Hydrodynamic Behavior Research Articles

The Characterization of Aquifer Parameters in Using Skimming Tubewells Through the Pumping Test Method: A Case Study of Tando Allahyar

Sindh is in the lower reaches of the Indus River; it is most vulnerable to a variety of upstream water development challenges. The aim of this research was to determine aquifer characteristics in the command area of Tando Allahyar-II distributary within the culmination of underground water potential. The hydraulic properties of the aquifer as well as the susceptibility of the formation to tedious extraction and saltwater upcoming were recognized. Three pumping tests were performed at head, middle, and tail reaches along the selected distributary. The drawdowns were measured at head reach (5.1667 h), at middle reach (6.0 h), and at tail reach (19.667 h) of the selected distributary by performing the pumping tests. Groundwater levels were lower at the tail reach compared to those at the head and middle reaches, likely due to a higher concentration of tubewells in the lower reach. The head and middle reaches showed higher groundwater levels, possibly due to constant head conditions promoting infiltration and recharge. The pumping test versus drawdown analysis revealed that the tubewells should be run with 7-h (on) and 4-h (off) operation. Further, the tubewells at all reaches (head, middle, and tail) should be closed for a minimum of 4 h between operations. This strategy would allow safe groundwater extraction, maintain water quality, and prevent water table depletion in the study area. The hydrodynamic and hydro-salinity behaviors were scrutinized in PWMIN 5.3 (version) by means of the MODFLOW mode. The results were estimated to compare the calibration and validation simulation outcomes using measured data. The model was successfully calibrated, and the root mean square (RMS) value of the head tubewell varied between 0.024 and 0.108, whereas it speckled between 0.0166 and 0.0349 for the middle tubewell and between 0.0659 and 0.0069 for the tail tubewell. The RMS values for hydrodynamic behavior for the head, middle, and tail reaches were less than 10%. These values represent a suitable match between the observed and simulated heads when a water table depletion of 1 to 2 m was observed due to extreme pumping. However, the average relative error values, for all validated procedures, were less than 10%.

Improvement of heat transfer in microchannels using nanofluids by numerical contribution on a sinusoidal shaped dissipator

This research conducts an extensive numerical investigation into the enhancement of heat transfer in wavy-walled channels using aluminum oxide-water nanofluids. The study examines the impact of key parameters, including geometric aspects (wave spacing ratio: 0-1), operational conditions (Reynolds number: 5,000-20,000), and varying nanofluid concentrations (1-6% by volume). The results indicate that zero wave spacing combined with a nanofluid concentration of 4% provides the most favorable thermal performance, resulting in a heat transfer enhancement of up to 2.5 times when compared to conventional smooth channels. While the wavy channel geometries significantly improve heat transfer, they also impose additional pressure drops, revealing a critical trade-off between enhanced thermal performance and the increased pumping power required. The study highlights the balance necessary between maximizing heat transfer and maintaining operational efficiency, particularly in systems where space is limited. These findings contribute valuable insights to the design of heat exchange systems that demand both high thermal efficiency and compact dimensions, such as those used in electronics cooling or energy-efficient HVAC systems. Additionally, the study explores the influence of the Reynolds number on both thermal and hydrodynamic behavior within the wavy channels, providing a thorough performance evaluation across different operational ranges. The conclusions drawn from this investigation offer practical guidance for optimizing heat exchanger designs, taking into account both thermal resistance and overall system performance under varying conditions.

Analysis of hydrodynamic behavior in response to diverse pile arrangements adjacent to an impermeable dike

