Evolution Of Free Surface Research Articles

Numerical investigation on the slamming loads of a truncated trimaran hull entering regular waves

For ship slamming, waves can disturb the water entry progress and thus affect the slamming load characteristics. This paper studied the slamming loads of a trimaran entering regular waves based on the CFD method. The results of a trimaran model impacting calm water and wedge impacting waves are used to verify the present method. The free surface evolution and load characteristics of the trimaran model considering wave effects are discussed. The results showed that the position at which the structure touches the wave surface depends on the formation, deformation and escape of bubble flows, which cause obvious asymmetrical flow. The enclosure of the air cavity induces a step increase in pressure, and the pressure peak appears when the bubble fully escapes. Three typical positions, wave crest, wave cross and wave through, are chosen to explore the influence of waves on slamming loads. The impact load shows a 98% difference at different wave locations. In ship load forecasting, the position of the waves relative to the hull is noteworthy. The influence of the water entry velocity on the slamming load is further discussed. Bubble retention related to the water entry velocity is the key factor affecting the peak load.

Stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances

An analysis is presented for the stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances under the action of gravity and surface tension. Using momentum-integral method, the nonlinear free surface evolution equation is derived by introducing the self-similar semiparabolic velocity profiles along the flow (x- and y-axis) directions. A normal mode technique and the method of multiple scales are used to obtain the theoretical (linear and nonlinear stability) results of this flow problem, which conceive the physical parameters: Reynolds number Re, Weber number We, angle of inclination of the plane θ and the angle of propagation of the interfacial disturbances ϕ. The temporal growth rate ωi+ and second Landau constant J2, based on which various (explosive, supercritical, unconditional, subcritical) stability zones of this flow problem are categorized, contain the shape factors B and β owing to the non-zero steady basic flow along the y-axis direction. A novel result which emerges from the linear stability analysis is that for any given value of Re, We and θ, any stability that arises in two-dimensional disturbances (ϕ = 0) must also be present in three-dimensional disturbances. For ϕ = 0, there exists a second explosive unstable zone (instead of unconditional stable zone) after a certain value of Re (or θ) due to the involvement of B and β in the expression of J2. This explosive unstable zone vanishes after a certain value of ϕ depending upon the values of Re, We and θ, which confirms the stabilizing influence of ϕ on the thin film flow dynamics irrespective of the values of Re, We and θ.

Numerical study on the motion characteristics of free fall lifeboats entering calm water and rough sea

As ocean engineering operations extend into deeper seas, the working environment becomes increasingly complex, making free fall lifeboats (FFLBs) more vital for maritime disaster rescues. Unlike traditional davit-launched lifeboats, FFLBs are propelled into the water at a specific velocity and angle, engaging in a complex motion process of launch, impact, submersion, and resurfacing. Therefore, to assess the safety of FFLBs, this paper regarding the lifeboat as a rigid body aims to investigate the six-degree-of-freedom motion characteristics of lifeboat entering the water with different entry angles θ and wave environment, with a specific focus on analyzing the primary causes of capsizing. The numerical simulations of water entry with various θ, wave heights H, and relative entry positions are carried out by combining large eddy simulation and overset mesh technology. The free surface is captured by the volume of fluid method, and the attitude change, acceleration change, motion trajectory, and free surface evolution law of lifeboats are analyzed. The findings suggest that lifeboats can enter calm water safely at θ of 20°–50° and maintain a stable posture. Moreover, in extreme conditions where θ is either 0° or 90°, there is a high risk of entry failure due to excessive vertical acceleration and poor motion attitude, respectively. Furthermore, when facing waves, lifeboats experience reduced horizontal displacement when entering at peak and downward zero point compared to calm water conditions, which poses challenges for avoiding potential dangers.

