Hydraulic design of stilling basins in steep channels

Dam Engineering Vol XIX Issue 4 1

Hydraulic design of stilling basins in steepchannels

Armando CarravettaAssociate ProfessorDipartimento di Ingegneria Idraulica, Geotecnica e AmbientaleUniversità degli Studi di Napoli “Federico II”Via Claudio 21I-80125 NapoliItalyEmail: [email protected]

Andrea VaccaAssociate ProfessorDipartimento di Ingegneria CivileSeconda Università degli Studi di NapoliVia Roma 29I-81121 Aversa (CE)ItalyEmail: [email protected]

AbstractThis paper investigates the design guidelines for stilling basins located within steepchannels, i.e. in the presence of supercritical downstream flow conditions. A large num-ber of experiments have been carried out varying both the terminal step height and thehydraulic characteristics of the upstream supercritical current. A regime chart in dimen-sionless parameters is built up, and the limited working conditions of the basin are uni-vocally individuated. Total head, local bottom pressures, and velocity field measure-ments, are employed to fully characterize the investigated flow conditions.

1. IntroductionStilling basins are widely used to dissipate a stream’s energy excess in open channels.The simplest structure is the hydraulic jump basin, where the dissipation process iscaused essentially by the jump itself [4]. This waterwork is generally equipped with afinal step, which may be negative or positive, and these two kinds of basin are denotedwith NS and PS, respectively. With specific reference to the PS basin different behav-iours may be observed depending on the flow conditions in the downstream channel:

Dam Engineering Vol XIX Issue 42

subcritical (PS-sub) or supercritical (PS-super). In both NS and PS configurations sever-al flow regimes (B-jump, oscillating jump, standing wave, etc.) have been identified forflow rates exceeding the design value ([3], [2], [10], [8], [9], [7], [1]).In what follows we shall focus only on the PS basin. Design conditions of a PS sub-

basin are generally defined with reference to the A-jump regime (see Figure 1a). Hager& Sinniger [3] firstly suggested the possibility to employ PS sub-waterworks for flowrates above the design value, owing to the persistency within the basin of a surfaceroller, even in the B-jump regime (see Figure 1b). The limiting conditions in the basinwere defined by the formation of a hydraulic jump in the downstream channel, renderingthe structure worthless (see Figure 1c). Theoretical and experimental results showed that,up to the limiting conditions, the energy dissipation in the basin was still appreciable([3], [2]). Stilling basins in the PS-super configuration, on the other hand, have not beenso deeply investigated, although they are commonly encounterd in steep slope mountainstreams.

The present paper reports the results of an experimental study carried out on differentPS basins characterized by several final step heights, with supercritical downstream flowconditions. The limited working conditions, beyond which a stable jump in the basincannot occur, have been identified. The results have led to the construction of regimeand efficiency charts, in terms only of dimensionless parameters. Measurements of bot-tom turbulence pressure fluctuation and averaged two-dimensional velocity field havebeen finally carried out to relate the dissipative process to the hydrodynamic characteris-tics of the flow field.

(a)

(b)

(c)

Figure 1. (a) A-jump, (b) B-jump, (c) standing wave in the PS-sub basin [2].


2. Experimental methodThe stilling basin, which is 0.8m long, was located at the final part of a horizontal pris-matic rectangular flume, b = 0.7m in width. The basin was limited downstream by a pos-itive step, having a 45° inclination, whose height was varied among s = 0.045, 0.052,0.058, 0.064, 0.070m. The selected step inclination accounts for the possible presence ofsediment in the basin. The channel ends with an abrupt drop of 0.7m downstream fromthe positive step (Figure 2). Hydrodynamic inflow conditions were fixed, operating onan upstream slice gate.