ABSTRACT Intense energy flow near the dike head significantly influences the development of the dike field zone (DFZ), momentum exchange zone (MEZ), and mainstream zone (MSZ), leading to potential partial or full failure of the dike in the MEZ. To address this, laboratory experiments were conducted to observe flow changes and rate of energy reduction around a single impermeable dike, with alterations made to the pile group length (HL: half-length = 11.5 cm and FL: full length = 23 cm), location (U: upstream, D: downstream), and shape (C: Circular, DV: Delta Van, ST: Streamlined tapered, APF: Angled Plate footing). Modifications in the MEZ flow structure were studied to mitigate concerns about intense energy vortices and dike head flows. These piles helped to assess factors like flow deflection, backwater rise, energy reduction rate, velocity fluctuations, and discharge distribution percentages across the zones. The data revealed that when the pile group length was increased from HL to FL, there was an inverse effect on depth-averaged velocity, MEZ discharge distribution percentage, and flow deflection toward the DFZ. Conversely, there was a direct influence on the rise in backwaters, rate of energy reduction, and discharge distribution percentages in the DFZ. The U-FL-APF pile dike showcased optimal results, displaying a reduction in maximum energy by 52% and streamwise velocity by 96%, while also increasing the backwater rise and discharge distribution by 22% and of only 5% in the MEZ, respectively, compared to a single impermeable dike. During flood events, these suggested measures can mitigate the intensified swirls formed in the DFZ, protect the dike head from direct momentum exchanges in the MEZ, and enhance flow deflection into the MSZ.

Hydrodynamic performance comparison of planing catamarans with mono-hulls using numerical and experimental methods

This study addresses the hydrodynamic performance of high-speed planing catamarans compared to equivalent mono-hulls using numerical simulations and experimental validation. The study includes computational fluid dynamics (CFD) simulations to analyse the hydrodynamic behaviour of the catamarans under various operating conditions, such as different speeds, deadrise angles, and static trim angles. Comparison of the numerical simulation results with model tests reveals that the numerical results for the resistance of planing catamarans at high speeds deviate significantly from the experimental data due to strong spray. This discrepancy is systematic (rather than random) and has been recognised and modified. The modified numerical results are sufficiently accurate for further pursuit. Generally, the resistance of a planing catamaran compared to an equivalent planing mono-hull is significantly larger, approximately 25–60 %, while the absolute sinkage is lower. A positive feature of the catamaran is its ability to prevent porpoising instability, especially in boats with a small deadrise angle. Choosing a planing catamaran over a mono-hull must offer other substantial advantages, such as better seakeeping performance, which compensate the higher resistance.

Studying Dynamical and Hydraulic Characteristics of the Hydraulically Suspended Passive Shutdown Subassembly (HS-PSS) and Validating with a Prototypic Test Sample

The pool-type demonstrative China Fast Reactor 600 (CFR-600) adopted a series of improved safety designs, among which the hydraulic suspended passive shutdown subassembly (HS-PSS) is employed for inherent safety enhancement, especially suitable against unprotected loss of flow accident (ULOF). In this article, functional requirements for HS-PSS design in hydro-dynamic aspects are proposed, with the corresponding performance indicators discussed. To address these functional requirements, qualitative analysis on the equilibrium solution properties of the nonlinear dynamical model equation of the hydraulic moving body (HMB) in the HS-PSS are conducted, which leads to the determination of an applicable design parameter domain of the HMB for its practical design from the broad range of structural and parametric design options available for HS-PSS. Furtherly, hydraulically characterizing and modeling the constituent paths and consequent fluid network, hydraulic characteristics of the HS-PSS, as well as the coupled hydro-dynamic motion behaviors of the HMB for suspension and dropping states, were simulated and test-validated. Considering the HS-PSS hydro-dynamic behaviors, key indicators such as critical flowrate, drop time, hydraulic self-tightening performance, as well as the hydraulic characteristics curve are for fulfilling the functional requirements. Meanwhile, through sensitivity study of some structural parameters‘ impact on hydraulic characteristics, some most sensible structural parameters for adjusting and optimizing detailed design are observed. The work is quite significant in supporting the conceptual design of the HS-PSS as well as its engineering improvement.

A Novel BEM for the Hydrodynamic Analysis of Twin-Hull Vessels with Application to Solar Ships

A novel Boundary Element Method (BEM) is presented for predicting the hydrodynamic behavior of twin-hull vessels, traveling at low speeds, aiming to quantify the benefits of integrating solar technology onboard. In particular, the power requirements of an electric 33 m long twin-hull ship are examined. The study discusses the placement of solar panels on deck and assesses their utilization in terms of real-time energy generation, aiming to extend the autonomy range while also reducing carbon emissions. The discussed methodology predicts the power needs by considering various operational variables, design specifications and hydrodynamic principles. In addition, it addresses the viability and possible advantages of integrating solar technology onboard and provides preliminary estimates regarding the extent to which solar energy may compensate for power needs, based on several factors, including the velocity, the prevailing sea state and the incident solar irradiance. The results provide useful information regarding the utilization of solar energy in the shipping sector, in addition to advancing sustainable maritime propulsion.

