KARAKTERISTIK LONCATAN HIDROLIK UNDULAR DI HILIR PINTU AIR
CHARACTERISTICS OF UNDULAR HYDRAULIC JUMP DOWNSTREAM
OF A SLUICE GATE
KARAKTERISTIK LONCATAN HIDROLIK UNDULAR DI HILIR PINTU AIR
Komang Arya Utama 1), Bambang Yulistiyanto 2), and Budi S. Wignyosukarto 2)
Lecturer in Civil Engineering Department, Faculty of Engineering, Gorontalo State University
2)
Lecturer in Civil and Environmental Engineering Department, Faculty of Engineering, Gadjah Mada University
1)
ABSTRACT
Undular hydraulic jump is a hydraulic jump with a low Froude number which is marked by the emergence of a fixed roller.
Information about the characteristics of undular hydraulic jump is still very poor. In order for the interests of the development
of science, it is necessary to in-depth study of the hydraulic characteristics and phenomenon that appear on the undular hydraulic jump. This research is applying the 2D physical model that used a tilting flume. Sluice gate is used as a tool to generate the undular hydraulic jump. Measurement of distance and depth using a point gauge while the flow velocity was measured using a Nixon Streamflo 422 Currentmeter. Circulation flow is driven by using water pumps with discharge 15 l/s and 30
l/s. The results of this study indicate that the maximum flow velocity of dimensionless velocity distribution are at 0.5 - 0.9.
Lowest value of Froude number obtained in running model Q9A1 is Fr1 = 1.197 and its highest value obtained in running model Q3A1 is Fr1 limit = 2.258. The wave steepness is mild with a slope range are 0.1 to 0.3 or 10% to 30%. The length and
height of the wave form are reduce at the first, second, third and so on until the condition of conjugate depth (y3). The Energy
loss occurs with the value ∆E = 0.03 to 1.039 cm or 0,3% - 10,3%. For more information, the phenomenon of recirculation
and flow separation are formed under of the first crest and near of the channel bed. The significant difference value of point
velocity gradient near the channel bed between the wave crest to wave trough raises the potential for scouring beneath the
wave trough for the mobile bed channel.
Keywords: Undular hydraulic jump, Froude number, Velocity profile
ABSTRAKSI
Loncatan hidrolik undular adalah lompata hidrolik dengan angka Froude yang rendah akibat adanya pintu roller tetap. Informasi tentang karakteristik lompatan hidrolik undular masih sangat kurang. Untuk kepentingan pengembangan ilmu pengetahuan, sangat diperluka penelitian yang mendalam tentang karakteristik dan fenomena yang muncul pada lompatan hidrolik
undular. Penelitian dilakukan dengan mengaplikasikan pemodelan fisik 2D yang menggunakan saluran air curam. Pintu air
digunakan sebagai alat untuk memba ngkitkan lompatan hidrolik undular. Alat pengukur jarak dan kedalaman menggunakan
point gauge, sedangkan alat pengukur kecepatan aliran menggunakan Nixon Streamflow 422 Currentmeter. Air dialirkan
menggunakan pompa air dengan kapasitas 15 l/s dan 30 l/s. Hasil penelitian menunjukkan bahwa kecepatan aliran maksimum
dari distribusi tidak berdimensi adalah 0,5 – 0,9. Angka Froude terendah dicapai pada model Q9A1 adalah Fr1 = 1,197 dan
nilai tertinggi pada model Q3A1 is Fr1 limit = 2,258. Kecuraman gelombang sedang dengan kemiringan antara 0,1 dan 0,3 atau
10% sampai 30%. Panjang dan lebar bentuk gelombang berkurang di awal, ke dua dan ke tiga dan seterusnya sampai kondisi
kedalaman yang diperkirakan (y3). Energi hilang terjadi pada ∆E = 0,03 sampai 1,039 cm atau 0,3% - 10,3%. Selanjutnya,
fenomena sirkulasi balik dan aliran terpisah terbentuk di bawah puncak pertama dan di dekat saluran dasar. Perbedaan yang
signifikan pada gradient kecepatan di dekat saluran dasar antara puncak gelombang dengan lembah gelombang menyebabkan
potensi gerusan di bawah lembah gelombang untuk saluran dasar yang begerak.
Kata-kata Kunci : loncatan hidrolik undular, angka Froude, profil kecepatan
INTRODUCTION
Hydraulic jump is a phenomenon that occurs due to suddenly flow changes from supercritical to subcritical flow. The
first type of hydraulic jump is undular hydraulic jump. The undular hydraulic jump formed by supercritical flow at the upstream
that has a low Froude number value which is the value of Fr is 1
to 1.7 (Chow, 1985). The form of undular hydraulic jump can be
found in irrigation channel or flow under the vertical sluice gate
and it also usually found at the weir, where the roll of the waves
can cause erosion on the channel banks (Chanson, H., 1995).
Undular hydraulic jump type are rare. The form of undular
hydraulic jump can be observed in three different types. The first
type is standing undular jump with flat bed. This condition is
usually found in the flow under the sluice gate. The second type
is a moving undular hydraulic jump or generally called undular
bore. This form can be observed due to the tides in estuaries. The
third type is the undular hydraulic jump caused by the submerge
weir at the bottom of the channel, such as the groin in a river.
The purpose and the objective of this present research was
to make observations and analysis of the characteristics of undular hydraulic jump at the downstream of the sluice gate, which is
to look for the lower limit value (Fr1) and the upper limit of
Froude number (Fr1limit) that cause an undular hydraulic jump and
also the velocity distribution and flow characteristics at the
bottom of the channel that occurs in undular hydraulic jump.
Figure 1. Sketch of undular hydraulic jump
Dinamika TEKNIK SIPIL/Vol. 11/No. 2/Mei 2011/Komang Arya Utama, dkk./Halaman : 101 - 106 101
LITERATURE REVIEW
Undular hydraulic jump is a series of steady free surface
waves that causes jump in downstream areas. Undular hydraulic
jump have Froude numbers 1 to 1.7 (Chow, VT, 1985). Further,
the hydraulic conditions to form an undular hydraulic jump in
flow under a sluice gate can be predicted by using hydraulic formulations at the vena contracta and the toe of the jump location
(Ohtsu et al, 2001). An Undular hydraulic jump can affect a
distribution channel and irrigation during the period of tides in
estuaries and in the rapid flow that has a low depth. When this
undular hydraulic jump come into the channel, waves with large
periods will cause a jump in downstream areas. Waves can cause
runoff (over-topping) and damage to the banks of the channel
(Chanson and Montes, 1995).
