Number Fr Research Articles

Thermal analysis in Darcy-Forchheimer hybrid nanofluid through a Riga plate: An ANN optimization

In the present study, a double-hybrid nanofluid's Darcy-Forchheimer flow behavior over a Riga plate with the presence of radiation and heat source impacts is examined. Two distinct nanoparticles as Silicon Carbide (SIC), and Graphite (C) with a base fluid of Ethylene glycol (C2H6O2) are taken into consideration. The model of Cattaneo-Christov heat flux is discussed in the energy and mass equation. The symmetry variables are utilized to remodel the boundary conditions and governing flow models into non-linear ordinary differential equations. The redesigned ordinary differential equations are numerically computed using bvp4c in MATLAB. Graphical representations are used to study how distinct parameters create variations in the concentration, temperature, and velocity profile. The present study shows that the velocity profile decreases with an upsurge in the Hartmann number. The current analysis determined that the fluid velocity declines and the Forchhiemer number (Fr) increases. The fluid concentration increases when temperature temperature-dependent coefficient (B) rises. The significance of emerging parameters on skin friction, Nusselt number, and Sherwood number are computed in tabular shape. Artificial neural networking (ANN) is applied to optimize physical quantities of data, by training, validation, and testing, to check the accuracy of the data.

Numerical and Experimental Analysis of Lifting Forces of Fin Stabilizers with Fin–Hull Interaction

A fin stabilizer is one of the most effective and frequently used anti-roll devices for maintaining a ship’s operational safety and passengers’ comfort. However, the discrepancy between theoretical hydrofoil-based predictions and the actual dynamic lift force of fin stabilizers due to fin–hull interactions requires more research attention. This study investigates the effect of fin stabilizers on mitigating roll motion through the performance of extensive computational fluid dynamic (CFD) simulations over a range of fin angles and ship speeds. Model tests were carried out to validate the drag and motion results obtained from numerical analyses. The results show that fin stabilizers significantly reduce the roll motion, with the lift coefficient values influenced by the Reynolds number, leading to differences between the theoretical and Reynolds-averaged Navier–Stokes (RANS) calculations. At a high Froude number (Fr), the actual fin lift is about half of the theoretical value. These findings highlight the requirement of selecting an adequate fin area at the predominant ship speeds and ensuring an effective anti-roll effect with fin–hull interaction. This study provides a significant reference for ship design, as well as stabilization system control and optimization.

Non-similar analysis of suction/injection and Cattaneo-Christov model in 3D viscoelastic non-Newtonian fluids flow due to Riga plate: A biological applications

Bioconvective non-Newtonian fluids with motile microorganisms have diverse applications in biology and medicine, offering numerous research opportunities. This article presents a comprehensive investigation into the non-similar analysis of bio-convective micropolar flow induced by a Darcy-Forchheimer exponentially stretchable sheet, considering the effects of suction/injection and thermal radiation in a three-dimensional framework. The fluid under scrutiny is a viscoelastic tangent hyperbolic nanofluid, the impact of Cattaneo-Christov heat subjected to Riga plate is considered for novelty. The role of activation energy and heat source are also computed. The governing equations of viscoelastic tangent hyperbolic nanofluids are transformed into couple of ordinary differential equations via similarity approximations. The resulting ODEs are tackled numerically via bvp4c tool of MATLAB. The impression of appropriate parameters like magnetic parameter, bio-convection parameter, viscoelasticity parameter suction/injection parameter etc. on involved profiles are computed via graphical and tabulated trends. It is observed that velocity layer f′ is dwindled for growing value of Forchheimer number Fr, while reverse relation in velocity curve is noted for developing value of mixed convection parameter δ. Micropolar fluids find biomedical engineering applications in modeling blood flow in microvessels, understanding cerebrospinal fluid dynamics, and optimization of biomedical devices and therapies and simulating drug delivery in tissues.

Experimental investigation of the characteristics of flame geometry and heat transfer from wind-driven pool fires

Wind-driven pool fire is a frequently encountered thermal hazard in cases of liquid fuel leakage accidents. Given the intricate interplay between wind flow and thermal buoyancy, understanding the flame geometry and external heat transfer behavior of pool fires is vital for effective liquid fuel security management. This paper presents a study to investigate these characteristics under various square pool sizes (side length, D = 0.31, 0.38, 0.44, 0.49, and 0.54 m) and wind speeds (u = 0, 0.5, 1, 2, 4, and 6 m/s). Five parameters pertaining to global flame geometry and two parameters concerning external heat transfer were measured. The findings indicate that the change rate of overall flame geometry parameters accelerates at first and then decelerates with wind speed. The ratio of the net flame horizontal length dominated by inertia force (Li) and the net flame horizontal length dominated by buoyancy force (Lb) to the total horizontal flame length (Lh) (Li / Lh and Lb / Lh) present a non-monotonic trend with increasing Fr number. To further comprehend the global flame geometry, a corresponding physical model is developed based on the ratio of Grs number to the 5/2 power of Rem number (Grs / Rem5/2). Due to the effects of flame thickness and flame attachment length, the variation in radiant heat transfer with wind speed can be bifurcated into two categories. The convective heat coefficient increases with wind speed, enhancing the local convection. Finally, the new models of radiant and convective heat transfers are established using dimensionless wind speed (u*, u∗=u(ṁ″g/ρ0)1/3) and Ri number. To ascertain the suitability of these new models, they have been validated against two classic flame models.

