Numerical Modelling of Turbulent Free Surface Flows over Rough and Porous Beds Using the Smoothed Particle Hydrodynamics Method

Understanding turbulent flow structure in open channel flows is an important issue for Civil Engineers who study the transport of water, sediments and contaminants in rivers. In the present study, turbulent flows over rough impermeable and porous beds are studied numerically using the Smoothed Particle Hydrodynamics (SPH) method.
A comprehensive review is carried out on the methods of turbulence modelling and treatment of bed boundary in open channel flows in order to identify the limitations of the existing particle models developed in this area. 2D macroscopic SPH models are developed for simulating turbulent free surface flows over rough impermeable and porous beds under various flow conditions. For the case of impermeable beds, a drag force model is proposed to take the effect of bed roughness into account, while for the case of porous beds, macroscopic governing equations are developed based on the SPH formulation, incorporating the effects of drag and porosity.
To simulate the effect of turbulence on the average flow field, a Macroscopic SPH-mixing-length (MSPH-ML) model is proposed based on the Large Eddy Simulation (LES) concept where the mixing-length approach is applied to estimate the eddy-viscosity rather than employing the standard Smagorinsky model. The difficulty in reproducing steady uniform free surface flow is tackled by introducing novel inflow/outflow techniques for the situations in which the flow quantities are unknown at the inflow and outflow boundaries.
The performance of these models is tested by simulating different engineering problems with an insight developed into turbulence modelling and bed/interface boundary treatment. The accuracy of the models is tested by comparing the predicted quantities such as flow velocity, water surface elevation, and turbulent shear stress with existing experimental data.
The limitations of the models are mainly attributed to the macroscopic representation of the roughness layer and porous bed, difficulty in the determination of the values of the empirical coefficients in the closure terms, and limitations with the use of fine computational resolution. On the other hand, the main strength of the model is describing the complicated processes occuring at the bed using simple and practical computational treatments so that the momentum transfer is estimated accurately. It is shown that if the closure terms in the momentum equation which represent the effect of bed drag and flow turbulence are determined carefully based on the physical conditions of bed and flow, the model is capable of being employed for different civil engineering applications.