Xu Weilin, Deng Jun and Yang Yongquan
State Key Hydraulics Laboratory of High Speed Flows, Sichuan University,
Chengdu, 610065, China
Abstract: In flood discharge tunnels with free flow, because of the influence of the roofs, the characteristics of self-aerated flows is different from that in the open channels. In order to test the influence of the roofs on the characteristics of self-aerated flows, the experiments on self-aerated flows in open channels and flood discharge tunnels were made and the influence of the roof on the air concentration distribution was studied. The measured results show: the air concentration decreases with the increasing height near the roof; besides, the air concentration in the water drop zone will decrease, even the maximum value of the air concentration on the vertical line may be lower than 99%. Therefore, the influence should be noticed in the calculations of the air concentration distribution, the aerated flow depth, even the air flow rate in the flood discharge tunnel with free flow.
Keywords: self-aerated flow, air concentration, flood discharge tunnel, remaining height
In 1926, the earliest experiment on air-water two-phase flows was made by R. Ehrenburger from Austria.[1] Sixteen years later, L. S. Hall made the first prototype survey in the world. [2] In 1950's, L. G. Straub and A. G. Anderson made a series of experiments on air concentration of self-aerated flows and obtained a lot of valuable experimental data, [3] which have been cited by many scholars in the world. Since then, more and more scholars have studied the self-aerated flows through experiment, theory and calculation, and significant results have been achieved. Wu Chigong advanced a set of theory on self-aerated flows in open channels and deduced the theoretical formulae to calculate the air concentration distribution, by which the calculated results are in good agreement with the experimental data. [4] However, the aims of their researches are all the self-aerated flow in open channels. In fact, the self-aerated flow often occurs in not only the open channels but also the flood discharge tunnels. In the latter, because of the influence of the roofs, the characteristics of self-aerated flows is different from that in the former. In order to test the influence of the roofs on the characteristics of self-aerated flows, a series of experiments on the self-aerated flows in flood discharge tunnels with free flow was made in the State Key Hydraulics Laboratory of High Speed Flows in China.
The experiments were made in a slope-adjustable steep flume with a length of 18m. The slope may change from 0¡ã to 72¡ã. The maximum flow rate is 0.75 m3/s. In experiment, a roof was added on the flume to form a flood discharge tunnel with free flows. The height of the roof may be changed by adjust the binder bolts. In order to measure and observe conveniently the flows in the flume, the roof was made of polymethyl methacrylate. The sensor of the air concentration instrument was led into the aerated flow through the hole in the roof. The layout of the flood discharge tunnel is shown in Fig.1.
For the sake of the comparison between the air concentration distribution of self-aerated flow in flood discharge tunnels and that in open channels, the air concentration distributions were measured firstly under the condition of the open channel without roof. Fig.2 and Fig.3 show the measured results with the flow rate Q=0.26m3/s and 0.33 m3/s respectively. Under this condition, the form of the air concentration distribution has been known very well and can be calculated by the existing methods, e.g. the Straub-Anderson Method,[3] the Wu Method,[4] etc.
According to the definition of the depth of the aerated flow, i.e. the depth (haw) is equal to the height under the point of C=0.99 (C is the air concentration), the haw can be determined from the measured air concentration distribution. In Fig.2 and Fig.3, the haw is equal to 7.5cm and 8.4cm respectively.
After adding the roof, the air concentration distribution was measured under the same flow rate as that in the open channel. Fig.4~Fig.6 show the measured results with Q=0.18, 0.26 and 0.33 m3/s respectively. The height of the tunnel is 9.5cm. Under the condition of Q=0.18 m3/s, the roof has little influence on the air concentration distribution, because the remaining height of the tunnel is enough (the remaining height means the distance between the roof and the point of C=0.99).
Then the flow rate is increased to 0.26 m3/s, the remaining height is 2.5cm and the percentage of the remaining height over the tunnel height is 26%, which is about equal to the upper limit in the design standard of the flood discharge tunnel with free flow (15%~25% is the suggested remaining height of the flood discharge tunnel with high-velocity free flow[5] ). It can be seen that the air concentration distribution is affected a little by the roof.
When the flow rate is increased further, the remaining height decreases and the air concentration distribution has the form shown in Fig.6. The flow rate in Fig.6 is the same as that in Fig.3. The remaining height is 1.6cm and the percentage of the remaining height over the tunnel height is 17%, which is close to the lower limit in the design standard. The influence of the roof on the air concentration distribution is very obvious. Near the roof, the air concentration decreases with the increasing height (H in Figures). At the same time, the air concentration in the upper reach of the water drop zone decreases. The air concentrations on the whole vertical line are all lower than 0.99 under the run condition in Fig.6. Therefore, it should be noticed that the air concentration distribution, the aerated flow depth, even the air flow rate will be affected by the roof.
When the remaining height of the tunnel is enough, the roof has little influence on the air concentration distribution of the self-aerated flow in the tunnel. However, if the percentage of the remaining height over the tunnel height is lower than 20%~25%, The influence of the roof on the air concentration distribution may be very obvious. The influence includes two hands: the air concentration decreases with the increasing height near the roof; the air concentration in the upper reach of the water drop zone decreases. The maximum value of the air concentration on the vertical line may even be lower than 0.99 under certain condition. Therefore, the influence should be noticed in the calculations of the air concentration distribution, the aerated flow depth, even the air flow rate in the flood discharge tunnel with free flow.
[1] Ehrenburger, R., Aerated flow in steep flumes, in: The Translated Papers on High Velocity Flows, Vol.1, No.1, Science Press of China, 1958, 176:185. (in Chinese).
[2] Hall, L.S., Aeration of high velocity flows in open channels, in: The Translated Papers on High Velocity Flows, Vol.1, No.1, Science Press of China, 1958, 1:38. (in Chinese).
[3] Straub, L.G. and Anderson, A.G., Experiments on self-aeration flow in open channels, Proc. ASCE, Hydr. Div., Vol.84, No.Hy7, 1958, 1890-1:35.
[4] Wu, C., Water-air two-phase flows in open channels, Press of the Chengdu University of Science and Technology, 1989, 63:105. (in Chinese).
[5] China Association of Electric-power Enterprises£¬Standards of electric-power industry (Hydro-electric power), Water Resource and Electric Power Press of China, 1995, 285:286. (in Chinese).
Fig.1 Layout of the flood discharge tunnel
Fig.2 Air concentration distribution without the roof (Q=0.26 m3/s)
Fig.3 Air concentration distribution without the roof (Q=0.33 m3/s)
Fig.4 Air concentration distribution with the roof (Q=0.18 m3/s)
Fig.5 Air concentration distribution with the roof (Q=0.26 m3/s)
Fig.6 Air concentration distribution with the roof (Q=0.33 m3/s)
* Supported by the National Natural Science Foundation of China (59709004).