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Coupled, parametric oscillators are often studied in applied biology, physics, fluids, and many other disciplines. In this paper, we study a parametrically driven, coupled oscillator system where the individual oscillators are subjected to varying frequency and phase with a focus on the influence of the damping and coupling parameters away from parametric resonance frequencies. In particular, we study the long-term statistics of the oscillator system's trajectories and stability. We present a novel, robust, and computationally efficient method, which has come to be known as an auxiliary function method for long-time averages, and we pair this method with classical, perturbative-asymptotic analysis to corroborate the results of this auxiliary function method. These paired methods are then used to compute the regions of stability for a coupled oscillator system. The objective is to explore the influence of higher order, coupling effects on the stability region across a broad range of modulation frequencies, including frequencies away from parametric resonances. We show that both simplified and more general asymptotic methods can be dangerously un-conservative in predicting the true regions of stability due to high order effects caused by coupling parameters. The differences between the true stability region and the approximate stability region can occur at physically relevant parameter values in regions away from parametric resonance. As an alternative to asymptotic methods, we show that the auxiliary function method for long-time averages is an efficient and robust means of computing true regions of stability across all possible initial conditions. [ABSTRACT FROM AUTHOR]

This work describes the effects of waves on the hydroelastic response of a hydrofoil in fully wetted and ventilated flows. In the absence of vaporous cavitation (described in Part 2 of this paper series), shallow long-period non-breaking waves delayed ventilation inception because velocity fluctuations prevent the formation of a stably separated region of flow at the foil's leading edge. Aerated von Kármán vortex shedding occurred from the blunt trailing edge, producing vortex-induced vibration of the hydrofoil at a near-constant Strouhal number. Regular waves led to near sinusoidal oscillations of the load and deformations at the wave encounter frequency, while the mean response and the dynamic response at other frequency peaks corresponding to hydrodynamic and structural modes remained mostly unaffected. Significant dynamic load amplification was observed at a submerged aspect ratio of 2 for cases with low angles of attack because of coalescence between the second and third wetted structural modes; at high angles of attack, the amplitude of the load fluctuations and flow-induced vibrations reduced because energy was diverted away from the coalescence frequencies to the nearby vortex shedding frequency. In both calm water and wave conditions, transition from fully wetted to fully ventilated flow resulted in sudden and significant reduction in the load coefficients, as well as foil deflections. An impulse-like signature was observed in the time-frequency spectra during these transitions. In many of the cases, transition to fully ventilated flow also led to substantially reduced amplitudes in the load and deformation fluctuations. [ABSTRACT FROM AUTHOR]

The storm surge associated with Hurricane Katrina caused tremendous damage along the Gulf Coast in Louisiana, Mississippi, and Alabama. Similar damage was observed subsequent to the Indian Ocean tsunami of December 26, 2004. In order to gain a better understanding of the performance of engineered structures subjected to coastal inundation due to tsunami or hurricane storm surge, the writers surveyed damage to bridges, buildings, and other coastal infrastructure subsequent to Hurricane Katrina. Numerous lessons were learned from analysis of the observed damage, and these are reported herein. A number of structures experienced significant structural damage due to storm surge and wave action. Structural members submerged during the inundation were subjected to significant hydrostatic uplift forces due to buoyancy, enhanced by trapped air pockets, and to hydrodynamic uplift forces due to wave action. Any floating or mobile object in the nearshore/onshore areas can become floating debris, affecting structures in two ways: impact and water damming. Foundation soils and foundation systems are at risk from shear- and liquefaction-induced scour, unless designed appropriately. DOI: 10.1061/(ASCE)0733-950X(2007)133:6(463) CE Database subject headings: Storm surge; Hurricanes; Tsunamis; Coastal structures; Hydraulic loads; Debris; Structural failures.

