Viscous Free Surface Flows Research Articles

On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators

On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators

Establishment and validation of a viscous-potential coupled and graphics processing unit accelerated numerical tank based on smoothed particle hydrodynamics and high-order spectral methods

The smoothed particle hydrodynamics (SPH) method is an entirely Lagrangian and truly meshless numerical tool that is inherently suitable for simulating violent viscous free-surface flows, whilst it usually renders considerable simulation time when solving large-scale engineering problems. The high-order spectral (HOS) method is an accurate and very efficient numerical tool for modeling a large-scale inviscid gravity wave field, whilst it is hard to tackle complex physical phenomena due to the dependence on the potential flow theory. This paper aims to propose a viscous-potential coupled and graphics processing unit accelerated numerical model for establishing a high-fidelity and high-efficiency numerical wave tank. In this coupling scheme, the SPH method is applied in the near-field where violent physical processes exist to accurately capture complex free-surface behaviors such as overturning and breaking, whilst the HOS method is applied in the far-field where the water undergoes gentle motion to efficiently generate a desired gravity wave. A dedicated SPH–HOS coupling interface is also presented to accurately transmit the flow information from the HOS side to the SPH side. Meanwhile, an SPH–HOS buffer region with several key techniques is also proposed to ensure a successful coupling between the two numerical methods. Different benchmarks demonstrate that the present SPH–HOS coupling method absorbs the respective advantages of the two numerical methods and shows great feasibility and reliability in solving hydrodynamic problems involving gravity wave generation, propagation, deformation, and its interaction with marine structures.

NUMERICAL INVESTIGATIONS ON THE FREE SURFACE FLOW AROUND WING-BODY JUNCTIONS

Starting with January 2013, all ships greater than 400 tons engaged in international voyages must comply with the Energy Efficiency Design Index (EEDI), and starting with January 2023 also with the Efficiency Existing Ship Index (EEXI), issued by the International Maritime Organization, (IMO). Knowing that, in general, a ship hull is the result of a compromise between the main dimensions imposed by the size of the locks, navigation route depth, port depth, taxes, transport capacity (deadweight, volume), ship equipment (machinery, deck installations, piping systems), hydrostatic performances and last but not least the hydrodynamic performances, from ship hydrodynamics point of view the available approaches are the optimization of the ship size and hull forms or the design of propellers adapted to the ship's wake. The main purpose is to reduce the ship resistance and increase the efficiency of the propulsion system which ultimately leads to a reduction in the power placed on board the ship. For this, there can be used the so-called flow control devices or Energy Saving Devices (ESD hereafter), as hydrofoils or nozzles, to improve the flow parameters entering the propeller disc in order to increase the efficiency of the propulsion system and decreasing the fuel consumption leading to reducing of the carbon and greenhouse gasses emissions. For ballast loading condition the ESD may intersect the free surface, the flow becoming complicated and combining nonlinear, three-dimensional and turbulent phenomena such as the boundary layer on solid surfaces, the horseshoe vortex system developed around junctions and their effects turbulence, and also wave breaking. Therefore, this paper presents the results of the numerical study on the viscous free surface flow around junctions between a hydrofoil mounted on a plate, more precisely the study of the influence of the angle between hydrofoil and plate. It was observed that from a hydrodynamic point of view the angle between hydrofoil and base plate to be less than 15 degrees in respect to the vertical direction on the hydrofoil so that horseshoe vortex to be reduced in intensity and the value of the hydrofoil drag to be minimal.

A 3D Fully Non-Hydrostatic Model for Free-Surface Flows with Complex Immersed Boundaries

A fully non-hydrostatic hydrodynamic model is developed to simulate a three-dimensional, incompressible, and viscous free-surface flow passing downstream rigid rectangular and circular cylinders. A direct numerical simulation (DNS) based on the volume of fluid (VOF) and immersed boundary (IB) method is presented for solving the Navier–Stokes equations. The numerical scheme provides accurate solutions with high efficiency using the novel computational procedure to model severe surface deformations. A staggered finite difference method with a Cartesian mesh coordinate system is used to discretize the governing equations with the complexity of the deformed free-surface flow, for which the numerical schemes include a free-surface tracking technique based on the VOF and a VOS-based IB method to simulate 3D dam-break flows passing the slender objects. Additionally, the case studies demonstrate the accuracy and flexibility of the proposed model to predict the impact forces of the surface flow against the different configurations of structures. The results reveal that the temporal variation of the impact force acted on the rectangular obstacle is dominated by the aspect ratio. The force increases with the increase in the shape parameter. The resistance caused by a thin obstacle is considerably less than the blunt shape.

