Single-phase Level Set Method Research Articles

A partitioned functional-decomposition scheme for modelling wave-ship-sloshing interaction

A novel partitioned function decomposition method is proposed and validated for accurately and effectively solving the interaction between waves and ships with sloshing effect. This scheme employs a hybrid functional-decomposition method that utilizes both potential and viscous flows to accurately and efficiently solve the wave-ship interaction in the external domain, while employing the original viscous method for simulating sloshing in the internal domain. To further enhance computational efficiency, a single-phase Level-set method is employed. Firstly, the issue of non-conservation in the level-set model is addressed through the application of a mass correction method. Additionally, based on the principle of mass conservation, modifications are made to the boundary conditions for free surface motion. As a result, an improved single-phase Level-set method is developed, which combines jump condition correction and mass correction. Through simulations involving linear and nonlinear free surfaces, impulsive pressures, overall forces on the tank, as well as comparisons with experimental data, it is observed that the proposed Level-set method effectively solves the sloshing in the internal domain, a problem for which the traditional single-phase Level-set method often fails to tackle with. Subsequently, by adopting a multi-block grid technique to mark tank and non-tank grid blocks and integrating the improved single-phase Level-set method with the SWENSE model, a partitioned function decomposition method is established to handle ship motions with sloshing effect in waves. It is found that simultaneously solving the internal and external flow problems using traditional implicit and explicit motion-solving methods poses certain challenges. Therefore, an implicit-inner-iteration solution method is proposed. By combining the proposed motion-solving method with the partitioned function decomposition model, satisfactory results are achieved for the wave-ship-sloshing interaction.

Simulation of large-scale additive manufacturing process with a single-phase level set method: a process parameters study

In this work, a numerical method is presented in order to simulate the deposition of molten polymer bead onto a substrate and its cooling down in the large-scale extrusion-based additive manufacturing process. The polymer flow is treated as a single-phase flow with a free surface. This method reduces the computation time without loss of accuracy as polymer behavior significantly dominates air behavior. The governing equations of the fluid motion are solved with the finite element method on moving mesh, whereas the free surface is captured based on the level set method on another fixed mesh. Since the free surface is captured “implicitly” by the zero level of the level set function, coalescence between filaments is well defined and naturally performed. Numerical algorithm and implementation method are described in detail. This model provides detailed information on the cooling process and the bonding formation during the molten polymer deposition process. The effects of control parameters (nozzle velocity, flow rate and extrusion temperature, etc.) on the final deformed shapes of the printed parts are investigated. And finally, the numerical result from 2D simulations is compared to optical micro-graphs of the longitudinal cross-section of the printed sample, which shows good agreement between numerical and experimental results.

Analysis of landslides employing a space–time single-phase level-set method

Landslide dynamics are characterized by a phase transition from a solid like behavior to a fluid one. Since the material is moving through space special discretization techniques are required. Four-dimensional space–time finite elements for fluid–structure interactions are applied together with the single-phase level-set method to investigate the dynamics of 3D landslides interacting with flexible walls. The wall is modeled as a geometric nonlinear solid with elastic–viscoplastic material behavior, whereas the liquefied soil is described with the Navier–Stokes equations for incompressible Bingham fluids. Between fluid and solid advanced coupling conditions are taken into account incorporating friction. In order to solve the governing equations of the multi-field problem, the weighted-residuals method is applied, which is discretized by time-discontinuous space–time elements. Within the monolithic solution procedure for the coupled problem, the kinematics of both solid and fluid are described using velocities as primary variables. A pseudo-structure adapts the coordinates of the fluid mesh to the deformations of adjacent structures. The single-phase level-set method describes the motion of the free surface of the sliding material. To accurately transport the free surface a pde-based extrapolation is used for the velocities. Various effects in 3D landslide dynamics are investigated.

Accurate prediction of complex free surface flow around a high speed craft using a single-phase level set method

