Free-surface Detection Research Articles

High spatiotemporal resolution free surface detection using cost-effective video equipment and computer vision techniques in nearly stationary flow along a transparent wall in the laboratory

The identification of the air–water interface in free surface flows traditionally involves intrusive techniques or costly equipment. Non-intrusive alternatives, such as computer vision, are emerging as highly effective substitutes or supplements for more invasive techniques in laboratory measurements, thanks to their straightforward implementation and cost efficiency. This research specifically delves in the conjunction of various naive techniques, exploring their collective precision in detecting the air–water interface along transparent walls in laboratory. A detection technique based on the double gradient of the image is applied and thoroughly examined. The study progresses through multiple refinement stages, culminating in a method that is both cost effective and easy to implement. This methodology allows for large-scale, high resolution measurements (200 mm × 1800 frames per video at a 0.25 mm, 50 Hz resolution), offering both spatial and temporal measurements by adeptly detecting the free surface along transparent walls.

Investigation on algorithms for simulating large deformation and impact loads

It is a challenge to simulate the hydrodynamic problems covering the large deformation of the free surface arising in severe circumstances with intense flow. This paper investigates algorithms based on the moving particle semi-implicit method for simulating large deformation and impact loads. The algorithm discretizes the fluid domain into a series of particles, each representing a part of the fluid. The pressure field calculation is implicit, and the velocity field calculation is explicit. Three models, including the gradient model, source term, and free-surface detection, have been improved and compared to determine which improvement is the best to enhance the accuracy and stability. The enhanced pressure gradient guarantees that momentum conservation can be satisfied. Particle density and velocity divergence are incompressible conditions combined in the mixed source term approach. The arc approach is used in the free-surface judging process. The results show that the combination of three models is the most effective in exploring the problems of hydrodynamic pressure and dam break. The issue of liquid sloshing including roll and sway investigates the effect of the initial distance and time step. It is found that the simulation accuracy of impact pressure can be increased as the initial distance and the time step decrease. Finally, the free surface breaking and liquid splashing phenomena are easily observed, and the method can accurately simulate the massive deformation of the free surface. These findings are helpful for hazard assessments of the various fluid mechanics-related problems.

Numerical investigations on water entry and/or exit problems using a multi-resolution Delta-plus-SPH model with TIC

As a classical Fluid-Structure Interaction (FSI) problem, water entry and/or exit of marine structures involve large deformations of free-surface and splashing, which have long been a great challenge for numerical modeling. Smoothed Particle Hydrodynamics (SPH) is a meshless Lagrangian particle method that has natural advantages in dealing with the non-linear variation of free-surface and moving interfaces. However, the characteristics of weakly-compressible SPH itself may lead to deficiencies such as pressure noise, tensile instability, heterogeneous particle distributions and computational inefficiency. Therefore, in this work, an acoustic damper term is formulated in the momentum equation to eliminate the amount of acoustic pressure waves induced by liquid impacts. Meanwhile, the Adaptive Particle Refinement (APR) is applied to obtain sufficiently fine particle resolution and reduce the computational cost. For the tensile instability issues induced by negative pressures, especially at the water exit stage, the Tensile Instability Control (TIC) is adopted into the SPH simulations to suppress its adverse impact. Furthermore, the Particle Shifting Technique (PST) is beneficial to the two schemes above, and it is also employed in this study. That is to say, PST can effectively solve the problem of particle disorder, which increases the accuracy and robustness of APR and reduces the momentum conservation error caused by TIC. Finally, we propose an improved Free-Surface Detection Method (FSDM) to allow the flow separation from the structure surface at the water entry stage that is impacted by PST. The fairly good agreements between the numerical results and the experimental data indicate the present SPH model can be treated as a reliable numerical tool for accurately solving such problems of structures penetrating fluid interfaces.

Stabilized mixed material point method for incompressible fluid flow analysis

This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational fluid dynamics (CFD) solver, the proposed approach adopts a monolithic displacement–pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). To satisfy the inf–sup stability condition, two stabilization strategies are integrated into the formulation: the variational multiscale method (VMS) and the pressure-stabilization Petrov–Galerkin method (PSPG). By concurrently solving the displacement and pressure fields, the developed monolithic solver obviates the need for free-surface detection as well as Dirichlet and Neumann pressure imposition, in contrast to the fractional-step method. This attribute mitigates spurious pressure and velocity oscillations in simulating dynamic and transient flow problems. This study also addresses other prevalent challenges in MPM simulations, such as the pressure oscillations triggered by cell-crossing errors, particle-distribution-induced quadrature errors, and particle-grid information transfer. To resolve these issues, the quadratic B-Spline basis function, the delta-correction method, and the Taylor particle-in-cell method are incorporated into the proposed mixed MPM formulation, thereby enhancing numerical stability. The efficacy of the proposed stabilized incompressible MPM framework is validated through several benchmark cases, comparing the obtained results with other numerical methods and analytical solutions. Furthermore, the method’s capability in simulating real-world problems involving violent free-surface fluid motion is demonstrated through comparisons with experimental results of water sloshing and dam break scenarios.