For each step height, s, and supercritical water depth, h1, the flow rate, Q, wasincreased starting from the design value, evaluated by the relation [6]:

(1)

in which F denotes the Froude number of the supercritical current (F = u1/(gh1)1/2, withu1 being the depth-averaged velocity) and S = s/h1.A sequence of steady-state conditions was explored up to the occurrence of the oscil-

lating or standing wave phenomena. Tests carried out with decreasing flow rate haveshown the absence of appreciable hysteresis.Total head (H2) was measured by a 1mm diameter Pitot tube located 0.1m upstream

from the abrupt drop. Seven pressure transducers were mounted at different locations onthe channel axis, downstream from the positive step. The first three transducers, DruckPDCR-200 model, were installed with their membranes aligned with the bottom, located atdistances from the edge of the positive step x = 5, 15, 30mm. The remaining transducers,Druck PDCR-1830 model, were connected to the bottom through 2.7mm diameter taps,located at x = 80, 130, 200, 270mm. The signals of the transducers were simultaneouslysampled by a processing computer supplied with an A/D and D/A electronic board

Slide gate

Stilling basin Positive step

0.8m s

y

x

s

0.7m

Figure 2. Sketch of the channel.


ATMIO16E10. More details on pressure measurements may be found in the references [1].An acoustic profiler, Signal Processing DOP2000 (equipped with acoustic probes

0.01m diameter, 1MHz emission frequency) was used to acquire the local velocities alongchannel axis. Vertical and longitudinal components were measured separately and 0.01mspacing was used for both horizontal and vertical alignments. For the longitudinal compo-nent, two probes were mounted horizontally, on an incline of 50° with the x axis, at a dis-tance of 0.05m from the mid-plane. Preliminary analyses were performed to assess theabsence of appreciable disturbances due to the presence of probes and air bubbles.

3. Results

3.1. Regime and efficiency chartsThe limited working conditions of the basin have been defined as the transition from B-jump to oscillating jump or standing wave. Table I reports the details of the experimentaldata in these limited conditions.Figure 3 shows the limiting conditions in the (F, S), along with the design values.

Different symbols have been used to indicate the experimental results corresponding todifferent step heights. All the experimental points collapse on a single curve showingthat the limiting working conditions are completely defined by the non-dimensional Fand S parameters, independently on the basin geometry.

4.0

3.0

2.0

1.0

0.0

design conditionsLimiting conditionss=0.045m0.0520.0580.0640.070

2 4 6 8F

S

Figure 3. Regime chart.


Table I. Experimental data in limited conditions.


Regression of experimental data furnishes the following interpolation relation:

(2)

Moreover, the displacement between the design curve (1) and the limiting curve (2) isstrongly dependent on S and it attains its maximum for S ranging between 2 and 3.The measured values of total head H2 were used to evaluate the stilling basin efficien-

cy defined as:

(3)

in which denotes the total head of the supercritical current. The efficien-cy values in the experimented conditions (see Table II) are plotted in Figure 4, along withthe design efficiency curve:

(4)

derived from (3) accounting for (1).

Design conditionsLimiting conditionss=0.045m0.0520.0580.0640.070

0.7

0.5

0.3

0.1

S=1.0

S=1.5

S=2.0

S=2.5S=3.0

S=3.5S=4.0

2 4 6 8F

Figure 4. Efficiency chart.


Table II. Efficiency measurements.


s h1 Q H1 H2 S F h(m) (m) (m3/sec) (m) (m) (-) (-) (-)

