spillways labyrinth discharge coefficients according to position in

E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
SPILLWAYS LABYRINTH DISCHARGE COEFFICIENTS ACCORDING TO POSITION IN RELIEF
CHANNEL
(1)
GUSTAVO A. DELGADO F.
(1)
(2)
& OSCAR PAZ PAIZ
(2)
Universidad Central de Venezuela, Caracas, Venezuela,
guszzz@hotmail.com
Universidad Nacional de Oriente, Chiquimula, Guatemala,
oscar1990_6@hotmail.com
ABSTRACT
In recent times more dams are starting to use labyrinth weirs to replace structures due to the fact that the original structure
is insufficient. This weir increases the volume of discharge in a high event situation. The advantage is the actual increase
of the body's normal level of water to replace dam volume losses, while maintaining the same level of high water. These
losses might be due to sedimentation and incomplete hydrology. The position of the weir in the discharge channel
influences the increase of the discharge, and it is well known that the larger amount of water that is placed above this
structure, far from the effects of the channel walls, the larger the discharge coefficient becomes. The numerical
specification (graphics discharge coefficient) is important to be implemented in any design or rehabilitation. This aspect is
important in cases where spill weirs are replaced by maze cornices, which seek to maximize the available space.
Keywords: Dams, Weirs, Coefficients, Upstream, Labyrinth
1.
INTRODUCTION
The dams’ designer starts to use labyrinth weirs in the spillways because dams’ original design is insufficient due to
climate changes. The implementation of these structures has been indicated as beneficial elements in water reservoirs
due to the increase of the discharge in high events. The characteristic advantage in case of rehabilitation reservoir is that it
can increase the body´s normal level of water to replace dam volume losses while maintaining the same level of “high
water”. In recent times the climate change has caused a different basin hydrologic regime. This new regime can increase
the input water over the dam and as a consequence, in the spillway. This structure can be used in a new design too,
because some developing projects can bear this situation in the future.
The first important characteristic in labyrinth weirs is the position of weirs segments in alternative position, looking in plant
view like teeth. It increases effective length of spillway discharge for the same channel width. There is extensive literature
that provides the design of a labyrinth weir[1]. However, many aspects of the functioning of these structures have not been
investigated. Even in simple cases, it is still advisable to carry out the study of the hydraulic operation reduced to physical
models.
In some studies, information on the effects of the discharge coefficient's position can be found with respect to the reservoir
spillway. The author [2] found that the discharge coefficient increases to the extent that the weir goes into the approach
channel and decreases when placed within the channel. This Study presents effects on the discharge coefficient
according to the first wall adjacent to the spillway chute but no numerical conclusions.
It is important to build a hydraulic model for research to visualize the effects of the position of the weir and starting point of
the channel, to provide more quantitative information. For this reason, it is necessary the study of this device, according to
a physical scale geometric equivalent of a labyrinth spillway weir, to perform a quantitative and qualitative behavior of the
hydraulic analysis for various situations. This analysis will be done through observations made to the various forms of the
model under study.
2.
PROCEDURE
Obtaining discharge coefficients is performed by evaluation activities discharge into the hydraulic model, which is a
generic, non-specific scale model built on a material which usually provides a rough equivalent to the roughness of the
concrete.
Specification of dimensions and shapes of the elements are based on the previous studies to be implemented. Other
authors have conducted research on features and experiences on the hydraulic performance of the Labyrinth spillways.
They have expressed their conclusions and construction procedures with respect to a specific characteristic. There is an
unification of criteria in this regard, although there are some that have matches at certain points.
__________________________________________
[1] Tullis, and Amanian Waldron, ASCE (1995).
[2] Houston (1998).
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
Many of these items have led to construction procedures and technical indication, which have been consulted. The
purpose of this information is to select design data to optimize the operation of the model. Availability of structure in the
laboratory to design implementation model are also evaluated. It is stressed that the components to be implemented are
the number of cycles, cycle width, spillway crest length, opening angle between the walls of the cycle and height of weir
wall.
Figure 1. Cycle dimensions.
The implemented approach is characteristic to evaluate in this research, in which the weir position was designed with
respect to the upstream channel. All four modes by varying the channel length of relief were implemented. Were named A,
B, C and D. It can be seen in Figure 2, the four types of approach implemented.
Figure 2. Approach configurations.
The request to supply air to flow at the time of discharge, resulting in constructive need to implement structures in the
model for the air supply to the flow discharge, without altering the geometry of the model. This action is to prevent the flow
adheres to the wall weir. In the model developed a series of ducts was created within the walls of the weir, whose outputs
are under the discharge. The location of the outlet ducts is determined at the geometric center of the wall weir discharge.
Finally, the model is placed in a channel and is given a high flow from the constant level reservoir in order to provide flow
and stabilize downloading instantly through the spillway. The primary measurement to take into the model is the height of
water above the edge of the spillway, which is called hydraulic load. It is considered measurement routines to various
hydraulic loads and assessing the volume of discharge. The margin of systematic errors and measurement, corrections
are considered. In Figure 3 shows the model built in operation.
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E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
Figure 3. The model in operation.
3.
CHARACTERISTIC OF THE MODEL
The model needed several characteristics to develop a high performance, so it uses previous studies to keep high
conditions in the coefficients. This previous studies is about the physical characteristics y design.
