Surface Tracking Method Research Articles

Numerical studies of the breakup of the water jet by a shock wave in the barrel of the fire extinguishing installation

This scientific paper delves into the numerical studies of the process of filling the barrel with water and the subsequent breakup of the water jet and water atomization in the barrel of the fire extinguishing installation. The numerical model of the process of water injection into the barrel with the subsequent breakup of water by a shock wave was substantiated. To simulate these processes, the ANSYS software was used. VOF (volume of fluid) method-based model was applied where it is assumed that there is no penetration of one medium into another. The solution is based on the surface tracking method applied to a fixed Eulerian grid. According to the results of the numerical study, it was established that the water injection time significantly exceeds the duration of the gas detonation cycle in the fire extinguishing installation. In particular, we found out that it takes 8 ms just to spread the water jet from one side of the barrel to the other. It was observed that a high quality of water atomization under the action of a high-speed gas flow including the water located along the barrel wall. We stated that it is unreasonable to use the pulse injection of water into the barrel in the designed fire extinguishing installation due to a high fregiency of the shock wave generation exceeding 23 Hz.

Fluid-evolving landform interaction by a surface-tracking method

This paper introduces a continuous finite element model to simulate fluid flow-bedform interaction problems. The approach utilizes a non-oscillatory finite element algorithm to compute the fluid dynamics by solving the complete Navier–Stokes equations. Additionally, it addresses the evolution of the fluid–bedform interface as a consequence of spatially non-balanced sediment fluxes through the solution of a conservation equation for the erodible layer thickness. A sign preservation algorithm is particularly relevant for landform tracking because a positive definite thickness of the erodible sediment layer is essential to model the interaction between evolving cohesionless sediment layers and rigid beds. The fluid/terrain interface is explicitly captured through a surface tracking methodology. First, new nodes fitting the interface are incorporated into the finite element mesh; then, elements beneath this interface are deactivated, while intersected elements are restructured to get a mesh composed exclusively of tetrahedral elements. Numerical experiments demonstrate capabilities of the method by exploring relevant problems related with civil engineering, such as the evolution of trenches and the scour of a submerged pile.

Features of the process of water filling the barrel of a periodic-pulse fire extinguishing installation

In the work, research was carried out, which made it possible to reveal the peculiarities of the process of filling the barrel of the periodic-impulse fire extinguishing installation with water. At the same time, a mathematical model for simulating the processes of water injection into a pipe with subsequent crushing of water by a shock wave was substantiated and proposed. To simulate the processes of water injection and water crushing in the shaft of the installation, a VOF model (volume of liquid model) is used, according to which there is no penetration of one medium into another, and which is based on the surface tracking method applied to a fixed Euler grid. On the basis of the developed mathematical model in the ANSYS software environment, numerical studies of the process of filling the barrel of a periodic-impulse fire extinguishing installation with water were carried out. According to the results of a numerical study of the process of filling the barrel of the periodic-impulse fire extinguishing installation with water, a relatively high inertia in the time of the water injection processes in relation to the gas detonation processes occurring in the periodic-impulse fire extinguishing installation was revealed. In particular, the time interval between detonation cycles in the installation operating at a frequency of 23 Hz is about 43,5 ms. If we discard the purge cycle, then we have a time interval of 21 ms, during which it is necessary to inject water into the barrel of the intermittent-impulse fire extinguishing installation. According to the results of the above studies, we have that only the time for the spread of the stream of water from one side to the other side of the barrel of the periodic-impulse fire extinguishing installation is 8 ms. The conducted research makes it possible to investigate the influence of the parameters of the fire extinguishing installation on the formation of a finely sprayed water jet, and the obtained results will significantly increase the level of operational readiness of the personnel of fire and rescue units during operational actions to extinguish internal fires.

Numerical investigation of structural models equipped with tuned liquid damper

Tuned liquid dampers (TLDs) are introduced in structural systems to suppress vibration of the structure due to dynamic actions. Using a grid-based Finite Volume Method-Finite Element Method (FVM/FEM), efficiency of TLDs of cylindrical and rectangular geometries was evaluated by performing a two-way Fluid-Structure Interaction (FSI) analysis. The nonlinear sloshing response of fluid was simulated by employing a three-dimensional Navier–Stokes equation as the governing equation and occurrence of wave breaking was accounted by using Volume of Fluid (VOF) method for free surface tracking. Utilizing the developed numerical model, a series of three-dimensional transient analysis were conducted on a structure with and without TLDs aiming to investigate effect of base excitation amplitude. The result show that maximum performance of TLDs at resonance is obtained when the forcing ratio is limited to 0.1, and for this case, both cylindrical and rectangular TLDs displayed comparable efficiency. Effect of excitation frequency fe was also investigated under a wide range of the forcing ratio showing that as fe increases, the natural frequency of coupled TLD-structural system approaches the natural frequency of un-damped structural system.

