Comparing Suspended Sediment Diffusivity Formulated with Different Turbulence Models
|Keywords||Sediment-laden flow Lagrangian integral timescale Sediment diffusivity Turbulence model|
The sediment diffusion in the open-channel flow is a basic question in sediment research, and sediment diffusivity research is one of the most important aspects. Extensive experiments and field surveys showed that, sediment vertical diffusivityεs may have different distributions, such as parabolic, parabolic-constant, or a gradually increasing distribution toward to the flow surface. Due to the sediment-turbulence and sediment-sediment interactions under the side wall influence, the mechanisms of sediment diffusion are very complex, and the quantifying of sediment diffusivity is always empirical or semi-empirical. The modelling results are different in thousands ways, also can’t reasonably reflect results of experiments and surveys. In additional to mechanical limitations in sediment diffusivity formulations, the fluid turbulence models used to calculating the sediment diffusivity may be another reason.Based on the kinetic model of fluid-sediment two phase flows, also based on the diffusivity model that contains mechanisms of sediment drift-diffusion and fluid turbulent diffusion, this paper analyzed different turbulence models’influences to the sediment diffusivity calculation. Among that, based on the turbulence mixing length theory, according to the flow velocity distribution’s log-wake law or modified log-wake law, Model A and Model B is constructed to calculate sediment diffusivity. In the meantime, using the turbulence two-equation theory, Model C and Model D is established, the former one is based on empirical k-εformulations, and the other is based on k-εtransport equation.Under different experimental conditions, such as narrow and wide open channels, the four models’modeling and reappearance capability to fluid eddy viscosityνft,、fluid Lagrange integral timescale TL and sediment diffusivityεs are compared. The results showed that different turbulence models have remarkable influence to the quantifying ofνft、TL andεs:(1)νft、TL andεs given by Model A are zero on the maximal flow velocity point, and between this point and the channel bed, they are parabolic distribution.(2) In the wide open channel, Model B have a similar behaviour to Model A. But in the narrow open channel,νft andεs are approximately constants in the middle and upper part of the flow, TL is about linearly increasing from the bed to the surface. (3) TL given by Model C and Model D is about linearly increasing from the bed to the surface too. In the middle and upper part of the flow,νft given by Model C is decreasing slowly toward to the surface;εs is increasing or slowly decreasing to the surface. Under the Model D,νft is nearly constant or increasing slowly to the surface,εs is increasing or decreasing gradually, or nearly a constant toward to the surface.Generally speaking, the models based on the turbulence mixing theory are formally simple, but have a limited application area. The models based on k-εturbulence model can reappear different types of sediment diffusivity distribution, and have a broad application area. Deepening the research on fluid Lagrangian integral timescale will advance development of sediment diffusivity models.