General correlation for pressure drop through randomly-packed beds of spheres with negligible wall effects

Pressure drop in fixed beds has been studied for over a century and a large number of conflicting correlations exist in the literature. Contributing factors to these differences include the use of particles of different shapes, the presence of wall effects in beds of low tube-to-particle diameter ratio (N) and parameter fitting over limited ranges of modified Reynolds number ${\mathit{Re}}_m=\frac{\mathit{\rho v}{d}_p}{\mu \left(1-\epsilon \right)}$. The present work, in contrast, considers the entire Reynolds number range for perfect spheres in unbounded (high-N) random-packed beds. An asymptote-based correlation has been developed based on published data for extremely high ${\mathit{Re}}_m$ and on new particle-resolved computational fluid dynamics (PRCFD) results for extremely low ${\mathit{Re}}_m$. The resulting equation is given by: $\frac{∆P}{L}\frac{d_p}{\rho v^2}\frac{{\epsilon }^3}{\left(1-\epsilon \right)}=\frac{160.0}{{\mathit{Re}}_m}+\left(0.922+16{\mathit{Re}}_m^{-0.46}\right)\frac{{\mathit{Re}}_m}{\left({\mathit{Re}}_m+52\right)}$. This equation fits a literature data set of 541 points with average error 5.66%, and shows correct limits for both high and low ${\mathit{Re}}_m$.     

积雪最低含水饱和度的野外测定

在野外对处于融化期的自然积雪的最低含水饱和度进行了测定。结果显示，当下渗水流流速在毛管力起着不可忽视作用的约3×10-8～1.39×10-7ms-1时，所对应的积雪平均含水饱和度为0.05～0.07。流速在约10-8ms-1以下时，达到最低含水饱和度，平均值为0.02～0.03。在毛管力起作用的范围内，积雪的不同层位的含水饱和度有较大差异，而且差异随流速的减小而显著增加。