Study on Model Tests and Hydrodynamic Force Models for Free Spanning Submarine Pipelines Subjected to Earthquakes

A test rig is built to model the dynamic response of submarine pipelines with an underwater shaking table in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. Model tests are carried out to consider the effects of exciting wave directions and types. Based on the experimental results, two hydrodynamic force models derived from Morisen equation and Wake model are presented respectively. By use of hydrodynamic force models suitable for free spanning submarine pipelines under earthquakes, diseretized equations of motion are obtained and finite element models are established to analyze dynamic response of free spanning submarine pipeline subjected to multi-support seismic excitations. The comparison of numerical results with experimental results shows that the improved Morison and Wake hydrodynamic force models could satisfactorily predict dynamic response on the free spanning submarine pipelines subjected to earthquakes.

Hydrodynamic Forces and Instability of Submarine Pipelines Under Waves and Currents:A Review

Stability design of submarine pipelines is a very important procedure in submarine pipeline engineering design. The calculation of hydrodynamic forces caused by waves and currents acting on marine pipelines is an essential step in pipeline design for stability. The hydrodynamic forces-induced instabilities of submarine pipelines should be regarded as a wave/ current-pipeline-seabed interaction problem. This paper presents a review on hydrodynamic forces and stability research of submarine pipelines under waves and currents. The representative progress including the improved design method and guideline has been made for the marine pipelines engineering design through experimental investigations, numerical simu- lations and analytical models. Finally, further studies on this issue are suggested.

Modeling of fluid-induced vibrations and identification of hydrodynamic forces on flow control valves

Dynamics and vibration of control valves under flow-induced vibration are analyzed. Hydrodynamic load characteristics and structural response under flow-induced vibration are mainly influenced by inertia, damping, elastic, geometric characteristics and hydraulic parameters. The purpose of this work is to investigate the dynamic behavior of control valves in the response to self-excited fluid flow. An analytical and numerical method is developed to simulate the dynamic and vibrational behavior of sliding dam valves, in response to flow excitation. In order to demonstrate the effectiveness of proposed model, the simulation results are validated with experimental ones. Finally, to achieve the optimal valve geometry, numerical results for various shapes of valves are compared. Rounded valve with the least amount of flow turbulence obtains lower fluctuations and vibration amplitude compared with the flat and steep valves. Simulation results demonstrate that with the optimal design requirements of valves, vibration amplitude can be reduced by an average to 30%.

Hydrodynamic Forces on Smooth Inclined Cyh'nders in Oscillatory Flow

-The hydrodynamic forces on a smooth inclined circular cylinder exposed to oscillating flow were experimentally investigated at Reynolds number (Re) in the range 40000-200000 and Keulegan-Capenter number (KC) in the interval from 5-40. In the test, Re number and KC number were varied systematically. The inertia force coefficient (Cu) and the drag force coefficient (CD) in Morison equation were determined from the measured loads and the water particle kinematics. In this analysis a modified form of Morison equation was used since it uses the normal velocity and acceleration. Thus, the applicability of the Cross Flow Principle was assumed. This principle, simply stated, is as follows: the force acting in the direction normal to the axis of a cylinder placed at some oblique angle with the direction of flow is expressed in terms of the normal component of flow only, and the axial component is disregarded. Both the total in-line force coefficient (CF) and transverse force (lift) coefficient (Cf) were analyzed in terms of their maximum and root mean square values. All the in-line and lift force coefficients were given as a functions of Re and KC number. F'rom this research, it can be seen that the Cross-Flow Principle does not always work well. It seems valid for the total in- line force at high Re and large KC numbers. The Cu for a = 45 is larger and the CD for a = 45 is smaller than that for a = 90 ?and Re> 80000. The hydrodynamic force coefficients CD and Cu for the inclined cylinder are only the functions of the oblique angle (a) and KC number, but not of the Re number.

