In this study, we applied the variational model to fluidization of small spherical particles. Fluidization experiments were carried out for spherical particles with 13 diameters between d_p = 0.13 and 5.00 mm. We propose a generalized form of our variational model to predict the superficial velocity U and interphase drag coefficient β by introducing an exponent n to describe the different dependences of the drag force F_d on fluid velocity for different particle sizes (different flow regimes). By comparing the predictions with the experimental results, we conclude that n=1 should be used for small particles (d_p < 1 mm) and n = 2 for larger particles (d_p > 1 mm). This conclusion is generalized by proposing n = 1 for particles with Re_t < 160 and n = 2 for particles with Re_t > 160. The average mean absolute error was 5.49% in calculating superficial velocity for different bed voidages using the modified variational model for all of the particles examined. The calculated values of β were compared with values of literature models for particles with d_p < 1.0 mm. The average mean absolute error of the modified variational model was 8.02% in calculating β for different bed voidages for all of the particles examined.

在这项研究中，我们将变分模型应用于小球形颗粒的流化。对直径在d _p  = 0.13和5.00 mm之间的13个球形颗粒进行了流化实验。我们提出了一种变分模型的广义形式，通过引入指数n来描述表观速度U和相间阻力系数β，以描述对于不同粒径（不同流态），阻力F _d对流体速度的不同依赖性。通过将预测结果与实验结果进行比较，我们得出结论：对于小颗粒，应使用n = 1（d _p <1 mm）， 对于较大的粒子（d _p  > 1 mm），n = 2 。这个结论是通过提出一种广义Ñ 与= 1颗粒重新_吨 <160和Ñ  = 2用于与粒子重新_吨 > 160平均平均绝对误差在使用用于改性变模型计算用于不同的床空隙率表面速度为5.49％所有检查过的颗粒。β的计算值与d _p  <1.0 mm的颗粒的文献模型值进行了比较。修正的变分模型在计算β时的平均平均绝对误差为8.02％ 对于所有检查过的颗粒，床的空隙率都不同。