Effect of Sediment Concentration on Hydraulic Characteristics ... - MDPI

applied sciences Article

Effect of Sediment Concentration on Hydraulic Characteristics of Energy Dissipation in a Falling Turbulent Jet Wenjuan Gou 1 , Huiping Li 1, *, Yunyi Du 2 , Hongxia Yin 1,3 , Fang Liu 1 1

2 3

*

and Jijian Lian 1

State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China; [email protected] (W.G.); [email protected] (H.Y.); [email protected] (F.L.); [email protected] (J.L.) Environmental Technology Development of TIWTE (Tianjin) Co., Ltd., Tianjin Research Institute for Water Transport Engineering, M.O.T., Tianjin 300072, China; [email protected] School of Water Conservancy and Hydroelectric Power, Heibei University of Engineering, Handan, Hebei 056038, China Correspondence: [email protected]; Tel.: +86-022-27401137

Received: 29 July 2018; Accepted: 13 September 2018; Published: 15 September 2018

Featured Application: This study establishes a foundation that links behavior with sediment concentration to enable further research into energy dissipator function in large dams on sediment-laden rivers. Abstract: The effect of sediment on the hydraulics of jet energy dissipation is an urgent issue for high dams built on sediment-laden rivers. Accordingly, flume experiments were conducted using a ski-jump type energy dissipator in flows of four sediment concentrations (0 kg/m3 , 50 kg/m3 , 150 kg/m3 , and 250 kg/m3 ) to determine the effects on discharge, flow regime, and hydrodynamic pressure in a plunge pool. The results demonstrate that the effect of sediment on discharge is constant, regardless of sediment concentration, when compared to fresh water. The width of the nappe decreased with increasing concentrations of sediment. The length of the jet trajectory increased with upstream water head. The time-averaged pressure and fluctuation pressure both exhibited peaks, describing the impact of the jet on the bottom of the plunge pool. The maximum time-averaged pressure and maximum fluctuating pressure both noticeably increased with upstream water head and slightly increased with sediment concentration for a given flow condition. The results also demonstrated that the dominant frequency of fluctuation trends to lower values, and that both the fluctuating energy and vortex scale increase with increasing sediment concentrations due to increased viscosity. These findings can be used to improve energy dissipation in dams on sediment-laden rivers. Keywords: sediment; concentration; energy dissipation; plunge pool; hydraulic characteristics

1. Introduction The interest in energy dissipation in hydraulic structures has developed at an appropriate time, given the significant increase in the construction of large dams worldwide since the 1950s [1]. The design of hydraulic energy dissipators for these dams is often a challenge, especially when dam parameters include high water head and large discharge [2]. The hydraulic jump [3] and ski-jump [4] are common energy dissipation features, as is the plunge pool [5]. However, when a dam is built on a hyperconcentrated sediment-laden river, energy dissipation is complicated by sediment effects [6]. Energy dissipation is an important issue in the design of a hydraulic structure. The hydraulic characteristics of the impinging jet or plunge pool of an energy dissipator have been extensively studied Appl. Sci. 2018, 8, 1672; doi:10.3390/app8091672

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in fresh water. Deep outlets with a plunge pool should be considered a standard, common design for energy dissipation [7] and flushing sediment from reservoirs [8]. Nappe flows, in which water is dropped through the atmosphere into a pool or water cushion, exhibit rapid diffusion of the jet in the pool, dissipating the energy of the falling water and attenuating fluctuations at the base of the pool [9]. Many papers have been published on methods to determine the shape and size [10] of a plunge pool and the bottom slab thickness [11], and others have paid special attention to hydraulic plunge pool scour [12]. The safety of plunge pools has also been a subject of close attention, e.g., the hydraulic pressure [13] and uplift force [14]. Other research has concentrated on the mechanism of the impinging jet [15]. The entire flow of an energy dissipator is divided into a free jet region, an impinging region, and wall jet region. Beltaos and Rajaratnam [16] discussed the time-averaged characteristics of an impinging jet and Gutmark et al. [17] presented an experimental study of the turbulent structure on the centerline of a two-dimensional impinging jet. Energy dissipation depends on the turbulence of flow and the fluctuation of turbulent flow based on the formation of coherent structures [18,19]. Using experiments and calculations, Adrian et al. [20] concluded that the vortex structure in a wall turbulent flow takes the form of a hairpin. Chakraborty et al. [21] systematically analyzed, summarized, and compared popular vortex identification criteria and vortex structure recognition methods. The scale, intensity, and density of vortex structures have also been studied [22,23]. With the continued development of experimental technology, new advanced simulation methods [24] and devices [25], such as direct numerical simulation (DNS) [26], large eddy simulations (LES) [27], and particle image velocimetry [28], have been used to research turbulence characteristics. However, turbulent flow is a complicated subject, and many details describing turbulent structures still remain inconclusive. Hyperconcentrated sediment-laden flow has been studied using experiments and simulations over the past century as either a Newtonian fluid [29] or Bingham fluid [30]. The presence and characteristics of particles have been found to affect the turbulent structure of a suspension [31]. Samanta et al. [32] simulated porous turbulent flows using DNS and observed that stream-wise turbulence intensity decreased in a porous duct. The turbulent velocity profile in sediment-laden flows has been studied by experiments [33] and simulations [34,35]. Guo and Julien [36] performed a theoretical analysis and determined that sediment suspension increases main flow energy loss and weakens turbulent diffusion in the vertical direction, and increases the velocity gradient. Wang and Qian [37] performed experiments to study the turbulence structure of open channel flow and confirmed that the turbulence of a sediment-laden flow is less intense, with a smaller frequency and larger turbulence eddies in the longitudinal direction compared with clear water flow; the distribution of density probability and the autocorrelation coefficients of the fluctuating velocity were similar to that of a clear water flow. These results suggested that the fundamental turbulence structure of a sediment-laden Newtonian flow remains unchanged, but Wang et al. [38] found different experimental results. Omid et al. [39] and Nasrabadi et al. [40] performed experiments demonstrating that suspended sediment increases flow resistance as a result of decreased maximum flow velocity. Though a great deal of the literature published in the last century has addressed the transport of sediment and turbulent structure of sediment-laden flow using experiments [41] and simulations [42], it remains necessary to clarify the effects of sediment-laden flow on ski-jump type energy dissipators, as they appear to complicate the turbulence structure and energy dissipation mechanisms of a fluid. For a high dam in a hyperconcentrated, sediment-laden river, an impinging jet from a deep outlet and plunge pool are combined to act as an energy dissipator. Deep outlets perform the critical function of flushing sediment from behind a dam, so the hydraulics of hyperconcentrated flows should be determined in order to ensure safe operation. The effect of sediment on energy dissipation is an urgent issue for dams on hyperconcentrated sediment-laden rivers. In this paper, experiments were conducted using a re-circulating flume and deep outlet discharge subjected to flow of four sediment concentrations (0 kg/m3 , 50 kg/m3 , 150 kg/m3 , and 250 kg/m3 ) and three upstream water heads (1.8 m, 1.85 m, 1.9 m) to study the effects of sediment concentration on the hydraulics of energy