Froude number (Fr) is a dimensionless number that states
the characteristics of flow in a transverse (cross-sectional flow
characteristic) which shows the ratio of inertial forces with the
force of gravity. Froude number can be obtained by the following
formula:
Fr =
U
gy
(1)
Conjugate Depth
Conjugate depth formulations of undular hydraulic jump
can be written as:
(
)
y3 1
=
1 + 8 Fr12 − 1
y1 2
(2)
Energy loss of undular hydraulic jump
Loss of energy (energy dissipation) is the energy difference
between the specific energy before and after the jump. The amount of energy loss that occurs in a hydraulic jump can be written
as:
(3)
∆E = E1 − E3
By doing a mathematical operation, Equation 3 above becomes
∆E = E1 − E 3 =
( y3 − y1 )3
du z
dz
RESEARCH METHOD
Equipment
Research carried out by using the facilities of prismatic
standard tilting flume with acrylic base material on the walls and
aluminum on the bottom. This channel has a width (B) 30 cm,
length (L) 1000 cm, and height 50 cm with a channel wall thickness is 10 mm. Bottom slope of this channel can be set manually
with a range of channel bed slope +1% and -1%.
Sluice gate that was used is an Armfield brand vertical sluice gate that has material specification of steel with dimensions of
width 30 cm, height 45 cm, the maximum aperture (a) 15 cm and
a minimum aperture (a) 0 cm. Velocity measurements using a
current meter Nixon Streamflo
(1) type 422 with a brand of
Armfield. Point gauge used to measure the depth of flow and is
also used to measure and control the high flow to ensure that the
flow is uniform. This present study is using water pump as a
regulator of the circulation flow. Discharge used around 7 l/s to
30 l/2 with 10 experimental models.
(2)
Examination Tools
1. Initial examination flume circuit
2. This examination is conducted in the form of checks readiness
and condition of the circuit including the pump and flume slope of the channel to match the desired conditions of the study.
3. Examination of velocity measuring devices
4. In this examination, the reading speed is using measuring devices called current meter which is compared with theoretical
(3)
discharge of direct velocity measurement results.
5. Checking flow rates
6. This examination aims to find out exactly how much discharge is flowing in the channel in the experiment this time.
(4)
4 y1 y 3
Velocity distribution and gradient of flow
velocity
Velocity distribution is uneven at every point. Distribution
of vertical velocity can be known by measuring the vertical direction at various depths. The gradient of flow velocity studied based on the velocity distribution with the formula as follows:
mu =
Determination of surface profile of a hydraulic jump will
help us in designing of the free board or retaining walls of a stilling basin where stepping occurred. In addition, knowing the
surface of a hydraulic jump will also help us to estimate the amount of pressure at the channels bed.
(5)
Implementation of Measurement
(4)
In this research, the implementation
of the measurement is
done by starting to prepare the materials and equipment which
necessary. The steps of procedures for the implementation of this
research are:
1. After the power switch is turned on and the engine pump is
turned on, then we open the water tap to drain water into the
channel. Do not forget to check the slope of the channels we
happened to order in accordance with the desired in this
research.
Figure 2. The scheme of depth and distance measurement of an undular hydraulic jump
102 Dinamika TEKNIK SIPIL, Akreditasi BAN DIKTI No : 110/DIKTI/Kep/2009
2. Having monitored the flow is stable, thus we install the sluice
gate on the channel. By doing a variation of discharge (Q)
and the variation of aperture (a), each experiment was given a
name or label for each experiment.
3. For each model, running was done until the model is formed
an undular hydraulic jump.
4. Water surface elevation in both the upstream and downstream
of the sluice gate were investigated by using point gauge and
mica ruler attached to the channel wall.
5. Vertical velocities were measured for each respective model
running. This measurement is done in 10 point depth of flow
at various points namely at the beginning of vena contracta,
at the beginning of stepping, and at three waves of undular
hydraulic jump.
RESULTS AND DISCUSSION
Velocity Profiles
Measurements were taken at the center lain of the channel
on the supercritical flow and subcritical flow regions. Velocity
measurement results are given in Figure 3 and 4 below. Generally
it can be seen that the velocity profile occurring along the undular
hydraulic jump formed shows that there is a relationship between
Froude number before the jump with the form of the wave that
occur.
It shows that the velocity profile at the toe of the jump to
give the maximum value is at y/y1d = 0.5 - 0.6. As for the first
wave, the wave crest giving a maximum velocity value is at y/y2a
= 0.5 - 0.7 and the maximum value for the wave trough is at y/y2b
= 0.7 to 0.8. For the data on second wave, the data obtained for
the maximum velocity of the first wave is at y/y2c = 0.7 to 0.8,
while in the wave tough is at y/y2d = 0.8 to 0.9.
Froude Number
Froude number calculations performed on all models of
running are done. Froude number value at the upstream of
undular hydraulic jump will determine the type of undular
hydraulic jump that occur. This present research has obtained
variety value of Froude number. Table 1 shows the lowest Froude
number value is on the model Q9A1 Fr1 = 1.197 and the highest
one is on Q3A1 model as Fr1limit = 2.258. These results have a
same results of other research obtained by Iwao Ohtsu and
Hubert Chanson is the latest research to obtain the highest Froude
number value is Fr1limit = 2.3 and = 2.4.
Characteristics of Free Water Surface of
Undular Hydraulic Jump
Measurement of the undular hydraulic jump free water
surface profile at the centre line of the channel is using measuring
instruments called points gauge, and for the canal walls water
surface profiles were observed using a mica ruler.
Figure 7 above had been seen that the results of research
data showed that the ratio of depth to the depth of critical flow
rate is 0.7 to 1.5. This value resembles the results obtained by
Chanson in his research.
