Hans-Erwin Minor

Bed erosion in steep open channels

A new model is proposed to predict the bed topography in steep open channels once the bed stability is exceeded. Existing relationships describe bed stability by defining an entrainment state, usually expressed by a threshold shear stress or a discharge. The approach proposed herein focuses the self-stabilization potential of the channel bed at discharges larger than the entrainment value for which there is no sediment supply from upstream. Flume experiments carried out at the Laboratory of Hydraulics, Hydrology and Glaciology (VAW) of the Swiss Federal Institute of Technology (ETH) Zurich, indicated that the self-stabilization potential occurs in various geomorphologic scales. These scales are associated with typical features of the channel bed morphology. As the self-stabilization process is always combined with erosion, the novel approach interrelates the product of water discharge and channel gradient with the channel bed degradations associated with the different geomorphologic scales.

Air Transport Caused by Chute Aerators

Chutes with flow velocities in excess of some 20 m/s are typically prone to cavitation. In order to avoid damages, these flows are aerated using chute aerators. The current literature describes the efficiency of these aerators mainly in terms of the air entrainment coefficient as the ratio of the entrained air and water discharges. However, this is a global coefficient neither specifying the precise air distribution in the flow nor its detrainment rate. As cavitation damages occur along the chute boundaries, the associated air concentration is of prime interest. The present investigation focuses on the flow structure and the air transport downstream of chute aerators. Systematic hydraulic model tests were conducted including a data analysis of the spatial air concentration distribution in the near and the far fields downstream of chute aerators. Based on these and other measurements, general air transport zones were described. Three flow zones were introduced, namely the: (1) Jet zone; (2) Re-attachment and spray zone; and (3) Far-field zone. It was further found that aerators have primarily an effect on the average air concentration, whereas they increase the bottom air concentration only slightly. A large de-aeration gradient was found near the bottom downstream of the re-attachment point. It was concluded that the bottom air concentration downstream of chute aerators is smaller than generally assumed. Nevertheless, these air concentrations obviously suffice to inhibit cavitation damages on spillways equipped with aerators.

Closure to “Hydraulic Performance of Step-Aerator” by Anina Schiess Zamora, Michael Pfister, Willi H. Hager, and Hans-Erwin Minor

The authors are to be congratulated for providing a detailed study of a step aerator to counter cavitation damage for relatively large unit discharges over a stepped chute. As shown in Fig. 2 of the paper, the step aerator is provided on the first step. The potential for cavitation is along the black water reach from the first step to the point of incipient bottom aeration xi . Boes and Hager 2003 demonstrated that the distance xi increases essentially with the critical flow depth hc . Also, Semenkov and Lantyev 1973a,b proposed an average air detrainment of c=0.04 to 0.80% per meter length of chute. Based on experimental data, Chanson 1997 suggested that an average air concentration of 30% is required for obtaining a bottom concentration of about 5%. Also according to Eq. 4 , the maximum air concentration in the bottom air water boundary layer decreases with x /hc. Hence, the discussers would like to know whether a single step aerator provided on the first step is sufficient to meet the required bottom air concentration for higher discharges to avoid cavitation up to the distance xi, or will additional aerators need to be provided. We would like the authors to comment on the following points: 1. For higher discharges, the values of Cb /Cbu in the region −10 x−xi /hc 0 are very close to zero as shown in Fig. 5 b . Therefore it is doubtful whether the provision of an aerator will serve to reduce the cavitation in this region for higher values of discharges. 2. Advantages and performance of the aerator suggested in this paper compared to the aerator suggested by Pfister et al. 2006 . 3. Generally, steps are provided on spillways to increase energy dissipation so that the cost of the energy dissipator is reduced. The energy dissipation over the surface of stepped spillway decreases with the increase in unit discharge. This