The effects of formation inclination on the operational performance of compressed carbon dioxide energy storage in aquifers

Compressed CO2 energy storage in aquifers (CAESA) is a net-zero energy storage technology. Due to the widespread existence of inclined aquifers in nature, it is of practical significance to study the influence of inclined reservoirs on CO2 migration, safety and energy efficiency of the storage system. We build 3D numerical models with different dips (0°–16°), analyze the hydrodynamic and thermodynamic behavior of the system, and discuss the effects of injection schemes (temperature and pressure) on wellbore pressure, temperature, and energy efficiency. The results show that formation dip affects the energy storage characteristics of the system mainly by affecting the migration and distribution of CO2 in the aquifer. The greater the formation dip, the greater the difference in CO2 distribution, and the farther the CO2 diffuses upward along the dip direction. The farthest migration distances in the low- and high-pressure aquifers, occurring in the case of 16° formation dip, increase by 100 and 53 m, respectively, compared with those of the flat formation. The average daily energy storage efficiency decreases with the increase in formation dip angle. The dip angle of aquifer which is selected for compressed CO2 energy storage should not exceed 8°.

A CFD and experimental study of hydrodynamic and heat transfer behavior in ribbed fluidized beds

Abstract The study focuses on enhancing the performance of fluidized bed systems, which are widely used in industrial processes requiring efficient heat and mass transfer. By integrating ribs at angles of 135, 150, and 165° on the riser wall, the research assesses their impact on hydrodynamic behavior and heat transfer using CFD simulations. The simulations, confirmed through experimental data, revealed that the 150° ribbed model outperforms others by improving particle mixing and achieving the highest heat transfer coefficient. The investigation also covered static pressure, solid volume fraction, and particle velocities at different bed heights (30, 60, 90, and 120 mm), showing that ribbed models significantly enhance turbulence and particle distribution, with the 150° ribs providing a balance between dynamic mixing and stable flow.

Assessment of pillar-array electrodes for electrochemical flow reactors using a novel hydrodynamic electrode performance factor

This work introduces and validates a Hydrodynamic Electrode Performance Factor (HEPF) for flow reactors. Traditional approaches to electrode optimization often rely on separated mass transfer and pressure drop metrics, hindering comparisons. We address this issue by combining electrochemical and hydrodynamic parameters through a new mathematical expression. This formulation draws inspiration from established equations in heat transfer and the widely recognized Chilton-Colburn analogy, aiming to develop a quantification method independent of the experimental arrangement. The HEPF is complementary to the well-established volumetric mass transfer coefficient and to Storck’s energetic effectiveness postulates for electrochemical reactors. Additionally, this study validates the proposed equation experimentally and then applies it to evaluate pillar array electrodes using 2D computational fluid dynamics simulations for laminar flow conditions. Both experimental and simulation approaches are used to analyze the hydrodynamic behaviour of the electrodes, utilizing the Forchheimer and Hagen-Poiseuille numbers. Notably, preliminary turbulence effects are observed at Reynolds numbers as low as 50 to 125. Visualization of velocity streamlines revealed distinct wake formation behind the pillars at these low Reynolds numbers. This study also explores how reactor inlets, outlets, and tubing pressure losses affect electrode performance. Results emphasize the importance of considering pressure drop, which is integral to the new hydrodynamic performance factor. Analysis of pillar array electrodes demonstrates that reducing both interpillar distance and pillar radius leads to improved electrochemical performance

Molecular modelling of active oil droplet propulsion: Insights from dissipative particle dynamics simulation

This study employed dissipative particle dynamics (DPD) simulations to investigate the self-propelled motion of oil droplets in water–oil–surfactant systems. It is the first attempt to replicate self-propulsion models of oil droplets at the molecular level, contrasting previous simulations focused on Brownian motion and hydrodynamic behavior of colloidal particles. The DPD model reproduced droplet propulsion and visualized internal Marangoni flow, showing that larger droplet radii and greater interfacial tension differences increase propulsion speeds. Additionally, surfactants with stronger oil–oil repulsion enhanced propulsion speed, suggesting that surfactant-induced local structures are crucial for the self-propulsion mechanism.