(a) velocity profile , Fr = 1,197 ; y1 = 0,083
(b) velocity profile, Fr = 1,450 ; y1 = 0,080
(c)
velocity profile, Fr = 1,725; y1 = 0,0675
Figure 3. velocity profile of undular hydraulic jump
Dinamika TEKNIK SIPIL/Vol. 11/No. 2/Mei 2011/Komang Arya Utama, dkk./Halaman : 101 - 106 103
y/y2a
y/y1d
1,000
1,000
y1 = 0,075 ; Fr1 = 1,404
y1 = 0,083 ; Fr1 = 1,197
y1 = 0,065 ; Fr1 = 1,349
y1 = 0,080 ; Fr1 = 1,450
y1 = 0,075; Fr1 = 1,725
Chanson - Fr = 1,48
Chanson - Fr = 1,7
0,900
0,800
0,700
y/y2b
1,000
0,900
0,700
0,600
0,600
0,500
0,500
0,900
y2 = 0,146 ; Fr2a = 0,559
y2 = 0,137 ; Fr2a = 0,660
y2 = 0,120 ; Fr2a = 0,558
y2 = 0,140 ; Fr2a = 0,634
y2 = 0,140; Fr2a = 0,697
Chanson - Fr1 = 1,57
Ohtsu - Fr1 = 1,48
Ohtsu - Fr1 = 2,08
0,800
0,700
0,600
0,500
0,400
0,400
0,300
0,300
0,300
0,200
0,200
0,200
0,100
0,100
u/uc
0,000
0,000
0,500
1,000
1,500
0,400
0,100
0,000
0,000
2,000
y2 = 0,093 ; Fr2 = 0,81
y2 = 0,098 ; Fr2 = 0,91
y2 = 0,08 ; Fr2 = 0,96
y2 = 0,09 ; Fr2 = 0,94
y2 = 0,09 ; Fr2 = 0,90
Chanson - Fr1 = 1,57
0,800
u/U c
0,200
0,400
0,600
0,800
1,000
1,200
0,000
0,000
1,400
(a)
0,200
0,400
0,600
0,800
1,000
1,200
u/Uc
1,400
(b)
y/y2c
y/y2d
1,000
1,000
0,900
0,900
y2 = 0,142; Fr2c = 0,57
0,800
0,700
0,600
y2 = 0,125 ; Fr2c = 0,65
0,800
y2 = 0,1024 ; Fr2d = 0,78
y2 = 0,092 ; Fr2d = 0,85
y2 = 0,08; Fr2d = 0,84
y2 = 0,12 ; Fr2c = 0,55
0,700
y2 = 0,135 ; Fr2c = 0,61
y2 = 0,135; Fr2c = 0,62
y2 = 0,10 ; Fr2d = 0,85
y2 = 0,12; Fr2d = 0,84
0,600
Chanson - Fr1 = 1,57
0,500
Chanson - Fr = 1,48
0,500
0,400
0,400
0,300
0,300
0,200
0,200
0,100
0,100
u/U c
0,000
0,000
0,500
0,000
0,000
1,000
0,200
0,400
0,600
0,800
1,000
1,200
u/Uc
1,400
(c)
Figure 4. (a) Velocity distribution at the toe of the jump, (b) Velocity distribution at the 1st wave, and
(c) Velocity distribution at the 2st wave
Table 1. Calculation of Froude number at the toe of the jump
g
No
Model
U1
y1
2
(m/d )
(m)
y1
U1
(m/d )
(m)
(m/d)
g
(m/d)
Fr1
No
Model
2
Fr1
1
Q1A1
9.81
0.0255
1.088
2.175
8
Q8A1
9.81
0.0720
1.220
1.452
2
Q2A1
9.81
0.0340
0.919
1.592
9
Q9A1
9.81
0.0830
1.080
1.197
3
Q3A1
9.81
0.0325
1.275
2.258
10
Q9A2
9.81
0.0750
1.204
1.404
4
Q3A2
9.81
0.0410
0.919
1.449
11
Q10A1
9.81
0.0675
1.404
1.725
5
Q4A1
9.81
0.0525
1.101
1.534
12
Q10A2
9.81
0.0750
1.299
1.514
6
Q5A1
9.81
0.0500
1.197
1.709
13
Q10A3
9.81
0.0800
1.285
1.450
7
Q6A1
9.81
0.0650
1.077
1.349
14
Q10A4
9.81
0.0840
1.178
1.298
Source: data analysis
y2 /y1
3,50
y = 1,354x + 0,024
R² = 0,906
3,00
2,50
2,00
Data [y2/y1 = 1,354 Fr1 + 0,024]
1,50
Ohtsu [h2/h1 = 1,51Fr1 - 0,35]
Linear (Teoritis)
1,00
Fr1
1
1,2
1,4
1,6
1,8
2
2,2
2,4
Figure 5. Experimental relationship of Fr1 with y2/y1 for
undular hydraulic jump
Figure 6. Undular hydraulic jump, Fr = 1,450; y1 = 0,008 m
104 Dinamika TEKNIK SIPIL, Akreditasi BAN DIKTI No : 110/DIKTI/Kep/2009
2.
y/yc
1,8
1,6
3.
1,4
1,2
1
0,8
4.
0,6
Data Q6A1 [Fr1=1,349 ; y1=0,065]
Data Q9A1 [Fr1=1,197 ; y1=0,083]
Chanson, H [Fr1=1,26 ; y1=0,082]
0,4
0,2
x/yc
0
0,0
5,0
10,0
15,0
20,0
25,0
30,0
For Froude number value, the lowest values obtained on
running the model Q9A1 is Fr1= 1.197 and highest value
in model Q3A1 is Fr1limit = 2.258.
This undular hydraulic jump is also has a loss of energy
∆E = 0.03 to 1.039 cm or 0,297% - 10,276%. The value
of energy coefficient is (α) = 0.94 -1.11 and the coefficient value of force / momentum (β) is = 0.89 to 1.20.
There is a difference in significant value of bed gradient
of flow velocity between the under of the wave crest with
the under of wave trough. This difference is potentially
caused scour beneath the wave trough in a mobile bed
channel.
Suggestion
Figure 7. Free water surface profile
Specific Energy and Specific Momentum
In this research, using Equation (3) dan (4) the result of
energy loss analysis of the models Q10A3 amounted ∆Es =
0.1953 cm. In general, the values of energy loss that occurs in
this research varies for each model, and it ranged ∆E = 0.03 to
1.039 cm or atau 0,297% - 10,276%. In addition, from analysis of all experimental models in this research, the researcher
obtained value α = 0.94 -1.11 and the value β = 0.89 to 1.20
In general, the bed gradient of flow velocity under the
wave trough has a greater value than the bed gradient of flow
velocity under the wave crest. This significant difference, by
the author, is indicated to cause the occurrence or provide the
potential for scour on the mobile bed channel.
