MASS-TRANSFER FROM SMALL PARTICLES SUSPENDED IN TURBULENT FLUID
MASS-TRANSFER FROM SMALL PARTICLES SUSPENDED IN TURBULENT FLUID
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DOI：
10.1017/s0022112080000304
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发表时间：
1980-01-01
影响因子：
3.7
通讯作者：
BATCHELOR, GK
中科院分区：
文献类型：
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作者：
BATCHELOR, GK
小的刚性球形颗粒悬浮在流体中，物质通过对流和扩散从每个球体的表面转移。由某种搅拌装置维持的流体处于统计上稳定的湍流运动。假设绕流的psamclet数相对于单位较大，因而在颗粒表面存在浓度边界层，且绕流的雷诺数足够小，使得颗粒表面附近的速度分布可以用Stokes方程给出。粒子周围的流动是(a)由于粒子相对于流体的平移运动而产生的流动，其速度与密度差成正比，以及(b)由于周围流体的速度梯度而产生的流动。利用这两个叠加流场的统计参数，得到了大psamclet数下的平均传输速率的渐近精确表达式。由于粒子旋转对对流传递的部分抑制，唯一相关的参数是粒子在环境涡度矢量方向上的平均平动速度和在环境涡度方向上的平均环境扩展速率。前者在一般湍流流场中为零，后者在湍流小尺度分量的平衡理论中得到了平均耗散率ε的表达式。传递速率的最终无因次表达式为0·55（a2ε½/κν½）1/3，其中a为粒子半径。这与以前发表的一些值小于102的数据集非常吻合。
Small rigid spherical particles are suspended in fluid, and material is being transferred from the surface of each sphere by convection and diffusion. The fluid is in statistically steady turbulent motion maintained by some stirring device. It is assumed that the Péclet number of the flow around a particle is large compared with unity, so that a concentration boundary layer exists at the particle surface, and that the Reynolds number of the flow around the particle is sufficiently small for the velocity distribution near the particle surface to be given by the Stokes equations.The flow around a particle is a superposition of (a) a streaming flow due to a translational motion of the particle relative to the fluid with a velocity proportional to the density difference, and (b) a flow due to the velocity gradient in the ambient fluid. An expression for the mean transfer rate which is asymptotically exact for large Péclet numbers is obtained in terms of statistical parameters of these two superposed flow fields. As a consequence of the partial suppression of convective transfer by particle rotation, the only relevant parameters are the mean translational velocity of the particle in the direction of the ambient vorticity vector and the mean ambient rate of extension in the direction of the ambient vorticity. The former is shown to be zero in common turbulent flow fields, and an expression for the latter in terms of the mean dissipation rate ε is obtained from the equilibrium theory of the small-scale components of the turbulence. The final non-dimensional expression for the transfer rate is 0·55(a2ε½/κν½)1/3, where a is the particle radius. This is found to agree well with some previously published sets of data for values of less than 102.