Discharge of a gas jet into a stationary bed of granular material

An experimental study is made of the discharge of a gas jet into a stationary bed of granular material. The physical pattern of development of the jet is established and an approximate method is developed for calculating the dimensions of the gas tongue.     

Dynamics of a gas bubble rising through a thin immersed layer of granular material: an experimental study

 Packings of non-cohesive grains, immersed in a fluid, differ significantly from classical porous media as the grains, subjected to stresses and flows, can move within the sample, changing then the local properties of the material. We study experimentally the conditions for a gas to pass through a layer of immersed granular material. Above a threshold pressure, which depends mainly on the grains size and on the surface free energy of the liquid-gas interface, the gas creates a channel within the whole thickness of the layer. Received: 23 January 2002     

Depth of penetration of solid particles injected into a gas flow

The depth of penetration of a spherical particle into a uniform transverse flow was determined experimentally and theoretically for both a continuous medium and a free molecule flow.Translated from Inhenerno-Fizicheskii Zhurnal, Vol. 40, No. 6, pp. 993–996, June, 1981.     

Distribution of gas streams in neighborhood of a plane jet in a high granular layer

Formulation of problems about the flow generated by jets in a fixed or fluidized granular bed is discussed. The solution of such a problem is considered for a single plane jet in a high layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 4, pp. 586–595, October, 1977.     

Deflection of a jet injected into a stream

A solution is given for the deflection of the axis of two-dimensional and circular jets by an entraining stream. Design formulas are obtained and compared with experiment.     

Compression and shear of a layer of granular material

A classical problem in metal plasticity is the compression of a block of material between rigid platens. The corresponding problem for a layer of granular material that conforms to the Coulomb-Mohr yield condition and the double-shearing theory for the velocity field has also been solved. A layer of granular material between rough rigid plates that is subjected to both compression and shearing forces is considered. Analytical solutions are obtained for the stress and velocity fields in the layer. The known solutions for steady simple shear and pure compression are recovered as special cases. Yield loads are determined for combined compression and shear in the case of Coulomb friction boundary conditions. Numerical results which describe the stress and velocity fields in terms of the normal and shear forces on the layer at yield are presented for the case in which the surfaces of the platens are perfectly rough. Post-yield behaviour is briefly considered.     

Compression and shear of a layer of granular material

A classical problem in metal plasticity is the compression of a block of material between rigid platens. The corresponding problem for a layer of granular material that conforms to the Coulomb-Mohr yield condition and the double-shearing theory for the velocity field has also been solved. A layer of granular material between rough rigid plates that is subjected to both compression and shearing forces is considered. Analytical solutions are obtained for the stress and velocity fields in the layer. The known solutions for steady simple shear and pure compression are recovered as special cases. Yield loads are determined for combined compression and shear in the case of Coulomb friction boundary conditions. Numerical results which describe the stress and velocity fields in terms of the normal and shear forces on the layer at yield are presented for the case in which the surfaces of the platens are perfectly rough. Post-yield behaviour is briefly considered.     

The resistance of a dense moving layer through which a gas stream is injected from below

For a tall and narrow vessel with an opening in the bottom — through which granular material is discharged under conditions of a gas countercurrent — we have experimentally confirmed the equality of the resistance factors for a moving and a nonmoving layer. We have established the practical equality for the porosity of a dense layer — at the threshold of fluidization — and the porosity of a moving bed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 3, pp. 423–428, March, 1969.     

Characteristics of the motion and distribution of the solid phase in a jet discharging into a fluidized bed

A model of the motion of the solid phase from the bed into a jet is proposed. A method for calculating the velocity field and solid-particle concentration field in the volume of the jet is developed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 3, pp. 436–443, September, 1986.     

Motion of a granular material discharging through an orifice

An experimental investigation is presented concerning particle motion in a column of granular material. The effect of gas flow on the motion of material discharging through an orifice is studied.     

Distribution of the disperse fraction of an injected polydisperse jet in a gas flow

The distribution of a polydisperse droplet jet over a gas flow is theoretically investigated. Results are given for specific nozzles.     

