Characteristics of Undular Hydraulic Jump Downstream of a Sluice Gate

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) 1) 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

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 gene- rate 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. Infor- masi tentang karakteristik lompatan hidrolik undular masih sangat kurang. Untuk kepentingan pengembangan ilmu pengeta- huan, 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

to look for the lower limit value (Fr ) and the upper limit of INTRODUCTION 1 Froude number (Fr1limit) that cause an undular hydraulic jump and Hydraulic jump is a phenomenon that occurs due to sud- also the velocity distribution and flow characteristics at the denly flow changes from supercritical to subcritical flow. The bottom of the channel that occurs in undular hydraulic jump. 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 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 Determination of surface profile of a hydraulic jump will Undular hydraulic jump is a series of steady free surface help us in designing of the free board or retaining walls of a stil- waves that causes jump in downstream areas. Undular hydraulic ling basin where stepping occurred. In addition, knowing the jump have Froude numbers 1 to 1.7 (Chow, VT, 1985). Further, surface of a hydraulic jump will also help us to estimate the amo- the hydraulic conditions to form an undular hydraulic jump in unt of pressure at the channels bed. 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 RESEARCH METHOD distribution channel and irrigation during the period of tides in estuaries and in the rapid flow that has a low depth. When this Equipment undular hydraulic jump come into the channel, waves with large Research carried out by using the facilities of prismatic periods will cause a jump in downstream areas. Waves can cause standard tilting flume with acrylic base material on the walls and runoff (over-topping) and damage to the banks of the channel aluminum on the bottom. This channel has a width (B) 30 cm, (Chanson and Montes, 1995). length (L) 1000 cm, and height 50 cm with a channel wall thick- Froude number (Fr) is a dimensionless number that states ness is 10 mm. Bottom slope of this channel can be set manually the characteristics of flow in a transverse (cross-sectional flow with a range of channel bed slope +1% and -1%. characteristic) which shows the ratio of inertial forces with the Sluice gate that was used is an Armfield brand vertical slui- force of gravity. Froude number can be obtained by the following ce gate that has material specification of steel with dimensions of formula: width 30 cm, height 45 cm, the maximum aperture (a) 15 cm and a minimum aperture (a) 0 cm. Velocity measurements using a U Fr = (1) current meter Nixon Streamflo (1) type 422 with a brand of gy 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 Conjugate Depth Conjugate depth formulations of undular hydraulic jump regulator of the circulation flow. Discharge used around 7 l/s to can be written as: 30 l/2 with 10 experimental models. (2) y3 1 2 = () 1 + 8 Fr 1 − 1 (2) Examination Tools y1 2 1. Initial examination flume circuit Energy loss of undular hydraulic jump 2. This examination is conducted in the form of checks readiness Loss of energy (energy dissipation) is the energy difference and condition of the circuit including the pump and flume slo- between the specific energy before and after the jump. The amo- pe of the channel to match the desired conditions of the study. unt of energy loss that occurs in a hydraulic jump can be written 3. Examination of velocity measuring devices as: 4. In this examination, the reading speed is using measuring devices called current meter which is compared with theoretical ∆E = E − E (3) (3) 1 3 discharge of direct velocity measurement results. By doing a mathematical operation, Equation 3 above be- 5. Checking flow rates comes 6. This examination aims to find out exactly how much dischar- ()y − y 3 ge is flowing in the channel in the experiment this time. ∆E = E − E = 3 1 (4) 1 3 4y y 1 3 Implementation of Measurement In this research, the implementation(4) of the measurement is Velocity distribution and gradient of flow done by starting to prepare the materials and equipment which velocity necessary. The steps of procedures for the implementation of this Velocity distribution is uneven at every point. Distribution research are: of vertical velocity can be known by measuring the vertical direc- 1. After the power switch is turned on and the engine pump is tion at various depths. The gradient of flow velocity studied ba- turned on, then we open the water tap to drain water into the sed on the velocity distribution with the formula as follows: channel. Do not forget to check the slope of the channels we happened to order in accordance with the desired in this du z research. m u = (5) dz

