# Energy Dissipation in Stilling Basins with Side Jets from Highly Convergent Chutes

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Aim and Scope

- Increasing the spillway capacity.
- Protecting the downstream toe of the dam abutments against potential scour caused by overtopping.
- Enhancing the reservoir storage by increasing the full supply level, preserving the existing freeboards and the former capacity of the spillway.

- To establish objective criteria for the suitable hydraulic conditions of the flow downstream from the stilling basin to enable the appropriate restitution of the flow to the riverbed according to widely accepted technical guidelines.
- To perform a conceptual study of the effect of key HCCs design parameters on the energy dissipation at the stilling basin.
- To assess the design adaptation needs of existing stilling basins depending on the increase in the outlet discharge.
- To obtain experimental data to calibrate and validate numerical models for future research.

## 3. Methodology

#### 3.1. Experimental Facility

- Maximum length of the weir (W
_{w}): 5 m - Height of the weir over the bottom of the stilling basin (H
_{w}): 1.5 m - Vertical upstream slope of the cross-section of the gravity dam
- Downstream slope of the cross-section of the gravity dam: 0.8 H:V
- Width of the stilling basin (W
_{b}): 1 m - Maximum length of the stilling basin (L
_{b}): 3.7 m - Maximum height of the sidewalls of the stilling basin (H
_{b}): 0.5 m

_{s}) and frontal (Q

_{f}) discharges were combined. In every test, the symmetry of the inlet flow at the stilling basin remained unchanged. Two vertical steel plates (inlet plates in Figure 2), transversely placed to the longitudinal axis of the gravity dam, were placed on both sides of the upstream area of the weir to maintain appropriate inlet conditions over the weir, i.e., to ensure an orthogonal direction of the inlet flow with respect to the longitudinal axis of the weir in all tests.

^{3}s

^{−1}.

#### 3.2. Instrumentation

- An electromagnetic flowmeter installed at the inlet pipe of the facility. The measured discharge was used as the variable controlling the inlet flow provided by the pumping system.
- An ultrasonic limnimeter for measuring the water level at the inlet tank, placed upstream of the gravity dam.
- A total of 21 dynamic pressure gauges located at the bottom of the stilling basin (Figure 4). The measurements analyzed in this study were those obtained from the 11 sensors located along the longitudinal axis of the basin.
- A set of three limnimeters attached to a movable carriage located at the stilling basin, 3.2 m downstream of the dam toe.
- An electronic limnimeter located upstream of the rectangular thin-plate weir at the returning channel, downstream of the model. This sensor provided an indirect measurement of the testing discharge through the calibrated rating curve of the weir.
- Photo and video cameras. The images showed the elapsed time of each test provided by the large chronometer located next to the right sidewall of the experimental facility.
- A self-programmed data acquisition system to gather real-time measurements of the devices. The system included acquisition cards controlled by a laptop computer.

#### 3.3. Research Approach

#### 3.3.1. Phase 1: Scope and Selection of Parameters

_{b}, H

_{w}, L

_{b}, and W

_{b}; the geometry of the HCCs corresponding to each configuration (B, C, and D); and the geometry of the gravity dam, including the shape of the weir, remained unchanged in every test. The size of the experimental facility limited the maximum suitable discharge to 0.15 m

^{3}s

^{−1}. The parameters that were modified during the tests were P, the ratio (K

_{Q}) between the discharge from the side jets (Q

_{s}) and the total discharge (Q), and the value of the angle of the bottom of the HCCs with respect the horizontal plane (α). The reference case for the comparison of each test was the one corresponding to frontal discharge only (i.e., Q

_{f}= Q), with energy dissipation achieved by a classical hydraulic jump.

