Jian-hua WU （吳建華）， Shang-tuo QIAN （錢尚拓）， Fei MA （馬飛）

College of Water Conservancy and Hydropower Engineering， Hohai University， Nanjing 210098， China，E-mail: jhwu@hhu.edu.cn

A new design of ski-jump-step spillway*

Jian-hua WU （吳建華）， Shang-tuo QIAN （錢尚拓）， Fei MA （馬飛）

College of Water Conservancy and Hydropower Engineering， Hohai University， Nanjing 210098， China，E-mail: jhwu@hhu.edu.cn

A new kind of ski-jump-step spillway was reported. By means of the effects of the aeration basin， it supplies the sufficient aeration flow from the first step for stepped chutes， especially for large unit discharge. The physical model experiments demonstrated that， this spillway makes a far better hydraulic performance as regards energy dissipation and cavitation damage protection than the current and conventional stepped spillways， and the unit discharge can be enlarged from about 50 m3/s-60 m3/s·m to 118 m3/s·m in order to significantly reduce the width of the spillways.

cavitation， energy dissipation， pre-aeration， ski-jump-step spillway

Over the last 30 years， several dozens of hydropower projects， characterized by high water head， large discharge and narrow valley， have been constructed within China. Stepped spillways， thanks to their simple structure and high energy dissipation， are widely used in the designs of the release works for high dams. However， there are the limits of unit discharge about 50 m3/s·m-60 m3/s·m for those stepped spillways. Both low energy dissipation and cavitation damage risk， due to insufficient air entrained into the flow in several foregoing steps of the spillways， may be brought about if the discharge exceeds the limit. So， many investigations on the enlargement of the unit discharge of the stepped spillways have paid much attention to in order to reduce the width of the spillways， especially in arrangement of those release works in narrow valley.

Pfister et al.［1］and Wu et al.［2］proposed the bottom aeration method using an aerator device at the first step. But， non-aeration zones still appear in two sidewalls. Furthermore， Pfister et al.［3］and Zamora et al.［4］presented another aeration method through placing a deflector at the vertical wall of the first step. However， in common with the method of the bottom aerator device， there are also non-aeration zones in two sidewalls in the deflector method.

Here， we will report a kind of ski-jump-step spillway， developed in the present work （Fig.1）， which can produce a sufficient aeration flow from the first step of the stepped chutes （i.e.， no non-aeration zones） so that it could achieve high energy dissipation and low cavitation damage risk， especially under the operation conditions of large unit discharge.

Figure 1 shows the definition sketch of ski-jumpstep spillway geometry， including five parts as an entrance section， a ski-jump， a pre-step section， an aeration basin， and a stepped chute. When the discharge is small， the flow passes through every part in turn， and it is the nappe flow regime that appears in each step of either the pre-step section or the stepped chute. In this flow regime， the flow energy is mainly dissipated by jet break in the air， jet impact and mixing on the step，and formation of full or partial hydraulic jump. Meanwhile， cavitation and atomization phenomena are virtually weak because of the low flow velocity.

With the continuously increasing discharge， the ski-jump and the aeration basin begin to play the role of pre-aeration. A large amount of air is entrained through ski-jump jet splashing in the air， and flow impact， diffusion and recirculation in the aeration basin. The sufficient aeration flow is formed by means of the pre-aeration effects of the aeration basin and is supplied to the stepped chute.

Fig.1 Definition sketch of ski-jump-step spillway geometry and flow regime at large discharge

Fig.2 Description and photos of skimming flow

In order to verify the advantages of the ski-jumpstep spillway presented in this work， the experiments were conducted in the High-speed Flow Laboratory of Hohai University in Nanjing， China. The physical model was designed according to the gravity similarity criterion at a scale of 1:40 in order to obtain the unit discharge in prototype［5］.

For the test physical model， the entrance section，with the horizontal length and vertical height of 0.33 m and 0.21 m， consisted of three parts as WES，tangent and drop. At the pre-step section and the stepped chute， each step was of the length a=0.11m and of the height b=0.09m . The ski-jump was 0.33 m in length and connected to the aeration basin by the pre-step section with 6 steps. The aeration basin was 0.88 m in length and 0.27 m in height， and the stepped chute downstream contained 16 steps.

The unit discharges varied between 0.01 m3/s·m and 0.47 m3/s·m in model， and then between 2.52 m3/s·m and 118.00 m3/s·m in prototype on the basis of the model scale of 1:40， resulting in the relative critical depthsc/hb between 0.24 and 3.12， here， hcis the critical depth.

The energy dissipation is defined as η=1-Hres/ Hmax， with Hmax=h1+H1+/（2g） to be the energy head in Section 1 and Hres=h2+/（2g） the one in Section 2， respectively （see Fig.1）.