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upstream water Appl. Sci. 2018, 8, 1672heads

(1.8 m, 1.85 m, 1.9 m) to study the effects of sediment concentration on 3 ofthe 15 hydraulics of energy dissipation, as quantified by discharge, flow regime of nappes, and hydraulic pressure on the slab in the plunge pool. dissipation, as quantified by discharge, flow regime of nappes, and hydraulic pressure on the slab in the plunge pool. Setup 2. Experimental

The experiments 2. Experimental Setupwere conducted using a re-circulating flume, shown schematically in Figure 1a. The flume mainly consisted of an upstream tank with a water level indicator supporting a The experiments were conducted using a re-circulating flume, shown schematically in Figure 1a. stabilized water head, a plunge pool, and a pump with a flow meter. The upstream tank was 1 m The flume mainly consisted of an upstream tank with a water level indicator supporting a stabilized wide, 1.3 m long and 2.6 m high. The 0.61 m deep plunge pool was 4 m long and of a trapezoidal water head, a plunge pool, and a pump with a flow meter. The upstream tank was 1 m wide, 1.3 m cross-section, 0.8 m and 0.4 m wide at the top and bottom, respectively. A deep outlet was fixed at long and 2.6 m high. The 0.61 m deep plunge pool was 4 m long and of a trapezoidal cross-section, the upstream tank 1.28 m above the bottom plate of the plunge pool, as shown in the schematic 0.8 m and 0.4 m wide at the top and bottom, respectively. A deep outlet was fixed at the upstream tank diagram in Figure 1b. The tank and the plunge pool were connected by 12 cm diameter pipes and a 1.28 m above the bottom plate of the plunge pool, as shown in the schematic diagram in Figure 1b. mud pump. The tank and the plunge pool were connected by 12 cm diameter pipes and a mud pump. The tests were conducted in a room-temperature environment of about 20 ± 2 °C. Upstream The tests were conducted in a room-temperature environment of about 20 ± 2 ◦ C. Upstream and downstream water levels were controlled within an experimental error of ± 1 mm. The flow and downstream water levels were controlled within an experimental error of ± 1 mm. The flow discharge was measured by a flow meter, and each experiment case was conducted three times to discharge was measured by a flow meter, and each experiment case was conducted three times to determine the average discharge. Diaphragm-type TS202 pressure transducers (Beijing Tiantai determine the average discharge. Diaphragm-type TS202 pressure transducers (Beijing Tiantai Xingye Xingye Technology co. Ltd, Beijing, China)with a diameter of 20 mm were spaced at 0.1 m intervals Technology co. Ltd, Beijing, China)with a diameter of 20 mm were spaced at 0.1 m intervals along along the centerline of the plunge pool to measure the hydrodynamic pressure. A DASP data the centerline of the plunge pool to measure the hydrodynamic pressure. A DASP data collection collection system sampled the transducers at 100 Hz on the basis of Nyquist’s law [43], equivalent system sampled the transducers at 100 Hz on the basis of Nyquist’s law [43], equivalent to a sampling to a sampling time interval of 0.01 s. The transducers were calibrated in the air and the hydrostatic time interval of 0.01 s. The transducers were calibrated in the air and the hydrostatic pressures pressures were measured prior to the experiments in order to provide a comparison of water level were measured prior to the experiments in order to provide a comparison of water level before before and after the experimental hydrodynamic pressures were applied. At least 8192 effective and after the experimental hydrodynamic pressures were applied. At least 8192 effective samples samples were taken in every experimental case. The complete set of samples was first analyzed for were taken in every experimental case. The complete set of samples was first analyzed for effective effective data, then decomposed using an infinite impulse response (IIR) filter in MATLAB (The data, then decomposed using an infinite impulse response (IIR) filter in MATLAB (The MathWorks, MathWorks, Inc., Natick, MA, U.S.). Finally, the parameters of the hydrodynamic pressures were Inc., Natick, MA, U.S.). Finally, the parameters of the hydrodynamic pressures were calculated calculated using MATLAB. using MATLAB. The sediment used was from the Yellow River and was classified as fine silt and clay of particle The sediment used was from the Yellow River and was classified as fine silt and clay of particle sizes ranging from 0.001 mm to 0.05 mm and a median particle size of 0.008 mm. The concentration sizes ranging from 0.001 mm to 0.05 mm and a median particle size of 0.008 mm. The concentration of mud was determined by its concentration at the nappe. Viscosity was measured by an NDJ-8S of mud was determined by its concentration at the nappe. Viscosity was measured by an NDJ-8S (Shanghai Yueping Scientific Instrument Co. Ltd., Shanghai, China) rotational viscometer. After (Shanghai Yueping Scientific Instrument Co. Ltd., Shanghai, China) rotational viscometer. After testing testing each case, the viscosity of the sediment-laden flow was measured at room temperature. Each each case, the viscosity of the sediment-laden flow was measured at room temperature. Each case was case was repeated five times and the results were averaged for analysis. repeated five times and the results were averaged for analysis.

(a)

(b)

Figure 1. Schematic diagram of the experimental (a) re-circulating flume; and and (b) (b) deep deep outlet. outlet.

Experiments were conducted conducted in in two two sets sets for for aa downstream The first first set Experiments were downstream water water depth depth of of 0.1 0.1 m. m. The set of evaluated fresh fresh water water at at three three upstream upstream water water heads heads (1.80 (1.80 m, m, 1.85 1.85 m, m, and and 1.90 1.90 m) m) to to of experiments experiments evaluated determine its energy dissipation in the plunge pool. The second set of experiments consisted of three determine its energy dissipation in the plunge pool. The second set of experiments consisted of 3 , 150 kg/m 3 , and3250 kg/m3 ) of sediment-laden 3, 150 kg/m concentrations (50 kg/m flow toflow determine its energy three concentrations (50 kg/m , and 250 kg/m3) of sediment-laden to determine its dissipation at each of three heads. The heads. densities of densities the suspensions energy dissipation at the each of evaluated the three upstream evaluated water upstream water The of the 3 3 3 3 3, and for were 1.02 kg/m kg/m concentrations of 50 kg/m3 ,of150 suspensions were, 1.05 1.02kg/m kg/m3,, and 1.05 1.08 kg/m 1.08sediment kg/m3 for sediment concentrations 50kg/m kg/m3,, and 250 kg/m3 , respectively. The details of all twelve experimental cases are presented in Table 1. The experimental errors were controlled to less than 1%.


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150 kg/m3, and 250 kg/m3, respectively. The details of all twelve experimental cases are presented in Table 1. The experimental errors were controlled to less than 1%. Appl. Sci. 2018, 8, 1672

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Table 1. Experimental cases.