Investigation of hydrodynamic characteristics of an oyster reef under regular waves

Oyster reef living shorelines are popular solutions to mitigate coastal hazards while providing ecosystem services, and their hydrodynamic characteristics deserve further examination. This paper reports an experimental and numerical study of the hydrodynamic behavior of a bagged oyster shell (BOS) reef under regular waves. The dependence of the pore pressure within the reef and the hydrodynamic coefficients on the reef height, length, porosity, and wave parameters are investigated. The results show that the normalized maximum pore pressure ps_m∗ decreases from the seaside of the BOS reef to its leeside and decreases with increasing dimensionless reef length. With increasing wave steepness, ps_m∗ fluctuates with an overall increasing trend. With increasing BOS reef porosity, ps_m∗ decreases at seaside locations and increases at leeside locations; simultaneously, the wave reflection coefficient Kr and the wave dissipation coefficient Kd decrease, and the wave transmission coefficient Kt increases. With increasing wave steepness for a given wave period, Kr and Kt tend to increase, but Kd exhibits the opposite trend. As the dimensionless reef height and length increase, Kt decreases and Kd increases. Multivariate nonlinear regression and genetic programming-based symbolic regression methods are individually used to derive two formulas for predicting the wave transmission coefficient, with the formula from the latter method being found to give a higher prediction accuracy.

Layout Optimization of Wave Energy Park Based on Multi-Objective Optimization Algorithm

Abstract In this paper, both semi-analytical method and numerical simulation is applied to investigate the hydrodynamic behavior of large arrays of point-absorber wave energy converters (WECs). To analyze wave interactions among multiple WECs within an array, a semi-analytical model is developed based on the potential flow theory and the matched eigen-function expansions method. The fluid domain is divided into two kinds of regions: interior regions underneath the cylinders and an exterior region surrounding all the cylinders. The matched eigenfunction expansions method is employed to solve the radiation potential problem in each domain, and the hydrodynamic coefficients and motion response of the cylinders in the array are evaluated. To validate the accuracy of the semi-analytical method, WAMIT is adopted to simulate the wave energy park numerically and compared with the results by the semi-analytical model. The hydrodynamic characteristics and power absorption performance of the WECs within the wave energy park are analyzed. The power performance of a wave energy park is studied as functions of layout geometry, incident wave direction and separation distance between WECs respectively. Finally, MOPSO based on a surrogate model is used to optimize the layout of wave energy array.

Experimental study on the effect of mixing parameters on the rheological behaviour and micro-flocculation structure of ultrafine Portland cement slurry

The penetration diffusion of ultrafine Portland cement (UPC) slurry is closely related to its rheological behaviour and micro-flocculation structure. To date, there has been a need for more research investigating the impact of mixing parameters on the macro-micro hydrodynamic behaviour of UPC slurries. In this study, a series of macroscopic rheomechanical characterisation tests and microscopic in-situ tests of the flocculation structure of UPC slurries under various mixing parameters were conducted systematically by using a rotational rheometer and a focused beam reflectance measurement (FBRM) system. The effects of mixing speeds and times on the macroscopic shear stress-shear rate curves, rheological patterns, rheomechanical parameters, and the distribution of micro-flocculated particles of UPC slurries were investigated. The results indicate that the macroscopic rheomechanical parameters and microscopic flocculation coefficient of UPC slurry exhibit a decrease with increased slurry mixing speed. However, a “decrease and then increase” trend is observed with increased slurry mixing time. The smaller the powder size of cement and the lower the water-cement ratio of the slurry, the more sensitive the rheomechanical properties of the slurry are to the influence of the mixing parameters. A positive correlation exists between the macroscopic rheomechanical properties of UPC slurry and its microscopic flocculation coefficient. Increasing the slurry mixing speed or prolonging the early mixing time can destroy the microscopic flocculation particles of UPC slurry, a reduction in the flocculation coefficient of the slurry, and an improvement in the macroscopic fluidity properties. The research findings provide a foundation for improving the effectiveness of UPC grouting in the engineering field.