CFD SIMULATION OF MOTION RESPONSES OF A TRIMARAN IN REGULAR HEAD WAVES

CFD has proved to be an effective method in solving unsteady Reynolds–Averaged Navier-Stokes (RANS) equations for analysing ships in free surface viscous flow. The research reported in this paper is intended to develop a better understanding of the parameters influencing high-speed trimaran motions responses. Variations of gridding system and time step have been investigated and reliability analysis was performed in solving the RANS equations. Different turbulence models were investigated, and the SST Menter K Omega turbulence model proved a more accurate model than Realizable K-epsilon model. In order to validate the CFD method, the results of the motions response of a high- speed trimaran are compared against a set of experimental and numerical results from a 1.6 m trimaran model tested in various head seas conditions. The results suggest that CFD offers a reliable method for predicting pitch and heave motions of trimarans in regular head waves when compared to traditional low speed strip theory methods. Unlike strip theory, the effect of breaking waves, hull shape above waterline and green seas are considered in CFD application. A wave resonance phenomenon was observed and wave deformation as a result of wave-current-wind interaction in CFD was identified as the main source of discrepancy. The results from this work form the basis for future analysis of trimaran motions in oblique seas for developing a better understanding of the parameters influencing the seakeeping response, as well as passenger comfort.

HYDRODYNAMIC HULL FORM DESIGN SPACE EXPLORATION OF LARGE MEDIUM-SPEED CATAMARANS USING FULL-SCALE CFD

Large medium-speed catamarans are a new class of vessel currently under development as fuel-efficient ferries for sustainable fast sea transportation. Appropriate data to derive design guidelines for such vessels are not available and therefore a wide range of demihull slenderness ratios were studied to investigate the design space for fuel-efficient operation. Computational fluid dynamics for viscous free-surface flow simulations were utilised to investigate resistance properties of different catamaran configurations having a similar deadweight at light displacement, but with lengths ranging from 110 m to 190 m. The simulations were conducted at full-scale Reynolds numbers (log(Re) = 8.9 – 9.6) and Froude numbers ranged from Fr = 0.25 to 0.49. Hulls of 130 m and below had high transport efficiency below 26 knots and in light loading conditions while hulls of 150 m and 170 m showed benefits for heavier displacement cases and speeds up to 35 knots. Furthermore, the study concluded that the lowest drag was achieved with demihull slenderness ratios between 11 and 13.

Developed liquid film passing a smoothed and wedge-shaped trailing edge: small-scale analysis and the ‘teapot effect’ at large Reynolds numbers

Recently, the authors considered a thin steady developed viscous free-surface flow passing the sharp trailing edge of a horizontally aligned flat plate under surface tension and the weak action of gravity, acting vertically, in the asymptotic slender-layer limit (J. Fluid Mech., vol. 850, 2018, pp. 924–953). We revisit the capillarity-driven short-scale viscous–inviscid interaction, on account of the inherent upstream influence, immediately downstream of the edge and scrutinise flow detachment on all smaller scales. We adhere to the assumption of a Froude number so large that choking at the plate edge is insignificant but envisage the variation of the relevant Weber number of$O(1)$. The main focus, tackled essentially analytically, is the continuation of the structure of the flow towards scales much smaller than the interactive ones and where it no longer can be treated as slender. As a remarkable phenomenon, this analysis predicts harmonic capillary ripples of Rayleigh type, prevalent on the free surface upstream of the trailing edge. They exhibit an increase of both the wavelength and amplitude as the characteristic Weber number decreases. Finally, the theory clarifies the actual detachment process, within a rational description of flow separation. At this stage, the wetting properties of the fluid and the microscopically wedge-shaped edge, viewed as infinitely thin on the larger scales, come into play. As this geometry typically models the exit of a spout, the predicted wetting of the wedge is related to what in the literature is referred to as the teapot effect.