Characterization on the impact load of a local corner region of a liquid tank entering water

This study conducts a detailed examination of the characteristics of impact loads in complex triangular areas within liquid tanks via the volume of fluids (VOF) method, with a general understanding of impact loads. By comparing the numerical results with previous experimental data of oblique wedge impacts on water surfaces, the effectiveness of the VOF method was confirmed. Complex dynamic phenomena such as fluid climbing, jet impact, and air cavity effects in corner areas were analyzed through 3D flow characteristics. By examining two types of impacts (a structure impacting fluid and a fluid impacting structure), the equivalence between them is verified. An in-depth exploration of the load characteristics in different areas is conducted by combining the free surface evolution. The multipeak characteristics of the load and synchronicity of the peak loads at different parts are closely related to the phenomenon of the climbing fluid being obstructed. Bubble flow also plays a crucial role in affecting the load characteristics. Further exploration of the effects of structural motion on load characteristics reveals complex load variability. These findings provide a valuable reference for understanding the impact loads in complex corner areas of liquid tanks.

Multiphysics Simulation of Battery Electrode Drying

Scaling Li-ion battery production to meet the demands of increasingly electrified grids and transportation systems will require higher throughput at all levels of the battery cell production process. One of the more energy intensive battery manufacturing steps is the necessary drying of solvents which persist in the electrodes after the initial slurry coating of their current collectors. It is critical to both optimize this drying process to minimize the time and resources required, as well as to understand the effect that the drying has on the electrode microstructure. As it is both expensive and time-intensive to iteratively test different temperatures on multiple initial electrode microstructures, it is necessary to have reliable, high-fidelity simulations which can model the evaporation process. Furthermore, it is easier to control microstructural features such as porosity, and particle size in a simulated environment, Indeed, by simulating evaporation, the design-of-experiments space can be minimized, and process conditions can be established to accelerate the production of high quality, lower cost electrodes. To that end, we develop a multiphysics model of solvent evaporation using Sandia’s in-house finite element software. By coupling the solvent equations of motion to species conservation equations for the carbon binder material and energy flux driven by evaporative cooling, we demonstrate good agreement between simulation and simple evaporation experiments. This model tackles several difficult aspects of evaporation, namely the evolution of free surfaces and gas-liquid phase-changes. We additionally extend our model to account for mesoscale features (i.e. particle size, porosity, binder distribution) and determine how different temperature profiles and microstructures affect the heating requirements for the electrode. These extensions present a key advantage over conventional 1D models, as these features can have a significant effect on the evaporation process and the final distribution of conductive additive and binder. We leverage this advantage to examine how several design parameters such as porosity, particle size distribution, and heating rate affect the resulting electrode structure and binder distribution. These results demonstrate a pathway to optimizing the electrode drying process and promise to inform the development of improved multiphysics models in the future.SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Study on the free surface evolution and slamming pressure of curved-wedge water entry using a Riemann-smoothed particle hydrodynamics method

The present study aims to provide a deep understanding of curved wedge water entry. It involves a numerical simulation investigation into the kinematic and dynamic properties of water entry for two curved wedges with deadrise angles of 25° and 35°. The meshless Riemann-smoothed particle hydrodynamics (SPH) model embedded with an acoustic damper is developed to simulate these violent water entries. The validation of the Riemann-SPH accuracy is confirmed through comparison with experimental data, and subsequently, we make a systematical simulation study on curved wedge water entry, including a comparative study of free surface evolution and pressure distribution at different curvatures and drop heights. Furthermore, the kinematics analysis of velocity and displacement of curved wedges and time domain characteristics of slamming pressure loads on both sides of the wedge are investigated. It is revealed that the pressure distribution is symmetrical, with high-pressure regions forming near the bottom of the wedge and gradually propagating outward. The free surface profiles are symmetrical, with deeper depressions formed by sharper wedges. The entry depth and velocity are correlated with the initial theoretical entry velocity, and the rate of speed decline varies with the curvature of the wedge. The slamming pressure loads exhibit distinct time-domain patterns, with lower pressure loads by sharper wedges.

