Linear Potential Flow Theory Research Articles

Undamped eigenperiods of a sea-based gravity monotower

An analytically approximate method was proposed in [1] to estimate undamped eigenperiods of a sea-based gravity monotower by accounting for sloshing inside the shaft. These results are generalised to include the soil feedback and the inertia moment of the top rigid body as well as to describe the external hydrodynamic loads using the linear three-dimensional potential flow theory of an incompressible liquid. A mathematical model of the multicomponent mechanical system is presented. The virtual work principle is used to express the Euler–Bernoulli governing equation and all fluid-structure dynamic transmission conditions. Numerical examples of the eigenperiods versus geometric and physical input parameters typical for the Draugen platform and some monopiles are given. The highest eigenperiod of the horizontal vibrations belongs to experimentally-known ranges. These eigenperiods increase with increasing mass, radius of gyration and mass centre of the top body; they also increase with the shear modulus of the soil. Three classes of eigenmodes are detected. They express dominant character of structural vibrations and sloshing, respectively, or a mixed type. Sloshing is less important for existing monopiles.

Analytical determination of the reflection coefficient by the evanescent modes model during the wave–current–horizontal plate interaction

Our work presents an analytical study of the determination of the reflection coefficient during the interaction between the regular wave current and a horizontal plate. This study was done using the linearized potential flow theory with the evanescent modes model, while searching for complex solutions to the dispersion equation that are neither real pure nor imaginary pure. To validate the established model, it has been confronted with the experimental results of V. Rey and J. Touboul, in a first phase, and then compared to those of the numerical study by H.-X. Lin et al. Then, this model was used to study the effect of current on the reflection coefficient. On présente dans ce travail une étude analytique de la détermination du coefficient de réflexion lors de l'interaction houle–courant–plaque. Cette étude a été faite dans le cadre de la théorie potentielle linéarisée moyennant le modèle des modes évanescents, en cherchant des solutions complexes de l'équation de dispersion qui ne soient, ni réelles pures, ni imaginaires pures. Pour valider le modèle établi, on l'a d'abord confronté aux résultats expérimentaux de V. Rey et J. Touboul, puis à ceux, issus de la modélisation, de H.-X. Lin et al. Ensuite, on a utilisé ce modèle pour étudier l'effet du courant sur le coefficient de réflexion.

Fluid–structure interaction for nonlinear response of shells conveying pulsatile flow

Circular cylindrical shells with flexible boundary conditions conveying pulsatile flow and subjected to pulsatile pressure are investigated. The equations of motion are obtained based on the nonlinear Novozhilov shell theory via Lagrangian approach. The flow is set in motion by a pulsatile pressure gradient. The fluid is modeled as a Newtonian pulsatile flow and it is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier–Stokes equations. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior. The case of shells containing quiescent fluid subjected to the action of a pulsatile transmural pressure is also addressed. Geometrically nonlinear vibration response to pulsatile flow and transmural pressure are here presented via frequency-response curves and time histories. The vibrations involving both a driven mode and a companion mode, which appear due to the axial symmetry, are also investigated. This theoretical framework represents a pioneering study that could be of great interest for biomedical applications. In particular, in the future, a more refined model of the one here presented will possibly be applied to reproduce the dynamic behavior of vascular prostheses used for repairing and replacing damaged and diseased thoracic aorta in cases of aneurysm, dissection or coarctation. For this purpose, a pulsatile time-dependent blood flow model is here considered by applying physiological waveforms of velocity and pressure during the heart beating period. This study provides, for the first time in literature, a fully coupled fluid–structure interaction model with deep insights in the nonlinear vibrations of circular cylindrical shells subjected to pulsatile pressure and pulsatile flow.

