Search Results (35)

This study investigates the numerical modeling of a high-velocity circular free-water jet impinging into a plunge pool, focusing on the simulation and validation of mean and fluctuating dynamic pressures on the pool floor. Numerical simulations were performed using two different computation methods, two-phase volume-of-fluid and Euler–Euler, under conditions replicating experimental data obtained at a jet velocity of 7.4 m/s and plunge pool depth of 0.8 m. The models, based respectively on the Volume of Fluid (VoF) and Euler–Euler methods, were evaluated for accuracy in replicating experimentally measured pressures and air concentration values. The Euler–Euler solver, coupled with the k-Omega SST turbulence model, demonstrated mesh independence for mean dynamic pressures with a mesh resolution of 24 cells across the jet diameter. In contrast, two-phase volume-of-fluid exhibited mesh dependency, particularly near the jet stagnation point and pressure values higher than the experimental ones. While the Euler–Euler accurately captured mean pressures and air concentration in close agreement with experimental data, its Reynolds-Averaged Navier–Stokes (RANS) formulation limited its ability to simulate pressure fluctuations directly. To approximate these fluctuations, turbulent kinetic energy values were used to derive empirical estimates, yielding results consistent with experimental measurements. This study demonstrates the efficacy of the Euler–Euler method with the k-Omega SST model in accurately capturing key dynamic pressures and air entrainment in plunge pools while highlighting opportunities for future work on pressure fluctuation modeling across a broader range of jet conditions. Full article

A scour hole in the pre-excavated plunge pool bed downstream of a dam can develop if the energy dissipation of the plunging jet from a spillway is underestimated. The objective of the research was to predict the equilibrium geometry of the scour hole downstream of a high-head dam to safeguard the stability of the dam foundation. A study incorporating both physical and numerical modeling was undertaken to examine the hydrodynamic and geo-mechanical aspects involved in rock scour. Experimental tests were performed to determine equilibrium scour hole profiles in an open-ended, jointed, movable rock bed under various conditions, including different flow rates, dam heights, plunge pool depths, rock sizes, and joint structure orientations. Based on the experimental findings, non-dimensional equations that describe the scour hole geometry were developed. The proposed innovative three-dimensional fluid–solid coupled numerical model is capable of realistically reproducing the equilibrium scour hole profile observed in the experimental tests. The numerical model allows detailed scour computations of fully developed rectangular jets plunging into shallow plunge pools. Full article

Turbulent water jets remain a critical study area, particularly the relation of the water flow with air entrainment and its role in energy dissipation at different hydraulic structures. Plunge pools, formed by the impact of jets on water cushions, play a pivotal role in energy dissipation. Understanding the complex flow dynamics within these pools is essential for designing efficient hydraulic structures. In this research, we present a comprehensive investigation of different numerical simulations, defining two-phase (air-water) in different ways, and them compare with experimental measurements. The primary objective is to analyze the pressure distribution at the bottom of a plunge pool induced by a vertical jet and understand the importance of accurately defining air-water flow in the dynamics of the jet into the pool. Our study bridges the gap between empirical data and computational modeling, shedding light on the intricate behavior of such flows with different method-based solvers: VOF, sub-grid, and multi-phase Euler. Various computational domains, mesh configurations, and analyses spanning different time periods, frequencies, and scales were considered. Full article

The hydrodynamic and thermal interaction of water with the high-temperature melt of a heavy metal was studied via the Volume-of-Fluid (VOF) method formulated for three immiscible phases (liquid melt, water, and water vapor), with account for phase changes. The VOF method relies on a first-principle description of phase interactions, including drag, heat transfer, and water evaporation, in contrast to multifluid models relying on empirical correlations. The verification of the VOF model implemented in OpenFOAM software was performed by solving one- and two-dimensional reference problems. Water jet penetration into a melt pool was first calculated in two-dimensional problem formulation, and the results were compared with analytical models and empirical correlations available, with emphasis on the effects of jet velocity and diameter. Three-dimensional simulations were performed in geometry, corresponding to known experiments performed in a narrow planar vessel with a semi-circular bottom. The VOF results obtained for water jet impact on molten heavy metal (lead–bismuth eutectic alloy at the temperature 820 K) are here presented for a water temperature of 298 K, jet diameter 6 mm, and jet velocity 6.2 m/s. Development of a cavity filled with a three-phase melt–water–vapor mixture is revealed, including its propagation down to the vessel bottom, with lateral displacement of melt, and subsequent detachment from the bottom due to gravitational settling of melt. The best agreement of predicted cavity depth, velocity, and aspect ratio with experiments (within 10%) was achieved at the stage of downward cavity propagation; at the later stages, the differences increased to about 30%. Adequacy of the numerical mesh containing about 5.6 million cells was demonstrated by comparing the penetration dynamics obtained on a sequence of meshes with the cell size ranging from 180 to 350 µm. Full article

