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Investigation of flow characteristics above trapezoidal broad-crested weirs
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Investigation of flow characteristics above trapezoidal broad-crested weirs Mohamad Reza Madadi, Ali Hosseinzadeh Dalir , Davood Farsadizadeh
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Flow Measurement and Instrumentation
Received date: 12 January 2014 Revised date: 24 April 2014 Accepted date: 11 May 2014 Cite this article as: Mohamad Reza Madadi, Ali Hosseinzadeh Dalir, Davood Farsadizadeh, Investigation of flow characteristics above trapezoidal broadcrested weirs, Flow Measurement and Instrumentation, http://dx.doi.org/10.1016/j. flowmeasinst.2014.05.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1 2
Investigation of flow characteristics above trapezoidal broad-crested weirs
3 4 5
Mohamad Reza Madadi*1, Ali Hosseinzadeh Dalir2, Davood Farsadizadeh3
6 7 8 9 10 11 12 13 14 15 16 17 18
1- Ph.D., Department of Water Engineering, Shahid Bahonar University of Kerman, Kerman, Iran., P.O.Box: 76169-133, Email: [email protected], Tel: +989119231606, Fax:+983413222043. (*Corresponding Author)
19
In this study the effect of upstream face slope of a trapezoidal broad-crested weir on discharge
20
coefficient and water surface profile was investigated using the laboratory models. The velocity
21
and pressure distribution profile were determined. The location of the critical section above the
22
weir was specified. The dimensions of flow separation zone were also measured for different
23
upstream face slopes. The results showed that decreasing the upstream face slope prevents
24
development of separation zone. In this case, the flow was passed through the weir more
25
regularly and the water surface and pressure drop were decreased. Decreasing the upstream face
26
slope to 210, increased the discharge coefficient up to 10% and reduced the separation relative
27
length and height up to 80% and 95% respectively.
28
Keywords: Trapezoidal Broad-Crested Weir, Discharge Coefficient, Flow Separation, Velocity
29
Profile, Critical Depth.
2- Professor, Department of Water Engineering, University of Tabriz, Tabriz, Iran., Email: [email protected], Tel: +989143166284. 3- Associate Professor, Department of Water Engineering, University of Tabriz, Tabriz, Iran., Email: [email protected], Tel: +989143135801. Abstract
30 31
1- Introduction
32
Flow measurement structures are one of the main categories of hydraulic structures which are
33
generally designed to act as a control in the open channels to provide a unique relationship
34
between the upstream head and the discharge (Bagheri and Heidarpour 2010, Biotin 2002).
35
Weirs are among the major types of measuring structures which because of their low cost, easy
36
installation and good accuracy have met with great interest. They are generally classified into
37
three groups, namely, broad-crested, short-crested and sharp-crested weirs depending on the ratio
38
of the weir upstream head to the weir crest length. For a broad crested weir, the ratio of crest
39
length (Lcrest) to upstream head over crest ( H − Z ) must be typically greater than 3 (Henderson
40
1966; Chanson 2004).
Lcrest H −Z
> 1.5 − 3
(1)
41
Hydraulically, a broad-crested weir is a flat-crested structure with a crest length large compared
42
to the flow thickness (Harrison 1967; Montes 1969) for the streamlines to be parallel to the crest
43
invert and the pressure distribution to be hydrostatic (Bos 1976; Henderson 1966; Montes 1998;
44
Chanson 2004). In this case, critical flow conditions occur on the crest (Woodburn 1932, Singer
45
1964, Goodarzi et al. 2012). If the up- and downstream faces of the broad crested weir be vertical
46
(namely as Standard Broad Crested Weir), it will operate with a rather significant loss in head
47
and also the sediment or solids may be deposited at the upstream side of the weir, which will
48
adversely affect its accuracy and increase the operating costs. To deal with such problems, the
49
broad-crested weir’s structural design can present some flexibility to provide better hydraulic
50
characteristics and discharge efficiency. For example, if the weir upstream entrance condition
51
changes from square-edged to the round-nosed corner, the weir discharge coefficient will be
52
increased (Ramamurthy et al. 1988). A review on previous studies shows that, to prevent
53
deposition of sediment or solids in the upstream side of the weir as well as to prevent cavitation
54
at the downstream corner of the weir, the upstream and downstream faces of broad crested weirs
55
can be sloped (Sargison and Percy 2009). This type of weirs can be classified as trapezoidal
56
profile weirs (Zerihun and Fenton, 2009), embankment-shaped weirs (Hager and Fritz 1998),
57
ramped broad crested weirs (Azimi et al. 2013), or broad-crested weirs with upstream and
58
downstream side slopes (Sargison and Percy 2009). In this paper, the term trapezoidal broad
59
crested weir is used because the models of weirs which were used in this study are in the range
60
of broad crested weirs (Eq. 1) and also, they have trapezoidal shape in the longitudinal section.
61
According to Fritz and Hager (1998), the discharge equation under free flow condition for this
62
type of weirs can be calculated by: Q = C D B 2 gH 3
(2)
63
Where H is total overflow head, g is the acceleration due to gravity, B is the weir width, and C D
64
is the discharge coefficient and is obtained by:
C D = 0.43 + 0.06 Sin[π (ε − 0.55)]
ε=
(3)
H is relative crest length. Sargison and Percy (2009) modified the Eq. (3) H + Lcrest
65
Where,
66
to account for the effect of upstream face slope (θ ) , resulting in the following equation:
C D = 0.43 + 0.06 Sin[π (ε − 0.55)] − 0.0396θ + 0.0029
(4)
67
The trapezoidal broad crested weir has many advantages which make it very attractive in practice
68
as a discharge measuring device. Thus, further laboratory experiments concerning the flow
69
characteristics above weirs of such type need to be conducted. In this study, a comprehensive set
70
of laboratory experiments have been conducted to investigate the main characteristics of flow
71
(i.e. water surface profile, head-discharge relations, velocity profile, pressure distribution profile,
72
discharge coefficient, dimensions of separation zone) over trapezoidal broad-crested weirs with
73
different upstream face slopes.
74 75
2- Literature review
76
A review of literature indicates that the characteristics of flow over broad-crested weirs have
77
been studied extensively by many researchers (Woodburn 1932, Doeringsfeld and barker 1941,
78
Kindsvater and Carter 1957, Tracy 1957, Kikkawa et al. 1961, Hall 1962, Singer 1964,
79
Kindsvater 1964, Harrison 1967, Hulsing 1968, Ranga Raju and Ahmad 1973, Bos 1976, Isaacs
80
1981, Montes 1998, Johnson 2000, Sarker and Rhodes 2004, Gogus et al. 2006, Jan et al. 2009,
81
Parilkova et al 2012). Ramamurthy et al. (1988) experimentally investigated the effect of
82
rounding the upstream corner of broad-crested weirs on the flow properties and discharge
83
coefficient. Hager and Schwalt (1994) performed laboratory experiments on broad-crested weirs
84
to study the flow features. This study showed that the broad-crested weir with 90º upstream face
85
slope is more accurate than with a round-edged upstream face. They also presented design
86
guidelines for a sharp-cornered vertical-faced broad-crested weir. Based on critical flow theory,
87
Gonzalez and chanson (2007) measured pressure and velocity distributions of flow over two
88
configurations of a near full-scale broad-crested weir. Azimi and Rajaratnam (2009) studied the
89
flow pattern above weirs of finite crest length with square edged or rounded entrance. They
90
classified the finite crest length weirs into four categories including sharp-crested, short-crested,
91
broad-crested and long-crested weirs. In an experimental study carried out by Felder and
92
Chanson (2012), they measured velocity and pressure distribution of flow over an upstream
93
rounded broad-crested weir for a wide range of flow. They declared that the discharge coefficient
94
for rounded edged broad-crested weirs is larger than for square edged broad-crested weirs. Some
95
authors demonstrated that the trapezoidal or embankment weirs have more advantages than
96
vertical faced broad-crested weirs. Because of the upstream face slope, they have higher
97
discharge coefficient (Sargison and Percy, 2009), and deposition of sediments and debris at their
98
upstream is low. Furthermore, Providing a sloped face downstream prevents formation of
99
cavitation at high flow rates (Inozemtsev 1969, Fortner 2003, Sargison and Percy 2009) and
100
improve the sensitivity to downstream submergence ratio (Farhoudi and Shokri 2007). The
101
problem of flow over such weirs has been studied experimentally and numerically (Bazin 1898,
102
Horton 1907, Govinda Rao and Muralidhar 1961, Govinda Rao and Muralidhar 1963,
103
Rajaratnam and muralidhar 1970, Ranga Raju et al. 1990, Wang et al. 2010). Hager and Fritz
104
(1998) conducted a series of experiments on trapezoidal shape weirs with different crest lengths
105
and both the upstream and downstream slopes at 1V:2H. They demonstrated that the discharge
106
coefficient for a vertical-sided standard broad-crested weir is approximately 10% less than its
107
corresponding value over the embankment weir. Sargison and Percy (2009) showed that the
108
slope of the downstream side of trapezoidal broad-crested weir has negligible effect on discharge
109
coefficient, but the upstream side slope can obviously affect on the discharge coefficient. Azimi
110
et al. (2013) performed laboratory experiments on broad-crested weirs with positive and negative
111
crest slopes, broad-crested weirs with upstream and downstream ramps and triangular weirs.
