摘要:

The results of numerical simulations of the lattice‐Boltzmann equation in three‐dimensional porous geometries constructed by the random positioning of penetrable spheres of equal radii are presented. Numerical calculations of the permeability are compared with previously established rigorous variational upper bounds. The numerical calculations approach the variational bounds from below at low solid fractions and are always within one order of magnitude of the best upper bound at high solid fractions ranging up to 0.98. At solid fractions less than 0.2 the calculated permeabilities compare well with the predictions of Brinkman’s effective‐medium theory, whereas at higher solid fractions a good fit is obtained with a Kozeny–Carman equation.

ISSN:0899-8213    

DOI:10.1063/1.857793

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The equations of motion for perturbed uniformly rotating flows with uniform axial‐time periodic strain, are derived from the Navier–Stokes equations in the low Mach number limit. The perturbation equations admit exponentially growing three‐dimensional solutions for which the amplification factors per period are computed for a range of compression and swirl ratios. It is found that for a given compression ratio, the flow is stable for low swirl ratios, but at high swirl ratios the flow is unstable with the amplification factor dependent on wave angle but independent of wavelength. For an unstable swirl ratio, higher compression ratios yield larger amplification factors.

ISSN:0899-8213    

DOI:10.1063/1.857794

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Shaqfeh and Fredrickson [Phys. Fluids A2, 7 (1990)] renormalized the multiple reflection expansion for hydrodynamic fiber interactions in a semidilute suspension,nl3≫1 and &fgr;≪1, where &fgr; is the fiber volume fraction,nis the number of fibers per unit volume, andlis the fiber half‐length. We use the results of Shaqfeh and Fredrickson to obtain the average rotation rate of a fiber in linear shear flows of a semidilute suspension. Specific results are obtained for the case where most of the fibers are oriented in a preferred direction, as occurs in simple shear and extensional flows. The correction to theO(&ggr;˚) Jeffrey rotation rate [Proc. R. Soc. London Ser. A102, 161 (1922); J. Fluid Mech.14, 284 (1962)] due to hydrodynamic interactions is shown to beO[&ggr;˚/ln(1/&fgr;)], where &ggr;˚ is the shear rate.

ISSN:0899-8213    

DOI:10.1063/1.857795

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The evolution of the shape of an initially nonspherical drop translating at low Reynolds number through a quiescent fluid is investigated experimentally. It is found that the drop reverts to a spherical shape when the degree of initial deformation is small enough. However, drops that are highly deformed initially are shown to deform continuously. Specifically, a prolate drop breaks up into multiple droplets as it rises, while an oblate drop deforms into a double‐emulsion drop as it translates. The experimental results agree well with results obtained earlier from numerical simulations [Phys. Fluids A1, 1309 (1989)].

ISSN:0899-8213    

DOI:10.1063/1.857796

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A study has been carried out on some of the influences of particle shape and orientation on the drag, lift, and heat transfer characteristics of nonspherical particles at intermediate Reynolds numbers, 10≤Re≤66. The geometry that has been employed in the investigation has been an ellipsoid of revolution with variation in angle of attack, and the aspect ratio (ratio of the major to the minor axis) has been varied by a factor of 3. The method of solution consists of a second‐order, finite volume formulation of the Navier–Stokes equations, which is capable of being extended to time‐dependent and variable density low Mach number flows. For relatively small increases in the ratio of major to minor axis the behavior of the pressure and skin friction distributions becomes substantially different in both qualitative and quantitative ways. The skin friction distribution as well as the heat flux to the particle surface exhibit a maxima near the major axis of the ellipsoid regardless of orientation, and the total friction drag and the total particle heat transfer exhibit a strong correlation. The total drag coefficient and the lift coefficient behave in a much different manner and they are strongly influenced by the Reynolds number, aspect ratio, and angle of attack. It appears that the total drag and lift force depend strongly on the particle shape, and it appears difficult to develop simple correlation schemes. The numerical methods that have been used performed well and they will be extended to more complex problems in the future.

