Froude Number Fr Research Articles

Fast Prediction of Solute Concentration Field in Rotationally Influenced Fluids Using a Parameter-Based Field Reconstruction Convolutional Neural Network

Many high-performance fluid dynamic models do not consider fluids in a rotating environment and often require a significant amount of computational time. The current study proposes a novel parameter-based field reconstruction convolutional neural network (PFR-CNN) approach to model the solute concentration field in rotationally influenced fluids. A new three-dimensional (3D) numerical solver, TwoLiquidMixingCoriolisFoam, was implemented within the framework of OpenFOAM to simulate effluents subjected to the influence of rotation. Subsequently, the developed numerical solver was employed to conduct numerical experiments to generate numerical data. A PFR-CNN was designed to predict the concentration fields of neutrally buoyant effluents in rotating water bodies based on the Froude number (Fr) and Rossby number (Ro). The proposed PFR-CNN was trained and validated with a train-validation dataset. The predicted concentration fields for two additional tests demonstrated the good performance of the proposed approach, and the algorithm performed better than traditional approaches. This study offers a new 3D numerical solver, and a novel PFR-CNN approach can predict solute transport subjected to the effects of rotation in few seconds, and the PFR-CNN can significantly reduce the computational costs. The study can significantly advance the ability to model flow and solute transport processes, and the proposed CNN-based approach can potentially be employed to predict the spatial distribution of any physical variable in the lentic, ocean, and earth system.

Reliable prediction of the discharge coefficient of triangular labyrinth weir based on soft computing techniques

Weirs are important hydraulic structures widely used to control the flow rates in open channels and rivers. As a remarkable parameter, the discharge coefficient (Cd) determines the weirs' passing capacity. In this research, to more accurately predict the Cd of triangular labyrinth weir, the machine learning (ML) models, including least square support vector machine (LS-SVR), quantile regression forest (QRF), and Gaussian process regression (GPR) were developed and assessed. Several statistical and visual methods were utilized to assess ML accuracy. Data management was performed to objectively evaluate these models' performance, and the optimal training/testing proportion was determined reliably. Sensitivity analysis determined that the highest effective parameters in prediction Cd are l/h and Froude number (Fr). The prediction results of the GPR model with R2 = 0.986 and RMSE = 0.009 are superior to those of the QRF and LSSVR. Compared to empirical models, GPR provides much better accuracy and stability. Furthermore, ML models were adopted for probabilistic Cd prediction for its nature of high variability. The examination of models demonstrates that GPR can obtain an appropriate prediction interval on the Cd prediction of triangular labyrinth weir in comparison with LSSVR and QRF. Furthermore, the GPR model is strongly recommended for predicting Cd; because this model indicates good learning performance and can represent point prediction coupled with prediction intervals.

Characteristics of Vegetation Resistance Variation in Muddy Water Flows

The shoal area of the lower Yellow River in China is not flooded with water during the dry season, so various plants can grow. When floods overflow the plains in the flood season, the complexity of water resistance is increased due to the resistance to water flow by vegetation, which directly affects flood discharge in the beach area. The drag force coefficient (CD), Manning’s roughness coefficient (n), and Darcy-Weisbach resistance coefficient (f) are commonly used to characterize vegetation drag force. Such studies are commonly conducted in clear water, but flood water in the lower Yellow River is generally muddy. In order to study the effect of the same sediment content and different sedimentation thicknesses on the resistance of muddy waters containing vegetation, this study conducted experiments in a flume (length = 28 m, width = 0.5 m, and height = 0.5 m) under different deposition thicknesses. The results showed that the vegetation drag force coefficient (CD), vegetation roughness (nb), and Darcy-Weisbach drag coefficient (f) all decreased logarithmically with increasing Reynolds number (Re) and Froude number (Fr). When Re > 30,000, under the conditions of different siltation thicknesses of vegetation, the vegetation roughness tended to stabilize near its minimum value. When the Reynolds number of the water flow is large (Re > 20,000), the variation of the Darcy-Weisbach drag coefficient f slows down with the Reynolds number Re. Logarithmic functions were established for the above resistance coefficients and flow coefficients, and the corresponding correlation coefficients were high, indicating that the conclusions were reliable.