0.058 0.029 0.053 0.371 0.147 2.000 4.860 0.4480.058 0.029 0.051 0.346 0.136 2.000 4.674 0.4390.058 0.039 0.071 0.393 0.190 1.500 4.281 0.3700.058 0.039 0.071 0.387 0.185 1.500 4.244 0.3710.058 0.039 0.069 0.369 0.176 1.500 4.136 0.3650.058 0.039 0.067 0.355 0.167 1.500 4.045 0.3660.058 0.058 0.099 0.361 0.214 1.000 3.234 0.2470.058 0.058 0.098 0.352 0.209 1.000 3.185 0.2420.058 0.058 0.095 0.336 0.197 1.000 3.094 0.2410.058 0.058 0.093 0.324 0.188 1.000 3.031 0.2420.058 0.058 0.092 0.318 0.185 1.000 2.996 0.2370.064 0.021 0.042 0.430 0.136 3.000 6.215 0.5370.064 0.021 0.041 0.411 0.125 3.000 6.069 0.5410.064 0.021 0.040 0.400 0.117 3.000 5.983 0.5480.064 0.021 0.040 0.392 0.116 3.000 5.919 0.5420.064 0.021 0.039 0.383 0.111 3.000 5.847 0.5440.064 0.025 0.050 0.436 0.155 2.500 5.686 0.4990.064 0.025 0.050 0.428 0.149 2.500 5.631 0.5050.064 0.025 0.049 0.412 0.143 2.500 5.518 0.5000.064 0.025 0.048 0.395 0.133 2.500 5.395 0.5020.064 0.025 0.047 0.376 0.124 2.500 5.254 0.5010.064 0.032 0.063 0.444 0.183 2.000 5.096 0.4440.064 0.032 0.062 0.423 0.171 2.000 4.964 0.4440.064 0.032 0.061 0.410 0.161 2.000 4.881 0.4520.064 0.032 0.059 0.390 0.152 2.000 4.750 0.4470.064 0.032 0.056 0.360 0.135 2.000 4.547 0.4490.064 0.042 0.083 0.443 0.214 1.500 4.351 0.3730.064 0.042 0.082 0.436 0.210 1.500 4.312 0.3730.064 0.042 0.081 0.422 0.201 1.500 4.235 0.3730.064 0.042 0.079 0.408 0.192 1.500 4.156 0.3740.064 0.042 0.076 0.374 0.173 1.500 3.958 0.3670.064 0.064 0.113 0.394 0.233 1.000 3.226 0.2470.064 0.064 0.112 0.386 0.228 1.000 3.187 0.2440.064 0.064 0.109 0.372 0.218 1.000 3.117 0.2430.064 0.064 0.106 0.351 0.204 1.000 3.009 0.2370.070 0.018 0.036 0.460 0.121 4.000 7.111 0.5860.070 0.018 0.036 0.455 0.117 4.000 7.071 0.5890.070 0.020 0.042 0.472 0.135 3.500 6.723 0.5670.070 0.020 0.041 0.465 0.131 3.500 6.671 0.5680.070 0.020 0.041 0.453 0.126 3.500 6.580 0.5670.070 0.020 0.040 0.441 0.117 3.500 6.488 0.5750.070 0.023 0.048 0.470 0.152 3.000 6.187 0.5290.070 0.023 0.048 0.462 0.147 3.000 6.131 0.5300.070 0.023 0.047 0.451 0.142 3.000 6.054 0.5300.070 0.023 0.046 0.429 0.127 3.000 5.896 0.5410.070 0.028 0.058 0.482 0.176 2.500 5.692 0.4900.070 0.028 0.058 0.477 0.173 2.500 5.661 0.4900.070 0.028 0.057 0.461 0.160 2.500 5.559 0.5020.070 0.028 0.055 0.435 0.147 2.500 5.391 0.5000.070 0.028 0.054 0.413 0.136 2.500 5.244 0.5020.070 0.035 0.073 0.491 0.203 2.000 5.106 0.4450.070 0.035 0.072 0.477 0.197 2.000 5.027 0.4400.070 0.035 0.071 0.465 0.190 2.000 4.958 0.4420.070 0.035 0.070 0.449 0.183 2.000 4.865 0.4370.070 0.035 0.067 0.420 0.165 2.000 4.692 0.4400.070 0.047 0.095 0.479 0.230 1.500 4.303 0.3730.070 0.047 0.093 0.464 0.222 1.500 4.228 0.3700.070 0.047 0.092 0.449 0.213 1.500 4.151 0.3690.070 0.047 0.089 0.424 0.199 1.500 4.020 0.3660.070 0.047 0.086 0.402 0.185 1.500 3.902 0.365

Table II (cont). Efficiency measurements.


No residual dependence on the s value may be appreciated. Furthermore, for a fixed Svalue the efficiency does not vary appreciably up to the limiting conditions. In limitingconditions the efficiency can be expressed by the following functional expression:

(5)