112
They investigated the effect of upstream and downstream ramps on discharge coefficient of
113
embankment and triangular weirs.
114
Despite these appropriate studies on hydraulics of trapezoidal broad-crested weirs, some aspects
115
of flow behaviors over such weirs are still not available. Less attention has been given to
116
dimensions of flow separation zone at the upstream corner of trapezoidal broad-crested weir.
117
Only few studies investigated the detailed flow information such as the pressure and velocity
118
distributions above these weirs. Particularly, the pressure fluctuations along the downstream face
119
have received no attention. The discharge coefficient as well as the head-discharge relations of
120
these weirs can be of interest. In addition, the determination of water surface profiles and the
121
exact location of control section (where critical depth is formed) above the weir needs more
122
consideration. These issues will be answered through this study.
123 124
3-Materials and methods
125
This research was carried out in the Hydraulic Laboratory of Water Engineering Department of
126
University of Tabriz, Iran. Experimental data were obtained by calibrated instruments and
127
standard techniques which were highly accurate and reliable. A schematic representation of the
128
experimental set-up is shown in Fig. (1) and a photo of experimental equipments can be seen
129
through Fig. (2). In the laboratory, the water is supplied to a constant head tank from a sump
130
using a centrifugal pump and thereafter is fed to the experimental flume through 254 mm
131
diameter pipe with a valve for controlling the discharge. After that, it is returned to the sump and
132
recirculated through this system. Provisions are made at the inlet to the flume to ensure that the
133
approach flow is free of surface waves, vortices and turbulence. The flume is rectangular with
134
cross section 0.25 m wide, 0.50 m deep and 12 m long with a 0.0022 bed slope. It has vertical
135
glass sidewalls and metal bottom. The longitudinal water surface profiles were determined using
136
a manual pointer gauge of reading accuracy 0.1 mm and sidewall photography undertaken with
137
camera. The pointer gauge mounted on rails along the channel and consisted of a vertically
138
mounted sharp brass rod with a vernier scale. The vernier zero point was set up with the base of
139
the flume. The distance along the flume from the channel entrance was measured with a meter
140
line; the error was less than 1 mm. In addition, photographs were taken during the experiments
141
and used to visualize the flow patterns. A miniature propeller meter was used to measure the
142
velocity profiles along the flow direction and over the weir crest at selected sections and each 10
143
mm in height. As the probe was not turnable relative to the horizontal, only the stream wise
144
velocity component was determined. From upstream to downstream there were 5 locations for
145
measurements of velocity distribution including three sections along the weir and a section
146
upstream of the weir. A series of pressure tappings were located along the centerline of weir, at
147
the upstream and downstream faces and at the horizontal weir crest. The maximum distance
148
between the tappings was 100 mm, but the spacing was much closer near the upstream and
149
downstream corners to obtain a good insight in the separation process. These pressure tappings
150
were connected to vertical water piezometers of reading accuracy to 1 mm by long plastic tubes.
151
The weir models were constructed from three parts: wedges as the upstream and downstream
152
faces, and the rectangular part or core segment. The upstream wedges could be changed in order
153
to produce different upstream slopes, with a constant crest length. The upstream slopes ( θ )
154
tested were 21, 40, 54, 74 and 90 (as the control) while the downstream slope was fixed at 54.
155
(See the photo of models in Fig. 2 and model dimensions and configurations in Table 1). The
156
models were manufactured from polyvinyl chloride (PVC).
157
Series of experiments carried out for a wide range of flow rates (discharge rates of 3 to 20 L/s)
158
and with various upstream face slopes. In all series, the flow characteristics which mentioned
159
previously were measured. The tests were performed in such a way that, initially the motor was
160
started and inlet butterfly valve was opened slightly. Flow to the flume was gradually increased
161
to the desired flow. There was no exit control at the downstream of the weir model and flow was
162
entirely supercritical, discharging into an outlet box. Volumetric flow rate was measured using a
163
calibrated 53° V-notch weir located at the downstream wall of the outlet box. The head over the
164
V-notch was measured in the gage pit by means of a point gage with ±0.1 mm of reading
165
accuracy.
166
167
4-Dimensional analysis
168
By working with non-dimensional combinations of variables instead of working with single
169
parameters one by one, the number of analyses can be significantly reduced and the results will
170
be more general, universal and useful [Tuyen 2006]. Dimensional analysis is a method for
171
reducing the number and complexity of experimental variables which affect a given physical
172
phenomenon, by using a sort of compacting technique [White, 2011]. Referring to Fig. 3, free
173
flow over a trapezoidal broad-crested weir can be written as a function of total upstream head
174
( H ) , dynamic viscosity of the fluid ( μ ) , surface tension (σ ) , weir crest length measured in the
175
flow direction (Lcrest ) , acceleration due to gravity ( g ) , height of the weir ( Z ) , mass density of
176
the fluid ( ρ ) , weir width ( B ) , weir upstream and downstream face slope angle (θ and β ). So,
177
the flow discharge is known in form of following equation:
178
q = F ( H , ρ , μ , σ , g , L crest , B, Z , θ , β )
179
In which, q is discharge over the weir per unit width. Using the Buckingham π theorem, the
180
dimensionless parameters in functional forms can be obtained as below:
181
q gH
3 2
= f ( 1
ν gH
3 2
,
σ ρ gH
2
,
(6)
Lcrest B Z , , ,θ , β ) H H H
(7)
182
Where ν is the kinematic viscosity of the fluid. The value of the first term on the right hand side
183
of Eq. (7) can be neglected ( Re y nolds Number 2000 ). Also, except when the head is
184
very small, the effect of surface tension is negligible. Regarding the minimum flow depth above
185
the weir in the experiments (0.05 m ), the surface tension force can also be ignored [Novak and
186
Cabelka 1981] and has hence been omitted from consideration under the flow conditions of this
187
work. Also the parameters Lcrest , B , Z and β have constant value through all experiments.
188
Referring the above discussions, the Eq. (7) can be simplified as Eq. (8): q
189
gH
3 2
= f1(θ )
(8)
190
According to the Eq. (8), the upstream face slope angle is the most effective parameters on the
191
flow discharge among the other dimensionless parameters. In the present study the effect of this
192
parameter on the flow characteristics is investigated.
193
194
5- Results and discussion
195
As previously mentioned, in this study the experiments on trapezoidal broad crested weirs were
196
performed for several upstream face slopes and a wide range of flow conditions. It should be
197
noted that in all cases, the flow upstream of the weir is subcritical, Transitional flow occurs on
198
the weir crest and the flow along the downstream weir face is supercritical. Following are the
199
results obtained according to the measurements. They are presented in the form of graphs, charts
200
and tables for the characteristics of flow.
201 202
5-1- Flow surface profile
203
The flow surface profiles were measured for all tests (all configurations and all discharge levels).
204
As a sample, the water surface profiles on the weir with 21D upstream face slope are plotted for
205
different discharge rates in Fig. (4). Based on the observations, by adjusting the flow discharge
206
three types of flow surface profiles were observed above the weirs:
H −Z
1 ) a wavy profile was observed above the crest.
207
(1) In the cases with low discharges (
208
This type of flow is classified as undular weir flow (Chanson 1996, Madadi et al., 2013). Hager
209
and Schwalt (1994) said that the origin of undular weir flow is viscousity. Issacs (1981) reported
210
that the undular flow is caused by the interactions between developing boundary layer and main
211
flow. This paper is not intended to investigate the undular weir flow. More information about
212
undular weir flow was completely reported by Madadi et al (2013).
213
(2) With increasing the flow discharge level, the typical (normal) surface profile occurred
214
without undular waves. In this case, the flow gradually decreases from the approach to the tail
215
water.
216
(3) In the range between two above mentioned flow conditions, the flow was formed as a
217
standing wave pattern which the flow depth increases along the crest.
218
As can be seen from Fig. (4), the critical flow conditions take place above the crest in all
219
discharge rates. From this figure, with increasing the discharge levels, the critical section is
220
shifted downstream. When the flow discharge increases from 6.9 L/s to 19.8 L/s, the ratio of Xc
221
to Lcrest (Xc denote the distance between upstream corner of the weir and the point which the
222
critical depth occur above the weir) increases up to 40.45% (Fig. 5). The observations showed
223
that, reducing the upstream face slope makes the water surface profile fall into smooth curvature
224
and becomes flatter. This is presented by Fig. (6-a) where the flow surface profiles are plotted for
225
all upstream slopes at the discharge of 19.8 L/s. Referring to the figure, the weir with a 90 D
226
upstream face slope shows a highly steep flow profile at the weir crest entrance. Reducing the
227
upstream face slope decreases approach flow curvature and water profiles asymptotically reach
228
to a horizontal streamline over the weir crest. Finally, near the downstream end of the crest, a
Z
229
reduction in surface profile is occurred to follow the downstream slope. For a constant upstream
230
head (H), as is shown in Fig. (6-b), when the upstream face slope (θ ) decreases, the critical
231
section is shifted downstream and vice versa.