Computation of the Viscous Hydrodynamic Forces on a KVLCC2 Model Moving Obliquely in Shallow Water

The viscous hydrodynamic force and moment on ships moving obliquely in shallow water are important for ship navigation safety.In the paper,the viscous flow field around a KVLCC2 model moving obliquely in shallow water is simulated and the hydrodynamic drag,lateral force and yaw moment acting on the hull are obtained by a general purpose computational fluid dynamics(CFD) package FLUENT with shear-stress transport(SST) k—ωturbulence model.The numerical computation is performed at different drift angels and water depths.The numerical results are compared with experimental results,and a good agreement is demonstrated.

EFFECTS OF WATER-DEPTH ON HYDRODYNAMIC FORCE OF ARTIFICIAL REEF

The effects of water-depth on the hydrodynamic force of the artificial reef were studied by simulating regular and irregular waves. The computational results show that the water-depth has a substantial effect on hydrodynamic force. The hydrodynamic force increases with the decrease of water-depth in shallow. Especially, in the ultra-shallow water these loads increase very evidently with the decrease of water-depth. The long-term values of hydrodynamic force increase with the decrease of the ratio of water-depth to reef height, and are about 10% larger than those of deep water when the ratio of water-depth to reef height is 4.0. However water-depth hardly affects the long term values of hydrodynamic force when the ratio of water-depth to reef height is larger than 6.0.

HYDRODYNAMIC FORCES FOR OVERTOPPING SPILLWAYS

Expressions are derived for calculating hydrodynamic forces from the unit dis- charge,channel slope,and flow and velocity profiles on an overflow spillway.A sample prob- lem is included to illustrate the use of the ideas presented and magnitudes of hydrodynamic forces for a 50-foot-high embankment dam.

RESEARCH ON HYDRODYNAMIC FORCES OF CAVITATING GRID FINS

Hydrodynamic forces and flow pattern of four kinds of cavitating grid fins with cavitation number from 2.5 to 0.25 were simulated numerically with a bubble two-phase flow model embodied in the commercial CFD code Fluent 6.0. Comparison with experimental datum showed that rules of hydrodynamic forces changing with cavitation number were coordinated with experiment, and cavitation made the ratio of lift to resistance decrease. Calculated axial force and chordal pressure center in all-wetted condition or those at cavitation number less than 0.75 agreed well with experiments. Normal force in all-wetted condition was less by 20 per cent. The differences between computation and experiment in the total range of cavitation number were mainly because that the incipient cavitation number in computation was less than that at experiment.

CALCULATION OF VISCOUS HYDRODYNAMIC FORCES ON A SHIP HULL IN OBLIQUE MOTION

This paper focuses on computations of viscous hydrodynamic forces acting on aship in oblique motion by solving the three-dimensional Reynolds-Averaged Navier-Stokes (RANS)equations. The standard k-ε turbulence model with wall function was applied. The conservationequations were discretized by a cell-centered second-order Finite Volume Method (FVM) in ablock-structured body-fitted grid and the coupling of velocity and pressure was resolved with theSIMPLE method. Computations were performed for a Wigley hull model to investigate the viscous flowsaround it. The results show good agreement with experimental data and more reasonable prediction ofhydrodynamic forces and moments than other numerical results available.

COMPUTATION OF SHIP MANOEUVRING RELATED VISCOUS FLOW AND HYDRODYNAMIC FORCES

An efficient multi block incompressible viscous flow solver based on solving the Reynolds Averaged Navier Stokes (RANS) equations numerically has been developed that can be applied to simulation of a variety of ship maneuvering related flows and calculation of hydrodynamic forces. Validation and verification of the solution procedure were carried out on several model problems with good agreement to experimental and numerical results.

A fast mapping method to evaluate immersed boundary hydrodynamic forces

Immersed boundary method is a crucial method to deal with particle suspension flow.Particle shapes involved in such flow are usually simple geometry,such as sphere and ellipsoid,which can be conveniently represented by the triangular surface grid.When the number of particles and resolution of the surface grid increase,calculating the hydrodynamic force on the particle surface through integration can be time-consuming.Hence,the present paper establishes a fast mapping method to evaluate immersed boundary hydrodynamic force.Firstly,the particle surface grid is generated by an initial triangular element grid.Subsequently,the initial surface grid is refined by bisection refinement to the desired resolution.The final step is to find the triangular element index on the particle triangular surface grid,which contains the projective point.Test cases show that the present mapping algorithm has good accuracy and efficiency for calculating hydrodynamic forces of particles.

