Froude Number Fr Research Articles

A water model study on mixing behaviour in a Kaldo furnace using acid–base neutralization decolourization method combined with RGB-based image analysis

Mixing time is usually used as an important parameter for quantifying the mixing performance of multiphase flow in a metallurgical bath. However, the topic of the mixing time of a Kaldo furnace for copper anode slime treatment has received little attention from scholars to date; this concept is important for guiding the optimization of high-efficiency smelting in the Kaldo furnace. In the present work, the mixing behaviour of gas-liquid two-phase flow in a Kaldo furnace was simulated using a scaled-down 1:4.5 water model fabricated from transparent acrylic plastic. A visualization technique and a quantitative characterization method for mixing performance in the Kaldo furnace—acid-base neutralization decolourization combined with RGB-based image analysis—were innovatively proposed. This approach can not only determine the global mixing level η¯(t) and track the frequency distribution of the local mixing performance ξk(t) of the fluid region during the mixing process but also quantify the mixing time. In addition, based on the proposed method and by using dimensional analysis, the effects of operating parameters (such as the gas flow rate Q, injection lance height h, rotation speed ω, liquid volume fraction φ, inclination angle θ, and liquid viscosity μl) on the mixing time of gas-liquid two-phase flow in the molten bath were discussed. On this basis, the empirical equation of the mixing time as a function of h, ω, φ, the modified Froude number (Fr'), μl and θ was established as the first quantitative relationship of the mixing time for the Kaldo furnace.

Forecasting particle Froude number in non-deposition scenarios within sewer pipes through hybrid machine learning approaches

Sediment deposition has a substantial effect on the hydraulic capacity of channels in urban drainage and sewer systems. In this sense, the self-cleaning concept has been extensively used in the construction of urban drainage and sewer systems. In this regard, the design of the sewer system heavily depends on the accurate forecasting of the particle Froude number (Fr). This study is conducted on experimental data sets collected from existing studies, including a wide range of dimensionless grain size of particles (Dgr), sediment median size (d), hydraulic radius (R), volumetric sediment concentration (Cv), and pipe friction factor (λ) for the condition of clear bed. We forecasted the particle Froude number using four different input combinations. We employed the Random Tree (RT) and Reduced Error Pruning Tree (REPT) methods as standalone methods, as well as Random Committee (RC) and Bagging (BA) methods as hybrid machine learning (ML) methods in particle Froude number forecasting. Hybrid machine learning methods demonstrate enhanced performance compared to both standalone machine learning methods and empirical equations. In the context of sewer system design under non-deposited bed conditions, there is a need to accurately forecast the particle Froude number, RC-RT (IA = 0.96, R = 0.928, MSE = 0.718, RRMSE = 0.197, NSE = 0.86, and PBias = −0.284) performed the best, followed by BA-RT, RC-REPT, BA-REPT, RT, and REPT. In our research, it was found that, in forecasting the particle Froude number under non-deposited bed conditions, Cv emerges as the most responsive input parameter among others.

Integrating machine learning and image processing for void fraction estimation in two-phase flow through corrugated channels

There is a substantial amount of information embedded in images of two-phase flow captured through high-speed video (HSV) or high-resolution photography. However, accurate image segmentation is necessary to unlock a meaningful analysis of the data. In this study, we discuss how to estimate the flow void fraction in chevron-type corrugated channels typical of compact plate heat exchangers (CPHE) from back-lit front-view HSV images, using machine learning (ML) algorithms and data processing techniques. A U-Net neural network was employed for image segmentation, demonstrating robust performance with evaluation metrics consistently exceeding 0.9. The binary masks (indicating gas or liquid phases) derived from segmentation were processed in MATLAB® to estimate void fraction through a 3D reconstruction algorithm of the gas cluster’s volume. In contrast to conventional void fraction estimates based on the area ratio of binary masks, this algorithm models the curvature of the liquid-vapor interface through the corrugated channel. When compared to other methods, our algorithm predicts very similar void fraction contour maps. However, the average discrepancy between our algorithm and the area-ratio approach can be as high as 80%, underscoring the importance of the processing method in analyzing the data and developing correlations. Finally, a drift flux model was introduced to predict the void fraction distribution using a two-part equation accommodating the dependency of the distribution coefficient C0 on the liquid flow rate for a corrugation Froude number Fr∼ larger than 1. The proposed model can predict the void fraction dataset with a mean average percentage error of 8.17%. In summary, U-Net’s pixel-level accuracy facilitates deep and precise post-processing of HSV images, enabling meaningful void fraction measurements. Thanks to its generality and minimal training effort requirements, the discussed methodology can be applied to estimate void fractions in various two-phase flow experiments and operating conditions.

