Numerical modeling of flow and scour below a pipeline in currents: Part I. Flow simulation

The performance of the standard k–ε, Wilcox high-Reynolds-number k–ω, Wilcox low-Reynolds-number k–ω and Smagorinsky's subgrid scale (SGS) turbulence models is examined against the flow around a circular cylinder 0.37 diameter above a rigid wall. The governing equations are solved using finite difference method in a non-orthogonal boundary-fitted curvilinear coordinate system. A mesh dependence study for the four turbulence models is carried out on computational meshes with different densities. In addition, the performance of the k–ω models with either wall function or no-slip boundary condition on the cylinder surface is examined on the finest mesh. It is found that the SGS model over-predicts the shedding of vortices from the cylinder and is sensitive to the computational mesh and the model constant C_s used. The standard k–ε and the Wilcox k–ω models predict the mean velocity field quite well but generally under-predict the velocity and hydrodynamic force oscillations using wall functions on the cylinder surface. It is also found that the Wilcox k–ω models with the no-slip boundary condition on the cylinder surface give better predictions on the shedding of vortices than their counterparts using the wall function boundary condition.     

Steady streaming around a circular cylinder in an oscillatory flow

Steady streaming induced by an oscillatory flow around a circular cylinder is investigated using a numerical method. Two-dimensional Reynolds-averaged Navier-Stokes equations are solved using a finite element method with a k-ω turbulent model closure. The range of the Keulegan-Carpenter (KC) number investigated is between 2 and 40, which is substantially higher than those reported in literature related to steady streaming to date. A constant value of Stokes number (β) of 196 is chosen in this study. The steady streaming structures and velocity distribution are analysed in detail. It is found that the characteristics of steady streaming are strongly related to the vortex shedding flow regimes.     

Numerical evaluation of passive control of VIV by small control rods

Flow past a circular cylinder with multiple small control rods is studied by numerical simulation for Re_D ranging from 1161.3 to 6387.1. The Reynolds-Averaged-Navier–Stokes (RANS) equations and shear stress transport (SST) k − ω turbulence model are used to calculate the vortex field, while a fourth-order Runge–Kutta method is employed for evaluating the structure dynamics of the cylinder group. Comparisons with experimental results demonstrate the validation of this method. This study is concerned with the vortex induced vibration (VIV) suppression efficacy of small control rods placed around a main cylinder. The effects of control rod number, diameter ratio, spacing ratio and Reynolds number on the hydrodynamics and vibration responses of the main cylinder are investigated. The reduced percents of in-line and cross-flow amplitudes and the increased percents of the whole cross-sectional area of cylinders and the drag coefficient are used to give a comprehensive evaluation. Results of simulation indicate that placing small rods with appropriate number at appropriate locations can achieve good suppression effectiveness at a wide range of Reynolds number. The numerical result for the case with nine control rods, diameter ratio of 0.15 and spacing ratio of 0.6 shows the best suppression effect among the cases investigated in this study.     

Numerical simulation of flow around a circular cylinder close to a flat seabed at high Reynolds numbers using a k–ε model

High Reynolds number flows around a circular cylinder close to a flat seabed have been computed using a two-dimensional standard high Reynolds number k–ε turbulence model. The effects of gap to diameter ratio, Reynolds number and flat seabed roughness for a given boundary layer thickness of the inlet flow upstream of the cylinder have been investigated. Hydrodynamic quantities and the resulting bedload transport have been predicted, and the vortex shedding mechanisms have been investigated. Predictions of hydrodynamic quantities around a cylinder located far away from the bed (so that the effect of the bed is negligible) are in satisfactory agreement with published experimental data and numerical results obtained for the flow around an isolated cylinder. Results for lower Reynolds number flows have also been computed for comparison with the high Reynolds number flow results. Overall it appears that the present approach is suitable for design purposes at high Reynolds numbers which are present near the seabed in the real ocean.     

