Effect of intake head wall and trash rack on vortices

Abstract

The effect of the intake head wall slope and the installation of a trash rack on the type and strength of vortices are studied experimentally. The strength within each vortex was determined by measuring its tangential velocity utilizing an Acoustic Doppler Velocimeter (ADV). Experiments were carried out with a projected intake and an intake with various head wall slopes, discharges and submerged depths. The results from the projected intake tests indicated that Type 6 vortex was present. However, the vortex strength and type reduced as the intake head wall slope increased up to the vertical position. In addition, increasing the intake head wall slope increased the vortex instability. All tests were repeated with a trash rack. A relationship was developed for vortex strength and the intake critical submerged depth based on the intake Froude number and the head wall slope. Moreover, a relationship has been found between vortex strength and type.

Keywords:

• Circulation number
• critical submergence
• experimentation
• head wall
• trash rack
• vortex

1 Introduction

Vortex formation at power intakes may occur at lower reservoir levels. The intake submerged depth and the geometry and layout of the intake have a direct effect on the vortex strength. Vortices can draw debris and air into an intake causing vibration and damage to turbines. Based on the visual classification of Alden Research Laboratory (Fig. 1), vortices can be divided into six types (Knauss 1987).

Figure 1 Types of vortices (Knauss 1987)

Vortex strength is evaluated by its circulation at the irrotational vortex region as

where Γ is the vortex circulation and v_θ the tangential velocity at a distance r from the vortex axis. To prevent formation of air core vortices, a minimum operating depth, called critical submerged depth S _c , is recommended. The distance between the water surface and the intake axis is defined as S (Fig. 2).

Figure 2 Schematic side view of physical model

The critical submerged depth of air core vortices was found to vary with the intake Froude number F = V/(gD)^1/2, where V is the average tunnel flow velocity, D tunnel diameter and g gravitational acceleration. The critical (subscript cr) submerged depth of air core vortices was described by Gordon (1970)

or by Amphlett (1976)

where λ = 2.3 for asymmetric intake geometry is selected here for comparison. In Eq. (3), C = 3.3 if B/D = 4 and C = 3.95 if B/D = 0.5, where B is the distance between intake axis and approach flow invert.

A reduction in vortex strength in general means a lower critical submerged depth, i.e. as the vortex strength decreases, the safe operating submerged depth is reduced. Any disturbance or obstacle within a vortex increases internal friction and therefore reduces the vortex strength and S _c /D. The proximity of, for example, an adjacent wall (Fig. 2) reduces the vortex strength. In addition, a trash rack induces disturbances in the vortex path reducing its strength. Although these effects on the type and stability of vortices are known, no comprehensive study is as yet available. In the present study, tests were conducted on a projected intake as well as an intake with different head wall slopes 1 : Z (Fig. 2) to investigate their effect on the type and strength of vortices. Relationships are also developed for vortex strength and critical submergence depth. In addition, a relationship is found between vortex strength and vortex type.

2 Dimensional analysis

Using the principles of the dimensional analysis, the relationship among parameters affecting the vortex circulation Γ can be expressed as (Anwar et al. 1978, Jain et al. 1978, Anwar and Amphlett 1980, Knauss 1987, Yildirim et al. 2009)

where ρ is the water density, υ kinematic fluid viscosity, σ fluid surface tension, Z intake head wall slope, T percentage of trash rack opening, N_Γ  = Γ/(2πg ^1/2 D ^3/2) the circulation number, S/D relative intake submergence and R = VD/υ and W = ρV ² D/σ the intake Reynolds and Weber numbers, respectively. If R and W are large enough (see below), their effects can be neglected and therefore Eq. (4) may be written as

3 Experimental set-up

Froude similarity was considered as the basis of the model studies (Anwar et al. 1978, Hite and Mih 1994). As the diameter of typical power tunnels in medium and large dams is between 4 and 10 m, and usual tunnel flow velocities are between 4 and 10 m/s, for a usual model with scales between 1/30 and 1/60, the herein selected model tunnel diameter was 16 cm and discharge was between 0.015 and 0.030 m³/s. The intake had a rounded entrance radius of r = 0.15D (USBR 1974). Model observations indicated that asymmetric flow from the reservoir was necessary to form a stable Type 6 vortex in a wide range of flow conditions.