An accurate FSI-SPH modeling of challenging fluid-structure interaction problems in two and three dimensions

The recently developed FSI-SPH model (Sun et al., 2019c), by combining the multi-resolution δ+-SPH scheme and a Total Lagrangian SPH method, is further extended for more complex three-dimensional (3D) Fluid Structure Interaction (FSI) problems. The FSI-SPH model is strengthened with advanced numerical techniques, in which a combination of the Particle Shifting Technique (PST) and the Tensile Instability Control (TIC) is adopted to prevent flow voids induced by the tensile instability. The Adaptive Particle Refinement (APR) is used to refine particles in the boundary layer region and coarsen particles in the far-field to increase local accuracy but reduce overall computational cost. Moreover, the δ+-SPH and Total Lagrangian SPH solvers are coupled through a Modified Sequential Staggered (MSS) algorithm which, on one hand, ensures the numerical accuracy and stability and, on the other hand, improves the efficiency when magnitudes of time steps between the two solvers differ from each other significantly. In the numerical results, challenging 2D and 3D FSI cases are simulated to test the accuracy of the proposed FSI-SPH model. A new FSI benchmark with free-surface is proposed to highlight the advantage of this FSI-SPH model in simulating free-surface viscous flows. In addition, 3D effects in the FSI dam-breaking and sloshing cases are investigated.

Comparison between Model Test and Three CFD Studies for a Benchmark Container Ship

An alternative to experiments is the use of numerical model tests, where the performances of ships can be evaluated entirely by computer simulations. In this paper, the free surface viscous flow around a bare hull model is simulated with three Computational Fluid Dynamics (CFD) software packages (FINE Marine, ANSYS CFD and SHIPFLOW) and compared to the results obtained during the experimental tests. The bare hull model studied is the Duisburg Test Case (DTC), developed at the Institute of Ship Technology, Ocean Engineering and Transport Systems (ISMT) for benchmarking and validation of the numerical methods. Hull geometry and model test results of resistance, conducted in the experimental facility at SVA Postdam, Nietzschmann, in 2010, are publicly available. A comparative analysis of the numerical approach and experimental results is performed, related to the numerical simulation of the free surface viscous flow around a typical container ship. Further, a comparative analysis between the results provided by NUMECA, ANSYS and SHIPFLOW is performed. Regarding the solution obtained, a satisfactory agreement between the towing test results and the computation results can be noticed. The minimum mean error was obtained through the SHIPFLOW case, 2.011%, which proved the best solution for the case studied.

Viscous free-surface flows past cylinders

Free-surface flows of viscous liquid down an inclined plane and past cylinders of various cross-sections are studied theoretically and experimentally. For relatively wide cylinders, a pond of nearly stationary fluid forms upstream of the cylinder, and a dry region without fluid occurs downstream of it. The flow structure in the pond region depends on the cylinder cross-section and curvature at the upstream stagnation point. The theory is used to deduce simplified asymptotic expressions of the force on the cylinders. The work is relevant to volcanic lava flow deflection by barriers.

Shallow free-surface Stokes flow around a corner.

The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle α to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of α using analytical and numerical methods. Far downslope after detachment, it is shown that the motion is accurately modelled in terms of a similarity solution. Moreover, the detachment point is well approximated by a simple expression for a broad range of opening angles. The results are corroborated through a series of laboratory experiments and the implication for the design of barriers to divert lava flows are discussed. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

CFD Simulation of Motion Response of a Trimaran in Regular Head Waves

CFD has proved to be an effective method in solving unsteady Reynolds–Averaged Navier-Stokes (RANS) equations for analysing ships in free surface viscous flow. The research reported in this paper is intended to develop a better understanding of the parameters influencing high-speed trimaran motions responses. Variations of gridding system and time step have been investigated and reliability analysis was performed in solving the RANS equations. Different turbulence models were investigated, and the SST Menter K Omega turbulence model proved a more accurate model than Realizable K-epsilon model. In order to validate the CFD method, the results of the motions response of a highspeed trimaran are compared against a set of experimental and numerical results from a 1.6 m trimaran model tested in various head seas conditions. The results suggest that CFD offers a reliable method for predicting pitch and heave motions of trimarans in regular head waves when compared to traditional low speed strip theory methods. Unlike strip theory, the effect of breaking waves, hull shape above waterline and green seas are considered in CFD application. A wave resonance phenomenon was observed and wave deformation as a result of wave-current-wind interaction in CFD was identified as the main source of discrepancy. The results from this work form the basis for future analysis of trimaran motions in oblique seas for developing a better understanding of the parameters influencing the seakeeping response, as well as passenger comfort.