Investigation of drag crisis phenomenon using CFD methods

When fluid flow passes a cylinder, the drag crisis phenomenon occurs between the sub-critical and the super-critical Reynolds numbers. The focus of the present studies was on the numerical prediction of the drag crisis based on CFD methods. In this work, block structured meshes with refined grids near the cylinder surface and in the downstream were employed. Both 2D and 3D simulations were performed using various turbulence models, including the SST k − ω model, the k − ϵ model, the SST with LCTM, the DES model, and the LES model. In the convergence studies, the effects of the grid size, the time step, the first grid size and the aspect ratio (for 3D simulations) on the solutions were examined. The errors due to spatial and time discretizations were quantified according to a V&V procedure. Validation studies were carried out for various Reynolds numbers between Re = 6.31 × 10⁴ and 7.57 × 10⁵. The averaged drag force, the RMS of lift force and the Strouhal number were compared with experimental data. The studies indicated that standard 2D and 3D RANS methods were inadequate to capture the drag crisis phenomenon. The LES method however has the potential to address the problem.     

Numerical computations of resonant sloshing using the modified isoAdvector method and the buoyancy-modified turbulence closure model

Sloshing is an interfacial-flow phenomenon which brings two challenges on how to locate the position of the interface and avoid the unphysical motion of the interface. In order to locate the the position of the interface, a new geometric Volume-of-Fluid (VOF) method called isoAdvector is adopted to pursue a sharp interface. Aiming to make the isoAdvector method compatible with the dynamic mesh adopted to handle the tank motion, the motion-flux correction is introduced, and a moving-velocity correction for face-interface intersection line (FIIL) is proposed. An approximation formula is adopted to effectively reconstruct the moving-velocity field of the meshes at each cell center based on the motion fluxes on each cell face. In order to avoid the unphysical motion of the interface due to the excessive turbulence level in the transition region at the interface, the buoyancy-modified k − ω SST model is adopted. The numerical results of wave elevations and forces are compared with the experiments. The comparisons suggest that (i) the moving-velocity correction for FIIL is important to update the volume fraction; (ii) the modified isoAdvector method can capture the the position of the interface more accurately than the algebraic VOF method; (iii) the unphysical motion of the interface can be avoided by using the buoyancy-modified k − ω SST model in long-time simulations. In addition, a new post-processing approach is proposed to evaluate the interface thickness. The decrease of interface thickness improves the accuracies of wave elevations by using the modified isoAdvector method. The adoption of both the modified isoAdvector method and the buoyancy-modified k − ω SST model improves the computational accuracies of wave elevations and hydrodynamic loads in long-time simulations.     

Influences of winglets on the hydrodynamic performance of horizontal axis current turbines

A novel tidal turbine with winglet is given, and the influences of winglets on the hydrodynamic performance of horizontal axis current turbines (HACT) are investigated. The incompressible Reynolds-Averaged Navier–Stokes (RANS) Equations with the k − ω shear stress transport (SST) turbulence model are solved. Two HACTs with the winglet that bent towards the pressure side or suction side are designed as the conceptual designs. The pressure distribution and tip vortices are analyzed and compared to investigate the effect of the winglets. Based on the simulation results, the parameter study of the winglet is performed to investigate the effect of length, tip chord and cant angle on the hydrodynamic performance. Results demonstrate that the numerical simulation shows good agreement with the experimental data. The performance of HACT could be improved only when the winglet bends towards the suction side. At the optimum tip speed ratio (TSR), the best design can achieve 4.66% power increase rate compared with that of the baseline turbine. The proper length, tip chord and cant angle of the winglet could improve power at the whole conditions.     

