Investigation of the Interaction Between the Free Surface and A Semi/Shallowly Submerged Underwater Vehicle

The present study aims to investigate the interaction between the free surface and a semi/shallowly submerged underwater vehicle,especially when the submergence depth h is smaller than 0.75D(D:submarine maximum diameter).In this respect,the straight-ahead simulations of the generic SUBOFF underwater vehicle geometry are conducted with constant forward velocities using the Unsteady Reynolds-Averaged Navier-Stokes(URANS)equations with a Shear-Stress Transport(SST)k-ωturbulence model in commercial code Fluent,at submergence depths and Froude numbers ranging from h=0 to h=3.3D and from Fn=0.205 to Fn=0.512,respectively.The numerical models are verified against the existing experimental data.The analysis of the obtained results indicates that in the case of the semi and shallowly submerged underwater vehicle(UV),both the submergence depth and forward velocity have a great effect on the behaviors of hydrodynamic forces acting on the UV.The magnitude of maximum total resistance may reach almost five times the value of resistance exerted on the totally submerged hull.Both the forces acting on the UV and the generated waves when the submergence depth h is smaller than 0.75D are significantly different from those whenr h is larger than 0.75D.The conclusions can be used as reference for future research on near free surface motions of underwater vehicles and the design of small water-plane area twin hull.

Numerical study of three-dimensional free surface dynamics

The dynamic problem of three-dimensional free surface is numerically studied in this paper. The ALE （Arbitrary Lagrange-Euler） kinematic description is introduced into the control equation system. The ALE description method is used to track free surface. Accurate formulations for calculating the normal vector on the free surface are presented. The discrete numerical equations by finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by a differential geometry method derived in the present paper. The effect of contact angle is incorporated in the numerical algorithm. Furthermore, the numerical computations are performed and the comparison between computational and analytical results validated the effectiveness of the method. The results of this paper provide a fundamental understandings of the dynamics of liquid free surfaces, in which the surface tension and contact angle boundary conditions are taken into account. Finally, numerical simulation of largescale amplitude sloshing of liquid in a cylindrical container is performed and a numerical analysis of the effect of an annular ring-shaped rigid damping baffle on liquid sloshing oscillations in a cylindrical tank is also carried out.

A CIP-Based Numerical Simulation of Free Surface Flow Related to Freak Waves

An enhanced numerical model for simulating two-dimensional incompressible viscous flow with distorted free surface is reported. The numerical simulation is carried out through the CIP （Constrained Interpolation Profile）-based method, which is described in the paper. A more accurate interface capturing scheme, the VOF/WLIC scheme （VOF：Volume-of-Fluid;WLIC：weighed line interface calculation）, is adopted as the interface capturing method. To assess the developed algorithm and its versatility, a selection of test problems are examined, i.e. the square wave propagation, the Zalesak’s rigid body rotation, dam breaking problem with and without obstacles, wave sloshing in an excited wave tank and interaction between extreme waves and a floating body. Excellent agreements are obtained when numerical results are compared with available analytical, experimental, and other numerical results. These examples demonstrate that the use of the VOF/WLIC scheme in the free surface capturing makes better results and also the proposed CIP-based model is capable of predicting the freak wave-related phenomena.

Numerical and experimental investigation of rock breaking method under free surface by TBM disc cutter

To study the rock breaking method under the free surface induced by disc cutter,the rock breaking simulations were first conducted based on the discrete element method,and the dynamic process of rock breaking under the free surface was studied including stressed zone,crush zone,crack initiation and propagation.Then the crack propagation conditions,specific energy,etc.under different free surface distance(S)were also investigated combined with linear cutting experiments.The results show that the rock breaking process under the free surface induced by disc cutter is dominated by tension failure mode.There exists a critical S to promote crack propagation to free surface effectively.And this rock breaking method can improve the rock breaking force and breaking efficiency significantly when proper.

Numerical Simulation of Sloshing with Large Deforming Free Surface by MPS-LES Method

Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.