A modified Kushner-Moore approach to characterising small-scale blender performance impact on tablet compaction

Continuous Direct Compaction (CDC) has emerged as a promising route towards producing solid dosage forms while reducing material, development time and energy consumption. Understanding the response of powder processing unit operations, especially blenders, is crucial. There is a substantial body of work around how lubrication via batch blender operation affects tablet critical quality attributes such as hardness and tensile strength. But, aside from being batch operations, the design of these blenders is such that they operate with low-shear, low-intensity mixing at Froude number values significantly below 0.4 (Froude number Fr being the dimensionless ratio of inertial to gravitational forces). The present work explores the performance of a mini-blender which has a fundamentally different mode of operation (static vessel with rotating blades around a mixing shaft as opposed to rotating vessel with no mixing shaft). This difference allows a substantially wider operating range in terms of speed and shear (and Fr values). The present work evaluates how its performance compares to other blenders studied in the literature. Tablet compaction data from blends produced at various intensities and regimes of mixing in the mini-blender follow a common trajectory. Model equations from literature are suitably modified by inclusion of the Froude number Fr, but only for situations where the Froude number was sufficiently high (1 < Fr). The results suggest that although a similar lubrication extent plateau is eventually reached it is the intensity of mixing (i.e. captured using the Froude number as a surrogate) which is important for the lubrication dynamics in the mini-blender, next to the number of revolutions. The degree of fill or headspace, on the other hand, is only crucial to the performance of common batch blenders. Testing using alternative formulations shows the same common trend across mixing intensities, suggesting the validity of the approach to capture lubrication dynamics for this system.

Experimental investigation on fluid-induced vibration of a semi-submerged flexible pipe in oncoming flows

Fluid-induced vibration (FIV) features of the semi-submerged flexible pipe in an oncoming flow are experimentally investigated in this paper. The flexible pipe is towed to simulate the equivalent uniform oncoming flow with a Froude number (Fr) ranging from 0.2 to 2.5. The overtopping states are determined and divided into three regions by the Fr numbers, including non-overtopping, intermitting overtopping, and continuous overtopping regions. Through the displacement reconstruction and wavelet transform methods, the displacement response, frequency, trajectory, and the chaotic characteristics of the semi-submerged pipe are studied. The results show that the FIV displacement responses are evidently affected by the intensity of the overtopping phenomenon. A significant mean displacement in the cross flow (CF) direction can be seen and a maximum value of 0.88D can be reached. The unexpectedly larger FIVs with standard deviation values of around 0.52D can be witnessed in the in-line (IL) direction than those for a fully submerged pipe. Moreover, the FIV frequency response in the IL direction is found to be consistent with that in the CF direction under intermitting overtopping and continuous overtopping state, and the corresponding Strouhal numbers are 0.24 and 0.28, respectively. The FIV response is found to be chaotic in non-overtopping states, while it behaves periodic and quasiperiodic features as overtopping occurs. The “O” shape of the motion trajectory is observed at such overtopping regions. The present work improves the basic understanding of the FIV features of the semi-submerged flexible pipe in the oncoming flow and can provide useful references for designing the relevant marine structures.