Numerical simulation of free-surface evolution in laser polishing of 100 Cr6 bearing steel

Abstract This research focuses on the laser surface polishing process of 100 Cr6, employing a moving Gaussian heat source. It establishes a two-dimensional transient model for laser polishing, taking into account the integrated effects of fluid flow and temperature fields, as well as the combined influence of capillary and thermocapillary forces. The model was used to perform numerical simulations to study the evolution of surface morphology during the laser polishing process. The investigation specifically examines how laser power and scanning speed influence the quality of the polishing outcome. The results demonstrate that an optimal surface roughness of approximately 0.571 μm is attained at a laser power setting of 200 W and a scanning speed of 300 mm/s.

Dynamics of a thin film of viscoelastic fluid flowing down an inclined or vertical plane

The stability characteristics of a thin film of viscoelastic (Walters’ B′ model) fluid flowing down an inclined or vertical plane are analyzed under the combined influence of gravity and surface tension. A nonlinear free surface evolution equation is obtained by using the momentum-integral method. Normal mode technique and multiple scales method are used to obtain the results of linear and nonlinear stability analysis of this problem. The linear stability analysis gives the critical condition and critical wave number kc which include the viscoelastic parameter Γ, angle of inclination of the plane θ, Reynolds number Re and Weber number We. The weakly nonlinear stability analysis that is based on the second Landau constant J2, reveals the condition for the existence of explosive unstable and supercritical stable zone along with the other two (unconditional stable and subcritical unstable) flow zones of this problem which is 3(1+3Γ)Re−3cotθ−4ReWek2 = 0. It is found that all the four distinct flow zones of this problem exist in Re-k-, θ-k- and Γ-k-plane after the critical value of Rec,θc and Γc, respectively. A novel result of this analysis is that the film flow is stable (unstable) for a negative (positive) value of Γ irrespective of the values of Re and θ, as for example, a solution of polyisobutylene in cetane, compared with the viscous (Γ=0) film flow case. Finally, we scrutinize the effect of Γ on the threshold amplitude and nonlinear wave speed by depicting some numerical examples in supercritical stable as well as subcritical unstable zone of this problem.

Different scenarios in sloshing flows near the critical filling depth

In the present paper, the sloshing flow in a cuboid tank forced to oscillate horizontally is investigated with both experimental and numerical approaches. The filling depth chosen is $h/L=0.35$ (with h the water depth and L the tank height), which is close to the critical depth. According to Tadjbakhsh & Keller (J. Fluid Mech., vol. 8, issue 3, 1960, pp. 442–451), as the depth passes through this critical value the response of the resonant sloshing dynamics changes from ‘hard spring’ to ‘soft spring’. The experimental tank has a thickness of $0.1L$ , reducing three-dimensional effects. High-resolution digital camera and capacitance wave probes are used for time recording of the surface elevation. By varying the oscillation period and the amplitude of the motion imposed on the tank, different scenarios are identified in terms of free-surface evolution. Periodic and quasi-periodic regimes are found in most of the frequencies analysed but, among these, sub-harmonic regimes are also identified. Chaotic energetic regimes are found with motions of greater amplitude. Typical tools of dynamical systems, such as Fourier spectra and phase maps, are used for the regime identification, while the Hilbert–Huang transform is used for further insight into doubling-frequency and tripling-period bifurcations. For the numerical investigation, an advanced and well-established smoothed particle hydrodynamics method is used to aid the understanding of the physical phenomena involved and to extend the range of frequencies investigated experimentally.

Simulation of viscoelastic free-surface flows with the Particle Finite Element Method