Three-dimensional numerical simulation of crown spike due to coupling effect between bubbles and free surface

The motion of gas bubbles beneath a free surface will lead to a spike of fluid on the free surface. The distance of the bubbles to the free surface is the key factor to different phenomena. When the inception distance varies in some range, crown phenomenon would happen after the impact of weak buoyancy bubbles, so this kind of spike is defined as crown spike in the present paper. Based on potential flow theory, a three-dimensional numerical model is established to simulate the motion of the free-surface spike generated by one bubble or a horizontal line of two in-phase bubbles. After the downward jet formed near the end of the collapse phase, the simulation of the free surface is performed to study the crown spike without regard to the toroidal bubble＇s effect. Calculations about the interaction between one bubble and free surface agree well with the experimental results conducted with a high-speed camera, and relative error is within 15%. Crown spike in both single- and two-bubble cases are simulated numerically. Different features and laws of the motion of crown spike, depending on the bubble-boundary distances and the inter-bubble distances, have been investigated.

Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method

n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.

Vertical 2D Modeling of Free Surface Flow with Hydrodynamic Pressure Using SIMPLE Arithmetic in σ Coordinates

A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged Navier-Stokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k-ε turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a current over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.

Validation of a CIP-based tank for numerical simulation of free surface flows

A constrained interpolation profile CIP-based numerical tank is developed to simulate violent free surface flows.The numerical simulation is performed by the CIP-based Cartesian grid method,which is described in the present paper.The tangent of hyperbola for interface capturing（THINC） scheme is applied for capturing complex free surfaces.The new model is capable of simulating a flow with violently varied free surface.A series of computations are conducted to assess the developed algorithm and its versatility.These tests include the collapse of water column with and without an obstacle,sloshing in a fixed tank,the generation of regular waves in a tank,the generation of extreme waves in a tank.Excellent agreements are obtained when numerical results are compared with available analytical,experimental,and other numerical results.

Experimental Investigation of the Effect of Bow Profiles on Resistance of an Underwater Vehicle in Free Surface Motion

In this paper, towing tank experiments are conducted to study the behavior of flow on a model of the underwater vehicle with various shapes of bows, i.e. tango and standard bows in free surface motion tests. The total resistances for different Froude numbers are considered experimentally. The towing tank is equipped with a trolley that can operate in through 0.05-6 m/s speed with ±0.02 m/s accuracy. Furthermore, the study is done on hydrodynamic coefficients i.e. total, residual and friction resistance coefficients, and the results are compared. Finally, the study on flow of wave fields around bows is done and wave filed around two bows are compared. The Froude number interval is between 0.099 and 0.349. Blockage fraction for the model is fixed to 0.005 3. The results showed that the residual resistance of the standard bow in 0.19 to 0.3 Froude number is more than the tango bow in surface motion which causes more total resistance for the submarine. Finally, details of wave generated by the bow are depicted and the effects of flow pattern on resistance drag are discussed.

Interaction of a submerged horseshoe vortex with a free surface

In this paper a submerged horseshoe vortex under a free surface is discussed and the algebraic expression of the wave elevation is obtained. From this expression, some characteristics of the ship wave are described. There exists a smooth region nearθ=0°, but when the uniform stream passes the other singularities （source, sink, doublet, etc.） there is no smooth region. The mechanism of synthetic aperture radar （SAR） images of the narrow ship wakes is also explained.

Simulation of Free Surface Flows Based on MapReduce in Cloud Computing

Simulating turbulent liquids with breaking waves and splashes is among the most desired features in fluid animation. Lagrangian methods such as Smoothed Particle Hydrodynamics method (SPH) are a promising way to capture such properties. However, the Particle-based liquid surface simulation has not been applied very well since its consumption is way too large. This paper derives the governing equations in SPH approaches and parallelizes the dynamics-based surface simulation with the MapReduce program models which apply the SPH approach in Cloud Computing. Compared to the serial methods, this approach obtained a 3.11 times speedup on the experimental platform.

THE NONLINEAR INTERACTION OF VORTEX RINGS WITH A FREE SURFACE

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.

Theoretical Mechanism Analysis of 3D Free Surface Electrospinning

Electrospinning is a new type of free-end spinning built on the electric field. The electric force of polyacrylonitrile( PAN)polymer solution overcomes the surface tension of the solution,and then it causes wave and forms jet flow. In the process of injection,the solution is evaporated or solidified,eventually forming a fiber on the receiving device. Different from ordinary single needle head,in the study,a new type of 3D free surface spinneret is used to produce multiple jets at the same time, and this will greatly improve production efficiency. In the paper,the model of 3D free surface is analyzed by the theory of fluid mechanics. The relationship among the wave length,surface tension and the electric field is obtained.After the mechanical analysis on the stable period of the jet,the relationship between the jet radius and the distance from the spinneret to jet is carried out. At the same time the relationship between the jet velocity and the tensile force is carried out. After mechanics analyzing on the unstable period of the jet,it can be concluded that the radius of the jet is inversely proportional to one half power of the distance from the jet to the spinneret,and the electrostatic spinning jet's velocity is directly proportional to one half power of the tensile force. After the mechanical analysis of the unstable period of the electrospinning jet,it can be concluded that the radius of the jet is inversely proportional to one fourth power of the jet intercept point distance.

