Labyrinth Weir Paper

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1 BACKGROUND FOR STUDY OF LABYRINTH WEIR IN ECUADOR The objective of the study is to study the performance of a proposed labyrinth weir to be used as spillway on a planned dam in Ecuador. The labyrinth weir is modelled in DHI’s three-dimensional (3D) numerical model, NS3. One section of the weir is included in the set-up. The flow approaching the upstream of the dam/weir is modelled by MIKE 21 HD model. The design discharge is 3660 m 3 /s The weir and spillway that are investigated is shown in Fig 1 .1. The left side of the figure shows the dam, and on the right-hand side the labyrinth weir is shown with a spillway leading the water to a stilling basin. Fig 1.1 Overview of the proposed dam and labyrinth weir The total width of the labyrinth weir is 186m and consists of 12 sections (teeth), each 15.5m wide. Upstream the labyrinth weir, the bed level is 112m. The crest level of 1

Transcript of Labyrinth Weir Paper

Page 1: Labyrinth Weir Paper

1 BACKGROUND FOR STUDY OF LABYRINTH WEIR IN ECUADOR

The objective of the study is to study the performance of a proposed labyrinth weir to be used as spillway on a planned dam in Ecuador. The labyrinth weir is modelled in DHI’s three-dimensional (3D) numerical model, NS3. One section of the weir is included in the set-up. The flow approaching the upstream of the dam/weir is modelled by MIKE 21 HD model. The design discharge is 3660 m3/s

The weir and spillway that are investigated is shown in Fig 1.1. The left side of the figure shows the dam, and on the right-hand side the labyrinth weir is shown with a spillway leading the water to a stilling basin.

Fig 1.1 Overview of the proposed dam and labyrinth weir

The total width of the labyrinth weir is 186m and consists of 12 sections (teeth), each 15.5m wide. Upstream the labyrinth weir, the bed level is 112m. The crest level of the labyrinth weir is 116m. The top of the dam is located at 120m.

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2 ANALYSIS OF LABYRINTH WEIR

The flow over one of the 12 sections is modelled with DHI’s in-house CFD tool, NS3. The results are compared with text book results, /4/.

2.1.1 Computational Set-upThe length, L, of a single section is 59.4m, the width 15.5m, and the angle of the labyrinth part is 11.98°.

The flow towards and over the weir is found directly from the NS3 computations. In the present calculations, no turbulence model has been used because the flow upstream and over the weir is very close to be a potential flow. On the downstream side of the weir, the flow will be highly turbulent.

The spatial discretisation is based on the finite-volume approach on a multi-block grid. The time integration of the Navier-Stokes equations is performed by application of the fractional step method. Figure 2.2 shows an example of the multi-block grid with one section, cf the labyrinth weir. The grid has only been shown at the bed and on the weir. The grid consists of 23 blocks.

Figure 2.2 Example of the computational grid

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2.2 Results

The discharge over one section of the labyrinth weir has been found by NS3 for six upstream water levels. Based on the flux and the H, the discharge coefficient in the for-mula from Tullis (1995) can be found from equation (4).

(4)

Q is the discharge over one labyrinth section, CT the discharge coefficient, L the entire length of one labyrinth weir, g the gravitational acceleration and H the total head above the weir level, which includes the velocity head.

In the present case, L is 59.4m as only one out of twelve sections is included in the sim-ulations. g is 9.81m/s2.

The flow over the weir has been estimated for six upstream water levels. Figure 2.3 shows the in-flow development in time from the initial conditions until stationary condi-tions have been achieved. The correct inlet velocity is not known, as it has to be found automatically. Therefore, waves will be created on the upstream side of the weir. As the inlet level is kept constant, the inlet velocity will change until equilibrium of the incoming flow and the flow over the weir has been achieved. This gives a high stagna-tion pressure, which generates a wave back to the in-let. Here, the water level is kept constant and therefore the inlet velocity is reduced. After some time, more water has gone over the weir than into the domain and therefore a sloping surface towards the weir increases the inlet velocity. This cycle is repeated, but with smaller and smaller amplitude. In all the six cases, stationary conditions are found before 50s after the initial conditions.

A comparison between the discharge and coefficients found from Tullis (1995) and NS3 is given in Fig 2.4. The agreement is very good for all six cases.