By studying the layout of typical existing dams, it became evident that the slope of the intake head wall varies between 2 : 1 to nearly vertical. Walls with Z = 2 : 1, 3 : 1, 4 : 1 and a vertical wall were installed (Fig. 2) and vortex strength and type in each test determined and compared with the projected intake. The reservoir walls, the intake structure and the tunnel were made of Perspex. The side walls and the reservoir bottom were more than 4D away from the intake axis to eliminate effects on vortex formation (Anwar et al. 1978).

To avoid scale effects relative to viscosity and surface tension, minimum values proposed are R ≥ 5 × 10⁴ (Daggett and Keulegan 1974), R ≥ 7.7 × 10⁴ and W > 600 (Padmanabhan and Hecker 1984), R ≥ 1.1 × 10⁵ and W > 720 (Odgaard 1986) and W > 120 (Jain et al. 1978). Minimum R and W values in the present work were 1.2 × 10⁵ and 1.2 × 10³, respectively, i.e. more than the above minimum values.

To study the effect of intake head wall slope on vortices, tests were first carried out with an intake projecting one diameter into the reservoir. By applying 4 different discharges and 3 different submergences, 12 Type 6 vortices formed at the intake and their strength was determined. Then, the effect of Z was investigated (Fig. 2) for the same hydraulic conditions. Finally, a trash rack made of copper wire nets was installed at the intake face to study its effects on the vortex strength.

An electromagnetic flow meter installed in the closed piping system was employed to measure water discharge. The water surface elevation was measured by reading the scales marked on the reservoir wall. The tangential flow velocity of the vortices in the reservoir was measured by an ADV of 25 Hz. The correlation factor was above 0.8 in all tests. Measurements were conducted at more than D/2 distance from the vortex axis in the free vortex zone. To measure velocity at each point, data over some 20 s were collected and then averaged. Observations indicated that the proximity of the intake head wall to the location of the vortex caused vortex instability. In these conditions, measurements were made only if the vortex was steady.

4 Experimental results

4.1 Effect of intake head wall slope on vortex type

Measurements were conducted for four different values of F and S/D = 1.5, 1.75 and 2. All vortex types observed are listed in Table 1, indicating that as the slope of the intake head wall increases, the type of vortex reduces. Note that with a projected intake and for the same flow conditions as in Table 1, all vortices were of Type 6.

Table 1 Types of vortices for various flow conditions with different intake head wall slopes

4.2 Effect of intake head wall slope on vortex stability

Experiments indicated that vortices become unstable as the intake head wall slope increases toward the vertical position. To study vortex instability, additional tests with the lowest and highest F and 2 : 1 and vertical intake walls were conducted for three different S/D. In each experiment, the time percentage of vortex presence corresponding to the measurement time was recorded and referred to as the vortex stability. It was determined that at least 20 min of run time was required during each test to measure the vortex stability with confidence. Note that with the exposed intake and for identical flow conditions, all vortices were stable and of Type 6. Since vortices became unstable for steep walls and the vortex type under the unsteady condition was difficult to recognize, vortex Types 6 and 5 were classified together as Class A. Similarly, vortex Types 4 and 3 were classified as Class B (Table 2) and weaker vortices 2 and 1 as Class C. Note that if R is large enough in a model and so scale effects remain insignificant, conditions leading to vortex Class A should be avoided. However, owing to scale effects and the possibility of the formation of weaker model vortices, vortices stronger than Class B (Type 3 or 4) are inacceptable.

