Self-entrainment of air on stepped spillways
Introduction
Numerous Roller-Compacted Concrete (RCC) gravity dams were built in the past decades, typically including a stepped spillway with modified flow features as compared to smooth standard spillways. A main difference relates to self-aeration of the flow located further upstream for stepped chutes (Chanson, 1994), due to increased turbulence generated by the rougher bottom.
Stepped spillway flow is accelerated from the spillway crest, where typically a standard-crest profile as hydraulic control is provided. A turbulent boundary layer develops, whose thickness mainly depends on the streamwise location and the roughness height (Amador et al., 2006a). At a certain location denoted as surface-inception point, the turbulent boundary layer reaches the free surface (Takahashi et al., 2006). If turbulence overcomes surface tension, air is entrained into the flow. Chamani (2000) visualized the surface-inception point with high-speed camera imagery for a step height of s = 0.125 m and a normalized discharge expressed as hc/s = 1, with hc = (q2/g)1/3, q = unit discharge and g = acceleration of gravity. For such small discharges, the surface-inception point was observed at the first step, due to turbulence generated at flow impact on the first horizontal step face. The thickness of the aerated zone then increases in the streamwise direction, protruding to the steps, so that the entire flow becomes aerated (Fig. 1). The pseudo-bottom-inception point I is located at Li, corresponding to the distance between the spillway crest and the location where the pseudo-bottom (subscript b) air concentration is Cb = 0.01. This definition is suitable for the present purpose, relates to earlier work (e.g. Boes and Hager, 2003) and is relevant for cavitation protection (Rasmussen, 1956). The pseudo-bottom is formed by the plane tangent to the step edges (Fig. 1), and does not correspond to the channel bottom surface. Both points, i.e. surface-inception (Chamani, 2000) and the bottom-inception are located close to each other (Boes and Hager, 2003). The flow near the pseudo-bottom and in the step niches consists of black-water upstream of point I, and of air–water mixture flow downstream, reaching ultimately equilibrium flow conditions.
The location of point I on a stepped spillway is of particular interest, because of
- 1.
Upstream cavitation risk. Pfister et al. (2006) demonstrate that unit discharges exceeding q ≅ 80 m3/ms require chute aeration upstream of point I, given that the same incipient cavitation index is considered as on smooth spillways. It is probable that the incipient cavitation indices are larger on stepped than on smooth spillways and, as a consequence, the corresponding maximum black-water discharges are smaller. Amador et al. (2006b) mention q ⩾ 15 m3/ms as critical discharge, if no cavitation protection measures are provided. Prototype experiences indicate, however, that discharges of q ≅ 78 m3/ms are conveyed without damage if flare gate piers are installed, thereby aerating the flow (Lin and Han, 2001). The difference between these observations seems exclusively due to the use of these flare gate piers, which are obviously efficient to aerate the flow. Aerated flows are known to prevent cavitation damages (Bradley, 1945).
- 2.
Drag reduction along aerated stepped spillway flow (Chanson, 2004), so that energy dissipation is smaller than in black-water flow, requiring a dissipation structure at the spillway toe.
The concept of air entrainment and air transport was intensively discussed (Chanson, 2002). Wilhelms and Gulliver (2005) distinguished between entrapped and entrained air transport in developed turbulent chute flows, based on optical visualization and on water surface measurements. A rough flow surface induced by turbulence similar to a breaking surface wave was observed, containing irregular crests and troughs. Entrained air is transported within the flow as bubbles, whereas entrapped air is transported above the coherent water body between two surface wave crests. The sum of entrapped and entrained air is the totally conveyed air.
The purposes of the present investigation are to describe visual observations made on a hydraulic model in the vicinity of the self-aeration point I, and their qualitative interpretation relative to the flow characteristics. The totally conveyed air and related parameters were measured and the results are discussed in terms of the air transport mechanism, again focusing on the vicinity of the inception point.
Section snippets
Hydraulic model
The data and photos presented below were collected on a stepped spillway model of the Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich (Fig. 2, Pfister, 2002). The channel was 0.5 m wide and 3.4 m long. A standard-crest profile (Hager, 1991) was inserted at its upstream end, designed for the maximum unit discharge of 0.864 m3/sm (Chanson, 2006). The transition from the smooth standard-crest to the stepped chute was abrupt, i.e. without a smaller step reach (Yasuda et al., 2006
Self-entrainment mechanism of air
The flow in the vicinity of the inception point I was filmed with a CCD high-speed camera (Speedcam Pro, Weinberger®, Germany) across the model glass sidewall with a rate of 1000 frames per second and a resolution of 512 × 512 pixels. A precise shutter speed is not provided in the camera files, but it is presumably below 1/1000 s. Around 4 kW of permanent light were installed. The time interval between two images of Fig. 3 is approximately 0.015 s. The rough flow surface appears white whereas the
Description
Two tests with different discharges were selected for a detailed discussion, namely Test 2 (Table 1) of which the inception point I was located at the model beginning to generate a large aerated flow length within the test reach (hc/s = 1.8, similar to Fig. 2b), and Test 5 (Table 1) with an inception point I close to the chute end (hc/s = 3.3, similar to Fig. 2c), to study the reach immediately upstream of air self-entrainment. As hc/s differs in these two tests, i.e. the discharges are different,
Conclusions
The pseudo-bottom-inception point I of stepped spillways is characterized by a pseudo-bottom air concentration of 1%. It is located further upstream than on a smooth spillway, because of a higher increase of the turbulent boundary layer thickness and the high turbulence level close to the bottom. The location of the inception point I is of interest related to the mixture flow depth, cavitation aspects and flow losses.
The zone close to the pseudo-bottom-inception point was visualized with a
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