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In the paper a numerical approach to the four equation model of water hammer (WH) with fluid–structure interaction (FSI) is presented. An algorithm for numerical solution of that model in time domain based on the method of characteristics (MOC) is proposed. Special attention is paid to modeling of the influence of viscoelastic pipe supports. The boundary condition at the support is formulated as a differential equation of junction motion which is solved numerically concurrently with the MOC compatibility equations. Numerical simulations were done with the use of an own computer program. The tests were conducted for a model of real pipeline built in the lab and fastened with specific, complex, supporting system. The numerical results were compared to the experimental records and after some modeling and calibration quite a good agreement was achieved. Basic behaviors in the pressure records were identified and existed discrepancies were discussed and explained. The other physical model tested and preliminary analyzed in the paper is a straight pipeline fixed to the floor only with viscoelastic supports. Such a design created the possibility of significant displacements of the pipeline on the supports and thus allowing for effective testing of the influence of supports stiffness and damping properties on the WH behaviors. The specific initial conditions for that case were formulated, solved and implemented in a computer code. It was found that proper selection of support parameters may produce significant reduction of WH pressure amplitudes, mainly due to effective energy absorption and dissipation at the supports. [ABSTRACT FROM AUTHOR]

Abstract A special type of fluid–structure interaction (FSI) problems are problems with periodic boundary conditions like in turbomachinery. The steady state FSI response of these problems is usually calculated with similar techniques as used for transient FSI analyses. This means that, when the fluid and structure problem are not simultaneously solved with a monolithic approach, the problem is partitioned into a fluid and structural part and that each time step coupling iterations are performed to account for strong interactions between the two sub-domains. This paper shows that a time-partitioned FSI computation can be very inefficient to compute the steady state FSI response of periodic problems. A new approach is introduced in which coupling iterations are performed on periodic level instead of per time step. The convergence behaviour can be significantly improved by implementing existing partitioned solution methods as used for time step coupling (TSC) algorithms in the time periodic coupling (TPC) framework. The new algorithm has been evaluated by comparing the convergence behaviour to TSC algorithms. It is shown that the number of fluid–structure evaluations can be considerably reduced when a TPC algorithm is applied instead of a TSC. One of the most appealing advantages of the TPC approach is that the structural problem can be solved in the frequency domain resulting in a very efficient algorithm for computing steady state FSI responses. Highlights • A time periodic coupling (TPC) is introduced for computing the FSI response of periodic problems. • A quasi-Newton inverse least squares (QN-ILS) method is included in the TPC for stabilization. • The QN-ILS TPC method converges for any case, irrespective of the amount of damping and added mass. • Computation time can be significantly reduced with the QN-ILS TPC approach. [ABSTRACT FROM AUTHOR]

This work addresses the problem of numerical simulation of the dynamic loads generated during a dry dam break flow impact on a wall. The numerical model used is the multi-fluid Navier–Stokes Volume Of Fluid (VOF) model THETIS. The results are compared with two experiments allowing pressure evolution validation at two relative positions on the wall. A first analysis of the results shows the large spatial and temporal variability of the pressure field after impact, highlighting the need for extreme care when performing measurements. When using first a free-slip boundary conditions on the bottom, the computed pressure peaks are found to behave differently depending on the distance to the stagnation point. Above a certain position, which is determined in the paper, computed peak pressures are stable with resolution while under this position, a divergent behavior is observed. This divergence is attributed to the shape of the bore tip which is poorly resolved with our model when a free-slip condition is used. This is confirmed by showing that starting from an identical free surface profile right before impact, the pressure peaks are convergent. The pressure peak instability problem can be solved by resolving the boundary layer structure with a suitable model (in our paper a v 2 − f RANS model) but this requires much more CPU resources. [ABSTRACT FROM AUTHOR]