#### 3.3.2. Phase 2: Determination of the Acceptance Criteria for the Energy Dissipation

_{V}) of the dynamic pressure measured at the pressure gauges located along the longitudinal axis of the stilling basin. The objective of this selection was to characterize the degree of turbulence at the end of the basin. For this purpose, we decided to use C

_{V}because it could be obtained from the measurements of the dynamic pressure (p). To apply a criterion based on the C

_{V}index, we needed to determine the reference values of the index according to widely accepted technical guidelines. As such, a set of tests with only frontal discharge (i.e., without discharge from side jets) was performed at the experimental facility. The tailwater elevation downstream of the stilling basin was imposed by the control gate for different discharges between 0.010 and 0.150 m

^{3}s

^{−1}until a stable hydraulic jump was generated with its upstream end located at the toe of the dam. The water depth downstream the jump was termed d

_{f2}. Applying the hydraulic jump equation [24] between the inlet (subscript 1) and outlet (subscript 2) sections of the hydraulic jump, the water depth of the flow entering the hydraulic jump (d

_{f1}) could be calculated as follows (Equation (1)):

_{f2}is the Froude number of the flow downstream of the hydraulic jump, which can be obtained through:

_{f2}) corresponding to the inlet cross-section of the basin is related to the discharge (Q) according to Equation (3):

_{f2}and Q were known through the measurements for the tests (W

_{b}is constant and equal to 1 m), V

_{f2}was obtained using Equation (3). Then, substituting V

_{f2}in Equation (2), F

_{f2}was calculated (Equation (2)). Finally, d

_{f1}and V

_{f1}were determined applying Equations (1) and (3), respectively (changing subindex 2 for 1 in Equation (3)).

_{f1}and V

_{f1}). This was considered necessary due to the low and fluctuating values of d

_{f1}that were reached during the tests. This finding prevented the accurate measurement of the values of d

_{f1}, so we used the more reliable measurements of the water depth registered downstream of the hydraulic jump.

_{f1}, V

_{f1}, and F

_{f1}were known, the length of the basin with only frontal discharge (L

_{f}) was obtained following the recommendations of BOR [19] according to Figure 5.

_{V}(Equation (4)) of each of the series of records corresponding to each device.

_{p}is the standard deviation of the pressure values, and $\overline{p}$ is the mean of the pressure values.

_{V}values in adjacent devices was used to calculate the C

_{V}corresponding to the length of the stilling basin recommended by the BOR (C

_{Vf}). This C

_{Vf}was adopted as the reference index for each tested discharge (Q, coincident with Q

_{f}in phase 2). Next, the sets of pairs (Q, L

_{f}) and (Q, C

_{Vf}) could be obtained and applied as an acceptance criterion of the energy dissipation of the basins with inlet flows from HCCs. In this phase, the maximum discharge was limited by the length of the jump. Thus, for discharges above 0.147 m

^{3}s

^{−1}, this length was so high that the jump was out of the area of the basin equipped with pressure sensors and it was not possible to obtain the C

_{Vf}. The total of 49 tests were conducted in phase 2.

#### 3.3.3. Phase 3: Core of the Experimental Research

_{T}): 0.010, 0.025, 0.050, 0.100, and 0.150 m

^{3}s

^{−1}. The target discharge was defined as the flowrate that was required by the pumping system for the inlet discharge at the facility. However, the variability in the discharge values registered by the flowmeter necessitated a more reliable measurement of the flow discharge (Q). The values of Q

_{T}and Q were similar for each test.

_{T}values indicated above were applied for every geometrical configuration (i.e., at every couple of values of α and K

_{Q}) when possible. In some cases, for the highest value of Q

_{T}(0.150 m

^{3}s

^{−1}), the maximum sidewall height was not high enough to obtain the needed water depth to produce a suitable dissipation of energy. Conversely, the tests with a lower value of Q

_{T}(0.010 m

^{3}s

^{−1}) were considered useless after the review of the registered pressure data. Therefore, the tests corresponding to this target discharge were not considered in the discussion.

_{Vf}(corresponding to the acceptance criteria for each Q) between the C

_{V}registered in the consecutive pressure gauges located along the longitudinal axis of the basin (i.e., gauges SP_03, SP_07, SP_10, SP_13, SP_15, SP_16, SP_17, SP_18, SP_19, and SP_20). An example of this is shown in Figure 6.