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 = 0.5 - 0.7 and the maximum value for the wave trough is at y/y2b gate on the channel. By doing a variation of discharge (Q) = 0.7 to 0.8. For the data on second wave, the data obtained for and the variation of aperture (a), each experiment was given a the maximum velocity of the first wave is at y/y2c = 0.7 to 0.8, name or label for each experiment. while in the wave tough is at y/y2d = 0.8 to 0.9. 3. For each model, running was done until the model is formed an undular hydraulic jump. Froude Number 4. Water surface elevation in both the upstream and downstream Froude number calculations performed on all models of of the sluice gate were investigated by using point gauge and running are done. Froude number value at the upstream of mica ruler attached to the channel wall. undular hydraulic jump will determine the type of undular 5. Vertical velocities were measured for each respective model hydraulic jump that occur. This present research has obtained running. This measurement is done in 10 point depth of flow variety value of Froude number. Table 1 shows the lowest Froude at various points namely at the beginning of vena contracta, number value is on the model Q9A1 Fr = 1.197 and the highest at the beginning of stepping, and at three waves of undular 1 one is on Q3A1 model as Fr = 2.258. These results have a hydraulic jump. 1limit same results of other research obtained by Iwao Ohtsu and

Hubert Chanson is the latest research to obtain the highest Froude RESULTS AND DISCUSSION number value is Fr1limit = 2.3 and = 2.4.

Velocity Profiles Characteristics of Free Water Surface of Measurements were taken at the center lain of the channel Undular Hydraulic Jump on the supercritical flow and subcritical flow regions. Velocity Measurement of the undular hydraulic jump free water measurement results are given in Figure 3 and 4 below. Generally surface profile at the centre line of the channel is using measuring it can be seen that the velocity profile occurring along the undular instruments called points gauge, and for the canal walls water hydraulic jump formed shows that there is a relationship between surface profiles were observed using a mica ruler. Froude number before the jump with the form of the wave that Figure 7 above had been seen that the results of research occur. data showed that the ratio of depth to the depth of critical flow It shows that the velocity profile at the toe of the jump to rate is 0.7 to 1.5. This value resembles the results obtained by give the maximum value is at y/y = 0.5 - 0.6. As for the first 1d Chanson in his research. wave, the wave crest giving a maximum velocity value is at y/y2a

(a) velocity profile , Fr = 1,197 ; y1 = 0,083

(b) velocity profile, Fr = 1,450 ; y1 = 0,080

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/y2b y/y1d 1,000 1,000 1,000 y1 = 0,075 ; Fr1 = 1,404 0,900 y1 = 0,083 ; Fr1 = 1,197 0,900 y2 = 0,146 ; Fr2a = 0,559 0,900 y1 = 0,065 ; Fr1 = 1,349 y2 = 0,093 ; Fr2 = 0,81 0,800 y2 = 0,137 ; Fr2a = 0,660 y2 = 0,098 ; Fr2 = 0,91 y1 = 0,080 ; Fr1 = 1,450 0,800 y2 = 0,120 ; Fr2a = 0,558 0,800 y2 = 0,08 ; Fr2 = 0,96 y1 = 0,075; Fr1 = 1,725 0,700 y2 = 0,140 ; Fr2a = 0,634 y2 = 0,09 ; Fr2 = 0,94 0,700 Chanson - Fr = 1,48 0,700 y2 = 0,09 ; Fr2 = 0,90 y2 = 0,140; Fr2a = 0,697 Chanson - Fr = 1,7 Chanson - Fr1 = 1,57 0,600 Chanson - Fr1 = 1,57 0,600 0,600 Ohtsu - Fr1 = 1,48 0,500 Ohtsu - Fr1 = 2,08 0,500 0,500 0,400 0,400 0,400 0,300 0,300 0,300 0,200 0,200 0,200 0,100 0,100 0,100