CONCLUSIONS AND SUGGESTIONS
Conclusion
The conclusions that can be obtained from the research
of undular hydraulic jump characteristics at the downstream of
sluice gate are:
1. In general, the maximum velocity at the wave crest is
below the surface while in the wave trough is on the surface flow.
It is recommended to perform measurements with the
ADV instrument side-looking and doing research with a mobile bed channel.
REFERENCES
Chanson, H., and Montes, J.S. (1995). “Characteristics of Undular Hydraulic Jumps. Experimental Apparatus and Flow
Patterns.” Journal of Hyd. Eng., ASCE, Vol. 121, No. 2,
pp. 129-144
Chow, V.T. (1985). Open Channel Hydraulics (translation),
Erlangga, Jakarta.
Montes, J.S., and Chanson, H. (1998). “Characteristics of Undular Hydraulic Jumps. Results and Calculations.” Journal
of Hyd. Eng., ASCE, Vol. 124, No. 2, pp. 192-205.
Ohtsu, I., Yasuda, Y., and Gotoh, H. (2001). “Hydraulic Condition for Undular-Jump Formations.” Journal of Hyd.
Res., IAHR, Vol. 39, No. 2, pp. 203-209.
Raju, K.G.R., (1986). Flow Through Open Channels (translation), Erlangga, Jakarta.
Wols, B.A. (2005). “Undular Hydraulic Jump.” M.Sc. Thesis,
Delft University of Technology, Delft.
Kurva Gaya Spesifik
Kurva Energi Spesifik
(Running-Q10A3)
y (cm)
18
18
Lengkung energi teoritis
Lengkung energi a ktua l
Lengkung gaya teoritis
Lengkung gaya aktua l
16
16
Esy2a 16,5179
14
12
10
(Running-Q10A3)
y (cm)
5055,020
Fsy2a
14
15,5157
Esy3
12
Esy2d14,9350
10
Fsy3
4659,672
4461,028
Esy2b
8
15,7110
8
Esy1
Esya 18,9848
∆Es
6
4
2
Es (cm)
0
0
2
4
6
8
10
12
14
16
18
20
4661,284
Fsy1
5342,475
6
Fsya
4
Fs1 = Fs3
2
Fsy1=Fsy3
0
0
1000
Fs
2000
3000
1 = Fs
3
4000
5000
600
Gradient of Flow Velocity
Figure 8. Curve of specific energy and specific momentum at the undular hydraulic jump for model Q10A3
Dinamika TEKNIK SIPIL/Vol. 11/No. 2/Mei 2011/Komang Arya Utama, dkk./Halaman : 101 - 106 105
F r = 1,197
Y
y
τz /µ
2,65
12,64
-1 ,3 1
1,86
-2,42
29,84
-17,17
20,87
-28,84
-7,52
-12,37
-11,89
-32,51
14,09
11,01 -2 5 ,9 8
-3 9 ,4 1
19,15
13,43 -1 0 ,7 9
2 9 ,2 8
-25,91
9 ,0 3
3 1 ,4 8
11 ,4 5
-18,81
-1,24
-11,11
-5,85
-8,48
-5,85
-15,50
-7,31
-6,68
4,02
-2,55
-14,02
-19,65
3,02
-74,43
-4 ,1 5
1 ,4 2
-10,10
1,77
17,21
-3 ,8 4
-3 ,0 7
-5 ,7 0
-2 ,5 2
-1 3 ,0 4
-6 ,1 4
-5 4 ,9 4
6,43
- 9 ,2 7
7 ,8 5
-6 ,1 3
- 9 ,5 8
-5 ,0 3
-6 7 ,8 2
-1 2 ,2 5
- 9 ,7 4
0 ,0 0
- 7 ,1 8
- 6 ,6 2
- 3 ,0 3
-1 ,0 7
-4 ,4 2
-1 3 ,11
2 ,1 3
- 4 ,8 2
-5 ,3 8
-6 9 ,4 7
-6 1 ,3 8
-11 ,8 9
-4 ,2 7
-1 2 ,5 0
1 ,8 3
X
F r = 1,450
Y
y
τ z /µ
2,59
12,37
0,10
3,20
-9,88
1,82
44,04
44,04
-43,23
4,32
0,81
-34,7
-1,94
-10,43
9,46
6,31
3,72
2,97
4,03
-8,26
-34,26
2,82
-6,71
-2,49
-13,71
-11,41
-14,68
-1,3
-19,88
-12,05
3,93
-8,84
-12,05
-9,64
-10,76
-11,73
-8,52
1,12
-4,40
-0,80
0,20
-2,10
-2,30
-8,89
-6,69
2,50
-2,83
-9,91
-3,40
-8,92
-6,09
-5,10
-9,77
24,20
1,27
-5,94
-4,14
1,98
-8,86
-0,94
-0,94
-4,90
-8,55
-1,07
-2,27
-11,89
-3,61
-7,75
-5,74
2,40
1,60
X
F r = 1,725
Y
y
τz/µ
2,5 9
1 2,37
-9,88
1,8 2
-0,73 1,21
-7,28
6,07
-14,32
18,20
-12,37
-8,49
-2,43
13,34
1,70
-9 ,22
-2 5,96
-16,50
14 ,80
-9,9 3
-1,39
7,76
-1 0,85
-0 ,64
-1,46
-2,54
22,6 2
-6,71
3,93
-2,49
-1 3,71
-19 ,65
-82,52
-5,14
-9,37
-12,80
-2,51
-9,49
4,34
-51,64
-0,8 0
-11,29
-9,9 9
-6,29
-11 ,29
-3,10
-3,7 0
2 2,08
-82,68
-7,09
-3,69
-8,69
-6,74
-5,72
-4,12
11 , 7 8
- 2 ,1 9
2,97
0 ,2 1
- 1 2 ,3 1
- 5 ,4 2
- 7 ,3 0
-6 ,9 9
- 7 ,9 3
- 4 4 ,7 0
-9,25
-83,84
Figure 9. Velocity profile and Gradient of flow velocity profile of undular hydraulic jump
Figure 10. Sketch of scour under the wave trough for a mobile bed channel
106 Dinamika TEKNIK SIPIL, Akreditasi BAN DIKTI No : 110/DIKTI/Kep/2009
-0,47
-2,58
-6,79
-3,40
-4,80
-1,99
X
OF A SLUICE GATE
KARAKTERISTIK LONCATAN HIDROLIK UNDULAR DI HILIR PINTU AIR
Komang Arya Utama 1), Bambang Yulistiyanto 2), and Budi S. Wignyosukarto 2)
Lecturer in Civil Engineering Department, Faculty of Engineering, Gorontalo State University
2)
Lecturer in Civil and Environmental Engineering Department, Faculty of Engineering, Gadjah Mada University
1)
ABSTRACT
Undular hydraulic jump is a hydraulic jump with a low Froude number which is marked by the emergence of a fixed roller.
