Hydrotopics

December 21, 2014

Discharge characteristics of submerged crest barrages

Filed under: Uncategorized — Rajnikant Khatsuria @ 11:31 am

R.M.Khatsuria
Formerly Addl. Director
Central Water and Power Research Station
Pune, India

email: rmkhatsuria@rediffmail.com

While discharge characteristics of submerged ogee spillways have been investigated widely, very little has been done to study the effect of submergence of crest of low head barrages by downstream water levels. The results in respect of submerged ogee spillways can not be applied to broad crested barrages. The only reference available in this regard is the outcome of a study made by the Punjab Irrigation Research Institute, Malikpur, India, in the form of a drawing showing variation of the coefficient of discharge C, in the equation Q= C L H^3/2 with the Drowning ratio defined as (downstream water depth over crest/upstream water depth over crest), expressed in percentage. It is seen that the value of C starts decreasing as the drowning ratio increases beyond about 70% or so. This result has also been adopted in Indian Standard IS 6966 (Part 1):1989 titled Hydraulic Design of Barrages and Weirs- Guidelines, Part 1 Alluvial Reaches.

Recently, an attempt was made to assess the discharging capacity of a low height barrage by applying the above results. A 2-D flume model was also available for verification. The barrage had its crest near the river bed and had 45 spans each 15.5m wide separated by 4.5m thick piers. A typical section of the barrage is shown in Figure 1.It was found that the calculated values of discharges varied widely form those obtained from model study. This is shown in Figure 1. An analysis revealed that the Malikpur curve related the coefficient of discharge C only with the drowning ratio, while other parameters likely to influence C, such as length of the crest and  height of the crest above the river bed in terms of head over the crest were not considered.

Since a low height barrage with high piers can be treated as a bridge also, it was decided to explore the possibility of applying the concept of bridge pier losses to arrive at the discharge passing under the bridge (i.e. over the barrage) with help of standard charts prepared by US WES in their Hydraulic Design Criteria. In this regard, charts under Open Channel Flow, Bridge Pier Losses, No. 010-6/1 and 010-6/2 were relevant. Using these charts, it is quite easy to calculate upstream water level corresponding to a set of total discharge and downstream water level. The upstream water levels for different discharges, as calculated above, are plotted in the same figure. It would be seen that the agreement between the observed and calculated water levels was excellent.

Fig 1

Figure 1: Comparison of observed and calculated values of discharges and upstream water levels.

The above case study reveals that a barrage with its crest level at or near the river bed can be treated as a bridge and the bridge pier losses can be added to the downstream water levels to obtain corresponding upstream water levels with good accuracy. On the other hand, application of Malikpur curve in such a situation will not result in reliable assessment of discharges since this is not akin to an overflow weir condition.

 

REFERENCES

  1.  Indian Standard IS 6966 (Part 1):1989 titled Hydraulic Design of Barrages and Weirs- Guidelines, Part 1 Alluvial  Reaches.
  2. US WES : Hydraulic Design Criteria.  Open Channel Flow, Bridge Pier Losses, Chart No. 010-6/1 and 010-6/2

April 30, 2013

 Predicting scour below ski jump spillways- Damle Equation  

Filed under: Uncategorized — Rajnikant Khatsuria @ 2:07 pm

 

 

 R.M.Khatsuria

Formerly Addl.Director

Central Water and Power Research Station

Pune, India

  

A detailed and reliable estimation of scour downstream of a ski jump spillway requires study on a comprehensive model. Yet, there are reservations regarding the acceptability of results in view of difficulty of simulating river bed, which might be composed of heterogeneous rock of complex mass. The scour levels thus obtained on a fully erodible bed are assumed to be of ultimate nature. In the preliminary assessment of a design, estimation of scour is often made with the use of a formula, although it gives an indication of single value of deepest possible scour unlike the areal pattern in the downstream vicinity.

 A question always arises as to which of the formulae should be used? There are some 50 formulae evolved by researchers in various countries.

 Scour prediction formulae are generally classified according to method of approach as:

  •  Theoretical analysis coupled with laboratory experiments like Yuditsky, Zvorykin, Mirtskhulava etc.
  • Theoretical analysis coupled with prototype observations like Taraimovich, Spurr etc.
  • Empirical relationships based on prototype observations, like Damle, Martins, Incyth etc.

 Another classification based on use of parameters may be as follows:

  • Formulae involving simplest parameters like discharge intensity, head and tail water depth, as for example Damle, Martins, Taraimovish etc.
  • Formulae involving additional parameter like bed material size, as for example Mason, Chee and Kung etc.
  • More complex formulae involving several parameters representing bed characteristics, rock properties and structure geometry etc. Most of these formulae have been developed by Russian researchers like Akhmedow, Mirtskhulava, Zvorykin etc.
  • Recently, Bollaert has proposed a comprehensive scour model based on experimental and numerical investigations of dynamic water pressure in rock joints.

However, according to author’s experience, use of even a comprehensive formula does not offer better result than obtained with a simpler formula. In this context, results given by Damle equation have been found to be quite reliable. A review of evolving of Damle equation is quite interesting and is the subject matter of this discussion.

Damle equation was evolved by a group of researchers at the Central Water and Power Research Station, Pune, India, ( a Government of India organization devoted to research in hydraulic and allied engineering), namely, P.M.Damle, C.P.Venkatraman and S.C.Desai in 1966. Data comprising results of scour observations from 6 prototype and 15 model studies was available then. The only hydraulic parameters responsible for causing scour were considered to be the stream power q x h (product of discharge intensity and head) and the tail water depth ds No account of bed material size was taken as it was assumed that the process of hydro-fracturing would ultimately lead to breakage of jointed rock mass into size that could be transported out of scour hole, to result into scour depth, considered to be ultimate. Study of prototype scour revealed that development of scour was in stages as the discharges of various magnitudes passed for different durations. Accordingly, the following set of equations was derived. Figure 1 shows the above mentioned relationships.