Concentrations Upstream Downstream Concentrations Upstream Downstream 1. Depth Experimental of Sediment Water Table Water No. cases. of Sediment Water Water Depth 3) 3) (kg/m Head (m) (m) (kg/m Head (m) (m) Downstream Upstream Downstream Concentrations Upstream Concentrations 0 1.80 0.1 150 1.80 0.1 Water Depth Water Water No.7 of Sediment Water of Sediment 3) (m) Head1.85 (m) Depth0.1 (m) (kg/m Head (m) (kg/m 0 3) 1.85 8 150 0.1 1.90 150 1.90 00 1.80 0.10.1 7 9 150 1.80 0.10.1 050 1.85 0.10.1 8 10 150 1.85 0.10.1 1.80 250 1.80 050 1.90 0.10.1 9 11 150 1.90 0.10.1 1.85 250 1.85 50 1.80 0.1 10 250 1.80 0.1 50 1.90 0.1 12 250 1.90 0.1 50 50

1.85 1.90

0.1 0.1

11 12

250 250

1.85 1.90

0.1 0.1

3. Experimental Results and Analysis

3. Experimental Results and Analysis 3.1. Flow Discharge 3.1. Flow FlowDischarge discharge is a critical control factor in the design of a hydraulic structure. A satisfactory flow Flow rate ensures theissafe operation of afactor dam in in the a hyperconcentrated sediment-laden so the discharge a critical control design of a hydraulic structure. Ariver, satisfactory effect of sediment on safe flowoperation dischargeofisa an important and urgent issue. The experiments flow rate ensures the dam in a hyperconcentrated sediment-laden river,in sothis the study were conducted to determine the relationship between flow rate and upstream water head effect of sediment on flow discharge is an important and urgent issue. The experiments in this for sediment-laden flow. The experimental results are presented Figure in whichwater the dark study were conducted to determine the relationship between flowinrate and 2, upstream headline for is the flow rate of fresh water and the dots areare thepresented flow ratesinofFigure the sediment-laden various sediment-laden flow. The experimental results 2, in which theflow darkof line is the sediment concentrations. The observed to the increase exponentially the square root flow rate of fresh water and theflow dotsrate are was the flow rates of sediment-laden flowwith of various sediment of the upstream The water head. dots were close to the line, indicatingwith that the the square flow rate is stable concentrations. flow rateThe was observed to increase exponentially root of the regardless of sediment concentration, which is the same conclusion reached by references [44,45]. upstream water head. The dots were close to the line, indicating that the flow rate is stable regardless Therefore, when a hydraulicwhich structure is designed, the flowreached rate need be evaluated terms of of sediment concentration, is the same conclusion by only references [44,45]. inTherefore, fresh whenwater. a hydraulic structure is designed, the flow rate need only be evaluated in terms of fresh water.

Relationshipbetween between flow flow rates rates and and upstream upstream water water head head to to deviations deviations at different Figure 2. Relationship sediment concentrations.

3.2. Jet Properties 3.2. Jet Properties Jet properties affect the mean or fluctuating pressure on the floor slab of a plunge pool because Jet properties affect the mean or fluctuating pressure on the floor slab of a plunge pool because the break-up and air entrainment of the jet is influenced by surface tension and turbulence effects. the break-up and air entrainment of the jet is influenced by surface tension and turbulence effects. These effects, in turn, determine the thickness of the slab. Nappe regimes at various sediment These effects, in turn, determine the thickness of the slab. Nappe regimes at various sediment concentrations are shown in Figure 3. The air entrainment of the falling jet is obvious. The break-up of concentrations are shown in Figure 3. The air entrainment of the falling jet is obvious. The break-up the jet in the air is best understood by vertically dividing it into three major flow regimes. The first of the jet in the air is best understood by vertically dividing it into three major flow regimes. The region was characterized by the initial formation of waves on the surface of the jet. Surface tension first region was characterized by the initial formation of waves on the surface of the jet. Surface resists the growth of these disturbances. The flow exiting the outlet was glassy and smooth, and the tension resists the growth of these disturbances. The flow exiting the outlet was glassy and smooth, nappe section was similar to that of a sharp outlet. This glassy smooth region increased in length with increasing sediment concentrations. The second region was characterized by the growth of instabilities on the water surface. Small, regularly spaced waves formed and were amplified in the direction of flow. Notably, the falling jet of sediment-laden flow was smoother than that of fresh water, and the


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and the nappe section was similar to that of a sharp outlet. This glassy smooth region increased in and thewith nappeincreasing section was similar to that of a sharpThe outlet. This region glassy smooth region increased in length sediment concentrations. second was characterized by the length increasing on sediment concentrations. Theregularly second region characterized the growth with of instabilities the water surface. Small, spaced was waves formed andbywere growth of instabilities on the water surface. Small, regularly spaced waves formed and were amplified in8,the direction of flow. Notably, the falling jet of sediment-laden flow was smoother5 than Appl. Sci. 2018, 1672 of 15 amplified in the direction of flow. Notably, the falling jet of sediment-laden flow was smoother than that of fresh water, and the small waves appeared slightly later. The third region was characterized that of transition fresh water, the small waves appeared slightly vortex later. The third region was characterized by the of and the surface waves into circumferential elements. Jet break-up was clearly small waves appeared slightly later. Theinto third region was characterized by theJet transition ofwas the surface by the transition of the surface waves circumferential vortex elements. break-up clearly observed and was less intense in sediment-laden flow than in fresh water, as was the air waves into circumferential vortex elements. Jet break-up was clearly observed and was less intense in observed and was less intense in sediment-laden flow than in fresh water, as was the air entrainment. This behavior has been attributed to the higher viscosity of sediment-laden flow [46]. sediment-laden flow than in fresh water, as was the entrainment. This of behavior has been attributed entrainment. This behavior has been attributed to air the higher viscosity sediment-laden flow Figure 4 presents the relationship between viscosity and sediment concentration at 10 °C, 20 °C, [46]. and to the higher viscosity of sediment-laden flow [46]. Figure 4 presentsconcentration the relationship between viscosity Figure 4 presents the relationship between viscosity and sediment at 10 °C, 20 °C, and 30 °C. Clearly, the viscosity of flow◦ increases with increasing sediment concentration and decreases ◦ C. Clearly, the viscosity of flow increases with and sediment atflow 10 C, 20 ◦ C, and 30 °C. Clearly,concentration the viscosity of increases with30increasing sediment concentration and decreases with increasing temperature. The increasing viscosity of the sediment-laden flow likely results in an increasing sediment concentration and decreases with increasing temperature. flow The increasing viscosity with increasing temperature. The increasing viscosity of the sediment-laden likely results inthe an increase in surface tension [9], and, as a result, the falling jets exhibit different nappe regimes at of the sediment-laden flow likely results inresult, an increase in surface tensiondifferent [9], and, nappe as a result, the falling increase in surface tension [9], and, as a the falling jets exhibit regimes at the different sediment concentrations. jets exhibit differentconcentrations. nappe regimes at the different sediment concentrations. different sediment

Figure 3. Nappe regimes at different sediments concentrations. Figure 3. Nappe regimes at different sediments concentrations.

