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  • Cambridge University Press  (12)
  • 1
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    Nonlinear mechanics of fluidization of beds of spherical particles (1987)
    Cambridge University Press
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    Publication Date: 1987-04-01
    Description: Experiments on fluidization with water of spherical particles falling against gravity in columns of rectangular cross section are described. All of them are dominated by inertial effects associated with wakes. Two local mechanisms are involved: drafting and kissing and tumbling into stable cross stream arrays. Drafting, kissing and tumbling are rearrangement mechanisms in which one sphere is captured in the wake of the other. The kissing spheres are aligned with the stream. The streamwise alignment is massively unstable and the kissing spheres tumble into more stable cross stream pairs of doublets which can aggregate into larger relatively stable horizontal arrays. Cross stream arrays in beds of spheres constrained to move in two dimensions are remarkable. These arrays may even coalesce into aggregations of close packed spheres separated by regions of clear water. A somewhat weaker form of cooperative motion of cross stream arrays of rising spheres is found in beds of square cross section where the spheres may move freely in three dimensions. Horizontal arrays rise where drafting spheres fall because of greater drag. Aggregation of spheres seems to be associated with relatively stable cooperative motions of horizontal arrays of spheres rising in their own wakes. © 1987, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 2
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    Two-fluid spin-up in a centrifuge (1978)
    Cambridge University Press
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    Publication Date: 1978-02-13
    Description: The behaviour of the interface between two immiscible fluids of different density and viscosity in a centrifuge is investigated both analytically and experimentally. The study includes the interfacial shape and behaviour during both steady and transient operation of the centrifuge. The interface shape is investigated for rigid-body rotation and during slow steady acceleration or deceleration of the centrifuge. The dependence of the interface shape on time is investigated during a rapid spin-up to a slightly different value of the angular velocity, which then remains constant. Some aspects of interface stability are also reported. © 1978, Cambridge University Press. All rights reserved.
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  • 3
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    The vortical flow above the drain-hole in a rotating vessel (1985)
    Cambridge University Press
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    Publication Date: 1985-06-01
    Description: The problem of slow draining of incompressible fluid from a rotating cylindrical vessel is considered. Transient effects, internal viscosity, boundary friction and finite cylindrical boundaries are included. In addition a tornado model formulated by Turner is solved and compared with some experiments on rotating turbulence of Hopfinger, Browand & Gagne. © 1985, Cambridge University Press. All rights reserved.
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  • 4
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    Microburst modelling and scaling (1992)
    Cambridge University Press
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    Publication Date: 1992-06-01
    Description: A microburst can be modelled by releasing a volume of fluid that is slightly heavier than the ambient fluid, allowing it to fall onto a horizontal surface. Vorticity develops on the sides of this parcel as it descends and causes it to roll up into a turbulent vortex ring which impinges on the ground. Such a model exhibits many of the features of naturally occurring microbursts which are a hazard to aviation. In this paper this model is achieved experimentally by releasing a volume of salt water into fresh water from a cylindrical dispenser. When care is taken with the release the spreading rate of the surface outflow is measurable and quite repeatable despite the fact that the flow is turbulent. An elementary numerical approximation to this model, based on in viscid vortex dynamics, has also been developed. A scaling law is proposed which allows experiments with different fluid densities to be compared with each other and with the numerical results. More importantly the scaling law allows us to compare the model results with real microbursts. © 1992, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Transition to turbulence in an elliptic vortex (1996)
    Cambridge University Press
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    Publication Date: 1996-01-25
    Description: Stability and transition to turbulence are studied in a simple incompressible two-dimensional bounded swirling flow with a rectangular planform - a vortex in a box. This flow is unstable to three-dimensional disturbances. The instability takes the form of counter-rotating swirls perpendicular to the axis which bend the vortex into a periodic wave. As these swirls grow in amplitude the primary vorticity is compressed into thin vortex layers. These develop secondary instabilities which roll up into vortex tubes. In this way the flow attains a turbulent state which is populated by intense elongated vortex tubes and weaker vortex layers which spiral around them. The flow was computed at two Reynolds numbers by spectral methods with up to 2563 resolution. At the higher Reynolds number broad three-dimensional shell-averaged energy spectra are found with nearly a decade of Kolmogorov k-5/3 law and small-scale isotropy.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Asynchronous whirl in a rotating cylinder partially filled with liquid (1985)
    Cambridge University Press
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    Publication Date: 1985-01-01
    Description: Experimental and analytical results are presented for the self-excited oscillations that occur in a partially filled centrifuge when centrifugal forces interact with shallow-water waves. Periodic and aperiodic modulations of the basic whirl phenomena are both observed and calculated. The surface waves are found to be hydraulic jumps, undular bores or solitary waves. © 1985, Cambridge University Press. All rights reserved.
