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ENERGY DISSIPATION IN THE STILLING BASIN DOWNSTREAM OF BLOCK RAMPS

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ENERGY DISSIPATION IN THE STILLING BASIN DOWNSTREAM OF BLOCK RAMPS Powered By Docstoc
					     ENERGY DISSIPATION IN THE STILLING BASIN DOWNSTREAM OF BLOCK
                 RAMPS IN PRESENCE OF ROCK MADE SILLS

                                        S. Pagliara1 and M. Palermo2
            1 Department of Civil Engineering, University of Pisa, Italy, Via Gabba 22, 56122, Pisa
            2 Department of Civil Engineering, University of Pisa, Italy, Via Gabba 22, 56122, Pisa

Abstract: The dissipative process is one of the main topics for river engineers. It is deeply affected by both river
morphology and the geometric configuration of the structures which can eventually be present in the river branch. In
presence of a block ramp, previous studies allowed to analyze the energy dissipation mechanism for prismatic channels.
The analysis was conducted for both submerged and free hydraulic jumps located at the toe of the block ramp with
different stilling basin materials and different scale roughness conditions for scour equilibrium configuration, but in the
absence of any protection structure in the stilling basin. Conversely, the aim of the present study is to analyze the
dissipative process which occurs in correspondence and downstream of a block ramp when a rock made sill is located in
the stilling basin. Moreover, the analysis of the dissipative process was conducted varying the spatial positions of the
sill and the results were compared with the cases where no protection sills are present. The tests were performed using
different stilling basin materials and varying the ramp slope. Moreover, in all the tests, the hydraulic jump was entirely
located in the stilling basin, never submerging the ramp toe.

INTRODUCTION

The energy dissipation which occurs in correspondence of hydraulic structures is a fundamental topic for hydraulic
engineers. Different types of structures produce different dissipative mechanisms which has to be carefully analyzed for
their optimal design. Namely, block ramps are peculiar hydraulic structures which produce high energy dissipation.
They are structures made of loose or fixed blocks and either a fixed or a mobile stilling basin can be present
downstream. They have become more popular in the last decades as they can assure a great energy dissipation and, in
the meantime, they have the characteristic to be eco-friendly structures.
Generally the approaching flow is in sub-critical condition and a passage from sub- to super-critical condition occurs in
correspondence with the ramp entrance. The sudden slope variation downstream of the block ramp and the downstream
hydraulic conditions in the stilling basin determine a further passage from super- to sub-critical condition resulting in a
hydraulic jump which can be entirely localized in the stilling basin or partially submerge the ramp. The presence of a
hydraulic jump in the downstream stilling basin causes a bed erosion in the case in which it is movable. The scour
process has to be carefully controlled in order to avoid structural risks that can even lead to a structural collapse. The
optimal functionality of the ramp is assured if the ramp bed is stable. Thus, one of the main problem which was studied
and solved in the past is the ramp stability (see for example Whittaker and Jäggi 1986 and Robinson et al. 1997). In the
case of mobile bed, the erosion occurring in the downstream stilling basin is another important factor which has to be
carefully analyzed. In the last years, many studies have been conducted in order to understand the erosive mechanism
downstream of hydraulic structures (among these Bormann and Julien 1991, Breusers and Raudkivi 1991, Hoffmans
and Verheij 1997, Hoffmans 1998, D’Agostino and Ferro 2004, Dey and Raikar 2005). More recently, scour
downstream of block ramps was deeply analyzed both in the case in which protection structures are present or absent in
the stilling basins. Pagliara (2007) analyzed the scour mechanism in various geometric and hydraulic conditions
furnishing useful relationships in order to calculate the scour lengths. Successively, Pagliara and Palermo (2008a-b)
studied the effect of the presence of different sills located in various spatial positions in the stilling basin in order to
reduce the maximum scour depth and the scour hole length. The dissipative process occurring in correspondence of a
block ramp was deeply analyzed in different hydraulic conditions and geometric configuration. Pagliara and
Chiavaccini (2006) analyzed the energy dissipation occurring in correspondence with the block ramp between the
entering section and the toe of the ramp. They conducted experiments for fixed stilling basins and in presence of a
hydraulic jump entirely occurring downstream of the ramp itself. Successively, Pagliara et al (2008) extended the
analysis of the dissipative process to the case in which the stilling basin was movable and the hydraulic jump
submerged the ramp. Moreover, they analyzed the complete energy dissipation process as they evaluated the energy
dissipation between the entering section of the ramp and downstream of the hydraulic jump.
No studies known by authors deal with the energy dissipation process in correspondence and downstream of a block
ramp when protection structures, namely rock sills are located in the stilling basin. The present paper aims to evaluate
the energy dissipation occurring between the entering section of the ramp and downstream of the hydraulic jump
varying the spatial positions of rock made sills located in the stilling basins. Moreover, both the energy dissipations
occurring on the ramp and in the stilling basin were evaluated in order to understand each single contribute to the entire
dissipative process.