3.1 Configuring a trapezoidal labyrinth weir
Numerous weirs are designed using this type of structure for discharge, in which the number and the direction of cycles
vary. Changing the direction of cycles is performed in order to be able to extend the effective length or adding more
cycles. Orientation can project cycle in a linear way, being located next to each other considered including an axis
perpendicular to the flow.
Previous studies [3] show that according to empirical tests on the structure geometry with three cycles (N = 3), it was
possible to observe the highest rates of discharge of the options studied. This fact can be attributed to the low interference
suffered by the nape effluent to pass through the weir crest because ground geometry provides increased effective length
straight discharge.
Figure 4. View plant. Flow over three labyrinth weirs cycles.
3.2 Crest Length.
The trapezoidal labyrinth weir type crest length for a cycle is given by the equation:
Lt = 2b + 4a
[1]
Where "b" is the measure weir wall and "a" is the value of half the apex.
But another study [4] developed a methodology of calculation for which they developed a graph, where present the weir
discharge length with respect to a length of spillway crest is drawn straight.
________________________
[3] Sartor (2011)
[4] Taylor and Hay (1970)
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
3.3 Angle between walls weirs. (α)
Other study [5] developed a series of assemblies to determine the angle that occurs between the cycle´s walls in a
Trapezoidal weir where the author can throw graphics results for different values subjected to experimentation. It
expresses values for angle from 6 ° to 90 ° is equivalent to a weir crest rect. The value of 8º is the value for which the best
discharge coefficient is obtained.
3.4 Apex. (a)
The complete equation for calculating the apex is deduced previously [6] that in his research indicates that the lowest
value, which the interference of a trapezoidal weir discharge occurs, is given by:
A = sin ((w-4 α) / (α L-4))
[2]
The complete equation for calculating the apex indicates that the lowest value which the interference of a trapezoidal weir
discharge happen.
3.5 Approach Conditions
Others highlights [7] say the need to develop experimental models symmetrical lateral approach. It is further based on the
chess-river dam studies for the structure design approach channel. It conducted important studies regarding variants of
the approach flow, breaking schemes to locate the weir structure entirely within the reservoir. The labyrinth cycles
extension the within the reservoir for observations in discharge were his initiative, but it does not express graphics about
results.
The labyrinth cycles extension the within the reservoir for observations in discharge were his initiative, but it does not
express graphics about results [8].
Using a linear model of a generic type scale concluding that if the weir is introduced into the water reservoir influences the
discharge [9].
3.6 The channel output.
From this author, in a previous studies can determinate that the best conditions to the output pieces between the weirs
segments is 0,5 inclination. [10]
3.7 Dimensionless scaling factors.
The dimensionless parameters included in this relationship are typical fluid mechanics problems and special names
associated with those who have made significant contributions to related aspects, or that have been proposed for specific
problems, among them are: R, Reynolds number; F, Fraud Number; M, Mach number; W, Weber number; E, Euler
number.
3.8 Crest form.
The crest used in the weir top was Quarter Round type, because it is the best performance opposite to nape interference.
Figure 5. The Quarter round Profile.
________________________
[5] Tullis (1994)
[6] Falvey (2002)
[7] Tullis (1996)
[8] Houston (1983)
[9] [10] Delgado (2009)
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E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
Finally the model characteristic is the following:
Table 1. Dimensions used in the model.
Dim
LON
W
WC
LC
B
60 cm
20 cm
83 cm
36,5 cm
2,5cm
8º
8 cm
3
249 cm
A
α
P
N
Lt
4.
DISCHARGE COEFFICIENT
It is a dimensionless coefficient implies characteristics of the weirs and the flow increase. Many authors have considered
developing its own discharge coefficient equation, but in the same way have pointed out shortcomings in the results, to
make comparisons between obtained experimental setups and measured on the prototype. Tullis (1995) uses a discharge
coefficient equation widely cited by some researchers, such as Falvey (2003). The equation is based on elements of the
weir and the discharged flow, the hydraulic head (height H). The discharge coefficient can be determined by various
formulas, but the most relevant, directed from previous studies is that developed by Tullis (1995). This equation states that
the discharge coefficient is a function of the weir and the values of Ho extent discharge.
=
∗
2
∗ ∗ √2 ∗
3
2
3
[3]
5. RESULTS
Finally, after the testing, the flow rate values are obtained, and these are computed, to obtain the coefficients of discharge.
These values are entered in graphs that are nominated according to the terms Cd according to Ho/P. “Cd” is obtain from
the equation “3”, “Ho” is the flow level over the crest weir and “P” is the weir height. The results are relevant to A, B, C and
D approach configurations.
Figure 6. The graphics for the discharge coefficients to the A, B, C and D approach configurations
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
6. RESULTS ANALYSIS
When low hydraulic load values were used in all the configurations, can find almost similar load values in magnitude.
When the weir is observed within the reservoir, increase in the coefficient. In high hydraulic case heads, approaches were
equally discharge amount.
As a possible direct cause of the discharge coefficient variations can be on the influence of the wall channel in the flow.
Can directly observe the discharge coefficient increased when this feature reduces its area. The results and observations
derived are specific, and can’t be an extrapolation of data to other equivalent configurations and geometries. It is
emphasized that the two configurations without approach channel, increase the interference of the discharge in the
chutes. To implement these structures in labyrinth spillways new projects is recommended type "Introduced in the
reservoir approximation". Decreasing the weir approach channel sidewalls, decreases flow friction and up the flow speed.
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