VOF with center of mass and Lagrangian particles (VCLP): a surface tracking and advection method for incompressible fluids

VOF with center of mass and Lagrangian particles (VCLP): a surface tracking and advection method for incompressible fluids

Research on Surface Tracking Method of Industrial Robot Based on Model Predictive Control

Research on Surface Tracking Method of Industrial Robot Based on Model Predictive Control

Extremely high-order convergence in simulations of relativistic stars

We provide a road towards obtaining gravitational waveforms from inspiraling material binaries with an accuracy viable for third-generation gravitational wave detectors, without necessarily advancing computational hardware or massively-parallel software infrastructure. We demonstrate a proof-of-principle 1 + 1-dimensional numerical implementation that exhibits up to 7th-order convergence for highly dynamic barotropic stars in curved spacetime, and numerical errors up to 6 orders of magnitude smaller than a standard method. Aside from errors associated with overshoot in high-order extrapolation from the interior of the star to the surface, there are no obvious fundamental obstacles to obtaining convergence of even higher order. The implementation uses a novel surface-tracking method, where the surface is evolved and high-order accurate boundary conditions are imposed there. Computational memory does not need to be allocated to fluid variables in the vacuum region of spacetime. We anticipate the application of this new method to full 3 + 1-dimensional simulations of the inspiral phase of compact binary systems with at least one material body. The additional challenge of a deformable surface must be addressed in multiple spatial dimensions, but it is also an opportunity to input more precise surface tension physics.

Finite difference solutions for nonlinear water waves using an immersed boundary method

AbstractIn this article, high‐order finite difference solutions of the exact potential‐flow problem for nonlinear water waves are developed which treat both the free surface and the uneven sea bottom boundary conditions using an immersed boundary method (IBM). The convergence, accuracy, and stability of this approach is first established for the linear problem, using various orders of scheme and different grid discretization strategies. The nonlinear wave problem on a flat bottom is then considered, and the solutions are compared with the highly accurate stream function theory solution. The convergence performance of the numerical solution for this nonlinear wave problem is established. Finally, linear wave shoaling and nonlinear wave propagation over a submerged bar are also tested. A preconditioned iterative solution strategy is also developed and shown to provide optimal scaling of the solution effort with increasing number of unknowns. Compared with existing free surface tracking methods, the IBM retains the same level of accuracy and stability when solving the linear problem. For the nonlinear problem, the IBM behaves reasonably in terms of accuracy, but generally with slightly higher computational effort. When it comes to the wave–body interaction problem, it is expected that the IBM will be advantageous compared with the σ‐transform method, since it removes the necessity of constructing an artificial continuous free‐surface inside the body.

A Coupled Grid-Particle Method for Fluid Animation on GPU

In digital production environments, high-quality visual effects play a key role in our mobile device such as game and film. The simulation of fluid animation with free surface is an important area in computer graphic. However, the tracking of fluid surface is a challenging problem because of its instability. In this paper, a coupled grid-particle method for fluid animation surface tracking and detail preserving is proposed. Firstly, based on the nonequilibrium extrapolation method, we design a novel method for reconstructing distribution functions (DFs) of interface grids of lattice Boltzmann method (LBM) and couple the reconstruction method with LBM and volume of fluid (VOF) to track the free surface, which can obtain the accurate surface. Secondly, in order to avoid the loss of details caused by weaknesses in the traditional LBM-VOF method, we design a coupled grid-particle method that not only makes full use of the advantages of the coupled grid-particle method but also realizes the two-way coupling between grid method and particle method. Furthermore, for achieving the real-time requirements of fluid animation, we use GPU parallel computing to accelerate the simulation and use an improved screen space fluid (SSF) rendering method for realistic rendering. The various experiments show that this work can track the fluid surface with high precision and preserve the details of the fluid surface, and it also achieves good real-time performance in large-scale fluid simulation.