Despite so many investigations on the WEC-breakwater integration system, the practical wave energy extraction efficiency still needs to be improved. Recently, using specially designed arc breakwaters to focus the wave energy to a certain area was found to be a feasible method. In this paper the integration strategy of setting a heaving WEC at the central of a semicircle opening of a vertical solid breakwater is investigated based on the linear potential flow theory, with a semicircle thin curtain wall set outside the opening to give protection on the heaving WEC. The boundary value problem is solved using the method of separation of variables and eigenfunction expansion matching, and the multi-term Galerkin method is adopted to handle the singularity at the thin curtain wall. After successful validation of the proposed theoretical model, a comparison study between the proposed integration systems with different permeability of the curtain wall is conducted, and the cases with a heaving WEC in front of a flat vertical wall and an isolated heaving WEC are considered as a comparison. Then a parametric study is carried out on the effects of the incident wave angle, the porosity, radius, and draft of the semicircle curtain wall, and the dimension of the heaving WEC. • Analytical model of heaving WEC in the semicircle opening of a vertical wall. • A permeable thin curtain wall is set outside to reduce the horizontal wave load. • Validated using published results, far-field coefficients, and Haskind relation. • Comprehensive comparative study between different configurations. • Parametric study on incident wave angle and critical geometrical parameters. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the vibration behavior of a flexible cylinder subjected to an axial flow is investigated numerically. Therefore a methodology is constructed, which relies entirely on fluid–structure interaction calculations. Consequently, no force coefficients are necessary for the numerical simulations. Two different cases are studied. The first case is a brass cylinder vibrating in an axial water flow. This calculation is compared to experiments in literature and the results agree well. The second case is a hollow steel tube, subjected to liquid lead–bismuth flow. Different flow boundary conditions are tested on this case. Each type of boundary conditions leads to a different confinement and results in different eigenfrequencies and modal damping ratios. Wherever appropriate, a comparison has been made with an existing theory. Generally, this linear theory and the simulations in this paper agree well on the frequency of a mode. With respect to damping, the agreement is highly dependent on the correlation used for the normal friction coefficients in the linear theory. [Copyright &y& Elsevier]

Abstract: This paper explores cantilevered beam flutter for both clamped and pinned leading edge boundary conditions. Specifically, a three-dimensional vortex lattice panel method is coupled with a classical Lagrangian one-dimensional beam structural model to predict the linear flutter boundary for finite size rectangular plates. The paper explores the change in flutter characteristics as a function of the fluid to structure mass ratio and the structural aspect ratio. The paper also presents an exploration of the non-monotonic transition in flutter velocity between the pinned-free and clamped-free boundary conditions which is modeled using a leading edge torsional spring. The theoretical results are compared to vibration and aeroelastic test results collected in the Duke University wind tunnel as well as previous theoretical and experimental results for the leading edge clamped configuration. The aeroelastic experiments confirmed the validity of the three-dimensional vortex lattice aerodynamic model over a subset of mass ratios. [Copyright &y& Elsevier]

Abstract: The plunging wave-breaking process for impulsive flow over a bump in a shallow water flume is described, which is relevant to ship hydrodynamics albeit for an idealized geometry since it includes the effects of wave–body interactions and the wave breaking direction is opposite to the mean flow. This paper consists of two parts, which deal with experimental measurements and numerical simulations, respectively. In Part I, ensemble-averaged measurements are conducted, including the overall flume flow, 2-D particle image velocimetry (PIV) center-plane velocities, turbulence inside the breaking wave, and bottom pressures under the breaking wave. A series of individual plunging wave-breaking tests were conducted, which all followed a similar time line consisting of startup, steep wave formation, plunging wave breaking, and chaotic wave breaking swept downstream time phases. The plunging wave breaking process consists of four repeated plunging events each with three [jet impact (plunge), oblique splash and vertical jet] sub-events, which were identified first using a complementary computational fluid dynamics (CFD) study. Video images with red dye display the plunging wave breaking events and sub-events. The wave profile at maximum height, first plunge, bump and wave breaking vortex and entrapped air tube trajectories, entrapped air tube diameters, kinetic, potential, and total energy are analyzed. Similarities and differences are discussed with the previous deep water or sloping beach experimental and computational studies. The numerical simulations using the exact experimental initial and boundary conditions are presented in Part II of this paper. [Copyright &y& Elsevier]