Nonlinear Model of Mean Free Surface of Waves

A nonlinear model of mean free surface of waves or wave set-up is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the Weighted-Average Flux (WAF) method (Watson el al., 1992), with Time-Operator-Splitting (TOS) used for the treatment of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modeling wave set-up. The short wave (or primary wave) energy equation is solved by use of a more traditional Lax-Wendroff technique. A nonlinear wave theory (James, 1974) is introduced. The model described in this paper is found to be satisfactory in most respects when compared with the measurements conducted by Stive (1983) except in modeling the mean free surface very close to the mean shoreline.

ON THE RESONANT GENERATION OF WEAKLY NONLINEAR STOKES WAVES IN REGIONS WITH FAST VARYING TOPOGRAPHY AND FREE SURFACE CURRENT

The effect of nonlinearity on the free surface wave resonated by an incident flow over rippled beds, which consist of fast varying topography superimposed on an otherwise slowly varying mean depth, is studied using a WKBJ-type perturbation approach. Synchronous, superharmonic and in particular subharmonic resonance were selectively excited over the fast varying topography with corresponding wavelengths. For a steady current the dynamical system is autonomous and the possible nonlinear steady states and their stability were investigated. When the current has a small oscillatory component the dynamical system becomes non-autonomous, chaos is now possible.

Isoparametric Boundary Element Method Applied to the Rectangular and Delta Hydrofoils near the Free Surface

In this paper, the hydrodynamic characteristics and flow field around rectangular and delta hydrofoils, moving with a constant speed beneath the free surface are numerically studied by means of isoparametric boundary element method （IBEM）. The quantities （source and dipole strengths） and the geometry of the dements are represented by a linear distribution. Two types of three-dimensional hydrofoils （rectangular and delta） are selected with NACA4412 and symmetric Joukowski sections. Some numerical results of pressure distribution, lift, wave-making drag coefficients and velocity field around the hydrofoils are presented. Also, the wave pattern due to moving hydrofoil is predicted at different operational conditions. Comparisons are made between computational results obtained through this method and those from the experimental measurements and other numerical results which reveal good agreement.

Analysis on MHD Stability of Free Surface Jet flow in a Gradient Magnetic Fields

The simplified modeling for analysis on MHD stability of free surface jet flow in a gradient magnetic fields is based on the theoretical and experimental results on channel liquid metal MHD flow, especially, the results of MHD flow velocity distribution in cross-section of channels (rectangular duct and circular pipe), and the expected results from the modeling are well agreed with the recent experimental data obtained. It is the first modeling which can efficiently explain the experimental results of liquid-metal free surface jet flow.

A New Efficient Finite Volume Modeling of Small Amplitude Free Surface Flows with Unstructured Grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.

Dynamics of a Rotating Sphere on Free Surface of Vibrated Granular Materials

We investigate the rotational dynamics of a low-density sphere on the free surface of a vertically vibrated granular material（VGM）. The dynamical behavior of the sphere is influenced by the external energy input from an electromagnetic shaker which is proportional to ε,where ε is equal to the ratio between the square of the dimensionless acceleration Γ and the square of the vibration frequency f of the container. Empirical results reveal that as the VGM transits from local-to-global convection,an increase in ε generally corresponds to an increase in the magnitudes of the rotational ω（RS） and translational v（CM） velocities of the sphere, an increase in the observed tilting angle θ（bed） of the VGM bed, and a decrease in the time t（wall） it takes the sphere to roll down the tilted VGM bed and hit the container wall. During unstable convection, an increase in ε results in a sharp decrease in the sphere＇s peak and mean ω（RS）,and a slight increase in t（wall）.For the range of ε values covered in this study, the sphere may execute persistent rotation, wobbling or jamming, depending on the vibration parameters and the resulting convective flow in the system.