Gas distribution in a deep granular bed injected by flat jets

The gas-flow distribution is examined for a set of identical equidistant flat jets entering a deep immobile or fluidized bed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 3, pp. 424–431, September, 1978.     

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.     

New aspects for friction coefficients of finite granular avalanche down a flat narrow reservoir

This work examines the bulk internal friction coefficient, \(\mu \), and effective wall friction coefficient, \(\mu _w\), for finite number of nearly identical dry glass spheres in avalanche down a narrow inclined reservoir of smooth frictional bed using a validated discrete element scheme. Instantaneous deviatoric strain rate tensor \(\dot{\gamma }^d_{ij}\) and stress tensor \(\tau _{ij}\) are computed locally to evaluate a three-dimensional constitutive model developed based on the rheology of steady homogeneous surface flows. On one side, the algebraic \(\mu -I\) relation conforms to conventional relation for glass beads, \(\mu =0.34+0.31/(1+0.15/I)\) (Jop et al. in J. Fluid Mech. 541:167–192, 2005, Midi in Eur. Phys. J. E 14:341–365, 2004, Jop in Comptes Rendus Phys. 16:62–72, 2015), when the inertial number \(I>I_{c}=2\times 10^{-2}\). The assumption of collinear \(\tau _{ij}\) and \(\dot{\gamma }^d_{ij}\), however, does not hold and such misalignment agrees to the findings in non-uniform inhomogeneous flows (Cortet et al. in Europhys. Lett. 88(1):14001, 2009). Below \(I_c\), we observe a decaying \(\mu -I\) as found in slowly deforming rheology tests and a simplified model is developed in view of shear-induced dilatation upon yielding. Non-constant effective wall friction coefficient is measured to grow in time and with I towards the sphere-wall sliding friction coefficient in the contact model while preserving the depth-weakening feature as in confined steady surface flows (Richard et al. in Phys. Rev. Lett. 101:248002, 2008, Brodu et al. in Phys. Rev. E 87:022202, 2013). The fact that rotation at one sphere center can divert surface relative velocity across the contact area to render lower sliding friction is considered to develop a model describing how \(\mu _w\) drops with the ratio between rotation-induced velocity and sliding velocity, \(\varOmega \). The simulation data compares fairly well to the predicted monotonic decay of \(\mu _w\) with \(\varOmega \).     

Valve effect in a granular bed

The appearance of a pronounced velocity-field nonuniformity beyond the granular bed has been established experimentally for the case in which a stream compresses the bed. This effect is absent in the opposite case, when the bed is made friable by a stream.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 3, pp. 389–393, March, 1978.     

Relaxation autooscillations of a granular bed

Instability and autooscillations of a fluidized bed having an empty space under the gas distributor plate are investigated experimentally. The results are used to test a theoretical model proposed earlier.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 1, pp. 45–49, January, 1977.     

Heat exchange in a ring granular bed

On the basis of a theoretical model of heat exchange in a granular bed, a simple dependence has been obtained for calculation of the heat-exchange coefficient in an extended ring bed. A comparison the dependence and the available experimental data has been made.     

Vibration-induced arching in a deep granular bed

Forced vertical vibration of a granular layer can drive flow phenomena such as heaping, convection, fluidization, densification, surface waves and arching. Food, mineral processing, and pharmaceuticals industries all utilize vibratory processes for the handling and transport of granular materials. Understanding how a granular material responds when subjected to vibration is essential for equipment design. Three-dimensional discrete element simulations have been used in this study to investigate the convective motion leading to arching in a vertically vibrated, deep granular bed. The undulating granular layer contains alternating regions that first compact and then relax. The dynamics of these regions may depend on material properties such as restitution and friction coefficients; as well as particle shape. The effects of these factors on the kinematics and dynamics of the arching pattern are investigated here. The arching pattern is found to arise from synchronised momentum transfer between the rise and fall of the deforming granular layer and horizontally travelling waves. The arching pattern was found to be stable across a broad range of restitution and friction levels and particle shapes. Particles with high restitution tend to disrupt the timing between the vertical and horizontal periodic flows and affect the stability of the pattern selection. Large friction results in shear resistance, higher bed pressures, lower bulk densities, and delays in the timing of the vertical and horizontal momentum transfer. Non-sphericity leads to increased dilation of the bed, slower sideways velocities, and increased loading on the floor and dissipation rate in the bed.     

Propagation of vibrations in a suspended granular bed

The influence of the elasticity and relative motion of the continuous medium on the hydrodynamics of a suspended vibrating bed is discussed. A solution is given for the boundary-value problem of small pressure disturbances propagating in the bed. The results are compared with experimental data and calculations based on existing models.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 2, pp. 188–197, February, 1988.     

Particles impacting on a granular bed

An asymptotic analysis is made to find the penetration depth and the stopping time for a particle impacting a granular bed. Newton’s equation is solved with a drag force with two terms, one term proportional to the square of the velocity and one term linear in the depth. The penetration depth is found to increase with the logarithm of the impact velocity, while the stopping time is found to decrease with the inverse of the square root of the logarithm of the impact velocity.     

Dynamic properties of a loose granular bed

A dynamic model of a loose granular medium is developed, and with its help the process of sudden arrest of the bed is studied. The model is compared with experiment.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 5, pp. 795–802, May, 1987.     

Vibrational fluidization of a shallow granular bed

A model is given for a vibrationally fluidized bed that incorporates the density reduction and allows one to calculate the pressure difference across the bed averaged over the period of oscillation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 3, pp.394–403, March, 1978.     

Thermal characteristics of a ventilated granular bed

The rate of heat removal by a gas current in a ventilated granular bed has been estimated and measured.     

Radiative heat transfer in a flat nonisothermal bed

A general formula is derived for the radiation flux impinging on the surface of the bed. The problem of self-radiation of a non-thick nonisothermal bed is solved, as well as the problem of self-radiation of a semi-infinite medium whose temperature remains constant everywhere except for a non-thick boundary layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 5, pp. 836–840, November, 1969.     

Nonsteady-state heat transfer in a high-temperature granular bed

Specific features of heat transfer in a high-temperature granular bed are studied based on a two-region model which takes into account the existence of an elevated porosity area.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 421–425, April, 1993.     

Wall gas-dynamic inhomogeneity in a fixed granular bed

The porosity variation in a granular bed near a wall has been used to calculate the gas profile there for spherical and other surface shapes. Sectioning in a fixed bed affects the uniformity in the gas distribution.Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 599–605, October, 1988.     

On free convection in a heat-releasing granular bed

Free convection in a heat-releasing granular bed for constant and exponential forms of heat release has been mathematically modeled on the basis of a two-temperature model. The extremum character of the dependence of the flow rate of the gaseous heat-transfer agent on the heat-release power and bed "choking" (cessation of the heat-transfer-agent filtration) for higher-than-average heat releases have been established. Dimensionless dependences for calculation of the flow rate of the heat-transfer agent and its outlet temperature in the region of stable convection have been obtained.     

Discharge of a turbulent jet in a monodisperse fluidized bed

The velocity of initial circulation is calculated and explanations are given for the mechanism of jet collapse and the existence of bubble and jet regimes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 6, pp. 913–918, December, 1982.     

Fluidization of a granular bed (theory)

On the basis of a simple physical model, it is shown that four basic mechanisms are possible for the conversion of a granular bed into the fluidized state in apparatuses of constant cross section. Conditions for the practical realization of these mechanisms are discussed as functions of bed parameters.