Scale effects on the hydrodynamic performance of a submerged body

The increasing development and utilization of submerged bodies in ocean exploration have led to significant challenges due to their unique working environment. Conducting experiments with a full-scale submerged body is exceptionally difficult. To investigate scale effects on the hydrodynamic characteristics of submerged bodies, a three-dimensional numerical model for submerged bodies was established based on the Reynolds-averaged Navier–Stokes (RANS) equations and utilizing the Realizable k-ɛ turbulence model. The volume of fluid (VOF) method was used for interface capture. Initially, the reliability of the numerical model was verified through result validation and convergence analysis of the grid and time steps. Subsequently, SUBOFF model of different scales were adopted using the established numerical model considering the influence of the Froude number (Fr). The present study focused on investigating the effect of model scales on the wave pattern, resistance characteristics, and nominal wake fields. Research has shown that the scale effects on the frictional resistance and the wake field of the submerged body are significant. The numerical model used in the present study demonstrated good accuracy. A comprehensive analysis of the scale effects on submerged bodies was conducted, providing valuable insights for the application of model data to full-scale scenarios.

Experimental Study on Double Jet Flames with Different Nozzle Diameters

Double jet flames are commonly observed in the energy industry. A facility consisting of a double jet flames apparatus, was designed to experimentally simulate the interaction of double jet fires with different spaces and nozzle diameters. It has been found that the exit momentum, nozzle diameters and nozzle spacing significantly affect the flame behavior. The experimental results show that the flame merging probability (Pm) of double jet fires with different nozzle diameters can be fitted with dimensionless parameters that couple the Froude number(Fr) and the distance between fire sources. Additionally, it has been observed that the difference in height between the two flames can be used as a parameter to determine the correlation between flame height and the distance to the nozzle center.

Vortex bifurcation and air entrainment mitigation using multi-point intakes

Air entrainment is a concern of paramount importance in the process industries, including nuclear power plant, hydraulic machines, water treatment plants, hydrocyclones, and power generation turbines. The ingression of the air into the equipment results in the reduction of the hydraulic efficiency. In the current paper, a combined experimental and numerical investigation has been performed using the commensurate high-speed photography and volume of fluid-based numerical simulations. The mitigation strategies for the reduction of the air ingression include the reduction of the critical height by increasing the number of intakes and changing the intake configuration. The viability of these solutions and the hydrodynamics behind the interfacial evolution leading to the air entrainment have been studied in detail. The air ingression progresses with the establishment of the flow patterns ranging from bubbly flow, slug flow, to the annular flow. The reduction of the critical height can be accomplished by increasing the number of intakes for the same cross-sectional area leading to the reduction in the Froude number Fr=Vdown/gHlocal&amp;lt;1. Further increasing the number of intakes beyond four leads to the minimal reduction in the critical height in the tank.

Formation and growth of wipe blockages due to a vertical obstruction in sewers: Experimental analysis to policy and management strategies

Improper disposal of wipes results in significant sewer blockages, especially during the COVID-19 pandemic. However, the formation and growth of wipe blockages and their backwater effect in sewers have not been studied. This study employed a vertical rod to simulate sewer obstructions such as tree root intrusion in sewers. Stochastic interactions among wipes, turbulent flow, and the obstruction were experimentally studied in a circular pipe (diameter D = 25 cm), with systematic variations in flow Froude number (Fr), wipe length (L), flow depth (H), submerged rod length (hrod), and rod diameter (drod). It was found that the mean area ratio of wipes (ratio of projected area in water to original surface area of the wipe) ranged from 0.14 to 0.30, indicating the distorted shapes in water. The entrapment probability P (ratio of entrapped to released wipes) for a single wipe was closely correlated with Fr, H/D, L/H, drod/H, and hrod/H, with a maximum value of 0.90. With the increase in the number of wipes released, the influence of the obstruction on wipe accumulation processes became negligible. New equations were developed for characterizing entrapment probability, blockage length, and backwater rise, which can be used to predict the development of wipe blockages and sewage levels. Based on the research findings, policy and management strategies were proposed for wipe blockage reduction in sewers.