A confined plunging liquid jet reactor (CPLJR) is an unconventional efficient and feasible aerator, mixer and brine dispenser that operates under many operating conditions. Such operating conditions could be challenging, and hence, utilizing prediction models built on machine learning (ML) approaches could be very helpful in giving reliable tools to manage highly non-linear problems related to experimental hydrodynamics such as CPLJRs. CPLJRs are vital in protecting the environment through preserving and sustaining the quality of water resources. In the current study, the effects of the main parameters on the air entrainment rate, Q_a, were investigated experimentally in a confined plunging liquid jet reactor (CPLJR). Various downcomer diameters (D_c), jet lengths (L_j), liquid volumetric flow rates (Qj), nozzle diameters (d_n), and jet velocities (V_j) were used to measure the air entrainment rate, Q_a. The non-linear relationship between the air entrainment ratio and confined plunging jet reactor parameters suggests that applying unconventional regression algorithms to predict the air entrainment ratio is appropriate. In addition to the experimental work, machine learning (ML) algorithms were applied to the confined plunging jet reactor parameters to determine the parameter that predicts Q_a the best. The results obtained from ML showed that K-Nearest Neighbour (KNN) gave the best prediction abilities, the proportion of variance in the Q_a that can be explained by the CPLJR parameter was 90%, the root mean square error (RMSE) = 0.069, and the mean absolute error (MAE) = 0.052. Sensitivity analysis was applied to determine the most effective predictor in predicting Q_a. The Qj and V_j were the most influential among all the input variables. The sensitivity analysis shows that the lasso algorithm can create an effective air entrainment rate model with just two of the most crucial variables, Qj and V_j. The coefficient of determination (R²) was 82%. The present findings support using machine learning algorithms to accurately forecast the CPLJR system’s experimental results. Full article

Low-head dams can be dangerous to recreational river users when a submerged hydraulic jump forms downstream, with recirculating surface flows that repeatedly carry trapped recreationists upstream into the high-velocity jet plunging over the dam crest. The flow endangers those who pass over the dam from upstream and can also entrap those who approach too closely from downstream. A national task force is using a range of methods to identify potentially dangerous structures, but definite determination requires field data and an analysis of the hydraulic conditions for each site’s range of likely flow rates. The spreadsheet tool described here determines the submergence created by site-specific tailwater levels and uses previous research results to estimate the associated magnitude of reverse flow velocities. The spreadsheet also determines the crucial tailwater level at which the jet passing over the dam stops plunging into the tailwater pool and instead flips to the surface, creating safer, downstream-directed velocities. The article describes application to specific sites and provides insight about the dangerous flow range of typical low-head dams. Full article

Plunging liquid jet reactor (PLJR) has gained popularity as a feasible and efficient aerator and mixer. However, the measurement of air disentrainment rate (Q_ads), which affects aeration performance, has been overlooked by many researchers. In this work, a newly invented Al-Anzi disentrainment ring (ADR) device was incorporated in CPLJR to experimentally measure Q_ads and its effect on the net air entrainment rate. Furthermore, the effect of new variables (l_ADR and d_s) and old variables (L_j and V_L) on Q_anet were also investigated. Results showed that shorter d_s and l_ADR produced higher Q_anet for the same ADR device. A new net entrainment jet velocity at the impingement point (V_Lnet) was measured at about 651 cm/s, above which bubbles left the base of downcomer as Q_anet. Q_anet increased linearly with V_L; however, Q_ads increased until it reached maximum value, and then decreased. Bubble penetration depth and liquid rise height increased for all V_L until they reached maximum, and then leveled off for the same l_ADR. A significant increase in Q_anet values was achieved with this downcomer in comparison with the conventional one. The increase in Q_anet was measured to be approximately 2.5–15 times of that measured by the standalone downcomer. Full article