EXPERIMENTAL SET-UP

Experiments were conducted in one channel whose geometric dimensions are: 0.25 m wide, 3.5 m long and 0.30 m
high. The ramp was simulated using an iron sheet on which stones were glued. The stones used for the ramp had the
following granulometric characteristics: D50 = 0.01046 m, D65 = 0.01094 m, D90 = 0.0117 m and σ=(D84/D16)0.5=1.17.
Three different ramp slopes i were tested: 0.25, 0.125 and 0.083. The mobile bed was simulated using two different
granular materials, m1 and m2, both non-uniform, whose main granulometric characteristics are synthesized as follows:
for material m1 d50=0.0053 m, d90=0.0105 m and σ=(d84/d16)0.5=1.8, whereas for material m2 d50=0.0051 m, d90=0.0168
m and σ=(d84/d16)0.5=2.8. The rock made sill was simulated using crushed rocks whose mean diameter was 0.046 m.
The rock made sills were located in the stilling basin in different spatial positions. Some preliminary tests were
conducted without any type of protection (reference test) in order to evaluate the energy dissipation in absence of sills
and in the same hydraulic and geometric conditions. Moreover, the preliminary tests allowed to evaluate the average
maximum scour depth zm (obtained averaging the transverse depth measurements in the section of maximum scour), and
the scour hole length l0 (see Fig. 1a). The sills were located in two different vertical positions and four different
longitudinal positions. The vertical positions Zop=zop/zm tested were 0 and 0.5, in which zop is the vertical position of the
upper sill corner point measured from the original bed level and zm is the maximum average scour depth for the
respective reference test. The longitudinal positions λ=xs/l0 tested were 0.25, 0.5, 0.75 and 1, in which xs is the
longitudinal position of the protection structure measured from the ramp toe and l0 the scour hole length of the
respective reference test (see Fig. 1b). Prior to each experiment the channel bed was carefully levelled. When the
asymptotic scour equilibrium was reached, the bed morphology and the water depths were measured. Particular
attention was paid in measuring the water depth h1 in section 1-1, which is the water depth at the ramp toe, and h2 in
section 2-2 which is the water depth downstream of the hydraulic jump (see Fig. 1). All tests were conducted in clear
water conditions and the discharge varied between 2.9 and 9.3 l/s. Moreover, all the experiments were done in
intermediate scale roughness condition (see Pagliara and Chiavaccini 2006), thus for 2.5<k/D50<6.6, where k is the
critical depth. In Fig. 2a-b two pictures of the experimental apparatus are shown. In fig. 2a the rock made sill is located
at Zop=+0.5 and λ=1 and in Fig. 2b Zop=+0.5 and λ=0.25.



                                            0              1                                2

                                        k
                                                                      l0
                                  (a)
                                        H
                                                      h1                                        h2
                                                                           zm
                                            0              1                                2
                                            0              1                                2

                                        k
                                                                      ls
                                  (b)
                                        H                        xs
                                                      h1                                        h2
                                                               zms              zop

                                            0              1                                2




 Figure 1 Definition sketch of (a) ramp in reference test condition and (b) with sill protection with the indication of the main
                                             geometric and hydraulic parameters
                   Figure 2 Pictures of experimental apparatus: (a) view from upstream and (b) side view

RESULTS AND DISCUSSION

The energy dissipation between the sections 0-0 and 2-2 was analyzed in presence of rock made sill located in the
stilling basin in different spatial positions and compared with the respective dissipation obtained in preliminary
reference tests. The data relative to reference tests confirmed the findings of Pagliara et al (2008), who furnished an
equation by which it is possible to estimate the relative energy dissipation ΔE2=(E0-E2)/E0, in which E0=1.5k+H is the
total upstream energy and E2=h2+q2/(2gh22) is the energy at downstream end of jump, where H is the ramp height and
q is the unit discharge. Pagliara et al. (2008) analyzed the dissipative phenomenon both in the case in which the
hydraulic jump submerges the ramp and in the case in which it is entirely located in the stilling basin, proposing the
following formula:


ΔE2 = A + (1 − A)e( B )k / H                                                                                           (1)

In which A and B are parameters depending on the scale roughness and the submergence condition of the ramp. In case
of intermediate scale roughness condition and for hydraulic jump entirely located in the stilling basin, A=0.249 and
B=-1.863. Note that in the tested range ΔE2 does not depend on the uniformity of stilling basin material and on the ramp
slope.
A preliminary analysis was conducted in order to understand if there is any effect of non uniformity in the dissipative
process being the same hydraulic conditions, geometric configuration and location of the sill in the case of either m1 or
m2 was the stilling basin material. It was experimentally proved that the effect of material non uniformity is negligible
also in presence of a protection structure in the stilling basin. Successively, the data were distinguished for various Zop
and i values and for all λ tested, in order to put in evidence the dependence of the dependent variable ΔE2 on these
parameters. Figure 3 shows the result of the comparison.

                                 1
                                         ΔE 2
                                                                                  Equation (1) for IR
                                                                                  i=0.25, Zop=+0.5
                                                                                  i=0.25, Zop=0
                               0.8
                                                                                  i=0.125, Zop=+0.5
                                                                                  i=0.125, Zop=0
                                                                                  i=0.083, Zop=+0.5
                                                                                  i=0.083, Zop=0
                               0.6




                               0.4



                                                                                                  k/H
                               0.2
                                     0          0.2   0.4   0.6   0.8   1   1.2   1.4       1.6         1.8

                                     Figure 3 ΔE2(k/H) for various i and Zop and all λ tested

It is worth noting that in the case in which a stilling basin is protected by a rock made sill, the energy dissipation
between sections 0-0 and 2-2 is slightly bigger than in the case in which the stilling basin is unprotected. This mainly
due to the fact that the sill presence partially deflects the flow creating a local recirculation upstream of the structure
itself which contributes to dissipate energy. Moreover, it is clearly visible that practically there is no difference in data
trend varying λ and Zop in the tested range. Thus, it can be stated that the effect of the sill position on the dissipative
phenomenon is negligible. As the differences in energy dissipation between the reference tests (whose trend is
represented by Eq. (1) in Fig. 3) and the respective tests conducted in the same geometric and hydraulic conditions but
in presence of a rock sill is very slight, Eq. (1) can satisfactorily estimate also the data relative to the last case. The
comparison between measured and calculated (with Eq. 1) values of the variable ΔE2 for protected basins is shown in
Fig. 4.
                                 1

                                          ΔE 2 meas

                                0.8



                                0.6


                                                                                                     data
                                0.4                                                                  perfect agreement
                                                                                                     20% deviation


                                0.2

                                                                                                                 ΔE 2 calc
                                 0
                                      0                        0.2          0.4          0.6         0.8                          1

   Figure 4 Comparison between measured and calculated (with Eq. 1) values of the variable ΔE2 for protected basin tests

The analysis of the dissipative process was further specialized and developed. Especially for practical purposes it is
very useful to know where the energy is mainly dissipated, namely on the ramp itself or in the stilling basin. Thus the
following non dimensional variables were introduced and estimated: ΔE1-2=(E1-E2)/E0 and ΔE’1-2=(E1-E2)/(E0-E2). ΔE1-2
represents the amount of the total upstream energy (in section 0-0) dissipated in the stilling basin (between sections 1-1
and 2-2), whereas ΔE’1-2 represents the amount of the total energy dissipation (between sections 0-0 and 2-2) which is
dissipated in the stilling basin (between sections 1-1 and 2-2). E1 is the energy in section 1-1 evaluated using Eq. (2)
proposed by Pagliara and Chiavaccini (2006), who found that the relative energy dissipation between section 0-0 and 1-
1 can be expressed as follows:

        E0 − E1
ΔE1 =           = A + (1 − A)e( B + C ⋅i ) k / H                                                                                      (2)
          E0

Where A,B,C are parameters depending on the scale roughness conditions of the ramp. In particular for intermediate
scale roughness condition Pagliara and Chiavaccini (2006) found that A=0.25, B=-1.2 and C=-12.0. Based on Eq. (2)
and knowing the hydraulic and geometric conditions (discharge, ramp configuration and material) one can easily derive
the value of E1. It is worth noting that ΔE1-2= ΔE2- ΔE1, in which ΔE1 is evaluated using Eq. (2).
Also in this case the analysis was conducted by steps. It was experimentally proved that the effect on non-uniformity σ,
Zop and λ on both the dependent variables ΔE1-2 and ΔE’1-2 can be considered negligible for practical purposes. Both the
variables ΔE1-2 and ΔE’1-2 were plotted versus k/H for all Zop and λ tested as shown in Figure 5a-b respectively.
                                      1
                                                                                   (a)
                                              ΔE 1-2