Numerical study of turbulent flow in USBR VI stilling basin

The USBR VI stilling basin is one of the oldest basins designed to dissipate the energy at the outlet of pipes. In this study, the effect of two parameters including the Froude number (Fr) of inlet flow to the basin and the ratio of basin width to equivalent depth of the inlet flow (W/D) on the characteristics of mean and turbulent flow inside the USBR VI stilling basin were investigated, numerically. Reynolds Averaged Navier–Stokes (RANS) equations were solved with Re-Normalization Group (RNG) k-ε turbulence model. Results showed that by increasing W⁄D, from 3.50 to 9.23, decreasing rate of the average velocity at the end of the basin to the average velocity of the inflow increases from 80 to 97% and decreasing rate of the maximum velocity at the end of the basin to the average velocity of the inflow increases from 40 to 87%. Also, by increasing W⁄D, from 3.50 to 9.23, the average turbulent dissipation rate in the whole basin increases to 4.5 times, moderately. Moreover, by increasing W⁄D, from 3.50 to 9.23, the dissipation of turbulent flow energy in the basin becomes four times. Therefore, to design a USBR VI stilling basin based on the existing conditions, W⁄D recommended to increase as much as possible until nearly 10.

Investigation of heavy gas dispersion characteristics in a static environment: Spatial distribution and volume flux prediction

The unexpected release of hazardous gases due to natural/industrial accidents or man-made disasters can have tragic consequences. Compared with other gaseous pollutants, heavy gases easily accumulate in personnel working areas and are more difficult to eliminate through existing mechanical ventilation systems. In this paper, to improve air quality in enclosed environments, the spatial characteristics of heavy gas dispersion were obtained based on an analysis of the basic properties of heavy gas dispersion. Schlieren experiments and image processing were conducted with shadow correction and noise reduction. The computational fluid dynamics (CFD) was used for predicting the dispersion of heavy gas. The numerical simulations cover a wide range of the densimetric Froude number (Fr) from 6.45 to 25.79, and a best-fit relation of Fr and the height of heavy gas fountain was provided. The radial velocity, radial density and axial density at cross-section of heavy gas dispersion were normalized using the unified scaling law. The axial density reached a minimum value at a height of 10 times the inlet diameter. Further decreases in the inertial force or decreases in the buoyant force can reduce the dilution of heavy gas by ambient fluids, which means that heavy gases diffuse faster and farther. An alternative method for estimating volume flux during gas dispersion using Fr was also proposed.

Plunging Flow and Coherent Turbulent Structures in a Straight Pool‐Riffle

AbstractPool‐riffle units are naturally occurring topographical elements of rivers. Various hypotheses have been proposed to describe how the hydrodynamics in pool‐riffle units may lead to scour and sediment transport. However, most hypotheses have focused on time averaged properties, and a physical mechanism for observations of high near‐bed velocities has not been proposed. In this study, we apply Large Eddy Simulations to examine the dynamics of flow over straight riffles. We show that a high velocity core of fluid can alternately skim or plunge toward the bed as a function of the Froude number (Fr) at the crest of the riffle, even within a subcritical flow regime. Coherent turbulent structures are generated in the pool and induce high magnitude fluctuations of shear stress and bed pressure. Four different turbulent structures are described and the concept of vortex resistance is used to discuss how turbulence can induce the observed bifurcation in pool hydrodynamics. Despite the simple geometry, the hydraulic scaling means that the results provide a novel physical explanation of near‐bed high velocity flow observations in natural pool‐riffles. The results are also significant because turbulent shear stresses in the head of a pool exceed what occurs elsewhere in the channel, including the riffles. Further research should examine the conditions under which plunging flow may occur and turbulence may lead to sediment entrainment in other riffle pool geometries.