Interaction of viscous free-surface flows with topography

The interaction of gravitationally driven, free-surface flows of viscous fluid with topographic features is investigated theoretically. The motion is studied in the regime where the depth of the flow is much smaller than the streamwise extent of the topography. A lubrication model of the motion is developed, integrated numerically and analysed asymptotically. For small mounds, it is shown that the flow surmounts the obstacles, but for larger mounds the flow is deflected around it and can form dry zones in its wake into which fluid does not flow, as well as forming deeper ponded regions upstream. Which of these phenomena prevails is shown to depend upon the amplitude of the mound height and the thickness of the oncoming flow relative to the streamwise length scale over which the topography varies. By using numerical and asymptotic results, we demonstrate that relatively wide mounds lead to the development of deep ponds of material upstream, which may lead to flow overtopping if the mound is not sufficiently high. These insights can be used to inform the design of barriers that defend built infrastructures from lava flows, and it is shown how this model can also provide an upper bound on the force exerted by the flow on them.

Viscous flow past a cylinder close to a free surface: Benchmarks with steady, periodic and metastable responses, solved by meshfree and mesh-based schemes

The question of whether it is possible to set relevant, robust and reliable benchmarks for viscous free-surface flows with complex free-surface dynamics is investigated in this work. The proposed method for finding an answer to this question consists of selecting three conditions leading to increasing flow complexity and to simulate them using three well established solvers based on diverse numerical techniques. In the three conditions, a submerged horizontal cylinder in an uniform current perpendicular to its axis is considered, the Reynolds number is fixed to 180, and the analysis is limited to a 2D framework. While the unbounded solution for such flow is well established, adding a free surface and setting the submergence ratio and the Froude number in certain ranges, challenging free-surface dynamics takes place. In the specific conditions selected, phenomena of increasing complexity are identified and studied with: (i) δ+-SPH, an enhanced version of the Smoothed Particle Hydrodynamics method, (ii) a single-phase Finite Volume scheme with a Level Set function for tracking the free-surface (LS-FVM), and (iii) a two-phase Finite Volume with a Volume-of-Fluid algorithm to treat the gas/liquid interface (VOF-FVM). It is shown that the test-cases, even being geometrically simple, present intricate complexities, such as alternate metastable states in the wake, linked to the strong non-linearities induced by the interactions between the wake’s vorticity and the free surface. It is also shown that the solvers considered are able to depict a consistent representation of these complex flows, useful as benchmarks for other solvers and methods. An additional research question, investigating whether the improvements of the δ+ variant of the SPH method are necessary for simulating specific aspects of the flows treated in the paper, is also posed and discussed.

Grid‐Free Modelling Based on the Finite Particle Method for Incompressible Viscous Flow Problems

In this paper, we present a grid‐free modelling based on the finite particle method for the numerical simulation of incompressible viscous flows. Numerical methods of interest are meshless Lagrangian finite point scheme by the application of the projection method for the incompressibility of the Navier–Stokes flow equations. The moving least squares method is introduced for approximating spatial derivatives in a meshless context. The pressure Poisson equation with Neumann boundary condition is solved by the finite particle method in which the fluid domain is discretized by a finite number of particles. Also, a continuous particle management has to be done to prevent particles from moving into configurations problematic for a numerical approximation. With the proposed finite particle technique, problems associated with the viscous free surface flow which contains the study on the liquid sloshing in tanks with low volumetric fluid type, solitary waves movement, and interaction with a vertical wall in numerical flume as well as the vortex patterns of the ship rolling damping are circumvented. These numerical models are investigated to validate the presented grid‐free methodology. The results have revealed the efficiency and stability of the finite particle method which could be well handled with the incompressible viscous flow problems.