There is growing interest in using lighter and more flexible foils with active and/or passive smart actuation mechanisms to increase efficiency and maneuverability. For efficient operations, airfoils and hydrofoils tend to have an effective aspect ratio greater than two, which permits spanwise flexibility depending on the choice of material and architectural design. The fluid density plays an important role in the steady and dynamic performance, including the governing hydroelastic instability mechanism. To understand the influence of spanwise flexibility, we examine the response of a rectangular cantilevered foil as a canonical proxy for more complex lift generating devices. This research aims to investigate the influence of key geometric, material, and flow parameters on the steady and dynamic responses of the spanwise flexible airfoils vs hydrofoils. The results are obtained using an inviscid frequency- and time-domain fluid-structure interaction model that accounts for flow-induced bend-twist coupling terms and are compared with inviscid theory results without the flow-induced bend-twist coupling terms. The results show that the flow-induced bend-twist coupling effects impact the natural frequencies and damping coefficients, and such effects grow with increasing fluid density and flow speed. Hence, the flow-induced bend-twist coupling effects are more critical for hydrofoils than airfoils, particularly for the twisting mode. Ignoring the flow-induced bend-twist coupling terms leads to an incorrect prediction of flutter speed and over-prediction of the damping, which is dangerous because the actual vibrations and dynamic load amplification may be higher than the prediction, which could lead to accelerated fatigue. The results demonstrate that flexible hydrofoils have much lower natural frequencies and higher damping coefficients than airfoils due to higher fluid inertial and damping forces, both of which are proportional to the fluid density. While all components of the fluid forces are proportional to the fluid density, the fluid damping forces grow with the velocity, and the fluid disturbing forces grow with velocity square. Therefore, divergence tends to be the governing instability mode for hydrofoils, while flutter is typically the governing instability mode for airfoils. The maximum aero/hydro-elastic bending and twisting deformations are limited by the corresponding reduced stable velocity to avoid divergence or flutter. [ABSTRACT FROM AUTHOR]

The influence of fluid–structure interaction on cloud cavitation about a hydrofoil is investigated by comparing results from a relatively stiff reference hydrofoil, presented in Part 1, with those obtained on a geometrically identical flexible hydrofoil. Measurements were conducted with a chord-based Reynolds number $Re=0.8\times 10^{6}$ for cavitation numbers, $\unicode[STIX]{x1D70E}$ , ranging from 0.2 to 1.2 while the hydrofoil was mounted at an incidence, $\unicode[STIX]{x1D6FC}$ , of $6^{\circ }$ to the oncoming flow. Tip deformations and cavitation behaviour were recorded with synchronised force measurements utilising two high-speed cameras. The flexible composite hydrofoil was manufactured as a carbon/glass-epoxy hybrid structure with a lay-up sequence selected principally to consider spanwise bending deformations with no material-induced bend–twist coupling. Hydrodynamic bend–twist coupling is seen to result in nose-up twist deformations causing frequency modulation from the increase in cavity length. The lock-in phenomenon driven by re-entrant jet shedding observed on the stiff hydrofoil is also evident on the flexible hydrofoil at $0.70\leqslant \unicode[STIX]{x1D70E}\leqslant 0.75$ , but occurs between different modes. Flexibility is observed to accelerate cavitation regime transition with reducing $\unicode[STIX]{x1D70E}$. This is seen with the rapid growth and influence the shockwave instability has on the forces, deflections and cavitation behaviour on the flexible hydrofoil, suggesting structural behaviour plays a significant role in modifying cavity physics. The reduced stiffness causes secondary lock-in of the flexible hydrofoil's one-quarter sub-harmonic, $f_{n}/4$ , at $\unicode[STIX]{x1D70E}$ = 0.4. This leads to the most severe deflections observed in the conditions tested along with a shift in phase between normal force and tip deflection. [ABSTRACT FROM AUTHOR]

The physics associated with various cavitation regimes about a hydrofoil is investigated in a variable-pressure water tunnel using high-speed photography and synchronised force measurements. Experiments were conducted on a relatively stiff stainless steel hydrofoil at a chord-based Reynolds number, Re = 0.8 × 106 for cavitation numbers, &#963, ranging from 0.2 to 1.2, with the hydrofoil experiencing sheet, cloud and supercavitation regimes. The NACA0009 model of tapered planform was vertically mounted in a cantilevered configuration to a six-component force balance at an incidence, &#945, of 6° to the oncoming flow. Tip deformations and cavitation behaviour were recorded with synchronised force measurements utilising two high-speed cameras mounted underneath and to the side of the test section. Break-up and shedding of an attached cavity was found to be due to either interfacial instabilities, re-entrant jet formation, shockwave propagation or a complex coupled mechanism, depending on &#963. Three primary shedding modes are identified. The Type IIa and IIb re-entrant jet-driven oscillations exhibit a non-linear dependence on &#963, decreasing in frequency with decreasing &#963 due to growth in the cavity length, and occur at higher &#963 values (Type IIa: 0.4–1.0; Type IIb: 0.7–0.9). Shockwave-driven Type I shedding occurs for lower &#963 values (0.3–0.6) with the oscillation frequency being practically independent of &#963. The Type IIa oscillations locked in to the first sub-harmonic of the hydrofoil's first bending mode in water which has been modulated due to the reduced added mass of the vapour cavity. Supplementary movies are available with the online version of the paper. [ABSTRACT FROM AUTHOR]