  

Image

 

 Figure 1: Damle Equation with original constants

 It may be mentioned that several other formulae derived from the results of prototype observations or model studies in the form of ds=K qa x hb, where values of a and b were based on regression analysis. Only in Damle equation, the exponents of the product (qh) were predetermined to conform to the concept of stream power.

 Some 20 years later, from a study of scour development at Kariba dam, Mason and Arumugm (1985) found that the depth of scour was indeed a function of stream power viz. ds=F (Q0.5 H0.5) if it was assumed that the depth was proportional to the cube root of volume of scour. This substantiated the assumptions underlying Damle equation.

 It must be noted that equations developed from laboratory experiments under controlled conditions give scour depths that are ultimate and stabilized. This is not so for the field where scouring may still be in the process. The equations developed from field studies must be updated and refined as and when additional data becomes available. In the years that followed, data on scour in respect of several projects became available. Khatsuria (1992 and 2005) analyzed these data and plotted superimposed on the original data, which revealed that the coefficient for the ultimate scour K was 0.90 instead of 0.65. The revised plot is shown in Fig 2.

Image

 

   Figure 2:  Damle Equation- Modifications based on additional Data

 Interestingly, a further refinement taking into effect latest data from Azamathulla (2008) also validates this equation (Figure 2). Only those data sets that represented deepest scour for a given (qh) value were plotted.

 It may thus be concluded that Damle equation is a reliable tool for prediction of scour downstream of ski jump spillways.

 REFERENCES:

  1. Damle,P.M., Venkataraman,C.P. and Desai,S.C.- Evaluation of scour below ski-jump buckets of spillways, CWPRS Golden Jubilee Symposia, Vol 1, 1966
  2. Mason,P.J. and Arumugm,K- A review of 20 years of scour development at Kariba Dam, 2nd International Conference on The Hydraulics of Floods and Flood Control,Cambridge, England, September 1985
  3. Khatsuria, R.M- State of Art on Computation, Prediction and Analysis of Scour in Rocky Beds Downstream of Ski Jump Spillways, CWPRS Platinum Jubilee, 1992
  4. Khatsuria, R.M.- Hydraulics of Spillways and Energy Dissipators, Publishers- Marcel Dekkers, New York, 2005
  5. Azamathullah,H., Ghani,A., Zakaria,N.A., Lai,S.H.,Chang,C.K. and Leow,C.S.-Genetic programming to predict ski jump bucket spillway scour, Science Direct, 20(4), 2008 pp-477-484

 

 

May 23, 2012

Desilting basins: Are they indispensable?

Filed under: Uncategorized — Rajnikant Khatsuria @ 12:01 pm

R.M.Khatsuria

Formerly Additional Director

Central Water and Power Research Station, Pune, India

E mail: rmkhatsuria@rediffmail.com

 

Mountainous streams with dependable flows and considerable heads are ideally suited for run-of-river schemes with relatively small reservoirs and almost no possibility of long term storage. Such schemes have been effectively commissioned in the north Indian states of Himachal Pradesh, Uttarakhand, Arunachal Pradesh and  Sikkim as also in countries likeNepal and Bhutan. However, such streams carry large amounts of sediments. On an average, such rivers carry sediment load of about 1000 ppm, which in some cases may go up to even 10,000 ppm during monsoon floods. Of this, coarser materials settle in the reservoir to reduce its capacity while finer particles travel up to turbines to cause abrasion damage. Desilting basins are generally provided to settle sediment before the flow reaches the turbines.Flushingof the reservoir is carried out to evacuate the coarser material deposited in the reservoir.

 Desilting basins are designed such that particles coarser than a specified size (about 0.2 mm inIndia) is settled in the basin and emptied through flushing tunnels at the bottom of the desilting basin. The general features of typical desilting basins are:

  • About 90% removal of particles coarser than 0.2 mm size
  • Flow through velocity in the basin of about 0.3 m/s.
  • Gates on the upstream and downstream for operation and control
  • Flushingducts and flushing tunnels for desilting
  • Minimum two chambers for ease of selective operation

 Figure 1 shows schematic of a dam- desilting basin-power house complex.

Figure 1: Typical layout of Dam-Desilting basin complex 

It would be obvious that the entire set up of desilting basins would involve huge expenditure, which may even be disproportionate to the cost of the barrage and water conductor system. As for example, one can imagine the cross sectional area of the chamber required for passing the design discharge with a flow through velocity as low as 0.3 m/s.

 Even under such circumstances, desilting basins have been provided in many schemes. Unfortunately, the prototype experience has not been encouraging. Turbine runners have been damaged due to abrasion. Fig 2 shows typical view of runner damage.

Figure 2: Abrasion damage to the turbine runners 

In view of this, there is serious reconsideration among the civil and power engineers about dispensing with the provision of desilting basins in run-of-river plants.

 Although the desilting basins are designed to remove about 90% of the material coarser than 0.2 mm or so, this constitutes only about 30% of the total sediment load. The remaining 70% comprising finer material in the range 0.2mm to 0.075mm pass through turbines. If this is predominantly quartz, then it is capable of causing abrasion damage. Further, the desilting system is designed for a particular discharge (generally the design discharge of the power plant) and sediment concentration. If the discharge is less, reduction in the flow through velocity will cause more deposition of sediment which in turn would overload the flushing capacity. On the other hand, if sediment concentration is more than the design value, more sediment will enter the turbines. In addition, discharge for silt flushing tunnel- of the order of 5-10% of the design discharge would have to be provided separately in the design. It would thus be seen that desilting basins can not be expected to fully solve the problem of sediment management.