The prediction of external flow field and hydrodynamic force with limited data using deep neural network

Predicting the external flow field with limited data or limited measurements has attracted long-time interests of researchers in many industrial applications.Physics informed neural network(PINN)provides a seamless framework for combining the measured data with the deep neural network,making the neural network capable of executing certain physical constraints.Unlike the data-driven model to learn the end-to-end mapping between the sensor data and high-dimensional flow field,PINN need no prior high-dimensional field as the training dataset and can construct the mapping from sensor data to high dimensional flow field directly.However,the extrapolation of the flow field in the temporal direction is limited due to the lack of training data.Therefore,we apply the long short-term memory(LSTM)network and physics-informed neural network(PINN)to predict the flow field and hydrodynamic force in the future temporal domain with limited data measured in the spatial domain.The physical constraints(conservation laws of fluid flow,e.g.,Navier-Stokes equations)are embedded into the loss function to enforce the trained neural network to capture some latent physical relation between the output fluid parameters and input tempo-spatial parameters.The sparsely measured points in this work are obtained from computational fluid dynamics(CFD)solver based on the local radial basis function(RBF)method.Different numbers of spatial measured points(4–35)downstream the cylinder are trained with/without the prior knowledge of Reynolds number to validate the availability and accuracy of the proposed approach.More practical applications of flow field prediction can compute the drag and lift force along with the cylinder,while different geometry shapes are taken into account.By comparing the flow field reconstruction and force prediction with CFD results,the proposed approach produces a comparable level of accuracy while significantly fewer data in the spatial domain is needed.The numerical results demonstrate that the proposed approach with a specific deep neural network configuration is of great potential for emerging cases where the measured data are often limited.

HYDRODYNAMIC FORCE ON SMOOTH HORIZONTAL CYLINDER IN UNIFORM OSCILLATORY FLOW

The hydrodynamic forces on a smooth horizontal circular cylinder exposed to oscillating flow have been experimentally investigated at Reynolds numbers (Re) in the range 20, 000 - 260, 000 (subcritical and transcritical regimes) and Keulegan- Carpenter numbers (Kc) in the interval from 5 to 40. In the tests, the Re number and Kc number were varied inertia systematically. The drag force coefficnent CD and inertia force coefficient CM in Morison equation have been determined through the use of Least Square Method. Both total in-line force coefficient CF and transverse force (lift) coefficient CL have been analysed in terms of their maximum and root mean square values. All the in-line and lift force coefficinets were given as a function of Re and Kc number, and also their deviations with the average value have been shown. The principal results are as follows: for the Re ≥80, 000, all the hydrodynamic force coefficients, including CD, CM, CP and CL,are at best very weak functions of Reynolds number, and each of them tends towards a certain constant with increasing Kc number; for the Re< 80, 000, the drag force coefficient CD decreases with increasing Re number, and inertia force coefficient CM increases with increasing Re number.The tendencies of drag and inertia coefficients versus Kc number for the Re ≥10￣5 are very similar to the others, which are very close to the Rodenbusch and Cutierrez's (1983) but are somewhat larger than the Sarpkaya's (1976 and 1986) and Bearman et al.' s(1985).

Influence of temperature and salinity on hydrodynamic forces

The purpose of this study is to introduce an innovative approach to offshore engineering so as to take variations in sea temperature and salinity into account in the calculation of hydrodynamic forces.With this in mind,a thorough critical analysis of the influence of sea temperature and salinity on hydrodynamic forces on piles like those used nowadays in offshore wind farms will be carried out.This influence on hydrodynamic forces occurs through a change in water density and viscosity due to temperature and salinity variation.Therefore,the aim here is to observe whether models currently used to estimate wave forces on piles are valid for different ranges of sea temperature and salinity apart from observing the limit when diffraction or nonlinear effects arise combining both effects with the magnitude of the pile diameter.Hence,specific software has been developed to simulate equations in fluid mechanics taking into account nonlinear and diffraction effects.This software enables wave produced forces on a cylinder supported on the sea bed to be calculated.The study includes observations on the calculation model’s sensitivity as to a variation in the cylinder’s diameter,on the one hand and,on the other,as to temperature and salinity variation.This software will enable an iterative calculation to be made for finding out the shape the pressure wave caused when a wave passes over will have for different pile diameters and water with different temperature and salinity.

