Revisiting the model-prototype similarity issue arising from investigations of submarine debris flow passing a downscaled pipeline in normal gravity

Abstract

In this study, the model-prototype similarity issue arising from investigations of submarine debris flow passing a downscaled pipeline in normal gravity is revisited. Theoretical analyses of the similarity issue for Power-law and Herschel–Bulkley fluids passing downscaled pipelines are performed based on the dimensionless governing equations. It is observed that, for a Power-law fluid, the similarity criterions of Reynolds number and power index can be readily satisfied in theory and practice. However, for a Herschel–Bulkley fluid, the similarity criterions of Oldroyd number, Reynolds number, and power index should be used in theory, but hardly be satisfied simultaneously in practice. Instead, the similarity criterion of plastic Reynolds number is suggested as an approximate alternative for a Herschel–Bulkley fluid. Based on these similarity criterions, the scaling laws for Power-law and Herschel–Bulkley fluids are derived, respectively. The applicability of scaling laws is demonstrated based on Computational Fluid Dynamics (CFD) simulations. The scaling laws are fully applicable to a Power-law fluid, while they can only reach an approximate similarity of drag coefficient for a Herschel–Bulkley fluid. These updated insights will facilitate a more rational design of a downscaled model to study the debris flow passing a pipeline in normal gravity.