The performance of waterworks equipped with different geometries of the upstream gatemay be determined by the combined use of Figures 3 and 4. For a clear explanation wewill show the procedure used in the frontal overflow with standard crest configuration.Two geometries of the overflow have been considered, characterized by a different valueof the ratio A = z/s, with z being the drop of inflow zone (A = 4.50 and A = 5.21). Forincreasing flow rate, the corresponding F and S values have been calculated according tothe discharge characteristics of the gate, and plotted in both the regime (Figure 5) and effi-ciency charts (Figure 6). Points B and C refer to design conditions for A = 4.50 (F = 6.02,S = 3.30, � = 0.57), and A = 5.21 (F = 7.52, S = 4.69, � = 0.64), respectively. By increas-ing the flow rate, the discharge characteristics lead to the limited working conditionsdenoted with b (A = 4.50; F = 4.07, S = 1.35, � = 0.35), and c (A = 5.21; F = 5.254,S = 2.10, � = 0.46). For the considered geometries, the gain in terms of flow rate was con-sistent (about 145 percent), whereas a 30-35 percent efficiency reduction has to be consid-ered.

Present results indicate that existing stilling basins may therefore be used even forflow rates much larger than the design value, with an appreciable residual efficiency.This corresponds to a direct increment in the return period of the critical event for the

5.0

4.0

3.0

2.0

1.0

0.02 4 6 8

F

Design conditions

Limiting conditions

A=4.50

A=5.21

S

c

b

C

B

Figure 5. Working conditions for stilling basin equipped with standard crest.


waterwork. On the other hand, from a design point of view, Equation 2 can be usedinstead of Equation 1 with an appreciable reduction of the dimensionless step height, i.e.of the construction cost.

3.2. Local measurementsLocal measurements, in terms of velocity fields and bottom pressure, have been carriedout in order to relate the results presented in the previous section of this paper to theflow field hydrodynamics.Velocity measurements in the limiting conditions for four S values (1.5, 2.5, 3.5, and

4.0), are plotted in Figure 7. The supercritical stream behaves like a plane turbulent jet,sweeping over the step and generating an evident recirculation zone (bottom vortex).The jet, sandwiched between the surface roller and the bottom vortex, reaches a maxi-mum elevation and finally impinges on the bed of the downstream channels.For the lowest S value (i.e. S = 1.5) the current separates approximately 0.15cm down-

stream of the step, and the longitudinal extension of the bottom vortex is 0.15m. Forlarger S, both location and vertical extension of the bottom vortex change. The currentseparates closer to the positive step for the increasing S, whereas the vertical extensionreduces when S is increased.For the same S values, Figures 8-11 show the velocity field closer to the step, the rms

distributions, and the spatial correlation functions of the turbulent pressure fluctuations.The presence of the bottom vortex induces a local increment in the rms pressure distribu-tions. Similar results have been found by Kiya et al [5] in studying the separation bubbleover a two-dimensional blunt flat plate. We note that in the case of S = 4.0 only theoccurrence of the local maximum in the rms distribution witness the presence of the bot-

0.7

0.5

0.3

0.12 4

c

b

C

B

86F

Design conditions

Limiting conditions

A=4.50

A=5.21

Figure 6. Efficiency for stilling basin equipped with standard crest.


tom vortex, probably because of the small extension of the vortex compared with thevertical location of the first velocity measurement point.

0.10

0.05

0.00

y(m)S=1.5

-0.3 -0.2 -0.1 0.1 0.2x (m)

x (m)

0.3 0.4 0.5 0.6 0.70

0.10

0.05

0.00

y(m)S=2.5

-0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.70

x (m)

0.10

0.05

0.00

y(m)S=3.5

-0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.70

x (m)

0.10

0.05

0.00

y(m)S=4.0

-0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.70

Figure 7. Velocity vector plots.


The presence of the bottom vortex induces a sign change in the spatial correlation ofpressure signals. In the case of S = 2.5 and S = 3.5 the two zero points allow exact local-ization of this vortex. As far as S = 4.0 is concerned, the spatial pressure correlationappears to confirm the hypothesis of a presence of a small separation zone not detachedby the velocity measurements.

0.050

0.025

0.000

y(m)

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

0.03

0.02

0.01

0.00

p’(m)

0 0.05 0.1 0.15x (m)

0.2 0.25 0.3

1.0

0.5

0.0

-0.5

r(-)

Figure 8. Velocity vector plot, pressure fluctuation, spatial correlation for S = 1.5.