This paper focuses on the analysis of a challenging free surface flow problem involving a surface vessel moving at high speeds, or planing. The investigation is performed using a general purpose high Reynolds free surface solver developed at CNR-INSEAN. The methodology is based on a second order finite volume discretization of the unsteady Reynolds-averaged Navier–Stokes equations (Di Mascio et al. in A second order Godunov—type scheme for naval hydrodynamics, Kluwer Academic/Plenum Publishers, Dordrecht, pp 253–261, 2001; Proceedings of 16th international offshore and polar engineering conference, San Francisco, CA, USA, 2006; J Mar Sci Technol 14:19–29, 2009); air/water interface dynamics is accurately modeled by a non standard level set approach (Di Mascio et al. in Comput Fluids 36(5):868–886, 2007a), known as the single-phase level set method. In this algorithm the governing equations are solved only in the water phase, whereas the numerical domain in the air phase is used for a suitable extension of the fluid dynamic variables. The level set function is used to track the free surface evolution; dynamic boundary conditions are enforced directly on the interface. This approach allows to accurately predict the evolution of the free surface even in the presence of violent breaking waves phenomena, maintaining the interface sharp, without any need to smear out the fluid properties across the two phases. This paper is aimed at the prediction of the complex free-surface flow field generated by a deep-V planing boat at medium and high Froude numbers (from 0.6 up to 1.2). In the present work, the planing hull is treated as a two-degree-of-freedom rigid object. Flow field is characterized by the presence of thin water sheets, several energetic breaking waves and plungings. The computational results include convergence of the trim angle, sinkage and resistance under grid refinement; high-quality experimental data are used for the purposes of validation, allowing to compare the hydrodynamic forces and the attitudes assumed at different velocities. A very good agreement between numerical and experimental results demonstrates the reliability of the single-phase level set approach for the predictions of high Froude numbers flows.

Near-field flow of submarines and ships advancing in a stable stratified fluid

A methodology is presented to predict density stratified flows in the near-field of naval vessels. The approach uses a single-phase level set method for the free surface, a dynamic overset technique to handle motions and controllers for self-propulsion and maneuvering. The density is solved with a higher-order transport equation coupled with momentum and mass conservation. Turbulence is implemented with a k−ε/k−ω based Delayed Detached Eddy Simulation (DDES) approach modified to add density gradients. Evaluation tests were performed for a two-dimensional square cavity, including grid and time step studies, and the stratified flow past a sphere, showing good agreement with available data. The stratified flow was studied for a self-propelled ship and a submarine. Density, velocity, pressure and turbulent quantities at the exit plane of the near-field contain a description of the relevant scales of the flow and can be used to compute the far-field stratified flow. It is shown that, as is the case of surface waves, the generation of internal waves requires energy that results in an increase in resistance. Moreover, the presence of a density interface against the hull results in a thickening of the boundary layer, just as in a solid/free surface juncture flow.

A mechanistic model of bubble entrainment in turbulent free surface flows

A framework for the development of models of bubble entrainment in free surface turbulent flows is presented. The framework uses mechanistic processes to model the stages involved in the entrainment of bubbles due to interaction of turbulence with a free surface. Entrainment is modeled as a chain of events for a bubble that is formed at the free surface, then pulled into the fluid against buoyancy, and interacts with vortices that break it up into smaller bubbles, or with other bubbles by coalescence. The main entrainment mechanism is modeled as a vortex/free surface interaction process that can entrain bubbles if the vortices located a given distance from the surface are strong enough. This approach overcomes limitations of approaches where the entrainment is determined only by turbulence parameters, which in the case of objects interacting with a free surface entrain bubbles on the boundary layers irrespective of the distance to the free surface. Depending on the computational fluid dynamics approach used to solve the flow, these processes may need different levels of modeling; more resolved approaches like large-eddy simulation with a volume of fluid method of the free surface will require less modeling complexity than a less resolved RANS method, since some of the involved processes of entrainment are directly accounted for. In this paper a standard RANS approach is used with the free surface modeled using a single-phase level set method, and models are presented for each of the relevant processes to produce a complete mechanistic model of turbulent bubble entrainment. The model was calibrated and tested for two relevant problems: a 2D+T breaking wave in model scale, and the full scale bubbly flows around the US Navy Research Vessel Athena. For the second case a grid study is carried out to analyze grid convergence performance of the model. Comparisons with experimental data show that the model predicts well location and magnitude of entrainment.

Transient filling modelling at meso-level for RTM process using a single phase LSM

A single phase level set method for capturing the propagating front within textile unit-cells is presented. The computational domain is embedded within an artificial Cartesian grid in order to avoid the difficulties associated with the meshing step. The flow is modelled by using the Stokes/Brinkman equations. Hence, the necessity of describing the yarn boundaries is avoided. The propagating front is represented by using a level set formulation where the extra step of reinitialization is avoided. The flow equations are solved only in the filled part of the domain. The velocity in the unfilled part is obtained through a harmonic continuation. Numerical tests on simple configurations in 2D and 3D space are presented in order to demonstrate the proposed method.