Geometrical features and global radiant heat of double turbulent jet flames

In energy industry, double jet fires are often reported to occur with a large release momentum at the leakage exit. The available literature considered the double buoyancy-controlled jet flames, and also neglected the restrictive effect of ground or tank surface. In this paper, an experimental setup is built to model the interaction of double turbulent jet fires with different spacings. Different nozzle diameters and exit velocities are chosen to achieve the transition from flame buoyancy to exit momentum for the dominance of turbulent jet flames. Comparative tests are also conducted between with and without a plate near the nozzle exit. It is found that the flame buoyancy, exit momentum and nozzle spacing significantly affect the flame merging behavior. A new dimensionless parameter coupling the Froude number (Fr) and the spacing is proposed to well fit the merging probability (Pm) of double jet flames dominated by the flame buoyancy (Fr < 105 for propane) and the exit momentum (Fr ≥ 105 for propane), respectively. The interaction of double jet flames leads to a less lift-off height than a single jet flame, and the lift-off height can also be reduced by a plate near the nozzle exit. A correlation coupling the spacing, the exit diameter and Froude number, is developed for the mean flame height of double jet fires. The distributions of radiant heat flux are intensively measured around the double jet flames, which can help to calculate the radiative fraction. The radiative fraction of double jet flames at the full merging state (Pm = 1) follows the law of a single jet flame, and it decreases at the intermittent (0 < Pm < 1) and no merging (Pm = 0) states, as compared to that of a single jet flame. In addition, the available line source radiation model of a single jet flame is revised to predict the thermal radiation of double jet flames in the three different merging states.

Laboratory-Scaled Investigation into Combined Impacts of Temporal Rainfall Patterns and Intensive Tillage on Soil and Water Loss

Many studies have focused on the impacts of rainfall duration and intensity, while overlooking the role of rainfall patterns on intensive tillage erosion in hilly agricultural landscapes. The objective of this study was to determine the combined effects of rainfall patterns and tillage erosion on surface runoff and soil loss on sloping farmland in the purple soil area of China. Five simulated rainfall patterns (constant, rising, falling, rising–falling, and falling–rising) with the same total precipitation were designed, and the intensive tillage treatment (IT) and no-tillage treatment (NT) were subjected to simulated rainfall using rectangular steel tanks (2 m × 5 m) with a slope of 15°. To analyse the differences in the hydrological characteristics induced by tillage erosion, we calculated the flow velocity (V), Reynolds number (Re), Froude number (Fr), and Darcy–Weisbach resistance coefficient (f). The results indicate that significant differences in surface runoff and sediment yield were found among different rainfall patterns and rainfall stages (p &lt; 0.05). The falling pattern and falling–rising pattern had a shorter time gap between the rainfall initiation and runoff occurrence as well as a larger sediment yield than those of the other rainfall patterns. The value of f varied from 0.30 to 9.05 for the IT and 0.48 to 11.57 for the NT and exhibited an approximately inverse trend to V and Fr over the course of the rainfall events. Compared with the NT, the mean sediment yield rates from the IT increased the dynamic range of 8.34–16.21% among the different rainfall patterns. The net contributions of the IT ranged from 2.77% to 46.39% in terms of surface runoff and 10.14–78.95% in terms of sediment yield on sloping farmland. The surface runoff and sediment yield were positively correlated with rainfall intensity, V, and Fr, but negatively correlated with f irrespective of tillage operation (p &lt; 0.05). The results showed that the tillage erosion effects on soil and water loss were closely related to rainfall patterns in hilly agricultural landscapes. Our study not only sheds light on the mechanism of tillage erosion and rainfall erosion but also provides useful insights for developing tillage water erosion prediction models to evaluate soil and water loss on cultivated hillslopes.

Experimental study on tail cavity structure and pressure characteristics of underwater vehicle with tail jet