Viscoelastic fluids are central in numerous applications from polymer manufacturing to the pharmaceutical industry and biological research. However, since analytical solutions are generally not available or too complex, it is common practice to study free-surface viscoelastic flows through numerical simulation techniques. This work proposes the use of the so-called particle finite element method (PFEM), a Lagrangian approach combining standard FEM techniques with a remeshing strategy. The PFEM is able to efficiently handle mesh distortion and to accurately track the free-surface evolution. Therefore, it is exploited in this work to deal with large displacements problems in the context of nonlinear viscoelasticity. An implementation of the Oldroyd-B constitutive model in the PFEM framework is here presented including details regarding how to deal with the transfer of the internal variables during remeshing events. Additionally, an innovative approach to impose unilateral Dirichlet boundary conditions ensuring optimal mass conservation is presented. The implementation is verified with two free-surface highly viscous benchmark flows: the impacting drop and the jet buckling problems. The results show perfect agreement with those obtained with other numerical techniques. The proposed framework opens the way for using PFEM in various applications, ranging from polymer extrusion to more sophisticated scenarios involving viscoelastic and viscoelasto-plastic constitutive laws.

An immersed boundary method coupled non-hydrostatic model for free surface flow

An efficient numerical model has been developed for the study of three-dimensional free surface flow, which combines a non-hydrostatic model with the immersed boundary method (IBM). The model utilizes the transformed σ coordinate in the vertical direction, which has been found to be highly effective in accurately capturing the free surface and uneven bottom. In addition, IBM is implemented by introducing a virtual boundary force into the momentum equations to emulate the natural boundary conditions. This implementation enhances the ability of the model in simulating the interactions of wave and solid structures. A robust boundary recognition method is used to identify the location of IB cells neighboring the virtual boundary. Furthermore, a water elevation correction method has been proposed to handle the integral discontinuity in the vertical direction caused by the submerged solid bodies. By adding the virtual boundary forces to the IB cells, the no-slip velocity condition at the solid boundary is effectively enforced. To validate the performance of the model, the numerical results have been compared with experimental data. The benchmark tests focused on the free surface evolution, velocity distributions and the dynamic pressures verified the performance of the numerical model and the robust strategy of the IBM.

An adaptive harmonic polynomial cell method for three-dimensional fully nonlinear wave-structure interaction with immersed boundaries

To accurately simulate wave-structure interaction based on fully nonlinear potential flow theory, a three-dimensional (3 D) high-order immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method is proposed. Both the free surface and body surface are immersed in background octree cells that are adaptively refined near the boundaries of interest, thereby dramatically reducing computational costs without loss of accuracy. We also propose an easy-to-implement IB strategy to deal with possible instabilities in the time-domain solution arising from the intersection of Dirichlet–Neumann boundaries. For a linearized problem of wave-wall interaction, a matrix-based stability analysis is performed, providing mathematical support for the robustness of the proposed IB strategy. In contrast to the two-dimensional HPC method, compressed cells are found to offer superior stability compared to stretched cells in the vertical direction, while equal mesh aspect ratio in the horizontal plane is superior. Cubic octree cells are, however, still preferred in practice. The free surface is primarily described by a set of massless background wave markers; however, to address the challenges of IB methods in tracking the free surface evolution near the structure, additional body-fitted wave markers are introduced close to the waterline. The information exchange between these two sets of wave markers is realized by radial basis function (RBF) interpolation. While standard RBF schemes have grid-size-dependent filtering performance, we propose a normalized RBF scheme, which is then optimized in terms of the number of neighboring nodes, a smoothing coefficient and the basis functions. Excellent accuracy properties of the proposed 3 D IB-AHPC method are demonstrated by studying fully nonlinear wave propagation. The method is further applied to study relevant fully nonlinear wave-structure interaction problems, including sloshing in 3 D rectangular tanks and wave diffraction of a bottom-mounted cylinder in regular waves. Satisfactory agreement is demonstrated with existing experimental and numerical results, suggesting that the proposed 3 D IB-AHPC method is a promising potential-flow method in marine hydrodynamics.

