AIR ENTRAINMENT OF FREE-SURFACE TUNNEL FLOW

 

Juerg Speerli

 

Laboratory of Hydraulics, Hydrology and Glaciology (VAW)

at the Swiss Federal Institute of Technology

CH-8092 Zurich, Switzerland

Tel.: +411 632 66 10 , Fax: +411 632 11 92

e-Mail: speerli@vaw.baum.ethz.ch

 

 

Abstract

High-speed flow in bottom outlet tunnels involve air-water mixture flow. The air flow results from the subpressure downstream from the gate. The air entrained by the high-speed flow is supplied by the air supply pipe and the tunnel portal. As demonstrated, there is a relation between the two air supply discharges, independent of the individual supply rate. The present project refers to spray flow and free surface mixture flow. The latter flow configuration is recommended to inhibit choking of the tunnel flow. Further, a design equation for the required air supply discharge across the supply pipe is presented that inhibits significant subpressures in the gate vicinity. The effects of energy head on the gate, relative tunnel width, degree of gate opening and head loss coefficients are particularly significant, whereas the effect of tunnel length is only moderate.

 

Keywords: Air Entrainment, Free-Surface Tunnel Flow, Air-Water Flow, Air Supply System

 

Introduction

Laboratory experiments on the air entrainment of a free-surface tunnel flow downstream of a bottom outlet gate are presented. A bottom outlet is an essential safety element of a dam. The most important flow conditions in the tailrace tunnel are spray flow for small gate openings and free-surface flow (Sharma 1976). Air is entrained due to large velocities of the water flow downstream of the bottom outlet gate (Wood 1991). The flow is highly turbulent, with a rough mixture surface. Therefore, negative air pressures result in the space downstream of the bottom outlet gate, which may induce vibrations of the gate as well as cavitation. The entrained air will be replaced through the air supply pipe and through the tailrace tunnel to limit the negative air pressure. In the case of free-surface flow an interaction between the air supply pipe and the tailrace tunnel occurs (Ghetti and Di Silvio 1967). For spray flow the spray prevents this interaction, and the ventilation takes place only through the air supply pipe (Speerli 1998). The air demand of the water flow is influenced by the approach energy head, the relative gate opening, the loss characteristics of the air supply pipe and the geometry of the tailrace tunnel (Speerli and Volkart 1997). Depending on the general layout of the dam, bottom outlets are long for embankment dams, or when diversion is made across the dam flanks. Experimental results relating to the study of air entrainment in long bottom outlet tailrace tunnels with free surface flow are presented. The interaction of the air flow with the air supply pipe and the air flow in the tailrace tunnel are described in detail.

 

Experimental Installation

The experimental set-up may be subdivided into pumping station and approach conduit, gate chamber with a vertical gate, tailrace tunnel and return flow system. Downstream from the gate of height 0.30 m, the tailrace tunnel height increased under 45^o to the tunnel height of 0.45 m. The tailrace tunnel had a width of 0.30 m and a maximum length of 21.0 m with a bottom slope of 2 %.The tunnel lengths were set to 2.3, 11.1, or 20.0 m, the relative gate openings varied from 0 to 45 %, the approach energy heads were 10, 15, 20 and 25 m, and the throttling degree of orifice between 0 and 100 %.

 

 

Fig.1: Definition sketch of measured parameters and variables.

 

The air supply pipe of 0.10 m diameter runs vertically into the tunnel at the location of height increase (fig. 1). The loss characteristic of the air supply pipe was varied by different throttling degrees of orifice between 100 % (open) and 0 (closed), Rabben (1984). The air discharge was measured with a thermo probe located in the air supply pipe. The water discharge was measured by inductive discharge measurement upstream of the gate. To measure the tunnel air discharge Q_au, a flap gate was located at the outlet section positioned on the mixture flow depth; upstream from this gate, a second air conduit was used for ventilation, with the air flow into or out of the tunnel measured with a miniature propeller meter, to compute the air discharge. The air pressure p_a was measured with piezo-resistive pressure transducers.

 

Air discharges Q_ao and Q_au

 

Influence of the air supply system

Reducing the throttle opening D_o results in a decrease of the air discharge Q_ao through the air supply system, resulting in a simultaneous increase of air discharge Q_au into the tunnel as long as a sufficiently large air cross-section above the mixture flow is available. The total of these two air discharges Q_ao + Q_au = Q_at remains almost constant for all throttle openings as well as for the examined energy heads H_E and tunnel lengths L_u. A reduction of the air discharge Q_ao through the air supply pipe due to a throttling increases the air discharge Q_au into the tunnel. This suggests a certain air entrainment capacity of the water discharge.

 

Concerning the air discharge Q_au, the tailrace tunnel shows a loss characteristic similar to the air supply pipe. With larger gate openings the losses of air flowing into the tailrace tunnel increase, because the air cross-section above the mixture flow decreases. This reduced the air discharge Q_au, and may become zero for choking flow, i.e. if the entire tunnel section is filled with mixture flow. A larger approach energy head causes a higher flow velocity of the mixture discharge and a "rougher" mixture surface. Both effects tend to increase the flow resistance of the air flow into the tailrace tunnel, resulting in increased "friction losses". Figure 2 shows the air discharges Q_ao, Q_au and Q_at as functions of the relative gate opening S for a tunnel length L_u = 20 m. The approach energy head varied from 10 to 20 m.

