A scaling law for designing a downscaled model to investigate submarine debris-flow impact on a pipeline in normal gravity

In recent years, many downscaled physical hydraulic tests and Computational Fluid Dynamics (CFD) numerical simulations in normal-gravity environments have been conducted to study the submarine debris-flow impact on a pipeline. However, a lack of model-prototype similarity has inhibited robust applications of the downscaled models. In this study, the pressing issue of model-prototype similarity is addressed. The debris flow is described as a Herschel–Bulkley fluid. The generic scaling law is derived based on the Reynolds similarity criterion, and its applicability is demonstrated by a series of CFD models carefully designed to simulate laminar fluids passing downscaled and prototype pipelines. The scaling law is found to be completely applicable to design a downscaled model of a Newtonian fluid passing a pipeline, whereas it is limited to the design of a downscaled model of Power-law or Herschel–Bulkley fluids passing a pipeline with shear strain rates below a critical value. Beyond this value, the downscaled model will overestimate the drag and lift coefficients and underestimate the Strouhal number. Results from a number of numerical simulations prove that the scaling law provides a basis for the design of a downscaled model of debris-flow impact on a pipeline in normal-gravity environments.