Tailwater Level Research Articles

An adaptive optimization system and point tracking technique for estimation of variable-speed seawater pumped storage

There are few kinds of researches on the capacity optimization of seawater pumped storage with variable-speed units. First, the pumped storage effects are investigated to smoothing the large-scale offshore wind power. From the perspective of energy saving and improving efficiency, a method on maximum efficiency tracking is proposed, based on the synthetic characteristic curve of the pump turbine. Second, under the background of the time-of-use electricity price in the power market, the relevant model is established, taking full account of the characteristics of random seasonal fluctuation of tailwater level. Besides, this model satisfies the constraints of variable-speed units (especially under the pump mode). Finally, the key factors influencing profit growth, such as the fluctuation rate, the unit type, and the optimal capacity, are investigated based on a real case. The results show that the variable-speed unit can give full play to the efficiency advantage when the operating head and power demand of the plant change sharply. Because the output range of the variable-speed unit is extensive and can be continuously adjusted (especially in pump mode), the joint system will actively curtail the offshore wind to seek the maximum profit.

Vertically Averaged and Moment Equations for Dam-Break Wave Modeling: Shallow Water Hypotheses

The dam-break wave modeling technology relies upon the so-called shallow water equations (SWE), i.e., mass and momentum vertically averaged equations by implementing the shallow water hypotheses, namely (i) horizontal velocity component independent of the vertical coordinate, (ii) vertical velocity component is null, (iii) pressure distribution is hydrostatic, (iv) turbulence is neglected. While this model often yields a satisfactory answer from an engineering standpoint, flows with vertical length scales not negligible cannot be modeled with accuracy, including the undular surge generated after a dam break for relatively high tailwater levels. These flows are modeled by the Serre–Green–Naghdi equations (SGNE), which fail to mimic wave breaking for low tailwater levels, however. Neither SWE nor SGNE produce a fully satisfactory answer for modeling dam break waves, therefore. A higher-order model using vertically averaged and moment equations (VAM) is used in this work to simulate dam break waves, thereby showing good results for arbitrary values of the tailwater level. The model contains four perturbation parameters implemented to overcome the shallow water hypotheses; two for the velocity components and two for fluid pressure. The role of each parameter in relaxing the limitations of the SWE is systematically investigated, depicting a complex and necessary interplay between the dynamic component of fluid pressure and the modeling of the velocity profile in producing accurate solutions for both non-hydrostatic and broken waves in dam break flows. The results highlight how the shallow water hypotheses can be relaxed in the vertically averaged modeling of dam break waves, producing an outcome of both theoretical and practical interest in the field. The results generated are tested with available experimental data, resulting in acceptable agreement.

Short-term generation scheduling of cascade hydropower plants with strong hydraulic coupling and head-dependent prohibited operating zones

A lot of large hydropower plants have been built in China in the past few decades. Large-capacity hydropower units usually have multiple prohibited operating zones (POZs) varying with the net head. Many cascade hydropower plants are hydraulically coupled because the distance between the upstream and downstream reservoirs is so small that the forebay water level of the downstream reservoir will influence the tailwater level of its immediate upstream reservoir. The integrated consideration of the strong hydraulic coupling between cascade hydropower plants, the head-dependent POZs of individual units, and other operation constraints make the daily operation of cascade hydropower plants very challenging for both operators and researchers. Therefore, this paper has developed an accurate optimization model for determining the hourly generation scheduling of cascade hydropower plants with strong hydraulic coupling and head-dependent POZs. The objective is to maximize the total profits of the cascade hydropower plants from selling electricity in the day-ahead market. To solve such a complicated mathematical model with non-convex and nonlinear features, the model is converted into a mixed-integer linear programming (MILP) formulation using multiple linear approximation techniques so as to take full advantage of the effective and mature commercial solvers. The MILP formulation focuses mainly on addressing two nonlinearities, namely the three-dimensional tailwater level curves and head-dependent POZs, which are approximated through the piecewise linear interpolations based on the meshing and triangulation technique. The developed model is applied to the optimal operation of the Tianshengqiao cascade hydropower plants which are located on the Hongshui River, China. The optimization results demonstrate that the proposed model is able to be applied in the short-term generation scheduling of cascade hydropower plants in different hydrological conditions, and the optimized total profits for the cascade hydropower plants on typical days in dry season and flood season are 1,809,842 USD and 1,856,964 USD, respectively. Moreover, the developed model is computationally efficient and produces more realistic and executable generation scheduling than the state-of-the-art optimization model which only considers the head-dependent characteristics of POZs without considering the strong hydraulic coupling.