 Thus, engineers are in favor of dispensing with desilting basins by taking recourse to modification in the basic concepts of planning, design and operational aspects of run-of-river plants.

 The first recourse is to treat the reservoir itself as a large desilting basin! Such plants are operated with reservoir at FRL during no-floods periods when the incoming discharges and sediment loads are relatively small and deposition of finer contents can be managed. Thus, relatively silt free water would enter the power plant.  During floods, the plant is generally operated with reservoir at MDDL to obviate the possibility of deposition of large amount of sediment in the reservoir. This must be changed to operation at FRL. This would of course induce deposition starting from the river-reservoir junction and move towards downstream in the form of sediment wave. But if the reservoir topography, plant discharge and relevant levels such as spillway crest and intake are favorable, an average flow velocity in the neighborhood of 0.3 m/s can be ensured and in this case also, silt free water would enter the power plant. The deposited sediment can be effectively flushed out of the reservoir at appropriate time during the floods. However, this would require specific planning and design.

 Reservoir flushing would be an integral part of the design and operation of these plants. The layout of the dam and power intake as well as the design of spillway would have to be tuned to meet this requirement efficiently. The relative position of the power intake with reference to the spillway is an important design consideration. Figure 3 shows possible layouts with preference. Thus, layouts 1 and 2 would be most effective in flushing operation.

 

Figure 3: (top)- Preferred layouts of dam-power intake

(bottom)- Section of low level spillway

The design of the spillway requires special consideration. It should be so designed that most of the storage is contained by the gates with the crest of the spillway at or near the river bed level. In addition to allowing an efficient flushing operation, this would also allow placing the sill of the intake at higher levels. A typical section of the low level spillway discussed above is shown in figure 3. For a detailed discussion on these aspects, refer Chapter 13- Spillways for Flood and Sediment Disposal of reference 1.

 The above measures would largely ensure relatively silt free water to the turbines. However, there are possibilities that even with operation at FRL, the flow velocity in the reservoir may be somewhat higher than 0.3 m/s or some of the silt content coarser than about 0.2 mm enters the turbines. This would cause abrasion damage to the turbine runners. At some plants, coating of under water parts with Tungsten Carbide in Cobalt Chromium matrix using HVOF process with thickness of coating in the range of 500-600 microns, has given good results. Alternatively, provision of spare runner with the provision of runner replacement gallery in the power house design, could also be explored since the cost of spare runner would be a fraction of the capital cost of the desilting basin complex.

And as a last measure, the plant can be shut down for a day or two during the period of floods carrying large amount of sediment. This situation can then be utilized for flushing operation.

 It would thus be seen that desilting basin may be dispensed with in most of the cases with appropriate planning, design and operation of the power plants.

 Reference:

 1. Khatsuria, R.M.(2004)- Hydraulics of Spillways and Energy Dissipators- Marcel Dekkers,New York.

May 6, 2012

Discharge characteristics of spillways and barrages silted up to crest

Filed under: Uncategorized — Rajnikant Khatsuria @ 5:17 am

R.M.Khatsuria

Formerly Addl. Director

Central water and Power research Station, Pune, India

E mail: rmkhatsuria@rediffmail.com

 

All other factors remaining the same, coefficient of discharge of a spillway decreases as the height of the crest relative to the head on the crest (P/Hd) decreases. The crest shape, though, has an influence to some extent as seen from figure 1. The elliptical shape retains some superiority over other shapes. However, trying to estimate the reduction in the coefficient Cd corresponding to the zero approach depth, viz. P=0, from figure 1 would not yield any result. The flow conditions substantially change as the approach depth diminishes to zero. No specific reference is available in the literature. Theoretically, a level broad crested weir should have a value of Cd =1.706 or C=0.577 in the equation Cd=2/3 (2g)0.5 C.

 

Figure 1:  Effect of approach depth on coefficient of discharge

This issue was particularly addressed by B.D.Suryavanshi, then Director, Irrigation Research, MP, India, in 1972. He conducted studies on a 1:24 scale model of a 7m high ungated weir which was getting silted up. In his experiments, in addition to the original bed, he also simulated a hypothetical condition whereby the weir was silted up fully up to the crest level. It was found that the coefficient of discharge in the equation q=Cd H3/2, of 2.143 corresponding to the original bed condition (P/Hd =1.33) decreased to a value of 1.96 for the bed silted up to the crest (P/Hd =0), a reduction of about 9.5%. Both the above values were worked out considering the head due to the velocity of approach. The corresponding C values were 0.725 and 0.663 respectively, considerably higher than theoretical. The head over the crest, however, reduced from 5.27 m for the original bed condition to 4.52 m corresponding to the silted bed condition, for the design discharge of 28 cumec. It is surmised that the free over fall just downstream of the level crest may be the reason for increase in C beyond the theoretical vale of 0.577.

 A noticeable finding from the above studies was that the afflux upstream of the reach increased in comparison to that caused by the original bed condition. Also, the maximum additional afflux was caused at a section up to which silting was extended. Therefore, if a reservoir behind a low dam or barrage is likely to be silted up in future, the additional afflux should be considered and provided for in the design itself. The results are shown in figure 2.

 

Figure 2: Effect of siltation upstream on flow profiles

In the above case, although the reservoir was silted up to the spillway crest, a free over fall in the downstream contributed to a better value of C. However, in the case of low height barrages, silted up to the crest level, such a free over fall would not be available as the downstream portion would not be too deep. In such a case, C value of 0.577 would be applicable, provided the downstream water level is not more than about 80 percent of the upstream level. For higher submergence, weir formula can not be applied and discharge should be calculated assuming fully developed open channel flow and corresponding velocity profile.