An AUV stability estimation method by considering rudder design parameters

Stability is a critical characteristic of Autonomous Underwater Vehicles (AUVs). During the initial design stage, selecting an appropriate rudder design is essential to ensure the overall stability performance of the AUV. This study introduces a method for predicting the stability of AUVs equipped with different rudder configurations. By parametric modeling based on the geometric characteristics of X-rudders, the rudder area, aspect ratio, and position parameters, which significantly impact AUV stability, were selected as the primary research objects. Formulas were derived to estimate the associated hydrodynamic forces and moments critical for assessing the stability index. Validation of this approach is conducted through comparison with Computational Fluid Dynamics (CFD) simulations. The results show that this method effectively predicts the hydrodynamic behavior of AUVs, facilitating stability assessments across various rudder designs.

Heat transfer and friction factor analysis for tomato puree flowing in a concentric-tube heat exchanger.

The heat and momentum transfer of tomato puree through a concentric-tube heat exchanger over a range of generalized Reynolds number (0.05<Re<66.5) was experimentally and numerically analyzed. Thermophysical and rheological properties of tomato puree (12°Brix) were measured from 20 to 60°C. The velocity, pressure, and temperature were calculated using the computational fluid dynamics (CFD) software FLUENTTM with temperature-dependent transport properties. The thermal operation of the concentric-tube exchanger was satisfactorily predicted using CFD, indicating accurate measurement of tomato puree properties with temperature variations. A concordance was found between the calculated Fanning friction factor and generalized Reynolds with the experimental correlation. A modified Sieder-Tate correlation was established, which allows properly expressing the Nusselt number as a function of the Peclet number. Simple correlations for the mechanical work and the heat transfer rate as a function of the volumetric flow rate were derived. The thermal efficiency was high at low puree flow rates but decreased with higher rates. However, at high flow rates, ceased its decline, instead showing a slight improvement. The analysis confirmed higher heat transfer rates in the concentric-tube heat exchanger compared to a plain tube at low puree flow rates. The results offer valuable insights for assessing diverse operational conditions in dairy, beverage, sauce, and concentrated food industries. Additionally, they also enhance the analysis and design of concentric-tube heat exchangers. PRACTICAL APPLICATION: The knowledge of the rheological and hydrodynamical behavior of fluids in concentric-tube heat exchangers allows to explore a set of different operating conditions to improve the yield and effectiveness on the system heating/cooling design.

Influence of hollow droplet impact and spreading characteristics on the cylindrical lateral surface

In this study, 3D model of a hollow glycerin droplet impacting on a cylindrical cross-section was numerically analyzed to coat the lateral surface of the cylinder. The hollow droplets had exterior diameters of 5.5 mm, 5.25 mm, and 5 mm, and the impact velocity was 1 m/s. To model, the influence of droplets on OpenFoam software, the Volume Of Fluid technique was utilized (VOF). The Newtonian, incompressible, and laminar fluid phase of a glycerin droplet was investigated using air with a diameter of 4 mm as the gas phase. The hydrodynamic behavior of droplet collisions as well as fluid properties were investigated. As a result, when can be observed in the simple cylinder, as the outer diameter increased, the spread diameter shrank. The least amount distributed diameter in Case 3 was 1.404, whereas the highest amount in Case 4 was 1.625. The situations with a simple lateral surface, uniform spread occurred, while in cases with a spiral lateral surface, non-uniform spread occurred. Observed the maximum length in Case 3 was 4.12 mm and the minimum was 1.83 mm in Case 4.

New characterization models for macroscopic chemical-hydrodynamic behavior of catalytic cracking riser-reactor with interactive patterns of severe operating conditions using CFD calculations

BackgroundFCC is the core of refining technologies for production of high-valued chemicals including, light olefins, and fuels. Global capacity of catalytic cracking unites is projected to grow from 14.4 to 15.8 million barrels per day from 2022 to 2026. Moreover, global production of 57 % ethylene, 42 % propylene and 69 % butylene is based on deep/fluid catalytic cracking. Therefore, optimization of catalytic cracking process is our indispensable industrial approach. MethodsThis study is optimization of industrial catalytic cracking unit for maximizing the yield of light gases, gasoline and gasoil conversion using CFD calculations. Hydrodynamic behavior and performance of the riser-reactor was investigated at severe operating conditions, including feed temperature, catalyst temperature and catalyst to oil ratio (CTO) in the range of 788–903 K, 813–1013 K and 6–18, respectively. New characterization models were proposed for macroscopic chemical-dynamic behavior of the process. Models validated with ANOVA analysis, RSM methodology. Significant findingsResults showed that the maximum products yield and gasoil conversion occur between 4 and 8 s. It was obtained that the maximum yield of nearly 12 wt% light gases, 38–39 wt% gasoline and 54 % conversion is possible for this geometry of industrial unit via optimization of operating conditions. Coefficients of obtained models and interactive patterns of operating conditions showed that CTO is the most influential parameter on riser-reactor performance.