Shock waves are gaining interests in biological and medical applications. In this work, we investigated the mechanical characteristics of shock waves that affect cell viability. In vitro testing was conducted using the metastatic breast epithelial cell line MDA-MB-231. Shock waves were generated using a high-power pulse laser. Two different coating materials and different laser energy levels were used to vary the peak pressure, decay time, and the strength of subsequent peaks of the shock waves. Within the testing capability of the current study, it is shown that shock waves with a higher impulse led to lower cell viability, a higher detached cell ratio, and a higher cell death ratio, while shock waves with the same peak pressure could lead to different levels of cell damage. The results also showed that the detached cells had a higher cell death ratio compared to the attached cells. Moreover, a critical shock impulse of 5 Pa·s was found to cause the cell death ratio of the detached cells to exceed 50%. This work has demonstrated that, within the testing range shown here, the impulse, rather than the peak pressure, is the governing shock wave parameter for the damage of MDA-MB-231 breast cancer cells. The result suggests that a lower-pressure shock wave with a longer duration, or multiple sequential low amplitude shock waves can be applied over a duration shorter than the fundamental response period of the cells to achieve the same impact as shock waves with a high peak pressure but a short duration. The finding that cell viability is better correlated with shock impulse rather than peak pressure has potential significant implications on how shock waves should be tailored for cancer treatments, enhanced drug delivery, and diagnostic techniques to maximize efficacy while minimizing potential side effects. [ABSTRACT FROM AUTHOR]

A study on the effects of Hurricane Katrina, which will help in safeguarding coastal construction, is presented.

It is important to understand and accurately predict the static and dynamic response and stability of flexible hydro/aero lifting bodies to ensure their structural safety, to facilitate the design/optimization of new/existing concepts, and to test the feasibility of using advanced materials. The present study investigates the influence of solid-to-fluid added mass ratio ([formula]) and viscous effects on the fluid-structure interaction (FSI) response and stability of a flapping foil in incompressible and turbulent flows using a recently presented efficient and stable numerical algorithm in time-domain, which couples an unsteady Reynolds Average Navier-Stokes solver with a two degrees-of freedom structural model. The new numerical coupling method is able to stably and accurately simulate the FSI behavior of light foils in dense fluids: a limit which is known to be numerically difficult to study with classical FSI coupling methods. The studied FSI responses include static/dynamic divergence and flutter instabilities, which are compared with inviscid, linear potential theory predictions obtained with both time and frequency domain formulations, as well as with several published experimental data. In general, the results show that the critical reduced flutter velocities and reduced divergence velocities both decrease as [formula] decreases, and are captured with good accuracy using the viscous FSI solver for a wide range of relative mass ratios that are typical to air/hydrofoils. The comparative analyses showed that the classic frequency-domain linear potential theory is severely unconservative for predicting the flutter velocity for cases with [formula]: this includes the typical operating conditions of most marine and biomedical lifting devices, where the fluid forces are comparable to the solid forces, and strong nonlinear interactions may develop. In addition, the viscous FSI solver is shown to correctly predict the experimentally reported critical divergence speed of a light foil in a dense fluid for a case where the classical potential theory predicts an infinite divergence speed as the foil's elastic axis (E.A.) coincided with the aerodynamic center. The results show that static/dynamic divergence will occur before flutter for light hydrofoils with an E.A. downstream of the center of pressure. However, for high solid-to-fluid added mass ratios ([formula]), flutter tends to occur prior to divergence. In addition, in between the regions governed by static divergence ([formula]) and flutter ([formula]), there is a dynamic divergence region, where the foil deformations oscillate with an increasing mean amplitude, and the oscillation frequency decreases toward zero as the deformation increases; this region could only be captured by using a viscous FSI solver. [ABSTRACT FROM AUTHOR]

