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# CFD Modelling of Scour in Flows with Waves and Currents

Nicholas S Tavouktsoglou,1[1] [2] David MKelly1 and John MHarris'

## Introduction

When it comes to sediment transport and scour modelling, the science must precede the engineering practice: simply measuring waves and currents and employing back of the envelope formulae is seldom adequate. Instead, performing detailed numerical modelling of multiple scenarios can offer real insight into a design problem. Moreover, in order to predict the sediment budget or the sediment transport , in relation to coastal works, a wide range of conditions need to be considered; thus, numerical models cannot be ignored. This begs the fundamental question: are accurate sediment transport predictions possible?

One reason sediment transport calculations are difficult is because the sediment transport is highly dependent on the hydrodynamics. To obtain reliable estimates of erosion rates we need to accurately predict the hydrodynamics of waves, currents and turbulence before the sediment flux can be determined. Importantly, the currents could result from processes at different time scales (for example, winds and cyclic loading etc.) developed within different generating locations (remote, fairly local or immediate vicinity) and can be highly variable in both space and time. The waves can also be driving currents, and they may initiate sediment motion themselves. This results in a complex fully three dimensional problem. In sediment transport, we are primarily dealing with a boundary layer of 1 2cm. but within this zone there are numerous factors that may contribute to high uncertainty in the final calculations.

Further to the effects the local hydrodynamics have, it has been observed that the bed has different responses depending on its local composition (sand, clay or silt) which in turn effects the movement of the sediment (Soulsby, 1997). The main sediment transport mechanisms can be divided into two categories:

These modes of sediment transport are in turn characterised by other processes and properties such as the bed pore pressure, median sediment size intra-particle forces etc. The result of all these properties, in conjunction with the local hydrodynamics and turbulence, are used to determine the sediment flux. To better understand and determine how sediment moves in oceanic, coastal and fluvial environments it is of essential importance to understand fundamentally how sediment particles move under the forcing of the hydrodynamics. The latest research is moving towards such solutions and by taking into consideration the increasing capabilities of computers, more direct methods to calculate sediment t ransport are being developed. These methods are based on Lagrangian approaches where each sediment grain is modelled as a particle or, for computational efficiency, a number of grains are collected together and modelled as a sediment parcel. Better measurements have led to better theory and better computer simulations. Sediment transport still remains challenging, but major advances in hardware, modelling and science have made it more and more accurate.

This chapter examines some of the authors’ research into numerical models for sediment transport using computational fluid dynamics (CFD) in non-cohesive sediments. In addition, this chapter will provide a summary of key studies that lead us to the current state of sediment transport numerical modelling along with a summary of the current methods used to model sediment transport using CFD.

## Types of sediment transport models in CFD

In recent years, with the rapid development of CFD and computational power, numerical studies of local scour have become increasingly popular. Numerical models for the simulation of scour usually comprise two distinct elements:

• • A hydrodynamic module to solve the fluid flow; and
• • A morphological module to deal with the sediment transport and bed erosion.

The hydrodynamic module solves the (Reynolds Averaged) Navier-Stokes equations for the flow field. The sediment-laden flow can be treated as a two-phase flow, which includes the water phase and the sediment phase, or as a single-phase flow, in which the two phases are modelled as a mixture. The two-phase flow model can be categorized into an Euler-Euler type (Chen et al., 2011), Lagrange-Lagrange type (Zubeldia et ah, 2018) and an Euler- Lagrange type (Li et ah, 2014). The Euler-Lagrange type of model treats the sediment phase as representing the motion of a certain number of individual particles. This approach succeeds in capturing the individual and collective dynamics of natural sand grains and many very good numerical models of the Euler-Lagrange type have been proposed recently such as those by Li et ah (2014), Finn et ah (2016) and Sun & Xiao (2016). However, this approach requires a large number of particles to simulate practical problems which translates into a huge demand on computational resources. The Euler-Euler approach describes the dispersed phase in a similar manner to that used for the continuous phase, and efforts have been made to develop such sediment transport models; representative examples are the models of Jha & Bombardelli (2010) and Chen et ah (2011). More recently a new type of Euler-Euler approach has been developed that makes use of two different intergranular stress models, the kinetic theory of granular flows and the dense granular flow rheology (Chauchat et ah, 2017 and Mathieu, 2019). However, the Euler-Euler type of two-phase models are typically complicated (Chen et ah, 2011). The two-phase model needs to solve the continuity and momentum equation for both of the phases and the most difficult part is to properly describe the turbulence characteristics of the two phases. For this reason, in hydraulic engineering applications, including scour estimations, single phase models are typically used.