0,000 u/uc 0,000 u/U c 0,000 u/Uc 0,000 0,500 1,000 1,500 2,000 0,000 0,200 0,400 0,600 0,800 1,000 1,200 1,400 0,000 0,200 0,400 0,600 0,800 1,000 1,200 1,400 (a) (b) y/y2c y/y 1,000 2d 1,000 0,900 0,900 y2 = 0,142; Fr2c = 0,57 y2 = 0,1024 ; Fr2d = 0,78 0,800 y2 = 0,125 ; Fr2c = 0,65 0,800 y2 = 0,092 ; Fr2d = 0,85 y2 = 0,12 ; Fr2c = 0,55 y2 = 0,08; Fr2d = 0,84 0,700 y2 = 0,135 ; Fr2c = 0,61 0,700 y2 = 0,10 ; Fr2d = 0,85 0,600 y2 = 0,135; Fr2c = 0,62 y2 = 0,12; Fr2d = 0,84 0,600 Chanson - Fr1 = 1,57 Chanson - Fr = 1,48 0,500 0,500 0,400 0,400 0,300 0,300 0,200 0,200 0,100 0,100

0,000 u/Uc 0,000 u/Uc 0,000 0,500 1,000 0,000 0,200 0,400 0,600 0,800 1,000 1,200 1,400 (c) st Figure 4. (a) Velocity distribution at the toe of the jump, (b) Velocity distribution at the 1 wave, and (c) Velocity distribution at the 2st wave

Table 1. Calculation of Froude number at the toe of the jump

g y1 U1 g y1 U1 No Model Fr No Model Fr (m/d2) (m) (m/d) 1 (m/d2) (m) (m/d) 1 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/y 1 3,50

y = 1,354x + 0,024 3,00 R² = 0,906

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 11,21,41,61,822,22,4 Figure 6. Undular hydraulic jump, Fr = 1,450; y = 0,008 m Figure 5. Experimental relationship of Fr1 with y2/y1 for 1 undular hydraulic jump

104 Dinamika TEKNIK SIPIL, Akreditasi BAN DIKTI No : 110/DIKTI/Kep/2009 2. For Froude number value, the lowest values obtained on y/yc 1,8 running the model Q9A1 is Fr1= 1.197 and highest value 1,6 in model Q3A1 is Fr1limit = 2.258. 1,4 3. This undular hydraulic jump is also has a loss of energy 1,2 ∆E = 0.03 to 1.039 cm or 0,297% - 10,276%. The value 1 of energy coefficient is (α) = 0.94 -1.11 and the coeffi- 0,8 cient value of force / momentum (β) is = 0.89 to 1.20. 0,6 4. There is a difference in significant value of bed gradient 0,4 Data Q6A1 [Fr1=1,349 ; y1=0,065] of flow velocity between the under of the wave crest with Data Q9A1 [Fr1=1,197 ; y1=0,083] the under of wave trough. This difference is potentially 0,2 Chanson, H [Fr1=1,26 ; y1=0,082] caused scour beneath the wave trough in a mobile bed 0 x/yc 0,0 5,0 10,0 15,0 20,0 25,0 30,0 channel. Suggestion Figure 7. Free water surface profile It is recommended to perform measurements with the ADV instrument side-looking and doing research with a mobi- Specific Energy and Specific Momentum le bed channel. In this research, using Equation (3) dan (4) the result of energy loss analysis of the models Q10A3 amounted ∆Es = REFERENCES 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 Chanson, H., and Montes, J.S. (1995). “Characteristics of Un- 1.039 cm or atau 0,297% - 10,276%. In addition, from analy- dular Hydraulic Jumps. Experimental Apparatus and Flow sis of all experimental models in this research, the researcher Patterns.” Journal of Hyd. Eng., ASCE, Vol. 121, No. 2, obtained value α = 0.94 -1.11 and the value β = 0.89 to 1.20 pp. 129-144 In general, the bed gradient of flow velocity under the Chow, V.T. (1985). Open Channel Hydraulics (translation), wave trough has a greater value than the bed gradient of flow Erlangga, Jakarta. velocity under the wave crest. This significant difference, by Montes, J.S., and Chanson, H. (1998). “Characteristics of Un- the author, is indicated to cause the occurrence or provide the dular Hydraulic Jumps. Results and Calculations.” Journal potential for scour on the mobile bed channel. of Hyd. Eng., ASCE, Vol. 124, No. 2, pp. 192-205.