Dynamic behaviour of a Francis turbine during voltage regulation in the electrical power system

Hydroelectric units can be operated in synchronous condenser mode to provide reactive power to the electrical power system (EPS) for voltage regulation. In this operating mode, the hydraulic turbine consumes active power and in case of hydroelectric units equipped with a Francis turbine, pressurized air is injected in the draft tube to decrease the tailwater level below the runner for decreasing the friction losses. Several dynamic phenomena have been recorded during full-scale hydraulic turbine operation due to the air–water mixing causing pressure and torque fluctuations which may compromise the operation and safety of both the hydraulic machine and the EPS.In this paper, the study of the dynamic response of a Francis turbine prototype during synchronous condenser mode operation is performed to evaluate the transposition of the machine behaviour from the homologous reduced scale model to the full-scale prototype. Measurements of the pressure in draft tube cone, machine vibrations, and torque are performed in both full scale prototype and reduced scale model. The analysis of the dynamic behaviour of the hydraulic turbine focuses on the critical vibrations and power fluctuations. The onset of a sloshing wave in the draft tube cone is highlighted as predicted by the reduced scale model tests. Rotor–stator interactions (RSI) are analyzed and compared to the RSI during generating mode operation. The advantages of decreasing the pressure in the vaneless gap between the runner blades and the closed guide vanes by installing a draining pipe are emphasized to limit the amplitude of the fluctuations and to avoid unwanted two-phase flow phenomena in the vaneless gap which can perturb the machine operation and safety.

Experimental investigation on the effects of bed slope and tailwater on dam-break flows

Understanding of the characteristics of dam-break flows moving along a sloping wet bed can help to timely issue flood warning and risk mitigation. In this study, laboratory experiments are carried out in a large flume for a wide range of upstream water depth, bed slopes and tailwater depth. The water level is recorded and processed to calculate the mean velocity and wave celerity. Results show that the increase of the bed slope will significantly accelerate the wave-front celerity for the downstream dry bed, while the negative wave celerity will decrease. When water depth ratio α ≥ 0.3 (defined as the ratio of initial downstream water depth over the upstream water depth of dam), there are extra negative waves propagating towards the reservoir area after the flow has developed for a period of time. When α ≥ 0.6, there are the Favre waves propagating downstream. The water level and the mean velocity fluctuate due to the influence of the extra negative waves and the Favre waves. Such fluctuant frequency increases with the increase of the water depth ratio. The empirical formulas are obtained for the celerity of the first extra negative wave and the first downstream wave. The variation of wave-front height is very similar under three bed slopes investigated in this study, while the maximum wave-front height occurs when α = 0.2. The present study broadens the understanding of the effects of the bed slope and the tailwater level on the movement of the dam-break flows. Furthermore, experimental results are also compared with some analytical solutions. The validity of the assumptions made during the development of these analytical solutions and their limitations are discussed by comparing with the experimental measurements.

Improved dynamic model of a bulb turbine-generator for analysing oscillations caused by mechanical torque disturbance on a runner blade

Generic dynamic models of hydraulic turbines are unable to capture power oscillations phenomena originating from a torque disturbance on a single runner blade. In this paper, an improved dynamic model of a double-regulated hydraulic turbine which takes into account torque oscillations identified from draft tube pressure measurements was presented. It was experimentally identified that specific power oscillations of a bulb turbine operating with low tailwater level can be connected to cavitation-related phenomena on a single runner blade. Furthermore, it was shown that these oscillations do not originate from grid fault-induced resonance between the turbine rotor and generator, nor from the excitation system. The proposed simulation model was validated against measurement data of hydro power plant Dubrava and the validation shows good agreement between measured and simulated results.