Information about the characteristics of undular hydraulic jump is still very poor. In order for the interests of the development
of science, it is necessary to in-depth study of the hydraulic characteristics and phenomenon that appear on the undular hydraulic jump. This research is applying the 2D physical model that used a tilting flume. Sluice gate is used as a tool to generate the undular hydraulic jump. Measurement of distance and depth using a point gauge while the flow velocity was measured using a Nixon Streamflo 422 Currentmeter. Circulation flow is driven by using water pumps with discharge 15 l/s and 30
l/s. The results of this study indicate that the maximum flow velocity of dimensionless velocity distribution are at 0.5 - 0.9.
Lowest value of Froude number obtained in running model Q9A1 is Fr1 = 1.197 and its highest value obtained in running model Q3A1 is Fr1 limit = 2.258. The wave steepness is mild with a slope range are 0.1 to 0.3 or 10% to 30%. The length and
height of the wave form are reduce at the first, second, third and so on until the condition of conjugate depth (y3). The Energy
loss occurs with the value ∆E = 0.03 to 1.039 cm or 0,3% - 10,3%. For more information, the phenomenon of recirculation
and flow separation are formed under of the first crest and near of the channel bed. The significant difference value of point
velocity gradient near the channel bed between the wave crest to wave trough raises the potential for scouring beneath the
wave trough for the mobile bed channel.
Keywords: Undular hydraulic jump, Froude number, Velocity profile
ABSTRAKSI
Loncatan hidrolik undular adalah lompata hidrolik dengan angka Froude yang rendah akibat adanya pintu roller tetap. Informasi tentang karakteristik lompatan hidrolik undular masih sangat kurang. Untuk kepentingan pengembangan ilmu pengetahuan, sangat diperluka penelitian yang mendalam tentang karakteristik dan fenomena yang muncul pada lompatan hidrolik
undular. Penelitian dilakukan dengan mengaplikasikan pemodelan fisik 2D yang menggunakan saluran air curam. Pintu air
digunakan sebagai alat untuk memba ngkitkan lompatan hidrolik undular. Alat pengukur jarak dan kedalaman menggunakan
point gauge, sedangkan alat pengukur kecepatan aliran menggunakan Nixon Streamflow 422 Currentmeter. Air dialirkan
menggunakan pompa air dengan kapasitas 15 l/s dan 30 l/s. Hasil penelitian menunjukkan bahwa kecepatan aliran maksimum
dari distribusi tidak berdimensi adalah 0,5 – 0,9. Angka Froude terendah dicapai pada model Q9A1 adalah Fr1 = 1,197 dan
nilai tertinggi pada model Q3A1 is Fr1 limit = 2,258. Kecuraman gelombang sedang dengan kemiringan antara 0,1 dan 0,3 atau
10% sampai 30%. Panjang dan lebar bentuk gelombang berkurang di awal, ke dua dan ke tiga dan seterusnya sampai kondisi
kedalaman yang diperkirakan (y3). Energi hilang terjadi pada ∆E = 0,03 sampai 1,039 cm atau 0,3% - 10,3%. Selanjutnya,
fenomena sirkulasi balik dan aliran terpisah terbentuk di bawah puncak pertama dan di dekat saluran dasar. Perbedaan yang
signifikan pada gradient kecepatan di dekat saluran dasar antara puncak gelombang dengan lembah gelombang menyebabkan
potensi gerusan di bawah lembah gelombang untuk saluran dasar yang begerak.
Kata-kata Kunci : loncatan hidrolik undular, angka Froude, profil kecepatan
INTRODUCTION
Hydraulic jump is a phenomenon that occurs due to suddenly flow changes from supercritical to subcritical flow. The
first type of hydraulic jump is undular hydraulic jump. The undular hydraulic jump formed by supercritical flow at the upstream
that has a low Froude number value which is the value of Fr is 1
to 1.7 (Chow, 1985). The form of undular hydraulic jump can be
found in irrigation channel or flow under the vertical sluice gate
and it also usually found at the weir, where the roll of the waves
can cause erosion on the channel banks (Chanson, H., 1995).
Undular hydraulic jump type are rare. The form of undular
hydraulic jump can be observed in three different types. The first
type is standing undular jump with flat bed. This condition is
usually found in the flow under the sluice gate. The second type
is a moving undular hydraulic jump or generally called undular
bore. This form can be observed due to the tides in estuaries. The
third type is the undular hydraulic jump caused by the submerge
weir at the bottom of the channel, such as the groin in a river.
The purpose and the objective of this present research was
to make observations and analysis of the characteristics of undular hydraulic jump at the downstream of the sluice gate, which is
to look for the lower limit value (Fr1) and the upper limit of
Froude number (Fr1limit) that cause an undular hydraulic jump and
also the velocity distribution and flow characteristics at the
bottom of the channel that occurs in undular hydraulic jump.
Figure 1. Sketch of undular hydraulic jump
Dinamika TEKNIK SIPIL/Vol. 11/No. 2/Mei 2011/Komang Arya Utama, dkk./Halaman : 101 - 106 101
LITERATURE REVIEW
Undular hydraulic jump is a series of steady free surface
waves that causes jump in downstream areas. Undular hydraulic
jump have Froude numbers 1 to 1.7 (Chow, VT, 1985). Further,
the hydraulic conditions to form an undular hydraulic jump in
flow under a sluice gate can be predicted by using hydraulic formulations at the vena contracta and the toe of the jump location
(Ohtsu et al, 2001). An Undular hydraulic jump can affect a
distribution channel and irrigation during the period of tides in
estuaries and in the rapid flow that has a low depth. When this
undular hydraulic jump come into the channel, waves with large
periods will cause a jump in downstream areas. Waves can cause
runoff (over-topping) and damage to the banks of the channel
(Chanson and Montes, 1995).
