REDUCTION OF STILLING BASIN LENGTH WITH TALL END SILL*

FATHI-MOGHADAM Manoochehr

Department of Hydraulic Structures, Shahid Chamran University, Ahvaz, Iran, E-mail: mfathi@scu.ac.ir

HAGHIGHIPOUR Sadegh

Department of Hydraulic Structures, Shahid Chamran University, Ahvaz, Iran

LASHKAR-ARA Babak

Department of Civil Engineering, Jundishapur University of Technology, Dezful, Iran

AGHTOUMAN Peyman

Soil Conservation and Watershed Management Research Institute, Tehran, Iran

REDUCTION OF STILLING BASIN LENGTH WITH TALL END SILL*

FATHI-MOGHADAM Manoochehr

Department of Hydraulic Structures, Shahid Chamran University, Ahvaz, Iran, E-mail: mfathi@scu.ac.ir

HAGHIGHIPOUR Sadegh

Department of Hydraulic Structures, Shahid Chamran University, Ahvaz, Iran

LASHKAR-ARA Babak

Department of Civil Engineering, Jundishapur University of Technology, Dezful, Iran

AGHTOUMAN Peyman

Soil Conservation and Watershed Management Research Institute, Tehran, Iran

Experiments were conducted to characterize forced hydraulic jumps in stilling basins for enforced cases due to tail water level or dam site arrangement and construction. The case with a single tall sill was simulated in a horizontal flume downstream of a sluice gate. Results of experiments are compared with the classical hydraulic jump, and significant effect of tall sill on dissipation of energy in shorter distance was confirmed. Furthermore, the generated jumps were classified based on the ratio of sill height to basin length, and a simple design criterion was proposed to estimate the basin length for a desired jump and particular inflow.

forced hydraulic jump, energy dissipater, sill, stilling basin length

Introduction

Kinetic energy of water over large spillways must be dissipated in the stilling basin through generation of a jump in order to prevent severe scouring of riverbed and failure of downstream structures as a result of the jump being wept out of the basin. The chute block and sills with different configurations are used in standard stilling basins to disturb water and dissipate water energy through forming a forced hydraulic jump. In basins with ordinary sill height, the type of generated jump (A- to D-type jumps as were described in Hager and Li[1]) is totally controlled by the water surface downstream of the basin. Unfavorable D-type jumps are likely to be generated when tail water is low, while A-, B-, and C-type jumps appear for higher tail water levels.

In most practical cases, the basins with a positive step end or slope end are constructed below the natural ground level to grant a forced jump inside of the basin. However, when hydraulic jump should be con-trolled in a shorter distance, or limitations associated with site arrangement and construction do not allow the lowering of the basin, a tall sill at the smallest possible distance from the jump toe is a novel alternative in practice. The tall sill should be high enough to dissipate considerable amount of energy, and the well being positioned to prevent extreme flow conditions (submergence of jump or splashing flow).

Review of the literature has drawn considerable attention to the effects of tail water on generation of forced hydraulic jumps. Based on tail water relative to inflow depth, and approaching Froude number, an extensive classification of forced hydraulic jump has been provided. Hager and Li[1]have presented extensive relationships for sill control jumps and classified jumps into five classes, namely A, B, minimum B, C, and D-jump. In their studies, the A-jump is the classical hydraulic jump which is characterized by the maximum sequent depth ratio for the Classical Hydraulic Jump (CHJ, where sill is far away to affect the jump). By decreasing the tail water depth, the jump toe moves toward the sill and a B-jump occurs in which the flow is considerably modified by the sill and the streamline pattern becomes curved over the sill. As the tail water depth decreases further and thedistance between the toe of the jump and upstream sill face are further reduced, the curved flow pattern over the sill is amplified. Moreover, the surface current starts to plunge behind the sill, yet without reaching the channel bottom. A further characteristic of such flow, referred to as minimum B-jump, is the formation of a second roller at the downstream of the sill and a C-jump is characterized by having the maximum difference between the depth of flow over the sill and the tail water depth. D-jump initiates when flow is disturbed further and roller waves can reach the bed and scouring becomes expectable. When tail water depth is small, D-jumps may appear sooner than normal conditions allow[2].