Abstract: The first objective of this paper is to present a series of accurate experimental measurements of the unsteady pressure in the annulus between two concentric cylinders, the outer one of which executes a harmonic planar motion, either transverse translational or rocking motion about a hinge, with and without annular flow. The second objective is the solution of the unsteady Navier–Stokes and continuity equations for the same annular geometry under the same boundary conditions for an incompressible fluid in the laminar regime. The solutions are obtained with a three-time-level implicit integration method in a fixed computational domain by assuming small amplitudes of oscillation of the outer cylinder. A pseudo-time integration method with artificial compressibility is used to advance the solution between consecutive real time levels. The finite difference method is used for spatial discretization on a stretched staggered grid. The problem is reduced to a scalar tridiagonal system, solved by a decoupling procedure which is based on a factored Alternating Direction Implicit (ADI) scheme with lagged nonlinearities. The third objective is the comparison of the experimental results with the theoretical ones. This comparison shows that the two are in good agreement in the case of translational motion, and in excellent agreement in the case of rocking motion. The experimental and theoretical work presented in this paper is useful for fluid–structure interaction and flow-induced vibration analyses in such geometries. [Copyright &y& Elsevier]

Abstract: Studying dynamic stability of a vertically suspended, fully submerged pipe conveying fluid upwards, researchers have found a contradiction between theoretical predictions and experiments. Experiments did not show any instability, while theory predicts instability at infinitesimally low fluid velocities for a pipe without dissipation mechanisms. To explain this contradiction, in 2005 Païdoussis and co-workers postulated a new description of the boundary condition at the free end of the pipe. Subject to this boundary condition the pipe is predicted to become unstable by divergence (stable node to saddle bifurcation) at a velocity higher than yet achieved in experiments. In this paper, it is shown that a realistic description of hydrodynamic drag in combination with conventional boundary conditions might result in even higher critical velocity, and hence, this could also be an explanation of the contradiction. The description of the hydrodynamic drag is based on experimental data available in literature. This data has been obtained by experimenting with submerged rigid cylinders. To make it applicable to flexible pipes, a key step is undertaken in this paper to translate the data from the frequency domain to the time domain. Using the time-domain description of the hydrodynamic drag in combination with the conventional boundary conditions at the free end, it is shown that the pipe becomes unstable by flutter (stable focus to unstable focus bifurcation) at a critical velocity, which is much higher than that attainable in small-scale experiments. For fluid velocities exceeding the critical one, the pipe motion reaches a steady oscillation of finite amplitude, i.e. a stable limit cycle. [Copyright &y& Elsevier]

This paper deals with the investigation of flow field due to clap and fling mechanism using immersed boundary coupled with lattice Boltzmann method. The lattice Boltzmann method (LBM), an alternative to Navier–Stokes solver, is used because of its simplicity and computational efficiency in solving complex moving boundary problems. Benchmark problems are simulated to validate the code, which is then used for simulating flow over two elliptic wing of aspect ratio 5 performing clap and fling flapping motion for different flow parameters such as Reynolds number (Re=75, 100, 150), advance ratio ( J =10E−3.10E−2,0.2) and frequency ( f =0.05 Hz, 0.25 Hz). Numerical simulation is able to capture typical low Reynolds number unsteady phenomena such as, ׳wake vortex wing interaction׳, ׳Kramer effect׳ and ׳delayed stall׳. The results are both qualitatively and quantitatively consistent with experimental observation. The parametric study involving different combinations of Re, f and J depict distinctly different aerodynamic performances providing physical insights into the flow physics. It is observed that a combination of low f , low J and high Re flow results in better aerodynamic performance. Pronounced lift enhancement via leading edge vortices are obtained in unsteady regime ( J <1) compared to quasi-steady regime ( J >1). The role of leading edge vortices in enhancing lift are investigated by studying the size and strength of these vortices for different flow conditions. For a given Re, the magnitude of maximum lift coefficient decreases with increasing f irrespective of the value of J ; while the same is enhanced with the increasing Re. [ABSTRACT FROM AUTHOR]