 A particular case of interest would be a low height barrage with crest piers and bridge. When silted up to the crest level, it would virtually be the case of a bridge with the intervening spans filled with level bed of concrete. This case offers calculations involving bridge pier losses. All the possible combinations of upstream and downstream water levels, shown in figure 3, are amenable to calculations by application of US Army Corps of Engineers Hydraulic Design Criteria charts 010-6 to 010-6/5.

Figure 3: Various combinations of upstream and downstream water levels

 

 

October 5, 2010

How and Why rivers meander?

Filed under: Uncategorized — Rajnikant Khatsuria @ 12:17 pm

 

 

R.M.Khatsuria

Formerly Additional Director

Central Water and Power Research Station, Pune, India

e mail:  rmkhatsuria@rediffmail.com

Meandering rivers have fascinated all sections of viewers; laymen, students, artists, poets, and scientists alike. It is believed that the river Sabarmati (meandering all along its course) in western India, has derived its name from a poetical expression- (saa bhramati) meaning- she (the river) is wandering. A meandering river originating form a valley formed by two mountains and a rising sun is the most likely sketch that a beginner in a drawing class would attempt. Crooked rivers with lazy loops and bends have been favorites of artists and photographers. Meandering river has been one of the most explored and investigated topics in hydraulic engineering. No less an intellectual luminary than Albert Einstein postulated in 1926 a theory explaining the process of meandering on the basis of simple physical laws. Since then understanding of the process has traversed from simple physics to stochastic, equilibrium and geomorphic theories on one hand and from empiricism to complex mathematical modeling on the other, and yet without a final word as to-why and how rivers meander!

According to Einstein, a slight change in the velocity of flow between the banks of a river (due to a bend in the river) would give rise to secondary circular currents in the plane perpendicular to the direction of the flow. Even where there is no bend, Coriolis force caused by the earth’s rotation can cause a small imbalance in velocity distribution such that velocity on one bank is higher than on the other. This can generate erosion on one bank and deposition of sediment on the opposite bank. The secondary currents cause the flow to proceed in the direction towards eroded portion until redistribution of velocity reverses the process. This result in formation of tortuous water course called meandering. Surprisingly, Einstein’s contribution to river engineering has not been acknowledged in the literature.

There are other theories as well. Stochastic theory ascribes random fluctuations in the flow velocity due to some obstacle or disturbance to affect velocity distribution across the section, for the formation of meanders. Equilibrium theory states that meandering is the process by which a river adjusts its gradient (length along the course divided by the drop in elevation) so that there is an equilibrium between the erodibility of the terrain and the erosive power of the stream. Geomorphic theory attributes tectonic features acting as obstacles to deflect the stream to cause meanders.

Attempts were also made in the past, to understand the process of initiation of meanders, on physical hydraulic models. Two such cases are known; Waterways Experiments Station (WES) at Vicksburg, USA and Central Water and Power Research Station, Pune, India. Experiments were conducted in wide and long sand laden trays, starting with the straight channel and varying discharge and silt load. However, there was no conclusive evidence of the cause of initiation of meanders, having observed that meanders may even develop spontaneously. In general, all the theories can explain how the meandering rivers continue to meander but fail to explain how meanders initiate.

It is believed that a necessary condition for the development of meander is erosion of the bed and its subsequent deposition further downstream. This is caused by the secondary currents, generated downstream of a bend, provided of course that the discharge and bed material are favorable for this process. The question, then is- how secondary currents are generated in a straight reach with almost symmetrical distribution of velocity? Explanations put forth were these: a sudden obstruction, external distribution, falling of a tree etc. These can no longer be acceptable, given the fact that meanders spontaneously formed even in straight experimental channels without any of these!

 Further discussing on this issue, it is argued that even if the cross section is symmetrical, the turbulence and the instantaneous maximum shear stress may be asymmetric. Experimental observations indicate this to be near the flanks, rather than in the centre of the channel. Thus, the most likely site for the initiation of bed erosion and subsequent deposition would be nearer to the flanks. This would force the otherwise parallel stream lines from the upstream, to deviate towards the opposite flank, which in turn cause another spot of bed erosion and subsequent deposition. If the above sequence of events is visualized graphically, it would look something like this:

 

Initiation of meandering

 

The course of events, when allowed to continue, would result in a meandering of river as shown below.

 

Equilibrium theory states that meandering is the process by which a river adjusts its gradient so that there is equilibrium between the erodibility of the terrain and the erosive power of the stream. This argument seems to be supported by the theory of entropy (having its basis in the second law of thermodynamics). Without going into details, it can be stated that a stream with a given discharge would tend to increase its entropy, which consequently would tend to reduce its average velocity. This can be achieved by flattening of its slope, which would require the stream to go in a tortuous way via meander.

At present, the above two postulations are generally accepted. However, the interesting aspect about meanders is that there is a consistency in their shapes and relationships among various geometric features, irrespective of the geomorphic conditions. The geometric features are shown in the drawing below.

The meander ratio or sinuosity index is the ratio of actual length along a meandering river (Lm) to the straight distance S between the end points (AB). It is an indication of quantification of meandering. Obviously, for a straight river course this ratio is equal to unity. A ratio varying from 1 to 1.5 defines the river course as sinuous and from 1.5 to 4 as meandering. Also, the following relationships hold good for a majority of rivers:

     Lm/W ~10;   Lm/Rc~5;   Rc/W~2

            It is observed that the meander length is a function of discharge also. Various investigators have studied this aspect and their findings could be generalized in the form  Lm  k Q0.5, where k is a constant and Q is the discharge. The value of k ranges from 1 to 31 depending on whether the discharge selected was dominant, mean, maximum or with a certain return period etc.