Figure 4. 4. Relationship between various sediment concentrations and fluid viscosity. viscosity. Figure Figure 4. Relationship between various sediment concentrations and fluid viscosity.

When the floor floor slab of aa plunge pool of of sufficient sufficient depth, the flow flow regime When aa falling falling jet jet impacts impacts the slab of plunge pool depth, the regime in in When a falling jet impacts the floor slab of a plunge pool of sufficient depth, the flow regime in the plunge pool can be divided into the three regions shown in Figure 5 to determine the hydraulic the plunge pool can be divided into the three regions shown in Figure 5 to determine the hydraulic the plunge pool can beThe divided into the shown injet Figure toIn determine hydraulic pressure distribution. first region (I) three is submerged jet region. In 5this region, the the flow velocity pressure distribution. The first region (I)the is regions the submerged region. this region, the flow pressure distribution. The first region (I) is the submerged jet region. In this region, the of the main stream remains approximately linear; the center of the main stream exhibits the highest velocity of the main stream remains approximately linear; the center of the main stream exhibitsflow the of the the main stream remains approximately thethe center of the main stream exhibits velocity while edge of the main stream the lowest velocity. The second region (II)region is the highest velocity while the edge of the mainexhibits stream linear; exhibits lowest velocity. The second highest velocity while the edge of the stream exhibits the lowest velocity. The second region main impact region, in which themain velocity ofthe the main stream decreases rapidly and streamlines (II) isstream the main stream impact region, in which velocity of the main stream decreases rapidly (II) theupon main meeting stream impact region, which the of main rapidly abruptly theupon slab, so theinpressure on the of the theon plunge poolofdecreases increases sharply. andisstreamlines abruptly meeting the slab, sovelocity theslab pressure thestream slab the plunge pool and streamlines abruptly upon meeting the slab, so the pressure on the slab of the plunge pool The third region (III) is the wall jet region, in which the main stream is ejected and flows to the wall increases sharply. The third region (III) is the wall jet region, in which the main stream is ejected increases The third region (III) is wall jet region, inand which the main isdiffuse. ejected and the slab of the plunge pool. Here, spirals begin to roll diffuse. Looking these three and along flowssharply. to the wall and along the slab ofthe the plunge pool. Here, spirals begin tostream rollatand and flows to thethe wall and impact along the slab ofis the plunge pool. Here, begin to roll and diffuse. regions, clearly design pressure caused by the effects of spirals the jet in the main stream impact region (II), where the maximum pressure on the slab occurs, and instability and failure of the slab are most likely.

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Looking at these three regions, clearly the design impact pressure is caused by the effects of the jet Looking at these threeimpact regions,region clearly(II), thewhere design the impact pressurepressure is causedonbythe theslab effects of theand jet in the main stream maximum occurs, in the main stream impact region (II), where the maximum pressure on the slab occurs, and instability and failure of the slab are most likely. Appl. Sci. 2018, 8, 1672 6 of 15 instability and failure of the slab are most likely. 3.3. Hydrodynamic Pressure 3.3. 3.3. Hydrodynamic Hydrodynamic Pressure Pressure Hydrodynamic pressure was measured along the centerline of the plunge pool by Hydrodynamic pressure measured thedata centerline ofsystem. the by plunge pool by Hydrodynamic pressure waswas measured along the centerline ofcollection the plunge pool diaphragm-type diaphragm-type TS202 pressure transducers andalong a DASP According to the diaphragm-type TS202 pressure transducers and a DASP data collection system. According to the TS202 pressure transducers and a DASP data collection system. According to the results of previous results of previous research [44], a sampling frequency of 100 Hz was used that satisfied Nyquist’s results of[44], previous research [44], ainterval sampling of 100 was used research aselection sampling of 100 Hz was used that satisfied Nyquist’s lawsatisfied [43]. selection law [43]. The offrequency sample andfrequency sampling time isHz related to thethat ability of The theNyquist’s collected law [43]. The selection of sample interval and sampling time is related to the ability of the collected of sample interval and sampling time is related to the ability of the collected data to accurately data to accurately reflect the reality of the experiment. According to the sampling theorem, the data tothe accurately the reality ofmust the experiment. According to the sampling the reflect reality ofreflect the According the sampling the truncation frequency of truncation frequency ofexperiment. Nyquist’s law betogreater than thetheorem, highest frequency of theorem, the sampling truncation frequency must befrequency greater than the highest frequency the sampling Nyquist’s law must beofgreater than law the highest of the sampling signal in theofselection. If the signal in the selection. IfNyquist’s the sampling interval is too large, the truncation frequency is too small, signal in the selection. If the sampling interval is too large, the truncation frequency is too small, sampling interval is too large, the truncation frequency is too small, causing spectrum aliasing. Asin a causing spectrum aliasing. As a result, at least 8192 samples were taken for every experiment causing spectrum aliasing. As a result, at least 8192 samples were taken for every experiment in result, at least 8192 samples were taken for every experiment in order to provide sufficient data to order to provide sufficient data to reduce uncertainty [25]. Figure 6 depicts a portion of the original order touncertainty provide sufficient data6todepicts reduce [25]. Figuretime 6 depicts portion the original reduce [25]. Figure a uncertainty portion the original history curve of of hydrodynamic time history curve of hydrodynamic pressures forofCase 3. These data were athen decomposed by an time history curve of hydrodynamic pressures for Case 3. These data were then decomposed bywith an pressures for Case 3. These data were then decomposed by an IIR filter before proceeding IIR filter before proceeding with the analysis. IIR filter before proceeding with the analysis. the analysis.

Figure 5. Schematic diagram of the flow regime. Figure 5. 5. Schematic Schematicdiagram diagramof ofthe theflow flow regime. regime. Figure

Figure 6. The time history curve of maximum hydrodynamic pressures for Case 3. Figure 6. The time history curve of maximum hydrodynamic pressures for Case 3.

Hydrodynamic pressure can can be be expressed expressed as as aa combination of mean Hydrodynamic pressure combination of mean pressure pressure and and fluctuating fluctuating Hydrodynamic pressure can be expressed as a combination of mean pressure and fluctuating pressure as pressure as pressure as Pi = P + P0 (1) (1) 𝑃𝑖 = 𝑃̅ + 𝑃′ 0 is 𝑃̅ + 𝑃′P is the mean pressure at this test point, and P(1) where Pi is the instantaneous pressure at a 𝑃 test 𝑖 =point, where 𝑃𝑖 is the instantaneous pressure at a test point, 𝑃̅ is the mean pressure at this test point, and the fluctuating Mean and fluctuating on the centerline of the slab is where 𝑃𝑖 fluctuating is the pressure. instantaneous at fluctuating a testdynamic point,dynamic 𝑃̅ pressure is thepressure mean pressure at this testfloor point, and 𝑃′ is the pressure.pressure Mean and on the centerline of the floor by the diffusion and air entrainment in the falling jet,pressure and the scale the turbulence the ′ 𝑃affected fluctuating pressure. andentrainment fluctuating dynamic on the theofscale centerline the in floor slabis isthe affected by the diffusionMean and air in the falling jet, and of theof turbulence plunge pool. slab is plunge affectedpool. by the diffusion and air entrainment in the falling jet, and the scale of the turbulence in the in the plunge pool. 3.3.1. Mean Pressure 3.3.1. Mean Pressure

