Rectangular Hopper Research Articles

Flapper Feed Device for Improved Productivity of Cassava Grater

A modified hopper design of the conventional cassava grater and its concomitant productivity improvement is presented. One of the sides of the inverted truncated rectangular pyramidal hopper was hinged at the lower end and swung through angle of 15 to 30 degrees. This flapper swing served as feed for the rotary grater. The flapper allowed the cassava tubers to be fed over a larger grater surface area permitting cassava feed over an angle of 120 degrees instead of the usual 90 degrees. It further allowed the variation of the space between the rotary grater and the hopper thereby enhancing complete maceration of the tubers. The presence of ungrated cassava chips in the macerated mash common feature with conventional graters was reduced to negligible proportions. A process improvement of up to 100 per cent in thru-put was obtained compared with the conventional graters.

Flow of sphero-disc particles in rectangular hoppers—a DEM and experimental comparison in 3D

Flows of “sphero-disc” granular particles in a rectangular hopper are studied both experimentally using high-speed video recording and mathematically using the discrete element method (DEM). The flow behaviour of particles and their arching and discharging in the hopper are analysed and compared with the DEM results for three hopper openings. In general, good agreement is shown on particle static packing, the flow behaviour and hopper discharging rates and the arching effect when flow ceases due to an inadequate hopper outlet opening. Spherical particles with a similar volume to the disc-like particles are also tested and compared and a clear effect of particle shape on flow rates is shown. Although some minor discrepancies are shown, these are likely to be caused by the practical difficulties in matching the exact particle parameters between the simulations and the experiments. The DEM is shown to be a powerful tool to analyse the interactions between irregularly shaped particles and demonstrates a great potential in analysing detailed particle packing structure and flow patterns, which may lead to the elaboration of a novel method for hopper design. Further work will focus on developing DEM to model a wider range of particle shapes and hopper geometries, use of DEM for flow and structure analysis, and the development of more sophisticated measuring tools such as tomography to validate the DEM model.

粉体シミュレーション その課題とブレークスルー Ｓｍｏｏｔｈｅｄ Ｐａｒｔｉｃｌｅ（Ｓ．Ｐ．）法を用いた流動粉体層の数値解析と実験値による検証

The numerical simulation of the velocity and stress fields for a flowing powder which consists of uncountablly numerous particles is one of the most difficult things to do. We have numerically simulated these fields of flowing powder using the Smoothed Particle (S. P.) method based on the relationships of the stress-strain rates obtained by D. E. M.. In the S. P. method, the partial differential equations, which are the governing equations of the flow fields, are transformed to ordinary differential equations which are Lagrangian-type equations of particle motions. The numerical analysis of ordinary differential equations is much easier than that of partial differential equations. Moreover, Lagrangian analysis is suitable for the description of the characteristics of discrete particles.The calculated results of the velocity and stress fields in a two-dimensional rectangular hopper are compared with the measured values obtained under nearly the same conditions, and a fairly good agreement among them is obtained. These results show that the S. P. method is an effective tool to simulate the various flow fields of powders which consist of uncountably numberous particles.

Numerical simulation for blockage of cohesive particles in a hopper using the distinct element method and its correlation with experimental results of real cohesive granular materials

We numerically simulated the blockage phenomena in the three-dimensional rectangular hopper using the distinct element method (DEM) in which the effects of cohesion forces between particles were taken into account. We also measured the critical blockage states using four different cohesive granular materials, i.e. talc, calcium carbonate, flyash and corn starch. The calculated results describe well the blockage, which is greatly affected by the cohesion force. The mass discharge rate decreases and its relative fluctuation increases with an increase of the cohesion force. The normal and shear stresses on the wall increase with an increase of the cohesion force. We found the critical blockage states by calculation and experiment under the various conditions, and calculated the blockage state diagram using the dimensionless numbers based on the properties which affect the blockage phenomena. The calculated and experimental critical blockage states are described by the same straight line (the critical blockage state line). The results of this study make it possible to predict the critical conditions under which the blockage occurs.

Three-dimensional numerical simulation of the motion of particles discharging from a rectangular hopper using distinct element method and comparison with experimental data (effects of time steps and material properties)

The distinct element method (DEM) is a simple numerical model which is capable of describing the motion of granular materials. In this study, the motion of particles discharging from a rectangular hopper has been numerically simulated by the DEM whose time steps are Δ t = 10 −6, 10 −5 and 10 −4s, which correspond to stiffness k n = 7.0 × 10 7, 7.0 × 10 5 and 7.0 × 10 3 N/m, respectively. The calculated results have been compared with the experimental data. All of the calculated results not only qualitatively describe the experimental results, but also approximately describe the quantitative characteristics of the measured data, although the stiffness of the calculations is greatly different from the real stiffness of the materials. However, the calculated result of the DEM using the smallest time step (Δ t = 10 −6s) could not give the best description of the experimental data. This suggests that the calculated results of the DEM could not accurately describe the real granular flow even if the time step is small enough to use the real stiffness of the materials. The most significant approximation of the DEM is that distinct particles do not interact with any other particles and displace independently from one another during one calculation time step. The discrepancy between the model based on this approximation and the real granular flow would not decrease as the time step is decreased.

ホッパーの流量特性に関する研究 案内板を用いたホッパーの流量特性

The maximum flow rate of hoppers that are widely used for feeding powder is depend on the area of the discharge opening at the bottom of the hopper.The way of increasing the flow rate without changing the area of the discharge opening has been studied, and it is confirmed that the flow rate increases by about 60% by attaching a cylinder to the inside of a conical hopper.The author succeeded in increasing the flow rate by 120% by adapting the fundamentals of the cylinder. This is a rectangular hopper to the inside of which two pairs of vertical plates, called “guide plate, ” are attached.This paper describes the flow characteristics of a model hopper using guide plates, and indicates its mechanism.