232 233
5-2- Velocity distribution
234
Investigation of velocity distribution over the flow depth is important to interpret flow structure
235
around the hydraulic structures. In this study, the vertical distribution of the velocity profiles was
236
measured for all tests at a section upstream of the weir, a section at heel of the weir, and three
237
sections above the crest. Figs. (7-a) to (7-e) show the vertical velocity distribution measured at
238
upstream and above the weir for all upstream slopes at discharge of 19.8 L/s. For all other
239
discharge levels, the velocity profile is the same in shape but different in the velocity
240
magnitudes. The concrete results obtained from the velocimetry are that: At the upstream of the
241
weirs (section 1) the velocity profiles are straight and uniform, almost have a constant value from
242
the bottom of the flume to the water surface (gradually increases over the depth). The flow
243
accelerates gradually when it reaches the weirs (section 2). There is a sharp increase when the
244
upstream face slope is steep and a gradual acceleration when the upstream face slope is mild. For
245
steep slopes, the flow behind the weir tends to stop at low depths (i.e. the velocity tends to be
246
zero near the bottom) and a reservoir condition occurs upstream of the weir. At the section (3),
247
the velocity has its highest value near the crest and decreases over the depth. The minimum
248
velocity occurs close to the water surface. It should be noted that, from the observations of dye
249
injection and video processing, the reverse velocity occurs at the separation zone. At the section
250
(4), the velocity distribution profile is parabolic, the maximum velocity appears at mid depth of
251
flow. Finally, at the section (5), the maximum velocity is shifted to near the crest surface and the
252
velocity decreases from the crest to the free surface. For all the upstream face slopes, the above
253
results were obtained. Although, the shape of velocity distribution profiles are similar, but the
254
velocity magnitudes increased when the upstream face slope decreased. In other word, more
255
upstream face slope leads to less velocity magnitude.
256
5-3- Pressure distribution
257
The piezometric head or hydraulic grade line ( P γ + Z ) was measured at pressure tappings
258
located on the surface of the weir, as previously described. Fig. (8) illustrates the values of
259
( P γ + Z ) over the weir with 21D upstream face slope for different discharge levels. The pressure
260
profiles represent two distinct dips at the upstream and downstream corners of the weir. As can
261
be seen from the figure, at the upstream corner of the weir, the hydraulic grade lines do not cross,
262
and the lowest pressure at this location occurs at the lowest discharge rate. On the contrary, at the
263
downstream corner of the weir, the hydraulic grade lines do cross with the lowest pressure
264
occurring for the highest flow rate (see the zoomed-in view of downstream face). Hence this
265
could potentially be a site for cavitation to take place if the flow rate is sufficiently high. Pressure
266
profile exhibits leaping flow along the downstream face and the weir face experiences
267
atmospheric or negative pressure. Fig. (9) shows the temporal variation of pressure at
268
piezometric tappings of D1 to D5 along the downstream face, respectively. Location of D1 to D5
269
is represented in figure (3). As can be seen from Fig. (9), at D1 piezometric tapping, the pressure
270
is negative over time, and strong fluctuations of pressure occur every few seconds. At D2, the
271
fluctuations severity is reduced but the pressure still remains negative. At D3, the pressure
272
fluctuations are greatly reduced and varied around zero between positive and negative values
273
over time. At D4, the pressure is positive without any strong fluctuations. At D5, the maximum
274
pressure is seen among all tappings and slight pressure fluctuations appear every few seconds.
275
Generally, regular fluctuations occur in all tappings along the downstream face every 10
276
seconds. At D1 and D2 where the pressure is negative, the cavitation is formed and to prevent of
277
this destructive phenomenon, the aeration facilities can be used at the area under the leaping
278
flow.
279
5-4- Flow separation
280
When flow reaches to a weir with sharp entrance, the flow separates from the upstream edge and
281
extends to a certain points over the crest. Some authors believe the flow separation does not
282
reattach to the weir before the flow leaves the weir (Azimi et al., 2013). This phenomenon
283
complicates the flow pattern over the weir and alters the velocity distribution in the stream
284
(Chow, 1959). Flow separation is known as the primary source of energy loss and dissipation of
285
this phenomenon leads to increase the discharge coefficient and prevent occurring of negative
286
velocity at the weir entrance (Tracy 1957; Ramamurthy et al., 1998; Goodarzi et al. 2012). From
287
the literature, the weir inflow geometry has a major impact on the dimensions of separation zone
288
over crest (Bazin 1896; Sargison and Percy 2009, Azimi et al. 2013). To obtain the dimensions
289
of flow separation zone in the experiments, the dye injection technique and video processing
290
procedure were used. Sawdust was also used in the flow and the camera was employed for
291
tracking the particle and the dye path. To demonstrate the effect of upstream face slope of the
292
trapezoidal broad crested weir on the dimensions of flow separation zone, the flow separation
293
length has plotted against the flow depth (both in dimensionless form), and is shown in Fig. (10).
294
Based on the figure, decreasing the upstream face slope from 90D to 21D increases the relative
295
L length of separation ( s
Lcrest
) up to 80% and the relative height of separation (
hs
Z
) about
296
95%. Ls and hs are the length and height of the separation zone, respectively (Fig. 3). At the
297
weir with 21D upstream face slope, the smallest separation zone occurred.
298 299
5-5- Discharge coefficient
300
In all experiments which were conducted in this study, the discharge coefficient ( C D ) of
301
trapezoidal broad-crested weirs was determined. Literature review indicates that, the weir inflow
302
geometry has a significant impact on the C D (Woodburn 1932, Harrison 1967, Fritz and Hager
303
1998, Sargison and Percy 2009). Meanwhile, from their laboratory experiments, Sargison and
304
Percy (2009) and Azimi et al. (2013) showed that the weir downstream face slope has low
305
impact on the C D , which can be neglected. Fig. (11) shows the variation of C D against angle (θ )
306
of the upstream face slope. It can be observed that, as the θ increases, the C D value decreases.
307
The weir with θ = 21D has the greatest C D value among the weirs including slope tests. Further
308
consideration on this figure reveals that, from the θ = 21D to θ = 54D , the C D decreases slightly
309
(low slope) while from θ = 54D to θ = 90D , the C D decreases precipitously (high slope). Fig. (12)
310
present the discharge coefficient as a function of the dimensionless head above crest
311
H
312
compared with those of Sargison and Percy (2009). Also, the C D values which were calculated
313
with Eqs. (3), (4) are presented in this figure. From this figure, by increasing the dimensionless
314
head, the discharge coefficient increases slightly. This result confirms the observation of
315
Sargison and Percy (2009). This figure also indicates that, the C D increases with the decrease of
316
the upstream face slope. The next result which can be obtained from this figure is that, there is a
( H + Lcrest ) . In this figure, the measured C D values for various
θ in current study were
317
good resemblance between values of C D in this study and experimental observation of Sargison
318
and Percy (2009), while it cannot be found a good agreement between the observed C D values
319
and the values calculated from the Eqs. (3), (4). As can be seen, the predicted values have higher
320
values than those of measured values in all tests.
321 322
5-6- Head-Discharge Relation for Trapezoidal broad crested weirs
323
In this study, the trapezoidal broad crested weir head-discharge relations were obtained and
324
plotted for each of the upstream face slopes (Fig. 13). it can be seen that, for low discharges (i.e.
325
for small head values), the head-discharge relations of all the weirs resemble each other while
326
increasing the discharge value leads to different head-discharge relations for different upstream
327
slopes. In other word, further increase in flow rate leads to further difference (divergence) in
328
weirs head-discharge relations. This figure revealed that for head value of H=0.132 m (or H/Z =
329
0.52), the discharge capacity of the weir with θ = 21D is Q=19 L/s (or Q2/gB5=0.038) which is
330
10.5 % higher than the weir with θ = 90D (where the Q=17 L/S or Q2/gB5=0.031).
