Radial void fraction distributions in randomly packed fixed beds of uniformly sized spheres in cylindrical containers

The radial void fraction distribution in randomly packed fixed beds of uniformly sized spheres in cylindrical containers is analyzed by a nondestructive method in which the center position coordinates of specially prepared spheres are experimentally obtained using X-ray radiography and the radial void fraction distribution is geometrically determined from these center coordinates. The geometrical solution for the radial void fraction distribution is derived by dividing the fixed packed bed of spheres into a large number of radial annular layers of equal thickness and the local void fraction in each layer is expressed in terms of the solid volume segments coming from each sphere. The radial void fraction distribution is presented for four different diameter aspect ratios, D/d, ranging from 2.02 to 7.99. The height aspect ratio, H/d, of each cylindrical container is approximately 7.84. Using the new data and existing data for the radial void fraction distribution, an empirical correlation with one principal equation is determined which accurately predicts the radial void fraction distribution for fixed packed beds of uniformly sized spheres in cylindrical containers. The correlation can be used for fixed packed beds with D/d > /2.02. The correlation can be also used in analytical and numerical transport models for fixed packed beds of uniformly sized spheres to closely approximate the radial void fraction in the near-wall region.