In this paper, the extended Hamilton׳s principle is used to obtain the linear equation of motion and boundary conditions for a cylinder flexibly supported by a translational and a rotational spring at the upstream end and free at the other, and subjected to axial flow. The equation of motion is solved numerically via Galerkin׳s method for a system in which the stiffness of the translational spring is infinitely large, while that of the rotational spring is zero, i.e. a pinned-free cylinder. For such a system, the condition for occurrence of non-oscillatory rigid-body instability is obtained analytically. Also, the Adomian Decomposition Method is used to obtain the critical flow velocity for divergence of pinned-free cylinders analytically. Finally, previously obtained experimental results for pinned-free cylinders are compared with those obtained numerically using the present theory. [ABSTRACT FROM AUTHOR]

Abstract: The partial slip boundary condition produced by a superhydrophobic surface in the Cassie state has been shown capable of reducing skin friction drag as well as influencing the flow around coated bodies including cylinders and spheres. In this paper, we investigated how the changes in vortex shedding and separation previously observed on superhydrophobic cylinders affects the rms lift force and the resulting oscillations induced on an elastically mounted cylinder. Two hydrophobic polytetrafluoroethylene cylinders were studied. The first was smooth and the second was roughened to make it superhydrophobic and to induce slip. The presence of slip was found to decrease rms lift and amplitude of the oscillating cylinder by up to 15% with no measurable impact on drag or the natural frequency of the elastically mounted system. We show that the observed reductions are a direct result of reduced fluid forcing on the superhydrophobic cylinder. [Copyright &y& Elsevier]

Abstract: When carrying out any numerical modelling it is useful to have an analytical approximation available to provide a check on the accuracy of the numerical results and to give insight into the underlying physics of the system. The numerical modelling of wave energy converters is an efficient and inexpensive method of undertaking initial optimisation and experimentation. Therefore, the main objective of this paper is to determine an analytical approximation for the wave excitation forces on a floating truncated vertical cylinder in water of infinite depth. The approximation is developed by solving appropriate boundary value problems using the method of separation of variables. A graphical representation of the analytical approximation for the truncated vertical cylinder and the cylinder of infinite depth are presented and are compared to the results from a computational fluid dynamics analysis, using a commercial boundary element package. The presented analytical approximation and the computational fluid dynamics analysis results were found to be in good agreement. Furthermore, the presented analytical approximation was found to be in good agreement with independent experimental data. [Copyright &y& Elsevier]

Abstract: This paper deals with the studies of sloshing of liquid in partially filled rectangular composite containers subjected to external excitation. The governing equation for inviscid fluid is written as pressure variable form. At each time step, the pressure is evaluated using the meshless local Petrov–Galerkin (MLPG) approach. A local symmetric weak form (LSWF) for linearized sloshing is developed, and a truly meshless method, based on LSWF and moving least squares (MLS) approximation, is presented for the solution of Laplace equation with the requisite boundary conditions. The effectiveness of the developed algorithm is demonstrated through few numerical examples. The comparison of results in terms of natural slosh frequencies, sloshing amplitudes and hydrodynamic pressures obtained in the present investigation are made with those available in the reported literature. To observe the change in the total liquid response due fluid–structure interaction effects, parametric studies are carried out for different cases by varying the fibre orientations and wall thicknesses in the laminated container wall. The present meshless method based on LSWF is found to be simple and attractive with a great potential in engineering applications. [Copyright &y& Elsevier]

Abstract: In this paper, the effect of aerodynamic asymmetries on the flutter characteristics of turbomachinery blades is investigated. Specifically, the present method is used to study the effect of leading edge blending in loaded and unloaded rotors. The unsteady aerodynamic response of the blades to self-excited vibrations is modeled using a harmonic balance method, which allows one to model the entire wheel using complex periodic boundary conditions and a computational grid spanning a single sector (symmetry group). This reduces the computational and memory requirements dramatically compared to similar time-accurate analyses. It is shown that alternate blending degrades the stability of a loaded rotor whereas it improves the stability of an unloaded rotor. On the other hand, when blends are spaced five blades apart their effect is less pronounced. [Copyright &y& Elsevier]