            The above relationship points to the dynamic nature of meandering. Any feature that brings about a change in discharge can alter the meander geometry; as for example, a dam constructed upstream or a diversion of discharge from the main stream or an unusual flood etc.

            Even when one concludes that meander results from the processes of erosion and deposition in alluvial rivers, there is no explanation as to why meanders also form on glaciers in the absence of sediment. Meanders are present even in oceans as formed by the well known Atlantic Gulf Stream, while passing along the coast of Florida towards north, alongside New England and then east ward to Europe. Meanders form even when there are no banks; as exemplified by the flow from a small nozzle on a slightly inclined glass plate. Interestingly, a discharge-meander length relationship similar to the one mentioned above holds good in this case also. How this could be explained?  There is no convincing answer for this. Perhaps, the theory of entropy can be extended to address these issues.

           

 

 

 

 

September 24, 2010

Pull out forces on concrete lined side walls of spillways

Filed under: Uncategorized — Rajnikant Khatsuria @ 10:23 am

 R.M.Khatsuria

Formerly Addl. Director

Central Water and Power Research Station, Pune, India

E Mail: rmkhatsuria@rediffmail.com

 

Widths of spillways to be located in relatively steep and narrow rocky river gorges often exceed the available waterways. As a result, one or both the ends of a spillway may have to be accommodated by excavating the flanks. Additional excavation in flanks is required for providing water way. When the energy dissipator is in the form of a stilling basin, construction of long and high side walls also poses a problem. If topography and geology permit, the side walls can be formed by providing concrete lining to the excavated and dressed rock face of the flank adjacent to the end of the spillway. The lining is secured to the rock with anchors. Such construction has been adopted for several spillways. However, the concrete lining may get dislodged due to the pull out force caused by the turbulence in the hydraulic jump.

            Estimation of hydrodynamic pull out force on the concrete lining is a tricky issue. The origin of such forces lies in the interaction between the fluctuating pressures on the water side face of the lining and pressures propagated behind the lining (at the rock-concrete interface) through joints/cracks in the lining. The magnitude of propagated pressures and hence the pull out force can not be estimated by analytical means. However, instantaneous fluctuating pressures can be experimentally measured by means of electronic pressure transducers. Assuming that at a given instance, the propagated pressure behind the lining reaches the instantaneous maximum value (Pmax), while at the same time, instantaneous minimum pressure (Pmin) exists on the water side face; the pull out pressure (Pl) would be (Pmax-Pmin). It is often argued that the magnitude of the propagated pressure behind the lining should be taken as RMS value of the fluctuating pressure (Prms) or hydrostatic pressure Hs. (whichever is larger). Thus

      Pl=Hs-Pmin    …………..Prms<Hs    or

      Pl=Prms-Pmin…………..Prms>Hs.

The above scheme of calculation is depicted in Figure 1.

 

               Figure 1: Scheme of calculation                                                                              

It is believed that effect of pressure fluctuations on areas as large as side wall monoliths are considerably less than those on the small diaphragm pressure transducers. It is quite likely that instantaneous fluctuating pressures vary with time as well in space. A reliable estimate of pull out force would therefore require averaging of pressure fluctuations over the area of interest with due consideration of space and time.

Averaging of pressure fluctuations over the entire area of a side wall monolith panel is based on the assumption that fluctuating pressures at all points over the area follow the normal distribution. The procedure consists of simultaneously measuring pressure fluctuations on ‘M’ sub areas of the monolith, each associated with a pressure transducer. This is described below:

 The above value of F’ is the RMS value. For obtaining the instantaneous maximum or minimum value, it should be multiplied by the coefficient of probability k, which, for the normal distribution, has a value of 3.09 corresponding to a probability of 99.8%. Thus (Fl) min=3.09 F’.

Pull out forces could also be estimated by direct measurement using a force transducer.

It will be apparent that determination of pull out force relies heavily on experiments on hydraulic model for the specific structure. The details of the spillway, stilling basin and side wall, for which, estimation of pull out force was carried out, are shown in Figure 2.

Figure 2:  Details of stilling basin, side wall profile and transducers

 The maximum head on the spillway, from MWL up to the stilling basin apron level, was 128m and the discharge intensity varied from 100 to 200 cumec/meter width. The maximum height of the side wall was 45m, consisting of both, the concrete lined portion at the base and gravity section above it.

Studies were conducted on a 1:55 scale model reproducing four spans of the spillway. Fluctuating pressures were measured with miniature piezoresistive pressure transducers having diaphragm diameter of 3.8mm. Direct measurement of pull out force was carried out with a force transducer having a capacity of 1kN.

A typical monolith panel of concrete lining, of 16.5m x 16.5m was fitted with 9 pressure transducers to form a symmetric matrix of 3 x 3. Another panel of the same size was fitted with the force transducer, structurally isolating it from the rest of the wall to allow freedom of movement in the direction transverse to the flow. It was found that the natural frequency of this system of about 48 hz was much higher than the dominant frequency of about 2 hz of the exiting forces. Thus, there was no possibility of resonance effects.

Measurements of fluctuating pressures as well as pull out force were carried out at location I to compare the results. At location II, only direct measurement of force was carried out. Measurements were recorded for the discharges of 100%, 75%, 50% and 45% of the design maximum discharge.