Object to End Effector Distance Control Method for Contactless Surface Tracking Works by a Teleopelated Humanoid Robot

Object to End Effector Distance Control Method for Contactless Surface Tracking Works by a Teleopelated Humanoid Robot

Numerical study of pore formation in thermal spray coating process by investigating dynamics of air entrapment

When a liquid droplet impacts onto a solid surface, a thin air film is generally entrapped between the droplet and the substrate at the central portion which eventually evolves into a spherical air bubble for minimizing the surface energy. It leads to the formation of pores in the thermal spray coatings. This interesting phenomenon during the impact of molten metal droplets in thermal spray deposition that involves freezing is not clearly understood because of opaque nature of the metal droplet. Earlier works have focused on hydrodynamics of air entrapment without considering the phase change. Without considering heat transfer and phase change, the actual conditions of thermal spray deposition were not represented. The current study numerically analyzes pore formation by investigating the entrapped air film dynamics during the high-speed impact of a micron-sized molten metal droplet onto a solid substrate for thermal spray conditions by considering fluid flow, heat transfer, solidification phase change and free surface evolution. The volume of fluid surface tracking method (VOF) coupled with the solidification and heat transfer model within a continuum formulation is utilized. Results show that initially a thin circular film of air was entrapped in the impacting droplet which subsequently grew into an air bubble. The formation of the air bubble from the entrapped air film involves a complicated evolutionary process consisting of retraction, contraction and toroid formation of the air film. The analysis of heat transfer shows that wall heat flux distribution has a strong relation with dynamic feature of the trapped air. Further, it is shown that wettability of the substrate affects the detachment of the air bubble, which suggests a method for air bubble elimination from the solidifying droplet. Trapped air film tends to detach easily from the surface for low contact angle.

Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure

Large floating structures, such as liquefied natural gas (LNG) ships, are subject to both internal and external fluid forces. The internal fluid forces may also be detrimental to a vessel’s stability and cause excessive loading regimes when sloshing occurs. Whilst it is relatively easy to measure the motion of external free surface with conventional measurement techniques, the sloshing of the internal free surface is more difficult to capture. The location of the internal free surface is normally extrapolated from measuring the pressure acting on the internal walls of the vessel. In order to understand better the loading mechanisms of sloshing internal fluids, a method of capturing the transient inner free surface motion with negligible affect on the response of the fluid or structure is required. In this paper two methods will be demonstrated for this purpose. The first approach uses resistive wave gauges made of copper tape to quantify the water run-up height on the walls of the structure. The second approach extends the conventional use of optical motion tracking to report the position of randomly distributed free floating markers on the internal water surface. The methods simultaneously report the position of the internal free surface with good agreement under static conditions, with absolute variation in the measured water level of around 4 mm. This new combined approach provides a map of the free surface elevation under transient conditions. The experimental error is shown to be acceptable (low mm-range), proving that these experimental techniques are robust free surface tracking methods in a range of situations.

Neural networks for determining the vector normal to the surface in CFD, LBM and CA applications

PurposeThe well-known discrete methods of computational fluid dynamics (CFD), lattice Boltzmann method (LBM), cellular automata (CA), volume-of-fluid (VoF) and others rely on several parameters describing the boundary or the surface. Some of them are vector normal to the surface, coordinates of the point on the surface and the curvature. They are necessary for the reconstruction of the real surface (boundary) based on the values of the volume fractions of several cells. However, the simple methods commonly used for calculations of the vector normal to the surface are of unsatisfactory accuracy. In light of this, the purpose of this paper is to demonstrate a more accurate method for determining the vector normal to the surface.Design/methodology/approachBased on the thesis that information about the volume fractions of the 3 × 3 cell block should be enough for normal vector determination, a neural network (NN) was proposed for use in the paper. The normal vector and the volume fractions of the cells themselves can be defined on the basis of such variables as the location of the center and the radius of the circumference. Therefore, the NN is proposed to solve the inverse problem – to determine the normal vector based on known values of volume fractions. Volume fractions are inputs of NNs, while the normal vector is their output. Over a thousand variants of the surface location, orientations of the normal vector and curvatures were prepared for volume fraction calculations; their results were used for training, validating and testing the NNs.FindingsThe simplest NN with one neuron in the hidden layer shows better results than other commonly used methods, and an NN with four neurons produces results with errors below 1° relative to the orientation of the normal vector; for several cases, it proven to be more accurate by an order of magnitude.Practical implicationsThe method can be used in the CFD, LBM, CA, VoF and other discrete computational methods. The more precise normal vector allows for a more accurate determination of the points on the surface and curvature in further calculations via the surface or interface tracking method. The paper contains the data for the practical application of developed NNs. The method is limited to regular square or cuboid lattices.Originality valueThe paper presents an original implementation of NNs for normal vector calculation connected with CFD, LBM and other application for fluid flow with free surface or phase transformation.