Abstract: Tuned liquid dampers (TLDs) have been installed in large engineering structures to suppress unwanted motions. They function by allowing fluid to slosh in a tank which is mounted rigidly to the structure and contain devices for dissipating energy. In this paper, the TLD is composed of a rectangular tank fitted with an arbitrary configuration of vertical slatted screens to provide damping when the fluid is in motion. The influence of the fluid motion in the tank is analysed by adopting classical linearised water wave theory and a boundary value problem formulated with linearised conditions both on the free surface and across the screens. These latter linearised screen conditions are designed to capture accurately both the added inertia effects of a slatted screen and the damping effects from an equivalent non-linear turbulent drag law, whose successful implementation has been reported earlier by Crowley and Porter. The rectangular tank TLD is coupled to a simple mechanical model for the displacement of an externally forced structure of large mass. Advantage is taken of the linearised theory used to demonstrate analytically key qualitative features of TLD systems. Numerical predictions are shown to compare very well with experimental results for particular screen arrangements. Different screen configurations are then considered to indicate general criteria for ‘optimising’ the TLD performance by reducing overall displacement across all forcing frequencies, by altering the number, placement and porosity of the slatted screens in the tank. [Copyright &y& Elsevier]

Abstract: Part II of this two-part paper presents the simulation results of the plunging wave-breaking generated by impulsive flow over a submerged bump fixed in a shallow water flume using the exact experimental initial and boundary conditions provided in Part I of this study. The overall plunging wave breaking process is described with major wave breaking events identified: jet plunge, oblique splash and vertical jet. These major events repeat up to four times before entering the chaotic breaking phase. The plunging wave breaking process of the simulations shows a similar time line as the experiments consisting of startup, steep wave formation, plunging wave, and chaotic wave breaking swept downstream time phases. Wave breaking profile, air entrainment, velocity, vorticity, flume bottom pressure, and energy are analyzed and compared with the experimental results. The simulations qualitatively predict all four time phases, all four plunging events and their sub-events. The wave profile and location at the maximum height is very close to the experiment results. The flume flow and velocity demonstrate the same flow trend as the experiments but with reduced velocity magnitudes. The simulations show similar bottom pressure to the experiments but with large oscillations, and the post-breaking water elevations are larger as compared to the experimental results. [Copyright &y& Elsevier]

Abstract: The paper addresses a theoretical study of the added mass effect in cavitating flow. The cavitation is considered to induce a strong time–space variation of the fluid density at the interface between an inviscid fluid and a three-degree-of-freedom rigid section. The coupled problem is then simplified to a Laplace equation written for the pressure with a boundary condition at the fluid–structure interface depending on the acceleration, the velocity of the structure and on the rate of change of flow density. It is shown that contrary to the homogeneous flow, the added mass operator is not symmetrical and depends on the flow through fluid density variation. The added mass coefficients decrease as the cavitation increases which should induce an increase of the natural structural frequencies. The model shows also an added damping operator related to the rate of change of flow density. Added damping coefficients are found to be positive or negative according to the rate of change of the fluid density, indicating the possibility of instability development between flexible structures and unsteady cavitating flows. [Copyright &y& Elsevier]

