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Restricting Hydraulic Jump Location Inside Stilling Basin for Maximum Energy Dissipation
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 919 Restricting Hydraulic Jump Location inside stilling Basin for Maximum Energy Dissipation Siddharth Upadhyay1, S Anbu kumar2 1 M. Tech in Hydraulic and Water Resource Engineering,DTU, New Delhi 2Associate professor, DTU, New Delhi ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - As per the report of InternationalCommission on Large Dams (ICOLD) 20% of dam mishaps happened because of poor arrangement of energy dissipation. Normally, energy dissipators are only intended for ‘design discharge'ofspillway. In this manner there is a need to build up a proper plan to perform expected function of energy dispersal even at lower discharge. Present work is focused on hydraulic jump type energy dissipators. It is found that in majority of failure cases of dam, the jump position is not specified – i.e. jump is either swept up or drowned. So it is required to manage the position of hydraulic jump so that the front of jump is positioned near toe of spillway or sluice gate to get clear jump. When the ideal post jump depth is equal to value obtained by Belanger momentum equation, then only clearhydraulicjumpoccur. To control and restrain the location of hydraulic jump in basin , a stepped weir is proposed at the end of apron. And mathematical method is performed to design the weir geometry which will form desired post jump depth corresponding to any discharge between design dischargeand 20% of the design discharge. Analysis in ansys fluent demonstrate that, for horizontal aprons, a designed weir section restricted the hydraulic jump to its desired location for different discharges. Key Words: Hydraulic jump, Position of jump, Ansys fluent, Stepped weir, Energy dissipation. 1. INTRODUCTION Energy dissipators in form of hydraulic jump are generally used for energy dissipation while planning the hydraulic structures like dams, weirs and barrages. They are popular for simplicity and proficiency, yet have certain restrictions when there is changes in discharge conditions. The energy dissipators agreeably work at design discharge condition. But if there is occurrence of fluctuatingdischargeconditions, they are not productive as the position of hydraulic jump tends to move from apron. This would bring about decrease in energy dispersal and thus harm hydraulic structures and unfavorably influence tail channel conditions. Henceforth with a plan to resolve this issue, an endeavor has been made to make a constrained hydraulic jump at sought area for fluctuating discharge conditions. The constrained hydraulic jumps are utilized for energy dispersal in stilling basin. It is a jump shapedwiththehelpof baffles and sill with or without sub critical tail water. A hydraulic jump occur when a high rate supercritical stream all of a sudden changes intoa moderatelylowratesubcritical stream, joined by development of vortexes, rollers and turbulence alongside air entrainment. At last the energy is dispersed as heat. The development of hydraulic jumpatthe toe of spillway or under the foot of sluiceway goes about as an energy dissipator. The most extreme energy dissipation happens when an clear hydraulic jump occur at the segment where the pre jump depth is least. Thisisonaccountofwhen pre jump depth is least, according to Belanger condition, it’s sequent depth i.e. post jump depth is most extreme and consequently the proportion of post jump depth to pre jump depth is greatest and thus the underlying Froude number is greatest. As energy dispersal is specifically related to initial Froude number, for the given inflow condition the energy dissipation is greatest. It is already understood that the length of the apron relies on the length and area ofthejump , which thus relies upon the pre jump depth (y1) and the relative extents of post jump depth (y2) and tail waterdepth (yt).In a rectangular channel withhorizontal slope,hydraulic jump forms at a location where these sequent depths satisfy Belanger equation. The sequent depths are referred relating to the segment at vena contracta as the perfect location of jump is at vena contracta of supercritical stream. In case of occurrence of spillway flows the vena contracta would be referred to a segment where the prejump depth (y1) isleast. In the case of tail water deficiency condition, the tail water rating curve is lower than the jump height curve for every single discharges. Because of this the hydraulic jump may occurs halfway or completely clear out of the basin and this condition is not recommended as it would bringaboutharm to stilling basin, tail channel and other downstream structures. Subsequently it turns out to be especially noteworthy to have the area of hydraulic jump in a stipulated zone, to effectively fulfill the purpose of energy dissipation. For this reason the depth of water on the apron might be artificially raised to such an extent, such that it becomes sequent to the pre jump depth at vena contracta and form the jump at vena contracta. This can be accomplished by presenting an obstruction as weir toward the finish of the apron. Normally the rectangular wide crested weirs are considered for this purpose. Theweirwith its height intended for fix discharge condition, is not appropriate under field conditions where discharges would differ by small and large and not as much as configuration discharges. Accordingly to address this issue an effort has been made to design an end weir geometry which would guarantee development of clear jump at vena contracta for the planned discharge and also for the lower discharges.