The mean dynamic pressure of the falling jet on the plunge pool floor slab can be determined by the average of the dynamic pressure over time, thus, the relative time average pressures (P*) can be given as 𝑃∗ = 𝑃̅ − ℎ0

(2)

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where 𝑃̅ is the time-averaged pressure at every test point and h0 is the static water depth in the plunge pool. The relative time-averaged pressure is a function of the location of the experimental measurement points, as presented in Figure 7. The experimental results illustrate that the relative 3.3.1. Mean Pressure time-averaged pressures remain stable before exhibiting a clear peak, as can be observed in Figure The mean dynamic pressure of the falling jet on the plunge pool floor slab can be determined by 7a–c. This peak in relative pressure mainly occurs in the main stream impact region, which is the average of the dynamic pressure over time, thus, the relative time average pressures (P*) can be clearly similar to the experimental results of Xu et al. [5]. In this region, the velocity of the jet is given as forced to sharply decrease, causing the pressure to abruptly increase [9]. The maximum value of the P ∗ = P − h0 (2) relative pressure, which affects the stability and safety of the plunge pool slab [13], can be seen in Figure 7 to increase with increasing sediment concentration, agreeing well with the experimental where P is the time-averaged pressure at every test point and h0 is the static water depth in the results Wang Qiantime-averaged [37]. This result was is expected, because higher pressure can be plunge of pool. Theand relative pressure a function of the the location of the experimental explained by points, the increase in the in viscosity of The the experimental liquid that accompanies increased sediment measurement as presented Figure 7. results illustrate that the relative concentration, diffusion and air entrainment of thepeak, jet toas decrease. time-averaged causing pressuresthe remain stable before exhibiting a clear can be observed in Figure 7a–c. increasing upstream water head,inthe peak moves downstream, as shown in This With peak in relative pressure mainly occurs the pressure main stream impact region, which is clearly similar Figure 7d, indicating that the impact region of the jet moves downstream travels further to the experimental results of Xu et al. [5]. In this region, the velocity of the jetasis it forced to sharply horizontally through air. The difference in the maximum values ofvalue relative pressure by decrease, causing the the pressure to abruptly increase [9]. The maximum of the relativecaused pressure, 3 fresh water and withsafety a concentration of 250 is approximately of whichwater affectsand theby stability of the plunge poolkg/m slab [13], can be seen instable, Figureregardless 7 to increase upstream water head. It is concentration, likely that the increase upstream water head has little influence on and the with increasing sediment agreeinginwell with the experimental results of Wang comparative degree turbulence of because fresh water and sediment-laden water. Clearly, pressure Qian [37]. This resultofwas expected, the higher pressure can be explained bywhile the increase in head does notofchange the relative effects of sediment-laden flow,concentration, the sediment causing concentration has an the viscosity the liquid that accompanies increased sediment the diffusion obvious influence onofthe pressure. and air entrainment theimpact jet to decrease.

(a)

(b)

(c)

(d)

Figure 7. Time-averaged Time-averagedpressure pressure and and location location for for different different upstream upstream water water heads heads at at different concentrations concentrations of of sediments: sediments: (a) (a) Upstream Upstreamwater waterhead headof of1.9 1.9 m; m; (b) (b) upstream upstream water water head head of of 1.85 1.85 m; m; (c) upstream water head of 1.8 m; (d) comparison of pressures at different upstream water heads due to fresh water and sediment-laden flow of 250 kg/m3 in concentration.

With increasing upstream water head, the pressure peak moves downstream, as shown in Figure 7d, indicating that the impact region of the jet moves downstream as it travels further

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horizontally through the air. The difference in the maximum values of relative pressure caused by fresh water and by water with a concentration of 250 kg/m3 is approximately stable, regardless of upstream water head. It is likely that the increase in upstream water head has little influence on the comparative degree of turbulence of fresh water and sediment-laden water. Clearly, while pressure head does not change the relative effects of sediment-laden flow, the sediment concentration has an obvious influence on the impact pressure. 3.3.2. Fluctuating Pressure The mean hydrodynamic pressure represents the average falling jet force on the floor slab of the plunge pool over a period of time, and the fluctuating pressure caused by turbulence represents the degree of turbulence at every point tested. The pressure fluctuation on the center line of the plunge pool was measured by transducers and the root mean squares (RMS) of the fluctuating pressure were determined by v u u1 N 2 (3) σ = t ∑ ( Pi − P) N i =1 where, P=

1 N

N

∑ Pi

(4)

i =1

in which σ is the RMS fluctuating pressure, Pi is the instantaneous pressure at a given point, i is the test number, P is the mean value of pressure at all test points, and N is total number of tests. As shown in Figure 8a–c, the experimental results indicate that the RMS fluctuating pressures remain stable at the beginning of the plunge pool, then increase sharply, exhibiting a peak before returning to a stable value at the end. For sediment-laden flow, the maximum values of the RMS pressure increased with increasing sediment concentration from 0 kg/m3 to 250 kg/m3 for a given upstream water head. The increasing concentration of sediment causes an increase in the viscosity of the flow, resulting in a decreased turbulence intensity [35] and an increased fluctuation in turbulence, which is consistent with the turbulence characteristics of sediment-laden flows in open channels [34]. Figure 8d shows that the maximum RMS increased with increasing upstream water head at a given concentration of sediment, and shows that the location of the maximum RMS moved downstream with the length of the region following the peak increasing with increasing water head. This indicates that the higher the upstream water head, the more energy carried by the jet and then applied to the slab, and the larger “hill” region following the peak of the RMS indicates that the main stream impact region is larger. Figure 8d, in which same color lines represent the RMS measured for different sediment concentrations at the same upstream water head, further demonstrates this relationship: The differences between the maximum RMS at different concentrations are similar, regardless of the upstream water head. Figure 9 depicts the maximum time-averaged pressure and the maximum fluctuating pressure for different sediment concentrations at different upstream water heads. The maximum time-averaged pressure can be seen to increase with both sediment concentration and water head, but the slopes at which the pressure increases with sediment concentration for all three water heads are nearly identical. The same trends are exhibited for the maximum fluctuating pressure. The results demonstrate that the pressure increases in a stable manner with the increasing sediment concentrations regardless of the upstream water head owing to the viscosity of the suspension and the accompanying flow resistance. Nasrabadi et al. [40] conducted experiments studying a submerged hydraulic jump with sediment-laden flow and determined that suspended sediment increased the flow resistance as a result of the decreased maximum flow velocity, which likely further confirms the presently observed effects of sediment in the flow.

This indicates that the higher the upstream water head, the more energy carried by the jet and then applied to the slab, and the larger “hill” region following the peak of the RMS indicates that the main stream impact region is larger. Figure 8d, in which same color lines represent the RMS measured for different sediment concentrations at the same upstream water head, further demonstrates this relationship: The differences between the maximum RMS at different Appl. Sci. 2018, 8, 1672 9 of 15 concentrations are similar, regardless of the upstream water head.