The tail of an underwater vehicle with a tail jet often creates an attached tail cavity when moving at high speed. The strong coupling between the tail cavity and high-speed jet affects the kinematics characteristics of underwater vehicles. This paper compares the influence of Froude number (Fr) and ventilation coefficient (CQv) on the tail cavity at area ratio A/Ae = 92.5 and 236.7 by water tunnel experiment. It was found that at a small Fr, the critical ventilation coefficient of the transition from intact (IC) to partially broken (PBC) and PBC to pulsating foam (PFC) at A/Ae = 92.5 is greater than that of A/Ae = 236.7. The cavitation number (σc) at A/Ae = 92.5 is generally smaller than that of A/Ae = 236.7. With increased CQv, PBC's dimensionless time-averaged length (Lc‾/D) decreases sharply and then gradually flattens. The Lc‾/D of A/Ae = 236.7 is larger than that of A/Ae = 92.5. The fluctuation amplitude of the PBC length is smaller than that of the PFC, and the fluctuation frequency (fLc) of the PFC length is about 120 Hz. The change in the tail cavity will affect the pressure characteristics of the vehicle's bottom. With the increase of CQv, the peak frequency of the bottom pressure fluctuation (fpeak) will continue to rise in the PBC until the transition to the PFC, and the fpeak will remain at about 120 Hz. The correlation coefficient is 0.74 between the fLc and the fpeak. In addition, the pressure oscillation intensity at the vehicle's bottom (pbrms) is small in the IC region. When the tail cavity changes from PBC to PFC, pbrms increases gradually at first, then tends to be flat.

Simulation and experimental research on hydrodynamic performance of fully attached submarine in the surface and near the surface modes

The switch between the surface and near-surface modes is critical to the hydrodynamic performance of the submarines. In this study, based on tank experiments, an improved delayed detached-eddy simulation (IDDES) method based on the shear stress transport (SST) K-Omega was tested for its ability to predict the hydrodynamic coefficients of submarines with satisfactory results. By expanding the simulation range, the changes in the hydrodynamic performance of the submarine on and near the water surface were analyzed with respect to force coefficient, flow field, maximum wave height, and maximum ray angle. The change in the drag coefficient of the hull has a water surface mode and near-water surface mode, which leads to a peak value of the drag coefficient at different submerged depths. When a "hump" phenomenon occurs at high Froude number(Fr = 0.5), the flow separation at the stern shoulder of the hull weakens, resulting in an increase in wake velocity and ray angle. The numerical simulation results showed that the Rabaud and Moisy model has better applicability, but when Fr > 0.8 and Hd > 1.5, the theory underestimates the maximum ray angle.

Unsteady vortex shedding dynamics behind a circular cylinder in very shallow free-surface flows

The turbulent wake generated by a horizontal circular cylinder in free-surface flows of increasing shallowness with submergence-to-diameter ratios between 0.5 and 2.1 are investigated using large-eddy simulation. At Froude number (Fr) = 0.26, the free-surface deformation is small with little influence on the wake, whereas at Fr = 0.53 there is a drop in the free-surface downstream of the cylinder that impacts the coherence of the vortex shedding. Irrespective to the relative submergence, the close location of the cylinder to the bottom wall generates an asymmetric von-Kármán vortex street. Proper Orthogonal Decomposition (POD) is used to analyse the spatio-temporal coherence of the turbulent structures shed in the cylinder wake. The spatial patterns of the first two POD modes, those containing the most energy, depict the von-Kármán vortices. As Fr increases, the energy content of the first pair of POD modes decreases from 56% at Fr = 0.26 to 26.8% at Fr = 0.53, as large-scale vortices lose coherence more rapidly with shallower conditions. This energy redistribution leads to the smaller flow structures to contain a relatively higher energy when Fr is larger. The frequency of the dominating vortex shedding determined from the spectra of the POD temporal coefficients unveils that the first two coefficients feature a dominant peak at the von-Kármán vortex shedding frequency. At Fr< 0.45, the reconstructed flow field using the first 20 POD modes agrees well with the instantaneous velocities from LES, whereas free-surface effects on the wake dynamics at increasing Fr requires more POD modes to reconstruct the flow field with reduced error.