A numerical model for onset of scour below offshore pipelines

A numerical model is developed to predict the onset of local scour below offshore pipelines in steady currents and waves. The scour is assumed to start when the pressure gradient underneath the pipeline exceeds the floatation gradient of the sediments. In this model, the water flow field above the bed is determined by solving the two-dimensional (2-D) Reynolds-averaged Navier–Stokes equations with a k-ω turbulence closure. The seepage flow below the seabed is calculated by solving the Darcy's law (Laplace's equation) with known pressure distribution along the common boundaries of the flow domains-seabed. The numerical method used for both the turbulent flow around the pipeline and Darcy's flow in the seabed is a fractional finite element method. The average pressure gradient along the buried pipe surface is employed in the evaluation of onset condition with a calibration coefficient. The numerical model is validated against experimental data available in literature. A unified onset condition for steady currents and waves is proposed. Influences of flow parameters, including water depth, embedment depth, boundary layer thickness, Reynolds number (Re) and Keuleagan–Carpenter (KC) number, on the pressure drop coefficient over the pipeline are studied systematically.     

Large-eddy simulation of the turbulent near wake behind a circular cylinder: Reynolds number effect

The purpose of the present work is <!–<query>The highlights are in an incorrect format. Hence they have been deleted. Please refer the online instructions: http://www.elsevier.com/highlights and provide 3-5 bullet points.</query>–>to study the effect of the Reynolds number on the near-wake structure and separating shear layers behind a circular cylinder. Three-dimensional unsteady large-eddy simulation is carried out and two different subgrid scale models are applied in order to evaluate the turbulent wake reasonably. The Reynolds number based on the free-stream velocity and the cylinder diameter is ranging from Re = 5500–41,300, corresponding to the full development of the shear-layer instability in the intermediate subcritical flow regime. For a complete validation of this numerical study, hydrodynamic bulk coefficients are computed and compared to experimental measurements and numerical studies in the literature. Special focus is made on the variations of both the large-scale near-wake structure and the small-scale shear-layer instability with increasing Reynolds numbers. The present numerical study clearly shows the broadband nature of the shear-layer instability as well as the dependence of the shear-layer frequency especially on the high Reynolds numbers.     

An experimental investigation of the characteristics of a cylinder interacting with waves and flow in the dominant-load regime

We describe in this paper the experimental investigations of the interaction of a bottom-pivoted vertical cylinder with water waves and flow, to determine the dominant-load-regime map by application of response step functions and response RAO. A rigid circular cylindrical mass-damper-spring oscillator system is investigated in regular waves and uniform flow to determine the response characteristics in the frequency domain. Interaction with waves dominates in the high frequency range f* = f_osc/ω_v = 0.862–1.547, with magnitude in the range of 0.1 rad. On the other hand, interaction with flow dominates at lower frequency range, f* = 0.442–0.862, with magnitude in the range of 0.01 rad. These are caused by the non-overlap peak positions of the magnitude response in waves and flow due to the change in added mass of the cylinder moving in different types of fluid loads. The frequency f* = 0.862 is the point where the dominant factors are transferred. The location of separation points determines the pressure distribution to induce the added mass changed. Separation positions determine the magnitude response, but do not determine the configuration of response RAO. That allows to enhance or reduce the magnitude response of the cylinder by taking advantage of the dominant-load-regime map in the frequency domain.     

Extending the k–ω turbulence model towards oceanic applications

Four different two-equation turbulence models for geophysical flows are compared: The k–ϵ model, two new versions of the k–ω model, and the Mellor–Yamada model. An extension of the k–ω model for buoyancy affected and rotating flows is suggested. Model performance is evaluated for a few typical oceanic flows. First, new analytical solutions of the models for the surface layer affected by breaking surface waves are discussed. The deficiencies of earlier attempts are high-lighted, and it is demonstrated why the Mellor–Yamada model and the k–ϵ model fail. It is illustrated that only one version of the k–ω model computes correct decay rates for turbulent quantities under breaking waves. Second, it is demonstrated that all models predict almost identical mixed layer depths and profiles for the turbulent kinetic energy in a classical stratified shear-entrainment experiment if the buoyancy term in the second equation is appropriately weighted. Third, the accuracy and numerical robustness of the new k–ω model in realistic oceanic situations is confirmed by comparison with the data-set of the Ocean Weather Ship ‘Papa’.     