                                  0.8
                                                                                                            data
                                                                                                            Eq. (3)

                                  0.6




                                  0.4



                                  0.2

                                                                                                                     k/H

                                      0
                                          0              0.2         0.4   0.6     0.8     1   1.2         1.4              1.6

                                      1
                                              ΔE ' 1-2                            (b)
                                                                                                            data
                                                                                                            Eq. (4)
                                  0.8



                                  0.6



                                  0.4



                                  0.2
                                                                                                                     k /H



                                      0
                                          0              0.2         0.4   0.6     0.8     1   1.2         1.4              1.6

                   Figure 5 (a) ΔE1-2 (k/H) and (b) ΔE’1-2 (k/H) for all the data relative to protected basin
For both the variables ΔE1-2 and ΔE’1-2 two different experimental equations are proposed:

             E1 − E2
ΔE1− 2 =             = 0.42 ⋅ e −1.77⋅( k / H )                                                                               (3)
               E0

and

             E1 − E2
ΔE '1− 2 =           = 0.53 ⋅ e −1.1⋅( k / H )                                                                                (4)
             E0 − E2

both valid for 0.2<k/H<1.6. In figure 6a-b the comparison between measured and calculated values with Eq. (3) and (4)
of the variables ΔE1-2 and ΔE’1-2 is shown.

                                  0.3
                                            ΔE 1-2 meas                       (a)




                                  0.2




                                                                                                 data
                                  0.1                                                            perfect agreement
                                                                                                 30% deviation




                                                                                                         ΔE 1-2 calc
                                    0
                                        0                         0.1                     0.2                           0.3

                                  0.5
                                                                              (b)
                                            ΔE ' 1-2 meas


                                  0.4



                                  0.3



                                  0.2                                                           data
                                                                                                perfect agreement
                                                                                                30% deviation
                                  0.1

                                                                                                        ΔE ' 1-2 calc
                                    0
                                        0                   0.1         0.2         0.3          0.4                    0.5



      Figure 6 (a) Comparison between measured and calculated (with Eq. 3) values of the variable ΔE1-2 and (b) between
         measured and calculated (with Eq. 4) values of the variable ΔE’1-2 for all the data relative to protected basins


From Figure 5a-b it is evident the effect of the presence of a block ramp on the entire dissipative process. In fact, from
fig. 5a, it is clearly visible that in the stilling basin it can be dissipated an amount of available energy which is less than
0.2 E0. The amount of energy dissipated in the stilling basin decreases increasing the ratio k/H and it results to be
independent from the parameters Zop and λ. Moreover, Figure 5b proves that the most part of energy dissipation occurs
on the ramp itself as the energy which can be dissipated in the stilling basin is always less than the 40% of the total
energy dissipation. This last result has a considerable practical importance as it proves that block ramps are structures
which can be satisfactorily used to dissipate energy. The energy dissipation process mainly occurs on them even if in
the stilling basin are located rock made sills which can be used to reduce the scour lengths, but which have not a
substantial effect on the dissipative process, if compared to the condition in which they are not present.

CONCLUSIONS

In the present paper the energy dissipation process in presence of both a block ramp and a protected granular stilling
basin was analyzed. The effect of the longitudinal and vertical position of rock made sills on the dissipative mechanism
was deepened. Namely, the energy dissipation between the upstream ramp section and downstream of the hydraulic
jump was evaluated and it was experimentally proved that the presence of protection structures slightly contributes to
increase the total amount of the dissipated energy. Moreover, a more detailed analysis was conducted to understand the
quantity of available energy which is dissipated on the ramp itself and in the stilling basin. The main result which was
achieved is that, in the tested range of parameters, in the stilling basin is dissipated less than 0.2E0. Moreover, if the
energy dissipation which occurs in the stilling basin is compared with that occurring both on the ramp and in the stilling
basin, it was proved that it decreases increasing the ratio k/H and it is always less than 0.4(E0-E2). The results found and
presented in this papers confirms that also in presence of a protected stilling basin, a block ramp plays a fundamental
role in the dissipative process as it mainly occurs on it.

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