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(a)

(b)

(c)

(d)

Relationshipbetween betweenfluctuating fluctuating pressure pressure and and upstream upstream water water head head for for different Figure 8. Relationship concentrations of of sediments: sediments: (a) (a) Upstream Upstream water waterhead headof of 1.90 1.90 m; m; (b) (b) upstream upstream water water head head of of 1.85 1.85 m; m; concentrations m;m; (d)(d) comparison of pressures measured at different upstream water (c) upstream upstream water waterhead headofof1.80 1.80 comparison of pressures measured at different upstream 3 in concentration. heads heads for fresh and sediment-laden flow offlow 250 of kg/m in concentration. water forwater fresh water and sediment-laden 2503kg/m

3.3.3.Figure Amplitude Characteristics 9 depicts the maximum time-averaged pressure and the maximum fluctuating pressure for different sediment concentrations at further different upstream heads. The maximum The maximum fluctuating pressure is studied here aswater a key characteristic of jet flow. time-averaged pressure can be seen to increase with both sediment concentration and water The probability density is an important statistical parameter describing fluctuating pressurehead, and but the slopesitsatoverall whichamplitude. the pressure increases with sediment concentration forthe allmaximum three water heads representing When the upstream water head was 1.90 m, pressure are nearly The pool samewas trends arefrom exhibited forofthe fluctuating on the slab identical. of the plunge 1.20 m the wall themaximum upstream tank. Figure pressure. 10 depictsThe the results demonstrate that the pressure increases in a stable manner with the increasing sediment probability density of the maximum fluctuating pressure for different concentrations of sediments at concentrations regardless the m. upstream water head owing to the viscosity of the suspension and an upstream water head ofof1.90 In this figure, the probability densities of the maximum pressure the accompanying flow resistance. Nasrabadi et al. distribution [40] conducted experiments studyingi.e., a at different concentrations basically satisfy a Gaussian and are positively skewed, submerged hydraulic jump with sediment-laden flow and determined that suspended sediment the positive fluctuations tend to be larger than the negative ones. The peaks of the probability densities increased the the flow resistance a result of the decreased flow sediment velocity, concentration. which likely decrease, and weights of theasprobability densities increase,maximum with increasing further confirms the presently observed effects of sediment in the flow. Wang and Qian [37] conducted experiments studying the turbulence structure of open channel flow and suggested that the turbulence in sediment-laden flow is less intense than that in clear water flow. 3.3.3. Amplitude Characteristics This further demonstrates that the turbulence intensity decreases, and the fluctuation of turbulence increases, with increasing sediment concentration. The maximum fluctuating pressure is further studied here as a key characteristic of jet flow. The probability density is an important statistical parameter describing fluctuating pressure and representing its overall amplitude. When the upstream water head was 1.90 m, the maximum pressure on the slab of the plunge pool was 1.20 m from the wall of the upstream tank. Figure 10 depicts the probability density of the maximum fluctuating pressure for different concentrations of sediments at an upstream water head of 1.90 m. In this figure, the probability densities of the maximum pressure at different concentrations basically satisfy a Gaussian distribution and are positively skewed, i.e., the positive fluctuations tend to be larger than the negative ones. The peaks of the probability densities decrease, and the weights of the probability densities increase, with increasing sediment concentration. Wang and Qian [37] conducted experiments studying the turbulence structure of open channel flow and suggested that the turbulence in sediment-laden flow is less intense than that in clear water flow. This further demonstrates that the turbulence intensity decreases, and the fluctuation of turbulence increases, with increasing sediment

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Figure 9. Relationship between pressures and sediment concentrations for different upstream water Figure 9. Relationship Relationship between pressures sediment concentrations for different upstream Figure 9. between pressures andand sediment concentrations for different upstream water heads. water heads. heads.

Figure 10. peak pressure at 1.20 from upstream tank at different Figure 10. Probability Probabilitydensities densitiesforfor peak pressure at m 1.20 m the from the upstream tank at sediment different Figure 10. Probability densities water for peak pressure at 1.20 m from the upstream tank at different concentrations and an upstream head of 1.90 m. sediment concentrations and an upstream water head of 1.90 m. sediment concentrations and an upstream water head of 1.90 m.

3.3.4. Frequency Domain Characteristics 3.3.4. Frequency Domain Characteristics 3.3.4.The Frequency Characteristics power Domain spectrum is an important parameter that represents the frequency domain The power spectrum is an important parameter that represents the frequency domain characteristics of fluctuating pressure, given by parameter that represents the frequency domain The power spectrum is an important characteristics of fluctuating pressure, given by characteristics of fluctuating pressure, given Zby∞ ∞ S( f = 4 ∞𝑅(𝑡)cos R(t) cos 2π f tdt (5) )= 𝑆(𝑓) 4∫ 2𝜋𝑓𝑡𝑑𝑡 (5) 0 𝑆(𝑓) = 4 ∫ 𝑅(𝑡)cos 2𝜋𝑓𝑡𝑑𝑡 (5) 0 0