Turbulence-induced steady streaming in an oscillating boundary layer: On the reliability of turbulence closure models

The accuracy of several closure models of the Reynolds-Averaged Navier–Stokes Equations in predicting the characteristics of an oscillating turbulent wall boundary layer is analyzed. The analysis involves four low Reynolds number k − ε models and a k − ω model and it is carried out by comparing the model results both with experimental data and with data obtained by a Direct Numerical Simulation (DNS) of the Navier–Stokes equations. The boundary layer is generated by a spatially constant time-oscillating pressure gradient given by the sum of two harmonic components characterized by angular frequencies Ω^∗ and 2Ω^∗ respectively, which generates a steady streaming because of the asymmetry of turbulence intensity during the cycle. Thus the results are relevant to the boundary layer at the bottom of nonlinear sea waves. The attention is therefore focused on the accuracy of the models in reproducing the period averaged profiles of the hydrodynamic characteristics of the steady streaming. The instantaneous quantities, such as time development of the wall shear stress, profiles of the streamwise velocity, Reynolds stresses and turbulent kinetic energy are also considered and analyzed. The results shows that a model can be judged better or worse than other models depending on the specific flow characteristic under investigation. However, an approach has been adopted which allowed to rank the models according to their accuracy in predicting the values of the hydrodynamic quantities involved in the present study.     

On a translating and transversely oscillating cylinder. Part 1—The effect of the strouhal number on the hydrodynamic forces and the near-wake structure

The problem of unsteady, laminar flow past a circular cylinder which starts translating and oscillating impulsively from rest in a viscous fluid is numerically investigated at a Reynolds number of R = 10³. The flow is incompressible and two-dimensional, and the cylinder oscillations are harmonic. The transverse oscillations are only allowed when the maximum oscillatory-to-translational velocity ratio is 0.5. The investigation is based on an implicit finite difference scheme for integrating the unsteady Navier-Stokes equations together with the mass-conservation equation in their vorticity stream function formulation. A non-inertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. Present calculations are performed within the range of sufficiently large oscillation amplitude to induce separation. The time variation of the in-line and transverse force coefficients are presented. The study also focuses on the laminar asymmetric flow structure in the near-wake region. In this flow regime, it is found that there is alternate shedding of vortices from either side of the cylinder over an oscillation cycle (as predicted experimentally); this is the classical mode of vortex shedding leading to formation of the Kármán street.     

Numerical flow and performance analysis of a water-jet axial flow pump

The purpose of the present study is to investigate the performance and three-dimensional flow fields in a water-jet pump. TASCflow is employed to simulate the rotator-stator coupling flow field. A standard k-ε turbulence model combined with standard wall functions is used. In order to investigate the effect of a rear stator on flow fields, the flows in two water-jet pumps with and without a rear stator are studied. Computational fluid dynamics (CFD)-predicted overall performances are in good agreement with the experimental results. Then the flow fields, such as the pressure distribution on the blade surfaces, and the axial and tangential velocity distribution, especially the radial loading distribution, are investigated at different flow rates. In addition, the effects of a rear stator and different spacings between the rotor and the stator on the overall performance and the flow fields of the water-jet pump are also investigated.     

Boundary layer approach in the modeling of breaking solitary wave runup

The boundary layer is very important in the relation between wave motion and bed stress, such as sediment transport. It is a known fact that bed stress behavior is highly influenced by the boundary layer beneath the waves. Specifically, the boundary layer underneath wave runup is difficult to assess and thus, it has not yet been widely discussed, although its importance is significant. In this study, the shallow water equation (SWE) prediction of wave motion is improved by being coupled with the k–ω model, as opposed to the conventional empirical method, to approximate bed stress. Subsequently, the First Order Center Scheme and Monotonic Upstream Scheme of Conservation Laws (FORCE MUSCL), which is a finite volume shock-capturing scheme, is applied to extend the SWE range for breaking wave simulation. The proposed simultaneous coupling method (SCM) assumes the depth-averaged velocity from the SWE is equivalent to free stream velocity. In turn, free stream velocity is used to calculate a pressure gradient, which is then used by the k–ω model to approximate bed stress. Finally, this approximation is applied to the momentum equation in the SWE. Two experimental cases will be used to verify the SCM by comparing runup height, surface fluctuation, bed stress, and turbulent intensity values. The SCM shows good comparison to experimental data for all before-mentioned parameters. Further analysis shows that the wave Reynolds number increases as the wave propagates and that the turbulence behavior in the boundary layer gradually changes, such as the increase of turbulent intensity.     

