A FLUID MECHANICAL DESCRIPTION OF FLUIDIZED BEDS
A FLUID MECHANICAL DESCRIPTION OF FLUIDIZED BEDS
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DOI：
10.1021/i160024a007
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发表时间：
1967-01-01
期刊：
影响因子：
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通讯作者：
JACKSON, R
中科院分区：
文献类型：
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作者：
ANDERSON, TB;JACKSON, R
原则上，悬浮在流体中的粒子系统的运动完全由流体的每一点满足的纳维-斯托克斯方程和每个粒子满足的牛顿运动方程决定。然而，当所关心的系统包括大量密集分布的颗粒时，如在流化床中，这个问题太复杂了，不能用这些术语直接求解，为了实际的目的，有必要寻求某种简化的方法，使它可以用相对较少的偏微分方程来描述。目前，文献包含几种尝试（Hinze，1962;杰克逊，1963; Murray，1965; Pigford和Baron，1965; Soo，1963;货车Deemter和货车der Laan，1961）以这种方式简化问题，所有这些都取代了点力学和流体力学变量，这些变量在与颗粒间距相当的尺度上迅速变化，通过在与粒子间距相比大但与整个系统相比小的区域上平均而获得的平滑变量。由此产生的方程，因此，描述了运动的流体和粒子，好像他们是相互渗透的连续。一个完整的解决方案的基本力学和流体力学方程将确定的数量，如流体颗粒的相互作用力和阻力的组件剪切，但在必要的更肤浅的看法提供的连续模型的数量，如这些出现在正式的条款，这些条款的形式必须确定经验。因此，对于描述连续统模型的方程的最终形式，存在着很大的意见分歧，而且事实上，迄今为止提出的两组方程并不完全一致，如果这些分歧仅仅是由于对待定项的形式的不同猜测而产生的，那么随着进一步的实验证据的出现，它们最终可能会得到解决。然而，差异比这更深，并且是由基本动量平衡的根本不同形式造成的。因此，似乎有必要用某种更为形式化的东西来取代构成现有连续体方程所依据的主要是直觉的考虑，这种形式化的东西将正确地把详细的点运动方程的力学基础纳入连续体模型，同时，清楚地把那些形式尚待经验确定的项分离出来。解决这个问题的方法肯定不止一种。例如，Murray（1966）应用了玻尔兹曼方程，在基本相同的基础上处理流体分子和固体颗粒，尽管它们的大小不同。在这里，我们采用了一种相当不同的方法，
In principle the motion of a system of particles suspended in a fluid is completely determined by the Navier-Stokes equations, to be satisfied at each point of the fluid, and the Newtonian equations of motion, to be satisfied by each particle. However, when the system of interestcomprises a large number of closely spaced particles, as in a fluidized bed, the problem is far too complicated to permit direct solutionwhen stated in these terms, and for practical purposes it is necessary to seek some method of simplifying it so that it can be described by a relatively small numberof partial differential equations. At present the literature contains several attempts (Hinze, 1962; Jackson, 1963; Murray, 1965; Pigford and Baron, 1965; Soo, 1963; Van Deemter and van der Laan, 1961) to simplify the problem in this way, all of which replace the point mechanical and fluid mechanical variables, which vary rapidly on a scale comparable with the particle spacing, by smoothed variables obtained by averaging over regions large compared with the particle spacing but small compared with the complete system. The resulting equations, therefore, describe the motionof the fluid and particles as though they were interpenetrating continua. A complete solution of thebasic mechanical and fluid mechanical equations would determine quantities such as the fluid-particle interaction forces and the resistance of the assembly to shear, but in the necessarily more superficial view provided bythe continuum models quantities such as these appear as formal terms in the equations, and the form of these terms must be determined empirically. Thus there is ample scope for differences of opinion about the final form of the equations describing the continuum model, and indeed no two sets of equations so far proposed are in complete agreement with each other.If these differences arose solely from different guesses at the forms of the undetermined terms, they might be expected eventually to be resolved as further experimental evidence becomes available. However, the differences run deeper than this and result from radically different forms of the basic momentum balance. It therefore seems desirable to replace the mainly intuitive considerations from which existing con-tinuum equations were constructed by something rather more formal, which will correctly translatethe mechanical basis of the detailed point equations of motion into the continuum model and, at the same time, clearly isolate those terms whose form remains to be determined empirically. There is certainly more than one way of approachingthis problem. Murray (1966), for instance, has applied Boltzmann’s equation, treating the fluid molecules and the solid particles on essentially the same basis despite the disparity in their sizes. Here we adopt a rather different approach, and