Search Results (81)

Ensuring the structural integrity of mechanical components operating in fluid environments requires precise and reliable monitoring techniques. This study presents a methodology for reconstructing the full-field deformation of a flexible aluminium plate subjected to unsteady water flow in a water tunnel, using a structural modal reconstruction approach informed by experimental data. The experimental setup involves an aluminium lamina (200 mm × 400 mm × 2.5 mm) mounted in a closed-loop water tunnel and exposed to a controlled flow with velocities up to 0.5 m/s, corresponding to Reynolds numbers on the order of ${10}^4$, inducing transient deformations captured through an image-based optical tracking technique. The core of the methodology lies in reconstructing the complete deformation field of the structure by combining a reduced number of vibration modes derived from the geometry and boundary conditions of the system. The novelty of the present work consists in the integration of the Internal Strain Potential Energy Criterion (ISPEC) for mode selection with a data-driven machine learning framework, enabling real-time identification of active modal contributions from sparse experimental measurements. This approach allows for an accurate estimation of the dynamic response while significantly reducing the required sensor data and computational effort. The experimental validation demonstrates strong agreement between reconstructed and measured deflections, with normalised errors below 15% and correlation coefficients exceeding 0.94, confirming the reliability of the reconstruction. The results confirm that, even under complex, time-varying fluid–structure interactions, it is possible to achieve accurate and robust deformation reconstruction with minimal computational cost. This integrated methodology provides a reliable and efficient basis for structural health monitoring of flexible components in hydraulic and marine environments, bridging the gap between sparse measurement data and full-field dynamic characterisation. Full article

Acid mine drainage (AMD) is an environmental concern that needs to be addressed by some mining industries because of its high concentrations of metals and acidity that destroy affected ecosystems. Its formation typically persists beyond the operating life of a mine site. Its management is even more challenging for sites that are abandoned without rehabilitation. In this study, a legacy copper–gold mine located in Sto. Niño, Tublay, Benguet, Philippines, generating a copper- and manganese-rich AMD (Cu, maximum 17.2 mg/L; Mn, maximum 2.90 mg/L) at pH 4.59 (minimum) was investigated. With its remote location inhabited by the indigenous people local community (IPLC), a novel limestone-based hybrid passive treatment system that combines a limestone leach bed (LLB) and a controlled modular packed bed reactor (CMPB) has been developed from the laboratory and successfully deployed in the field while investigating the effective hydraulic retention time (HRT), particle size, and redox conditions (oxic and anoxic) in removing Cu and Mn and increasing pH. Laboratory-scale and pilot-scale systems using simulated and actual AMD, respectively, revealed that a 15 h HRT and both oxic and anoxic conditions were effective in treating the AMD. Considering these results and unsteady conditions of the stream in the legacy mine, a hybrid multi-stage limestone leach bed and packed bed were deployed having variable particle size (5 mm to 100 mm) and HRT. Regular monitoring of the system showed the effective removal of Cu (88.5%) and Mn (66.83%) as well as the increase of pH (6.26), addressing the threat of AMD in the area. Improvement of the lifespan of the system needs to be addressed, as issues of Cu-armoring were observed, resulting in reduced performance over time. Nonetheless, the study presents a novel technique in implementing passive treatment systems beyond the typical treatment trains reported in the literature. Full article

To accommodate the integration of emerging energy sources such as wind and solar power, hydroelectric units are increasingly required to operate across a broader range of conditions. This operational expansion often leads to elevated pressure pulsations within turbines under non-design conditions, resulting in intensified hydraulic vibrations and, in some cases, structural damage and overall stability concerns. In this study, the Shear Stress Transport (SST) k-ω turbulence model is employed to perform unsteady numerical simulation calculation of a Francis-99 mixed-flow model turbine operating at a head of 400 m. Simulations are conducted for three operating regimes: low-flow and low-load conditions, optimal conditions, and high-flow and high-load conditions. Internal flow in the full flow channel of the turbine and pressure pulsation in the full flow channel components is systematically analyzed. The findings indicate that under low-flow and low-load conditions, the ability of the runner blades to constrain the water flow is significantly decreased. Across all three operational scenarios, the dominant pressure pulsation frequencies observed in both the stationary and guide vane are 30f_n, primarily influenced by dynamic and static disturbance caused by the rotation of the runner’s long and short blades. In low-flow and low-load conditions, a low-frequency component at 0.2f_n, due to the existence of vortices in the draft tube, exhibits the highest amplitude—up to 0.6%—in the straight cone section. Within the runner, pressure pulsation frequencies are predominantly associated with the rotation of the guide vane. Conversely, the draft tube region is characterized by frequency components related to both the runner’s dynamic-static interaction at 30f_n and vortex-induced pulsations at 0.2f_n. Full article