331 332
6- Conclusion
333
In this paper, a series of laboratory experiments were conducted to investigate the effect of
334
changing upstream slope of trapezoidal broad-crested weirs on discharge coefficient, velocity
335
profile, pressure distribution, flow separation zone, etc. Also, a comprehensive literature review
336
has been performed to survey the extent of the experimental results available in the literature on
337
broad-crested weirs. Based on the results, the upstream weir design has a significant effect on the
338
flow characteristics and discharge coefficient of trapezoidal broad-crested weir. By analyzing
339
experimental observations, the following conclusions can be drawn:
340
By increasing the dimensionless head H ( H + L , the discharge coefficient increases slightly. crest )
341
From the θ = 21D to θ = 54D , the C D decreases slightly while from θ = 54D to θ = 90D , the C D
342
decreases precipitously. Reducing the upstream slope from 90D to 21D increases the relative
343
length of the separation and the relative height of the separation up to 80% and 95%,
344
respectively. Over the time at the downstream face of the weir, pressure reduction alternately
345
occurs, as a result a pressure fluctuation on the downstream face of the weir is observed. This
346
could potentially be a site for cavitation to occur. As the flow rate increases from 6.9 L/s to 19.8
347
L/s, the ratio of Xc/Lcrest increases up to 40.45%. Reducing the upstream face slope decreases
348
approach flow curvature and water profiles asymptotically reach to a horizontal streamline over
349
the weir crest. When the upstream face slope (θ ) decreases, the critical section is shifted
350
downstream and vice versa. This paper presented considerable information that could be of use
351
in the design of flow control and measurement structures.
352
353
References
354 355 356
Azimi, A. H., Rajaratnam, N., and Zhu, D. Z., (2013). “Discharge Characteristics of Weirs of Finite Crest Length with Upstream and Downstream Ramps”, Journal of Irrigation and Drainage Engineering, Vol. 139, No. 1. 75-83.
357 358
Azimi A. H., Rajaratnam N., (2009). “Discharge characteristics of weirs of finite crest length”. J. Hydraul. Engng., Vol. 135, 12, 1081–1085.
359 360
Bagheri, S., Heidarpour, M., (2010). “Flow over rectangular sharp-crested weirs”, irrigation Science, , Volume 28, Issue 2, pp 173-179.
361 362 363
Bazin, H., (1896): Expériences Nouvelles sur l’Ecoulement par Déversoir. Recent experiments on the flow of water over weirs. (In French.) Mémoires et Documents, Annales des Ponts et Chaussées, Séries 7, 12, 2, 645–731.
364 365
Boiten, W. (2002). “Flow measurement structures”, Flow Measurement and Instrumentation, 13 (2002) 203–207.
366 367
Bos, M. G. (1976). “Discharge measurement structures”. Publication No. 161. Delft Hydraulic Laboratory. Delft. Netherlands. 464 pp.
368 369
Chanson, H. (1996). “Free-surface flows with near-critical flow conditions”. Canadian Journal of Civil Engineering.; 23(6): 1272-84.
370 371
Chanson, H. (2004). “The hydraulics of open channel flow: An introduction”. 2d edition. Department of Civil Engineering, University of Queensland. Australia.
372
Chow, V. T. (1959). “Open channel hydraulics”. New York: McGraw-Hill.
373 374
Doeringsfeld, H. A., Barker, C. L. (1941) “Pressure momentum theory applied to the broadcrested weir”. Trans. ASCE.106: 934-69.
375 376
Farhoudi, J. Shokri N. (2007). “Flow from broad crested rectangular weirs with sloped downstream face”. 32nd IAHR Congress. Venice, Italy.
377 378 379
Felder, S., Chanson, H. (2012). “Velocity and pressure measurements on a broad-crested weir: physical measurements”. 4th IAHR International Symposium on Hydraulic Structures. Porto, Portugal.
380
Fortner, B., (2003). “Water vapor almost busts dam”. Popsci.com.
381 382
Fritz, M, Hager, H. (1998). “Hydraulics of Embankment Weirs”. J. Hydraulic Engineering. 124(9):963-71.
383 384
Gogos, M., Defne, Z., and Ozkandemir, V. (2006). “Broad-Crested Weirs with Rectangular Compound Cross Sections”. J. Irri. Drain. Eng., 132(3), 272-280.
385 386 387
Gonzalez, C. A., Chanson, H. (2007). “Experimental measurements of velocity and pressure distributions on a large broad-crested weir”. Flow Measurement and Instrumentation. 18(34): 107-13.
388 389
Goodarzi, E., Farhoudi, J., Shokri, N., (2012). “Flow characteristics of rectangular broadcrested weirs with sloped upstream face”, J. Hydrol. Hydromech., 60( 2), 87–100.
390 391
Govinda Rao, N. S., and Muralidhar, D. (1961). "A new discharge formula for waste-weirs (bye washes)." Irrigation and Power, 18(10), 908-917; 19(7),546-549.
392 393
Govinda Rao, N.S. and Muralidhar, D. (1963). "Discharge Characteristics of Weirs of Finite Crest Width." Jl La Houille Blanche, Vol. 18, No. 5, Aug.-Sept., pp. 537-545.
394 395
Hager, W. H., Schwalt, M. (1994). “Broad-Crested Weir”. Journal of Irrigation and Drainage Engineering. 120 (1):13-26. Discussion: 121 (2):222-6.
396 397 398
Hall, G. W., Mech, E. (1962). “Analytical determination of the discharge characteristics of broad-crested weirs using boundary layer theory”. International J of civil Engineering. (22):177-90.
399 400
Harrison, A. J. M. (1967). “The streamlined broad-crested weir.” Proc., Institute of Civil Engineers, Vol. 38, ICE, London, 657–678.
401
Henderson, F. M. (1966). “Open channel flow”. New York: MacMillan Company.
402 403
Horton, R. E. (1907). "Weir experiments, coefficients, and formulas," Water Supply and Irrigation Paper 200. U.S. Dept. of Interior, Government Printing Office, Washington, D.C.
404 405 406
Hulsing, H. (1968). “Measurement of peak discharge at dams by indirect methods”. Techniques of Water Resources Investigations, U.S. Geological Survey, Book 3(A5). U.S. Government Printing Office, Washington, D.C.
407 408
Inozemtsev, Y. P. (1969). “Cavitation destruction of concrete and protective facings under natural conditions”. Power Technology and Engineering, 3(1), 24–29.
409 410 411
Isaacs, L. T. (1981). “Effects of laminar boundary layer on a model broad-crested weir”. Research report No. CE28. Department of Civil Engineering, University of Queensland, Australia, 21pp.
412 413 414 415 416
Jan, C., Chang, C., and Kuo, F. (2009). ”Experiments on Discharge Equations of Compound Broad-Crested Weirs.” J. Irrig. Drain Eng., 135(4), 511–515.
417 418
Kikkawa, H., Ashida, K., and Tsuchiya, A. (1961). "Study on the discharge coefficient of broad-crested weirs." J. Res. Of Public Works Res. Inst., Japan, 5(4), 1-20.
419 420
Kindsvater C. E., Carter, R. W. (1957). “Discharge characteristics of rectangular thin-plate weirs”. Journal of Hydraulic Division. 83(6):1-36.
421 422 423
Kindsvater, C. E. (1964). “Discharge characteristics of embankment shaped weirs.” Proc., U.S. Geological Survey Water Supply Paper 1617-A, Government Printing Office, Washington, DC.
Johnson, M. C. (2000). “Discharge coefficient analysis for flat-topped and sharp-crested weirs.” J. Irrig. Sci., 19(3), 133–137.
424 425 426
Madadi, M. R., Dalir A. H., Farsadizadeh, D., (2013). “Control of undular weir flow by changing of weir geometry”, Flow Measurement and Instrumentation, Volume 34, December 2013, Pages 160–167.
427 428
Montes J. S., Chanson, H. (1998). “Characteristics of undular hydraulic jumps. Results and calculations”. J Hydraulic Eng ASCE 124(2):192–205.
429 430
Montes, J.S. (1969). "The Streamlined Broad-Crested Weir. Discussion." Proc. Instn. Civil Engrs., London, Vol. 42, Mar., pp. 576-578.
431 432
Montes, J. S. (1998). “Hydraulics of open channel flow”. ASCE Press, New-York, USA, 697 pages.
433 434
Tuyen N. B., (2006). “Flow over oblique weirs”, Master of Science Thesis, Delft university of Technology, Faculty of Civil Engineering and Geosciences, 159 pp.
435 436
Novak P., Cabelka J. (1981). “Models in Hydraulic Engineering”. Boston. Pitman Advanced Publishing Program.
437 438 439
Parilkova, J., Riha, J., Zachoval, Z., (2012), “The influence of roughness on the discharge coefficient of a broad-crested weir”, Journal of Hydrology and Hydromechanics, 60(2): 101– 114.
440 441
Rajaratnam, N. and Muralidhar, D. (1970). “The trapezoidal free overfall”. IAHR Journal of Hydraulic Research, Vol. 8, No. 4, pp. 419-447.
442 443
Rajaratnarn, N., and Muralidhar, D. (1969). "Flow below deeply submerged rectangular weirs." J. Hydr. Res., 7(3), 355-374.
444 445 446
Ramamurthy, S. A., Tim, U. S., Rao, M. V., (1998)., “Characteristics of square-edged and round-nosed broad-crested weirs”. Journal of Irrigation and Drainage Engineering. 114(1): 61-73.