Figure 2 presents the description and photos experiment finished by the authors， of the skimming flows over the conventional stepped spillway and ski-jump-step spillway， respectively， which are of the same step geometries. For the conventional stepped spillway， there is clearly a non-aeration flow region whatever the unit discharge is， which may be characterized by the position1L of the inception point of air entrainment （see Figs.2（a） and 2（b））. It is this1L that is the material weakness due to the existence of cavitation damage risk for the conventional stepped spillway. However， no non-aeration flow region appears in the ski-jump-step spillway due to sufficient air entrained into the water in the aeration basin （see Figs.2（c） and 2（d））. The present ski-jump-step spillway geometry could effectively eliminate those non-aeration flow regions so that cavitation damage risk could be avoided， and this may be one of the best outstanding characteristics for the skijump-step spillway. Besides， comparing with the conventional stepped spillway， the flow through the present geometry could decrease the range of the varied flow region in order to rapidly develop a uniform flow state.

Fig.3 Variations of η with hc/b

Figure 3 shows the variations of η withc/hb，and the data of conventional stepped spillways with various slope θ are cited from Refs.［6-8］. For any givenc/hb， the ski-jump-step spillway has obviously higher η， and the advantage of the energy dissipation increases with the increasingc/hb， comparing with the others. Especially whenc/hb reached 3.12 （corresponding to the unit discharge of 118.00 m3/s·m in the prototype）， still， η=75.8% for the ski-jump-step spillway. In contrast， the energy dissipations of the conventional stepped spillways are obviously insufficient under this condition.

The pre-aeration effect of the ski-jump-step spillway can be illustrated by the air concentration C on the first step of the present stepped chute. Figure 4 shows the variations of C withc/hb. The air concentration was measured by CQ6-2005 aeration apparatus at the edge of the first step with the center line of the bottom and the side wall of 0.025 m from the bottom.

Fig.4 Variations of C with hc/b in first step of present stepped chute

Generally， C is always larger than 2.2% within the whole range of operation discharge. When hc/b= 0.24-2.05， C increases with the increasing hc/b. At hc/b=3.12 （corresponding to 118.00 m3/s·m in prototype）， the air concentrations of the bottom and side wall are still maintained at 4.2 % and 5.1%，respectively. It means that the air concentrations are sufficient to control the cavitation damage risk［9］.

In summary， the ski-jump-step spillway， developed in this work， shows better hydraulic performance with regard to energy dissipation and cavitation damage protection than the current and conventional stepped spillways， especially for large unit discharge. The unit discharge can be enlarged from about 50 m3/s·m-60 m3/s·m to 118 m3/s·m in order to drastically reduce the width of the spillways.

References

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［2］WU Shou-rong， ZHANG Jian-min and XU Wei-lin et al. Experimental investigation on hydraulic characteristics offlow in the pre-aerator stepped spillways［J］. Journal of Sichuan University， 2008， 40（3）: 37-42. （in Chinese）.

［3］PFISTER M.， HAGER W. H. and MINOR H. E. Stepped chutes: Pre-aeration and spray reduction［J］. International Journal of Multiphase Flow， 2006， 32（2）: 269-284.

［4］ZAMORA A. S.， PFISTER M. and HAGER W. H. et al. Hydraulic performance of step aerator［J］. Journal of Hydraulic Engineering， ASCE， 2008， 134（2）: 127-134.

［5］PFISTER M.， CHANSON H. Two-phase air- water flows: Scale effects in physical modeling［J］. Journal of Hydrodynamics， 2014， 26（2）: 291-298.

［6］CHINNARASRI C.， WONGWISES S. Flow regimes and energy loss on chutes with upward inclined steps［J］. Canadian Journal of Civil Engineering， 2004， 31（5）: 870-879.

［7］CHINNARASRI C.， WONGWISES S. Flow patterns and energy dissipation over various stepped chutes ［J］. Journal of Irrigation and Drainage Engineering， 2006，132（1）: 70-76.

［8］CHRISTODOULOU G. C. Energy dissipation on stepped spillways［J］. Journal of Hydraulic Engineering， ASCE，1993， 119（5）: 644-650.

［9］PETERKA A. J. The effect of entrained air on cavitation pitting［C］. Proceedings of Minnesota International Hydraulics Convention. Minneapolis， USA， 1953， 507-518.

（August 25， 2016， Revised September 13， 2016）

* Project supported by the National Natural Science Foundation of China （Grant No. 51479057）， the PAPD （Grant No. 3014-SYS1401）.

Biography： Jian-hua WU （1958-）， Male， Ph. D.， Professor