Towards an automated framework for the finite element computational modelling of directed energy deposition

In the present work, a comprehensive framework for finite element-based computational modelling of Directed Energy Deposition (DED) process is presented. The proposed approach can be fully automated and implemented on a complex real-life part geometry to accurately predict a thermo-mechanical response during the full-scale deposition process. The discrete material deposition modelling in Finite Element Analysis (FEA) leads to artificial increases in temperature gradients in the melt pool domain. A new method is therefore proposed that aims to mitigate these gradients. Additionally, an easy-to-implement free-surface detection algorithm to accurately prescribe the evolving heat transfer boundary conditions is presented. A three-dimensional sequentially coupled thermo-mechanical model of the process is then validated against experimental data obtained in a deposition case study. The simulation results show good agreement with the in-situ temperature measurements taken during the actual deposition. In addition, result analysis showed that the largest tensile residual stresses form in the hoop and axial direction on the outer domain of the thin-wall cylindrical part near the base plate while the inward material is compressed.

Numerical investigation on solitary waves traveling over rigid vegetation by a 3D-MPS method

In this study, a three-dimensional wave-vegetation numerical model based on the moving particle semi-implicit (MPS) method is established to investigate the interaction between solitary waves and rigid vegetation. Different from traditional wave-vegetation models, the effect of vegetation in the present numerical model is considered in terms of the stress between fluid and solid particles. Several improvements are put forward to increase the simulation accuracy, including a higher-order pressure gradient discrete model, a multi-term source involving a background mesh scheme, and multi-condition free surface detection. Based on the improved 3D-MPS method, the propagation of solitary waves on a flat bed with and without vegetation is simulated. The results show improvement in resolving the issue of numerical energy dissipation. Because of the intrinsic advantage of the particle method, the attenuation and deformation of a wave on a vegetation area can be realistically reproduced, as can detailed velocity and curl fields. In addition, a parametric study of the effects of wave height, plant relative height, and stem density on the wave attenuation rate is conducted. The result indicates that the relationship between wave attenuation rate and plant height is nonlinear.

Multi-level adaptive particle refinement method with large refinement scale ratio and new free-surface detection algorithm for complex fluid-structure interaction problems

Fluid-Structure Interaction (FSI) is a crucial problem in ocean engineering. The smoothed particle hydrodynamics (SPH) method has been employed recently for FSI problems in light of its Lagrangian nature and its advantage in handling multi-physics problems. The efficiency of SPH can be greatly improved with the Adaptive Particle Refinement (APR) method, which refines particles in the regions of interest while deploying coarse particles in the left areas. In this study, the APR method is further improved by developing several new algorithms. Firstly, a new particle refinement strategy with the refinement scale ratio of 4 is employed for multi-level resolutions, and this dramatically decreases the computational costs compared to the standard APR method. Secondly, the regularized transition sub-zone is deployed to render an isotropic particle distribution, which makes the solutions between the refinement zone and the non-refinement zone smoother and consequently results in a more accurate prediction. Thirdly, for complex FSI problems with free surface, a new free-surface detection method based on the Voronoi diagram is proposed, and the performance is validated in comparison to the conventional method. The improved APR method is then applied to a set of challenging FSI cases. Numerical simulations demonstrate that the results from the refinement with scale ratio 4 are consistent with other studies and experimental data, and also agree well with those employing the refinement scale ratio 2. A significant reduction in the computational time is observed for all the considered cases. Overall, the improved APR method with a large refinement scale ratio and the new free-surface detection strategy shows great potential in simulating complex FSI problems efficiently and accurately.

Numerical simulations of liquid-solid flows with free surface by coupling IMPS and DEM

Liquid-solid two-phase flow with free surface is a significant issue in nature and engineering fields. In present study, an in-house solver MPSDEM-SJTU based on a fully Lagrangian coupled method is developed to solve the problems of liquid-solid two-phase flows. The improved moving particle semi-implicit (IMPS) method is applied for the simulation of incompressible viscous liquid flows while the discrete element method (DEM) is used to model the interaction among the solid particles. The coupling strategy is based on the local averaging technique. Multiple time-step algorithm is adopted for those two methods to balance the stability and the efficiency. The free surface detection and the solid-fluid neighbor search are modified. A simulation of multi-balls collapse is conducted to verify the DEM program of the present solver. The distributions of solid balls at different instants are in good agreement with the experimental results. Then, this solver is applied for two typical problems of two-phase flows, including the two-phase dam-break and the liquid-solid flows in a rotating cylindrical tank. The flow front, flow patterns and the shape of solid beds all agree well with experimental observations.

