RIKU Tashiro 

Experimental and Real Scale Similarity of Rivers with Seepage Flows

LU Minjiao�@ TOSHIRO Kumakura�@YANG Hongxuan

�@In rivers, many hydraulic model experiments have been conducted to elucidate and study the phenomena. There are several similarity rules, but in general, fluid similarity is the standard similarity rule for rivers. Although model experiments on rivers are based on fluid similarity and other factors, they do not necessarily satisfy the seepage flow similarity in cases involving seepage flow. Therefore, model experiments do not take into account the similarity of seepage flow. To solve this problem, a numerical model was proposed to simultaneously calculate seepage flow and river flow by introducing a Darcy-Forchheimer resistance term into the VOF model. In this study, more realistic measures for simultaneous similarity of seepage flow and river flow are investigated through numerical experiments. After the study of similarity in Darcy flow, the study was extended to non-Darcy flow to investigate the similarity law between seepage flow and river flow. 
�@As a result, we obtained the following results. Although it is common to have multiple permeable zones with different permeability, the permeability to have seepage flow similarity does not have to be at a theoretical scale (velocity scale), and highly accurate pressure similarity can be obtained if the ratio of permeability between zones is maintained. A relatively small hydraulic conductivity ratio between the broken stone immediately below the structure and the sandy bedrock below it will generally increase the lift pressure. However, if the ratio is made extremely small, the similarity may be lost and lift pressure may decrease in some locations. Extended to non-Darcy high velocity turbulence, the theoretical conditions necessary for the similarity are induced. Under the Fr-similarity of river flow, the simultaneous similarity of river and seepage flow is obtained by reducing the permeability of the model to the scale of the flow velocity, so that the FL number matches the real one. Theoretical conditions were confirmed by analyzing the seepage flow in a one-dimensional multi-permeable zone. Theoretical conditions require matching both the material permeability k and the Forchheimer coefficient F, which is unrealistic, but one-dimensional seepage flow analysis shows that if Re is high, the turbulent term in the seepage flow becomes dominant and a realistic similarity law can be obtained by matching only the FL number.