where ff is is the thefrequency frequencyofoffluctuating fluctuatingpressure, pressure,t tisisthe thetest testtime, time,and and S(fis) the is the power spectrum where S(f) power spectrum of where f is the frequency of fluctuating pressure, t is the test time, and S(f) is the power spectrum of of the fluctuating pressure. maximum fluctuating pressure onslab theofslab the plunge the fluctuating pressure. The The maximum fluctuating pressure on the theof plunge pool ispool also is a the fluctuating pressure. The maximum fluctuating pressure on the slab of the plunge pool is also a also a key characteristic for studying the frequency domain characteristics. Figure 11 depicts the key characteristic for studying the frequency domain characteristics. Figure 11 depicts the key characteristic for studying the frequency domain characteristics. Figure 11mdepicts the relationships of spectrum andand frequency for an water water head ofhead 1.90 different relationships ofthe thepower power spectrum frequency forupstream an upstream of at1.90 m at relationships of the power spectrum and frequency for an upstream water head of 1.90 m at sediment sediment concentrations. The calculations show that the turbulence energy was most concentrated at different concentrations. The calculations show that the turbulence energy was most different sediment concentrations. The calculations show that the turbulence energy was most frequencies ofat 0–0.2 Hz and that the frequency of the fluctuating energy widen with increasing concentrated frequencies of 0–0.2 Hz and bands that the frequency bands of the fluctuating energy concentrated at frequencies of 0–0.2 Hz and that the frequency bands of the fluctuating energy sediment concentrations. The dominant frequencyThe trended to a lower frequency withtoincreasing widen with increasing sediment concentrations. dominant frequency trended a lower widen with increasing sediment concentrations. The dominant frequency trended to a lower sediment concentration. The sediment results demonstrate that the higher the demonstrate sediment concentration, the larger frequency with increasing concentration. The results that the higher the frequency with increasing sediment concentration. The results demonstrate that the higher the the viscosity of the flow and the lower the turbulent kinetic energy of the small-scale vortexes, sediment concentration, the larger the viscosity of the flow and the lower the turbulent kinetic sediment concentration, the larger the viscosity of the flow and the lower the turbulent kinetic which decrease gradually,vortexes, causing which the turbulent energy to become more concentrated in energy of the small-scale decreasekinetic gradually, causing the turbulent kinetic energy energy of the small-scale vortexes, whichunder decrease gradually, causing the turbulent kinetic energy large-scale energetic vortexes. Notably, these conditions, the turbulence eddies are longer. to become more concentrated in large-scale energetic vortexes. Notably, under these conditions, the to become more large-scale energetic vortexes. Notably, under these conditions, the These results areconcentrated similar to thein results of Wang Qian undertook to study turbulence eddies are longer. These results areand similar to[37] thewho results of Wangexperiments and Qian [37] who turbulence eddies are longer. These results are similar to the results of Wang and Qian [37] who turbulent structure of open channel flow with plastic particles. depicts theplastic relationships of undertook experiments to study turbulent structure of open Figure channel12flow with particles. undertook experiments to study turbulent structure of open channel flow10.4%) with of plastic particles. spectral density and frequency for four concentrations (0%, 1.4%, 5.6% and particles with Figure 12 depicts the relationships of spectral density and frequency for four concentrations (0%, 12 depictsofthe relationships spectral density and frequency for four concentrations (0%, aFigure mean5.6% diameter 0.266 mm. They of reveal the turbulent decreases the that increase 1.4%, and 10.4%) of particles with that a mean diameter frequency of 0.266 mm. Theywith reveal the 1.4%, 5.6% and 10.4%) of particles with a mean diameter of 0.266 mm. They reveal that the turbulent frequency decreases with the increase in concentration and the turbulence energy is turbulent frequency decreases with the increase in concentration and the turbulence energy is

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in concentration and the turbulence energy is transmitted to the eddy with low frequency and large transmitted to the eddy with low frequency and large size. However, the different values of size. However, values frequencies by large the two experiments result ofvalues different transmitted to the the different eddy with lowoffrequency and size. However,are thethe different of frequencies by the two experiments are the result of different turbulence and flow regimes. turbulence and flow regimes. frequencies by the two experiments are the result of different turbulence and flow regimes.

Figure 11. Relationships between power spectrum and frequency with an upstream water head of Relationships between between power power spectrum spectrum and and frequency frequency with with an an upstream water head of Figure 11. Relationships 1.90 m for different sediment concentrations. 1.90 m for different sediment concentrations.

Figure Relationships of of spectral spectral density density distribution distribution with with concentrations concentrations taken taken by by Wang and Figure 12. 12. Relationships and Figure 12. Relationships of spectral density distribution with concentrations taken by Wang and Qian [37]. Qian [37]. Qian [37].

3.3.5. 3.3.5. Time Time Domain Domain Characteristics Characteristics 3.3.5. Time Domain Characteristics The The coefficient coefficient of of association association is is an an important important parameter parameter used used to to analyze analyze the the turbulent turbulent structure structure The coefficient of association is an important parameter used to analyze the turbulent structure and dimensions of vortexes. The coefficient of association includes two parameters: The coefficient of and dimensions of vortexes. The coefficient of association includes two parameters: The coefficient and dimensionsand of vortexes. The coefficient of association includes two parameters: The coefficient autocorrelation the coefficient of cross-correlation. The point of maximum pressure is the critical of autocorrelation and the coefficient of cross-correlation. The point of maximum pressure is the of autocorrelation and the coefficient of cross-correlation. The point ofcalculated maximumbypressure is the location at whichatthe coefficient of association, R, should determined, critical location which the coefficient of association, R, be should be determined, calculated by critical location at which the coefficient of association, R, should be determined, calculated by Z T −τ 1 1 T  (6) R R = 1T − τT   px [pt x (t)p−x px]p· y pty (t+ τ)p−y pdt y dt (6) R  T   0 0 px  t   px  p y  t     p y dt (6)

T 



0



 



where thethe entire test test duration; t is thet test timetest andtime τ is an interval of time; px is of thetime; hydrodynamic where TTis is entire duration; is the and τ is an interval px is the where T atisa the entire test duration; t is the test timepressure and τ at is another an interval of time; px is the pressure given test point and p is the hydrodynamic test point; are x and py test hydrodynamic pressure at a giveny test point and py is the hydrodynamic pressure atpanother hydrodynamic pressure at a given test point and p y is the hydrodynamic pressure at another test the average hydrodynamic pressureshydrodynamic at test points xpressures and y, respectively; whenx pand represent a x andy,pyrespectively; point; 𝑝 and ̅̅̅ 𝑝 are the average ̅̅̅ at test points point; 𝑝𝑥𝑥 and ̅̅̅ 𝑝𝑦𝑦R are ̅̅̅ the average hydrodynamic pressures at test points x and y, respectively; single test point, represents the coefficient of auto correlation for R , and when p and p xx x y represent when px and py represent a single test point, R represents the coefficient of auto correlation for Rxx, when p x and py represent a single test point, R represents the coefficient of auto correlation for Rxx, two points, representstwo the coefficient cross-correlation for Rxy . the coefficient of and different when ptest x and py Rrepresent different of test points, R represents and The when px andofpautocorrelation y represent two different test points, R represents the coefficient of coefficient of the maximum hydrodynamic pressure, and the coefficient of cross-correlation for Rxy. cross-correlation for R xy. cross-correlation between the point with and the pressure, other points at 0.1 m The coefficient of autocorrelation ofthe themaximum maximumpressure hydrodynamic andlocated the coefficient The coefficient of autocorrelation of the maximum hydrodynamic pressure, and the coefficient intervals downstream, shouldthe be point calculated. By maximum comparingpressure the coefficients autocorrelation of the of cross-correlation between with the and theofother points located at of cross-correlation between the pointconcentration with the maximum pressure theinother points located at 3 , the and fresh water and water with a sediment of 250 kg/m results Figure 13 demonstrate 0.1 m intervals downstream, should be calculated. By comparing the coefficients of autocorrelation 0.1 m intervals downstream, should be calculated. By comparing the coefficients of autocorrelation of the fresh water and water with a sediment concentration of 250 kg/m33, the results in Figure 13 of the fresh water and water with a sediment concentration of 250 kg/m , the results in Figure 13 demonstrate that the eddy sizes in sediment-laden flow are larger than those in fresh water. demonstrate that the eddy sizes in sediment-laden flow are larger than those in fresh water.

