A new physics-based method for estimating the excess turbulence downstream of a structure

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Abstract

Erosion and sedimentation are natural processes that occur in natural flows.
If the erosion is a threat for a structure, a bed protection is necessary to stop this process. A bed protection usually consists of relatively large stones.
For calculating the required dimeter of the stones several formulae are available, of which the formula of Shields is the most well-known. In most of these formulae the required dimeter depends on the maximum flow velocity.
Almost all flows in hydraulic engineering are turbulent. This means that the velocities are not constant in time, but fluctuating. Due to this irregular nature, the flows are described in a statistical way with a mean velocity and a standard deviation. This standard deviation is called turbulence.
In a uniform flow, the amount of turbulent remains constant, but it increases rapidly just behind a hydraulic structure and decreases gradually further downstream. The situation that will be dealt with in this research is that of the Backward Facing Step.
The turbulence is often represented as the amount of turbulent energy.
If the relative turbulence is known, the maximum velocity can be calculated and from that follows the required stone diameter. Knowing the standard deviation of the velocities is therefore very important, since having too small stones can destroy the bed protection and too large stones are more expensive and their placement could lead to practical problems.
Voortman (2013) came up with a new method to predict the turbulent energy, based on the energy cascade. He assumed that the dissipation rate of the turbulent energy depends on the amount of energy itself. Hoeve (2015) concluded, based on earlier experiments, that the method might work for the increase of turbulence, but that not enough data was available for calibrating the method for predicting the decrease of turbulence further downstream.
For this reason, twelve new experiments were done in the Laboratory for Fluid Mechanics of the Delft University of Technology. The experiments consisted of a step and a certain combination of water depth, flow velocity and bed roughness behind the step.
In these experiments, the flow velocities were measured at various locations and levels, so that the mean velocity and standard deviations at various locations are known.
In combination with the measured water depths, the head levels and turbulent energy could be calculated at each location and from that the change in head level and turbulent energy could be calculated.
The measurement data was obtained in both the deceleration zone and behind the reattachment point.
After a careful analysis, it turned out that it is possible to describe the dissipation of the turbulence with an exponential function, as suggested by Voortman (2013).
With the obtained data it should be possible in the near future to find a better link between the generation and dissipation of turbulent energy as well, leading to the creation of a new turbulence method and resulting in better bed protections.