Froude number (Fr) is a dimensionless number that states
the characteristics of flow in a transverse (cross-sectional flow
characteristic) which shows the ratio of inertial forces with the
force of gravity. Froude number can be obtained by the following
formula:
Fr =
U
gy
(1)
Conjugate Depth
Conjugate depth formulations of undular hydraulic jump
can be written as:
(
)
y3 1
=
1 + 8 Fr12 − 1
y1 2
(2)
Energy loss of undular hydraulic jump
Loss of energy (energy dissipation) is the energy difference
between the specific energy before and after the jump. The amount of energy loss that occurs in a hydraulic jump can be written
as:
(3)
∆E = E1 − E3
By doing a mathematical operation, Equation 3 above becomes
∆E = E1 − E 3 =
( y3 − y1 )3
du z
dz
RESEARCH METHOD
Equipment
Research carried out by using the facilities of prismatic
standard tilting flume with acrylic base material on the walls and
aluminum on the bottom. This channel has a width (B) 30 cm,
length (L) 1000 cm, and height 50 cm with a channel wall thickness is 10 mm. Bottom slope of this channel can be set manually
with a range of channel bed slope +1% and -1%.
Sluice gate that was used is an Armfield brand vertical sluice gate that has material specification of steel with dimensions of
width 30 cm, height 45 cm, the maximum aperture (a) 15 cm and
a minimum aperture (a) 0 cm. Velocity measurements using a
current meter Nixon Streamflo
(1) type 422 with a brand of
Armfield. Point gauge used to measure the depth of flow and is
also used to measure and control the high flow to ensure that the
flow is uniform. This present study is using water pump as a
regulator of the circulation flow. Discharge used around 7 l/s to
30 l/2 with 10 experimental models.
(2)
Examination Tools
1. Initial examination flume circuit
2. This examination is conducted in the form of checks readiness
and condition of the circuit including the pump and flume slope of the channel to match the desired conditions of the study.
3. Examination of velocity measuring devices
4. In this examination, the reading speed is using measuring devices called current meter which is compared with theoretical
(3)
discharge of direct velocity measurement results.
5. Checking flow rates
6. This examination aims to find out exactly how much discharge is flowing in the channel in the experiment this time.
(4)
4 y1 y 3
Velocity distribution and gradient of flow
velocity
Velocity distribution is uneven at every point. Distribution
of vertical velocity can be known by measuring the vertical direction at various depths. The gradient of flow velocity studied based on the velocity distribution with the formula as follows:
mu =
Determination of surface profile of a hydraulic jump will
help us in designing of the free board or retaining walls of a stilling basin where stepping occurred. In addition, knowing the
surface of a hydraulic jump will also help us to estimate the amount of pressure at the channels bed.
(5)
Implementation of Measurement
(4)
In this research, the implementation
of the measurement is
done by starting to prepare the materials and equipment which
necessary. The steps of procedures for the implementation of this
research are:
1. After the power switch is turned on and the engine pump is
turned on, then we open the water tap to drain water into the
channel. Do not forget to check the slope of the channels we
happened to order in accordance with the desired in this
research.
Figure 2. The scheme of depth and distance measurement of an undular hydraulic jump
102 Dinamika TEKNIK SIPIL, Akreditasi BAN DIKTI No : 110/DIKTI/Kep/2009
2. Having monitored the flow is stable, thus we install the sluice
gate on the channel. By doing a variation of discharge (Q)
and the variation of aperture (a), each experiment was given a
name or label for each experiment.
3. For each model, running was done until the model is formed
an undular hydraulic jump.
4. Water surface elevation in both the upstream and downstream
of the sluice gate were investigated by using point gauge and
mica ruler attached to the channel wall.
5. Vertical velocities were measured for each respective model
running. This measurement is done in 10 point depth of flow
at various points namely at the beginning of vena contracta,
at the beginning of stepping, and at three waves of undular
hydraulic jump.
RESULTS AND DISCUSSION
Velocity Profiles
Measurements were taken at the center lain of the channel
on the supercritical flow and subcritical flow regions. Velocity
measurement results are given in Figure 3 and 4 below. Generally
it can be seen that the velocity profile occurring along the undular
hydraulic jump formed shows that there is a relationship between
Froude number before the jump with the form of the wave that
occur.
It shows that the velocity profile at the toe of the jump to
give the maximum value is at y/y1d = 0.5 - 0.6. As for the first
wave, the wave crest giving a maximum velocity value is at y/y2a
= 0.5 - 0.7 and the maximum value for the wave trough is at y/y2b
= 0.7 to 0.8. For the data on second wave, the data obtained for
the maximum velocity of the first wave is at y/y2c = 0.7 to 0.8,
while in the wave tough is at y/y2d = 0.8 to 0.9.
Froude Number
Froude number calculations performed on all models of
running are done. Froude number value at the upstream of
undular hydraulic jump will determine the type of undular
hydraulic jump that occur. This present research has obtained
variety value of Froude number. Table 1 shows the lowest Froude
number value is on the model Q9A1 Fr1 = 1.197 and the highest
one is on Q3A1 model as Fr1limit = 2.258. These results have a
same results of other research obtained by Iwao Ohtsu and
Hubert Chanson is the latest research to obtain the highest Froude
number value is Fr1limit = 2.3 and = 2.4.
Characteristics of Free Water Surface of
Undular Hydraulic Jump
Measurement of the undular hydraulic jump free water
surface profile at the centre line of the channel is using measuring
instruments called points gauge, and for the canal walls water
surface profiles were observed using a mica ruler.
Figure 7 above had been seen that the results of research
data showed that the ratio of depth to the depth of critical flow
rate is 0.7 to 1.5. This value resembles the results obtained by
Chanson in his research.