For the incipient forced jump, two cases, A and B, of the flow were discussed by Ohtsu et al.[3]. The sill height and tail water were the variables for the two cases. The criteria for the first case were previously proposed by Karki and Kumar[4]. Later, Ohtsu et al.[5]presented the upper limit of the inflow Froude number for undular-jump formations in smooth rectangular channels. It has been found that the formation of undular jumps depends not only on the inflow Froude number but also on the boundary-layer development at the toe of the jump.

The analyses of hydraulic jump occurring in rough bed channels and incorporation of roughness effect on the general equations is an interesting subject which was investigated by Pagliara et al.[6]. Yan et al.[7]and Dai et al.[8]also analyzed pressure fluctuations beneath of hydraulic jumps. A numerical simulation of minimum B-jumps in horizontal rectangular channels having an abrupt drop was given by Tokyay et al.[9]. Before that, an A-type jump at a positive step was simulated numerically by Altan-Sakarya and Tokyay[10]. More studies on submerged and non-submerged jumps and jets can be found in Yang and Wu[11], Ni and Liu[12], Wang et al.[13], and Wu and Ai[14].

The purpose of this study is to parameterize a rather wide range of forced hydraulic jumps for practice and propose design criteria for estimating the sill height required to truncate jump and basin lengths where site restrictions are present. To this end, sills relatively taller than before are used and the desired jumps are B, minimum B, and C-jumps where the second roller waves could not be observed near the channel bottom. In this study, a sill is considered to be tall when the ratio of sill height to the supercritical flow depth is between 2 and 3.5 for considerable range of the approaching Froude numbers. It should be noted that the results of preliminary experiments downstream of a chute spillway with the aforementioned ratio larger 3.5 was not satisfactory due to the production of a wide range for splashing flows and submerging jumps.

Fig.1 Forced hydraulic jump in stilling basin with a continuous tall sill

where h is the height of sill, y1and v1are depth and average velocity of the supercritical flow right in front of the jump toe, ymis the maximum flow depth upstream of the sill, y2is the sequent flow depth behind the sill, LB is the stilling basin length (distance from toe of jump to the upstream face of sill), g is acceleration due to gravity, and ρ and μ are water density and viscosity respectively.

Assume that the hydraulic jump being fully turbulent, flow is considered to be independent of the Reynolds number and viscous effect. To avoid the effects due to dependencies on y2and ym, their relationships with other parameters will be analyzed separately in the following form

1. Formulations

The effective hydraulic parameters for a tall and continuous end sill with variable heights and distances from jump toe are shown in the Fig.1. The following functional relationship among significant parameters is used to characterize the forced hydraulic jump due to tall sill in a horizontal channel

Through dividing the first parameter by the second one on the right hand side, the resulting geometric ratio of sill height to basin length (h/LB) is more useful in design and practice. According to the Belanger equation, the sequent depth ratio for a CHJ is given by,

where Y*is the sequent depth ratio for classical hydraulic jump and y2?is the sequent depth of CHJ. For Fr≥2.5, the sequent depth ratio can be appro-ximated as follows

Based on experimental observations of Hager and Li[1], the following relation is found for estimating sequent depth ratio for a forced jumpYdue to a continuous end sill

In Eq.(5), the sill effect (Ys) is expressed by the following relationship.

where the coefficientsαandβdepend on the type of hydraulic jump. According to Bretz (in Visher and Hager[2]), if the relative sill height (/1hy) becomes larger than1.645[1/6(Fr)], sill flow might change into weir flow.