Penentuan Faktor Koreksi Panjang Loncatan Hidrolik pada Kolam Peredam Energi Tipe Bucket

Abstrak Pada kolam olak tipe bucket, jari-jari (R) mempengaruhi loncatan hidrolik. Faktor koreksi panjang loncatan yang dipengaruhi oleh jari-jari kolam bucket. Nilai tersebut dapat digunakan menentukan panjang atau luas area pengamanan hilir sungai agar tidak terjadi tergerusan. Uji model fisik dilakukan dengan flum, panjangnya 4,1 m, lebar flume 0,15 m dan tinggi flume 0,24 m. Maka 3 variasi jari-jari kolam olak yaitu R1 = 6 cm, R2 = 7 cm dan R3 = 8 cm kemudian dialirkan air dengan 27 variasi percobaan. Diukur tinggi muka air diatas mercu bendung (Hd), saat meloncat (y1), setelah meloncat (y2) dan panjang loncatan hidrolik (Lj), didapatkan tinggi air saat meloncat (y1) dan bilangan Froude (Fr). Dengan memodifikasi persamaan Silvester (σ = 3,0 dan Ƞ = 1,17). panjang loncatan hidrolik mendekati hasil observasi dengan tingkat kesalahan relatif ΔE = 25,8%, NSE = 0,9, MAE = 6,0 dan RMSE = 3,1. Kata-kata Kunci: Kolam olak, tipe bucket, loncatan hidrolik, bilangan froude. Abstract In a bucket type still pond, radius (R) affects the hydraulic jump. The jump length correction factor is affected by the bucket pool radius. This value can be used to determine the length or area of the river downstream safeguard area so that erosion does not occur. The physical model test was carried out with a flume, the length of which was 4.1 m, the flume width was 0.15 m and the flume height was 0.24 m. Then 3 variations of the radius of the stilling pond, namely R1 = 6 cm, R2 = 7 cm and R3 = 8 cm then water was flowed with 27 experimental variations. Measured the water level above the crest of the weir (Hd), when jumping (y1), after jumping (y2) and the length of the hydraulic jump (Lj), obtained the water height when jumping (y1) and the Froude number (Fr). By modifying Silvester's equation (σ = 3.0 and Ƞ = 1.17). hydraulic jump length is close to the observed results with relative error rates ΔE = 25.8%, NSE = 0.9, MAE = 6.0 and RMSE = 3.1. Keywords: Stilling pond, bucket type, hydraulic jump, froude number. Abstract In a bucket type still pond, radius (R) affects the hydraulic jump. The jump length correction factor is affected by the bucket pool radius. This value can be used to determine the length or area of the river downstream safeguard area so that erosion does not occur. The physical model test was carried out with a flume, the length of which was 4.1 m, the flume width was 0.15 m and the flume height was 0.24 m. Then 3 variations of the radius of the stilling pond, namely R1 = 6 cm, R2 = 7 cm and R3 = 8 cm then water was flowed with 27 experimental variations. Measured the water level above the crest of the weir (Hd), when jumping (y1), after jumping (y2) and the length of the hydraulic jump (Lj), obtained the water height when jumping (y1) and the Froude number (Fr). By modifying Silvester's equation (σ = 3.0 and Ƞ = 1.17). hydraulic jump length is close to the observed results with relative error rates ΔE = 25.8%, NSE = 0.9, MAE = 6.0 and RMSE = 3.1. Keywords: Stilling pond, bucket type, hydraulic jump, froude number.

DESAIN KOLAM PEREDAM ENERGI BENDUNG PLAOSAN KABUPATEN SEMARANG

Hydraulic aspect of the weir is important factors in planning a stilling basin. Remaining energy on the stilling basin is expected to be as minimal as possible so that scour does not occur on the river bed. Plaosan Weir does not yet have a stiiling basin structure. Therefore it is necessary to recommend the design of stiliing basin.The analysis carried out hydrological analysis, including calculating return period rainfall, flood discharge (Q) using the Haspers method, and calculating Froude number (Fr) to determine pond type. Based on the recommendations for the type of stilling basin, a building design is carried out and also stability of design..From the results of calculation it is obtained that 50-year return period rainfall is 108.68 mm. Planned discharge for 50 years is 186.06 m3/s, and froude number : 4. The appropriate type of stilling basin is USBR Type IV. The pond is planned to have a length of L = 17 m, with a block face width of 0.68 m, height of 1.36 m, distance between front blocks of 1.69 m and total of 13 pieces. The results of stability control analysis during normal water conditions and flood water conditions produce values above the safety factor so that it can be concluded that the design is planned qualify.