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Figure 2.3 Development of the integrated flow over one labyrinth weir from the various initial conditions.

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Fig 2.4 Comparison between the NS3 results and the formula given in Tullis (1995) Discharge and discharge coefficients

2.2.1 Examples of Flow Field

Initial surface After 6s

After 20s After 45s

Figure 2.5 Free surface flow over the labyrinth weir from Case 6

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Figure 2.5 show examples of the flow field with a upstream water level of 2.375 m above the crest level of the weir.

When the nappes (the flow over the weir crest) from two weirs placed at an angle inter-act, it has an impact on the flow over a limited length of the weir crest. This is called nappe interference. According to /4/, nappe interference can reduce the performance of the weir. In all the cases examined, the nappe interference is small and has no signific-ant impact on the flow.

In order to test the approach of only modelling one section of the labyrinth weir, a sens-itivity test has been made. This test consisted of two sections at the labyrinth weir. Each section was configured exactly as the cases with one section. The flow is Case 6, which reflects the design flow case. An example of the flow at t = 25.2s is given in Fig 2.5.

The flux per section was found to be the same for one and for two sections. Therefore, the modelling of one section is adequate to study the performance of the labyrinth weir itself.

Fig 2.5 Example of the free surface flow with two sections at the labyrinth weir.

3 FLOW UPSTREAM THE DAM

In the previous section, it was found that the discharge formula given in Tullis (1995) gives an accurate estimate of the flow over the labyrinth weir when the flow approaches the weir perpendicular. However, the flow approaching the weir cannot be expected to be perpendicular a few depth away from the weir. In this section, the effect of the upstream flow on the overall weir performance is investigated.

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3.1 Methodology and Set-up

The flow upstream of the weir is modelled with MIKE 21 HD, /12/. MIKE 21 HD is a depth-averaged hydrodynamic model. It simulates water level variations and flows in response to a variety of forcing. For this study, it is used to simulate water level vari -ation and flows due to a sloping water surface. Locally, the surface slope is balanced by bed shear stress, momentum exchange, and acceleration.

The model requires the following input data: bathymetry, description of the driving forces, flow and/or water level conditions at the boundaries of the model and parameters describing the bed resistance and momentum exchange coefficients.

The bathymetry upstream of the dam and weir is shown in Fig 3.1. The weir is mod-elled as a flux boundary, and at the open boundary upstream of the dam the water level is assumed constant. The Manning number is set to M = 32m1/3/s, the eddy viscosity to 1.0m2/s.

The modelling approach is as follows. For a fixed upstream water level, an initial guess of the discharge at the weir is used to calculate the flow field in the entire domain. This results in a revised water level at the weir. Based on the varying water level along the weir, Tullis (1995) is used to give a better estimate of the discharge for the fixed water level. The procedure is repeated until convergence. In this way, the discharge over the labyrinth weir is found for one fixed value upstream water level. For other levels, the procedure is the same.

Fig 3.6 Bathymetry upstream of the dam and wei, and flow pattern upstream the dam and weir in the design case. Levels are relative to the weir crest

The bathymetry and flow in the main part of the domain is shown in Fig 3.1. The flow speed is in general small in the main basin upstream of the dam. It is clear that the flow approaches the labyrinth weir under a large angle. Here the flow speed increases signi-ficantly.

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Figure 3.7 illustrates the flow field close to the weir for the design case. Upstream the dam, the water level is set to 3.2m in this case. The level decreases significantly as the current approaches the labyrinth weir. The water level is relatively small at the northern side of the weir, and largest just south of the middle part.

Figure 3.7 Flow pattern close to the labyrinth weir in the design case. Levels are relative to the weir crest

The water level upstream the dam forces the water to be redirected towards the weir and accelerates the water. If no redirection was needed, as it would be the case for a perpen-dicular approaching flow, the total head, H0, would be constant until it reached the weir

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(apart from small energy loss due to bed friction, which can be neglected over shorter distances). In this case, a part of the total head can be said to redirect the flow.

Far away from the weir, the velocity head can be neglected and therefore the water level gives a direct measure of the total head. In Table 3.1, results from two converged MIKE 21 HD calculations are shown. From the table, it is clear that the effective dis-charge coefficient is reduced in the order of 16 to 17 percent. This change seems to be rather constant over a large regime of extreme flows.