447 448
RangaRaju, K. G., and Ahmad, I., (1973). "Discharge characteristics of suppressed and contacted broad-crested weirs." J. Irrigation and Power (India), 30(4), 157-166.
449 450
RangaRaju, K. G., Srivastava, R., and Porey, P. D. (1990). “scale effects in modelling flows over broad-crested weirs”, Journal of Irrigation and Power, Vol. 47, No. 30, pp. 101-106.
451 452
Sargison, J. E., Percy, A. (2009). “Hydraulics of broad-crested weirs with varying side slopes”. Journal of Irrigation and Drainage Engineering. 135(1):115-8.
453 454
Sarker, M. A., Rhodes, D. G. (2004). “Calculation of free-surface profile over a rectangular broad-crested weir”. Journal of Flow Measurement and Instrumentation. (15) 215-9.
455 456
Singer, J. (1964). “Square-edged broad crested weir as a flow measurement device.” Water Water Eng., 28(820), 229–235.
457 458
Tracy, H. J., (1957). “Discharge characteristic of broad crested weirs”, Circular 397, Geological survey, U.S. Department of Interior, Washington.
459 460
Wang, X., Hao, Z. and Tan, S. K., (2010). “Hydrodynamics of trapezoidal embankment weir”, Journal of Hydrodynamics, 22(5): 386-390.
461
White, F. M., (2011). “Fluid Mechanics”, Published by Tata McGraw-Hill Education.
462
Woodburn, J. G. (1932). “Tests on Broad-crested weirs”. Trans. ASCE. (96): 387-408.
463 464
Zerihun, Y. T., Fenton, J. D., (2009). “Discussion: A Boussinesq-type model for flow over trapezoidal profile weirs”, Journal of Hydraulic Research, IAHR, 2007, 45(4), 519–528.
465
466
467
468
Figure 1: Schematic representation of the flume, Hydraulic Laboratory of University of Tabriz 469
470
471
Figure 2: Photo of experimental equiipment an nd instrum ments 472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
Figure 3: Flow over trapezoidal broad-crested weir
492
493
494
495
496
497
498
499
500
501
502
503
Figure
4: Flow surface profiles over 21o weir for different discharges (Q=6.9 L/s ~ 19.8 L/s)
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
Figure 5: Variation of critical section location vs. flow discharge
521
522
523
524
525
526
527
528
Figure 6(a): Flow surface curvature vs. upstream face slope (Q= 19.8 L/s)
529
530
531
532
Figure 6(b): critical section location vs. upstream face slope (Q= 19.8 L/s)
533
534
535
536
537
538
Figure 7(a): Velocity vertical distribution at upstream of the weir (section 1)
539
540 541 542
Figure 7 (b): Velocity vertical distribution at weir heel (section 2) for various upstream face slopes
543
Figure 7 (c): Velocity vertical distribution at upstream corner (section 3) for various upstream face slopes 544 545 546 547
548 549 550
Figure 7 (d): Velocity vertical distribution at middle section of crest (section 4) for various upstream face slopes
551
552
553
554
555
556 557
Figure 7 (e): Velocity vertical distribution at downstream corner (section 5) for various upstream face slopes 558
559
560
561
562
563
564
565
566
567
568
Figure 8: Pressure distribution along the weir with a zoomed-in view of downstream face
Figure 9: pressure fluctuations along downstream face in the case of leaping flow condition 569
570 571 572 573 574
Figure 10: variations of separation zone altitudinal and longitudinal characteristics vs. upstream face slope 575 576 577 578 579 580 581
582 583 584 585
586
Figure 11: variation of discharge coefficient against upstream face slope
587 588
589
590
591
592
593
594
595
596
597
598
599
Figure 12: Variation of discharge coefficient for different dimensionless heads and different upstream face slopes 600
601
602
603
604
605
606
607
608
609
610
611
612
Figure 13: Dimensionless head-discharge curve for trapezoidal broad crested weir
613 614 615
616
617
618
619
620 621
Table 1: Geometrical dimensions of the models
Weir Weir length height Lcrest (m) Z (m)
Weir width B (m)
622
623
624
0.25
0.5
625
0.25
626
627
Weir configurations
Upstream Downstream slope slope
θD
βD
0.25
90
54
0.5
0.25
74
54
0.25
0.5
0.25
54
54
0.25
0.5
0.25
40
54
628
0.5
0.25
21
54
629
0.2 5
630
631
632
633
634
635
636
637
638
639
•
The flow characteristics on the trapezoidal broad-crested weir have been studied.
640
•
Increasing the upstream face slope decreased the discharge coefficient up to 10%.
641
•
Decreasing the upstream face slope prevents development of separation zone.
642
•
As the upstream face slope decreases, the critical section is shifted downstream.
643
•
By increasing the dimensionless head, the discharge coefficient increases slightly.
644 645 646
Investigation of flow characteristics above trapezoidal broad-crested weirs Mohamad Reza Madadi, Ali Hosseinzadeh Dalir , Davood Farsadizadeh
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PII: DOI: Reference:
S0955-5986(14)00060-0 http://dx.doi.org/10.1016/j.flowmeasinst.2014.05.014 JFMI951
To appear in:
Flow Measurement and Instrumentation
Received date: 12 January 2014 Revised date: 24 April 2014 Accepted date: 11 May 2014 Cite this article as: Mohamad Reza Madadi, Ali Hosseinzadeh Dalir, Davood Farsadizadeh, Investigation of flow characteristics above trapezoidal broadcrested weirs, Flow Measurement and Instrumentation, http://dx.doi.org/10.1016/j. flowmeasinst.2014.05.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1 2
Investigation of flow characteristics above trapezoidal broad-crested weirs
3 4 5
Mohamad Reza Madadi*1, Ali Hosseinzadeh Dalir2, Davood Farsadizadeh3
6 7 8 9 10 11 12 13 14 15 16 17 18
1- Ph.D., Department of Water Engineering, Shahid Bahonar University of Kerman, Kerman, Iran., P.O.Box: 76169-133, Email: [email protected], Tel: +989119231606, Fax:+983413222043. (*Corresponding Author)
19
In this study the effect of upstream face slope of a trapezoidal broad-crested weir on discharge
20
coefficient and water surface profile was investigated using the laboratory models. The velocity
21
and pressure distribution profile were determined. The location of the critical section above the
22
weir was specified. The dimensions of flow separation zone were also measured for different
23
upstream face slopes. The results showed that decreasing the upstream face slope prevents
24
development of separation zone. In this case, the flow was passed through the weir more
25
regularly and the water surface and pressure drop were decreased. Decreasing the upstream face
26
slope to 210, increased the discharge coefficient up to 10% and reduced the separation relative
27
length and height up to 80% and 95% respectively.
28
Keywords: Trapezoidal Broad-Crested Weir, Discharge Coefficient, Flow Separation, Velocity
29
Profile, Critical Depth.
2- Professor, Department of Water Engineering, University of Tabriz, Tabriz, Iran., Email: [email protected], Tel: +989143166284. 3- Associate Professor, Department of Water Engineering, University of Tabriz, Tabriz, Iran., Email: [email protected], Tel: +989143135801. Abstract
30 31
1- Introduction
32
Flow measurement structures are one of the main categories of hydraulic structures which are
33
generally designed to act as a control in the open channels to provide a unique relationship
34
between the upstream head and the discharge (Bagheri and Heidarpour 2010, Biotin 2002).
35
Weirs are among the major types of measuring structures which because of their low cost, easy
36
installation and good accuracy have met with great interest. They are generally classified into
37
three groups, namely, broad-crested, short-crested and sharp-crested weirs depending on the ratio
38
of the weir upstream head to the weir crest length. For a broad crested weir, the ratio of crest
39
length (Lcrest) to upstream head over crest ( H − Z ) must be typically greater than 3 (Henderson
40
1966; Chanson 2004).
Lcrest H −Z
> 1.5 − 3
(1)
41
Hydraulically, a broad-crested weir is a flat-crested structure with a crest length large compared
42
to the flow thickness (Harrison 1967; Montes 1969) for the streamlines to be parallel to the crest
43
invert and the pressure distribution to be hydrostatic (Bos 1976; Henderson 1966; Montes 1998;
44
Chanson 2004). In this case, critical flow conditions occur on the crest (Woodburn 1932, Singer
45
1964, Goodarzi et al. 2012). If the up- and downstream faces of the broad crested weir be vertical
46
(namely as Standard Broad Crested Weir), it will operate with a rather significant loss in head
47
and also the sediment or solids may be deposited at the upstream side of the weir, which will
48
adversely affect its accuracy and increase the operating costs. To deal with such problems, the
49
broad-crested weir’s structural design can present some flexibility to provide better hydraulic
50
characteristics and discharge efficiency. For example, if the weir upstream entrance condition
51
changes from square-edged to the round-nosed corner, the weir discharge coefficient will be
52
increased (Ramamurthy et al. 1988). A review on previous studies shows that, to prevent
53
deposition of sediment or solids in the upstream side of the weir as well as to prevent cavitation
54
at the downstream corner of the weir, the upstream and downstream faces of broad crested weirs
55
can be sloped (Sargison and Percy 2009). This type of weirs can be classified as trapezoidal
56
profile weirs (Zerihun and Fenton, 2009), embankment-shaped weirs (Hager and Fritz 1998),
57
ramped broad crested weirs (Azimi et al. 2013), or broad-crested weirs with upstream and
58
downstream side slopes (Sargison and Percy 2009). In this paper, the term trapezoidal broad
59
crested weir is used because the models of weirs which were used in this study are in the range
60
of broad crested weirs (Eq. 1) and also, they have trapezoidal shape in the longitudinal section.