Numerical simulation and experimental study of the hydrodynamics of a modeled reef located within a current

The hydrodynamic forces and flow field of artificial reef models in steady flow were numerically investigated using the RNG κ-ε turbulent model. The numerical simulation results are consistent with results observed by experimental means. A comparative study indicates that the corresponding errors of forces between calculated values and values observed in the experiment vary in the range of2.3%-11.2% and that the corresponding errors of velocities vary in the range of 1.3%-15.8%. The flow field numerical results show that upstream and vortices exist when the current passes over and through the surface of the reef model. This study suggests that the numerical simulation method can be applied to predict the forces and flow field associated with artificial reefs.

Particle image velocimetry and numerical simulations of the hydrodynamic characteristics of an artificial reef

This article reports a particle image velocimetry study and the comparative results of a numerical simulation into the hydrodynamic characteristics around an artificial reef.We reveal the process of flow separation and vortex evolution,and compare the force terms generated by our artificial reef model.The numerical simulation agrees well with experimental results,showing the applicability of computational fluid dynamics to the hydrodynamics of an artificial reef.Furthermore,we numerically simulate the hydrodynamics of the reef model for seven velocities.The results show that the drag coefficient is approximately 1.21 in a self-modeling region for Reynolds numbers between 2.123×104and 9×104.Therefore,the upwelling height and current width of the flow field do not change significantly when the inflow velocity increases.Our study indicates that computational fluid dynamics can be applied to study the hydrodynamics of an artificial reef and offer clues to its construction.

Characteristics from a hydrodynamic model of a trapezoidal artificial reef

Flume experiments and numerical simulation were conducted to characterize the hydrodynamics of a trapezoid artificial reef.Measurements in particle image velocimetry were conducted to observe the formation of upwelling and vortices;and forces for the reef model were measured by load cell.The results of flume experiments agree well with the numerical data.In addition,the flow structure around a reef combining trapezoidal and cubic blocks was simulated numerically under two deployment schemes,showing a more complicated flow structure than that of a stand-alone reef.Relationship between drag coefficient and Reynolds number suggest that the degree of turbulence can be assessed from the value of drag coefficient downstream from the reef.The role of the reef in water flow is to reduce flow velocity and generate turbulence.

Numerical Investigation of Submarine Hydrodynamics and Flow Field in Steady Turn

This paper presents numerical simulations of viscous flow past a submarine model in steady turn by solving the Reynolds-Averaged Navier-Stokes Equations（RANSE） for incompressible, steady flows. The rotating coordinate system was adopted to deal with the rotation problem. The Coriolis force and centrifugal force due to the computation in a bodyfixed rotating frame of reference were treated explicitly and added to momentum equations as source terms. Furthermore, velocities of entrances were coded to give the correct magnitude and direction needed. Two turbulence closure models（TCMs）, the RNG k-ε model with wall functions and curvature correction and the Shear Stress Transport（SST） k-ω model without the use of wall functions, but with curvature correction and low-Re correction were introduced, respectively. Take DARPA SUBOFF model as the test case, a series of drift angle varying between 0° and 16° at a Reynolds number of 6.53×10^6 undergoing rotating arm test simulations were conducted. The computed forces and moment as a function of drift angle during the steady turn are mostly in close agreement with available experimental data. Though the difference between the pressure coefficients around the hull form was observed, they always show the same trend. It was demonstrated that using sufficiently fine grids and advanced turbulence models will lead to accurate prediction of the flow field as well as the forces and moments on the hull.

Numerical Method for Wave Forces Acting on Partially Perforated Caisson

The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid–structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier–Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.

孔隙率对矩形沟槽上垂直多孔屏障的波浪散射效应影响

The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.