_{f2}, L

_{f}) to evaluate the required size depending on the inlet conditions.

## 4. Results and Discussion

_{Q}) are discussed; and (3) general conclusions about the flow pattern observed during the tests are provided.

#### 4.1. Energy Dissipation Criteria

_{V}decreases with increasing distance from the dam toe. As expected, $\overline{p}$ also increases with L given that the water depth is higher when subcritical flow conditions are achieved. The C

_{V}value that strictly fulfills the acceptance criteria for each particular discharge (Q) can be obtained through a linear interpolation between the immediately higher and lower values of C

_{Vf}in Figure 6 as the intersection between the horizontal line (C

_{Vf}) and the C

_{V}corresponding to each test.

_{Vf}with Q (coincident with Q

_{f}in this phase) shows that the interval of the registered values ranges between 0.5% and 3.0%. This evolution shows a gradual decrease as Q increases in the range of flow rates used in the tests. The C

_{Vf}values were not reliable for Q below 0.034 m

^{3}s

^{−1}. As described in Section 3.3, for discharges above 0.147 m

^{3}s

^{−1}, the length of the hydraulic jump exceeded the area of the basin where dynamic pressures could be registered. Therefore, the C

_{Vf}values that could be experimentally obtained ranged from 0.034 and 0.147 m

^{3}s

^{−1}. Within this interval, the C

_{Vf}could be fitted to a fourth-grade polynomic expression (Equation (5)) with a coefficient of determination of 0.96.

^{3}s

^{−1}, the C

_{Vf}considered for the acceptance criteria was constant, with a value of 3.05% (i.e., the minimum available discharge in this phase). As the maximum discharge used in phase 3 was 0.162 m

^{3}s

^{−1}, which is close to 0.147 m

^{3}s

^{−1}, a constant C

_{Vf}value of 0.5 % was adopted for discharges higher than 0.147 m

^{3}s

^{−1}. The criteria to assess the energy dissipation can be modified depending on the conditions (such as geological or environmental conditions, the potential scour, or others) of the downstream riverbed. However, as indicated in the methodology, in this case, the intention was to establish a consistent approach with the widely accepted criteria for Type I basins.

_{f}) for different discharges are shown in Figure 7. The results were adjusted to a simple linear regression (Equation (6)):

#### 4.2. Influence of the Parameters on the Performance of the Stilling Basin

_{Q}are jointly analyzed, specifically for the cases where P was more effective in terms of energy dissipation.

#### 4.2.1. Analysis of the Height of the Bottom of the HCCs over the Bottom of the Basin (P)

_{f2}(termed as condition I), L* < L

_{f}, (condition II), and both I and II, for different values of P and Q

_{T}. The latter condition (i.e., I and II) represents the percentage of cases where the size of the basin needed to dissipate the energy with side inlets from HCCs is smaller than the size with only frontal flow (i.e., with a dissipation achieved by a hydraulic jump). For this analysis, the freeboard needed for the sidewall height was neglected, so that the comparison focused only on the water depth and the length of the basin (note that the width of the basin was constant for every test) required to fulfill the acceptance criteria for the dissipation of energy.

_{f2}with respect to the mean value of d* ($\overline{{d}_{f2}}/\overline{{d}^{*}}$), and the mean value of L

_{f}with respect the mean value of L* ($\overline{{L}_{f}}/\overline{{L}^{*}}$).

^{3}s

^{−1}) among the tests conducted. Thus, for representative values of Q

_{T}, and when P equals zero, 56.8% to 70% of the tests complied with d* < d

_{f2}. Likewise, 75% to 100% of the tests complied with L* < L

_{f}, and 39.4% to 47.8% fulfilled both conditions. Therefore, if P is zero, i.e., if the bottom of the HCCs enters the basin at the same elevation of the sill of the basin, it is more likely that a smaller basin would be required. In other words, HCCs can be used to increase the capacity of existing spillways without any change in the original basin, especially when P is zero. In most of the tests performed with P equaling 0.20 m, both d* and L* were higher than when P was zero. This finding led to infer that the higher the depth of entry to the basin, the greater the dissipation of energy. This was observed especially when the basin operated in submergence conditions (i.e., when the tailwater level was high enough that the side jets impinged into the water mass).