61
According to Fritz and Hager (1998), the discharge equation under free flow condition for this
62
type of weirs can be calculated by: Q = C D B 2 gH 3
(2)
63
Where H is total overflow head, g is the acceleration due to gravity, B is the weir width, and C D
64
is the discharge coefficient and is obtained by:
C D = 0.43 + 0.06 Sin[π (ε − 0.55)]
ε=
(3)
H is relative crest length. Sargison and Percy (2009) modified the Eq. (3) H + Lcrest
65
Where,
66
to account for the effect of upstream face slope (θ ) , resulting in the following equation:
C D = 0.43 + 0.06 Sin[π (ε − 0.55)] − 0.0396θ + 0.0029
(4)
67
The trapezoidal broad crested weir has many advantages which make it very attractive in practice
68
as a discharge measuring device. Thus, further laboratory experiments concerning the flow
69
characteristics above weirs of such type need to be conducted. In this study, a comprehensive set
70
of laboratory experiments have been conducted to investigate the main characteristics of flow
71
(i.e. water surface profile, head-discharge relations, velocity profile, pressure distribution profile,
72
discharge coefficient, dimensions of separation zone) over trapezoidal broad-crested weirs with
73
different upstream face slopes.
74 75
2- Literature review
76
A review of literature indicates that the characteristics of flow over broad-crested weirs have
77
been studied extensively by many researchers (Woodburn 1932, Doeringsfeld and barker 1941,
78
Kindsvater and Carter 1957, Tracy 1957, Kikkawa et al. 1961, Hall 1962, Singer 1964,
79
Kindsvater 1964, Harrison 1967, Hulsing 1968, Ranga Raju and Ahmad 1973, Bos 1976, Isaacs
80
1981, Montes 1998, Johnson 2000, Sarker and Rhodes 2004, Gogus et al. 2006, Jan et al. 2009,
81
Parilkova et al 2012). Ramamurthy et al. (1988) experimentally investigated the effect of
82
rounding the upstream corner of broad-crested weirs on the flow properties and discharge
83
coefficient. Hager and Schwalt (1994) performed laboratory experiments on broad-crested weirs
84
to study the flow features. This study showed that the broad-crested weir with 90º upstream face
85
slope is more accurate than with a round-edged upstream face. They also presented design
86
guidelines for a sharp-cornered vertical-faced broad-crested weir. Based on critical flow theory,
87
Gonzalez and chanson (2007) measured pressure and velocity distributions of flow over two
88
configurations of a near full-scale broad-crested weir. Azimi and Rajaratnam (2009) studied the
89
flow pattern above weirs of finite crest length with square edged or rounded entrance. They
90
classified the finite crest length weirs into four categories including sharp-crested, short-crested,
91
broad-crested and long-crested weirs. In an experimental study carried out by Felder and
92
Chanson (2012), they measured velocity and pressure distribution of flow over an upstream
93
rounded broad-crested weir for a wide range of flow. They declared that the discharge coefficient
94
for rounded edged broad-crested weirs is larger than for square edged broad-crested weirs. Some
95
authors demonstrated that the trapezoidal or embankment weirs have more advantages than
96
vertical faced broad-crested weirs. Because of the upstream face slope, they have higher
97
discharge coefficient (Sargison and Percy, 2009), and deposition of sediments and debris at their
98
upstream is low. Furthermore, Providing a sloped face downstream prevents formation of
99
cavitation at high flow rates (Inozemtsev 1969, Fortner 2003, Sargison and Percy 2009) and
100
improve the sensitivity to downstream submergence ratio (Farhoudi and Shokri 2007). The
101
problem of flow over such weirs has been studied experimentally and numerically (Bazin 1898,
102
Horton 1907, Govinda Rao and Muralidhar 1961, Govinda Rao and Muralidhar 1963,
103
Rajaratnam and muralidhar 1970, Ranga Raju et al. 1990, Wang et al. 2010). Hager and Fritz
104
(1998) conducted a series of experiments on trapezoidal shape weirs with different crest lengths
105
and both the upstream and downstream slopes at 1V:2H. They demonstrated that the discharge
106
coefficient for a vertical-sided standard broad-crested weir is approximately 10% less than its
107
corresponding value over the embankment weir. Sargison and Percy (2009) showed that the
108
slope of the downstream side of trapezoidal broad-crested weir has negligible effect on discharge
109
coefficient, but the upstream side slope can obviously affect on the discharge coefficient. Azimi
110
et al. (2013) performed laboratory experiments on broad-crested weirs with positive and negative
111
crest slopes, broad-crested weirs with upstream and downstream ramps and triangular weirs.
112
They investigated the effect of upstream and downstream ramps on discharge coefficient of
113
embankment and triangular weirs.
114
Despite these appropriate studies on hydraulics of trapezoidal broad-crested weirs, some aspects
115
of flow behaviors over such weirs are still not available. Less attention has been given to
116
dimensions of flow separation zone at the upstream corner of trapezoidal broad-crested weir.
117
Only few studies investigated the detailed flow information such as the pressure and velocity
118
distributions above these weirs. Particularly, the pressure fluctuations along the downstream face
119
have received no attention. The discharge coefficient as well as the head-discharge relations of
120
these weirs can be of interest. In addition, the determination of water surface profiles and the
121
exact location of control section (where critical depth is formed) above the weir needs more
122
consideration. These issues will be answered through this study.
123 124
3-Materials and methods
125
This research was carried out in the Hydraulic Laboratory of Water Engineering Department of
126
University of Tabriz, Iran. Experimental data were obtained by calibrated instruments and
127
standard techniques which were highly accurate and reliable. A schematic representation of the
128
experimental set-up is shown in Fig. (1) and a photo of experimental equipments can be seen
129
through Fig. (2). In the laboratory, the water is supplied to a constant head tank from a sump
130
using a centrifugal pump and thereafter is fed to the experimental flume through 254 mm
131
diameter pipe with a valve for controlling the discharge. After that, it is returned to the sump and
132
recirculated through this system. Provisions are made at the inlet to the flume to ensure that the
133
approach flow is free of surface waves, vortices and turbulence. The flume is rectangular with
134
cross section 0.25 m wide, 0.50 m deep and 12 m long with a 0.0022 bed slope. It has vertical
135
glass sidewalls and metal bottom. The longitudinal water surface profiles were determined using
136
a manual pointer gauge of reading accuracy 0.1 mm and sidewall photography undertaken with
137
camera. The pointer gauge mounted on rails along the channel and consisted of a vertically
138
mounted sharp brass rod with a vernier scale. The vernier zero point was set up with the base of
139
the flume. The distance along the flume from the channel entrance was measured with a meter
140
line; the error was less than 1 mm. In addition, photographs were taken during the experiments
141
and used to visualize the flow patterns. A miniature propeller meter was used to measure the
142
velocity profiles along the flow direction and over the weir crest at selected sections and each 10
143
mm in height. As the probe was not turnable relative to the horizontal, only the stream wise
144
velocity component was determined. From upstream to downstream there were 5 locations for
145
measurements of velocity distribution including three sections along the weir and a section
146
upstream of the weir. A series of pressure tappings were located along the centerline of weir, at
147
the upstream and downstream faces and at the horizontal weir crest. The maximum distance
148
between the tappings was 100 mm, but the spacing was much closer near the upstream and
149
downstream corners to obtain a good insight in the separation process. These pressure tappings
150
were connected to vertical water piezometers of reading accuracy to 1 mm by long plastic tubes.
151
The weir models were constructed from three parts: wedges as the upstream and downstream
152
faces, and the rectangular part or core segment. The upstream wedges could be changed in order
153
to produce different upstream slopes, with a constant crest length. The upstream slopes ( θ )
154
tested were 21, 40, 54, 74 and 90 (as the control) while the downstream slope was fixed at 54.
155
(See the photo of models in Fig. 2 and model dimensions and configurations in Table 1). The
156
models were manufactured from polyvinyl chloride (PVC).
