Nonlinear Hydrodynamic Model Research Articles

Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability

Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.

Models of the formation of roughness on the surface of materials and the movement of molten flows under the laser melting processes

We used the nonlinear hydrodynamic model of the motion of molten flows to determine the basic geometric characteristics of the resulting coatings in a laser experiment. To test the capabilities of the developed algorithm, a series of calculations was performed for various values of Reynolds numbers (Re) and certain sizes of the computational domains with several cavities with different configurations. The influence of the channel geometry is clearly noticeable in the case of a deep depression. The direction of motion of different structures (e.g. the vortex) was predicted. Using the convection model, we estimate the temperature field and velocity distribution in the system under consideration for various initial conditions and experimental regimes selected. The profile of the arising island on the surface was modeled by a scaling computational domain with the number of particles N = pS, where the parameter p – determined the viscosity of melted material, and S - the area of the computational domain. The influences of the two key parameters, i.e. probability of adhesion (sc) and viscosity (p), on the obtained surface profile of materials can be estimated by our approach, and result in different deposition images, being finally principal for functional characteristics of the samples under the specific regimes of laser treatment.

Numerical investigation of parametric resonance due to hydrodynamic coupling in a realistic wave energy converter

Representative models of the nonlinear behavior of floating platforms are essential for their successful design, especially in the emerging field of wave energy conversion where nonlinear dynamics can have substantially detrimental effects on the converter efficiency. The spar buoy, commonly used for deep-water drilling, oil and natural gas extraction and storage, as well as offshore wind and wave energy generation, is known to be prone to experience parametric resonance. In the vast majority of cases, parametric resonance is studied by means of simplified analytical models, considering only two degrees of freedom (DoFs) of archetypical geometries, while neglecting collateral complexity of ancillary systems. On the contrary, this paper implements a representative 7-DoF nonlinear hydrodynamic model of the full complexity of a realistic spar buoy wave energy converter, which is used to verify the likelihood of parametric instability, quantify the severity of the parametrically excited response and evaluate its consequences on power conversion efficiency. It is found that the numerical model agrees with expected conditions for parametric instability from simplified analytical models. The model is then used as a design tool to determine the best ballast configuration, limiting detrimental effects of parametric resonance while maximizing power conversion efficiency.

Plasmon enhanced second harmonic generation by periodic arrays of triangular nanoholes coupled to quantum emitters

Optical properties of periodic arrays of nanoholes of a triangular shape with experimentally realizable parameters are examined in both linear and nonlinear regimes. By utilizing a fully vectorial three-dimensional approach based on the nonlinear hydrodynamic Drude model describing metal coupled to Maxwell's equations and Bloch equations for molecular emitters, we analyze linear transmission, reflection, and nonlinear power spectra. Rigorous numerical calculations demonstrating second and third harmonic generation by the triangular hole arrays are performed. It is shown that both the Coulomb interaction of conduction electrons and the convective term contribute on equal footing to the nonlinear response of metal. It is demonstrated that the energy conversion efficiency in the second harmonic process is the highest when the system is pumped at the localized surface plasmon resonance. When molecular emitters are placed on a surface of the hole array line shapes, the second harmonic signal exhibits three peaks corresponding to second harmonics of the localized surface plasmon mode and upper and lower polaritonic states.

Fast data assimilation for open channel hydrodynamic models using control theory approach

Model-driven forecasting, used for flood risks or big hydropower systems management, can produce results of unsatisfying accuracy even with best-calibrated hydrodynamic models. One of the biggest uncertainty sources is the inflow data, either produced by different hydrological models or obtained using unreliable rating curves. To keep the model in the up-to-date state, data assimilation techniques are used. The aim of the assimilation is to reduce the difference between simulated and observed state of selected variables by updating hydrodynamic model state variables according to observed water levels. The widely used data assimilation method applicable for nonlinear hydrodynamic models is Ensemble Kalman Filter (EnKF). However, this method can often increase the computational time due to complexity of mathematical apparatus, making it less applicable in everyday operations. This paper presents the novel, fast, tailor-made data assimilation method, suitable for 1D open channel hydraulic models, based on control theory. Using Proportional-Integrative-Derivative (PID) controllers, the difference between measured levels and simulated levels obtained by hydrodynamic model is reduced by adding or subtracting the flows in the junctions/sections where water levels are measured. The novel PID control-based data assimilation (PID-DA) is compared to EnKF. Benchmarking shows that PID-DA can be used for data assimilation, even coupled with simplified 1D hydraulic model, without significant sacrifice of stability and accuracy, and with reduction of computational time up to 63 times.