_{f2}and L

_{f}, respectively. In the table, values higher than one indicate that the tailwater depths and lengths of the basin (when HCCs are in operation) are lower than those corresponding to a classical hydraulic jump with only frontal flow for the same Q

_{T}. Focusing on representative target discharges (i.e., 0.025, 0.050, and 0.100 m

^{3}s

^{−1}), and considering the $\overline{{d}_{f2}}/\overline{{d}^{*}}$ rate, the ranges of values are 0.93 to 1.09 for P = 0 m, 0.96 to 1.08 for P = 0.1 m, and 0.90 to 0.94 for P = 0.2 m. The $\overline{{L}_{f}}/\overline{{L}^{*}}$ rate has a wider range of variation: 1.30 to 1.54 for P = 0 m, 0.64 to 1.24 for P = 0.1 m, and 0.58 to 1.18 for P = 0.2 m. Thus, the results presented in Table 3 indicate that the differences between the height of the basin (i.e., d* and d

_{f2}) for HCCs or hydraulic jump are not significant. Conversely, the effect of the operation of HCCs can achieve reductions of up to 54% of the required length of the basin, which can be meaningful from an economical point of view in actual cases. However, in some of the tests with P values of 0.10 or 0.20 m, reductions in d* and L* were also achieved; so, in some cases, it may be possible to design HCCs with inlets raised from the bottom of the basin that provide good performance.

#### 4.2.2. Influence of the Angle between the Bottom of the HCCs with Respect to the Horizontal Plane (α) and the Discharge Rate of the Side Jets (K_{Q})

_{Q}. As shown in Figure 9, which depicts results of the tests for a P of zero, most of the highest reductions in L* occurred for the lowest value of α (i.e., 10°). Such reductions are especially relevant for higher values of K

_{Q}(i.e., 0.75 and 0.80). The possible reason for this result may be the higher energy dissipation achieved by the impingement of the side jets. Thus, the lowest value of α (10°) more directly impinges the side jets, which produces a quasi-frontal impact. In addition, the higher the values of K

_{Q}, the higher the proportion of the discharge involved in the impact dissipation of the side jets in relation to the frontal discharge. Therefore, the results show that the combination of both effects has significative consequences for the reduction in L*.

_{f2}), with a usual range of variation in d*/d

_{f2}between 0.50 to 1.50. In general, with some exceptions (see Q

_{T}0.025 m

^{3}s

^{−1}and K

_{Q}0.8), the higher the α, the higher the d*. However, this tendency is not evident, as noted in the following cases: Q

_{T}0.1 m

^{3}s

^{−1}and K

_{Q}0.67, Q

_{T}0.1 m

^{3}s

^{−1}and K

_{Q}0.75, and Q

_{T}0.05 m

^{3}s

^{−1}and K

_{Q}0.5. However, no conclusive conclusions could be drawn about the effect of K

_{Q}on the value of d*.

_{f2}and L

_{f}, values (every filled circle below the dotted line in each figure). That is, it is highly probable that a smaller basin size can be found that can dissipate the energy. In other words, it may be possible to adapt an existing stilling basin to dissipate the energy of a larger outflow discharge without varying the size of the basin. This conclusion can be useful in cases where an increase in the capacity of the spillway is needed in gravity (or arch-gravity) dams with a stilling basin as the energy dissipator.

#### 4.3. Effect of Submergence on Flow Distribution

## 5. Conclusions

_{f}and d

_{f2}) of the Type I basins for a given flow discharge.

_{Q}was 0.8).