Fast detection of free surface and surface tension modelling via single-phase SPH

Surface tension plays a crucial role in many practical issues ranging from the bubble and droplet dynamics to the super-hydrophilic and hydrophobic bio-inspired designs. Current smoothed particle hydrodynamics models for surface tension are mostly multiphase-based and computationally expensive. In this work, we propose a single-phase model of surface tension based on fast free-surface detections. We develop two free-surface detection algorithms: (1) a two-step detection combining the number of neighboring particles method and the arc-method, and (2) a central angle-based method, which is proved to be much more efficient than the reference counterparts. The central angle method is incorporated into the single-phase model. We verify the single-phase model through several droplet dynamics simulations including initially squared droplets, the oscillating droplet, binary head-on coalescence of droplets, and the wetting problems. Compared with the multiphase solver, this single-phase model is much simpler in the algorithm, more efficient in computation, and meanwhile retains good accuracy and robustness. Although the problems studied in this work are limited to 2D cases, the single-phase model lends itself naturally to large-scale 3D scenarios. The free-surface detection algorithms can also be applied in other meshfree methods.

Enhanced weakly-compressible MPS method for violent free-surface flows: Role of particle regularization techniques

This paper develops a consistent particle method for capturing the highly non-linear behavior of violent free-surface flows, based on an Enhanced Weakly Compressible Moving Particle Semi-implicit (EWC-MPS) method. It pays special attention to the evaluation and improvement of two particle regularization techniques, namely, pairwise particle collision (PC) and particle shifting (PS). To improve the effectiveness of PC in removing noisy pressure field, and volume conservation issue of PS, we propose and evaluate several enhancements to these techniques, including a novel dynamic PC technique, and a consistent PS algorithm with new boundary treatments and additional terms (in the continuity and momentum equations). Besides, we introduce modified higher-order and anti-symmetric operators for the diffusive and shear force terms. Evaluation of the proposed developments for violent free-surface flow benchmark cases (2D dam-break, 3D water sloshing, and 3D dam-break with an obstacle) confirms an accurate prediction of the flow evolution and rigid body impact, as well as long-term stability of the simulations. The dynamic PC reduces pressure noises with low energy dissipation, and the consistent PS conserves the volume even for extreme deformations. Comparing the role of these new particle regularization techniques demonstrates the effectiveness of both in assuring the uniformity of the particle distribution and pressure fields; nevertheless, the implementation of PS is found to be more complex and time-consuming, mainly due to its need for free surface detection and boundary treatments with several tuning parameters.

An improved high-order ISPH method for simulation of free-surface flows and convection heat transfer

The present work introduces a modified Incompressible Smoothed Particle Hydrodynamics (ISPH) model for simulation of free-surface flows and convection heat transfer. First, two new gradient and Laplacian models are proposed based on the Taylor series expansion and then used for discretization of the diffusion terms, Pressure Poisson's equation (PPE), and divergence of velocity. To maintain overall high-order accuracy, an explicit third-order TVD Runge-Kutta scheme is employed for discretization of the transient terms in Navier-Stokes and energy equations. Moreover, a new Hybrid Particle Shifting Technique (HPST) is developed by combining the classical PST and a collision model. A new kernel function is developed by combination of the Gaussian and polynomial functions and is then applied to the simulation of classical 1D Sod shock tube. Furthermore, a novel Hybrid Free-surface Detection (HFD) technique is proposed for accurate imposition of Dirichlet pressure boundary condition at the free surface area. The validity and applicability of proposed numerical schemes are verified against the several challenging benchmark cases including: dam-break flows with/without an obstacles, stretching water drop, rotating square patch of fluid, Rayleigh-Taylor instability, energy and exergy analysis of natural convection heat transfer in differentially heated cavity. The results show that, the newly constructed kernel function can successfully guarantee the stability and convergence of the numerical solution. Furthermore, it is found that, the proposed Hybrid Particle Shifting Technique (HPST) can efficiently resolve the unphysical discontinuity and suppress spurious pressure fluctuations.