Understanding liquid-jet atomization cascades via vortex dynamics

Temporal instabilities of a planar liquid jet are studied using direct numerical simulation (DNS) of the incompressible Navier–Stokes equations with level-set (LS) and volume-of-fluid (VoF) surface tracking methods. $\unicode[STIX]{x1D706}_{2}$ contours are used to relate the vortex dynamics to the surface dynamics at different stages of the jet breakup – namely, lobe formation, lobe perforation, ligament formation, stretching and tearing. Three distinct breakup mechanisms are identified in the primary breakup, which are well categorized on the parameter space of gas Weber number ($We_{g}$) versus liquid Reynolds number ($Re_{l}$). These mechanisms are analysed here from a vortex dynamics perspective. Vortex dynamics explains the hairpin formation, and the interaction between the hairpins and the Kelvin–Helmholtz (KH) roller explains the perforation of the lobes, which is attributed to the streamwise overlapping of two oppositely oriented hairpin vortices on top and bottom of the lobe. The formation of corrugations on the lobe front edge at high $Re_{l}$ is also related to the location and structure of the hairpins with respect to the KH vortex. The lobe perforation and corrugation formation are inhibited at low $Re_{l}$ and low $We_{g}$ due to the high surface tension and viscous forces, which damp the small-scale corrugations and resist hole formation. Streamwise vorticity generation – resulting in three-dimensional instabilities – is mainly caused by vortex stretching and baroclinic torque at high and low density ratios, respectively. Generation of streamwise vortices and their interaction with spanwise vortices produce the liquid structures seen at various flow conditions. Understanding the liquid sheet breakup and the related vortex dynamics are crucial for controlling the droplet-size distribution in primary atomization.

Modeling of Rapid Solidification with Undercooling Effect During Droplet Flattening on a Substrate in Coating Formation

The coating deposit on the substrate in thermal spray coating process develops by solidification of individual molten particle which impacts, flattens and solidifies on the surface of the substrate. Droplet flattening and solidification typically involves rapid cooling. In this paper, a model for non-equilibrium rapid solidification of a molten droplet spreading onto a substrate is presented. Transient flow during droplet impact and its subsequent spreading is considered using the volume of fluid surface tracking method which was fully coupled with the rapid solidification model. The rapid solidification model includes undercooling, nucleation, interface tracking, non-equilibrium solidification kinetics and combined heat transfer and fluid flow as required to treat a non-stagnant splat formed from droplet flattening. The model is validated with the literature results on stagnant splats. Subsequently, using the model the characteristics of the rapidly solidifying interface for non-stagnant splat, such as interface velocity and interface temperature, are described and the effect of undercooling and interfacial heat transfer coefficient are highlighted. In contrast to the stagnant splat, the non-stagnant splat considered in this study displays interesting features in the rapidly solidifying interface. These are attributed to droplet thinning and droplet recoiling that occur during the droplet spreading process.

Intrinsic 3D Dynamic Surface Tracking based on Dynamic Ricci Flow and Teichmüller Map.

3D dynamic surface tracking is an important research problem and plays a vital role in many computer vision and medical imaging applications. However, it is still challenging to efficiently register surface sequences which has large deformations and strong noise. In this paper, we propose a novel automatic method for non-rigid 3D dynamic surface tracking with surface Ricci flow and Teichmüller map methods. According to quasi-conformal Teichmüller theory, the Techmüller map minimizes the maximal dilation so that our method is able to automatically register surfaces with large deformations. Besides, the adoption of Delaunay triangulation and quadrilateral meshes makes our method applicable to low quality meshes. In our work, the 3D dynamic surfaces are acquired by a high speed 3D scanner. We first identified sparse surface features using machine learning methods in the texture space. Then we assign landmark features with different curvature settings and the Riemannian metric of the surface is computed by the dynamic Ricci flow method, such that all the curvatures are concentrated on the feature points and the surface is flat everywhere else. The registration among frames is computed by the Teichmüller mappings, which aligns the feature points with least angle distortions. We apply our new method to multiple sequences of 3D facial surfaces with large expression deformations and compare them with two other state-of-the-art tracking methods. The effectiveness of our method is demonstrated by the clearly improved accuracy and efficiency.

