No abstract

Vortex units are commonly considered for various single and multiphase applications due to their process intensification capabilities. The transition from gas-only flow to gas-solid flow remains largely unexplored nonetheless. During this transition, primary flow phenomenon, jets, and secondary flow phenomena, counterflow and backflow, are substantially reduced, before a rotating solids bed is established.This transitional flow regime is referred to as the vortex suppression regime. In the present work, this flow transition is identified and validated through experimental and computational studies in two vortex units with a scale differing by a factor of 2, using spherical aluminum and alumina particles. This experimental data supports the proposed theoretical particle monolayer solids loading that allows estimation of vortex suppression regime solids capacity for any vortex unit. It is shown that the vortex suppression regime is established at a solids loading theoretically corresponding to a monolayer being formed in the unit for 1g-Geldart D-and 1g-Geldart B-type particles. The model closely agrees with experimental vortex suppression range for both aluminum and alumina particles. The model, as well as the experimental data, shows that the flow suppression regime depends on unit dimensions, particle diameter, and particle density but is independent of gas flow rate.This combined study, based on experimental and computational data and on a theoretical model, reveals the vortex suppression to be one of the basic operational parameters to study flow in a vortex unit and that a simple monolayer model allows to estimate the needed solids loading for any vortex device to induce this flow transition. K E Y W O R D Sgas-solid vortex reactor, gas-solid vortex units, monolayer model, process intensification, vortex suppression regime Abbreviations: GSVR, gas-solid vortex reactor; GSVU, gas-solid vortex unit; GVU, gasvortex unit; HDPE, high density polyethylene.

The kinematic theory of axisymmetric dynamos in the accretion disk of a rotating black hole differs in some important aspects from the nonrelativistic formulation; the gravitomagnetic potential couples the equations of the magnetic flux and current, rendering invalid the argument used in the proof of Cowling's antidynamo theorem. We prove that in this case no similar theorem may exist by showing that a sharp gradient in the angular velocity of the disk may cause a dynamo effect localized near the equatorial plane. [S0031-9007(97)03760-5] PACS numbers: 97.60. Lf, 95.30.Qd, 97.10.Gz When the motions of a conducting fluid are able to sustain or increase a magnetic field, it is said that a dynamo is present. For a number of simple geometries the induction equation alone is sufficient to prove that no dynamo is possible; the most famous of such antidynamo theorems, due to Cowling [1,2] shows that axisymmetric flows cannot sustain axisymmetric fields. The essence of the proof is that the poloidal field (i.e., the component lying in planes which contain the rotation axis) may have its field lines twisted by differential rotation and thus feed the toroidal (parallel to the equatorial plane) field, but no feedback from the toroidal to the poloidal field is possible. In the end the poloidal field vanishes, and deprived of its source term, the toroidal field decays too. The situation is different in a relativistic setting. A black hole's rotation stretches both magnetic and electric fields, thus being in principle able to feed poloidal field from the toroidal one. The early numerical studies of Khanna and Camenzind [3,4] seemed to show the existence of axisymmetric dynamo action, but the calculations were shown to be flawed by Brandenburg [5], and later work by Khanna, although highly interesting, has failed to confirm the existence of a working dynamo, and indeed, some partial antidynamo theorems exist [6]. We will see, however, that for some not unreasonable parameters there exist growing solutions of the induction equation, and therefore no general antidynamo theorem is to be expected. More realistic dynamos must take into account the constraints imposed upon the accretion disk velocity by some physical model. We must remember that we are dealing with kinematic dynamos only; i.e., we neglect the feedback of the magnetic field upon the fluid velocity through the Lorentz force. The axisymmetric induction equations, when posed in the Kerr metric and Boyer-Lindquist coordinates ͑t, r, u, f͒, have the form [4,6]where the meaning of the magnitudes is as follows: let M be the mass of the hole, J its momentum, a J͞M, D r 2 2 2Mr 1 a 2 , r 2 r 2 1 a 2 cos 2 u, S 2 ͑r 2 1 a 2 ͒ 2 2 a 2 D sin 2 u. Then R ͑S͞r͒ sin u, a g ͑r͞S͒ p D, v 2aMr͞S 2 , g p 1 2 y 2 (setting G c 1), h is the magnetic diffusivity, V the angular velocity of the accretion disk as measured by a global Boyer-Lindquist observer [hence y f R͑V 2 v͒͞a g , e f the basis vector ͑1͞R͒≠͞≠f], v p the poloidal component of the velocity, C the poloidal flux, and T the ...

The equations of magnetohydrodynamics of partially ionized plasmas have been known for a long time, but rarely studied. Instead, several simplifications have been applied to different physical models, ranging from magnetic reconnection to ambipolar drift. The original system relates the electric field to kinetic magnitudes by means of a non-local law, so that the equations describing it involve partial differentials as well as functional operators. We prove a theorem of existence and uniqueness of solutions for a finite time by means of a fixed point argument in an appropriate functional setting.

It is shown that wave conversion between fast and slow magnetosonic waves in the zone where the sound and Alfvén velocities coincide has a smoothing effect; unless the coming fast wave transfers entirely to a slow one, or vice versa, any incoming shock will emerge as two continuous waves. This is due to averaging between the Fourier modes of the outgoing waves.