Linear and nonlinear hydrodynamic models for dynamics of a submerged point absorber wave energy converter

This study compares the response of a submerged CETO-shaped point absorber wave energy converter using linear, partially-nonlinear, pseudo-nonlinear, and fully-nonlinear methods to model hydrodynamic effects. Linear potential flow models calculate hydrodynamic parameters to represent the fluid-structure interaction; typical dynamic models apply these parameters without pose-dependence. The partially-nonlinear method evaluates excitation forces at different poses to introduce a pose-dependent excitation force; in addition to the excitation force, the pseudo-nonlinear method calculates hydrodynamic coefficients using linear potential flow methods and includes pose-dependence through interpolating pre-calculated parameters to represent the radiation force. The fully-nonlinear CFD model is a numerical wave tank validated against published data. The applicability of linear-based methods has been explored by comparing the motion, force, and power of the system under various operating conditions against the fully-nonlinear results. It was expected that for low amplitude waves results tend towards the linear results; however, for both low amplitude waves and increased submergence depth, linear methods provided poor representations of the nonlinear CFD results. Geometric nonlinearities were insufficient to capture all the nonlinear behaviour. A frequency-dependent nonlinearity was identified in the water above the buoy resonating. For such submerged point absorbers, linear methods do not adequately represent the influential nonlinear effects.

Analysis of circulation near the coast of Western Crimea and the region of Sevastopol with assimilation of temperature and salinity observations

Hydrophysical fields which are continuous in time and space are reconstructed in the coastal zone of the Black Sea (near the coast of Western Crimea and the region of Sevastopol) by a three-dimensional nonlinear hydrodynamic model with assimilation of observational data of the 2007 hydrological survey. A sequential optimal interpolation of temperature and salinity observations is used as the assimilation procedure. We use real atmospheric forcing and a high resolution (a horizontal grid of ~1.6×1.6 km and 31 vertical layers from 1 m to 1300 m). Mesoscale features of the currents are obtained, and coastal upwelling in the Kalamitsky Bay is reconstructed and registered in satellite observations.

Temporal and Topographic Source Effects on Tsunami Generation

AbstractWe present a systematic study of the influence on tsunami waves generated by the uplift of a rectangular plug, of the rise time of the deformation, and of its topographic details (e.g., the presence of a sill). We are motivated by the fact that most simulation codes use an instantaneous deformation of a flat ocean floor as an initial condition of the problem, although Hammack (1973, http://resolver.caltech.edu/CaltechAUTHORS:HAMjfm73) performed pioneering laboratory studies as well as analytical computations featuring variable rise times. Here, we consider three 2‐D source shapes, including a flat seafloor, a simple elevated piston, and additional trapezoidal sill on top of it, all with variable rise times, and simulate the resulting waves using the fully nonlinear smooth particle hydrodynamic model graphics processing unit smooth particle hydrodynamic. We validate our results against Hammack's (1973) laboratory measurements and analytical results. We find that a relatively large sill, with height and width of more than half of the local depth and width of the source, has a profound effect on the spatiotemporal structure of the generated free surface wavefield. Specifically, we show that the maximum water surface elevation over the source region is not always the same as the bottom displacement, as assumed in most tsunami propagation models. Next, we obtain simple scaling relationships to predict the maximum height of the generated tsunami over and outside the source, based on the geometry of the sill and the nondimensional bed rise time. Last, we show that inertial effects may lead to an initial free surface displacement over the generation region greater than the maximum vertical displacement of the displaced seabed.