Study on the Viscoelastic Fluid Behavior in Hollow Fiber Membrane Fabrication Process Using Giesekus’ Model

In the present study, attempts are made to study the behavior of a viscoelastic fluid in hollow fiber membrane production process. For this purpose, the fluid is considered to obey the Giesekus’ model and flow is taken as steady, two-dimensional and isothermal flow. The flow field is obtained using DEVSS/SUPG scheme combined with a free surface tracking method. The obtained results are compared to the case of Newtonian fluid. It is shown that the extrudate swell is 20% more in the case of viscoelastic fluid. Moreover, the elastic behavior of the viscoelastic fluid significantly affects the velocity field in the extrudate outside the die. It causes the fluid flow to become reversed in the middle part of the extrudate as the direct result of the stress relaxation process, whereas such a behavior is not seen for Newtonian fluid. Also, the first normal stress difference (FNSD) distribution in the extrudate is obtained and its variation is discussed. Furthermore, the effect of operational parameters including die back pressure and take-up velocity are investigated. Finally, the predicted extrudate swell for various operation conditions is compared to experimental results showing a good agreement between experimental and simulated data.

An overlapping domain decomposition based near-far field coupling method for wave structure interaction simulations

This paper presents a newly developed Overlapping Domain Decomposition (ODD) method, which forms the basis of a near-far field coupling solver for a wide range of wave-structure interaction problems. In this method, the computational domain is decomposed into near and far fields which are then modeled separately by solving the viscous Navier-Stokes equations (NSE) and the Potential Laplacian equation (PLE) respectively. A Finite volume method (FVM) is adopted to discretize both the NS and PL equations. The free surface problem is solved in both domains but using totally different strategies. In the potential domain, a moving mesh free surface tracking method is adopted where arbitrary polyhedral mesh adapts to the time-varying shape of the interface using vertex-based automatic mesh motion solver. Meanwhile, at the free surface, the boundary conditions are formulated using an ordinary differential equation (ODE) derived from the Bernoulli's equation. In the viscous domain, however, the volume of fluid (VOF) method is used to predict the location of free surface. The novelty of the reported method lies in two-folds. First, the introduction of the so called overlapped buffer zone eliminates the need of performing time costing iterative schemes in the non-overlapping domain decomposition methods to ensure the matching of free surface elevation at the domain boundaries. The concept of a buffer zone is borrowed from the relaxation zone technique which is commonly used near the inlet to ensure a stable wave generation or near the outlet to absorb the reflected waves in numerical wave simulations. Second, an in-house developed OVERSET method is adopted for the viscous domain solver to handle large object displacement in the case of an extreme event. The proposed method has been implemented in the OpenFOAM platform (foam-extend-3.1). To validate the method, the propagation of a solitary wave is first simulated and the resulting wave parameters are compared with the corresponding analytical, as well as pure VOF solution. Meanwhile, a comparison of the CPU time between the single domain approach and the current method has been provided. Next, the measured wave impact loading for a single body which is partially submerged will be used to further test the method. Last but not least, the method is applied to simulate the spilling wave breaking near the beach. Various numerical examples presented in the paper demonstrate the accuracy and efficiency of the proposed method. Towards the end, computation of a sinking semi-submersible platform will be presented to demonstrate further the capability of the method.

Substrate Melting and Re-solidification During Impact of High-Melting Point Droplet Material

In this paper, impact, spreading, and solidification of molten droplet on a dissimilar substrate along with substrate melting and its re-solidification are investigated numerically. Volume of fluid surface tracking method coupled with the solidification model within a one-domain continuum formulation is used to model the transient flow during the droplet impact, its subsequent spreading, and solidification. Evolution of melting front in the substrate is modeled by solving the governing equations for solidification in the substrate, too. Simulations are performed for the impact of a heated droplet on a substrate. The model predicts substrate melting, which can give better insight of bonding between the coating material and substrate, where droplet and substrate are of different materials. It is observed that melting in the substrate in the present case starts soon after the impact of the heated droplet. The depth and the width of the melting front in the substrate increase with the time and after reaching a maximum they start to decrease because of start of re-solidification from the melted edge. In the central part of the splat droplet solidifies, while the substrate remains melted which can enhance the coating strength and its bonding with the substrate.

Fast grid-free surface tracking

We present a novel explicit surface tracking method. Its main advantage over existing approaches is the fact that it is both completely grid-free and fast which makes it ideal for the use in large unbounded domains. A further advantage is that its running time is less sensitive to temporal variations of the input mesh than existing approaches. In terms of performance, the method provides a good trade-off point between speed and quality. The main idea behind our approach to handle topological changes is to delete all overlapping triangles and to fill or join the resulting holes in a robust and efficient way while guaranteeing that the output mesh is both manifold and without boundary. We demonstrate the flexibility, speed and quality of our method in various applications such as Eulerian and Lagrangian liquid simulations and the simulation of solids under large plastic deformations.