157
Series of experiments carried out for a wide range of flow rates (discharge rates of 3 to 20 L/s)
158
and with various upstream face slopes. In all series, the flow characteristics which mentioned
159
previously were measured. The tests were performed in such a way that, initially the motor was
160
started and inlet butterfly valve was opened slightly. Flow to the flume was gradually increased
161
to the desired flow. There was no exit control at the downstream of the weir model and flow was
162
entirely supercritical, discharging into an outlet box. Volumetric flow rate was measured using a
163
calibrated 53° V-notch weir located at the downstream wall of the outlet box. The head over the
164
V-notch was measured in the gage pit by means of a point gage with ±0.1 mm of reading
165
accuracy.
166
167
4-Dimensional analysis
168
By working with non-dimensional combinations of variables instead of working with single
169
parameters one by one, the number of analyses can be significantly reduced and the results will
170
be more general, universal and useful [Tuyen 2006]. Dimensional analysis is a method for
171
reducing the number and complexity of experimental variables which affect a given physical
172
phenomenon, by using a sort of compacting technique [White, 2011]. Referring to Fig. 3, free
173
flow over a trapezoidal broad-crested weir can be written as a function of total upstream head
174
( H ) , dynamic viscosity of the fluid ( μ ) , surface tension (σ ) , weir crest length measured in the
175
flow direction (Lcrest ) , acceleration due to gravity ( g ) , height of the weir ( Z ) , mass density of
176
the fluid ( ρ ) , weir width ( B ) , weir upstream and downstream face slope angle (θ and β ). So,
177
the flow discharge is known in form of following equation:
178
q = F ( H , ρ , μ , σ , g , L crest , B, Z , θ , β )
179
In which, q is discharge over the weir per unit width. Using the Buckingham π theorem, the
180
dimensionless parameters in functional forms can be obtained as below:
181
q gH
3 2
= f ( 1
ν gH
3 2
,
σ ρ gH
2
,
(6)
Lcrest B Z , , ,θ , β ) H H H
(7)
182
Where ν is the kinematic viscosity of the fluid. The value of the first term on the right hand side
183
of Eq. (7) can be neglected ( Re y nolds Number 2000 ). Also, except when the head is
184
very small, the effect of surface tension is negligible. Regarding the minimum flow depth above
185
the weir in the experiments (0.05 m ), the surface tension force can also be ignored [Novak and
186
Cabelka 1981] and has hence been omitted from consideration under the flow conditions of this
187
work. Also the parameters Lcrest , B , Z and β have constant value through all experiments.
188
Referring the above discussions, the Eq. (7) can be simplified as Eq. (8): q
189
gH
3 2
= f1(θ )
(8)
190
According to the Eq. (8), the upstream face slope angle is the most effective parameters on the
191
flow discharge among the other dimensionless parameters. In the present study the effect of this
192
parameter on the flow characteristics is investigated.
193
194
5- Results and discussion
195
As previously mentioned, in this study the experiments on trapezoidal broad crested weirs were
196
performed for several upstream face slopes and a wide range of flow conditions. It should be
197
noted that in all cases, the flow upstream of the weir is subcritical, Transitional flow occurs on
198
the weir crest and the flow along the downstream weir face is supercritical. Following are the
199
results obtained according to the measurements. They are presented in the form of graphs, charts
200
and tables for the characteristics of flow.
201 202
5-1- Flow surface profile
203
The flow surface profiles were measured for all tests (all configurations and all discharge levels).
204
As a sample, the water surface profiles on the weir with 21D upstream face slope are plotted for
205
different discharge rates in Fig. (4). Based on the observations, by adjusting the flow discharge
206
three types of flow surface profiles were observed above the weirs:
H −Z
1 ) a wavy profile was observed above the crest.
207
(1) In the cases with low discharges (
208
This type of flow is classified as undular weir flow (Chanson 1996, Madadi et al., 2013). Hager
209
and Schwalt (1994) said that the origin of undular weir flow is viscousity. Issacs (1981) reported
210
that the undular flow is caused by the interactions between developing boundary layer and main
211
flow. This paper is not intended to investigate the undular weir flow. More information about
212
undular weir flow was completely reported by Madadi et al (2013).
213
(2) With increasing the flow discharge level, the typical (normal) surface profile occurred
214
without undular waves. In this case, the flow gradually decreases from the approach to the tail
215
water.
216
(3) In the range between two above mentioned flow conditions, the flow was formed as a
217
standing wave pattern which the flow depth increases along the crest.
218
As can be seen from Fig. (4), the critical flow conditions take place above the crest in all
219
discharge rates. From this figure, with increasing the discharge levels, the critical section is
220
shifted downstream. When the flow discharge increases from 6.9 L/s to 19.8 L/s, the ratio of Xc
221
to Lcrest (Xc denote the distance between upstream corner of the weir and the point which the
222
critical depth occur above the weir) increases up to 40.45% (Fig. 5). The observations showed
223
that, reducing the upstream face slope makes the water surface profile fall into smooth curvature
224
and becomes flatter. This is presented by Fig. (6-a) where the flow surface profiles are plotted for
225
all upstream slopes at the discharge of 19.8 L/s. Referring to the figure, the weir with a 90 D
226
upstream face slope shows a highly steep flow profile at the weir crest entrance. Reducing the
227
upstream face slope decreases approach flow curvature and water profiles asymptotically reach
228
to a horizontal streamline over the weir crest. Finally, near the downstream end of the crest, a
Z
229
reduction in surface profile is occurred to follow the downstream slope. For a constant upstream
230
head (H), as is shown in Fig. (6-b), when the upstream face slope (θ ) decreases, the critical
231
section is shifted downstream and vice versa.
232 233
5-2- Velocity distribution
234
Investigation of velocity distribution over the flow depth is important to interpret flow structure
235
around the hydraulic structures. In this study, the vertical distribution of the velocity profiles was
236
measured for all tests at a section upstream of the weir, a section at heel of the weir, and three
237
sections above the crest. Figs. (7-a) to (7-e) show the vertical velocity distribution measured at
238
upstream and above the weir for all upstream slopes at discharge of 19.8 L/s. For all other
239
discharge levels, the velocity profile is the same in shape but different in the velocity
240
magnitudes. The concrete results obtained from the velocimetry are that: At the upstream of the
241
weirs (section 1) the velocity profiles are straight and uniform, almost have a constant value from
242
the bottom of the flume to the water surface (gradually increases over the depth). The flow
243
accelerates gradually when it reaches the weirs (section 2). There is a sharp increase when the
244
upstream face slope is steep and a gradual acceleration when the upstream face slope is mild. For
245
steep slopes, the flow behind the weir tends to stop at low depths (i.e. the velocity tends to be
246
zero near the bottom) and a reservoir condition occurs upstream of the weir. At the section (3),
247
the velocity has its highest value near the crest and decreases over the depth. The minimum
248
velocity occurs close to the water surface. It should be noted that, from the observations of dye
249
injection and video processing, the reverse velocity occurs at the separation zone. At the section
250
(4), the velocity distribution profile is parabolic, the maximum velocity appears at mid depth of
251
flow. Finally, at the section (5), the maximum velocity is shifted to near the crest surface and the
252
velocity decreases from the crest to the free surface. For all the upstream face slopes, the above
253
results were obtained. Although, the shape of velocity distribution profiles are similar, but the
254
velocity magnitudes increased when the upstream face slope decreased. In other word, more
255
upstream face slope leads to less velocity magnitude.
256
5-3- Pressure distribution
257
The piezometric head or hydraulic grade line ( P γ + Z ) was measured at pressure tappings
258
located on the surface of the weir, as previously described. Fig. (8) illustrates the values of
259
( P γ + Z ) over the weir with 21D upstream face slope for different discharge levels. The pressure
260
profiles represent two distinct dips at the upstream and downstream corners of the weir. As can
261
be seen from the figure, at the upstream corner of the weir, the hydraulic grade lines do not cross,
262
and the lowest pressure at this location occurs at the lowest discharge rate. On the contrary, at the
263
downstream corner of the weir, the hydraulic grade lines do cross with the lowest pressure
264
occurring for the highest flow rate (see the zoomed-in view of downstream face). Hence this
265
could potentially be a site for cavitation to take place if the flow rate is sufficiently high. Pressure
266
profile exhibits leaping flow along the downstream face and the weir face experiences
267
atmospheric or negative pressure. Fig. (9) shows the temporal variation of pressure at
268
piezometric tappings of D1 to D5 along the downstream face, respectively. Location of D1 to D5
269
is represented in figure (3). As can be seen from Fig. (9), at D1 piezometric tapping, the pressure
270
is negative over time, and strong fluctuations of pressure occur every few seconds. At D2, the
271
fluctuations severity is reduced but the pressure still remains negative. At D3, the pressure
272
fluctuations are greatly reduced and varied around zero between positive and negative values
273
over time. At D4, the pressure is positive without any strong fluctuations. At D5, the maximum
274
pressure is seen among all tappings and slight pressure fluctuations appear every few seconds.
275
Generally, regular fluctuations occur in all tappings along the downstream face every 10
276
seconds. At D1 and D2 where the pressure is negative, the cavitation is formed and to prevent of
277
this destructive phenomenon, the aeration facilities can be used at the area under the leaping
278
flow.