Numerical investigation of the components of calm-water resistance of a surface-effect ship

The elements of the calm-water resistance of an surface-effect ship are studied with two different numerical methods. A potential-flow-based method that satisfies linearized free-surface boundary conditions is used to predict the wave resistance of the sidehulls and air cushion. A RANS-based program that employs a single-phase level set method is used to simulate the flow around an SES of a nonlinear viscous fluid. Detailed comparison of the dynamic wetted surface, the free-surface elevation, and the wave, cushion, and frictional drag is made for a geometry that has experimental resistance data. It is shown that the linear free-surface boundary conditions of an inviscid fluid are accurate for prediction of wave drag. Disagreement is present between the two methods for the free-surface elevation behind the vessel, which might possibly be due to the transom-stern model that is used in the potential-flow method. The small difference between the numerically predicted resistance and the experimental measurement is attributed to the error in the seal and air drag models that are used in this study.

비정상 RANS 법과 중첩격자계를 이용한 횡파중 선박운동 수치해석

The present paper presents the CFD result for a beam wave test case. An ONR tumblehome ship model with bilge keels is used. The beam wave test is for zero forward speed and roll and heave 2DOF with wave slope <TEX>$a_k=0.156$</TEX> and wavelength <TEX>${\lambda}=1.12L_{PP}$</TEX>, with <TEX>$L_{PP}$</TEX> the ship length. The problems is solved numerically with an unsteady Reynolds averaged Navier-Stokes approach. The free surface flow is computed using a single-phase level-set method and the motions in each time step are integrated using a predictor-corrector iteration approach which uses dynamic overset grids moving with relative ship motion. The predicted CFD results for motions and forces are compared with experimental data, showing a reasonable agreement.

Ship motions using single-phase level set with dynamic overset grids

The problem of surface ships free to pitch and heave in regular head waves is analyzed numerically with an unsteady Reynolds averaged Navier Stokes (URANS) approach. The unsteady single-phase level set method previously developed by the authors was extended to include six degrees of freedom (6DOF) motions. The method uses rigid overset grids that move with relative motion during the computation, and the interpolation coefficients between the grids are recomputed dynamically every time the grids move. The motions in each time step are integrated implicitly using a predictor–corrector approach. An earth-based reference system is used for the solution of the fluid flow, while a ship-based reference system is used to compute the rigid-body equations of motion. Predicted results for sinkage and trim and resistance at two Froude numbers (medium, Fr = 0.28 and large, Fr = 0.41) were compared against experimental data, showing good agreement. Pitch and heave motions were computed for near-resonant cases at Fr = 0.28 and 0.41, with regular linear head waves with slope ak = 0.025 and wavelength λ = 1.5 L, with L the ship length. The predicted motions compare favorably with existing experimental data. A solution for a large amplitude head wave case ( ak = 0.075) was also obtained, in which the transom wave breaks and extreme motions are observed. The medium Froude number case was subject to a verification and validation analysis. A problem with two ships pitching and heaving one behind the other is demonstrated.

Unsteady free-surface wave-induced separation: analysis of turbulent structures using detached eddy simulation and single-phase level set

Turbulent structures of the unsteady free-surface wave-induced separation around a surface-piercing NACA0024 are studied using a detached-eddy simulation with a single-phase level set method. Quantitative verification and validation show good agreement with experimental data. Instantaneous and mean flows show an owl-type separation with the same instability frequencies identified by unsteady Reynolds-averaged Navier–Stokes. Anisotropy invariant maps show that turbulence is anisotropic in the middle of the separation region and is at a two-component state near the foil surface. The turbulent kinetic energy and its budget have similarities to that of a separated turbulent boundary layer near the toe and a backward-facing step flow in the recirculation region, but with large three-dimensional and free-surface effects. The free-surface damps velocity and pressure fluctuations and moves the peaks of turbulence quantities from the high-speed to the low-speed side of the free shear layer.

RANS simulation of a container ship using a single-phase level-set method with overset grids and the prognosis for extension to a self-propulsion simulator

Steady flow simulations for the Korean Research Institute for Ships and Ocean Engineering (KRISO) container ship (KCS) were performed for towing and self-propulsion. The main focus in the present article is on the evaluation of computational fluid dynamics (CFD) as a tool for hull form design along with application of state-of-the-art technology in the flow simulations. Two Reynolds-averaged Navier-Stokes (RANS) equation solvers were employed, namely CFDShip-Iowa version 4 and Flowpack version 2004e, for the towing and self-propulsion cases, respectively. The new features of CFDShip-Iowa version 4 include a single-phase level-set method to model the free surface and an overset gridding capability to increase resolution in the flow and wave fields. The new features of Flowpack version 2004e are related to a self-propulsion scheme in which the RANS solver is coupled with a propeller performance program based on the infinitely bladed propeller theory. The present work is based on a close interaction between IIHR-Hydroscience and Engineering of the University of Iowa and Osaka Prefecture University. In the following article, overviews are given of the present numerical methods and results are presented and discussed for the KCS in towing and self-propulsion modes, including comparison with available experimental fluid dynamics (EFD) data. Additional evaluation is provided through discussion of the recent CFD Workshop Tokyo 2005, where both methods appeared to yield very promising results.