Experimental Study on Crescent Waves Diffracted by A Circular Cylinder

Crescent waves often observed on the sea surface are unusual wave pattern induced by the instability of Stokes wave. The paper presents the experimental results of the wave field around a circular cylinder generated by the diffraction of crescent wave in order to examine the difference of diffracted crescent waves from the commonly-used diffracted Stokes waves. The results show that with the existence of the cylinder, the crescent wave pattern can still get fully developed, and with the presence of this type of wave pattern, the symmetry breaking of the wave amplitude distribution occurs and there are extra wave components at the frequencies of 0.5ω₀, 1.5ω₀ and 2.5ω₀ (ω₀ is the frequency of Stokes waves) appearing in the wave amplitude spectrum.     

On a translating and transversely oscillating cylinder: Part 2: Effect of the velocity ratio on the hydrodynamic forces and the near-wake structure

The unsteady flow past a circular cylinder which starts translating and transversely oscillating from rest in a viscous fluid is investigated at a Reynolds numbers of R=10³ and at a Strouhal number of π/4 and for the maximum oscillatory to translational velocity ratios between 0.1 and 1.0. This study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations. The object of the study is to examine the effect of increase of velocity ratio on the near-wake structure as well as the hydrodynamic forces acting on the cylinder. For all velocity rates a periodic structure of vortex evaluation and shedding develops which is repeated exactly as time advances. Vortex dynamics close behind the body are affected by changing acceleration of the cylinder and a changeover from one mode to a different mode of vortex formation is observed with increase in velocity ratio. A comparison of the present results with the impulsively started translating case has been included to illustrate the effect of velocity ratio on drag at small values of velocity ratio.     

Numerical investigation of the scale effect of hydrodynamic performance of the hybrid CRP pod propulsion system

The scale effect of hydrodynamic performance of the hybrid CRP pod propulsion system was investigated numerically using the RANS method combined with SST k − ω turbulence model and moving mesh method. The pod resistance influence factor was introduced to represent the effect of wake field of CRP on the pod resistance. Results showed the pod resistance influence factor to be a function of the Reynolds number and revolution ratio. Representative function expression can be obtained by regression analysis using multiplication of multinomial polynomials and linear function. The standard ITTC 1978 extrapolation procedure can be utilized to predict hydrodynamic performance of forward propeller because of the slightness of the influence of the pod unit on the forward propeller. The thrust and torque coefficient influence factors of aft propeller were introduced, and they were found to represent the effect of wake field of forward propeller and blockage effect of the pod on the hydrodynamic performance of aft propeller. It shows that thrust and torque coefficient influence factors are independent of the Reynolds number and have a linear relationship with the revolution ratio. On this basis, a method of estimating the hydrodynamic performance was proposed for full scale propulsion system.     

Effect of time step size and turbulence model on the open water hydrodynamic performance prediction of contra-rotating propellers

A growing interest has been devoted to the contra-rotating propellers (CRPs) due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibration. Compared with the single-screw system, it is more difficult for the open water performance prediction because forward and aft propellers interact with each other and generate a more complicated flow field around the CRPs system. The current work focuses on the open water performance prediction of contra-rotating propellers by RANS and sliding mesh method considering the effect of computational time step size and turbulence model. The validation study has been performed on two sets of contra-rotating propellers developed by David W Taylor Naval Ship R & D center. Compared with the experimental data, it shows that RANS with sliding mesh method and SST k-ω turbulence model has a good precision in the open water performance prediction of contra-rotating propellers, and small time step size can improve the level of accuracy for CRPs with the same blade number of forward and aft propellers, while a relatively large time step size is a better choice for CRPs with different blade numbers.