Stability and vibration properties of a composite laminated plate subjected to subsonic compressible airflow

The stability and nonlinear vibration of a composite laminated plate with simply supported boundary conditions in subsonic compressible airflow subjected to transverse periodic external excitation are investigated. The equation of motion of the plate is established by using the von Karman’s nonlinear plate theory. The linear potential flow theory considering the compressibility of the airflow is adopted to formulate the aerodynamic model. The nonlinear ordinary differential equation of motion of the plate is obtained by applying the assumed mode method. The critical divergence velocity and the flutter velocity of the plate are obtained by analyzing the natural frequencies of the linear system. The effects of the ply angle and the compressibility of the airflow on the critical divergence velocities and the flutter velocities of the plate are investigated. For the nonlinear system, the displacement time response of the plate subjected to accelerating airflow and transverse harmonic excitation is presented to investigate the vibration properties. The effects of the subsonic airflow on the resonance properties of the system are analyzed from the amplitude frequency curves of the plate under different flow velocities. From the study, it can be seen that with the flow velocity increasing, the natural frequencies of the plate decreases and the plate may exhibit instability of the divergence or flutter type. With the ply angle increasing from 0° to 90°, the critical divergence velocity increases and then decreases, and the flutter velocity decreases. The critical divergence velocity and the flutter velocity of the plate obtained from the compressible aerodynamic model are smaller than those obtained from the incompressible model. When the plate is in instability of divergence type, the plate vibrates with smaller amplitude around a non-zero point of equilibrium, and when the plate is in instability of flutter type, the plate vibrates with larger amplitude around a non-zero point of equilibrium. When the flow velocity exceeds the divergence velocity, the amplitude frequency curve of the plate is an irregular curve with larger vibration amplitudes and the plate may be in a chaotic motion state.

Observations and computations of narrow Kelvin ship wakes

Computations of far-field ship waves, based on linear potential flow theory and the Hogner approximation, are reported for monohull ships and catamarans. Specifically, far-field ship waves are computed for six monohull ships at four Froude numbers F≡V/gL=0.58, 0.68, 0.86, 1.58 and for six catamarans with nondimensional hull spacing s≡S/L=0.25 at two Froude numbers Fs≡V/gS=1 and 2.5. Here, g is the gravitational acceleration, V and L denote the ship speed and length, and S is the separation distance between the twin hulls of a catamaran. The computations show that, although the amplitudes of the waves created by a ship are strongly influenced by the shape of the ship hull, as well known, the ray angles where the largest waves are found are only weakly influenced by the hull shape and indeed are mostly a kinematic feature of the flow around a ship hull. An important practical consequence of this flow feature is that the apparent wake angle of general monohull ships or catamarans (with arbitrarily-shaped hulls) can be estimated, without computations, by means of simple analytical relations; these relations, obtained elsewhere via parametric computations, are given here. Moreover, the influence of the two parameters Fs and s that largely determine the ray angles of the dominant waves created by a catamaran is illustrated via computations for three catamarans with hull spacings s=0.2, 0.35, 0.5 at four Froude numbers Fs=1, 1.5, 2, 2.5. These computations confirm that the largest waves created by wide and/or fast catamarans are found at ray angles that only depend on Fs (i.e. that do not depend on the hull spacing s) in agreement with an elementary analysis of lateral interference between the dominant waves created by the bows (or sterns) of the twin hulls of a catamaran. The dominant-waves ray angles predicted by the theory of wave-interference effects for monohull ships and catamarans are also compared with the observations of narrow Kelvin ship wakes reported by Rabaud and Moisy, and found to be consistent with these observations.

Inertia effects in TLD sloshing with perforated screens

Rectangular tanks equipped with perforated screens and partly filled with water have been proposed as Tuned Liquid Dampers (TLDs) to mitigate the vibratory response of slender buildings. In a previous paper (Molin & Remy 2013)an experimental campaign was reported and its results compared with a numerical model, based on linearized potential flow theory. Good agreement was generally obtained for the added mass and damping coefficients. In these experiments the screen had numerous circular openings, 4 mm in diameter, and it was assumed in the numerical model that the screen created a pressure drop proportional to the square of the relative traversing velocity. In this subsequent paper complementary experiments are described where the screen openings are increased in size, keeping constant the open-area ratio, and varied in shapes (vertical slots then circular holes). As a result of the solid parts of the screen getting larger, inertia effects come into play resulting in a shift of the resonant frequencies of the odd sloshing modes. With a proper modification of the discharge law in the numerical model, ccounting for inertia effects, good agreement is recovered between experimental and numerical hydrodynamic coefficients.