When a single location of fluctuating pressures was analyzed form the time-history records, maximum pressure of 52m of water against a minimum of -9m, with RMS values ranging from 1.5m to 43m were revealed. Obviously, any assessment of pull out force based on these results would be too excessive. Thus, a need for averaging the pressures over the time and space was underlined.

Results of averaging of the pressure fluctuations as per the scheme described above are given in Table 1. The pull out forces varied from 12,321 kN to 24,329 kN over the panel. In terms of head of water, these would be equivalent to 4.6m to 9.1m.

Direct measurement of pull out force was carried out at the same locations I and II, for all the four discharges. The results are shown in Table 1.

Table 1:   Pull out forces on concrete lining, kN

 

     Discharge  ( as % of the               maximum)                Location I Location II
PressureMeasurement ForceMeasurement ForceMeasurement
       45        12,321   12,439    12,500
       50        14,410   13,852    13,890
       75        19,210   19,480    15995
      100        24,329   23,995    17,800

  A comparison of the results for the location I shows that pull out forces obtained by both the methods agree well. The magnitude of the force increased with the discharge as expected and followed a linear variation as shown in Figure 3. It was also seen that the pull out force reduced from location I to II, which can be explained by the reduction of intensity of turbulence as one moves in the downstream direction.

Figure 3: Variation of pull out force with discharge 

 

The above studies confirmed the fact that any estimation of force exerted on a structure should not be based on measurement of pressure at a single or isolated location but should be based on averaging of pressures at several points in the time and space domain. On the other hand, direct assessment of force using suitable force transducer taking the entire precautions offer an equally reliable means.

August 9, 2010

Hydrostatic Vs Hydrodynamic bending moment on submerged divide walls in a stilling basin

Filed under: Uncategorized — Rajnikant Khatsuria @ 10:50 am

R.M.Khatsuria

Formerly Addl. Director

Central Water and Power Research Station, Pune, India

E mail: rmkhatsuria@rediffmail.com

Low height submerged divide walls are sometimes provided in large width hydraulic jump stilling basins. Unequal operation of spillway gates causing imbalance of discharge across the width of the stilling basin often results in large horizontal eddies that may also extend downstream of the stilling basin. These eddies have a potential to pick up loose material from downstream and bring inside the basin to cause abrasion damage. Several stilling basins were damaged due to abrasion caused by such eddies. Since simultaneous and equal operation of large number of gates may not be possible all the times, one of the remedies to prevent such damage is to ensure that eddies caused by unequal operation, is at least confined within the stilling basin. Incorporating divide walls in the stilling basin to segregate the basin into a number of bays has been found to be effective towards ensuring the above objective. The hydraulic design, mainly the number and height of such divide walls is finalized from hydraulic model studies. Their structural design requires assessment of bending moment on the divide walls. This is rather a tricky issue.

The conventional design of such divide walls is based on the assumption that the maximum bending moment a divide wall have to resist, would be equal to that caused by the water retained up to its top level on one of the sides, the other side having no water. This is so called hydrostatic bending moment. The calculation of hydrostatic bending moment along the height of a typical divide wall is explained in figure 1.

Figure 1: Comutation of hydrostatic bending moment

This assumption allows a solace that under the submerged condition a moment in the opposite direction from the other side would in fact, have balancing effect. However, divide walls designed on this assumption failed in some projects and the hind casting model studies revealed that the instantaneous forces caused by the turbulence of the hydraulic jump, were much higher than those accounted with the simple assumption and that submergence did not have compensating effect.  Thus, hydrodynamic bending moments must be considered in the design, as opposed to the hydrostatic bending moments.

This issue has been extensively studied on large size hydraulic models using specially designed bending moment transducers. The suitability of strain gauge to respond to the fluctuating forces is well known. Using this property of strain gauge, a transducer consisting of standard strain gauge Wheatstone bridge configuration was designed for these studies. The principle and details of construction of BM Transducer is depicted in figure 2. An apparatus was also designed for calibrating the transducer for the relationship volt output Vs bending moment.

 

 

Figure 2: Design of a bending moment transducer

Some results of model studies conducted using the BM transducer is shown in figure 3. In these studies, bending moments over the entire height of the divide wall were measured at two locations along the length. The flow entering the stilling basin had a pre-jump depth of 2.43m with a velocity of 46.1m/s (equivalent prototype), giving a Froude number of 9.44.  Discharges of lower magnitude were also considered.

 

 

Figure 3: Hydrostatic Vs Hydrodynamic bending moment

It was indicated that the measured values of hydrodynamic bending moments in the region of intense turbulence were about 1.8 to 2.7 times of those obtained from hydrostatic force distribution. Since these are the instantaneous values, the question a designer might ask is- What is the proportion of time the divide wall would be subjected to this loading? In other words, if this loading would be exerted, only for a small fraction of the time, some calculated risk may be taken and the design may consider a reduced value.

To address this question, the cumulative probability distributions of time history records of bending moment at critical locations were analyzed. It was seen that the divide wall would be subjected to bending moments exceeding the hydrostatic value for about 24 % of time. This is also shown in figure 3.

January 29, 2010

Converting an ogee spillway into a siphon spillway:Some considerations

Filed under: spillway,Uncategorized — Rajnikant Khatsuria @ 11:53 am

 

 

R.M.Khatsuria

Formerly Addl. Director

Central Water and Power research Station, Pune, India

E Mail: rmkhatsuria@rediffmail.com

 

The discharge over an overflow spillway is a function of the head measured above its crest. Enclosing the crest and making the resulting conduit flow full, thus converting an ogee spillway into a siphon spillway, can substantially increase the effective head. The head on the siphon spillway is then the difference in elevations between the reservoir level and the water level at the spillway outlet. This property can be utilized to increase the discharge capacity of a spillway without raising the reservoir level or lowering the crest level. This can be an effective way for the rehabilitation of a spillway that has undergone hydrologic re-assessment with an increased inflow.