Experimental analysis on the flow patterns and conversion mechanisms of condensing flow with non-azeotropic mixtures in spiral tube

The flow patterns have a significant impact on the flow and heat transfer characteristics of the working fluid, making it fundamental for the study of complex two-phase flows. To investigate the condensation flow pattern and flow pattern transformation mechanism with mixed hydrocarbon in a spiral tube, a two-phase flow pattern experimental system was designed. The effects of mass flux (196–540 kg/m−2·s−1), vapor quality (0–1), and operating pressure (2–4 MPa) on flow patterns of methane/ethane/propane/isobutane mixed fluid in spiral tubes were analyzed. The results showed that with the increase in vapor quality, flow patterns such as bubbly flow, intermittent flow, wavy-stratified flow, and annular flow were observed in sequence. Additionally, through a comparative analysis of the experimental observations with existing flow pattern maps, a new flow pattern map tailored for the condensation two-phase flow of mixed hydrocarbon working fluids has been established. Based on the influence of inertial force, surface tension, gravity, shear force and other forces, Martinelli number, Soliman We and Soliman Fr are selected for the development of flow pattern conversion criteria. The new flow pattern map accurately predicts the majority of flow patterns.

Recommendations on setup in simulating atmospheric gravity waves under conventionally neutral boundary layer conditions

Wind farm-induced atmospheric gravity waves have been the subject of recent research as they can impact wind farm performance. Pressure variations associated with gravity waves can contribute to the global blockage effect and wind farm wake recovery. Therefore, accurate numerical simulation of flow fields, where wind-farm-induced gravity waves may be produced, is important. Three main considerations in such simulations are the overall domain size, the use of Rayleigh damping near domain boundaries to dampen gravity waves, and advection damping at the inlet to prevent spurious oscillations. Often these considerations are treated ad hoc rather than systematically. This work aims to test and extend the systematic modelling of internal gravity waves proposed in a preliminary investigation to modelling of both internal and trapped gravity waves. The preliminary study identifies the length scales to set the domain and damping layer sizes and the time scale to configure the Rayleigh damping coefficient but under linearly stratified conditions. Large eddy simulations of flow through a wind farm canopy are performed under conventionally neutral boundary layer (CNBL) conditions to test the validity of proposed setups for CNBL conditions. Background atmospheric parameters, such as Froude number (Fr), inversion height (Hi ), and inversion layer Froude number (Fri ) control most of the atmospheric gravity wave characteristics. We validated for CBNL conditions that the effective wavelengths of the internal gravity waves are the correct length scale to configure the domain size and damping layer thickness. Likewise, the optimum damping coefficient to dampen the internal gravity waves relates to the free atmosphere’s buoyancy frequency or buoyant perturbations’ time scale. We infer that the damping coefficient in the inversion layer may relate to the inversion buoyancy frequency to effectively dampen the trapped gravity waves. Moreover, the advection damping length is linked to the horizontal wavelength of the trapped gravity waves in the inversion layer to prevent spurious waves at the inlet by retaining wave energy accumulation.

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.

Experimental analysis of self-propelled characteristics with uncertainty analysis of ONR tumblehome hull

In this paper, the self-propelled characteristics of the benchmark ONRT hull were studied experimentally at both Froude numbers, Fr = 0.20 and Fr = 0.30. The assessments were conducted under free-running conditions using a fully appended Office of Naval Research Tumblehome (ONRT), model 5613, scaled at 48.9, a customary proportion in academic research. To demonstrate the reliability of self-propulsion experiments conducted at the Istanbul Technical University, Ata Nutku Ship Model Testing Laboratory (ITU-AN), an uncertainty analysis method was applied to the ONRT results. The self-propulsion points from the studies in literature at both Fr = 0.20 and Fr = 0.30, were compared with the present test results. Based on the analysis results at self-propulsion points, it was noted that there was a high level of both intra-laboratory repeatability and inter-laboratory reproducibility characteristics. Through repeated tests, it was discerned that the uncertainties impacting essential parameters were, in descending magnitude, thrust, torque, and rotational rate. Consequently, this investigation enhances the precision and reliability of results by presenting the thrust and torque characteristics of the ONRT hull form, along with associated uncertainties for these Fr numbers.

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.

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.

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.

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.