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 920 2. METHODOLOGY 2.1 Important Factors The variables which represent design of stepped weir geometry are as per the following – Head on upstream = H Width of channel = B Maximum discharge in the range = Q max Minimum discharge in the range = Q min Coefficient of discharge = Cd Submerged flow coefficient = K Starting height of weir crest = y' 2.2 Mathematical procedure The stepped weir is designed for the range of configuration discharge (Qmax) to least dischargeequivalentto20%ofthe design discharge (Qmin). A stepped weir is considered to be made up of number of rectangular weirs. The equation for discharge Q over a rectangularsharpcrestedweir(freeflow) is given by following equation. Where h = y2 – y ′, the required width of weir can be found from above equation. Where, y′ = (y2)1 / 4 is designed for Q1 (i.e. Qmin) . (y2)1 is the post jump depth corresponding to Q1 and is calculated by Belanger momentum equation in the following manner. For Where , , To calculate width for any other discharge Qn, the width of the corresponding step can be calculated as follows Where an symbolizes the incremental width at nth step at every rise. And 2.3 Determination of Appropriate Cd for Free Flow Condition on Horizontal Apron In the mathematical design of stepped weir, for free flow condition, a constant value of Cd = 0.623 is adopted according to Francis formula. As there are different kinds of uncertainties involved in the flow conditions, the analytical determination of Cd is hardly possible. There is presence of hydraulic jump and associated turbulence on upstream of stepped weir. The upstream reach for the stepped weir, being equal to length of stilling basin, is small. Hence it is decided to empirically judge the appropriateness of Cd. Three weir models, each for Cd=0.6, 0.65 and 0.623 were designed and checked by their performance in ansys fluent. With Cd = 0.6, jumps were found to be shifted in the downstream direction. With Cd = 0.65, thejumps werefound to be drowned. With Cd = 0.623, the hydraulic jumps have formed inside the basin and the fronts of jumps in all the cases were found to be located near the sluicegate. ThusCd = 0.623 is confirmed empirically for the condition of free flow over the weir. Value of width and rise at every step for Cd = 0.623 is shown in following table. Table-1 : Output of Mathematical Procedure for Data(Horizontal apron and Cd = 0.623) Sr. no Q m3/s y1 m y2 m H m Fr1 M B M 1 0.002 0 0.002 4 0.060 5 0.045 5 18.335 0 0.111 9 2 0.005 0 0.006 2 0.096 5 0.081 4 11.370 9 0.166 0 3 0.006 8 0.008 1 0.109 8 0.094 8 9.9435 0.181 6 4 0.008 4 0.010 0 0.121 6 0.106 6 8.9466 0.194 9 5 0.009 2 0.010 9 0.127 0 0.112 0 8.5487 0.201 0 6 0.010 0 0.011 8 0.132 2 0.117 2 8.1997 0.206 7 The above analysis is performed by Mr. G.A. Hinge, 2012 for varying gate opening in laboratory but in this study, the gate opening at tail is kept 100% open and the results are still found to be satisfactory and reasonable in analysis in ansys fluent software.
3.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 921 3. RESULTS By analyzing the various discharge condition in flume with the help of ansys fluent software, it was found that in all the cases, hydraulic jump start forming at the toe or sluice gate opening. Which is most desirable location for formation of hydraulic jump for maximum energy dissipation. Following are results obtained through ansys fluent analysis. Fig-1: Designed stepped weir for varying Discharge condition Fig-2: Set up of stepped weir in flume Fig-3: Hydraulic jump formation starting at toe for 20 % discharge Fig-4: Hydraulic jump formation starting at toe for 50 % discharge Fig-5: Hydraulic jump formation starting at toe for 68 % discharge
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 922 Fig-6: Hydraulic jump formation starting at toe for 84 % discharge Fig-7: Hydraulic jump formation starting at toe for 92 % discharge Fig-8: Hydraulic jump formation starting at toe for 100 % discharge 4. CONCLUSIONS AND RECOMMENDATIONS The performance of stepped weir is checked for six discharges (20%, 50%, 68%, 84%, 92% and 100% of the design discharge). It is found that for all these discharges clear hydraulic jumps are formed and are located near toe of spillway. Sincethelocationof jump is restricted for most of discharge, it will be beneficial in attaining the purpose of maximum energy dissipation for all discharge. The method developed in the study is applicablefor steady flow only. Which is Fr1> 4.5 . Even though this seems to be better method for solving the erosion related problem of stilling basin, but due to too many rectangular sharp edges there are chances of cavitations in weir. Which can be removed on site practice by using least square method for designing cavitation free stepped weir which will be also free from sharp edges. REFERENCES [1] Achour, B., Debabeche, M. (2003). “Control of hydraulic jump by sill in triangular channel”. J. Hydr. Res., 41(3), 319-325. [2] Anderson, J.D. (1995). “Computational fluid dynamics”. McGraw-Hill book company, Inc., New York, 1995. [3] Chow, V.T. (1959). “Open channel hydraulics”. McGraw- Hill book company, Inc., New York, 1959. [4] Hinge G. A., Balkrishna S., Khare K.C. (2010), Pawana Dam Energy Dissipation – A Case Study, Australian Journal of Basin and Applied Sciences, Vol.4(8), pp. 3261-3267 [5] Hinge G. A., Balkrishna S., Khare K.C. (2010), Improved Design of Stilling Basin for Deficient Tail Water, Journal of Basic and Applied Scientific Research, Vol.1(1), pp. 31-40. [6] Subramanya, K. (1986). “Flow in open channels”. Tat a McGraw-Hill Publishing Co. Ltd., New Delhi, India.
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