An efficient local moving thermal-fluid framework for accelerating heat and mass transfer simulation during welding and additive manufacturing processes

Numerical prediction of melt pool morphology and temperature distribution of thermomechanical processes (welding, additive manufacturing) plays an important role in understanding the relationships between process parameters and the quality of manufactured parts. The heat conduction models are limited in their predictability because the transport phenomena relevant to the melt pool dynamic are ignored. In contrast, the multiphysics model allows consideration of the heat transfer, free surface evolution, and transport phenomena in the melt pool, leading to more accurate predictions. However, the computational cost of multiphysics models makes them impractical for part-scale simulations. In this paper, a local moving thermal-fluid framework based on the finite element method is presented, which allows solving the thermal-fluid problem only in the small moving zone containing the melt pool and the heat transfer problem in the rest part. Therefore, this new proposed moving thermal-fluid (MTF) framework is predictive as well as the full thermal-fluid model, while it is much more efficient than a full thermal-fluid model since there are much fewer degrees of freedom (DOF) to solve. Finally, numerical validation tests in welding and additive manufacturing simulations highlight its computational efficiency and high-fidelity, and a relative error of less than 2.6% was observed in predicting melting pool dimensions compared to full thermal-fluid model. In the part-scale simulation of laser welding benchmark, the MTF model takes only 62 h in place of about three weeks required by a full thermal-fluid model.

Numerical investigation of vehicle wading based on an entirely particle-based three-dimensional SPH model

Vehicle wading problems have received increasing attention from the automotive community in recent years because of the prosperous developments of electric vehicles, for which the performance of water tightness can be more important than conventional fuel vehicles. This paper presents an attempt to simulate vehicle wading problems based on an entirely meshless framework by using Smoothed Particle Hydrodynamics (SPH). First of all, an easy-to-implement but effective strategy is proposed to prevent the penetration between fluid particles and a wall boundary modeled by a set of solid particles when the distribution quality of the solid particles is poor. Subsequently, a comparative study is conducted to assess the feasibility and applicability of the SPH and Finite Volume (FV) methods in solving vehicle wading problems. Furthermore, the wading dynamics of a vehicle passing a puddle under different combinations of wading speeds and accumulating water depths is also investigated and discussed in detail by using the SPH method. It is suggested that the SPH method can be regarded as a potential candidate for solving vehicle wading problems, especially for those situations where the free-surface evolution during the wading process is particularly concerning.

Fully Nonlinear Evolution of Free-Surface Waves with Constant Vorticity under Horizontal Electric Fields

This work presents the results of a direct numerical simulation of the nonlinear free surface evolution of a finite-depth fluid with a linear shear flow under the action of horizontal electric fields. The method of time-dependent conformal transformation for the description of the combined effects of the electric fields and constant vorticity is generalized for the first time. The simulation results show that strong shear flow co-directed in the wave propagation direction leads to the formation of large-amplitude surface waves, and, for some limiting vorticity value, a wave breaking process with the formation of an air bubble in the liquid is possible. The oppositely directed shear flow can cause the retrograde motion of a surface wave (wave propagation in the opposite direction to the linear wave speed). The simulations conducted taking into account the electro-hydrodynamic effects demonstrate that a high enough external horizontal electric field suppresses these strongly nonlinear processes, and the surface waves tend to preserve their shape.

Numerical Simulation of Three-Dimensional Free Surface Flows Using the K-BKZ-PSM Integral Constitutive Equation.

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically the K-BKZ-PSM (Kaye-Bernstein, Kearsley, Zapas-Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation and the marker particle method (known as marker-and-cell) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.

Study of atypical particle flow and free surface evolution behaviour in stirred tanks

Stirred tanks are ideal vessels for material mixing reactions in the chemical sector. However, insufficient data on the complex contact collisions occurring inside these vessels hinder their appropriate design and utilization. This study employs a coupled discrete element method and volume of fluid method (DEM-VOF) to examine the evolutionary behaviour of atypical particle flow and free surface in stirred tanks. DEM is utilized to trace particle motion and interactions, while VOF is used to capture the phase interface between the gas and liquid phases. Simulations are conducted on three commonly used particle shapes-oblate ellipsoid, sphere, and prolate ellipsoid-varying their aspect ratios under the same volume of particles. The key results of the suspension, distribution, multiphase flow, and free surface behaviours in the stirred tanks were analysed. The results show that the suspension and distribution of the three particle shapes are not substantially different, with suspension stability primarily influenced. Notably, the suspension of oblate ellipsoid particles exhibits conspicuous fluctuations. Additionally, the particle shape influences the magnitude of turbulent kinetic energy in the paddle area, with oblate particles exhibiting the largest values and prolate ellipsoids the smallest values. The findings provide guidelines for designing and operating stirred tanks under optimal conditions.