(a) velocity profile , Fr = 1,197 ; y1 = 0,083
(b) velocity profile, Fr = 1,450 ; y1 = 0,080
(c)
velocity profile, Fr = 1,725; y1 = 0,0675
Figure 3. velocity profile of undular hydraulic jump
Dinamika TEKNIK SIPIL/Vol. 11/No. 2/Mei 2011/Komang Arya Utama, dkk./Halaman : 101 - 106 103
y/y2a
y/y1d
1,000
1,000
y1 = 0,075 ; Fr1 = 1,404
y1 = 0,083 ; Fr1 = 1,197
y1 = 0,065 ; Fr1 = 1,349
y1 = 0,080 ; Fr1 = 1,450
y1 = 0,075; Fr1 = 1,725
Chanson - Fr = 1,48
Chanson - Fr = 1,7
0,900
0,800
0,700
y/y2b
1,000
0,900
0,700
0,600
0,600
0,500
0,500
0,900
y2 = 0,146 ; Fr2a = 0,559
y2 = 0,137 ; Fr2a = 0,660
y2 = 0,120 ; Fr2a = 0,558
y2 = 0,140 ; Fr2a = 0,634
y2 = 0,140; Fr2a = 0,697
Chanson - Fr1 = 1,57
Ohtsu - Fr1 = 1,48
Ohtsu - Fr1 = 2,08
0,800
0,700
0,600
0,500
0,400
0,400
0,300
0,300
0,300
0,200
0,200
0,200
0,100
0,100
u/uc
0,000
0,000
0,500
1,000
1,500
0,400
0,100
0,000
0,000
2,000
y2 = 0,093 ; Fr2 = 0,81
y2 = 0,098 ; Fr2 = 0,91
y2 = 0,08 ; Fr2 = 0,96
y2 = 0,09 ; Fr2 = 0,94
y2 = 0,09 ; Fr2 = 0,90
Chanson - Fr1 = 1,57
0,800
u/U c
0,200
0,400
0,600
0,800
1,000
1,200
0,000
0,000
1,400
(a)
0,200
0,400
0,600
0,800
1,000
1,200
u/Uc
1,400
(b)
y/y2c
y/y2d
1,000
1,000
0,900
0,900
y2 = 0,142; Fr2c = 0,57
0,800
0,700
0,600
y2 = 0,125 ; Fr2c = 0,65
0,800
y2 = 0,1024 ; Fr2d = 0,78
y2 = 0,092 ; Fr2d = 0,85
y2 = 0,08; Fr2d = 0,84
y2 = 0,12 ; Fr2c = 0,55
0,700
y2 = 0,135 ; Fr2c = 0,61
y2 = 0,135; Fr2c = 0,62
y2 = 0,10 ; Fr2d = 0,85
y2 = 0,12; Fr2d = 0,84
0,600
Chanson - Fr1 = 1,57
0,500
Chanson - Fr = 1,48
0,500
0,400
0,400
0,300
0,300
0,200
0,200
0,100
0,100
u/U c
0,000
0,000
0,500
0,000
0,000
1,000
0,200
0,400
0,600
0,800
1,000
1,200
u/Uc
1,400
(c)
Figure 4. (a) Velocity distribution at the toe of the jump, (b) Velocity distribution at the 1st wave, and
(c) Velocity distribution at the 2st wave
Table 1. Calculation of Froude number at the toe of the jump
g
No
Model
U1
y1
2
(m/d )
(m)
y1
U1
(m/d )
(m)
(m/d)
g
(m/d)
Fr1
No
Model
2
Fr1
1
Q1A1
9.81
0.0255
1.088
2.175
8
Q8A1
9.81
0.0720
1.220
1.452
2
Q2A1
9.81
0.0340
0.919
1.592
9
Q9A1
9.81
0.0830
1.080
1.197
3
Q3A1
9.81
0.0325
1.275
2.258
10
Q9A2
9.81
0.0750
1.204
1.404
4
Q3A2
9.81
0.0410
0.919
1.449
11
Q10A1
9.81
0.0675
1.404
1.725
5
Q4A1
9.81
0.0525
1.101
1.534
12
Q10A2
9.81
0.0750
1.299
1.514
6
Q5A1
9.81
0.0500
1.197
1.709
13
Q10A3
9.81
0.0800
1.285
1.450
7
Q6A1
9.81
0.0650
1.077
1.349
14
Q10A4
9.81
0.0840
1.178
1.298
Source: data analysis
y2 /y1
3,50
y = 1,354x + 0,024
R² = 0,906
3,00
2,50
2,00
Data [y2/y1 = 1,354 Fr1 + 0,024]
1,50
Ohtsu [h2/h1 = 1,51Fr1 - 0,35]
Linear (Teoritis)
1,00
Fr1
1
1,2
1,4
1,6
1,8
2
2,2
2,4
Figure 5. Experimental relationship of Fr1 with y2/y1 for
undular hydraulic jump
Figure 6. Undular hydraulic jump, Fr = 1,450; y1 = 0,008 m
104 Dinamika TEKNIK SIPIL, Akreditasi BAN DIKTI No : 110/DIKTI/Kep/2009
2.
y/yc
1,8
1,6
3.
1,4
1,2
1
0,8
4.
0,6
Data Q6A1 [Fr1=1,349 ; y1=0,065]
Data Q9A1 [Fr1=1,197 ; y1=0,083]
Chanson, H [Fr1=1,26 ; y1=0,082]
0,4
0,2
x/yc
0
0,0
5,0
10,0
15,0
20,0
25,0
30,0
For Froude number value, the lowest values obtained on
running the model Q9A1 is Fr1= 1.197 and highest value
in model Q3A1 is Fr1limit = 2.258.
This undular hydraulic jump is also has a loss of energy
∆E = 0.03 to 1.039 cm or 0,297% - 10,276%. The value
of energy coefficient is (α) = 0.94 -1.11 and the coefficient value of force / momentum (β) is = 0.89 to 1.20.
There is a difference in significant value of bed gradient
of flow velocity between the under of the wave crest with
the under of wave trough. This difference is potentially
caused scour beneath the wave trough in a mobile bed
channel.
Suggestion
Figure 7. Free water surface profile
Specific Energy and Specific Momentum
In this research, using Equation (3) dan (4) the result of
energy loss analysis of the models Q10A3 amounted ∆Es =
0.1953 cm. In general, the values of energy loss that occurs in
this research varies for each model, and it ranged ∆E = 0.03 to
1.039 cm or atau 0,297% - 10,276%. In addition, from analysis of all experimental models in this research, the researcher
obtained value α = 0.94 -1.11 and the value β = 0.89 to 1.20
In general, the bed gradient of flow velocity under the
wave trough has a greater value than the bed gradient of flow
velocity under the wave crest. This significant difference, by
the author, is indicated to cause the occurrence or provide the
potential for scour on the mobile bed channel.