The radial spreading as a free surface layer of a vertical buoyant jet

Summary When the rising plume in a stagnant ambient fluid impinges the free surface it spreads radially as a surface layer flowing over a pool of heavier liquid. Initially the surface layer in the entrainment zone entrains the underlying fluid, but the entrainment decreases with the increasing distance from the boil. The radius of the entrainment zone depends on the initial buoyancy flux from the nozzle and also on submergence height. It was assumed that the flow in this zone has a self-preserving form. The theoretical results based upon this assumption showed that the maximum velocity and density difference of the layer decreases as powers of radius distance measured from centre of the boil and the depth varies linearly with the radius, so that the sectional Richardon's number based on maximum physical quantities of the section remain unchanged. It was further shown that the coefficient of the entrainment remains constant and is a function of the Richardson's number and the slope of the interface. The theoretical results were compared with those obtained experimentally and fair agreement was obtained.At the end of the entrainment zone the surface layer enters the zone of homogeneous flow in which the layer travels over the underlying fluid and behaves much like a free homogeneous flow over a rigid boundary: the friction at the interface replacing the friction of the boundary. In this zone the mean velocity of the layer in the radial direction was measured and found that it decreases inversely with the increase of radius. The thickness of the layer in the zone of homogeneous flow remains constant and depends, as far as experiments show, greatly on the submergence height.     

Self-excitation of oscillatory processes when a liquid is injected into a plasma jet

The process of cooling of a wall by a liquid injected into a plasma jet through a circular opening is studied experimentally. Different flow regimes in a vaporliquid system, including self-excited oscillatory regimes associated with the transfer of the region of boiling from the exterior side of the wall into the interior cavity of the casing, were obtained. Self-excited oscillations of the wall temperature are described with the help of approximation formulas.Translated from Inzherno-fizicheskii zhurnal, Vol. 61, No. 4, pp. 650–655, October, 1991.     

The propagation of elastic waves through a textured granular material

When an ultrasonic wave passes through a block of metal, the wave is attenuated, i.e. its amplitude decreases with distance. The principal cause of this attenuation is believed to be scattering of the wave at the grain boundaries. Since neighbouring grains will in general have different crystallographic orientations and the velocity of sound depends on the orientation, a proportion of the wave will be lost due to reflection and mode conversion at each grain boundary. This problem was first tackled by Lifshitz and Parkhomovski [1], who considered the problem of a cast material which has equiaxed grains with no preferred orientation. They also assumed that the anisotropy within a single grain is small and they obtained expressions for the attenuation of longitudinal and shear waves. Their results have subsequently been shown to be a useful approximation even for the case of steels where the anisotropy within a grain is not small. Many metals which have been worked in some way, e.g. forging or welding, exhibit a textured structure in which the grains may on average be elongated in a particular direction or there may be a preferred crystallographic orientation, or both. In this case the bulk metal will no longer be isotropic, and the results of Lifshitz and Parkhomovski will not apply. In this paper we show how the approach used by Lifshitz and Parkhomovski may be modified to tackle such problems. General results for the attenuation are presented in terms of averages over the particular distribution of orientations. Detailed results are presented for a particular distribution which is a representation of austenitic weld metal.     

Transfer processes when the surface material of a body and an injected material react with a laminar boundary layer

The article constitutes an analytical investigation of an unsteady (due to a change in the boundary of the porous body) laminar boundary layer. There is a chemical reaction (for infinitely large rates of heterogeneous and homogeneous reactions) between the wall surface material together with the injected material and a coolant contained in the external flow. For the particular case Pr=Sc_i=1, a solution in closed form is obtained for problem (31)-(32).     

Growth of a bubble of noncondensing gas injected into a liquid

The solution of the problem of growth of a gas-vapor bubble injected into a liquid is obtained. The growth of the bubble depends on mass transfer in the gas phase and heat transfer in the liquid phase. Experimental and theoretical data are compared.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 6, pp. 978–989, June, 1977.     

Temperature field through a layer of heat-generating granular packing in a pipe

The radial temperature profiles and their stability conditions were investigated for a layer of granular packing through which heat was being generated in a length of pipe.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 2, pp. 265–270, August, 1971.     

Structure of flow through an immovable granular layer

A solution of the problem of flow through an immovable granular layer is presented. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 390–393, May–June, 1997.     

Temperature field and dynamics of a vertical gas jet in a fluidized bed

Experimental results are presented on the determination of the range of a jet and the boundaries of temperature variation of a fluidized bed in its vicinity.