Influence of Lee Wave Breaking on Far‐Field Mixing in the Deep Ocean

AbstractBreaking of internal lee waves generated by flow‐topography interaction is an important driving mechanism for abyssal mixing. By assuming that lee‐wave‐driven mixing is a local process, direct measurements in the past mainly focused on the water column over rough topography. In this study, a non‐local role of lee waves on remote mixing is investigated by using mooring observations in the northwestern Philippine Basin and a series of 2‐dimensional high‐resolution numerical simulations. We find that the breaking of lee waves can generate near‐inertial waves (NIWs) which can propagate away from their generation sites. The NIWs have strong vertical shear which can significantly elevate turbulent dissipation and mixing over remote uneven seafloor. Based on the topography perturbations numerical experiments, we find that for the remote gentle topography with inverse Froude number (Fr−1) between 0 and 0.5, the arrival of upstream NIWs can elevate the near‐bottom layer (0–1,000 m above bottom) dissipation rate and vertical diffusivity by 9.2 and 10.4 times, respectively at 30–50 km away from the NIWs source. For the remote rough topography with Fr−1 between 0 and 4, the corresponding increases are 3.5 and 4.4 times, respectively. The mechanism of upstream NIWs to elevate the downstream dissipation and mixing is through strengthening the shear instability over the far‐field topography, which is associated with NIWs' interactions with the topography and the generated lee waves therein. The results of this study will provide a foundation for improving the mixing parameterizations associated with current‐topography interactions.

Performance analysis and modelling of circular jets aeration in an open channel using soft computing techniques

Dissolved oxygen (DO) is an important parameter in assessing water quality. The reduction in DO concentration is the result of eutrophication, which degrades the quality of water. Aeration is the best way to enhance the DO concentration. In the current study, the aeration efficiency (E20) of various numbers of circular jets in an open channel was experimentally investigated for different channel angle of inclination (θ), discharge (Q), number of jets (Jn), Froude number (Fr), and hydraulic radius of each jet (HRJn). The statistical results show that jets from 8 to 64 significantly provide aeration in the open channel. The aeration efficiency and input parameters are modelled into a linear relationship. Additionally, utilizing WEKA software, three soft computing models for predicting aeration efficiency were created with Artificial Neural Network (ANN), M5P, and Random Forest (RF). Performance evaluation results and box plot have shown that ANN is the outperforming model with correlation coefficient (CC) = 0.9823, mean absolute error (MAE) = 0.0098, and root mean square error (RMSE) = 0.0123 during the testing stage. In order to assess the influence of different input factors on the E20 of jets, a sensitivity analysis was conducted using the most effective model, i.e., ANN. The sensitivity analysis results indicate that the angle of inclination is the most influential input variable in predicting E20, followed by discharge and the number of jets.

Experimental study on the cavity dynamics of a sphere entering flowing water

This paper delves into the dynamics of a sphere entering flowing water at varying impact velocities and flow speeds. Using a high-speed photography system and image processing, we track the cavity evolution and trajectory. Flowing water is observed to tilt the cavity and postpone its detachment from the free surface. Beyond surface sealing, we identify a flowing-induced pinch-off phenomenon during water entry, marking a transition in closure regimes. This transition establishes a threshold impacting cavity tilt angle and pull-away length. By mapping the phase diagram of flow Reynolds number (Rew) against impact Froude number (Fr), we classify partial surface seal, pinch-off, and surface seal into distinct regimes. The Fr1/3 law effectively predicts the rising trend of cavity depth (H) and pinch-off depth (Hp) in flowing water. However, the Hp/H ratio differs from that reported in existing literature.