Errors due to a practical Green function for steady ship waves

Errors that stem from a practical analytical approximation La to the local flow component L in the Green function associated with steady linear potential flow around a ship hull are considered. Although the approximation La is not very accurate, the flow potentials evaluated via the exact local flow component L or the approximation La for Froude numbers F=0.15, 0.3 and 0.5 cannot be distinguished, except at F=0.15 for which relatively small differences can be observed. Moreover, the sinkage, the trim angle and the wave drag predicted by the Neumann–Michell (NM) theory, with the local flow potential evaluated using L or La, are in very close agreement. Despite its remarkably simplicity, the analytical approximation La can then be used to compute the local flow component L in the Green function, in the entire flow region, within the framework of the NM linear potential flow theory and the related Hogner approximation. The practical analytical approximation La is far more practical than the basic integral representation of L, and is an important element of the NM theory. Indeed, the analytical approximation La, and other features of the NM theory, make it possible to compute the flow around a steadily advancing ship hull in a highly efficient way, as required for routine practical applications to design and hull-form optimization.

Hydrodynamic analysis of oscillating water column wave energy devices

A 40-chamber I-Beam attenuator-type, oscillating water column, wave energy converter is analyzed numerically based on linearized potential flow theory, and experimentally via model test experiments. The high-order panel method WAMIT by Newman and Lee (WAMIT; a radiation–diffraction panel program for wave-body interactions, 2014, http://www.wamit.com ) is used for the basic wave-structure interaction analysis. The damping applied to each chamber by the power take off is modeled in the experiment by forcing the air through a hole with an area of about 1 % of the chamber water surface area. In the numerical model, this damping is modeled by an equivalent linearized damping coefficient which extracts the same amount of energy over one cycle as the experimentally measured quadratic damping coefficient. The pressure in each chamber in regular waves of three different height-to-length ratios is measured in the experiments and compared to calculations. The model is considered in both fixed and freely floating, slack-moored conditions. Comparisons are also made to experimental measurements on a single fixed chamber. The capture width ratio in each case is predicted based on the pressures in the chambers. Good agreement is found between the calculations and the experiments.

Diffraction and radiation loads on open cylinders of thin and arbitrary shapes

We study the effects of having an opening in a vertical cylinder of an arbitrary cross-sectional shape when subjected to incident waves from the outside field. Both the diffraction and radiation problems of linear potential-flow theory are addressed. The cylinders considered are bottom-mounted with vanishing thickness and the problem is formulated as a hypersingular boundary-integral method. A simple higher-order procedure is presented to handle the strong singularity. Comparisons are made between the hydrodynamic properties of open and closed cylinders, and the effects of increasing the opening size are discussed and explained. Results for square, circular and elliptical open cylindrical shells, presented as examples, indicate that wave loads on the structures could be dramatically decreased to zero (effectively) at certain frequencies and opening sizes. This leads to the surprising conclusion that directing an open structure into the incident-wave field results in lower loads on the structure. A model of an open harbour with a frontal breakwater in a wave field, inspired by the idea of the Portunus Project, is also analysed.

A simplified mechanical model with fluid–structure interaction for rectangular tank sloshing under horizontal excitation

Based on the spring–mass model, a novel mechanical model of sloshing with fluid–structure interaction under a horizontal excitation is proposed, and the coupled dynamic equation of sloshing system is established. Considering the flexibility of bulkhead, the effects of certain factors, such as bulkhead bending stiffness and filling ratios, on the mode of coupled sloshing system are investigated. It is found that these factors have significant influence on the mode. By comparing the present results with the results of ADINA based on the linear potential flow theory and published literatures, the proposed coupled sloshing model is verified. The results show that the simplified rigid mass, [Formula: see text], dominates the contributions to bending moment near the bottom of a bulkhead and the spring–mass, [Formula: see text], [Formula: see text], to bending moment near the liquid-free surface of a bulkhead. Furthermore, the computational cost is greatly reduced by using the proposed mechanical model with fluid–structure interaction for a rectangular tank sloshing.

