A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers/piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included in the paper

Mathematical modelling of scour: A review

The scour around a long fixed pipeline placed just above a non-cohesive sandy bed is numerically simulated using an Eulerian two-phase model that implements Euler–Euler coupled governing equations for fluid and solid phases and a modified k−ɛ turbulence closure for the fluid phase, the modeling system being a part of the CFD software package FLUENT. Both flow–particle and particle–particle interactions are considered in the model. During the simulations, the interface between sand and water is specified using a threshold volume fraction of sand, and the evolution of the bedforms is studied in detail. The predictions of bedform evolution are in good agreement with previous laboratory measurements. Investigations into the mechanisms of scour reveal that three sediment transport modes (bed-load, suspended-load and laminated-load) are associated with the scour development. While some previously proposed scour development formulae for cylindrical objects are in good general agreement with the simulations, scour prediction based on a commonly used operational mine-burial model (DRAMBUIE) shows disparities with present simulations.

Numerical simulation of scour around pipelines using an Euler-Euler coupled two-phase model

A numerical model for the equilibrium profiles of the local scour around pipelines is developed. The numerical model solves the turbulence flow field around the pipeline using a large eddy simulation model in a curvilinear coordinate system with frequent updates of the scoured seabed. The iteration method of determining the equilibrium scour profile is based on the assumption that the equilibrium seabed shear stress is equal to the critical shear stress of the sediment for clear-water scour or the undisturbed seabed shear stress for live-bed scour. Based on this assumption the model predicts the equilibrium scour hole without using any sediment transport formula. The calculation results clearly reveal that the lee wakes behind the pipeline contribute significantly to the local scour hole development, especially to the gentle scour slope observed in experiments. The predicted maximum scour depth and the shape of the scour hole compare favorably with the experimental data published in the literature.

Prediction of Lee-Wake Scouring of Pipelines in Currents

Numerical and experimental investigation of flow and scour around a half-buried sphere

Experimental Study Of Vortex-Induced Vibrations Of A Pipeline Near An Erodible Sandy Seabed

A morphological model for the local scour around pipelines is developed. Based on the Navier-Stokes equation and an erodible boundary adjustment technique the model predicts the equilibrium scour hole without using any sediment transport formula. The calculation results clearly reveal that the lee-wakes behind the pipeline contribute significantly to the local scour hole development, especially to the gentle scour slope observed in experiments. The predicted maximum scour depth and the shape of the scour hole compare favorably with the experimental data published in the literature.

Fangjun Li

Papers

Numerical Simulation of Pipeline Local Scour With Lee-Wake Effects