ISSN:0899-8213    

DOI:10.1063/1.857797

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The quasistatic thermocapillary motion of a compound drop in an unbounded fluid possessing a uniform temperature gradient is analyzed. For completeness, gravitational effects are included in the treatment. The general model is formulated, and the equations for the concentric case are solved using spherical polar coordinates, while the eccentric case is handled using bispherical coordinates. Results are given for the velocity of the drop as well as that of the droplet with respect to the drop, along with useful approximations. Illustrative results are presented graphically for the thermocapillary migration of a compound drop in the special case when the droplet is a gas bubble. In addition to the velocities of the drop and the bubble, representative isotherms and streamlines also are presented which display interesting qualitative features.

ISSN:0899-8213    

DOI:10.1063/1.857798

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The convective instability of a viscous liquid jet emanating into a inviscid gas with a swirl is investigated. Contrary to the known case of a swirling liquid jet in a quiescent gas, the swirl in the ambient gas is shown to have a stabilizing effect. The inertia force in the gas is shown to play dual roles of both stabilization and destabilization. The gas inertia associated with the swirl has a stabilizing influence, but that associated with the interfacial pressure fluctuation has a destabilizing effect. A physical explanation of the mechanism of stabilization by the gas swirl is given.

ISSN:0899-8213    

DOI:10.1063/1.857799

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

An array of flush‐mounted hot film probes has been used to measure the local shear stress reduction as a result of microbubble injection over an axisymmetric body at the four discrete, free‐stream speeds of 4.6, 10.7, 13.2, and 16.8 m/sec. Visualization of the bubble flow pattern supplement these results at intermediate free‐stream speeds. At speeds of 10.7 m/sec and above, a circumferential gradient in skin friction, with skin friction reduction larger at the top than at the bottom of the model occurs at some distance downstream of injection. For these speeds, the gradient is stronger at the lower speeds and higher gas injection conditions. Higher speeds tend to drive the axial location of the gradient farther from the injection location. At speeds below 10.7 m/sec, the flow is dominated by a double vortex structure that entrains the bubbles at the bottom and sides of the model and transports them to the top. At sufficiently high gas flow rates a cavity, large enough to be observed visually, is formed just upstream of the vortices, centered near the body midline. The axial position of the cavity is roughly independent of flow speed and gas flow conditions. The transport of bubbles by the vortices, to the top of the body, is the cause of the poor skin friction reduction performance of microbubble injection at low speeds on an axisymmetric shape. Integration of the current local skin friction results gives good agreement with earlier drag balance measurements. The persistence of the drag reduction phenomenon with axial distance as well as the statistics of the shear stress fluctuations are quite similar to what was observed earlier on flat plates.

ISSN:0899-8213    

DOI:10.1063/1.857800

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly [Phys. Rev. Lett.60, 700 (1988)]. The critical Reynolds numbers calculated from linear stability theory agree with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: (1) a truncated Fourier series representation in time and (2) a fundamental solution matrix based on a Chebyshev‐pseudospectral representation in space. For large‐amplitude, low‐frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent interval followed by rapid change in the perturbed flow velocities.

ISSN:0899-8213    

DOI:10.1063/1.857801

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Direct numerical simulations of two‐dimensional high Rayleigh (Ra) number, base‐heated thermal convection in large aspect‐ratio boxes are presented for infinite Prandtl number fluids, as applied to the Earth’s mantle. A transition is characterized in the flow structures in the neighborhood of Ra between 107and 108. These high Ra flows consist of large‐scale cells with strong intermittent, boundary‐layer instabilities. For Ra exceeding 107it is found that the heat‐transfer mechanism changes from one characterized by mushroom‐like plumes to one consisting of disconnected ascending instabilities, which do not carry with them all the thermal anomaly from the bottom boundary layer. Plume–plume collisions become much more prominent in high Ra situations and have a tendency of generating a pulse‐like behavior in the fixed plume. This type of instability represents a distinct mode of heat transfer in the hard turbulent regime. Predictions of this model can be used to address certain issues concerning the mode of time‐dependent convection in the Earth’s mantle.

ISSN:0899-8213    

DOI:10.1063/1.857802

出版商:AIP    

年代:1990

数据来源: AIP