The effect of a side wall on cavity dynamics during the water entry of a sphere at low Froude numbers

This paper comprehensively investigates the non-axisymmetric cavity dynamics of a vertically entering sphere under the influence of nearby side-walls through experimental, numerical, and theoretical analyses. Initially, we explore the characteristics of cavity evolutions with the sidewall effect. The emergence of a twin-vortex during cavity pinch-off is observed, and detailed numerical simulations provide insights into its underlying mechanisms. Both the dimensionless distance (λ) and the Froude number Fr significantly influence the pinch-off type. A phase diagram in the λ−Fr parameter space is presented, revealing the interplay between these variables. Moreover, we investigate the sidewall effect on the pinch-off time and location at low Froude numbers. The findings indicate that as λ decreases, both the pinch-off time and depth of the cavity increase. Generally, the wall effect is relatively weak when λ exceeds 4. Additionally, the pinch-off time can be described by τ=kr/g, with the constant k determined by λ. Utilizing 2D cavity theory, we estimate the pinch-off time of the water entry cavity with the sidewall effect, revealing a consistent collapse behavior with the mechanics of a two-dimensional cavity.

Modeling of GPM and LPM in Centrifugal Pump for Obtaining Hydraulic Flow Pattern Types

The types of hydraulic flow patterns in laboratory testing through the use of physical modeling tools often encounter several challenges when confronted with the use of empirical model scales, namely, the issue of scale. Water structures in the horizontal dimension do not experience highly complex issues because there are many measuring instruments available, whether self-made, home industry-produced, or industrial-grade. The presence of water volume in storage can only be tested at a clear scale, especially when it is already within a water tower (reservoir) installation with a specific height. Determining the need for water storage in a water tower is not an easy task to calculate due to differences in height, diameter, and storage capacity. Hydraulic experts often overlook these differences, which can become a problem when there is a demand for the volume of water during peak flow conditions. The solution to this issue needs to be verified by conducting model tests using a device known as the Centrifugal Pump, which has not been previously explored for laboratory research. GPM LPM model tests on this device make use of instruments and numerous pressure measuring tools supplied with pressurized water by a pump at specific, measurable volumes. To analyze the flow rate, flow coefficients, flow velocity, Reynolds number, Froude number, and test results with various speeds (speed meter), researchers test and measure the capacity of GPM LPM for each valve opening, starting with openings of 0.5, 0.75, 1.00, reading the instruments, shifting the speed from 1, 2, 3, 4, up to the highest speed, which is 12. A graph is created to display the test results of the GPM LPM speed booster device, which contains an electric motor. The test is conducted with three repetitions for each valve opening, and the speed and travel time values from the instruments on the test device are recorded and mapped. Subsequently, the analysis results of the GPM LPM test are recommended to provide information to construction planners of water structures. These results show that, under specific conditions of different speeds and valve openings, there are variations in the volume and travel time values. This information can be applied to determine the required storage capacity for each water tower building with a hydraulic flow pattern based on Reynolds number (Re) and Froude number (Fr).

Electrohydrodynamic peristaltic microfluidic flow with thermal and molecular analysis featuring sloped configurations

This study examines the simultaneous impacts of thermal and molecular transfer of non-Newtonian fluid propelled by the collective impact of electroosmosis and peristaltic pumping via inclined channel. Internal frictional heating and heat generation are also taken into consideration. The electrohydrodynamic phenomenon is described by the nonlinear Poisson–Boltzmann equation. The problem is modulated mathematically through a system of coupled non-linear differential equations in wave frame of reference. Using the regular perturbation method around a small wave number δ, we obtain sequential solutions for stream function ψ, electric potential ϕ, velocity u, pressure gradient dpdx, temperature θ and concentration Ω distributions. The influences of newly arising parameters such as the electroosmotic parameter me, relaxation time parameter λ1, retardation time parameter λ2, wave number δ, Reynold’s number Re, heat generation parameter β, Prandtl number Pr, Schmidt number Sc, Froude number Fr and Soret number Sr on physical characteristics are analyzed graphically. There is an inverse correlation between the parameters of relaxation time and retardation time and their effects on axial velocity, concentration, and temperature distributions. In particular, the temperature of the fluid increases as the EDL parameter, relaxation time parameter, viscous dissipation parameter, and Reynolds number increase, but decreases as the retardation time parameter increases. Moreover, the axial pressure gradient increases as Reynolds number and inclination angle increase, while it decreases as Froude number increases. The current model has applicability in the chemical industry, reservoir engineering, micro-fabrication, and biomedical applications, where electroosmotic effects on heat and mass movement are crucial.