Energeticheskie harakteristiki tsirkulyatsii vod Mramornogo morya v 2008 godu

Purpose. The main objectives of the study consisted in analyzing the Marmara Sea energy and in identifying the basic reasons for formation of its circulation features in 2008. Methods and Results. The numerical experiment on modeling the Marmara Sea circulation and evaluating its energy characteristics on the example of 2008 was carried out based on the eddy-resolving nonlinear hydrodynamic model of Marine Hydrophysical Institute, RAS. The horizontal resolution of the model was 1.22 × 0.83 km, 18 horizons were used over vertical and the time step was 0.5 min. Temperature, salinity and water discharge through the Bosporus and the Dardanelles were preset according to the available measurement data. The applied fields of atmospheric forcing were obtained from the calculation by the regional atmospheric model MM5. The volume-integrated and yearaveraged contributions of the terms in the equations of the kinetic and potential energy budgets were analyzed. The basic factors of change in the Marmara Sea kinetic energy consisted in the buoyancy force action, wind, and vertical and horizontal mixing. Having been analyzed, the volume-average summands in the equation of rate of the kinetic energy change have shown that the wind-induced energy influx was compensated mainly by vertical friction, and the buoyancy force action – by horizontal friction. On the average, in course of a year the potential energy changed mainly due to its horizontal transport conditioned by the effect of the currents located in front of the straits, vertical diffusion and the buoyancy force impact. The results of analysis of the energy transitions permitted to reveal that in the upper sea layer, the mesoscale vortices were formed directly under the wind influence and as a result of the currents’ baroclinic instability. Generation of the sub-mesoscale vortices in the coastal regions was affected predominantly by the processes of baroclinic instability. In the region near the Bosporus, increase of the horizontal gradients in the density field and, consequently, intensification of dynamic processes are the results of inflow of the Black Sea waters with lower density. Conclusions. Study of the energy characteristics of the Marmara Sea water circulation permitted to conclude that baroclinic instability and wind are two of the basic sources of eddy formation in this basin.

Dynamic characteristics of water-lubricated journal bearings

The increasing ecological awareness and stringent requirements for environmental protection have led to the development of water lubricated journal bearings. For the investigation of water-lubricated journal bearings, a new structured mesh movement algorithm for the CFD model is developed and based on this method, the nonlinear transient hydrodynamic force model is established. Then, with consideration of velocity perturbation, a method to determine dynamic coefficients and linear hydrodynamic forces is promoted. After validation of static equilibrium position and stiffness coefficients, a comparative linear and nonlinear hydrodynamic force analysis of multiple grooves water-lubricated journal bearings (MGWJBs) is conducted. The calculation results indicate that the structured mesh movement algorithm is suitable for the dynamic characteristics investigation of water-lubricated journal bearings. And the comparative study shows that there is a considerable difference between the linear and nonlinear hydrodynamic forces of MGWJBs. Further investigation should be carried to evaluate the dynamic responses of rotor supported by MGWJBs under difference force models.

Wave‐current interaction effects on structural responses of floating offshore wind turbines

AbstractThis paper proposes a model considering the wave‐current interactions in dynamic analyses of floating offshore wind turbines (FOWTs) and investigates the interaction effects on the FOWT responses. Waves when traveling on current are affected by the current, leading to frequency shift and shape modification. To include such interactions in FOWT analysis, which has not been considered by the researchers till date, a nonlinear hydrodynamic model for multicable mooring systems is presented that is able to consider the cable geometric nonlinearity, seabed contact, and the current effect. The mooring model is then coupled with a spar‐type FOWT model that handles the structural dynamics of turbine blades and tower, aerodynamics of the wind‐blade interaction, and wave‐current effects on the spar. The analytical wave‐current interaction model based on Airy theory considering the current effect is used in the computation of flow velocity and acceleration. Numerical studies are then carried out based on the NREL offshore 5‐MW baseline wind turbine supported on top of the OC3‐Hywind spar buoy. Two cases, (1) when the currents are favorable and (2) when the currents are adverse, are examined. Differences of up to 15% have been observed by comparing the cable fairlead tension obtained excluding and including the wave‐current interactions. In particular, when irregular waves interact with adverse current, a simple superposition treatment of the wave and the current effects seems to underestimate the spar motion and the cable fairlead tension. This indicates that the wave‐current interaction is an important aspect and is needed to be considered in FOWT analysis.

