Modelling chute delivery of grains in a food-sorting process
Modelling chute delivery of grains in a food-sorting process
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对食品分选过程中谷物的滑槽输送进行建模
DOI：
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发表时间：
2007
期刊：
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通讯作者：
A. Ellis
中科院分区：
文献类型：
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作者：
A. Ellis
整个论文的动机是一个特殊的问题，从食品分拣行业的粮食，典型的大米，流下来的斜槽。当它们落在斜槽中时，颗粒形成快速移动的单层。该项目从一个离散模型开始，在没有空气阻力的情况下，基于颗粒动力学处理单个颗粒。首先讨论单个颗粒，然后讨论多个颗粒，所使用的方法包括描述粒子路径、速度和其他关键特征的大型计算以及分析。此后，论文的大部分内容都是关于谷物斜槽流的连续模型的发展，灵感来自于上述计算中看到的集群和空洞，并基于与Lighthill-Whitham交通流模型的类比。这里的关键区别在于，流动不是单向的，因此需要多值流动-密度关系。引入这一定律后，流体的流动行为变得复杂而丰富。数学兴趣是在解决双曲和抛物偏微分方程，将冲击和风扇的解析和数值解的控制方程，在渐近方法中使用的分析特别限制，特别是那些有关的碰撞或分离的谷物，并在寻求稳态解决方案的密度分布。最后，研究了空气的影响。特别是，在晶粒之间的间隙中的局部粘性或非粘性的影响进行了研究，随后的许多晶粒上的相互作用的影响。
The whole of the thesis is motivated by a particular problem from the food-sorting industry in which grains of food, typically rice, flow down chutes. As they fall down the chute, the grains form a rapidly moving mono-layer. This project starts with a discrete model treating individual grains based on partcle dynamics without air resistance. Single grains and then many grains are addressed, and the methodology used includes large computations describing the particle paths, velocities and other key features accompanied by analysis. Much of the thesis thereafter is concerned with the development of a continuum model for the chute flow of grains, inspired by the clusters and voids seen in the above computations and based on analogies with the Lighthill-Whitham model of traffic flow. The crucial difference here is that the flow is not uni-directional and so a multi-valued flow-density relation is required. The introduction of such a law yields complex and rich flow behaviours. The mathematical interest is in solving hyperbolic and parabolic partial differential equations, incorporating shocks and fans into analytical and numerical solutions of the governing equation, in asymptotic methods used in analysis of particular limits, especially those relating to clashing or separation of grains, and in seeking steady state solutions for the density profile. Finally, air effects are studied. In particular, local viscous or inviscid effects in the gaps between grains are investigated, followed by the subsequent interaction effects on many grains.