Energy dissipation in a deep tailwater stilling basin with partial flaring gate piers

Flaring gate piers (FGPs) have been used to increase energy dissipation in stilling basins downstream of spillways. For projects with a low water head and large unit discharge together with a deep tailwater level, energy dissipation inside a conventional stilling basin is usually insufficient. This paper proposes a new partial flaring gate pier (partial FGP) scheme to intensify the energy dissipation inside the stilling basin. The results for the no FGP scheme, the conventional FGP scheme, and the partial FGP scheme were compared using a physical model study and numerical simulations. It was found that the partial FGP scheme (the alternation of flaring and no flaring gate piers in chambers) can contain the submerged hydraulic jump and high-speed water jet in the upstream region of the stilling basin. Thus, the water jet from the FGP chamber was forced to laterally diffuse, thereby intensifying the shear friction and turbulent kinetic energy and forming a vertical vortex from the bottom to the surface. Compared with the other two schemes, the flow pattern in the partial FGP scheme was improved significantly with much deeper air entrainment depth inside the stilling basin and much lower turbulent kinetic energy in the outgoing flow. The mean velocity of the outgoing flow also decreased by more than 20%. The common problems of secondary hydraulic jump outside the stilling basin were eliminated.

Estimation of maximum scour depth downstream of an apron under submerged wall jets

AbstractAn analysis of laboratory experimental data pertaining to local scour downstream of a rigid apron developed under wall jets is presented. The existing equations for the prediction of the maximum scour depth under wall jets are applied to the available data to evaluate their performance and bring forth their limitations. A comparison of measured scour depth with that computed by the existing equations shows that most of the existing empirical equations perform poorly. Artificial neural network (ANN)- and adaptive neuro-fuzzy interference system (ANFIS)-based models are developed using the available data, which provide simple and accurate tools for the estimation of the maximum scour depth. The key parameters that affect the maximum scour depth are densimetric Froude number, apron length, tailwater level, and median sediment size. Results obtained from ANN and ANFIS models are compared with those of empirical and regression equations by means of statistical parameters. The performance of ANN (RMSE = 0.052) and ANFIS (RMSE = 0.066) models is more satisfactory than that of empirical and regression equations.

Experimental investigation of erosion processes downstream of block ramps in mild curved channels

Eco-friendly low-head river restoration structures such as block ramps are of paramount importance with regard to the control of sediment grade in rivers, particularly in the mountains. They also help in the stabilization of river bed and prevent damages due to excessive downstream erosion by dissipating flow energy. Although the hydraulic characteristics of block ramps in straight channels have been thoroughly studied, there are very less studies dealing with the analysis of scour mechanism downstream of block ramps in curved channels. In fact, to the authors’ best knowledge, there are no studies till date investigating the scour process downstream of block ramps in river bends, involving the effect of tailwater and ramp bed slope. Therefore, this study aims to analyze the hydraulic behaviour of block ramps placed at various positions on a curved channel incorporating the effects of the mentioned parameters. Furthermore, the equilibrium morphology of the resulting downstream scour has been analyzed and classified. A dedicated hydraulic model was constructed, and a large range of in situ hydraulic conditions were simulated. Tests were carried out varying ramp slope and locating the structure at different positions along the channel bend. Data analysis revealed that the scour morphology is essentially three-dimensional and depends on flow characteristics, tailwater level and slightly on its location. Finally, a useful design relationship was also developed to evaluate the maximum scour depth taking into consideration the effect of channel curvature and the tailwater level.