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{V} | coefficient of variation of the water pressure, expressed in percentage. |

C_{Vf} | coefficient of variation of the pressure downstream the BOR’s Type I stilling basin, expressed in percentage. |

d_{f1} | water depth of the flow entering the jump in BOR’s Type I basin. |

d_{f2} | water depth downstream of the BOR’s Type I basin. |

d* | water depth downstream of the basin after energy dissipation with side jets discharge. |

F_{f1} | Froude number at the entrance of the hydraulic jump. |

F_{f2} | Froude number downstream the hydraulic jump. |

H_{b} | maximum height of the sidewalls of the stilling basin, equals to 0.5 m. |

H_{w} | height of the weir over the bottom of the stilling basin, equals to 1.5 m. |

K_{Q} | discharge rate of the side jets (i.e., Q_{s}/Q). |

L | horizontal distance from the toe of the dam along the longitudinal axis of the basin. |

L_{b} | maximum length of the stilling basin of the experimental facility: 3.7 m. |

L_{f} | length of the basin recommended by the BOR criteria for Type I basins. |

L* | length of the basin required to a suitable energy dissipation with side jets discharge. |

p | pressure. |

$\overline{p}$ | mean of the pressure values. |

P | height of the step from the bottom of the basin to the bottom of the downstream section of the HCCs. |

Q | total discharge. |

Q_{f} | frontal discharge. |

Q_{s} | side discharge from the HCCs inlet. |

Q_{T} | target discharge. |

V_{f1} | velocity of the flow entering the jump in BOR’s Type I basin. |

V_{f2} | velocity of the flow downstream of the BOR’s Type I basin. |

W_{b} | width of the stilling basin, equals 1 m. |

W_{w} | maximum length of the weir, equals 5 m. |

α | angle of the bottom of the HCCs with respect the horizontal plane, projected in the front view vertical plane. |