The most popular single-phase approach neglects the effects of the dispersed phase on the continuous phases and solves the volumetric concentration of the dispersed phase using an advection-diffusion model. The advection-diffusion model has been successfully applied to many numerical studies of scour problems; see, for example, the work of Liang et al. (2005) and Roulund et al. (2005). However, it should be noted that the advection-diffusion model, which neglects the effects of the dispersed phase, is only valid for dilute problems where the suspended load concentration is not large enough to influence the principle properties of the flow field. Another issue concerning the hydrodynamic module is whether to include free surface effects in the model, or not. The air-water interface is affected when the flow interacts with obstacles—this causes local variations in the water depth. If the variations are comparable with the water depth, they may have a significant influence on the flow field and thus on the scour formation. Free surface effects are very common in scour problems, as the obstacles causing scour can have significant dimensions and thus the variation of the flow depth can be large. Recently, many numerical models for scour, or bed erosion, problems have included the free surface effect in the model; see, for example, the model of Liu and Garcia (2008).

The final important issue concerning the hydrodynamic module is to properly choose the turbulence closure for solving the (Reynolds Averaged) Navier-Stokes equations. The flows in scour problems are often turbulent. A direct numerical simulation (DNS) Orszang (1970) of the full Navier-Stokes equations will resolve the whole range of spatial and temporal scales of the turbulence, but the computational meshes must be fine enough to ensure resolution of the smallest dissipative scale (Kolmogorov microscales); for many problems this can be 0(10“°) m. The computational resources required to solve this sort of problem exceed what is currently practical. The most commonly used turbulence closure conditions are based on Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) models. Various studies have investigated the influence of the choice of turbulence model on the results of scour simulations. Aghaee and Hakimzadeh (2010) simulated the scour caused by bridge piers with both RANS and LES turbulence models and concluded that although the LES model simulates the flow field more accurately, especially for the periodic behaviour of the vortex shedding, a RANS model was generally sufficient to give a satisfactory estimate of scour development . The morphological module for scour simulations generally includes a sediment transport model and a sediment conservation equation (the Exner equation) to calculate the bed level change. There are many possible choices for the sediment transport model which usually includes both suspended load and bed load. As mentioned above, the suspended load in scour problems is often solved by the advection-diffusion model with a reference concentration given at a certain reference height. The reference concentration is usually given by empirical models of sediment entrainment. Two entrainment models commonly used can be found in the work of van Rijn (1984) and Garcia and Parker (1991).

To determine the bed load, many empirical equat ions from laboratory flume data have been given by previous studies. Most of them depend on the bed shear stress ть, i.e., the Shields parameter в, the density ratio between the sediment and the flow (s = ps/pw) and the nominal sediment particle diameter drM. In order to facilitate the expression, a non- dimensional form of transport rate which is referred as the Einstein number in some papers Фь is defined:

An extensive summary of the main methods to determine Фь is found in Soulsby (1997).

• [1] 1 HR Wallingford, Wallingford, Oxon, 0X10 8BA. UK. 2 Centre for Environment Fisheries and Aquaculture Science (CEFAS), Pakefield Rd, Lowestoft, NR33 OHT, UK.
• [2] Corresponding author: This email address is being protected from spam bots, you need Javascript enabled to view it

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