Flow instabilities of second-grade fluid over a stretching sheet

The work at hand studies thin-film flow instabilities in a non-Newtonian second-grade fluid moving over a stretching sheet. The analysis considers the free surface evolution equation of the thin second-grade viscoelastic fluid model based on the long-wave approximation method. We undertook a linear stability analysis using a normal mode approach and obtained expressions for the linear time growth rate, linear phase speed, and critical wavenumber, which illustrates the linear stability structure of the flow system. Furthermore, the multi-scale analysis of the fluid’s weakly non-linear stability characteristics reveals the presence of subcritical instability in the linear stability zone. The study shows that the varying flow parameters affect the threshold amplitude, which influences the stable and unstable zones in the subcritical region. The outcomes show a stabilizing effect spanning the range of non-dimensional parameters, such as the second-grade parameter ranging from 0 to 100 in values, the surface tension parameter ranging from 0 to 100 in values, and the modified Froude number from 0 to 100 in values.

A new approach to aircraft ditching analysis by coupling free surface lattice Boltzmann and immersed boundary method incorporating surface tension effects

This study primarily addresses the phenomenon of aircraft ditching. This phenomenon presentspresenting a significant challenge for numerical simulations due to its highly nonlinear and multiphase-coupled water entry impact problem involving fluid-structure interaction. Traditional numerical methods have difficulties and deficiencies in free surface evolution and accuracy. An improved iterative velocity correction scheme has been presented by coupling the single-phase free surface-lattice Boltzmann method (FS-LBM) based on the volume of fluid method with the immersed boundary (IB) method to simulate water entry impact issues. Notably, this model incorporates the effect of surface tension, enhancing its ability to accurately simulate various phenomena, such as rolling, breaking, splashing, and fusion with the free surface in gas-liquid-solid multi-physical field conditions. Through the correction of the boundary force of the interface lattice and the gas lattice and the improved scheme, the non-slip boundary is satisfied, and the particle penetration is prevented. Furthermore, several benchmark tests have been conducted to verify the rationality and feasibility of the FS-LBM-IB method in simulating aircraft ditching. A scaled model of an aircraft has been developed to investigate the dynamic response characteristics of aircraft ditching at a specific attitude angle, with the simulation results confirming the accuracy of the FS-LBM-IB method in predicting the secondary head-up of the aircraft under suction force. This research highlights the efficiency of the FS-LBM-IB method as a novel approach for simulating aircraft ditching behavior.

Shear imposed falling liquid films on a slippery substrate with Marangoni effects: Effect of odd viscosity

We investigate the behavior of a thin fluid with disrupted time-reversal symmetry on a uniformly heated inclined surface under external shear stress using modified Navier–Stokes equations, an energy conservation equation, and incorporating a Navier slip condition. Critical conditions for instability onset are determined by a linear stability analysis within the Orr–Sommerfeld framework. We derive a first-order Benney-type evolution equation to study long-wave instabilities. We find slippery substrate, imposed shear stress along the flow direction, and Marangoni number consistently destabilize the flow, while odd viscosity and imposed counter-flow shear stabilize it. A weakly nonlinear analysis using multiple scales reveal distinct zones of instability. Marangoni number, slip length, odd viscosity, and imposed shear direction significantly impact stability and instability regions. Numerical simulations of the free surface evolution equation of a flow system under consideration provide clear evidence of the contributions of thermocapillary, slip length, odd viscosity, and imposed shear direction. Furthermore, our analysis of linear and weakly nonlinear stability, as well as our numerical simulations, exhibit remarkable consistency.