2. Experiments

Experiments were conducted in a horizontal flume downstream of a sluice gate in order to estimate the optimal ratio of sill height to stilling basin length for a range of acceptable jumps and the Froude number. The goal was to reduce the jump length as much as possible, while having an acceptable jump. The glass flume was 0.30 m in width and 3.8 m long, facilitated with a tail gate at the downstream end. Maneuvering of discharge and tail gate allowed the generation of desired jumps for any sill height and position. The extreme flow conditions for development of splashing and submerging jumps were avoided. The B, minimum B, and C-type jumps have been desired jumps in this study. Sills with five heights were tested at three distances from the toe of the jump.

The stabilized sequent flow depth (y2) and the maximum water depth (ym) were recorded at a frequency of 20 samples per second for 60 s using two identical pressure transducers (operating range of 0 mbar -100 mbar) connected to the pressure taps upstream and downstream of the sill. The data were translated using an analog/digital device (Data Translation, model DT 9801) compatible with the pressure transducers. Averages of the recorded data were checked with a precision point gage. To avoid separation effects due to high velocity, supercritical flow depth at toe of the jump was measured by a precision point gage with reading accuracy of 0.1 mm. The circulated flow was measured with a calibrated V-notch weir at the downstream end of the circulation system.

3. Results and discussions

Discharge and tail gates were used to adjust and generate a desired jump for a particular sill height and position. To assess the efficiency of tall sills in dissipation of energy, the results of depth ratios upstream and downstream of the sill were compared with the sequent depth ratio for a CHJ as follows.

Fig.2 Variation of the maximum depth ratio withFrandh/LBinside of the basin

Considering the functional relationships given in Eq.(2), a general increase of the flow depth upstream of the sill (ym/y1) with the increase of the sill height ratio (h/LB) and Froude number are shown in Fig.2. The rest of data are not shown in the figure to avoid masking of one another. For the same range of Froude numbers, sequent depth ratios (y2?/y1) are also calculated with Eq.(4) for CHJ and are shown in the figure by a solid line. The figure illustrates a significant increase of the depth ratios upstream of the sill (ym/y1) due to the presence of sill as they are compared withy2?/y1. It should be reminded that the CHJ line (Eq.(4)) is drawn for an ideal condition where wall friction effects are absent. However, the wall effects along with uncertainties associated with measurements are grounds for the variation of trends (experimental data and CHJ line) in the figure. In cases where sill effect is low, they even causeym/y1to be relatively lower thany2?/y1. In general and to some extent for a particularFr, flow depth upstream of the sill (ym) increases as the sill height ratio (h/LB) increases (Fig.2). This shows considerable effect of sill height (h) on the exchange and dissipation of energy for an identical basin length (LB).

To further clarify the results, Fig.3 demonstrates a partial decrease of the sequent depth ratios outsideof the basin (y2/y1) in contrast to the sequent depth ratios (y2?/y1) for CHJ. In this case, the flow downstream of tall sill has some more energy compared to the CHJ condition and the jump shifts toward the minimum-B and C-types. However, the experimental and tail water adjustment errors for development of a desired jump were coupled with losses and caused a non-uniform distribution of the experimental data around the CHJ lines.

Fig.3 Variation of the sequent depth ratio withFrandh/LB

Fig.4 Comparison of the results with previous studies (data extracted from[2-4])

Based on the results of this study, the correlation of the Froude number (Fr) and sill height ratio (h/y1) are plotted and compared with previous studies in Fig.4 (data extracted from[2-4]). Previous studies by large have concentrated on the conditions of minimum sill height required to initiate a favorite jump, while in this study, a minimum possible length for a non-critical jump in stilling basin is more important. To achieve that, sills taller than before (higherh/LB) were examined. Figure 4 shows the ratio ofh/y1versus the Froude number for this study and previous studies which show similar trends. In addition, a dashed line based on Bretz’ equation [1/6· (Fr1.645)] is overlaid to show that the tested ratios ofh/y1are below the restricted condition for weir flow. However, no cases of weir flow are included in the results of this study or in Fig.4. The differences in scale and flow boundary conditions might be sources of the inconsistency of results with Bretz’s ideal equation for the lower Froude numbers.