Dual-inlet tail escapes, combining an orifice and a weir, are key hydraulic structures that evacuate excess water from canal termini during maintenance and protect berms by discharging surplus irrigation flows. Conventional sizing methods typically depend on trial and error, which is time-consuming and may yield suboptimal design. This study introduces a graphical design approach and a MATLAB-based tool, TAILOPT, developed to streamline tail escape design. The tool incorporates both the Fanning and Darcy–Weisbach friction formulations for head loss estimation and can automatically generate an “.inp” file for EPA-SWMM, enabling direct unsteady-state hydraulic assessment. This integration reduces design effort and supports evaluation of alternative hydraulic and drainage scenarios within a single workflow. Two applications illustrate the framework. The first shows that overly steep drainage slopes (Sp > 2%) are impractical, while vertical drops may require larger pipe diameters. The second application applies TAILOPT to a distributary canal, determining the optimal pipe size and verifying its performance in EPA-SWMM under emergency surplus flow and routine dewatering conditions. The results demonstrate that the method yields economical, robust, and practitioner-friendly designs; however, modeling simplifications, such as assuming continuously submerged orifice flow, can introduce minor deviations in the predicted channel emptying times. Full article

Two-way channel irrigation pumping stations are widely used along rivers for irrigation and drainage. Due to fluctuating internal and external water levels, these stations often operate under ultra-low or near-zero head conditions, leading to poor hydraulic performance. This study employs computational fluid dynamics (CFD) to investigate such systems’ pressure fluctuation and chaotic dynamic characteristics. A validated 3D model was developed, and the wavelet transform was used to perform time–frequency analysis of pressure signals. Phase space reconstruction and the Grassberger–Procaccia (G–P) algorithm were applied to evaluate chaotic behavior using the maximum Lyapunov exponent and correlation dimension. Results show that low frequencies dominate pressure fluctuations at the impeller inlet and guide vane outlet, while high-frequency components increase significantly at the intake bell mouth and outlet channel. The maximum Lyapunov exponent in the impeller and guide vane regions reaches 0.0078, indicating strong chaotic behavior, while negative values in the intake and outlet regions suggest weak or no chaos. This integrated method provides quantitative insights into the unsteady flow mechanisms, supporting improved stability and efficiency in ultra-low-head pumping systems. Full article

In 2071, the Hydraulic community will commemorate the second centenary of the Baré de Saint-Venant equations, also known as the Shallow Water Equations (SWE). These equations are fundamental to the study of open-channel flow. As non-linear partial differential equations, their solutions were largely unattainable until the development of computers and numerical methods. Following 1960, various numerical schemes emerged, with Preissmann’s scheme becoming the most widely employed in many software applications. In the 1990s, some researchers identified a significant limitation in existing software and codes: the inability to simulate transcritical flow. At that time, Preissmann’s scheme was the dominant method employed in hydraulics tools, leading the research community to conclude that this scheme could not handle transcritical flow due to suspected instability. In response to this concern, several researchers suggested modifications to Preissmann’s scheme to enable the simulation of transcritical flow. This paper will demonstrate that these accusations against the Preissmann scheme are unfounded and that the proposed improvements are unnecessary. The observed instability is not due to the numerical method itself, but rather a mathematical instability inherent to the SWE, which can lead to ill-posed conditions if a specific derived condition is not met. In the context of a friction slope formula based on Manning or Chézy types, the condition for ill-posedness of the 1D shallow water equations simplifies to the Vedernikov number condition, which is necessary for roll waves to develop in uniform flow. This derived condition is also relevant for the formation of roll waves in unsteady flow when the 1D shallow water equations become ill-posed. Full article

As a core component in renewable energy systems for grid regulation, hydropower units are increasingly exposed to flow conditions that elevate the risk of cavitation and erosion, posing significant challenges to the safe operation of flow-passage components. In this study, model testing and computational fluid dynamics (CFD) simulations are employed to investigate the hydraulic performance and cavitation behavior of a bulb turbine operating under rated head conditions and varying cavitation numbers. The analysis focuses on how changes in cavitation intensity affect flow characteristics and efficiency within the runner region. The results show that as the cavitation number approaches its critical value, the generation, growth, and collapse of vapor cavities increasingly disturb the main flow, causing a marked drop in blade hydraulic performance and overall turbine efficiency. Cavitation predominantly occurs on the blade’s suction side near the trailing edge rim and in the clearance zone near the hub, with bubble coverage expanding as the cavitation number decreases. A periodic inverse correlation between surface pressure and the cavitation area is observed, reflecting the strongly unsteady nature of cavitating flows. Furthermore, lower cavitation numbers lead to intensified pressure pulsations, aggravating flow unsteadiness and raising the risk of vibration. Full article