 

 

Fig. 2: Influence of throttle opening D_o to air discharges Q_ao, Q_au and Q_at in [m³/s] for tunnel length L_u = 20.0 m.

D_o: n 100 %, l 80 %, s 50 %, u 20 %, ¨ 10 %, ¡ 5 %, D 0 %.

Approach energy head H_E a) 10 m and b) 20 m.

 

Influence of tailrace tunnel length

The length of the tailrace tunnel L_u affects both the air discharges Q_ao and Q_au. With increasing tailrace tunnel length, the air discharge Q_ao increases while the air discharge Q_au decreases, because the losses of the air flow in the tailrace tunnel increase. The design of the air supply pipe is, therefore, particularly important for long tailrace tunnels. The total air discharge Q_at is largest for all examined approach energy heads and throttle openings with the short tailrace tunnel (fig. 3).

 

 

Fig. 3: Influence of tailrace tunnel length L_u on air discharges Q_ao, Q_au and Q_at in [m³/s].

 

Analysis of experimental data

A comparison of figures 2 and 3 shows the dependency of the air discharge Q_ao of the relative gate opening S, the approach energy head H_E, the throttle degree D_o and the tailrace tunnel length L_u. An increase of each individual parameter results in an increasing air discharge Q_ao. The influence of an individual parameter was determined by systematic variation, as described by Speerli (1998). With the dimensionless air discharge q_ao

 

[1]

 

where g is the acceleration due to gravity, B_u the width of the tailrace tunnel and H_E the approach energy head upstream of the bottom outlet gate, the influence of the throttle opening on the dimensionless air discharge is

 

q_ai = D_o^0.9. [2]

 

If the dimensionless air discharge q_ao is divided by D_o^0.9, the parameter

 

q_aD = q_ao /D_o^0.9 [3]

 

can be related to the relative gate opening S as

 

q_aD = 1.6 S^0.5, [4]

 

or

. [5]

 

Equation [5] gives the functional relation between the air discharge Q_ao and the approach energy head H_E, the tunnel width B_u, the tunnel length L_u, the tunnel height H_u, the relative gate opening S and the throttle opening D_o.

 

The throttle opening D_o cannot be used in practice as a design parameter. Therefore, a relationship between the throttle opening and the total loss coefficient of the air supply pipe must be determined. The total loss coefficient of the air supply pipe for a prototype can be determined according to Blevins (1984). The total loss coefficient of the air supply pipe can be calculated with the present data as

 

. [6]

 

The correlation between throttle opening D_o and total loss coefficient of the air supply pipe gives further

 

. [7]

 

Inserting equation [7] in equation [5] gives

 

, [8]

 

or when transformed into the dimensionless air discharge

 

. [9]

 

All data can be reduced to a single curve after equation [9] (fig. 4).

 

 

Fig. 4: Experimental data and (--) equation [9].

 

Conclusions

The total air discharge Q_at (= Q_ao + Q_au) is independent of the throttling degree. The water discharge possesses therefore a maximum air entrainment capacity. For free-surface tunnel flow, air is discharged both through the air supply pipe and the portal section into the tailrace tunnel to the negative pressure area downstream of the bottom outlet gate. A bottom outlet should always be operated under supercritical free-surface flow, with the exception of spray flow for small gate openings. Choking flow is highly undesirable because it may severely damage a bottom outlet. A design formulae for the air discharge Q_ao is presented.

 

Acknowledgements

The author would like to thank the Projekt- und Studienfonds der Elektrizitätswirtschaft (PSEL of Switzerland), who generously funded this research project.

 

References

Blevins, R. D. (1984). Applied fluid dynamic handbook, Van Nostrand Reinhold Company Inc., New York.

Ghetti, A., and Di Silvio, G. (1967). "Investigation on the running of deep gated outlet works from reservoirs." Proc. 9th ICOLD Congress, Istanbul, 2, Q33, R48, 837-852.

Rabben, S. L. (1984). "Untersuchung der Belüftung an Tiefschützen unter besonderer Berücksichtigung von Massstabseffekten (Investigation of aeration of bottom outlet gates under particular consideration of scale effects)". Mitteilung Nr. 53, Institut für Wasserbau und Wasserwirtschaft, RWTH Aachen, Germany. (in German)

Sharma, H. R. (1976). "Air-entrainment in high head gated conduits." Journal of the Hydraulics Division ASCE, 102(HY 11), 1629-1646.

Speerli, J., and Volkart, P.U. (1997). "Air entrainment in bottom outlet tailrace tunnels." Proc. 27th IAHR Congress, San Francisco, Theme D, 613-618.

Speerli (1998). "Strömungsprozesse in Grundablassstollen (Flow processes in bottom outlets)", Dissertation ETHZ, Nr. 12583, Zürich, Switzerland.

Wood, I. R. (1991). "Air entrainment in free-surface flows." IAHR Hydraulic Structures Design Manual Nr. 4, A.A. Balkema: Rotterdam, The Netherlands.