Viscosity and nonlinearity effects on the forces and waves generated by a floating twin hull under heave oscillation

Nonlinear hydrodynamics of a twin rectangular hull under heave oscillation is analyzed using numerical methods. Two-dimensional nonlinear time-domain solutions to both inviscid and viscous problems are obtained and the results are compared with linear, inviscid frequency-domain results obtained in [26] to quantify nonlinear and viscous effects. Finite-difference methods based on boundary-fitted coordinates are used for solving the governing equations in the time domain [2]. A primitive-variables based projection method [6] is used for the viscous analysis and a mixed Eulerian–Lagrangian formulation [11] for inviscid analysis. The algorithms are validated and the order of accuracy determined by comparing the results obtained from the present algorithm with the experimental results of Vugt [22] for a heaving rectangle in the free surface. The present study on the twin-hull hydrodynamics shows that at large and non-resonant regular frequencies, and small amplitude of body oscillation, the fluid viscosity does not significantly affect the wave motion and the radiation forces. At low frequencies however the viscosity effect is found to be significant even for small amplitude of body oscillation. In particular, the hydrodynamic force obtained from the nonlinear viscous analysis is found to be closer to the linear inviscid force than the nonlinear inviscid force to the linear inviscid force, the reason for which is attributed to the wave dampening effect of viscosity. Since the wave lengths generated at smaller frequencies of oscillation are longer and therefore the waves could have a more significant effect on the dynamic pressure on the bottom of the hulls which contribute to the heave force, the correlation between the heave force and the wave elevation is found to be larger at smaller frequencies. Because of nonlinearity, the wave radiation and wave damping force remained nonzero even at and around the resonant frequencies – with the resonant frequencies as determined in [26] using linear potential flow theory. As to be expected, the nonlinear effect on the wave force is found to be significant at all frequencies for large amplitude of oscillation compared to the hull draft. The effect of viscosity on the force, by flow separation, is also found to be significant for large amplitude of body oscillation.

Optimizing wave energy parks with over 1000 interacting point-absorbers using an approximate analytical method

Large arrays of wave energy converters of point-absorber type are studied using an approximate analytical model. The model is validated against a numerical method that takes into account full hydrodynamic interactions based on linear potential flow theory. The low computational cost of the analytical model enables parameter studies of parks in the MW range and includes up to over 1000 interacting devices. The model is actuated by irregular wave data obtained at the Swedish west coast. In particular, focus is on comparing park geometries and improving park configurations to minimize the power fluctuations.

Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced facesheets using higher-order structural theory

In this paper, the supersonic flutter characteristics of doubly curved sandwich shell panels, viz., cylindrical and spherical shells, with carbon nanotube (CNT) reinforced facesheets are investigated using QUAD-8 shear flexible shell element developed based on higher-order structural theory. The formulation accounts for the nonlinear variation of the in-plane and transverse displacements through the thickness, and abrupt discontinuity in slope of the in-plane displacement at the interface. The strain–displacement relation is accurately introduced in the formulation. The first-order high Mach number approximation to linear potential flow theory is employed for evaluating the aerodynamic pressure. The solutions of the complex eigenvalue problem, developed based on Lagrange’s equation of motion, are obtained by QR algorithm. The accuracy of the present formulation is validated considering the problems for which solutions are available in the literature. A detailed numerical study is conducted to highlight the significance of the higher-order model over the first-order theory and also to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness, the shell thickness and the aspect ratio, radius-to-thickness ratio, and temperature on the flutter boundaries.

Hydroelastic response of a circular plate in waves on a two-layer fluid of finite depth

The hydroelastic response of a circular, very large floating structure (VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the plate-covered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.

Modeling of Finite-span Ram Wings Moving Above Water at Finite Froude Numbers

Power-augmented ram wings can be used for very fast transportation of heavy cargo over water and relatively flat solid surfaces. This article describes a coupled aerohydrodynamic model for a ram wing in steady forward motion. Effects of a finite wingspan and finite Froude numbers are accounted for by the extreme ground effect theory for airflow and a linearized potential flow theory for water. Representative results showing the influence of several variable parameters of the vehicle geometry and operational regimes are demonstrated for a selected ram-wing configuration. The developed method can be applied for modeling of airborne lifting surfaces operating in the strong ground effect on a variety of fast marine craft.