0.10

0.05

0.00

y(m)S=1.5

-0.3 -0.2 -0.1 0.1 0.2x (m)

x (m)

0.3 0.4 0.5 0.6 0.70

0.10

0.05

0.00

y(m)S=2.5

-0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.70

x (m)

0.10

0.05

0.00

y(m)S=3.5

-0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.70

x (m)

0.10

0.05

0.00

y(m)S=4.0

-0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.70



Both pressure and velocity measurements allow to attribute the displacement of thelimiting curve from the design one to the strength and location of the bottom vortex. Forsmall S values (S = 1.5) the strength of the vortex is appreciable, but is located far fromthe positive step. For intermediate S values (i.e. S = 2.5-3.5) the vortex does not reduceits intensity, and is localized very close to the step. Finally, for the large S value, it tends

0.050

0.025

0.000

y(m)

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

0.03

0.02

0.01

0.00

p’(m)

0 0.05 0.1 0.15x (m)

0.2 0.25 0.3

1.0

0.5

0.0

-0.5

r(-)



to disappear. Therefore, it follows that such coherent structures play a key rule in stabi-lizing the hydraulic jump in the basin, and for its contribution in the whole dissipativeprocess.

0.050

0.025

0.0000 0.05

y(m)

p’(m)

0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15x (m)

0.2 0.25 0.3

0 0.05 0.1 0.15x (m)

0.2 0.25 0.3

0.03

0.02

0.01

0.00

1.0

0.5

0.0

-0.5

r(-)

Figure 11. Velocity vector r plot, pressure fluctuation, spatial correlation for S = 4.0.


4. ConculsionsThe present paper concerns the working conditions of several stilling basins with posi-tive step and supercritical downstream flow conditions. Regression expressions indimensionless variables, based on the experimental results, are proposed to univocallyindividuate the limiting working conditions, and to evaluate the efficiency of the water-work. Such equations can be directly used for design purposes. Local velocity and pres-sure measurements show the key role played by a bottom vortex downstream of the posi-tive step in stabilizing the hydraulic jump in the basin and contributing to the dissipativeprocess.

NotationA = dimensionless drop of inflow zoneb = channel width (m)F = Froude numberg = gravity (m/sec2)h = water surface depth (m)H = total head (m)s = step height (m)S = dimensionless step heightu = depth-averaged velocity (m/sec)x = longitudinal coordinate (m)y = vertical coordinate (m)z = drop of inflow zone (m)� = efficiency

[subscripts]1 = upstream2 = downstream

References[1] Carravetta, A, Capuano, D & Vacca, A, ‘B-jump at the positive step of a stillingbasin’, Proceedings, XXX IAHR Congress, (C), pp213-219, 2003.

[2] Hager, W H & Bretz, N V, ‘Hydraulic jumps at positive and negative steps’, J HydrRes, 24(4), pp237-253, 1986.

[3] Hager, W H & Sinniger, R, ‘Flow characteristics of the hydraulic jump in a stillingbasin with an abrupt bottom rise’, J Hydr Res, 23(2), pp101-113, 1985.


[4] Hager, W H, ‘Energy dissipators and hydraulic jumps’, Kluwer AcademicPublishers, Dordrecht, Netherlands, 1992.

[5] Kiya, M & Sasaki, K, ‘Structure of a turbulent separation bubble’, J Fluid Mech,137, pp83-113, 1983.

[6] Muskatirovic, D & Batinic, B, ‘The influence of abrupt change of geometry onhydraulic regime characteristics’, Proceedings, XVII IAHR Congress, (2), pp397-404,1977.

[7] Nebbia, G, ‘Sui dissipatori a salto di Bidone. Ricerca sperimentale’, L’EnergiaElettrica, (6), pp327-355 (in Italian), 1940.

[8] Mossa, M, ‘On the oscillating characteristic of hydraulic jumps’, J Hydr Res, 37(4),pp541-558, 1999.

[9] Mossa, M, Petrillo, A & Chanson, H, ‘Tailwater level effects on flow conditions atan abrupt drop’, J Hydr Res, 41(1), pp1-13, 2003.

[10] Quraishi, A A & Al-Brahim, A M, ‘Hydraulic jump in sloping channel with posi-tive or negative step’, J Hydr Res, 30(6), pp769-782, 1993.

Hydraulic design of stilling basins in steep channels

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