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.     

Dynamical arching in a two dimensional granular flow

A study of grains flow in a two dimensional hopper using particle tracking and photoelastic methods is presented in this article. An intermittent network of contact forces consisting of force chains and arches is observed. This network is responsible for fluctuations in the average vertical velocity. The magnitude of these fluctuations depends on the hopper’s geometry, and it quickly reduces for large aperture size and small inclination angles. The average velocity field is described using a combination of harmonic angular functions and a power law of radial position. The mass flow rate is determined through the average velocity field and a Beverloo type scaling is obtained. We found that the effect of the inclination angle on the mass flow rate is given by ${\alpha/ \,(\sin\alpha)^{3/2}}$ . It is also found that the critical aperture size, approaching jamming, depends linearly on ${\sin\alpha}$ . At small D/d, the time average of the network of contact forces shows a boundary with characteristics resembling the free fall arch. We show that an arch can be built following the principal compression orientation of the stress tensor which captures the characteristics of the arches observed experimentally.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Instability in a granular bed fluidized by a gas flow

Stability in fluidization is considered in an approach in which the granular bed is considered as a structureless element with a definite working response, and the boundary to the stability region in parameter space is examined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 3, pp. 410–417, September, 1976.     

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.     

Statistical characteristics of convective exchange in a stationary granular bed

A statistical investigation of local coefficients of convective exchange in a stationary granular bed is made in the range of Re_e = 30–800.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 2, pp. 194–198, August, 1986.     

Heating rate in a dense bed of wet granular material

Measurements are reported on the heat transfer in a bed of wet granular material during drying.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No.1, pp.123–125, July, 1976.     

Periodic processes in localized gas injection into a granular bed

Physical principles are used in formulating conditions for occurrence of acoustic and relaxation oscillations in a bed of granular material in the presence of localized gas injection.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 1, pp. 94–101, January, 1979.     

A flat jet in a granular bed of finite height

The distribution of gas flows in the vicinity of the jet is discussed and the conditions of disruption of the static equilibrium of the bed, the formation and growth of a cavity, and the jet breakthrough of the bed are investigated qualitatively.Notation a, b functions calculated in [11] - C, C constants in (7) - F derivative of the complex potential - f function in (6) - G function defined in (19) - H dimensionless height of bed - h height of cavity - k coefficient introduced in (15) - p, po pressure inside bed and in cavity - p dimensionless pressure drop - Q, q dimensional and dimensionless jet flow rates - q₁, q₂ critical values - T dimensionless height of cavity - T₀, T₁ T₁, T₂ characteristic values of T - u,v filtration velocities - u, u_* initial filtration velocity in the bed and minimum fluidization velocity - u_o velocity scale introduced in (14) - u * velocity scale introduced in (14) - u* velocity of fictitious flow defined in (15) - U complex velocity - Z=X+iY, z=x+iy dimensionless coordinates - z=x+iy dimensional coordinates - coefficient of hydraulic resistance - parameter from (5) - specific weight of particles' material - porosity - =+i coordinates in the plane obtained from z=x+iy as a result a of conformai transformation - _m value of giving a minimum of the function G - f complex and real flow potentials - angle of internal friction - stream function - angle of inclination of boundaries of the region of plastic flow to the vertical Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 804–812, November, 1979.