Modeling of Finite-span Ram Wings Moving Above Water at Finite Froude Numbers

Power-augmented ram wings can be used for very fast transportation of heavy cargo over water and relatively flat solid surfaces. This article describes a coupled aerohydrodynamic model for a ram wing in steady forward motion. Effects of a finite wingspan and finite Froude numbers are accounted for by the extreme ground effect theory for airflow and a linearized potential flow theory for water. Representative results showing the influence of several variable parameters of the vehicle geometry and operational regimes are demonstrated for a selected ram-wing configuration. The developed method can be applied for modeling of airborne lifting surfaces operating in the strong ground effect on a variety of fast marine craft.

Stability analysis and active control of a nonlinear composite laminated plate with piezoelectric material in subsonic airflow

The stability analysis and active control of a nonlinear composite laminated plate in subsonic airflow are studied. The equation of motion of a plate with a piezoelectric patch in subsonic air flow is established by using the Hamilton’s principle with the assumed mode method. The perturbation aerodynamic pressure is derived from linear potential flow theory. For the linear system, the eigenfrequencies of the system are calculated for different flow velocities, and the critical instability flow velocity and the flutter flow velocity are obtained. For the nonlinear system, the bifurcation of the transverse displacement with respect to the flow velocity is analyzed by solving the equations of equilibrium of the nonlinear dynamic system. The effects of the ply angles on the critical instability flow velocities of the plate are analyzed. According to the mechanism for the instability of the plate in subsonic flow, the displacement feedback control strategy is adopted to stabilize the system. The influences of the control gain on the critical instability velocity of the plate are analyzed. From the analysis and numerical simulations, it can be concluded that with the ply angle increasing from \(0^{\circ }\) to \(90^{\circ }\), the critical instability flow velocity of the plate has a maximum at a finite critical angle. When the flow velocity exceeds the critical instability flow velocity, the stable point of the nonlinear system deviates from the zero point of the system. It also can be concluded that the displacement feedback control can effectively improve the aerodynamic properties of the plate by providing the active stiffness for the unstable system. With displacement feedback control gain increasing, the critical instability flow velocity increases.

Panel flutter characteristics of sandwich plates with CNT reinforced facesheets using an accurate higher-order theory

In this paper, the flutter characteristics of sandwich panels with carbon nanotube (CNT) reinforced face sheets are investigated using QUAD-8 shear flexible element developed based on higher-order structural theory. The formulation accounts for the realistic variation of the displacements through the thickness, the possible discontinuity in the slope at the interface, and the thickness stretch affecting the transverse deflection. The in-plane and rotary inertia terms are also included in the formulation. The first-order high Mach number approximation to linear potential flow theory is employed for evaluating the aerodynamic pressure. The solutions of the complex eigenvalue problem, developed based on Lagrange׳s equation of motion are obtained using the standard method for finding the eigenvalues. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to bring out the efficacy of the higher-order model over the first-order theory and also to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness, the plate thickness and the aspect ratio, damping and the temperature on the flutter boundaries and the associated vibration modes.

Scaling parameters and modeling flutter of a cylindrical shell

The similarity parameters in the problem of flutter of a cylindrical shell were studied. As a mathematical theory of shells there was adopted a technical theory in mixed form. For a manometric pressure either formula of piston theory or formula of linearized potential flow theory is accepted. Physical conditions of modeling were derived from the equation of similarity parameters of the model and full-scale processes.

Wave farm modelling of oscillating wave surge converters

A mathematical model is described to analyse the hydrodynamic behaviour of a wave energy farm consisting of oscillating wave surge converters in oblique waves. The method is a highly efficient semi-analytical approach based on the linear potential flow theory. Wave farms with a large number of such devices are studied for various configurations. For an inline configuration with normally incident waves, the occurrence of a near-resonant behaviour, already known for small arrays, is confirmed. A strong wave focusing effect is observed in special configurations comprising a large number of devices. The effects of the arrangement and of the distance of separation between the flaps are also studied extensively. In general, the flaps lying on the front of the wave farm are found to exhibit an enhanced performance behaviour in average, owing to the mutual interactions arising within the array. A random sea analysis shows that a slightly staggered arrangement can be an ideal layout for a wave farm of this device. The hydrodynamics of two flaps that oscillate back to back is also discussed.