Fabián A. Bombardelli, Ph.D.
Assistant Professor

Numerical Modeling of Sediment Transport Near the Bed Using a Two-Phase Flow Approach

Motivation

It is a notably difficult task to provide accurate  prediction of particle  motion and interaction among particles when they move close to the bed of rivers/channels. Some of the difficulties are associated to :

• Particles present different motion patterns near bed: sliding, rolling and saltation.
• Small particles can be ejected from the wall and be transported by suspension.
• Particles collide with the bed and among them.

How can we incorporate all these elements in a model to predict bedload transport, avoiding empirical correlations?

Project Objectives

The main objective of this work is to develop a two-phase flow model to integrate fluid and particle motion using an Eulerian-Lagrangian approach close to the channel bed. This work focuses on the water flow close to the wall and the transport of sediment in bed load motion, and it includes processes that have been disregarded in most existing models, most notably inter-particle collision.

The specific objectives of this study are:

• To develop and validate an Eulerian-Lagrangian model to simulate the saltation of particles close to the bed. The Lagrangian model is intended to be coupled with highly-resolved velocity fields, using Large Eddy Simulations (LES) or Direct Numerical Simulations (DNS). Validation of this model is accomplished via-comparison with experimental data.
• To optimize the computational effort of the Lagrangian model to calculate particle trajectories and velocities, by revisiting the formulations for all forces; with special emphasis is put on the Basset force.
• To examine existing bed-representation sub-models, to propose a simple yet realistic new approach and to validate it via comparison with experimental data.
• To gain more understanding about the response of saltating particles to the velocity fluctuations in the flow (i.e., to turbulence). To that end, a highly-resolved flow simulation, considering one-way coupling between phases, is developed.

Results

2-D Particle Tracking Code
A two-dimensional (2-D) particle tracking computational code was developed in FORTRAN, including a rebound sub-model and a bed roughness representation. The model was validated through comparison of numerical predictions with experimental data.

Figure 1 2D Validation

To optimize the computational cost of the particle tracking model, a new methodology to calculate the Basset force was developed and it was tested for particles of both small and large size (See Bombardelli, Gonzalez and Niño, In press).

3-D Particle Tracking Code
A three-dimensional (3-D) particle tracking model was developed in FORTRAN, which includes the description of both the particle translational and rotational velocity at every moment. An assessment of existing sub-models for bed roughness representation is introduced in this chapter together with a new sub-model. The validation of the best sub-model is accomplished by comparing its performance with experimental data. The computational code also considers the motion of multiple particles and an algorithm to treat the inter-particle collisions.

Multiple particle simulations under a non turbulent velocity were performed, using the inter-particle collision algorithm  presented in Yamamoto et al. (2001). A video featuring an example of two particles colliding using this methodology is presented here.

2D View of a bed collision and an interparticle collision event. (See video.)

3D View of a bed collision and an interparticle collision event. (See video.)

HR3D  Velocity Field Simulations
The proposed 3-D model coupled with a highly resolved 3-D (HR3D) turbulent velocity field. After its validation, the effect of the turbulence on the particle motion is studied in detail. The interaction between particles, the effect of particle size, volumetric concentration of particles and flow conditions on particle turbulent parameters are discussed in this chapter. A new filter to separate the fluctuating component of the particle velocity from the "mean" value is introduced. .

Figure 2 Two velocity fields

The particle tracking code was later coupled with a highly-resolved, 3-D, turbulent flow field, to study the effect of the flow turbulence on the particle motion. The one-way coupling model was validated with experimental observations, for the first time in bed load transport. Videos featuring multiple particles under a turbulent velocity field are presented:

Multiple particle simulation. Particle diameter: 0.7 mm, shear velocity: 0.028 m/s. (See video.)

Multiple particle simulation. Particle diameter: 1.0 mm, shear velocity: 0.037 m/s. (See video.)

When considering multiple particles, it is possible to calculate the bed load rate and compare the results with widely used expressions of bed load transport (Julien, 1998). The volumetric sediment transport rate q  is calculated directly by counting the number of particles that moves through a specific location of the simulated channel, in a given period, and multiplying this result by the particle volume. Good agreement between both simulation model and analytical expressions is found.

Figure 3 Bedload rate

Department of Civil & Environmental Engineering - University of California, Davis
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