Recycled scrap is used as a raw material in an electric arc furnace (EAF). Certain EAF systems preheat the scrap using its exhaust gas to save energy. However, the actual operations cannot recover sufficient thermal energy of gas owing to non-uniform flow distribution such as blow-out and stagnation to cause the portion that is not melted. This study investigated the relationship between packed structure and gas permeability in a tank filled with random-and multiple-shaped solids. Visualization and flow measurement experiments were conducted. The packing structure was measured using laser-induced fluorescence by scanning a laser sheet through the tank to measure the three-dimensional distribution of the packed structure. The flow velocity distribution was measured using particle image velocimetry by preparing multiple directions of the laser sheet with respect to the water tank and reconstructing a three-dimensional three-component velocity distribution. Under high packing ratio, the flow structure was obstructed by the packing material, resulting in stagnation areas with low flow velocity. In contrast, at low packing ratio, the stagnation area was smaller, and the global flow field was stable. Furthermore, histograms of the flow velocity distributions suggested that stagnation occurred under high packing ratio conditions, while a global flow field occurred at low packing ratios. These results are applicable in the design of preheating equipment, such as exhaust gas recycling, preheating furnace, or clamshell. Thus, this study provides valuable insights into flow nonuniformity and the design of preheating equipment to improve operational efficiency and safety.