In this paper, we present a monitoring program of loss control prevention for airlines to enhance aviation safety and operational efficiency. The assessments of dynamic stability characteristics based on the approaches of oscillatory motion and eigenvalue motion modes for jet transport aircraft response to sudden plunging motions are demonstrated. A twin-jet transport aircraft encountering severe clear-air turbulence in transonic flight during the descending phase was examined as the study case. The flight results in sudden plunging motions with abrupt changes in attitude and gravitational acceleration (i.e., the normal load factor) are provided. Development of the required thrust and aerodynamic models with the flight data mining and the fuzzy logic modeling techniques was carried out. The oscillatory derivatives extracted from these aerodynamic models were then used in the study of variations in stability characteristics during the sudden plunging motion. The fuzzy logic aerodynamic models were utilized to estimate the nonlinear unsteady aerodynamics while performing numerical integration of flight dynamic equations. The eigenvalues of all motion modes were obtained during time integration. The positive real part of the eigenvalues is to indicate unstable motion. The dynamic stability characteristics during sudden plunging motion are easily judged by the values in positive or negative. The present quantitative assessment method is an innovation to examine possible mitigation concepts of accident prevention and promote the understanding of aerodynamic responses of the jet transport aircraft. Full article

Coastal embankments often collapse due to the tremendous destructive energy of an overtopping tsunami flow due to a deep scour by nappe flow. Hence, to clarify the nappe flow formation condition due to the overtopping, a series of tests were carried out within a laboratory flume with immobile settings by lowering the downstream surface angle of an embankment model while keeping the upstream surface slope constant (1:1) with five non-dimensional overtopping depths and six different crest conditions. The conditions imposed on the embankment crest in the flow direction were without vegetation; horizontal crest, (−)4% descending crest slope, (+)4% ascending crest slope, and adding vegetation model with three different densities across the horizontal crest to improve resistance to the flow. The increased resistance provided by the vegetation models were categorized based on the spacing ratio between cylinders to diameter: sparse, intermediate, and dense. Increased vegetation density above the crest results in a significant reduction of flow energy by approximately 30–50% at the downstream brink edge and 40–60% at the downstream plunge basin. In contrast, the maximum energy reduction was found to be by the dense vegetation model. Additionally, owing to the steep slope of the water surface profile and the increasing vegetation density, the impinging jet’s impact point moved closer to the toe of an embankment. This implies that vegetation covers a smaller area while increasing density to mitigate the destructive intensity of flood/tsunami movement. Meanwhile, the descending crest scenario results in a faster nappe flow formation. In contrast, the ascending crest scenario delays the nappe formation while reducing the downstream slope angle. It maintains the sub-critical flow at the crest, except near the downstream brink edge. Full article

This companion paper investigates the hydrodynamics of turbulent bores that propagate on a horizontal plane and have a striking resemblance to dam break waves and tsunami-like hydraulic bores. The focus of this paper is on the propagation of a turbulent bore over a mitigation canal using both laboratory experiments and numerical simulations. In the first part of this paper, the effects of canal depth on the time histories of wave height and velocity were experimentally investigated, and the experimental results were used for the validation of the numerical model. The rapid release of water from an impoundment reservoir at depths of d_o = 0.30 m and 0.40 m generated bores analogous to tsunami-induced inundations. The time histories of the wave heights and velocities were measured at 0.2 m upstream and at 0.2 m and 0.58 m downstream of the canal to study the energy dissipation effect of the mitigation canal. The recorded time series of the water surface levels and velocities were compared with simulation outputs, and good agreement was found between the experimental and numerical water surface profiles, with a Root Mean Square Error (RMSE) of less than 6.7% and a relative error of less than 8.4%. Three turbulence models, including the standard k-ε, Realizable k-ε, and RNG k-ε, were tested, and it was found that all these models performed well, with the standard k-ε model providing the highest accuracy. The velocity contour plots of the mitigation canal with different depths showed jet streams of different sizes in the shallow, medium-depth, and deep canals. The energy dissipation and air bubble entrainment of the bore as it plunged downward into the canal increased as the canal depth increased, and the jet stream of the maximum bore velocity decreased as the canal depth increased. It was found that the eye of the vortex created by the bore in the canal moved in the downstream direction and plunged downward in the middle of the canal, where it then began to separate into two smaller vortices. Full article

Water circulation in storage tanks significantly impacts water quality in distribution networks since old water tends to have low residual chlorine concentrations that are insufficient to neutralize microbial regeneration. Their large capacity and long residence times result in uneven mixing, which can accelerate the disinfectant decay and the formation of potentially carcinogenic disinfection by-products. The phenomenon is strongly related to the tank inflow conditions, since there are no active mixing devices. This paper presents a comprehensive analysis of the flow dynamics in circular storage tanks using a three-dimensional computational fluid dynamics model. The main motivation is that the inflow—which mixing processes rely on—strongly influences the circulations. The numerical analysis provided includes a thorough investigation of interest in understanding flow dynamics for two inflow configurations: (i) the plunging jet modelling and comparison with published experimental data and (ii) the submerged jet as an improvement measurement for these storage tanks. Full article