A splitting method for free surface flows over partially submerged obstacles

Abstract The paper proposes a stable time-splitting method for the numerical simulation of free-surface viscous flows. The key features of the method are a semi-Lagrangian scheme for the level-set function transport improved with MacCormack predictor–corrector step with limiting strategy and an adaptive volume-correction procedure. The spatial discretization is done by a hybrid finite volume/finite difference method on dynamically adaptive hexahedral meshes. Numerical verification is done by comparing full-scale 3D numerical simulations of the sloshing tank and the coastal wave run-up with other numerical and experimental results known from the literature.

Harmonic Balance method for nonlinear and viscous free surface flows

The Harmonic Balance method applied to fully nonlinear, viscous, temporally periodic free surface flows is presented in this paper. The Harmonic Balance approach is used to project a transient periodic two phase flow into multiple coupled steady–state problems discretising the periodic time interval. The numerical framework is based on Finite Volume method for Computational Fluid Dynamics in the open–source software foamextend. The disability of the Harmonic Balance method to simulate flows with zero or close to zero mean velocity is overcome by coupling the Harmonic Balance steady–state equations implicitly, presenting a novelty in the field. Von Neumann stability analysis is performed for the governing Harmonic Balance equations to mathematically prove that zero mean velocity can be simulated using the proposed implicit coupling. The method is validated and verified on a periodic free surface flow over a ramp and regular surface wave propagation with current, both including grid convergence studies and spectral resolution sensitivity studies. All results are compared to fully transient computations. A detailed study is performed for wave propagation without current, confirming that convergence of free surface elevation can be achieved without mean velocity. The approach proved accurate and applicable for twophase flows, opening a new research field.

Numerical investigation into the interaction of resistance components for a series 60 catamaran

Numerical study of the flow around S60 catamaran and S60 monohull, as well as an investigation into interference phenomenon are performed within this paper. Numerical simulations of the free surface and double body viscous flow are carried out for six Froude numbers in the range 0.3–0.55, for four separation ratios in the range 0.226–0.4696 and for monohull. Verification and validation of the obtained results are provided. Validation is performed by comparison with available experimental data and satisfactory agreement is obtained. Firstly, catamaran interference resistance is studied through interference factor based on the total resistance of catamaran and monohull. Afterwards, the interference resistance is investigated through a procedure based on the resistance decomposition, in order to determine the viscous and wave interference effect on the total resistance of catamaran. The form factor for monohull is found to be different than the form factor for catamaran with identical demihulls. Also, form factor for catamaran is found to be in correlation with the separation. Analysing the flow around demihulls, it has been established that the strength of cross flow is correlated to interference resistance. Finally, benefits of CFD based on viscous flow as a tool in catamaran preliminary design are highlighted.

Viscous free-surface flows on rotating elliptical cylinders

Results from a 2D numerical model of liquid-film flow on a rotating elliptical cylinder reveal that large variations in substrate curvature lead to strong capillary flows. With a suitably chosen time-dependent rotation rate, more liquid can be supported relative to the constant-rotation-rate case.

Numerical simulation of submarine landslide tsunamis using particle based methods

This paper presents the simulation of tsunamis due to rigid and deformable landslides with consideration of submerged conditions by using particle methods. The smoothed particle hydrodynamics (SPH), as a particle based method, is for solving problems of fast moving boundaries in the field of continuum mechanics. Other particle based methods, like the discrete element method (DEM), are suitable for modeling the displacement and the collision related to the rigid landslides. In the present work, we use the SPH and the DEM to simulate tsunamis generated by rigid and deformable landslides with consideration of submerged conditions. The viscous free-surface flows are solved by a weakly compressible SPH and the displacement and the rotation of the rigid body slides are calculated using a multi-sphere DEM allowing for modeling solids of arbitrarily complex shapes. The fluid-solid interactions are simulated by coupling the SPH and the DEM. A rheology model combining the Papanastasiou and the Herschel-Bulkley models is applied to represent the viscoplastic behavior of the non-Newtonian flow in the submarine deformable landslide cases. Submarine landslide tsunamis due to rigid and deformable landslides are both simulated as typical landslide cases in this investigation. Our simulated results and the previous experimental results in the literatures are in good agreement, which shows that the proposed particle based methods are capable of modeling the submarine landslide tsunamis.