Abstract: An understanding of the fundamental system dynamics of wave energy converters (WECs) is required to safely and reliably benefit from the available wave energy resource to produce electricity. The effects of the geometry, mooring system, and mass distribution on the idealized power takeoff of a tethered wave energy absorber in irregular waves are examined. The effects on coupled pitch and sway motions are also considered using a linear frequency-domain method, based on potential flow theory, to obtain the hydrodynamic coefficients. Superposition is used to calculate the response in irregular waves. The objectives of this paper are to examine the characteristic system response of WECs, and to demonstrate the use of an efficient potential-based method for the optimization of a WEC to maximize the annual power takeoff while ensuring system safety at a given site. The analyses suggest that the idealized power takeoff damping increases with the size of the WEC, with the intensity of motion limited. A relatively light mooring system has little effect on the power takeoff, but it introduces a low-frequency coupled pitch-surge resonance that can cause system failure if subject to long-period swells. To mitigate the risk of coupled surge-pitch related failures, a low center of gravity and a low radius of gyration of the floater about the center of floatation are recommended. The results also demonstrate the importance of tuning the system for the site-specific probabilistic wave climate in order to maximize total energy capture and avoid potential failures. [Copyright &y& Elsevier]

Electroactive polymers such as piezoelectric elements are able to generate electric potential differences from induced mechanical deformations. They can be used to build devices to harvest ambient energy from natural flow-induced deformations, e.g., as flapping flags subject to flowing wind or artificial seaweed subject to waves or underwater currents. The objectives of this study are to (1) investigate the transient hydroelastic response and energy harvesting potential of flexible piezoelectric beams fluttering in incompressible, viscous flow, and (2) identify critical non-dimensional parameters that govern the response of piezoelectric beams fluttering in viscous flow. The fluid-structure interaction response is simulated using an immersed boundary approach coupled with a finite volume solver for incompressible, viscous flow. The effects of large beam deformation, membrane tension, and coupled electromechanical responses are all considered. Validation studies are shown for the motion of a flexible filament in uniform flow, and for a piezoelectric beam subject to base vibration. The predicted flutter velocities and frequencies also compared well with published experimental and numerical data over a range of Reynolds numbers for varying fluid and solid combinations. The results showed that for a heavy beam in a light fluid (i.e., high βρ regime), flutter incepts at a lower critical speed with a lower reduced frequency than for a light beam in a heavy fluid (i.e., low βρ regime). In the high βρ regime, flutter develops at the second mode and is only realized when the fluid inertial forces are in balance with the solid elastic restoring forces, which leads to large amplitude oscillations and complex wake patterns; the flutter speed is practically independent of the Reynolds number (Re) and solid to fluid mass ratio (βρ), because the response is dominated by the solid inertial forces. In the low βρ regime, fluid inertial forces dominate, flutter develops at higher modes and is only realized when the solid inertial forces are proportioned to the solid elastic restoring forces; the flutter speed depends on both Re and βρ, and viscous force and beam tension effects tend to delay flutter and reduce vibration amplitudes, leading to thinner, more simplified wake patterns. The results demonstrate that energy extraction via fluttering piezoelectric beams is possible. The overall efficiency was observed to be influenced by the piezoelectric circuit resistance, which is known to be directly related to the square of the piezoelectric coupling factor. The results show that the maximum strain limit of piezoelectrics may be exceeded, and hence careful optimization of the material and geometry is recommended to maximize the energy capture for a given range of expected flow conditions while satisfying safety and reliability requirements. [ABSTRACT FROM AUTHOR]