Image processing for hydraulic jump free-surface detection: coupled gradient/machine learning model

High-frequency oscillations and high surface aeration, induced by strong turbulence, make water depth measurement for hydraulic jumps a persistently challenging task. The investigation of hydraulic jump behaviour continues to be an important research theme, particularly with regards to the stilling basin design. Reliable knowledge of time-averaged and extreme values along a depth profile can help develop an adequate design of a stilling basin, improve safety, and aid the understanding of the jump phenomenon. This paper presents an attempt to mitigate certain limitations of existing depth measurement methods by adopting a non-intrusive computer vision-based approach to measuring the water depth profile of a hydraulic jump. The proposed method analyses video data in order to detect the boundary between the air–water mixture and the laboratory flume wall. This is achieved by coupling two computer vision methods: (1) analysis of the vertical image gradients, and (2) general-purpose edge detection using a deep neural network model. While the gradient analysis technique alone can provide adequate results, its performance can be significantly improved in combination with a neural network model which incorporates a ‘human-like’ vision within the algorithm. The model coupling reduces the likelihood of false detections and improves the overall detection accuracy. The proposed method is tested in two experiments with different degrees of jump aeration. Results show that the coupled model can reliably and accurately capture the instantaneous depth profile along the jump, with low sensitivity to image noise and flow aeration. The coupled model presented fewer false detections than the gradient-based model, and offered consistent performance in regions of high as well as low aeration. The proposed approach allows for automated detection of the free-surface interface and expands the potential of computer vision-based measurement methods in hydraulics.

Numerical simulation of solitary waves overtopping on a sloping sea dike using a particle method

Sea dikes, as a commonly used type of coastal protection structures, are often attacked or damaged by violent waves overtopping under tsunamis and storm surges. In this study, the behavior of solitary waves traveling on a sloping sea dike is simulated, and solitary wave overtopping characteristics are analyzed using a complete Lagrangian numerical method, the moving particle semi-implicit (MPS) method. To better describe the complicated fluid motions during the wave overtopping process, the original MPS method is modified by introducing a new free surface detection method, i.e., the area filling rate identification method, and a modified gradient operator to provide higher precision. Meanwhile, the approximation method for sloping boundaries in particle methods is enhanced, and a smooth slope approximation method is proposed and recommended. To verify the improved MPS method, a solitary wave traveling over a steep sloping bed is studied. The entire solitary wave run-up and run-down processes and exquisite water movements are reproduced well by the present method, and are consistent with the corresponding experimental results. Subsequently, the improved MPS method is applied to investigate the overtopping process of a single solitary wave over a sloping sea dike. The results show that the hydraulic jump phenomenon is also possible to occur during the run-down motion of the solitary wave overtopping. Finally, the characteristics of the propagation and overtopping of two successive solitary waves on a sloping sea dike are discussed. The result manifests that the interaction between adjacent solitary waves affects wave overtopping patterns and overtopping velocities.

Improved particle shifting technology and optimized free-surface detection method for free-surface flows in smoothed particle hydrodynamics

This paper presents an improved particle shifting technology (IPST) for smoothed particle hydrodynamics (SPH). It allows particles in the vicinity of the free-surface to be shifted in all the directions in case they are not uniformly distributed, rather than just shifted tangentially to the free-surface in some conventional particle shifting technologies. Therefore, with the new technique, the imprecise shifting due to the inaccurate evaluations of the local normal and tangential vectors of the free-surface can be avoided, and a more uniform particle distribution near the free-surface can be obtained even for long-term simulations, which improves the accuracy and stability of the SPH method. Besides, by combining the advantages of two existing free-surface detection methods, an optimized detection approach is provided. It is capable of detecting the free-surface particles accurately, and meanwhile, it is easier to implement and requires lower computational costs, especially for three-dimensional problems. Several numerical tests show that the proposed IPST and the optimized free-surface detection method are robust and accurate for the simulation of a variety of free-surface flows.

A particle-based free surface detection method and its application to the surface tension effects simulation in smoothed particle hydrodynamics (SPH)

A particle based algorithm for fluid surface detection and evaluation of the interface force due to surface tension for smoothed particle hydrodynamics (SPH) is presented in this work. The algorithm identifies the surface particles by examining the local geometry around them, and it presents sharp interface transition region. The curvature and normal for the identified surface particles are extracted from the geometry around the surface particles. The interface force is integrated into the SPH equation for fluid dynamics with full consideration of interface effects. The algorithm presented is capable of detecting arbitrary surface undergoing fragmentation and coalescence. The stability and accuracy of the interface force simulated with this algorithm are validated with test cases.