Analysis of influencing factors of the projectile entering the water through the ice hole

The ice hole, as a special constraint environment, affects the dynamics of water entry. In this paper, the finite volume method (FVM) is used to study the cavity dynamics of the projectile passing through the ice hole. The results show that the cavity evolution law of the projectile passing through the ice hole is different from that of the projectile entering the water freely, and the backflow of the splash crown occurs near the hole. As the Froude number (Fr) increases, the time when the splash crown flows back at the hole is earlier, and the time when the cavity pinch-off occurs at the tail of the projectile is also earlier. The fluctuation of force decreases, and the velocity variation becomes more stable as the Fr decreases. After the projectile with a large aspect ratio passes through the ice hole, the cavity collapse becomes more obvious, and the resistance increase. The constraint effect of the hole on the cavity strengthens as the hole thickness increases, and the cavity integrity after the pinch-off becomes worse. After the projectile passes through the hole, the resistance and force fluctuation increase as the hole thickness increases.

Estimating the energy dissipation of flow passing over triangular and trapezoidal plan weirs using the GMDH model

Abstract Weirs are one of the most common hydraulic structures used in water engineering projects. In this research, a group method of data handling (GMDH) was developed to estimate the energy dissipation of the flow passing over the labyrinth weirs with triangular and trapezoidal plans. To compare the performance of this model with other types of soft computing models, a multilayer perceptron neural network (MLPNN) was developed. The dimensionless parameters derived from dimensional analysis, including the relative upstream head (ho/P), the number of cycles (Ncy), the Froude number ( Fr), and the magnification ratio (Mr) were used as input variables. The error statistical indicators of the GMDH model in the training phase were R2 = 0.913, RMSE = 0.010, and in the testing phase were R2 = 0.829, RMSE = 0.015. The error statistical indicators of the MLPNN in the training phase were R2 = 0.957, RMSE = 0.007, and in the testing phase were R2 = 0.945, RMSE = 0.009. Examining the structure of the GMDH network shows that ho/P, Ncy, and Mr play more meaningful roles in the development network.

CFD Analysis into the Resistance Estimation of Hard-Chine Monohull using Conventional against Inverted Bows

There are many ways that ship designers can do to get the minimum engine power with the desire ship speed. One of the ways is to design the bow shape with the aim of minimizing ship resistance. In this study, the ship resistance of hard-chine monohull with two different bow shapes that conventional and inverted bows are analyzed. CFD (Computational Fluid Dynamics) approach by using Shear Stress Transport (SST) as turbulence model is used. Different ship speed by Froude numbers Fr 0.2 to 0.7 is applied. The simulation results give convincing evidence that the inverted bow produces lower total resistance compared to the conventional one by about 5% reduction

INVESTIGATING THE COMPARISON OF SHIP RESISTANCE COMPONENTS BETWEEN U AND V-SHAPED HULLS

The selection of a hull design with minimal drag is an important effort to reduce emission levels on ships. Two different hull shapes, U and V hulls, have unique properties that affect their drag production, which has been studied extensively in the past. This study aims to re-examine the differences between the two hull types by conducting a simple analysis of drag prediction results using empirical and numerical slender body methods. Both hull models in this study have the same size and volume. The results indicate that the U hull has a higher frictional resistance ( ) than the V hull due to its wider wetted surface area ( ). Additionally, the viscous pressure resistance ( ) and form factor coefficient ( ) of the U hull are also higher than those of the V hull. However, for Froude numbers (Fr) above 0.245, the U hull has lower wave resistance ( ) than the V hull, whereas for Fr below 0.245, the U hull has higher . Overall, the U hull produces a higher total resistance ( ) than the V hull at low speeds, but a lower at high speeds. Therefore, the choice of hull shape for minimizing a ship's resistance is influenced by the desired speed of service. If Fr is low, below 0.24, a V-shaped hull is more suitable. However, if Fr is higher than 0.24, a U-shaped hull is more appropriate.