DESIGN OF STILLING BASIN FOR DECREASING BACK WATER IN THE DAM FOOT

This research studies the hydraulic behavior and the problem solving alternatives of original until final design, and the most effective stilling basin and downstream regulator channel for decreasing back water from the upstream water level in the dam foot. The methodology consists of physical modeling in theLaboratory of River and Swamp, Department of Water Resources, Faculty of Engineering, University of Brawijaya. The methods include the USBR for the hydraulic analysis, the Hind’s formulation for the side channel analysis, the energy equation by analyzing the standard step for the transition and the chute way analysis, and the USBR type III for designing the stilling basin. A square cross-section with the Manning coefficient of 0.40 is used for determining the control of the Tail Water Level (TWL) and a trapezoidal crosssection with the Manning coefficient of 0.39 is used for the final design. However, the equation of Schotlischand Veronise is used for the local scouring analysis. The result of Model Test and analysis indicates that there are some differences among the analysis in every point of the building. Therefore, the relative error is needed to know how big the error in the comparison result.This research studies the hydraulic behavior and the problem solving alternatives of original until final design, and the most effective stilling basin and downstream regulator channel for decreasing back water from the upstream water level in the dam foot. The methodology consists of physical modeling in theLaboratory of River and Swamp, Department of Water Resources, Faculty of Engineering, University of Brawijaya. The methods include the USBR for the hydraulic analysis, the Hind’s formulation for the side channel analysis, the energy equation by analyzing the standard step for the transition and the chute way analysis, and the USBR type III for designing the stilling basin. A square cross-section with the Manning coefficient of 0.40 is used for determining the control of the Tail Water Level (TWL) and a trapezoidal crosssection with the Manning coefficient of 0.39 is used for the final design. However, the equation of Schotlischand Veronise is used for the local scouring analysis. The result of Model Test and analysis indicates that there are some differences among the analysis in every point of the building. Therefore, the relative error is needed to know how big the error in the comparison result.

Research on Cascade Reservoirs’ Short-Term Optimal Operation under the Effect of Reverse Regulation

Currently research on joint operation of a large reservoir and its re-regulating reservoir focuses on either water quantity regulation or water head regulation. The accuracy of relevant models is in need of improvement if the influence of factors such as water flow hysteresis and the aftereffect of tail water level variation are taken into consideration. In this paper, given the actual production of Pankou-Xiaoxuan cascade hydropower stations that combines two operation modes (‘electricity to water’ and ‘water to electricity’), a coupling model of their short-term optimal operation is developed, which considers Xiaoxuan reservoir’s regulating effect on Pankou reservoir’s outflow volume and water head. Factors such as water flow hysteresis and the aftereffect of tail water level variation are also considered to enhance the model’s accuracy. The Backward Propagation (BP) neural network is employed for precise calculation of the downstream reservoir’s inflow and the upstream reservoir’s tail water level. Besides, we put forth Accompanying Progressive Optimality Algorithm (APOA) to solve the coupling model with aftereffect. An example is given to verify the scientificity of the proposed model and the advantages of APOA. Through analysis of the model calculation results, the optimal operation rules of the cascade reservoirs are obtained in terms of water quantity regulation and water head regulation, which can provide scientific reference for cascade reservoirs’ optimal operation.

Tailrace surge shaft optimization procedure for minimum downsurge

Tailrace surge shafts are required in hydropower projects where the spent water is conveyed through a long tailrace tunnel under pressure to the recipient. Startup and shutdown of the turbine can cause sudden changes in water velocity and can develop dangerously high and low pressures. Surge shafts are provided in water conductor systems to significantly reduce these pressure surges. Based on numerous transient analyses carried out, it was observed that the cross-sectional area of the tailrace surge shaft can be optimized based on the relationship between the differences in the tailwater level and the minimum downsurge level at the tailrace surge shaft obtained with respect to the different lengths of the tailrace tunnel and different cross-sectional areas of the tailrace surge shaft. In this study, a procedure was proposed by which the tailrace surge shafts can be optimized and, hence, the cost of the hydropower projects with tailrace surge shafts can be minimized.

Experimental Investigation on Air-Water Interaction in a Hydropower Station Combining a Diversion Tunnel with a Tailrace Tunnel

Diversion tunnels are often used as tailrace tunnels in underground hydropower stations. The special layout results in complex flow regimes, including air-water two-phase flow. A set of experiments is conducted based on the model of a hydropower station which combines partial diversion tunnels with tailrace tunnels to investigate the interactions between the air and water phases in the combined diversion tunnels. Interactions between the air and water phases observed in the combined diversion tunnel significantly alter flow dynamics, and are classified into four types according to the initial tail water level. There is a range of initial tail water levels in which the interaction between the air and water phases cannot be neglected, and the range becomes greater when the change in flow rate increases. Such interactions may cause a pressure surge and the pressure surge reaches the maximum when the initial tail water level is approximately equal to the crown of the tunnel. The surge pressures do harm to the safety and stability of hydropower stations, so the condition should be considered and controlled.