On the application of the single-phase level set method to naval hydrodynamic flows

The application of the single-phase level set approach to the numerical simulations of three-dimensional free surface flows around complex geometries, at both non-breaking and breaking regimes is presented. In this approach only the liquid phase is simulated and the level set function is used as tracking device to locate the free surface position. The extrapolation of the solution in the dummy points in the gaseous phase is such that second-order accuracy is maintained also in the points adjacent to the free surface; the time evolution of the level set function and the re-initialization step have been merged so to get a function which is a distance function everywhere, and satisfies, at the same time, the kinematic condition on the free surface. The implementation of this technique into a general purpose Reynolds averaged Navier–Stokes (RANS) equations solver developed at INSEAN [Di Mascio A, Broglia R, Favini B. A Second Order Godunov-type Scheme for Naval Hydrodynamics. Kluwer Academic/Plenum Publishers; 2001, p. 253–61], is described in details; capabilities of the algorithm in dealing with non-breaking and breaking flows in the naval hydrodynamic context will be demonstrated by using a submerged hydrofoil and two different ship hulls in straight course as test cases. Comparisons with both experimental data and numerical surface fitting computations are presented; convergence properties of the algorithm, as well as validation and verification assessment will be also discussed.

URANS simulations for a high-speed transom stern ship with breaking waves

An exploratory study of high-speed surface ship flows is performed to identify modelling and numerical issues, to test the predictive capability of an unsteady RANS method for such flows, to explain flow features observed experimentally, and to document results obtained in conjunction with the 2005 ONR Wave Breaking Workshop. Simulations are performed for a high-speed transom stern ship (R/V Athena I) at three speeds Froude number (Fr) = 0.25, 0.43 and 0.62 with the URANS code CFDSHIP-IOWA, which utilizes a single-phase level set method for free surface modelling. The two largest Fr are considered to be high-speed cases and exhibit strong breaking plunging bow waves. Structured overset grids are used for local refinement of the unsteady transom flow at medium speed and for small scale breaking bow and transom waves at high-speeds. All simulations are performed in a time accurate manner and an examination of time histories of resistance and free surface contours is used to assess the degree to which the solutions reach a steady state. The medium speed simulation shows a classical steady Kelvin wave pattern without breaking and a wetted naturally unsteady transom flow with shedding of vortices from the transom corner. At higher speeds, the solutions reach an essentially steady state and display intense bow wave breaking with repeated reconnection of the plunging breaker with the free surface, resulting in multiple free surface scars. The high-speed simulations also show a dry transom and an inboard breaking wave, followed by outboard breaking waves downstream. In comparison to an earlier dataset, resistance is well predicted over the three speeds. The free surface predictions are compared with recent measurements at the two lowest speeds and show good agreement for both non-breaking and breaking waves.

Unsteady RANS simulation of the ship forward speed diffraction problem

The forward speed diffraction problem for a surface ship is analyzed numerically, using a RANS approach with a single-phase level set method to compute the free surface and a blended k– ε/ k– ω model for the turbulent viscosity. Simulations were run for a DTMB 5512 model under head incident waves at two speeds and two wavelengths with the same wave amplitude ( a = 0.006 L, with L the ship length). The medium speed case ( Fr = 0.28) with long wavelength incident waves ( λ = 1.5 L) behaves linearly and has been extensively compared against available experimental data for resistance and heave forces and pitching moment, unsteady free surface elevations, and unsteady velocity fields at the nominal wake plane ( x/ L = 0.935). Quantitative verification and validation was performed for this case by running three grids and three time steps with refinement ratio of 2 and the flow field analyzed in detail. The behavior of the boundary layer is analyzed to explain the origin of large first harmonic amplitudes on the axial velocity observed both experimentally and numerically. The high speed case ( Fr = 0.41) with short wavelength incident waves ( λ = 0.5 L) exhibits non-linear behavior on the forces and moment with a strong second harmonic component and an unsteady breaking bow wave. The second harmonic has been reproduced by the CFD computations and the breaking wave predicted. Analysis of the flow indicates that the breaking wave could be responsible for the non-linear behavior on the forces and moment.