PIV Measurements of Open-Channel Turbulent Flow under Unconstrained Conditions

Many open-channel turbulent flow studies have been focused on highly constrained conditions. Thus, it is rather conventional to note such flows as being fully developed, fully turbulent, and unaffected by sidewalls and free surface disturbances. However, many real-life flow phenomena in natural water bodies and artificially installed drain channels are not as ideal. This work is aimed at studying some of these unconstrained conditions. This is achieved by using particle image velocimetry measurements of a developing turbulent open-channel flow over a smooth wall. The tested flow effects are low values of the Reynolds number based on the momentum thickness Reθ (ranging from 165 to 930), low aspect ratio AR (ranging from 1.1 to 1.5), and Froude number Fr (ranging from 0.1 to 0.8). The results show that the mean flow has an inner region with a logarithmic layer with a von Kármán constant of 0.40–0.41, and a log law constant ranging from 5.0 to 6.0. The friction velocity and coefficient of skin friction are predictable using the formulations of Fr and Reθ presented in this work. The outer region is also characterized by a dip location, which is predictable using an equation associated with Reθ. The higher-order turbulence statistics, on the other hand, show distinguishing traits, such as correlation coefficients ranging from −0.1 to 0.5. Overall, this work demonstrates that for the unconstrained conditions studied, friction evaluations associated with Reynolds shear stress and some notable turbulence modelling functions used in conventional open-channel flows are inapplicable.

Dynamic characteristics of water entry under the effect of floating ice and an independent distance model of floating ice

An ice-constrained environment significantly affects the water entry of projectiles. In this paper, cavity evolution in the presence of floating ice is studied. The numerical method is validated by experiments. The effects of the layout of floating ice, Froude number (Fr), and distance between the floating ice and projectile (lg) on water entry dynamics are investigated. The dynamic model of the water entry under the effect of floating ice is established. The independent distance equation of the floating ice at different Fr is obtained. The results show that the floating ice affects the cavity surface closure and the deep pinch-off. In the presence of unilateral floating ice, the height variation of the splash crown on both sides of the projectile is different, and the height of the splash crown is lower than that under the effect of bilateral floating ice. The impact force of the projectile entering the water is the largest with bilateral floating ice, which is 20% higher than that without floating ice. As Fr increases, the splash crown completely seals on the free surface and the surface closure occurs. With the change of Fr, there are transition regions in the position and time of the cavity pinch-off plots. The effect of the floating ice on the splash crown weakens as lg increases, and the pressure on both sides of the projectile gradually reaches the pressure without floating ice. The fitted independent distance curve can predict the pressure on both sides of the projectile affected by the floating ice. This study provides a reference for the launch of projectiles and release of detectors in polar region with floating ices, and provides a new idea for water entry under environmental restrictions.

A hybrid ensemble machine learning model for discharge coefficient prediction of side orifices with different shapes

Side orifices are widely applied for flow control and regulation in channel systems. Accurate estimation of the discharge coefficient of the side orifice is significant for water management. The main objective of current research is to accurately predict the discharge coefficients of circular and rectangular side orifices. Considering that traditional empirical regressions are hard to estimate the discharge coefficient precisely due to the complex nonlinear relationship between the discharge coefficient and relevant parameters, a new hybrid boosting ensemble machine learning model, BO-XGBoost, is developed, which combines the advantages of the boosting ensemble model (XGBoost) and Bayesian Optimization. To further evaluate the proposed hybrid model, it is also compared with other tree-based machine learning models, including standalone XGBoost, Random Forest (RF) and Decision Tree (DT). Literature experimental data of the flow and geometric parameters relevant to the discharge coefficients of circular and rectangular side orifices are collected and applied to develop the models. Four dimensionless parameters of the relative channel width (B/L), the relative bottom height (W/L), the relative upstream depth (Y/L) and the upstream Froude number (Fr) are taken into consideration for the prediction of discharge coefficient (Cd). Furthermore, four different input combinations are designed and then compared to determine the best one on the basis of RMSE. By using the optimal input combination, our results demonstrate that BO-XGBoost provides the best comprehensive performance among all the involved machine learning models in the discharge coefficient prediction for both types of side orifices. Besides, the uncertainty analysis also reveals that BO-XGBoost shows the narrowest uncertainty bandwidth and gives the highest prediction reliability.