There are, however, several issues, which require serious considerations:

• An ungated spillway, preferably with crest piers supporting bridge would be an ideal choice from consideration of construction facility.
• The profile of the upper membrane forming the siphon would have to follow the profile of the spillway surface for obvious reasons. This would rather be an inefficient configuration as far as priming of the siphon spillway is concerned. A flow deflector suitably located downstream of the crest may be a solution.
• The height of the siphon barrel at the crest would have to be greater than the maximum depth of overflow for achieving a sizable increase in the discharge.
• The conversion to the siphon spillway would involve large scale construction modifications like provision of siphon inlet at the entrance, embedding the barrel in the existing crest piers, construction of the barrel portion downstream of the piers and provision of air vent for depriming.
• If the span width is significantly larger as compared to the depth of barrel proposed, the barrel may require to be divided into two or more compartments from structural considerations. This feature is known to result in reduced coefficient of discharge.
• Finally, model studies would be indispensable for arriving at a suitable design, keeping in view the scale effects involved in such a study.

There is no information about any of the existing ogee spillways converted into siphon spillway. However, if the above mentioned difficulties could be overcome, such a conversion has a potential for increasing the discharge capacity considerably without lowering the crest or increasing depth of overflow, as shown by the following example.

The spillway in question has a span width of 20m and the maximum depth of overflow of 10m, as shown in Figure 1. The discharge per span is calculated as 1382 m3/s, assuming a coefficient of discharge of 2.185.The difference between the FSL El 110m and water level El 65m at the spillway outlet is 45m.

Figure 1: The original spillway

This spillway is proposed to be converted into a siphon spillway as shown in Figure 2. The overall cross section of the barrel is 20m wide x 12m high, with a1m thick dividing wall forming two barrels of 9.5m x 12m.

Figure 2: Proposed conversion to siphon spillway

 This configuration is likely to reduce the coefficient of discharge C in the formula

substantially. A conservative value of C=0.37 has been assumed for the present. Because of the increased discharge, the water surface at the outlet of the spillway would now be around El 70m, giving an effective head Ha of 40m. With the values of C=0.37, A=228 sq.m, the discharge through the siphon is calculated as 2363 cum/s.

This shows that a considerable increase in discharge capacity can be achieved with the proposed modification. The required size of the siphon barrel can be calculated for a given increase in the discharge. It should be ensured that the velocity at any section of the barrel is not more than about 12m/s to avoid cavitation.

Copyright: Neither this article nor any part of it may be copied in any form without the written permission of the author.

November 26, 2009

TRASH RACK DAMAGE:CAUSES AND REMEDIES-PRESENT RESEARCH

Filed under: Uncategorized — Rajnikant Khatsuria @ 5:17 am

 

 

R.M.Khatsuria

Formerly Addl. Director

Central Water and Power Research Station, Pune, India

E mail: rmkhatsuria@rediffmail.com

Trash in rivers is a continuing problem for hydropower plants. Flowing water picks up solid matter like industrial waste, plastic, textiles, rubber and also trees, branches, leaves etc. This matter collects near the intake and enters into the turbines, if not prevented by suitable device like trash rack.  However, damages to the trash rack structures of several hydro plants all over world are of concern for designers, plant owners and operators alike.

 

Trash racks may be fixed structures embedded in the concrete around the inlet or may be removable, operated by a crane using a grappling. A typical trash rack panel is made up of vertical bars of rectangular section (say 15 cm x 1.2 cm) and horizontal bars of circular section (say 3.75 cm Ø). Vertical bars are closely spaced, typically 10-12 cm apart, whereas horizontal bars may be 100 cm apart. Although, trash rack cleaning machines are provided on top of dams, occasional surges of increased trash materials collide with trash rack bars and accumulate there, forming almost impenetrable wall. In addition to imposing excessive drag on trash rack bars, this also restricts smooth flow in to the intake and creates head loss resulting in loss of power generation. More seriously, this blockage induces change in the direction of approach flow towards the intake, resulting in vortices and vibrations. Besides, variable pattern of power generation with instantaneous change in intake discharge, common at hydro plants, adds to the problem of vortex shedding with a wide range of frequency. This is believed to be responsible for damage.

Several research studies are currently under way to understand the mechanism of damage and evolve remedial measures for averting such damage. Observations have shown that the most critical location for the origin of damage is the junction of the vertical rectangular bars with horizontal circular bars, where three pairs of vortices are generated. Varying degree of blockages and changes in discharge generate vortices of different patterns and frequencies.

 

                                                                                                

Both, physical and numerical modeling has been resorted to understand the flow structure responsible for damage. It is found that the origin of damage was fluid-structure interaction. Out of a wide range of frequencies of vortex shedding, caused by blockages of various degrees and sudden changes of discharge, some frequency lie in the neighborhood of natural frequency of the trash rack screen. This creates a resonant condition responsible for damage.

Efforts for eliminating condition of resonance include evolving shape of trash rack bars that would reduce/prevent formation of vortices. Instead of vertical bars of rectangular section, bars with wedge-shaped pointed end at the upstream followed by tapering on the downstream have been examined. Also, the circular horizontal rods were positioned nearer to the pointed end of vertical bars, rather than in the centre. This arrangement has indicated promising improvement in the flow conditions.

 

 While the research efforts towards improvements continue, there are at least three issues that need to be addressed.