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that the eddy the sizes in sediment-laden flow are larger fresh water. Additionally, coefficients of cross-correlation of thethan freshthose waterinand water withAdditionally, a sediment Additionally, the coefficients of cross-correlation of the fresh water and water with a sediment 3 the coefficients of cross-correlation of the fresh water and water with a sediment concentration of 250 kg/m3 indicate that the scale of the vortex increases with concentration the presence of of concentration of 250that kg/m indicate that the scale of the vortex increasesofwith the presence of 3 indicate 250 kg/min the scale the vortex increases with the presence sediment in theofflow. sediment the flow. The scale ofofthe vortex increases when sediment is present as a result the sediment in the flow. The scale of the vortex increases when sediment is present as a result of the The scaleinofturbulent the vortex increases sediment present as a result of the changes in turbulent changes structure andwhen surface tension is [47,48]. changes in turbulent structure and surface tension [47,48]. structure and surface tension [47,48]. Although different objects were studied, and different experimental details were produced, Although different objects were studied, and experimental details were different objects were studied, and different different details were produced, produced, theseAlthough results correspond well with those in reference [37], as experimental shown in Figure 14. Figure 14, taken these results correspond well with those in reference [37], as shown in Figure 14. Figure 14, Wang taken these results correspond well with those in reference [37], as shown in Figure 14. Figure 14, taken from from Wang and Qian [37] depicts the relationships of eddy sizes with particle concentrations. The fromQian Wang and Qian [37]relationships depicts the relationships of eddy sizes concentrations. with particle concentrations. The and [37] depicts of eddy sizes with particle The results reveal results reveal that thethe longitudinal sizes of the macroscale eddies increase with the increase in results reveal that the longitudinal sizes of the macroscale eddies increase with the increase in that the longitudinal sizes of the macroscale eddies increase with the increase in sediment concentration sediment concentration and is mainly decided by the low frequency, large-size eddies. When the sediment concentration and is mainly decided by the low frequency, large-size eddies. When the and is mainly by the low is frequency, eddies. When thecarried frequency turbulent eddies eddies frequency of decided turbulent eddies reduced,large-size the energy proportion byoflarge-size frequency of turbulent eddies is reduced, the energy proportion carried by large-size eddies is reduced,The thelongitudinal energy proportion by large-size increases. longitudinal sizes of increases. sizes ofcarried the microscale eddieseddies increase with an The increase in concentration increases. The longitudinal sizes of the microscale eddies increase with an increase in concentration the microscale eddies increase with an increase in concentration and is mainly decided by small-size and is mainly decided by small-size eddies with high frequency. For a sediment-laden flow, part of and is mainly decided by small-size eddies with high a sediment-laden flow, part of eddies withcarried high frequency. For a sediment-laden flow,frequency. partthe of smallest theFor energy carried by high frequency the energy by high frequency eddies decreases and eddies vanish. the energy carriedand by the high frequency eddies decreases and the smallest eddies vanish. eddies decreases smallest eddies vanish.

Figure 13. Relationships between coefficient of association at peak pressure and time for fresh water of association at peak pressure and time for fresh water Figure 13. Relationships between coefficient and sediment-laden flow of 250 kg/m33 concentration at an upstream water head of 1.90 m. and sediment-laden flow of of 250 250 kg/m kg/m 3concentration concentrationat atan anupstream upstreamwater water head head of of 1.90 1.90 m. m.

Figure particle concentrations taken by Wang and Qian [37]. Figure 14. 14. Relationships Relationshipsbetween betweeneddy eddysizes sizesand and particle concentrations taken by Wang and Qian Figure 14. Relationships between eddy sizes and particle concentrations taken by Wang and Qian [37]. [37]. Hence, the fluctuating pressure is the result of the movement and interaction of different scales of

vortexes in the pool,pressure caused by jet.the The results ofand the experiments calculations Hence, theplunge fluctuating is the the nappe result of movement interaction ofand different scales Hence, the fluctuating pressure is theconcentration result of the in movement and interaction of different scales demonstrate that the larger the sediment the liquid of the jet, the higher its viscosity. of vortexes in the plunge pool, caused by the nappe jet. The results of the experiments and of vortexes in the plunge pool,ofcaused by the and nappe jet. Theinresults ofofthe experiments and This causes ademonstrate decrease in vortexes smaller scales an increase vortexes larger calculations that the larger the sediment concentration in the liquid of the scales, jet, theleading higher calculations demonstrate that the larger the sediment concentration in the liquid of the jet, the higher to increase in causes fluctuating pressure and, thus, energy.scales The scale of increase vortexesinincreases the its an viscosity. This a decrease in vortexes of smaller and an vortexes with of larger its viscosity. This causes a decrease in vortexes of smaller scales and an increase in vortexes of larger scales, leading to an increase in fluctuating pressure and, thus, energy. The scale of vortexes scales, leading to an increase in fluctuating pressure and, thus, energy. The scale of vortexes

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increasing concentrations of sediments. The energy of fluctuation also increases with increasing concentrations of sediments. 4. Conclusions The effect of the concentration of fine sediments on the hydraulics of the energy dissipation of a turbulent jet is an important and urgent problem for dams on hyperconcentrated sediment-laden rivers. Experiments were conducted using a deep outlet in an upstream tank and a plunge pool consisting of 12 test cases at four sediment concentrations (0 kg/m3 , 50 kg/m3 , 150 kg/m3 and 250 kg/m3 ) under three upstream water heads (1.80 m, 1.85 m and 1.90 m). The results of these tests were used to study the hydraulic characteristics of energy dissipation in terms of flow discharge, jet properties, and hydrodynamic pressure. The main conclusions are: (1) (2)

(3)

(4)

Flow discharge is solely related to the upstream water head for a deep outlet and is independent of sediment concentration. The horizontal length of the jet from the deep outlet to the plunge pool increases with increasing upstream water head, and the width of the jet decreases with increasing sediment concentrations. The nappe of the jet also becomes smoother and exhibits decreased air entrainment as a result of the higher viscosity of suspensions with higher sediment concentrations. The time-averaged pressure in the plunge pool exhibits a peak around the impact region of the falling jet and the magnitude and distance from the outlet of this peak increases with increasing sediment concentration due to increased viscosity. The distance from the outlet to the peak also increases with increasing upstream water head. The RMS fluctuating pressure exhibits the same trend as the time-averaged pressure. The probability density, power spectrum, and coefficient of correlation of hydrodynamic pressure was calculated and the results demonstrate that as sediment concentration increases, the fluctuating energy increases, as does the scale of the vortexes, and the dominant frequency decreases.

The findings of this study provide invaluable insights into the effects of sediment on the behavior of energy dissipators in large river dams. The behaviors and relationships determined in this study establish a foundation for the informed design of dam energy dissipator structures such as plunge pools, improving the operational safety of the overall dam. In the future, the effects of sediment on the velocity profile of the flow will be studied further. Author Contributions: All authors contributed to the research work. J.L., H.L. and W.G. conceived and designed the experiments; Y.D., H.Y. and F.L. performed the tests; H.L. analyzed the data; and W.G. drafted the paper. Funding: The authors are grateful to the National Natural Science Foundation of China (Grant Nos. 51509180, 51579172 and 51409187) for financial support. Acknowledgments: The authors dedicate the manuscript to the memory of Min Yang who gave much advice. Conflicts of Interest: The authors declare no conflict of interest.

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