Local Scour: Influence of an exponential eddy viscosity distribution on the longitudial flow velocity

Local Scour: Influence of an exponential eddy viscosity distribution on the longitudial flow velocity

Hoffmans, G.J.C.M.

Civil Engineering and Geosciences

Hydraulic Engineering

1988-01-01

The general purpose of this research project is to model mathematically the local scour downstream of a structure (2-D). The model has to simulate the development of the scour as a function of the time. Basically two models are necessary namely a flow model and a morphological model. The latter model has to describe the bed and suspended load and the erosion of the bottom. In the present study a function (prescription) for the eddy viscosity with a variable parameter, which is a parameter in the exponential function, is discussed. A sensitivity study has been made in order to fit the parameter mentioned above for several flow types. In this study the hypothesis of Boussinesq and a linear shear stress distribution are applied. Using this eddy viscosity concept, it follows, that the profile of the longitudinal flow velocity is a logarithmic profile with a correction term. The differences between the traditional logarithmic flow velocity profile and the Coles flow velocity profile are small near the wall. A large difference occurs at the surface of a uniform flow or at the center of a pipe flow. There the gradient of the longitudinal flow velocity equals zero, while the eddy viscosity does not reduce to zero regardless of the value of the parameter in the exponential function for the eddy viscosity. CONCLUSIONS Uniform Flow: Using the Coles flow velocity profile with Pi = 0.20 (Nezu and Rodi, 1986) the velocities are approximated in a better way especially in the outer region (wake function!) than using a pure logarithmic flow or using the velocity profile which follows from an exponential eddy viscosity. Pipe Flow: Using a logarithmic flow velocity profile or the Coles flow velocity profile the boundary condition in the center of the pipe is not satisfactory, because there the gradient of the longitudinal flow velocity is discontinue. Also the eddy viscosity will not be equal to zero there. Then a correction has to be made on the eddy viscosity distribution which follows from the Coles flow velocity profile. Internal Boundary Layer: The Coles flow velocity profile using Pi = 0.55 describes the distribution of the velocities as well as the distribution of the eddy viscosity very well in a new wall-boundary layer with an undisturbed outer flow. However, the description is poor in case the outer flow is disturbed.

local scour
flow model
morphology
eddy viscosity
eddy
Coles
velocity profile

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TU Delft, Department of Hydraulic Engineering

Report no. 14-88

Institutional Repository

report

(c) 1988 TU Delft, Department of Hydraulic Engineering