Coupled Mathematical Modelling Of Shallow Water Flow And Substance Transport In Open Channels

In open channel,shallow water flow is often accompanied by material transport,the most common of which is sediment transport,such as the evolution of alternate bar,the turbidity current,and the debris flow with high sediment concentration.Meanwhile,the degradation of water quality due to the economic development and anthropogenic activities have been gaining more and more attention on the water pollutants transportation,like the industry and agriculture waste water and the sudden leakage of toxic substances or oil.This dissertation focuses on the transportation of sediment and water pollutants in shallow water flows by numerical modelling.It aims to have a better understanding of the physical mechanism on the specific sediment-laden flow conditions by improving and extending the existing mathematical model and also to study the pollutant transport considering the effects of sediments.Firstly,based on the conservation laws and the continuum assumption in fluid dynamics,the traditional SHSM(Shallow water hydrosediment-morphodynamic)model is elaborated,including the effects of unsteady flow,non-capacity sediment transport,interaction among water,sediment and bed,and non-uniform sediments.However,in a recent reformulation,the well-established SHSM equations are questioned for its incorrect incorporation of bed sediment entrainment effects.While the reformulation proposed some jump conditions at the bed surface to rectify the accounting for the effects of mass exchange.Theoretical analysis and case studies are carried out to illustrate that the reformulation is in fact problematic because it is incompatible with the continuum assumption and conflicts with principle of self-adaptation of river dynamics,while the traditional SHSM equations are correct and have seen widespread applications.Next,a FCNA(Fully Conservative Numerical Algorithm)is proposed to solve the SHSM equations.The numerical fluxes are estimated by the TVD(Total Variation Diminishing)version of a well-balanced weighted surface depth gradient method along with a slope-limited centred scheme,which is able to capture shock waves and discontinuities automatically.The CNA(Conventional Numerical Algorithm)needs to redistribute the variable water-sediment mixture density to the source terms of the governing equations so that the hyperbolic operator is rendered similar to that of the conventional shallow water equations for clear water flows,while the FCNA directly solves the original SHSM equations.A spectrum of test cases are carried out to compare these two algorithms.It is found that the CNA performs better than the FCNA in preserving mass conservation,but differences of the indexes were subtle,and both of the two algorithms can be satisfactorily applied in computational river modelling.Then,as the extension of the traditional SHSM model implemented by the FCNA,a quasi single-phase mixture model is proposed for debris flows over inclined bed slopes and the stresses due to fluctuations are incorporated based on analogy to turbulent flow.Also,a general one-dimensional double layer-averaged SHSM model is presented to study the processes of reservoir turbidity current.The former performs much better than the traditional SHSM models,and is attractive in terms of computational cost while the two-phase model performs even better appreciably.The latter illustrates that the general model successfully captures the interface of the two layers and reproduces the formation and propagation of the turbidity current.It is also conducted to investigate sediment flushing efficiency with different operations of the bottom outlets,in support of optimized reservoir sedimentation management.Finally,a water quality model is established based on the SHSM model to study the pollutant transport.One the one hand,the model explicitly incorporates the effects of changes in water volume,such as lateral inflow,evaporation and infiltration.On the other hand,the model involves the effects of sediments,such as the adsorption and desorption of suspended sediment and bed sediment,and the bed deformation.As applied to the Wei Canal in the Haihe River basin of China,it is found that the present model can successfully reproduce the hydrodynamic processes.It also shows that the model including the effects of sediments performs better than the clear water model in modelling pollutant transportation,thereby facilitating a promising modeling tool able to underpin water quality management.