  1. Trash rack cleaning devices:  Trash rack cleaning machines operating from top of dam, pick up material from the rack bars. Is it possible that some device sucks up the trash from the water surface, lifts it up, separates it out at the top and returns the clean water in the reservoir? This is something in line with the sediment sucking from the reservoir.
  2. Floating barriers: At some plants, floating barriers are placed at some distance away from the intake. Such barriers prevent trash from approaching towards intake. Boats or barges then collect the trash from the barriers. It is observed that some material that is in suspension with flow, escape from below the barriers and enter in to the intake. Some improvement in the design and operation of floating barriers is needed.
  3. Though the wedge-shaped bars described above are effective in improving flow conditions near the trash rack screens, a cost effective design must be evolved, because such shapes for the bars are very expensive to manufacture and handle.

 

(Copyright:  Neither this article nor any part thereof may be reproduced in any form without the written permission of the author)

July 5, 2009

Supercritical contraction on inclined plane: A new topic for research

Filed under: Uncategorized — Rajnikant Khatsuria @ 2:46 pm

           Contractions along spillway chutes are provided whenever reduction in the channel width becomes necessary. This may be due to geological, topographical, economical or hydraulic consideration. Since the flow along a spillway chute is supercritical, any deviation in the stream lines creates oblique standing waves that can propagate downstream unless a properly designed contraction is provided to minimize this effect.

             A supercritical contraction has three parameters viz. contraction ratio (b2/b1), upstream Froude number F1 (determined by discharge, channel width and flow depth prior to contraction) and angle of contraction θ or length of contraction Lc. The phenomenon of oblique standing waves has been studied extensively, both theoretically and experimentally, for the past half century. However, a direct solution to the governing equations is not possible and either a trial and error procedure or graphical solution is resorted to. The earlier approaches of Ippen and Dawson [1951] involved solution through four-quadrant graphs and that of Sturm [1985] of twin graphs, but as the analytical treatments improved, today  it is possible to design an optimal contraction by a single algebraic equation or a chart, refer Hsu et al.[2004], Subramanya et al.[1974]. In an optimal contraction, the positive and negative disturbances will cancel each other so that the flow is calm in the channel downstream of contraction.

       It is worth mentioning here that all the analytical and experimental studies related to supercritical contraction have involved only the three parameters listed above. The transition is assumed to be on a horizontal plane. The only change in the velocity is due to change in the width of the waterway. However, when a contraction is provided on a spillway chute having an inclination to horizontal, an additional parameter of chute slope α is introduced. Now the gravitational effect is also accompanied simultaneously along with the contraction in the width to affect the velocity. None of the analytical treatments so far has included the effect of channel slope on the performance of contraction. Although several contractions have been provided on various spillway chutes, their designs have not included the parameter of channel inclination.

        Recently, the first attempt towards inclusion of channel inclination has been made by a group of Algerian researchers; refer Berreksi et al. [2008]. They have applied St. Venant’s equations governing two-dimensional unsteady free surface flows, incorporating therein the parameter α, which in turn led to a system of non-linear hyperbolic equations. These are solved numerically by applying second order two step McCormack explicit finite difference scheme. Although there is experimental verification for the case of contraction on a horizontal plane, i.e. α=0, there is no direct verification for the case of inclined plane. The authors have applied the scheme to a rectangular channel with no contraction i.e (b2/b1) equal to unity, on an inclined plane, with good correlation between analytical and experimental results. It was assumed that the same scheme would apply equally well to a contraction on inclined plane with different values of (b2/b1) and α. Figure 1 shows a schematic of results for a contraction on an inclined plane.

 

Contraction

                   Figure 1:  Supercritical contraction on inclined plane- A shematic

 

            It would be seen that, as anticipated, flow depths decrease and velocities increase with increasing inclination. Another noteworthy feature of this analysis is that there is only one occurrence of wave, that too, just downstream of the end of contraction, along the centre line of contraction. Along the side walls, the water surface falls considerably and that the effect of increasing inclination is not significant.

           The above results have opened up a new chapter of studies on supercritical contractions on inclined planes. Further studies are required specifically to address the following issues:

  1. Correlation of analytical and experimental studies with different configurations of contraction on inclined planes.
  2. It is apparent that there would be an optimal configuration of such a contraction that would give acceptable conditions in the downstream channel.
  3. With steeply inclined channels, air entrainment and resulting bulking of flow also come into play.
  4. The results of such studies should be generalized on the lines of contractions on horizontal plane, in the form of algebraic equations or design charts that would obviate the need for complex computational procedures.

 

References

  1.  Berreksi,A, Kettab,A, Remini, B, and Benmamar, S (2008)-“Computation of two-dimensional unsteady supercritical flows in open channel contraction of spillway chutes”- Dam Engineering, Vol.XIX  Issue 3  December 2008, pp 149-168
  2. Ippen, A.T. and Dawson, J.H (1951)-“Design of channel contractions”- Symposium on high velocity flow in open channels, Trans ASCE, 116, pp 326-346
  3. Hsu, Ming-His, Su, Tung-Hung and Chang, Tsang-Jung (2004)-“Optimal channel contraction for supercritical flows”- Jnl of Hydraulic Research, Vol 42 No.6 (2004) pp 639-644
  4. Sturm, Terry W, (1985)-“ Simplified design of Contractions in Supercritical Flow”- Jnl of Hyd Engg, Vol111 No. 5 May 1985.pp 871-875
  5. Subramanya,S and Dakshinamurty,S  (1974)-“Design of Supercritical Flow Contractions by Least Square Error Minimization Technique”- 5th Australasian Conference on Hydraulics and Fluid Mechanics, Uni.of Canturbury, New Zealand, 1974

____________________________________________________________________________________________________________________________  © Neither   ©Neither this article nor any part of it may be reproduced in    any form without the permission of the author in writing.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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