279
5-4- Flow separation
280
When flow reaches to a weir with sharp entrance, the flow separates from the upstream edge and
281
extends to a certain points over the crest. Some authors believe the flow separation does not
282
reattach to the weir before the flow leaves the weir (Azimi et al., 2013). This phenomenon
283
complicates the flow pattern over the weir and alters the velocity distribution in the stream
284
(Chow, 1959). Flow separation is known as the primary source of energy loss and dissipation of
285
this phenomenon leads to increase the discharge coefficient and prevent occurring of negative
286
velocity at the weir entrance (Tracy 1957; Ramamurthy et al., 1998; Goodarzi et al. 2012). From
287
the literature, the weir inflow geometry has a major impact on the dimensions of separation zone
288
over crest (Bazin 1896; Sargison and Percy 2009, Azimi et al. 2013). To obtain the dimensions
289
of flow separation zone in the experiments, the dye injection technique and video processing
290
procedure were used. Sawdust was also used in the flow and the camera was employed for
291
tracking the particle and the dye path. To demonstrate the effect of upstream face slope of the
292
trapezoidal broad crested weir on the dimensions of flow separation zone, the flow separation
293
length has plotted against the flow depth (both in dimensionless form), and is shown in Fig. (10).
294
Based on the figure, decreasing the upstream face slope from 90D to 21D increases the relative
295
L length of separation ( s
Lcrest
) up to 80% and the relative height of separation (
hs
Z
) about
296
95%. Ls and hs are the length and height of the separation zone, respectively (Fig. 3). At the
297
weir with 21D upstream face slope, the smallest separation zone occurred.
298 299
5-5- Discharge coefficient
300
In all experiments which were conducted in this study, the discharge coefficient ( C D ) of
301
trapezoidal broad-crested weirs was determined. Literature review indicates that, the weir inflow
302
geometry has a significant impact on the C D (Woodburn 1932, Harrison 1967, Fritz and Hager
303
1998, Sargison and Percy 2009). Meanwhile, from their laboratory experiments, Sargison and
304
Percy (2009) and Azimi et al. (2013) showed that the weir downstream face slope has low
305
impact on the C D , which can be neglected. Fig. (11) shows the variation of C D against angle (θ )
306
of the upstream face slope. It can be observed that, as the θ increases, the C D value decreases.
307
The weir with θ = 21D has the greatest C D value among the weirs including slope tests. Further
308
consideration on this figure reveals that, from the θ = 21D to θ = 54D , the C D decreases slightly
309
(low slope) while from θ = 54D to θ = 90D , the C D decreases precipitously (high slope). Fig. (12)
310
present the discharge coefficient as a function of the dimensionless head above crest
311
H
312
compared with those of Sargison and Percy (2009). Also, the C D values which were calculated
313
with Eqs. (3), (4) are presented in this figure. From this figure, by increasing the dimensionless
314
head, the discharge coefficient increases slightly. This result confirms the observation of
315
Sargison and Percy (2009). This figure also indicates that, the C D increases with the decrease of
316
the upstream face slope. The next result which can be obtained from this figure is that, there is a
( H + Lcrest ) . In this figure, the measured C D values for various
θ in current study were
317
good resemblance between values of C D in this study and experimental observation of Sargison
318
and Percy (2009), while it cannot be found a good agreement between the observed C D values
319
and the values calculated from the Eqs. (3), (4). As can be seen, the predicted values have higher
320
values than those of measured values in all tests.
321 322
5-6- Head-Discharge Relation for Trapezoidal broad crested weirs
323
In this study, the trapezoidal broad crested weir head-discharge relations were obtained and
324
plotted for each of the upstream face slopes (Fig. 13). it can be seen that, for low discharges (i.e.
325
for small head values), the head-discharge relations of all the weirs resemble each other while
326
increasing the discharge value leads to different head-discharge relations for different upstream
327
slopes. In other word, further increase in flow rate leads to further difference (divergence) in
328
weirs head-discharge relations. This figure revealed that for head value of H=0.132 m (or H/Z =
329
0.52), the discharge capacity of the weir with θ = 21D is Q=19 L/s (or Q2/gB5=0.038) which is
330
10.5 % higher than the weir with θ = 90D (where the Q=17 L/S or Q2/gB5=0.031).
331 332
6- Conclusion
333
In this paper, a series of laboratory experiments were conducted to investigate the effect of
334
changing upstream slope of trapezoidal broad-crested weirs on discharge coefficient, velocity
335
profile, pressure distribution, flow separation zone, etc. Also, a comprehensive literature review
336
has been performed to survey the extent of the experimental results available in the literature on
337
broad-crested weirs. Based on the results, the upstream weir design has a significant effect on the
338
flow characteristics and discharge coefficient of trapezoidal broad-crested weir. By analyzing
339
experimental observations, the following conclusions can be drawn:
340
By increasing the dimensionless head H ( H + L , the discharge coefficient increases slightly. crest )
341
From the θ = 21D to θ = 54D , the C D decreases slightly while from θ = 54D to θ = 90D , the C D
342
decreases precipitously. Reducing the upstream slope from 90D to 21D increases the relative
343
length of the separation and the relative height of the separation up to 80% and 95%,
344
respectively. Over the time at the downstream face of the weir, pressure reduction alternately
345
occurs, as a result a pressure fluctuation on the downstream face of the weir is observed. This
346
could potentially be a site for cavitation to occur. As the flow rate increases from 6.9 L/s to 19.8
347
L/s, the ratio of Xc/Lcrest increases up to 40.45%. Reducing the upstream face slope decreases
348
approach flow curvature and water profiles asymptotically reach to a horizontal streamline over
349
the weir crest. When the upstream face slope (θ ) decreases, the critical section is shifted
350
downstream and vice versa. This paper presented considerable information that could be of use
351
in the design of flow control and measurement structures.
352
353
References
354 355 356
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463 464
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465
466
467
468
Figure 1: Schematic representation of the flume, Hydraulic Laboratory of University of Tabriz 469
470
471
Figure 2: Photo of experimental equiipment an nd instrum ments 472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
Figure 3: Flow over trapezoidal broad-crested weir
492
493
494
495
496
497
498
499
500
501
502
503
Figure
4: Flow surface profiles over 21o weir for different discharges (Q=6.9 L/s ~ 19.8 L/s)
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
Figure 5: Variation of critical section location vs. flow discharge
521
522
523
524
525
526
527
528
Figure 6(a): Flow surface curvature vs. upstream face slope (Q= 19.8 L/s)
529
530
531
532
Figure 6(b): critical section location vs. upstream face slope (Q= 19.8 L/s)
533
534
535
536
537
538
Figure 7(a): Velocity vertical distribution at upstream of the weir (section 1)
539
540 541 542
Figure 7 (b): Velocity vertical distribution at weir heel (section 2) for various upstream face slopes
543
Figure 7 (c): Velocity vertical distribution at upstream corner (section 3) for various upstream face slopes 544 545 546 547
548 549 550
Figure 7 (d): Velocity vertical distribution at middle section of crest (section 4) for various upstream face slopes
551
552
553
554
555
556 557
Figure 7 (e): Velocity vertical distribution at downstream corner (section 5) for various upstream face slopes 558
559
560
561
562
563
564
565
566
567
568
Figure 8: Pressure distribution along the weir with a zoomed-in view of downstream face
Figure 9: pressure fluctuations along downstream face in the case of leaping flow condition 569
570 571 572 573 574
Figure 10: variations of separation zone altitudinal and longitudinal characteristics vs. upstream face slope 575 576 577 578 579 580 581
582 583 584 585
586
Figure 11: variation of discharge coefficient against upstream face slope
587 588
589
590
591
592
593
594
595
596
597
598
599
Figure 12: Variation of discharge coefficient for different dimensionless heads and different upstream face slopes 600
601
602
603
604
605
606
607
608
609
610
611
612
Figure 13: Dimensionless head-discharge curve for trapezoidal broad crested weir
613 614 615
616
617
618
619
620 621
Table 1: Geometrical dimensions of the models
Weir Weir length height Lcrest (m) Z (m)
Weir width B (m)
622
623
624
0.25
0.5
625
0.25
626
627
Weir configurations
Upstream Downstream slope slope
θD
βD
0.25
90
54
0.5
0.25
74
54
0.25
0.5
0.25
54
54
0.25
0.5
0.25
40
54
628
0.5
0.25
21
54
629
0.2 5
630
631
632
633
634
635
636
637
638
639
•
The flow characteristics on the trapezoidal broad-crested weir have been studied.
640
•
Increasing the upstream face slope decreased the discharge coefficient up to 10%.
641
•
Decreasing the upstream face slope prevents development of separation zone.
642
•
As the upstream face slope decreases, the critical section is shifted downstream.
643
•
By increasing the dimensionless head, the discharge coefficient increases slightly.
644 645 646