Jet velocity is an important parameter affecting the air entrainment rate of plunging liquid jet processes. While the vast majority of researchers have investigated the effect of jet velocity, only a few of them considered the effect of jet length in calculating the jet velocity at impingement point. This study investigates the difference (ΔV) between the jet velocity at the inception of the nozzle (V_j) and the impingement point (V_L) for a range of operating conditions. Furthermore, bubble voidage inside the downcomer, another critical parameter in plunging jets, is estimated using three different voidage equations incorporated inside a momentum balance model to predict the two-phase elevation level (H_R) inside the downcomer. Results showed that ΔV is significant (V_L > V_j), especially at low jet flow rates and high jet lengths. Generally, the momentum balance model predicted the H_R well, and its prediction improves with downcomer diameter. Given that, the model still needs to be refined for more accuracy for a wide range of operating conditions. Full article

Spillways are a requirement for dams’ safety, mainly preventing overtopping during floods. A common spillway solution involves plunging jets, which dissipate a considerable flow energy in the plunge pool. Energy dissipation has to occur in a controlled manner to avoid endangering the dam foundation and river slopes. Indeed, a scouring process in the downstream riverbed will inevitably develop until equilibrium is reached, otherwise a suitable pre-excavated or concrete lined plunge pool has to be provided. This paper focuses on experimental studies in which particular attention was paid to the dynamic pressures in the plunge pool floor at the vicinity of the jet stagnation zone sampled at 2.4 kHz. A rectangular experimental facility, 4.00 m long and 2.65 m wide, was used as plunge pool. Tests involved a vertical circular plunging jet with velocity ranging from 5 to 18 m/s and plunge pool depth ranging from 4.2 to 12.5 jet diameters. Differences in dynamic pressure measurements are highlighted between transducers located in the inner and outer regions of the jet diameter footprint. Several parameters characterizing the dynamic pressures evidence trends tied with the jet velocity that, to the authors’ knowledge, were not dealt in previous research. These can derive from the coupling effects of consequent recirculating motions and air entrainment in the limited-size plunge pool. Both effects, increasing with velocity, cause an reduction in the efficiency of the diffusing jet shear layer. This aspect deserves further investigation to achieve a better understanding and more complete characterization. Full article

Hydrodynamic pressure exerted on a plunge pool slab by jet impingement is of high interest in high dam projects. The present study experimentally investigated the characteristics of pressure induced by a jet through a constant width flip bucket (CFB) and a slit flip bucket (SFB). A pressurized plane pipe was employed in the flume experiments to control the inlet velocities in the flip buckets. A concise method is proposed to predict the mean dynamic pressure field. Its implementation is summarized as follows: First, the position of the pressure field is determined by the trajectories of free jets, and to calculate its trajectories, an equation based on parabolic trajectory theory is used; second, the maximum mean dynamic pressure is obtained through dimensional analysis, and then the pressure field is established by applying the law of Gaussian distribution. Those steps are integrated into a concise computing procedure by using some easy-to-obtain parameters. Some key parameters, such as takeoff velocity coefficient, takeoff angle coefficient, and the parameter $k_2$, are also investigated in this paper. The formulas of these coefficients are obtained by fitting the experimental data. Using the proposed method, the easy-to-obtain geometric parameters and initial hydraulic conditions can be used to calculate the maximum mean dynamic pressure on the slab. A comparison between experimental data and calculated results confirmed the practicability of this model. These research results provide a reference for hydraulic applications. Full article

A more complete understanding of scour mechanisms for flows downstream of grade-control structures, including their temporal evolution, has the potential to lead to improved predicting tools for design. To date, design equations have been mostly derived empirically, i.e., by parametric modelling (at generally-small scales) corresponding to specific structure configurations, and for limited ranges of hydraulic conditions. Although these approaches allowed different authors to propose many empirical and/or semi-empirical equations, they lack generality and may lead to incorrect estimations when applied outside their ranges of validity. First-principles-based methods with solid calibration and validation procedures can overcome these issues. Following recent theoretical advancements presented elsewhere by the last three authors, in this work we analyze and test the predictive capability of a scour evolution model based on the phenomenological theory of turbulence (PTT) by using a large dataset pertaining to different grade-control structures. Although the PTT model was developed (and validated) for scour evolution caused by oblique and vertical plunging jets, we show that its basic assumptions are still valid for the addressed low-head structures, encompassing rock structures, stepped gabion weirs, rock and bed sills, and others. Furthermore, we also provide interesting insights on scour evolution by contrasting the predicting capability of our model against experimental data by different authors for specific structures. Results of the comparison conclusively show that the PTT model has a general validity and represents a trustable tool to estimate scour evolution regardless of the structure configuration and hydraulic conditions. Full article