Numerical procedure for free-surface detection using a Volume-of-Fluid model

During the design of a stepped spillway it is fundamental to predict the maximum water depth to define wall height. Many experimental and numerical studies have been made on this subject, however the combination of both, in order to enhance aspects related to free-surface characteristics and their numerical prediction, are still uncovered. While experimentally the free-surface position is defined as the line where air-concentration reaches 90%, numerically the free-surface is defined by the equilibrium of volume between the water and air. In this work, the free-surface, captured with a modified version of three-dimensional Volume-of-Fluid model for the combined air–water flow, is compared to the flow depths measured with three ultrasonic sensors in a stepped spillway. This comparison is used to reach an equilibrium between the theoretical definition of the numerical and experimental free-surface position and to propose a numerical procedure to predict the free-surface using the three-dimensional modified Volume-of-Fluid. The numerical model uses the Shear-stress transport k-ω model to calculate the turbulent characteristics of the flow in a uniform and orthogonal mesh. Fit coefficients between experimental and numerical free-surfaces are calculated along with this procedure to obtain the best relation. In non-aerated regions of the flow, free surface should be represented by α=0.7 while for the aerated region, α=0.1 should be used instead, both with errors of 2%.

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

SummaryPrecise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.

Numerical simulation of impinging jet flows by modified MPS method

Purpose – The jet impingement usually accompanying large interface movement is studied by the in-house solver MLParticle-SJTU based on the modified moving particle semi-implicit (MPS) method, which can provide more accurate pressure fields and deformed interface shape. The comparisons of the pressure distribution and the shape of free surface between the presented numerical results and the analytical solution are investigated. The paper aims to discuss these issues. Design/methodology/approach – To avoid the instability in traditional MPS, a modified MPS method is employed, which include mixed source term for Poisson pressure equation (PPE), kernel function without singularity, momentum conservative gradient model and highly precise free surface detection approach. Detailed analysis on improved schemes in the modified MPS is carried out. In particular, three kinds of source term in PPE are considered, including: particle number density (PND) method, mixed source term method and divergence-free method. Two...

Implementation of surface tension force in fluid flow during reactive rotational molding

During Reactive Rotational Molding (RRM), it is very important to predict the fluid flow in order to obtain the piece with homogeneous shape and high quality. This prediction may be possible by simulation the fluid flow during rotational molding. In this study we have used a mixture of isocyanate and polyol as reactive system. The kinetic rheological behaviors of thermoset polyurethane are investigated in anisothermal conditions. Thanks to these, rheokinetik model of polyurethane was identified. Then, to simulate the RRM, we have applied Smoothed Particles Hydrodynamics (SPH) method which is suited method to simulate the fluid flow with free surface such as occurs at RRM. Modelling and simulating reactive system flow depend on different parameters; one of them is the surface tension of reactive fluid. To implement force tension surface, the interface between polymer and air is dynamically tracked by finding the particles on this border. First, the boundary particles are detected by free-surface detection algorithm developed by Barecasco, Terissa and NAA [1, 2] in two and three dimension. Then, analytical and geometrical algorithms have been used for interface reconstructions. The aim of this work is the implementation of surface tension force in the SPH solver applied to RRM. To illustrate that, we used novel and simple geometric algorithm fitting circle and fitting sphere, in two and three dimensional configurations, respectively. The model has been validated using a well-known dam break test case which covered the experimental data.

PIV measurements of flow around an arbitrarily moving free surface

We present an image preprocessing method for particle image velocimetry (PIV) measurements of flow around an arbitrarily moving free surface. When performing PIV measurements of free surface flows, the interrogation windows neighboring the free surface are vulnerable to a lack, or even an absence, of seeding particles, which induces less reliable measurements of the velocity field. In addition, direct measurements of the free surface velocity using PIV have been challenging due to the intermittent appearance of the arbitrarily moving free surface. To address the aforementioned limitations, the PIV images with a curvilinear free surface can be treated to be suitable for a structured interrogation window arrangement in a Cartesian grid. The proposed image preprocessing method is comprised of a free surface detection method and an image transform process. The free surface position was identified using a free surface detection method based on multiple textons. The detected free surface points were used to transform PIV images of a curvilinear free surface into images with a straightened free surface using a cubic Hermite spline interpolation scheme. After the image preprocessing, PIV algorithms can be applied to the treated PIV images. The fluid-only region velocities were measured using standard PIV method with window deformation, and the free surface velocities were resolved using PIV/interface gradiometry method. The velocity field in the original PIV images was constructed by inverse transforming that in the transformed images. The accuracy of the proposed method was quantitatively evaluated with two sets of synthetic PIV images, and its applicability was examined by applying the present method to free surface flow images, specifically sloshing flow images.