Abstract: The aerodynamic forces on a stay cable under a rain-wind induced vibration (RWIV) are difficult to measure directly in a wind tunnel test. This paper presents a hybrid approach that combines an experiment with computational fluid dynamics (CFD) for the investigation on aerodynamic forces of a stay cable under a RWIV. The stay cable and flow field were considered as two substructures of the system. The oscillation of the stay cable was first measured by using a wind tunnel test of a RWIV under an artificial rainfall condition. The oscillation of the cable was treated as a previously known moving boundary condition and applied to the flow field. Only the flow field with the known moving cable boundary was then numerically simulated by using a CFD method (such as Fluent 6.3). The transient aerodynamic forces of the stay cable with a predetermined cable oscillation were obtained from numerical calculations. The characteristics of the aerodynamic forces in the time domain and frequency domain were then analysed for various cases. To verify the feasibility and accuracy of the proposed hybrid approach, the transient aerodynamic forces were applied to a single-degree-of-freedom model (SDOF) of the stay cable to calculate the RWIV of the cable. A comparison was performed between the oscillation responses of the stay cable obtained from the calculated (SDOF model) and experimental results, and the results indicate that the hybrid approach accurately simulates the transient aerodynamic forces of the stay cable. The equivalent damping ratios induced by the aerodynamic forces were obtained for various wind speeds. Furthermore, a nonlinear model of the aerodynamic force is proposed based on the calculation results, and the coefficients in the model were identified by a nonlinear least-squares technique. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with a novel computational formulation for the analysis of viscous flows past a solid body. The formulation is based upon a convenient decomposition of the flow field into potential and rotational velocity contributions, which has the distinguishing feature that the rotational velocity vanishes in much of, if not all, the region in which the vorticity is negligible. Contrary to related formulations implemented by the authors in the past, in the proposed approach, discontinuities of the potential and rotational velocity fields across a prescribed surface emanating from the trailing edge (such as the wake mid-surface) are eliminated, thereby facilitating numerical implementations. However, the main novelty is related to the application of the boundary condition: first, the expression for the velocity used for the condition on the body boundary is consistent with that for the velocity in the field; also—contrary to related formulations used by the authors in the past—in the proposed approach, the condition on the body boundary does not require the evaluation of the total vorticity (inside and outside the computational domain). The proposed algorithm, valid for three-dimensional compressible flows, is validated—as a first step—for the case of two-dimensional incompressible flows. Specifically, numerical results are presented for the aerodynamic analysis of two-dimensional incompressible viscous flows past a circular cylinder and past a Joukowski airfoil. In order to verify the desirable absence of artificial damping, we present also results pertaining to the flutter (i.e., dynamic aeroelastic) analysis of a spring-mounted circular cylinder in a viscous flow, free to move in a direction orthogonal to the unperturbed flow. In both cases (aerodynamics and aeroelasticity), the results are in good agreement with existing literature data. [Copyright &y& Elsevier]

Abstract: The paper deals with the early stage of impact of a solid cylindrical body on the surface of a cylindrical cavity for zero and non-zero gap between the cavity surface and the body surface. As a result, the stated mixed non-stationary boundary value problem with the unknown variable in the time boundary is formulated. Its solution is reduced to a joint solution of an infinite system of linear integral Volterra equations of the second kind and the differential equation of the body movement. In the case of simplified formulation, the solution is reduced to the infinite sequence of the linear integral Volterra equations. Hydrodynamic and kinematic characteristics are also obtained. [Copyright &y& Elsevier]

The present paper is dedicated to the development of a numerical model for the water impact of two-dimensional (2D) and axisymmetric bodies with imposed motion. The work is a first step towards the implementation of a 2D+t procedure to be used for the analysis of aircraft ditching. The problem is investigated under the assumptions of an inviscid and incompressible fluid, which is modeled by a potential flow model with fully non-linear boundary conditions at the free-surface. The unsteady boundary value problem with a free-surface is numerically solved through a boundary element method, coupled to a simplified finite element method to describe the thinnest part of the jet. The study is aimed at describing the entry and exit phases. Specific numerical solutions are developed to tackle the exit phase and to improve the stability of the model. Results are presented in terms of free-surface shape, pressure distribution and hydrodynamic load acting on the impacting body. The model is used to study the water entry and exit of a 2D wedge and an axisymmetric cone, for which numerical or experimental results are available in the literature. The numerical investigation shows that the proposed model accurately simulate both the entry and exit phases. For the exit phase, it is shown that the proposed model, being fully non-linear, provides a much better prediction of the loads and the wetted area compared to simplified (analytical) approaches. The effects of the gravity, usually missing in the approaches available in the literature, are also investigated, showing they are rather important, especially, in the exit phase. [ABSTRACT FROM AUTHOR]