Scour process caused by multiple subvertical non-crossing jets

The scour process induced by plunging jets is an important topic for hydraulic engineers. In recent decades, several researchers have developed new strategies and methodologies to control the scour morphology, including different jet arrangements and structures located in the stilling basin. It has been found that multiple jets can cause less scouring than single plunging jets. Based on this evidence, this study aimed to investigate the equilibrium morphology caused by multiple non-crossing jets. A dedicated laboratory model was built and experimental tests were carried out under different combinations of jet inclination angles, by varying the tailwater level and the virtual crossing point location, which was set below the original channel bed level. It was experimentally shown that the equilibrium scour morphology depends on the jet discharge, the differences in non-crossing jet inclination angles, the downstream water level, and the distance of the virtual crossing point from the original channel bed level. In particular, the last parameter was found to be one of the most influential parameters, because of the resulting flow patterns inside the water body. Furthermore, the analysis of experimental evidence allowed for a complete and detailed classification of the scour hole typologies. Three different scour typologies were distinguished and classified. Finally, based on previous studies, two novel relationships have been proposed to predict both the maximum scour depth and length within a large range of hydraulic and geometric parameters.

THE FRICTION RESISTANCE EFFECT ON THE HYDRAULIC JUMP LOCATION AND ENERGY DISSIPATION, A LABORATORY STUDY

The location of the jump downstream the hydraulic structures outlets is an important parameter taken into considerations within the construction of the downstream protection works. One of the ways of moving the jump into a closer distance from the outlets is to raise the tail water level. In this research, a flow partitioning structure, FPS, designed, carried out, and installed downstream a sluice gate to apportion the cross sectional area of the flow and, then, increase the resistance of the friction force by increasing the walls of flow. The FPS shaped as a sectioned triangular prism consists of sets of 2.6cm×2.6cm iron square-section pipes formed with direction of the flow. The FPS with a vertical front face consisting of 16×11, rows × columns, of pipes extended 10cm downstream and held by a 0.5cm, thickness, iron bars and welded together to prevent any egression of the pipes from the FPS. This combination of the pipes and bars made a width of 29.6cm and height of 42.6cm to fit, approximately, the flume cross sectional area dimensions. The downstream face made with an inclination of 45o to prevent the free fall of the water. The system (which consists of a sluice gate, FPS, and rising weir) installed in a horizontal flume of 0.3m width, 0.45m depth, and 15m length. The system operated with flow rates ranged from 11.11 to 36.24l/s with different gate openings in 27 tests. In each test, the hydraulic jump formed downstream the sluice gate and the FPS once placed downstream the jump and once removed, in the same test, with maintaining the same flow conditions, and measurements are taken to investigate the effect of the FPS on the jump. The results show that the additional friction resistance by the FPS increased the tail water level and forced the hydraulic jump towards the sluice gate, in which the FPS produced a converging distance ranged from 0.64m to 5.34m. This convergence of the jump lowered the head losses of the flow before the jump and then increased Froude Number, Fr, and produced higher y2/y1 value. The increased value of y2/y1 increased the energy dissipation of the jump, in which the jump produced energy dissipation ranged from 8.47 to 85.38% with the existence of the FPS instead of 5.91 to 66.14% without it, with same flow conditions. In spite of the considerable increase in the tail water level downstream the FPS, there was no significant differences of the dissipated energy with and without the FPS for the whole system, in which the energy dissipation ranged from 14.05 to 55.91% with the FPS and ranged from 13.57 to 55.09% without it.

Kariba Dam Plunge Pool Scour: quasi-3D Numerical Predictions

Kariba Dam is a 128 m high double-curvature arch dam located on the Zambezi River at the border between Zambia and Zimbabwe. The dam is known worldwide for its impressive plunge pool scour hole of almost 90 m below the tailwater level, which is an unprecedented value in dam history.This paper presents a numerical study performed to assess both past scour and future scour potential at the dam site. Based on gate opening durations and bathymetric surveys since 1960, quasi-3D time-dependent numerical scour computations have been made to assess the scour potential of the gneiss rock for the next 50 years.The computations use the Comprehensive Scour Model (CSM) [Bollaert, 2004]. This model is physics based and allows predicting rock scour evolution with time for the main rock break-up mechanisms (rock mass fracturing, rock block uplift and peeling off of rock blocks along the wall). The model has been calibrated based on past flooding and the corresponding scour observed. Dynamic pressures at the pool bottom have been analytically determined and compared with values measured on a 1/65 scaled model of the dam and its plunge pool constructed at the Laboratory of Hydraulic Constructions of the Swiss Federal Institute of Technology (LCH-EPFL). The numerical model automatically adapts these values during subsequent scour formation by applying a 2D turbulent jet diffusion model, downstream of each of the gates separately. Main assumptions and outcomes of the numerical scour study are presented. It specifically focuses on the potential for future scour as well as on the potential beneficial influence of several proposed countermeasures against further scour formation.