New empirical equations to assess energy efficiency of flow-dissipating vortex dropshaft

Vortex structures are generally considered the common energy-dissipating infrastructures in order to convey urban surface waters. During transferring wastewater in such urban networks, the major proportion of water energy is dissipated and additionally, the hydraulic performance of these infrastructures is evaluated on the basis of the dissipation of energy efficiency in the vortex dropshaft. Over the last decade, the literature review of vortex structures demonstrated that there is no reliable mathematical expression to predict energy efficiency although various experimental investigations were done to evaluate the hydraulics of vortex structures. In this research, robust numerical models based on conceptions of Artificial Intelligence (AI) methodologies (i.e., classification, non-parametric analysis, and evolutionary computing) were developed by using 144 experimental data extracted from a physical model of vortex dropshaft. Through analysis of experiments, three main factors, called flow Froude number (Fr), the ratio of sump height (Hs) to shaft diameter (D), and the ratio of drop total height (L) to shaft diameter (D) were determined to estimate the efficiency of flow energy dissipation. The numerical models were calibrated/trained by different algorithms such as multi/single-objective optimization strategies (e.g., Particle Swarm Optimization [PSO] and Multi-Objective Genetic Algorithm [MOGA]). Various statistical tests, known as quantitative assessments for training and testing stages of AI models, demonstrated that Evolutionary Polynomial Regression (EPR) had the best performance (Coefficient of Correlation [R] = 0.9736, Root Mean Square Error [RMSE] = 0.5923, and Mean Absolute Percentage Error [MAPE] = 0.5035) and followed by MT (R = 0.9665, RMSE = 0.7039, and MAPE = 0.6225), GEP (R = 0.9113, RMSE = 1.0803, and MAPE = 0.9535), and MARS (R = 0.8337, RMSE = 1.6473, and MAPE = 1.1010). Additionally, expressions given by AI models provided more accurate predictions of energy dissipation efficiency when compared with a regression-based equation (R = 0.9113, RMSE = 0.7039, MAPE = 0.6225) from the literature. Additionally, variations of three effective factors versus the predicted responses (values of energy dissipation efficiency given by AI models) were in coincidence with experimental observations. Overall, this study proved that the usability of mathematical expressions could provide new insights for experts to assess the hydraulic evaluation of vortex structures before their physical and prototype models are constructed.

Computation of aluminum droplet ejection and flight in microgravity

Persistent and frequent space explorations are limited by real-time parts supply and it is significant to achieve space manufacture, such as the droplet-based printing. In order to study the microgravity environment effect on droplet-based printing, this paper proposed an effective method to research the effect of space station environmental g-jitter (according to NASA experimental signal) on droplet ejection and flight process. The heat transfer, transient gravity acceleration and Marangoni effect are studied based on the improved model. The results show that the g-jitter is in the order of 10−3 magnitude and the effect on aluminum droplet ejection could be ignored when nozzle diameter (dn) is smaller than 0.1 mm and so do ground case. Combined with the ground microgravity simulation of SnPb alloy lateral ejection experiments, it can be obtained that the ejected single droplet is characterized by capillary number (Ca≤0.002), the droplet flight trajectory is dependent on the Froude number (Fr) and the laminar-turbulence transition exists during the droplet flight process. The relationship formulation between the deviation along gravity direction and the deposition distance is introduced to control and adjust the droplet flight trajectory. Moreover, the temperature effect on material property, such as surface tension and so on, has effect on the droplet breakup length. The g-jitter field enhances the Marangoni effect resulting in the deviation of droplet trajectory. In microgravity field, the computational droplet oscillation period is well coincidence with theoretical equation. Improved KIC-SST based model is available for simulating droplet-based printing in microgravity.

Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators

It is essential for mathematicians, physicists, and engineers to construct fractional mathematical models for specific phenomena and develop numerical or analytical solutions for these models. In this work, we implement the natural decomposition approach with nonsingular kernel derivatives to investigate the solution of nonlinear fractional forced Korteweg–de Vries (FF-KdV) equation. We first investigate the FF-KdV equation under the Caputo–Fabrizio fractional derivative. The similar equations are then examined using the Atangana–Baleanu derivative. This approach combines the decomposition method with the Natural transform method. The series solution of the suggested equations is thus obtained using the natural transform. The key benefit of this novel approximate-analytical approach is that it may provide an analytical solution for the FF-KdV problem in the form of convergent series with simple computations. For each equation, three unique situations are chosen to demonstrate and test the viability of the proposed method. To guarantee the competence and dependability of the proposed method, the nature for various values of the Froude number Fr have been provided. The present approach is also used to calculate solutions at various fractional orders. The approximate series solution’s behavior for various fractional orders has been graphically displayed. The outcomes demonstrate that the methodology is simple to use and reliable when applied to numerous fractional differential equations.

Application of an Open-Source OpenFoam for Fluid-Structure Interaction Analysis of the Horizontal-Axis Wind Turbine Blade

This study investigates numerical simulation for fluid-structure interaction in wind turbine blades, emphasizing the influence of dimensionless numbers. Utilizing OpenFoam, the Navier-Stokes equation is accurately solved with the PISO algorithm, ensuring proper interface conditions. The icoFsiFoam solver is validated through dynamic testing, demonstrating its effectiveness. In contrast to the widely adopted Blade Element Momentum Theory (BEMT), our approach focuses on analyzing blade deformation and resonance phenomena, capturing intricate deformations and stress concentrations. Our investigation explores the impact of reduced velocity on blade behavior across a range of 0.105 to 0.145, while consistently maintaining crucial dimensionless numbers such as Reynolds number (Re = 10⁶), Froude number (Fr = 4.93), and Cauchy number ( Cy = 10-5). The outcomes of this study significantly contribute to the understanding of fluid-structure interaction in wind turbine blades. By examining the oscillatory behavior of the blades, we observe trends similar to those predicted by BEMT. However, our approach surpasses BEMT by providing additional insights into stress concentrations and deformation modes. This advancement enables superior performance optimization and facilitates advanced blade analysis. The implications of our research are paramount for optimizing blade design and performance under varying reduced velocities. By incorporating the findings of this study, blade designers can make well-informed decisions to enhance the efficiency and durability of wind turbine technologies. The presented methodology and results provide a comprehensive investigation into the fluid-structure interaction of wind turbine blades, highlighting the importance of dimensionless numbers and their influence on blade behavior. Overall, this study offers valuable insights for improving wind turbine design and performance.

Flow regime transition and bubble behavior in gas-liquid two-phase impinging jet reactor

The gas-liquid flow regimes transition mechanism and bubble behavior in gas-liquid two-phase impinging jet reactor are studied by numerical method. The liquid phase velocity, gas-liquid flow regimes, bubble behavior in the impinging reactor under different gas and liquid velocities are analyzed to explore. The vortex in flow field changes periodically, and the period is 7.5 s. According to the dispersion mode of bubbles in the reactor, the gas-liquid flow regimes can be divided into three regimes: cluster upflow, gradual dispersion and complete dispersion. The critical condition equations of flow regimes transition are established combination of Flow number (Fl) and Froude number (Fr). The distribution range of bubble diameter in the reactor increases with the increase of gas velocity and decreases with the increase of liquid velocity. The turbulent kinetic energy, turbulent dissipation rate and the velocity in the flow field are gradually weakens from the impact center to the radial direction. Based on dimensionless analysis, the mathematical model of bubble Sauter diameter is established to predict bubble Sauter diameter accurately. This research provides a theoretical basis for the amplification and optimization of reactors.