Ohtsu, I., Yasuda, Y., and Gotoh, H. (2001). “Hydraulic Con- CONCLUSIONS AND SUGGESTIONS dition for Undular-Jump Formations.” Journal of Hyd. Res., IAHR, Vol. 39, No. 2, pp. 203-209. Conclusion Raju, K.G.R., (1986). Flow Through Open Channels (translation), Erlangga, Jakarta. The conclusions that can be obtained from the research Wols, B.A. (2005). “Undular Hydraulic Jump.” M.Sc. Thesis, of undular hydraulic jump characteristics at the downstream of Delft University of Technology, Delft. 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 sur-

face flow.

Kurva Energi Spesifik Kurva Gaya Spesifik (Running-Q10A3) (Running-Q10A3) y (cm) y (cm)

18 Lengkung energi teoritis 18 Lengkung gaya teoritis Lengkung energi aktual Lengkung gaya aktual 16 16 Es 16,5179 5055,020 y2a 14 14 Fsy2a

12 15,5157 12 Fsy3 4659,672 Es y3 10 Esy2d14,9350 10 4461,028

Esy2b 8 15,7110 8 4661,284 Esy1 Fsy1 5342,475 Esya 18,9848 6 6 Fsya 4 ∆Es 4 Fs1 = Fs3 2 2 Fsy1=Fsy3 0 Es (cm) 0 0 2 4 6 8 101214161820 0 1000Fs 2000 = Fs 3000 4000 5000 600 1 3

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

2,65 τz /µ -1,31 12,64 -4,15 -10,10 1,42 0,00 -3,84 1,86 6,43 -7,18 -1,07 -11,11 -3,07 -9,27 1,77 -6,68 7,85 -6,62 -4,42 -5,85 -5,70 -6,13 -3,03 -7,52 -2,42 14,09 29,28 17,21 4,02 -9,58 -13,11 29,84 -25,98 9,03 -25,91 -8,48 -2,52 -5,03 2,13 1,83 -17,17 11,01 31,48 -2,55 -5,85 -11,89 20,87 -15,50 -13,04 -4,82 -12,37 -39,41 -14,02 -12,25 -4,27 -18,81 -7,31 -6,14 -9,74 -5,38 -12,50 -11,89 -28,84 19,15 3,02 -74,43 -54,94 -67,82 -69,47 X -32,51 13,43 -10,79 11,45 -1,24 -19,65 -61,38

F r = 1,450

Y y

2,59 τ z/µ 0,10 2,50 12,37 3,20 -9,88 -4,40 -5,94 -4,14 1,82 24,20 -8,52 -0,80 -2,83 1,98 2,40 3,72 -6,71 1,12 0,20 -9,91 -8,86 -1,07 -12,05 1,27 -2,27 44,04 9,46 4,03 2,97 3,93 -8,84 -2,10 -3,40 -0,94 -11,89 6,31 -43,23 -2,49 -12,05 -2,30 -8,92 -0,94 -3,61 44,04 -1,94 -8,26 -14,68 -13,71 -9,64 -8,89 -6,09 -4,90 1,60 -10,43 -34,26 -1,3 -10,76 -5,10 -7,75 X 4,32 -34,7 2,82 -19,88 -11,41 -11,73 -6,69 -9,77 -8,55 -5,74 0,81

F r = 1,725

Y y

2,59 τz /µ 22,08 12,37 -0,80 11,78 -9,88 4,34 -7,09 -2,19 -0,47 -5,14 -11,29 -3,69 0,21 -2,58 1,82 2,97 -6,79 -9,37 -9,99 -8,69 -12,31 22,62 -6,71 -6,29 -3,40 13,34 14,80 -12,80 -6,74 -5,42 18,20 3,93 -11,29 -4,80 -12,37 -9,22 -9,93 -7,30 -2,49 -0,73 1,21 1,70 -1,39 -2,51 -3,10 -5,72 -6,99 -9,25 -8,49 7,76 -13,71 -7,28 -25,96 -10,85 -9,49 -3,70 -4,12 -7,93 -1,99 -0,64 -82,52 -51,64 -82,68 -44,70 -83,84 X -14,32 6,07 -2,43 -16,50 -1,46 -2,54 -19,65

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