This study presents a numerical investigation of the internal flow characteristics within the draft tube of a Kaplan turbine using computational fluid dynamics (CFD). The distribution and evolution of vortical structures, particularly the formation and development of vortex ropes under various operating conditions, are systematically analyzed. The study aims to explore the effects of blade angle and guide vane opening on the internal flow characteristics of the unit, thereby providing guidance for flow control strategies. The influence of guide vane opening and turbine head on vortex dynamics and flow stability is examined, with a focus on the pressure pulsations induced by vortex ropes through frequency-domain analysis. The results indicate that increased guide vane openings and higher heads lead to the expansion and downstream extension of the vortex rope into the elbow section, causing significant low-frequency pressure pulsations and enhancing flow instability. These findings contribute to a deeper understanding of unsteady flow behavior in Kaplan turbine draft tubes and provide a theoretical foundation for improving hydraulic stability and optimizing operational performance. Full article

In this paper, a novel approximate triangular fuzzy finite element method (FEM) is proposed to solve the one-dimensional second-order unsteady nonlinear fuzzy partial differential Boussinesq equation. The physical problem concerns the case of the drought flow of a horizontal unconfined aquifer with a limited breath B and special boundary conditions: (a) at x = 0, the water level is equal to zero, and (b) at x = B, the flow rate is equal to zero due to the presence of an impermeable wall. The initial water table is assumed to be curvilinear, following the form of an inverse incomplete beta function. To account for uncertainties in the system, the hydraulic parameters—hydraulic conductivity (K) and porosity (S)—are treated as fuzzy variables, considering sources of imprecision such as measurement errors and human-induced uncertainties. The performance of the proposed fuzzy FEM scheme is compared with the previously developed orthogonal fuzzy FEM solution as well as with an analytical solution. The results are in close agreement with those of the other methods, with the mean error of the analytical solution found to be equal to $1.19·{10}^{-6}$. Furthermore, the possibility theory is applied and fuzzy estimators constructed, leading to strong probabilistic interpretations. These findings provide valuable insights into the hydraulic properties of unconfined aquifers, aiding engineers and water resource managers in making informed and efficient decisions for sustainable hydrological and environmental planning. Full article

In the context of irrigation canal flow, numerical models developed to accurately estimate canal behavior based on gate trajectories are often highly complex. Consequently, hardware limitations make it significantly more challenging to implement these models locally at gate devices. In this regard, one of the most significant contributions of this paper is the concept of the hydraulic influence matrix (HIM) and its application as a linear model to estimate the water surface flow in irrigation canals, integrated within an irrigation canal controller to facilitate real-time operations. The HIM model provides a significant advantage by quickly and accurately computing water level and velocity perturbations in open-flow canals. This capability empowers watermasters to apply this linear free-surface model in both unsteady and steady flow conditions, enabling real-time applications in control algorithms. The HIM model was validated by comparing water-level estimates under various perturbations with results from software using the full Saint-Venant equations. The test involved introducing a 10% perturbation in gate movement over a specified time period in two different test cases, resulting in a flow discharge increase of more than 10% in each test case. The results showed maximum absolute errors below 7 cm and 0.2 cm, relative errors of 0.7% and 0.023%, root mean square errors ranging from 2.4 to 0.07 cm, and Nash–Sutcliffe efficiency values of approximately 0.95 in the first and second test cases, respectively, when compared to the full Saint-Venant equations. This highlights the high precision of the HIM model, even when subjected to significant disturbances. However, larger gate movement disturbances (exceeding 10%) should be planned in advance rather than managed in real time. Full article

This study proposes the water hammer energy difference (WHED) method based on unsteady flow energy and continuity equations, as well as the propagation laws of water hammer in closed pipes, and verifies its accuracy. Additionally, the parameter evolution patterns of typical transient conditions in pumped storage power plants are investigated based on WHED. The application of WHED in the transient processes of hydropower plants (HPs) is validated by experiments, showing a maximum error of about 7% between numerical and experimental results under conditions of initial load increase followed by decrease (H_R = 184 m). Additionally, WHED was validated under two critical conditions in pumped storage plants (PSPs): 90% load rejection in generating mode and emergency power-off in pumping mode. In PSPs, the results of WHED are consistent with those obtained using the method of characteristics (MOC), with a maximum fault tolerance rate Δ < 3%. Notably, WHED offers superior time efficiency when analyzing hydraulic transitions in complex pipe networks, as it directly considers boundary conditions at both ends of the pipeline and hydraulic machinery, whereas MOC requires dividing the pipeline into multiple segments with a series of boundary points. Lastly, WHED’s energy parameters are used to describe flow stability from a physics perspective, explaining the causes of pressure fluctuations during transient periods in HPs and PSPs. These findings offer valuable references and guidance for the safe operation of PSPs and HPs. Full article