The objective of this paper is to evaluate the predictive capability of three popular transport equation-based cavitation models for the simulations of partial sheet cavitation and unsteady sheet/cloud cavitating flows around a stationary NACA66 hydrofoil. The 2D calculations are performed by solving the Reynolds-averaged Navier-Stokes equation using the CFD solver CFX with the k-? SST turbulence model. The local compressibility effect is considered using a local density correction for the turbulent eddy viscosity. The calculations are validated with experiments conducted in a cavitation tunnel at the French Naval Academy. The hydrofoil has a fixed angle of attack of a = 6° with a Reynolds number of Re = 750,000 at different cavitation numbers s. Without the density modification, over-prediction of the turbulent viscosity near the cavity closure reduces the cavity length and modifies the cavity shedding characteristics. The results show that it is important to capture both the mean and fluctuating values of the hydrodynamic coefficients because (1) the high amplitude of the fluctuations is critical to capturing the extremes of the loads to ensure structural safety and (2) the need to capture the frequency of the fluctuations, to avoid unwanted noise, vibrations, and accelerated fatigue issues. [ABSTRACT FROM AUTHOR]

Hydrokinetic turbines extract energy from currents in oceans, rivers, and streams. Ducts can be used to accelerate the flow across the turbine to improve performance. The objective of this work is to couple an analytical model with a Reynolds averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) solver to evaluate designs. An analytical model is derived for ducted turbines. A steady-state moving reference frame solver is used to analyze both the freestream and ducted turbine. A sliding mesh solver is examined for the freestream turbine. An efficient duct is introduced to accelerate the flow at the turbine. Since the turbine is optimized for operation in the freestream and not within the duct, there is a decrease in efficiency due to duct-turbine interaction. Despite the decrease in efficiency, the power extracted by the turbine is increased. The analytical model under-predicts the flow rejection from the duct that is predicted by CFD since the CFD predicts separation but the analytical model does not. Once the mass flow rate is corrected, the model can be used as a design tool to evaluate how the turbine-duct pair reduces mass flow efficiency. To better understand this phenomenon, the turbine is also analyzed within a tube with the analytical model and CFD. The analytical model shows that the duct’s mass flow efficiency reduces as a function of loading, showing that the system will be more efficient when lightly loaded. Using the conclusions of the analytical model, a more efficient ducted turbine system is designed. The turbine is pitched more heavily and the twist profile is adapted to the radial throat velocity profile. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various research papers within the issue of the periodical on topics including design, numerical, and experimental modeling of marine propulsors and turbines.

The objective of this paper is to investigate cavitating flows around a pitching hydrofoil via combined physical and numerical studies. The aims are to (1) improve the understanding of the interplay between unsteady cavitating flow, hydrofoil motion, and hydrodynamic performance, (2) quantify the influence of pitching rate on subcavitating and cavitating responses, and (3) quantify the influence of cavitation on the hydrodynamic load coefficients and surrounding flow structures. Results are presented for a NACA66 hydrofoil undergoing controlled, slow (α=6°/s) and fast (α=63°/s) pitching motions from α = 0° to α = 15° and back to α = 0° for both subcavitating and cavitating conditions at a moderate Reynolds number of Re = 750 000. The experimental studies were conducted in a cavitation tunnel at the French Naval Academy, France. The numerical simulations are performed by solving the incompressible, multiphase Unsteady Reynolds-Averaged Navier-Stokes Equations via the commercial code CFX using a transport equation-based cavitation model; a modified k-ω SST turbulence model is used to account for the effect of local compressibility on the turbulent eddy viscosity. The results showed that increases in the pitching rate suppressed laminar to turbulent transition, delayed stall, and significantly modified post-stall behavior. Cavitation inception at the leading edge modified the pressure distribution, which in turn significantly changed the interaction between leading edge and trailing edge vortices, and hence the magnitude as well as the frequency of the load fluctuations. For a fixed cavitation number, increases in pitching rate lead to increase in cavitation volume, which in turn changed the cavity shedding frequencies and significantly modified the hydrodynamic loads. Inversely, the leading edge cavitation observed for the low pitching velocity case tends to stabilize the stall because of the decrease of the pressure gradient due to the formation of the cavity. The results showed strong correlation between the cavity and vorticity structures, which suggest that the inception, growth, collapse and shedding of sheet/cloud cavities are important mechanisms for vorticity production and modification. [ABSTRACT FROM AUTHOR]