Table 2 Vortex stability for various flow conditions and intake head wall slopes

As can be seen from Tables 1 and 2, the intake wall slope has a significant effect on reducing the type and stability of vortices, especially for lower F. For example, if F = 0.6, stable vortices of Type 6 were observed at the projected intake for all S/D, whereas with the vertical intake wall vortices were reduced to Class B with a stability of less than 5%.

4.3 Effect of trash rack

A trash rack disturbs the flow and can therefore reduce the strength and type of vortices. To study this effect, all the previous tests with various wall slopes, F and S/D were repeated to determine the vortex circulation with trash rack presence at the intake. Most prototype trash racks have an open area of 70–80%. A trash rack was therefore built with 75% opening with copper wires of 2 mm thick installed at the intake. A comparison of Tables 1 and 3 shows that trash rack presence reduces the vortex strength, especially the stronger vortices.

Table 3 Vortex type with presence of trash rack

4.4 Calculating vortex strength and type

With over 100 tests of vortex strength for the variable S/D, F and Z, with and without trash rack presence, an equation was developed for N_Γ with a correlation factor of 0.95 as

where T is the trash rack opening, equal to 0.75 for trash rack presence. Without a trash rack, T = 1.0. Based on all test data, a relationship was developed between the circulation number and the vortex type (Fig. 3). Three distinct zones of vortex types are observed. From Eq. (6), the vortex type can then be specified from Fig. 3.

Figure 3 Relationship between vortex type and measured circulation number N _Γ

4.5 Calculating critical submergence depth

As shown in Fig. 3, a vortex stronger than or equal to Type 5 results in N_Γ  > 0.016. Inserting into Eq. (6), the critical submerged depth then is

Similarly, from Fig. 3, N_Γ  > 0.011 defines a vortex stronger than Type 3. Thus, the critical submerged depth then is

To check Eqs. (7) and (8), additional data were collected for 10 various S/D for which the vortex type was measured in terms of F and Z. The submerged depth at which vortex Types 5 and 3 were formed was then compared with the predictions and the agreement was found to be good. Equation (7) for calculating the submerged depth of vortex Types 5 and 6 is also compared with the empirical Eqs (2) and (3) in Fig. 4. The slope of the intake head wall is observed to affect the relationship between F and S _c /D, an effect not considered in previous empirical equations.

Figure 4 Comparison of empirical Eqs (2) and (3) with Eq. (7)

5 Conclusions

Using physical model data, the effects of intake head wall slope and trash rack presence on the type and strength of intake vortices, as well as the critical submerged depth has been studied. The vortex strength was determined by measuring the tangential vortex velocity using ADV. The laboratory tests indicate that the intake head wall slope does affect the type and strength of the vortices, especially at lower Froude numbers F. In addition, it was demonstrated that as the intake head wall slope increases, vortices become more unstable. For example, for F = 0.6, stable vortices of Type 6 were always observed at the projected intake, whereas with the vertical intake head wall, vortices were reduced to Types 2 and 3. With trash rack presence, the vortex strength was further reduced, indicating a lower critical submergence depth. Equations among the circulation number, the vortex type and the remaining test parameters were developed. Finally, an equation for the critical intake submergence considering the intake head wall slope and trash rack presence is given. The slope of the intake head wall was demonstrated to affect these relationships significantly.

Notation

D	=	tunnel diameter
F	=	Froude number
g	=	gravitational acceleration
N Γ	=	circulation number
r	=	distance from vortex axis, radius
R	=	Reynolds number
S	=	submerged intake depth
S c	=	critical submerged depth
T	=	cross-sectional trash rack opening
V	=	average tunnel flow velocity
v θ	=	tangential velocity
W	=	Weber number
Z	=	intake head wall slope
Γ	=	vortex circulation
υ	=	kinematic fluid viscosity
ρ	=	fluid density
σ	=	surface tension of fluid

Acknowledgements

All experiments were conducted at the Water Research Institute, affiliated to the Ministry of Energy, Tehran, Iran, whose cooperation is highly appreciated.