid past a vertical flat plate in a channel of finite depth is described. It is found that there are time‐dependent oscillations in each vertical mode of the upstream advancing columnar disturbances which correspond to the unsteadiness in the drag coefficient found in previous experiments. The long‐time behavior of the upstream columnar disturbances shows that the time‐averaged strength of each mode approaches some constant value that is not zero. This determines the drag coefficient in the long‐time limit. In many points the numerical solutions of the Navier–Stokes equation agree with the solutions of the forced Korteweg–de Vries (KdV) equation with a cubic nonlinear term or the forced KdV–Burgers equation. It is also suggested that the strong downstream columnar disturbances predicted by linear theory for steady flow do not exist.

ISSN:0899-8213    

DOI:10.1063/1.857470

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

The inviscid, two‐dimensional interaction between a pair of counter‐rotating line vortices and a free surface has been studied. A solution to the linearized, small‐disturbance problem has been thoroughly explored. For the nonlinear problem numerical calculations were carried out for Froude numbers representing a range of very weak to very strong vortices. Strong vortices are little affected by the presence of the surface, rising to form a bubblelike disturbance; weaker vortices follow paths like vortices approaching a plane boundary. The experimentally observed scarring phenomena—surface depressions whose axes are perpendicular to the flow plane—are seen in the numerical results.

ISSN:0899-8213    

DOI:10.1063/1.857471

出版商:AIP    

年代:1989

数据来源: AIP

摘要:

Observations are reported of the interaction with a free surface of vortex rings and vortex pairs moving normal to the surface when different amounts of surface active agents are present on the surface. At a vortex ring Reynolds number &Ggr;/&ngr;≈3800, the interaction with a contaminated free surface results in the generation of secondary and tertiary vortex rings that limited the outward motion of the vortex ring core. When the experiment was repeated with a cleaner surface the formation of the secondary vortex ring was delayed so that the outward motion and stretching of the vortex ring core was much more than for the contaminated surface. At a Reynolds number &Ggr;/&ngr;≈18 000, the vortex pair was observed to rebound from the free surface contrary to what one would expect for an inviscid flat boundary. When the surface was cleaned by draining away a portion of the contaminated surface water the amount of rebound was reduced. These changes in interaction are believed to be caused by the reduction in concentration of the surface active agent which, in turn, results in a reduced generation of secondary vorticity ahead of the vortex ring or pair before and during the interaction with the surface.

ISSN:0899-8213    

DOI:10.1063/1.857472

出版商:AIP    

年代:1989

数据来源: AIP