σ_{p} | standard deviation of the pressure values. |

## References

- San Mauro, J.; Morera, L.; Salazar, F.; Rossi, R.; Toledo, M.; Morán, R.; Martínez, B.; Caballero, F.; Oñate, E. Modelación Física Y Numérica De Aliviaderos Con Cajeros Altamente Convergentes. In Proceedings of the III Jornadas De Ingeniería Del Agua, Valencia, Spain, 23–24 October 2013. [Google Scholar]
- Larese, A.; Salazar, F.; San Mauro, J.; Oñate, E.; Toledo, M.; Morán, R. Advanced Computational Methods for Dam Protections Against Overtopping. In Proceedings of the Protections 2018 (3rd International Conference on Protection against Overtopping), Grange-over-Sands, UK, 6–8 June 2018. [Google Scholar]
- Mauro, S.; Salazar, F. Mejora De La Seguridad Hidrológica E Incremento De La Capacidad De Embalse De Presas De Fábrica Mediante Aliviaderos Con Cajeros Altamente Convergentes. 2019. Available online: https://www.scipedia.com/public/Peraita_et_al_2019a (accessed on 1 October 2020).
- Lempérière, F.; Vigny, J.; Deroo, L. New Methods and Criteria for Designing Spillways could Reduce Risks and Costs Significantly; Hydropower & Dams: Wallington, UK, 2012; pp. 120–128. [Google Scholar]
- Hunt, S.L. Design of Converging Stepped Spillways. Ph.D. Thesis, Colorado State Univeristy, Fort Collins, CO, USA, 2008. [Google Scholar]
- Hunt, S.L.; Kadavy, K.C.; Abt, S.R.; Temple, D.M. Impact of Converging Chute Walls for Roller Compacted Concrete Stepped Spillways. J. Hydraul. Eng.
**2008**, 134, 1000–1003. [Google Scholar] [CrossRef] - Schleiss, A. From Labyrinth to Piano Key Weirs—A Historical Review. In Proceedings of the Labyrinth and Piano Key Weirs; Apple Academic Press: Palm Bay, FL, USA, 2011; pp. 3–15. [Google Scholar]
- Macián-Pérez, J.F.; Vallés-Morán, F.J.; Sánchez-Gómez, S.; De-Rossi-Estrada, M.; García-Bartual, R. Experimental Characterization of the Hydraulic Jump Profile and Velocity Distribution in a Stilling Basin Physical Model. Water
**2020**, 12, 1758. [Google Scholar] [CrossRef] - NVE. Guidelines for Embankment Dams. Guideline 4/2012. Norwegian Water Resources and Energy Directorate. 2012. Available online: https://www.nve.no/damsikkerhet-og-kraftforsyningsberedskap/damsikkerhet/regelverk/veileder-for-fyllingsdammer/ (accessed on 1 October 2020).
- Portland Cement Association. Design Manual for RCC Spillways and Overtopping Protection, 1st ed.; Portland Cement Association: Skokie, IL, USA, 2002; p. 100. [Google Scholar]
- FEMA. Technical Manual: Overtopping Protection for Dams; U.S. Department of Homeland Security: Washington, DC, USA, 2014.
- United States Bureau of Reclamation. Design of Small Dams; US Department of the Interior, Bureau of Reclamation: Washington, DC, USA, 1987.
- Morera, L.; San Mauro, J.; Salazar, F.; Toledo, M.Á. Highly-Converging Chutes as an Overtopping Protection for Concrete Dams: Physical and Numerical Modelling; Taylor & Francis Group: London, UK, 2015. [Google Scholar]
- Yang, J. Investigations at Vatnsfell. Int. Water Power Dam. Constr.
**2007**, 59, 9. [Google Scholar] - Zaitsoff, M. Overtopping modifications to Tygart Dam. In Proceedings of the National Dam Safety Technical Seminar: Overtopping Protection for Dams, Portland, OR, USA, 13–15 May 2003; pp. 20–21. [Google Scholar]
- Talbot, J.; Robinson, K.; Kadavy, K. Hydraulic Model Study of a Roller Compacted Concrete Stepped Spillway with Converging Chute Walls. In Proceedings of the Association of State Dam Safety Officials Annual Conference, Pittsburg, PA, USA, 7–10 September 1997. [Google Scholar]
- Hunt, S.L.; Temple, D.M.; Abt, S.R.; Kadavy, K.C.; Hanson, G. Converging Stepped Spillways: Simplified Momentum Analysis Approach. J. Hydraul. Eng.
**2012**, 138, 796–802. [Google Scholar] [CrossRef] - Hunt, S.L.; Kadavy, K.C.; Abt, S.R.; Temple, D.M. Impact of Converging Chute Walls for RCC Stepped Spillways. Impacts Glob. Clim. Chang.
**2005**, 1–12. [Google Scholar] [CrossRef] - Peterka, A.J. Hydraulic Design of Stilling Basins and Energy Dissipators; Department of the Interior, Bureau of Reclamation: Washington, DC, USA, 1978.
- Barjastehmaleki, S. Spillway Stilling Basins and Plunge Pools Lining Design. Ph.D. Thesis, University of Trieste, Trieste, Italy, 2016. [Google Scholar]
- Babaali, H.; Shamsai, A.; Vosoughifar, H. Computational Modeling of the Hydraulic Jump in the Stilling Basin with Convergence Walls using CFD Codes. Arab. J. Sci. Eng.
**2015**, 40, 381–395. [Google Scholar] [CrossRef][Green Version] - Vischer, D.; Hager, W. Energy Dissipators. Oceanogr. Lit. Rev.
**1996**, 1, 87. [Google Scholar] - Martín-Vide, J. The Design of Converging Overfall Spillways. Int. J. Hydropower Dams
**1995**, 2, 87. [Google Scholar] - Chanson, H. Hydraulics of Open Channel Flow; Elsevier: Amsterdam, The Netherlands, 2004. [Google Scholar]
- San Mauro, J.; Salazar, F.; Morán, R.; Peraita, J.; Toledo, M.Á.; Conde, M.J.; Flórez, V.; Labalde, B.; Alcalde, F. Aliviaderos Con Cajeros Altamente Convergentes. ¿Posible Solución Para La Presa De Oroville? In Proceedings of the V Jornadas de Ingeniería del Agua, A Coruña, Spain, 24–26 October 2017. [Google Scholar]

**Figure 1.**(

**a**) Scheme of the HCCs of a gravity dam from downstream [13]. (

**b**) View of one of the HCCs of Torre de Abraham Dam (Spain) in operation (courtesy of José R. González).

**Figure 2.**Experimental facility: (

**a**) 3D scheme with the main parts and the setup configurations A, B, C and D, and (

**b**) plan view and longitudinal cross-section.

**Figure 4.**Plan view of the location of the dynamic pressure devices at the bottom of the stilling basin. The flow traveled from left to right, being the left border of the dam toe.