Fig.5 Ratio ofh/LBand type of jump

4. Type of the generated jump and design criteria

To some extent, the taller the end sill is, the more energy that can be exchanged and dissipated in a shorter distance will be. This is shown in Fig.5, which represents the increase of the depth ratio (ym?y2?/y1) upstream of the sill and decrease of the sequent depth relative to CHJ (y2?y2?/y1) as the sill height ratio (h/LB) increases. However, the type of the desired jump, cost, and site implementation are key factors for the selection of a favorableh/LB. According to Fig.5, the most efficient range ofh/LBfor granting a B-type jump is estimated to be 0.02-0.06. In this range, the figure shows a minor difference in water levels and velocities from upstream to downstream of the sill. Based on the surface current observation and exchange of energy due to considerable difference of (ym?y2?/y1) and (y2?y2?/y1) lines in Fig.5, jumps are classified as minimum-B forh/LB＞0.06. Ath/LB=0.10, the jump is a solid C-type and scouring was imminent. In the range ofh/LB=0.10-0.14, jumps are D-type and scouring is serious. There is always a chance for weir flow to prevail as tail water is decreased particularly for higher ratios ofh/LB.

The errors associated with measurements and tail water adjustment produce a lower R-square fory2line than theymline in Fig.5. In an ideal condition, the lines forymandy2should be symmetric around the CHJ (zero horizontal dash line in Fig.5). However, more data is required to provide more accurate classification of jumps for design in practice.

The suggested order of design for the jumps generated by tall end sill is:

(1) Having design Froude number (Fr) andsupercritical flow depth (y1), the sill height ratio (h/y1) andhis estimated with Fig.4 (the current study curve).

(2) Based on site limitations and availableLB, ratio ofh/LBis calculated and type of generated jump could be estimated from Fig.5. If this is not the desired jump, eitherLBshould be increased or downstream of the sill should be protected against scouring.

(3) Using the decidedh/LB, the flow depths upstream and downstream of the sill (ymandy2) are measured from the correlated lines to zero CJH line in Fig.5.

In order to scale up the results in practice,y1andFrare principal hydraulic parameters for the Froude similarity in this study.

5. Conclusion

Tall sills are a novel alternative to ordinary sills where stilling basin length must be shrunk in order to fulfill restrictions associated with site arrangement and construction. They can create safe forced hydraulic jumps (i.e., B, minimum-B and C-jumps) before scouring is significant. Results of the experiments have proved considerable effect of sill height and position on the sequent depth ratio and shortening of the basin length, thus reducing costs. In contrast with ordinary sills, they are able to raise water level upstream of the sill (while draw it down downstream), and dissipate considerable amount of flow energy through sudden interexchange of kinetic and potential energies. Based onFrand selected ratio of (h/y1), a design criterion was proposed to estimate the required sill height for a desired jump (B-jump, minimum B-jump, and C-jump). The desired jumps are classified based on sill height ratio (h/LB), and maximum and sequent depths could be calculated for particular inflows. The proposed design criterion is flexible to fulfill the flow and site implementation requirements, and it is simple in practice.

Acknowledgements

The authors would like to acknowledge Professor Hager W. H. at the Laboratory of Hydraulics, Hydrology, and Glaciology, VAW, Swiss Federal Institute of Technology for his invaluable comments on this research. Acknowledgement is also extended to the Chamran University of Ahwaz, Jundishapur University of Technology, and the Centre of Shahid Excellence on Operation Management of Irrigation and Drainage Networks for financial support and facilitation of the experiments.

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March 8, 2011, Revised May 23, 2011)

* Biography: FATHI-MOGHADAM Manoochehr (1949-), Male, Ph. D., Professor

2011,23(4):498-502

10.1016/S1001-6058(10)60141-2