Table 3.1 Flow test cases for the MIKE 21 HD computations. H0 is the total head upstream of the dam in the MIKE 21 computation, while H0_uniform is the total head for a current approaching the weir perpendicular. Qtot is the total discharge.

Case H0 H0_uniform Qtot (H0/H0_uniform)1.5

1 2.0 1.77 2300 0.832 3.2 2.84 3660 0.84

Figure 3.8 and Figure 3.9 show the water level and discharge along the weir. It is quite clear that the flow in the northern part of the weir is significantly reduced by the uneven discharge. For the design flow, the flux in the northern part is smaller than 10m3/s/m and the maximum is 22m3/s/m. The average discharge is 19.7m3/s/m. This might not be a problem for the weir and the upstream area, but when the flow reaches the stilling basin an uneven hydraulic jump can be generated. If this happens, there will be a risk of the jump being swept-out of the stilling basin, and severe circulation might be generated in the stilling basin.

Figure 3.8 Water level along the weir for two discharge flows

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Figure 3.9 Uneven discharge along the labyrinth weir

A similar curve as the one shown in Fig 2.3 is given in Fig 3.5 including the upstream effects on the flux. The discharge coefficient is generally smaller for all flow cases due to the necessity of redirecting the flow close to the weir.

Fig 3.5 Modified discharge coefficient from MIKE 21 HD calculation due to redirection of the flow

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4 SUMMARY AND CONCLUSIONS

The performance at a labyrinth weir has been studied numerically. The result has been compared with results from the literature.

The following conclusions are made:

1. The discharge over the labyrinth weir can be found using the formula by Tullis (1995) as a very good agreement has been found between the formula and the numerical results.

2. Due to the bathymetry and flow pattern upstream the dam and weir, the discharge is ten percent smaller than the one found from Tullis (1995), for the same upstream total head. The water level upstream the dam is estimated to be 119.2 in the design case. No assessment of surge wave and wind waves due to overtopping has been made.

3. The performance of the weir might be improved in a number of ways. In order to have a better performance, the water level along the labyrinth weir has to be con-stant. This might be achieved by prolonging the guiding wall, excavating the bed perpendicular upstream at the weir, or for instance move the entire labyrinth weir downstream of the present proposed location.

5 REFERENCES

/4/ Falvey, HT.: ”Hydraulic design of labyrinth weirs”, Book from ASCE Press, 162 pp, 2003.

/5/ Christensen, ED., Zanuttigh, B. and Zysermann, J. (2003): ”Validation of Numer-ical Models Against Laboratory Measurements of Waves and Currents Around Low-Crested Structures”, In Proc of Coastal Structures 03, 26-29 August 2003, Portland, Oregon.

/6/ Emarat, N., Christensen, E. D., Forehand, D. I. M. and Mayer, S. (2000): "A study of plunging breaker mechanics by PIV measurements and a Navier-Stokes solver", in Proc. of the 27th Int. Conf. on Coastal Eng., ASCE, Sydney, Australia, Vol. 1, pp 891-901.

/7/ Hirt, C.W., and Nichlos, B.D. (1981): ”Volume of Fluid (VOF) method for the dynamics of free boundaries”, J. Comput. Phys. Vol. 39, pp 201-225.

/8/ Kawamura, T., Mayer, S., Garapon A. and Sørensen, L. (2002): ”Large eddy sim-ulation of a flow past a free surface piecing cylinder”, J. Fluids Eng. Vol. 124, pp 91-101.

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/9/ Mayer, S., Garapon, A. and Sørensen, L.S., 1998. “A fractional step method for unsteady free-surface flow with application to non-linear wave dynamics”, Intl. Journal for Numerical Methods in Fluids, Vol. 28, No. 2, pp 293-315.

/10/ Nielsen, KB, and Mayer, S., 2004. “Numerical prediction of green water incid-ents”, Ocean Engineering, Vol 31, pp 363-399.

/11/ Ubbink, O. (1997): ”Numerical prediction of two fluid systems with sharp inter-faces”, Ph.D. thesis, University of London.

/12/ MIKE 21 HD reference manual, DHI Water & Environment, 2004.

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