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  • 7
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    Slow flow through stationary random beds and suspensions of spheres (1972)
    Cambridge University Press
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    Publication Date: 1972-01-25
    Description: Stokes flow through a random, moderately dense bed of spheres is treated by a generalization of Brinkman's (1947) method, which is applicable to both stationary beds and suspensions. For stationary beds, Darcy's law with a permeability result similar to Brinkman's is derived. For suspensions an effective viscosity μ/(1–2·60ψ) is found, where ψ is the volume fraction of spheres. Also, an expression for the settling velocity is derived. © 1972, Cambridge University Press. All rights reserved.
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  • 8
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    Turbulent pair dispersion and scalar diffusion (1981)
    Cambridge University Press
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    Publication Date: 1981-10-01
    Description: A method of treating turbulent pair dispersion and scalar diffusion is presented. Use is made of Kraichnan's form of Richardson's diffusion equation by relating the turbulent pair diffusivity to single-time Eulerian velocity statistics (which are presumed known) by means of a statistical independence hypothesis. In this procedure the diffusivity itself is coupled to solutions of the diffusivity equation in a self-consistent way. The method is applied to both two- and three-dimensional flow. In three-dimensional inertial-range and dissipative-range turbulence the turbulent pair diffusivity is determined and used to find the values of the coefficients of the scalar spectrum in the k- and k-1 ranges with good agreement with experiment. The Obukhov-Corrsin constant is found to be 049 and the Batchelor constant is. In two-dimensional turbulence the results are compared with constant-pressure balloon dispersion experiments. Results are also found for the rate of decay of scalar intensity in the special case where the initial scalar spectrum peaks in the inertial range. © 1981, Cambridge University Press. All rights reserved.
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  • 9
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    Area-varying waves on curved vortex tubes with application to vortex breakdown (1989)
    Cambridge University Press
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    Publication Date: 1989-03-01
    Description: Equations which modify those derived by Widnall & Bliss (1971) and Moore & Saffman (1972) are presented in which jet-like flow along the axis of a vortex tube interacts with the motion of the tube. The equations describe two major effects. The first is the propagation of axial waves along the vortex tube which is similar to the flow of shallow water. A local decrease in cross-section area of the vortex tube produces higher swirling velocity and lower pressure. The resulting axial pressure gradient causes a propagating wave of area and axial velocity in order to move fluid into the region of smaller area. The second effect is instability to helical disturbances when the jet-like axial velocity is high enough to overcome the stabilizing effect of the swirling motion. An elementary nonlinear theory of vortex breakdown is presented which has an analogy with the formation of bores in shallow-water theory. A numerical example shows the growth of a helical disturbance behind a vortex breakdown front.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    Oscillations of drops in zero gravity with weak viscous effects (1988)
    Cambridge University Press
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    Publication Date: 1988-09-01
    Description: Nonlinear oscillations and other motions of large axially symmetric liquid drops in zero gravity are studied numerically by a boundary-integral method. The effect of small viscosity is included in the computations by retaining first-order viscous terms in the normal stress boundary condition. This is accomplished by making use of a partial solution of the boundary-layer equations which describe the weak vortical surface layer. Small viscosity is found to have a relatively large effect on resonant-mode coupling phenomena. © 1988, Cambridge University Press. All rights reserved.
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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