CONCLUSIONS AND SUGGESTIONS
Conclusion
The conclusions that can be obtained from the research
of undular hydraulic jump characteristics at the downstream of
sluice gate are:
1. In general, the maximum velocity at the wave crest is
below the surface while in the wave trough is on the surface flow.
It is recommended to perform measurements with the
ADV instrument side-looking and doing research with a mobile bed channel.
REFERENCES
Chanson, H., and Montes, J.S. (1995). “Characteristics of Undular Hydraulic Jumps. Experimental Apparatus and Flow
Patterns.” Journal of Hyd. Eng., ASCE, Vol. 121, No. 2,
pp. 129-144
Chow, V.T. (1985). Open Channel Hydraulics (translation),
Erlangga, Jakarta.
Montes, J.S., and Chanson, H. (1998). “Characteristics of Undular Hydraulic Jumps. Results and Calculations.” Journal
of Hyd. Eng., ASCE, Vol. 124, No. 2, pp. 192-205.
Ohtsu, I., Yasuda, Y., and Gotoh, H. (2001). “Hydraulic Condition for Undular-Jump Formations.” Journal of Hyd.
Res., IAHR, Vol. 39, No. 2, pp. 203-209.
Raju, K.G.R., (1986). Flow Through Open Channels (translation), Erlangga, Jakarta.
Wols, B.A. (2005). “Undular Hydraulic Jump.” M.Sc. Thesis,
Delft University of Technology, Delft.
Kurva Gaya Spesifik
Kurva Energi Spesifik
(Running-Q10A3)
y (cm)
18
18
Lengkung energi teoritis
Lengkung energi a ktua l
Lengkung gaya teoritis
Lengkung gaya aktua l
16
16
Esy2a 16,5179
14
12
10
(Running-Q10A3)
y (cm)
5055,020
Fsy2a
14
15,5157
Esy3
12
Esy2d14,9350
10
Fsy3
4659,672
4461,028
Esy2b
8
15,7110
8
Esy1
Esya 18,9848
∆Es
6
4
2
Es (cm)
0
0
2
4
6
8
10
12
14
16
18
20
4661,284
Fsy1
5342,475
6
Fsya
4
Fs1 = Fs3
2
Fsy1=Fsy3
0
0
1000
Fs
2000
3000
1 = Fs
3
4000
5000
600
Gradient of Flow Velocity
Figure 8. Curve of specific energy and specific momentum at the undular hydraulic jump for model Q10A3
Dinamika TEKNIK SIPIL/Vol. 11/No. 2/Mei 2011/Komang Arya Utama, dkk./Halaman : 101 - 106 105
F r = 1,197
Y
y
τz /µ
2,65
12,64
-1 ,3 1
1,86
-2,42
29,84
-17,17
20,87
-28,84
-7,52
-12,37
-11,89
-32,51
14,09
11,01 -2 5 ,9 8
-3 9 ,4 1
19,15
13,43 -1 0 ,7 9
2 9 ,2 8
-25,91
9 ,0 3
3 1 ,4 8
11 ,4 5
-18,81
-1,24
-11,11
-5,85
-8,48
-5,85
-15,50
-7,31
-6,68
4,02
-2,55
-14,02
-19,65
3,02
-74,43
-4 ,1 5
1 ,4 2
-10,10
1,77
17,21
-3 ,8 4
-3 ,0 7
-5 ,7 0
-2 ,5 2
-1 3 ,0 4
-6 ,1 4
-5 4 ,9 4
6,43
- 9 ,2 7
7 ,8 5
-6 ,1 3
- 9 ,5 8
-5 ,0 3
-6 7 ,8 2
-1 2 ,2 5
- 9 ,7 4
0 ,0 0
- 7 ,1 8
- 6 ,6 2
- 3 ,0 3
-1 ,0 7
-4 ,4 2
-1 3 ,11
2 ,1 3
- 4 ,8 2
-5 ,3 8
-6 9 ,4 7
-6 1 ,3 8
-11 ,8 9
-4 ,2 7
-1 2 ,5 0
1 ,8 3
X
F r = 1,450
Y
y
τ z /µ
2,59
12,37
0,10
3,20
-9,88
1,82
44,04
44,04
-43,23
4,32
0,81
-34,7
-1,94
-10,43
9,46
6,31
3,72
2,97
4,03
-8,26
-34,26
2,82
-6,71
-2,49
-13,71
-11,41
-14,68
-1,3
-19,88
-12,05
3,93
-8,84
-12,05
-9,64
-10,76
-11,73
-8,52
1,12
-4,40
-0,80
0,20
-2,10
-2,30
-8,89
-6,69
2,50
-2,83
-9,91
-3,40
-8,92
-6,09
-5,10
-9,77
24,20
1,27
-5,94
-4,14
1,98
-8,86
-0,94
-0,94
-4,90
-8,55
-1,07
-2,27
-11,89
-3,61
-7,75
-5,74
2,40
1,60
X
F r = 1,725
Y
y
τz/µ
2,5 9
1 2,37
-9,88
1,8 2
-0,73 1,21
-7,28
6,07
-14,32
18,20
-12,37
-8,49
-2,43
13,34
1,70
-9 ,22
-2 5,96
-16,50
14 ,80
-9,9 3
-1,39
7,76
-1 0,85
-0 ,64
-1,46
-2,54
22,6 2
-6,71
3,93
-2,49
-1 3,71
-19 ,65
-82,52
-5,14
-9,37
-12,80
-2,51
-9,49
4,34
-51,64
-0,8 0
-11,29
-9,9 9
-6,29
-11 ,29
-3,10
-3,7 0
2 2,08
-82,68
-7,09
-3,69
-8,69
-6,74
-5,72
-4,12
11 , 7 8
- 2 ,1 9
2,97
0 ,2 1
- 1 2 ,3 1
- 5 ,4 2
- 7 ,3 0
-6 ,9 9
- 7 ,9 3
- 4 4 ,7 0
-9,25
-83,84
Figure 9. Velocity profile and Gradient of flow velocity profile of undular hydraulic jump
Figure 10. Sketch of scour under the wave trough for a mobile bed channel
106 Dinamika TEKNIK SIPIL, Akreditasi BAN DIKTI No : 110/DIKTI/Kep/2009
-0,47
-2,58
-6,79
-3,40
-4,80
-1,99
X