Accurate knowledge of the flow rate is essential for hydraulic systems, enabling the calculation of hydraulic power when combined with pressure measurements. These data are crucial for applications such as predictive maintenance. However, most flow rate sensors in fluid power systems operate invasively, disrupting the flow and producing inaccurate results, especially under transient conditions. Utilizing pressure transducers represents a non-invasive soft sensor approach since no physical flow rate sensor is used to determine the flow rate. Usually, this approach relies on the Hagen–Poiseuille (HP) law, which is limited to steady and incompressible flow. This paper introduces a novel soft sensor with an analytical model for transient, compressible pipe flow based on two pressure signals. The model is derived by solving fundamental fluid equations in the Laplace domain and converting them back to the time domain. Using the four-pole theorem, this model contains a relationship between the pressure difference and the flow rate. Several unsteady test cases are investigated and compared to a steady soft sensor based on the HP law, highlighting our soft sensor’s promising capability. It exhibits an overall error of less than $0.15$% for the investigated test cases in a distributed-parameter simulation, whereas the HP-based sensor shows errors in the double-digit range. Full article

This paper aims to numerically assess the cavitation damage of hydrodynamic machines and hydraulic components and its development in time, based on cavitation erosion tests with samples of used materials. The theoretical part of this paper is devoted to the numerical simulation of unsteady multiphase flow by means of computational fluid dynamics (CFD) and to the prediction of the erosive effects of the collapses of cavitation bubbles in the vicinity of solid surfaces. Compressible unsteady Reynolds-averaged Navier–Stokes equations (URANS) are solved together with the Zwart cavitation model. To describe the destructive collapses of vapor bubbles, the modeling of cavitation bubble dynamics along selected streamlines or trajectories is applied. The hybrid Euler–Lagrange approach with one-way coupling and the full Rayleigh–Plesset equation (R–P) are therefore utilized. This paper also describes the experimental apparatus with a rotating disc used to reach genuine hydrodynamic cavitation and conditions similar to those of hydrodynamic machines. The simulations are compared with the obtained experimental data, with good agreement. The proposed methodology enables the application of the results of erosion tests to the real geometry of hydraulic machines and to reliably predict the locations and magnitude of cavitation erosion, so as to select appropriate materials or material treatments for endangered parts. Full article

Due to the effects of swing motion, the performances and internal flow characteristics of marine centrifugal pump undergo some unsteady variations in the marine environment. The hydraulic test system with six degree of freedom parallel motion platform is established to study the pump performance characteristics at the different heel angles of steady roll position and pitch position. The pump head gradually decreases as heel angle increases. The pump head has decreased by 7% to reach the minimum at the 15° heel angle of roll position. At the same heel angle, the head at the roll position is lower than that at the pitch position under the rated flow condition. The fluid in the impeller passage is subjected to the additional inertial force of roll motion or pitch motion under unsteady swing motion, inducing some flow bias phenomena in the velocity field. The unsteady development of flow velocity induces the intense vortex motion, and the shedding and dissipation of interblade vortices are affected. The periodic flow-induced pulsation characteristics obviously appear in the impeller passage. The pulsation periodicity and pressure amplitude are influenced due to the swing motion. The pitch motion induces the greater hydraulic excitation and fluid-induced vibration amplitude. In addition to the pressure pulsation at the low frequencies, the pulsation amplitude at 20 times the shaft frequency is evident under pitch motion. Full article

To address the escalating demand for power grid load regulation, pumped storage power stations must frequently switch between operational modes. As a key component of such stations, the pump turbine has seen extensive research on its steady-state flow behavior. However, the intricate dynamics of its transient flow have not yet been thoroughly examined. Notably, the no-load condition represents a quintessential transient state, the instability of which poses challenges for grid integration. Under certain extreme conditions, this could result in the impairment of the unit’s elements, interruption of its functioning, and endangerment of the security of the power station’s output as well as the stability of the power network’s operations. Thus, investigating the flow characteristics of pump turbines under no-load conditions is of significant practical importance. This paper focuses on the transient flow characteristics of a Weifang hydro-generator unit under no-load conditions, exploring the internal unsteady flow features and their underlying mechanisms. The study reveals that under no-load conditions, the runner channel is obstructed by a multitude of vortices, disrupting the normal pressure gradient within the runner and resulting in substantial hydraulic losses. Within the draft tube, a substantial reverse flow zone is present, predominantly along the walls. This irregular flow pattern within the tube generates a potent, stochastic pressure fluctuation. In addition to the interference frequencies of dynamic and static origins, the pressure pulsation frequency at each measurement point also encompasses a substantial portion of low-frequency, high-amplitude components. Full article