Fluidized-bed OCM reaction: A promising Mn2O3-Na2WO4/TiO2 catalyst and a numerical study

The fluidized-bed reactor with excellent heat and mass transfer features has great appeal for application in the oxidative coupling of methane (FB-OCM), whereas qualified fluid catalysts represent a grand challenge. Herein, we report a high-performance Mn2O3-Na2WO4/TiO2 fluid catalyst (5.4 wt% Mn2O3 and 2 wt% Na2WO4), which was obtained by the incipient-wetness impregnation method and examined in the OCM reaction in an electric-heating quartz fluidized-bed reactor (i.d., 2 cm). The standard normalization method on the basis of carbon atom was used for calculating the CH4 conversion and C2-C3 selectivity. This catalyst achieves 35.5 % CH4 conversion, 66 % C2-C3 selectivity and particularly 15.1 % single-pass yield of C2H4 for a feed of CH4/O2/H2O=3/1/1 with a catalyst dosage of 20 mL at 700 °C and a total GHSV of 7200 h−1. Such catalyst is stable for at least 50 h without signs of deactivation and agglomeration/defluidization. The catalyst particle size is crucial for the FB-OCM reaction with respect to the reaction light-off and catalyst fluidization. The catalyst with preferable particle size of 450–600 μm can not only trigger the OCM reaction at a relatively low temperature of 630 °C but also warrant active bubbling fluidization. Furthermore, thanks to the low amount of Na2WO4 and interpenetrating structure of TiO2-nanorod, such catalyst achieves good anti-aggregation and robust mechanical strength (with a low attrition index of 1.9 %). The effects of water-adding amount in feedstock and catalyst particle size distribution on the hydrodynamics behaviour were investigated in a laboratory-scale fluidized-bed OCM reactor by using numerical simulation method.

Generalized hydrodynamics for the volterra lattice: ballistic and non-ballistic behavior of correlation functions

Abstract In recent years, a lot of effort has been put in describing the hydrodynamic behavior of in- tegrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics to describe the Euler scale behavior of the correlation functions. We anticipate that the solution to the Generalized Hydrodynamics equations develops shocks at ξ0=x/t ; so this linear approximation does not fully describe the behavior of correlation functions. Intrigued but this fact, we performed several numerical investigations which show that, exactly when the solution to the hydrodynamic equations develops shock, the correlation functions show an highly oscillatory behavior. In view of this empirical observation, we believe that at this point ξ0 the diffusive contribution are not sub-leading corrections to the ballistic transport, but they are of the same order.

Appraisal of the Flooding Behaviour of Rotating Packed Beds

Rotating packed beds (RPBs) enhances mass transfer processes because a centrifugal force which is several -times greater than gravity is used as the driving force. The complexity of fluid flow across RPBs has made predicting and accurately determining their hydrodynamic behaviours difficult. The flooding point as a hydrodynamic characteristic is essential for the accurate design and scale-up of RPBs. However, variations in flooding point definitions and methodologies across the literature highlight the need for standardized approaches in studying RPB flooding phenomena. This study compared four approaches based on pressure drop fluctuations and the volume of liquid ejected from the RPB to determine the onset of flooding in RPBs using experimental results from a pilot-scale counter-current RPB. For rotational speeds of 300 -1500 rpm, gas flow rate of 100-300 Nm3/h, and liquid flow rates of 0.39-0.75 m3/h, the pressure drop varied from 314 to 2,100 Pa. Quantitative comparisons of the results based on different flooding point definitions showed wide variations with the values of the pressure drop at the onset of flooding differing by as much as 325 %. A quantitative approach based on virtual observations and the ejection of 8 % of the total liquid flow rate from the rotor’s eye is proposed as the standard method for identifying the onset of flooding in RPBs.