Kariba dam on Zambezi river: stabilizing the natural plunge pool

The paper presents the outstanding case history of the development of a deep scour hole downstream of Kariba arch Dam on Zambezi River, since its commissioning in 1959 for hydropower generation, and the reshaping project under development, designed as a remedial measure to stabilize the plunge pool evolution.The history of spilling through its gated spillway 9 000 m3/s capacity is summarized and the consequent deepening of a scour hole in the competent rocks of river bed, under the spillway impact zone, extending now about 80m below mean tail water level is depicted.The reshaping project development has been validated through an original progressive optimization methodology involving in various steps both civil engineering design and up to date hydraulic modelling, both physical and numerical. The reasonably feasible design of these exceptional civil works, while keeping in operation the dam and both powerhouses totalizing 1350 MW, is then described.

Analysis of Scour Characteristics in Presence of Aerated Crossing Jets

Jets scour is a major topic in hydraulic engineering. It has to be carefully analysed in order to understand the mechanism and predict its geometry. The jets conf guration has a deep inf uence on the scour features. In the present paper the analysis was conducted in presence of two symmetric crossing jets, varying the discharge, the air content, the tailwater level in the downstream stilling basin, the angle between the jets and the vertical distance of the jets crossing point from the water surface, for different vertical jets angle. It was proven that the presence of the air in the jets deeply affects the scour morphology. The scour geometry was analysed and compared with the respective obtained in black water conditions. Useful practical relationships are proposed to estimate the main scour hole dimensions. The analysis was also extended to non-dimensional prof les and it was proved that the effect of air content on them is negligible.

Analysis of scour characteristics in presence of aerated crossing jets

AbstractJets scour is a major topic in hydraulic engineering. It has to be carefully analysed in order to understand the mechanism and predict its geometry. The jets conf guration has a deep inf uence on the scour features. In the present paper the analysis was conducted in presence of two symmetric crossing jets, varying the discharge, the air content, the tailwater level in the downstream stilling basin, the angle between the jets and the vertical distance of the jets crossing point from the water surface, for different vertical jets angle. It was proven that the presence of the air in the jets deeply affects the scour morphology. The scour geometry was analysed and compared with the respective obtained in black water conditions. Useful practical relationships are proposed to estimate the main scour hole dimensions. The analysis was also extended to non-dimensional prof les and it was proved that the effect of air content on them is negligible.

Study of flow at side weir in narrow flume using visualization techniques

The purpose of the research was to quantify characteristics of a subcritical flow at a rectangular sharp-crested side weir in a rectangular main channel using non-invasive measuring techniques based on the visualization of the flow. Experiments were carried out in physical models, including nine different dimensions of the side weir and nine combinations of the inflow and tailwater level for each weir, amounting to 81 test runs. Velocity vector fields were measured in various horizontal planes along the side weir using a high speed digital camera and electrolysis-induced hydrogen bubbles as flow tracers. Recorded films were converted into sequences of images which were used for numerical calculation of local velocities. Components of velocity vectors were determined with great spatial and time resolution. Longitudinal profiles of water surface elevation at each side weir were determined using photos of laser-induced vertical section planes. Measured discharges and flow depths were used to formulate new equation for the side weir discharge coefficient using dimensional analysis. The principal results indicated that velocity distribution along the side weir was distinctly non-uniform, with various velocity ratios increasing along the crest. However, the calculated energy grade line was parallel to the main channel bed, indicating that only friction losses were present. The proposed equations for the side weir discharge coefficient gave results that were in good accordance with two other studies.