**Figure 5.**Length of the Type I basin recommended by the BOR (Adapted from Ref. [19]).

**Figure 6.**Example of the determination of the required length of the HCCs basin (L*) in phase 3 tests. The figure shows the results obtained from the measurements of the dynamic pressure gauges located in the longitudinal axis of the basin: mean dynamic pressure ($\overline{p}$), standard deviation (σ

_{p}), and coefficient of variation (C

_{V}).

**Figure 8.**Combinations of d* (m) and L* (m) of the phase 2 tests conducted to formulate the energy dissipation criteria with only frontal flow, and the phase 3 tests that fulfilled such criteria with side jet flow.

**Figure 9.**The L*/L

_{f}(−) rate with respect to α (°) for tests with a P of zero. The figure is organized in a matrix layout, with vertical columns representing K

_{Q}(−) and horizontal rows Q

_{T}(m

^{3}s

^{−1}). Filled circle represent cases where d* < d

_{f2}; empty circles represent d* > d

_{f2}. The size of every circle represents the d*/d

_{f2}(−) rate.

**Figure 10.**d*/d

_{f2}(−) with respect to α (°) for tests when P is zero. The figure is organized in a matrix layout, with vertical columns representing K

_{Q}(−) and horizontal rows representing Q

_{T}(m

^{3}s

^{−1}). Filled circles represent cases where L

^{*}< L

_{f}; empty circles represent L* > L

_{f}. The size of every circle represents L*/L

_{f}(−).

**Figure 11.**Pictures showing the hydraulic conditions in a stilling basin with low ((

**a1**,

**a2**), views from downstream and left side, respectively) and high submergence ((

**b1**,

**b2**), same positions as a1 and a2, respectively) due to different tailwater elevations in the test with Q

_{T}= 0.050 m

^{3}s

^{−1}, α = 28° (configuration B), P = 0, and K

_{Q}= 0.80.

Configuration | α (°) | K_{Q} (−) | Number of Tests |
---|---|---|---|

B | 47 | 0.50 and 0.67 | 132 |

C | 28 | 0.50, 0.67, 0.75, and 0.80 | 256 |

D | 10 | 0.50, 0.67, 0.75, and 0.80 | 261 |

**Table 2.**Number of tests that met the energy dissipation criteria for different basin dimension conditions for different values of P.

Condition | I (d* < d_{f2}) | II (L* < L_{f}) | I and II | ||||||
---|---|---|---|---|---|---|---|---|---|

P (m) | 0.0 | 0.1 | 0.2 | 0.0 | 0.1 | 0.2 | 0.0 | 0.1 | 0.2 |

Q_{T} (m^{3} s^{−1}) | Number of Tests Fulfilling the Condition/Total Tests for Each P and Q_{T} (%) | ||||||||

0.010 ^{1} | 21/49 | 15/34 | 10/29 | 8/49 | 8/34 | 6/29 | 0/49 | 0/34 | 0/29 |

(42.9) | (44.1) | (34.5) | (16.3) | (23.5) | (20.7) | (0.0) | (0.0) | (0.0) | |

0.025 | 17/33 | 23/39 | 18/31 | 26/33 | 13/39 | 9/31 | 13/33 | 1/39 | 0/31 |

(51.5) | (59.0) | (58.1) | (78.8) | (33.3) | (29.0) | (39.4) | (2.6) | (0.0) | |

0.050 | 25/36 | 28/40 | 16/34 | 27/36 | 16/40 | 16/34 | 16/36 | 4/40 | 0/34 |

(69.4) | (70.0) | (47.1) | (75.0) | (40.0) | (47.1) | (44.4) | (10.0) | (0.0) | |

