Peculiarities of air entrainment with a loose material flow at the variable aerodynamic resistance of falling particles

Abstract

Gravity flows of loose-matter particles are accompanied with aerodynamic forces that produce ejection of air in the loading and unloading chutes. A flow of loose matter acts like a blower. Head created by this blower (which we choose to call ejection head) comprises a sum total of aerodynamic forces of falling particles divided by cross-sectional area of the flow [1]. Flows of loose material in loading and unloading chutes that arise during operation of high-performance bucket elevators feature elevated volumetric concentrations as high as β0.01y. Estimates of air ejection caused by such flows should be based upon instantaneous rather than averaged aerodynamic drag coefficient ψy. Within the range of significant volumetric concentrations, varying volumetric concentration of falling particles leads to fluctuations in instantaneous values of the coefficient ψ. These fluctuations cause the ejection head, even in the case of short chutes, to significantly diverge from the head determined using averaged coefficient ψy. In order to compute ejection heads inside loading and unloading chutes, it is necessary to introduce an adjustment coefficient K (K is the ratio of the true value of ejection head in an inclined chute to the mean value of this pressure ) the value of which will noticeably diverge from one at small initial velocities of particle flow. It is possible to view flows of particles in chutes at 0.1В(B is the ratio of the average coefficient of drag encountered by a falling particle to the drag coefficient of an individual particle in the self-similarity area) as blowers with a performance curve determined with formula 330113ekkQQpQKznSvSv(Q is the volumetric flow rate of air ejected through the loading chute of the elevator, z is a relative velocity of particles in a pipe, defined as the difference vu,v is the velocity of falling particles, u is the velocity of ejected air, ,nkvvis the fall velocity of particles at outlet of the chute, /nknvv, S is the cross-sectional area of the chute) in view of the resulting coefficient 0K(0K is the ratio K absent ejection airflow). 636 For a flow of wheat (3ed mm) within the ranges 0.5nand β0.001y, increasing drag coefficient along the fall height is only able to produce negligibly small changes in the intensity of ejection head. The adjustment coefficient may be dispensed with (01KK), and head value will then be determined using formula 333τψε1φφ23ymmkeyKnGvPSa (.mGis mass flow rate of the material, τa is the acceleration which, for chutes installed at an angle to horizontal surface,ε is the ratio of air density to particle density, φ is ejection coefficient)

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