Hydrodynamic lifting surfaces usually include junctions. High-fidelity simulations are necessary to capture critical physics near these regions, such as separation, junction vortices, and cavitation. We present RANS-based hydrodynamic optimizations of a T-shaped hydrofoil, including changes in the junction geometry. The optimized hydrofoils avoid separation and delay cavitation compared to the baseline. The full optimization design with planform, cross-section, and junction geometry variables yields a total drag reduction of 6.4%. The optimized results show that the relative locations of the maximum foil thickness and the maximum strut thickness significantly impact the junction cavitation. Including the translation between the strut and the foil and more strut geometric variables as design variables will provide further improvement. The comparison between optimized designs demonstrates that optimizing planform and detailed junction geometry provides further improvement in addition to designing the cross-sectional geometry. The hydrostructural analyses show that the optimized T-foils have lower stress at the junction than the baseline because of the resultant junction fairing. However, these hydrodynamic-only optimized T-foils have higher deformation and maximum stress, which could result in accelerated fatigue, highlighting the need for hydrostructural responses in design optimization. The results demonstrate that the developed methodology is useful for designing next-generation complex hydrodynamic lifting surfaces. • Optimization is effective in designing hydrodynamic lifting surfaces with junctions. • Multipoint optimization reduces drag, delays cavitation, and avoids separation. • Planform and junction shape impact cavitation and separation performance. • Hydrostructural response consideration is needed to avoid accelerated fatigue. [ABSTRACT FROM AUTHOR]

This paper introduces a control scheme to vector thrust in marine cycloidal propellers with non-zero forward speed, despite the presence of measurement noise and current-like disturbances. Cycloidal propellers utilize 360° thrust-vectoring to provide agile maneuvering to surface vessels like tugboats and double ended ferries, but have yet to be utilized in present-day unmanned and autonomous marine vehicles. This work strategizes a low-level cycloidal propeller controller to track a reference thrust magnitude and direction for use in high-level control of underwater vehicles. Unlike previous work that assumes zero inflow-speed, the propeller-shaft speed and propeller-blade phase are hydrodynamically coupled in cases with non-zero inflow. The incorporation of this coupling enables thrust-tracking over varying advance-speeds necessary for propulsion and maneuvering of unmanned and autonomous underwater vehicles. A torque controller for screw propellers is extended for thrust-tracking in cycloidal propellers. A propeller-phase control loop is added and the resultant controller is verified through simulations for 360° thrust vectoring of cycloidal propellers in currents and varying cruise speeds. This low-level controller will enable use of cycloidal propellers for high maneuverability and thrust-augmentation in applications like station-keeping, seakeeping, maneuvering, and teaming of unmanned and autonomous marine vehicles in complex marine environments like surf zones and restricted waters. • A novel control scheme to vector thrust of marine cycloidal propellers is presented. • Hydrodynamic coupling between propeller-speed and phase angle is highlighted. • Measurement noise and disturbances like water currents are considered. • High maneuverability and high control authority of underwater vehicles in restricted waters can be achieved. [ABSTRACT FROM AUTHOR]

Accurate estimation of a surface vessel's added power in waves is essential to ensure efficient and safe operations. Propeller–hull interactions play significant roles in added power and are dominated by viscous effects. Therefore, numerical simulations of added power require the use of a Navier–Stokes based solver to account for viscous effects. To reduce the computational cost, the propeller is often modeled using an actuator disk, and hybrid techniques can be employed using potential flow methods. However, such approximations may not capture the nonlinear and viscous propeller–hull interactions in waves. On the other hand, reduced-scale experiments of added power are complicated by scaling effects because the Reynolds number is typically several orders of magnitude lower than that for full scale, and the higher relative contribution of viscous effects at model scale leads to over estimation of the added power. The objective of this work is to study the role of propeller–hull interactions in waves, related scaling effects, and numerical challenges. The results show that added power is not simply a linear function of the added resistance or the incoming wave amplitude squared because of complex propeller–hull interactions in waves. Moreover, the over prediction of added power increases with smaller model size. • Propeller–hull interactions in waves have a significant role in added power. • Nonlinear hydrodynamic and viscous effects have a significant role in added power. • Added power coefficient is nonlinearly dependent on wave elevation squared. • Added power coefficient is increasingly overpredicted with model size reduction. • Added power is overpredicted using an ideal axisymmetric disk loading distribution. [ABSTRACT FROM AUTHOR]