0.100 | 11/23 | 25/44 | 22/49 | 23/23 | 27/44 | 30/49 | 11/23 | 8/44 | 4/49 |

(47.8) | (56.8) | (44.9) | (100) | (61.4) | (61.2) | (47.8) | (18.2) | (8.2) | |

0.150 ^{2} | 0/0 | 0/4 | 0/1 | 0/0 | 4/4 | 1/1 | 0/0 | 0/4 | 0/1 |

(0.0) | (0.0) | (0.0) | (0.0) | (100.0) | (100.0) | (0.0) | (0.0) | (0.0) | |

All discharges | 74/141 | 91/161 | 66/144 | 84/141 | 68/161 | 61/144 | 40/141 | 13/161 | 4/144 |

(52.5) | (56.5) | (45.8) | (59.6) | (42.2) | (42.4) | (28.4) | (8.1) | (2.8) |

^{1}This target discharge was not be considered representative for the discussion as mentioned in Section 3.3.3.

^{2}Most of the tests performed for this target discharge did not meet the acceptance criteria due to the size limits of the facility so they were not considered statistically representative.

**Table 3.**Values of the rates between the mean value of d

_{f2}with respect to the mean value of d* ($\overline{{d}_{f2}}/\overline{{d}^{*}}$), and the mean value of L

_{f}with respect the mean value of L* ($\overline{{L}_{f}}/\overline{{L}^{*}}$) for every value of P.

P (m) | 0.0 | 0.1 | 0.2 | |||
---|---|---|---|---|---|---|

Q_{T} (m^{3} s^{−1}) | $\overline{{\mathit{d}}_{\mathit{f}2}}/\overline{{\mathit{d}}^{*}}$ | $\overline{{\mathit{L}}_{\mathit{f}}}/\overline{{\mathit{L}}^{*}}$ | $\overline{{\mathit{d}}_{\mathit{f}2}}/\overline{{\mathit{d}}^{*}}$ | $\overline{{\mathit{L}}_{\mathit{f}}}/\overline{{\mathit{L}}^{*}}$ | $\overline{{\mathit{d}}_{\mathit{f}2}}/\overline{{\mathit{d}}^{*}}$ | $\overline{{\mathit{L}}_{\mathit{f}}}/\overline{{\mathit{L}}^{*}}$ |

0.010 ^{1} | 0.85 | 0.51 | 0.83 | 0.43 | 0.76 | 0.49 |

0.025 | 0.93 | 1.30 | 0.96 | 0.64 | 0.92 | 0.58 |

0.050 | 1.09 | 1.35 | 1.08 | 0.89 | 0.90 | 0.98 |

0.100 | 0.97 | 1.54 | 1.02 | 1.24 | 0.94 | 1.18 |

0.150 ^{2} | - | - | 0.34 | 1.05 | 0.95 | 1.01 |

^{1}This target discharge was not considered representative for the discussion as mentioned in Section 3.3.3.

^{2}Most of the tests performed for this target discharge did not meet the acceptance criteria due to the size limits of the facility so they were not considered statistically representative.

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**MDPI and ACS Style**

Moran, R.; Toledo, M.Á.; Peraita, J.; Pellegrino, R. Energy Dissipation in Stilling Basins with Side Jets from Highly Convergent Chutes. *Water* **2021**, *13*, 1343.
https://doi.org/10.3390/w13101343

**AMA Style**

Moran R, Toledo MÁ, Peraita J, Pellegrino R. Energy Dissipation in Stilling Basins with Side Jets from Highly Convergent Chutes. *Water*. 2021; 13(10):1343.
https://doi.org/10.3390/w13101343

**Chicago/Turabian Style**

Moran, Rafael, Miguel Ángel Toledo, Javier Peraita, and Raffaella Pellegrino. 2021. "Energy Dissipation in Stilling Basins with Side Jets from Highly Convergent Chutes" *Water* 13, no. 10: 1343.
https://doi.org/10.3390/w13101343