Application of kinetic flux vector splitting scheme for solving viscous quantum hydrodynamical model of semiconductor devices

Abstract In this article, one-dimensional viscous quantum hydrodynamical model of semiconductor devices is numerically investigated. The model treats the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. The nonlinear viscous quantum hydrodynamic models contain Euler-type equations for density and current, viscous and quantum correction terms, and a Poisson equation for electrostatic potential. Due to high nonlinearity of model equations, numerical solution techniques are applied to obtain their solutions. The proposed numerical scheme is a splitting scheme based on the kinetic flux-vector splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct splitting of macroscopic flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the splitting scheme based on the NT central scheme. The effects of various parameters such as device length, viscosities, different doping and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations.

Surface plasmons modulated by ferromagnetic insulating layers on the surface of topological insulator

We study the spin-polarized surface plasmons on the surface of a three-dimensional topological insulator. The surface of the topological insulator is modulated by a pulsed exchange field provided by an array of ferromagnetic insulating (FI) stripes. A nonlinear quantum hydrodynamic model is adopted and solved self-consistently, in the presence of the quantum statistical effect and the spin effect. The exchange field can form and sustain the periodic polarization of the surface plasmons under a laboratory magnetic field condition. The nonlinear effect and increasing exchange field strength enhance the surface plasmon polarization. The quantum statistical effect inhibits the surface plasmon polarization. Different spin state leads to different sign of collective density polarization.

Critical assessment of non-linear hydrodynamic load models for a fully flexible monopile offshore wind turbine

This paper presents a comparison between experimental data of a model-scale 4 MW monopile offshore wind turbine subjected to extreme irregular sea states in finite water and the numerical models suggested in offshore wind energy standards to assess ULS conditions. The model is fully flexible with its 1st and 2nd eigenfrequencies and 1st mode shape tuned to fit those of the full-scale turbine. The measured and simulated bending moments at the sea bottom are decomposed around the eigenfrequencies of the structure, and the Morison equation with stream function wave kinematics is found to trigger transient 1st mode response (so-called ringing response). The amplitude of the simulated 1st mode response is proportional to the incoming wave steepness; such a relationship is not observed experimentally. Similarly, 2nd mode response is triggered by Wienke's slamming model, but generally does not match the experimental data. Although the numerical models from the design standards (Morison's equation with stream function kinematics, plus a slamming model) can give conservative estimates of the extreme responses, the models miss the balance between 1st and 2nd mode responses. The simplification of the physics in the numerical models can thus lead to inaccuracies in response prediction, such as the stress distribution along the monopile.

A coupled finite difference mooring dynamics model for floating offshore wind turbine analysis

This study develops a coupled nonlinear hydrodynamic model of a mooring system consisting of multiple cables for analyses of floating offshore wind turbines (FOWTs). The model is based on a finite difference model of submerged cables which considers cable-seabed interaction, current effect, cable bending and torsional stiffness. The implementation of the model proposes a parallelization scheme for solving the cable responses to improve the computational efficiency. The developed program is then coupled with a spar type FOWT and verified using an experimentally validated open source mooring simulation program. Furthermore, the model is used to study the impact of nonlinear dynamics of the mooring system on FOWT responses in the presence of current. Both static responses of a spar FOWT under current load and dynamic responses of the spar FOWT under wind, wave and current loads are investigated. Responses are compared where varied mooring models are used including the linear model, quasi-static model and nonlinear mooring models without and with current effect on cables considered. The results show that the current effect on cables can have a considerable impact on the restoring effect of the mooring system and hence the spar and cable responses. The current effect on mooring cables needs to be properly considered in the FOWT analysis.

Numerical Analysis of Surge Phenomena, Currents, and Pollution Transport in the Sea of Azov

Dynamic processes and features of transformation of pollution in the Sea of Azov, caused by the action of a real wind and atmospheric pressure in the presence of stationary currents, are studied using a three-dimensional nonlinear hydrodynamic model. On the basis of numerical calculations, conclusions are reached about the influence of the velocities of stationary background currents on maximal deviations and the velocities of nonstationary currents generated by wind fields in the SKIRON model. It is shown that the combined effect of the constant wind and wind in the SKIRON atmospheric model leads to a significant expansion of the polluted area and to a longer dispersion time compared to the effects of solely stationary currents.

Valley-polarized edge pseudomagnetoplasmons in graphene: A two-component hydrodynamic model

By means of a nonlinear two-component hydrodynamic model, we study the valley-polarized collective motion of electrons in a strained graphene sheet. The self-consistent numerical solution in real space indicates the existence of valley-polarized edge plasmons due to a strain-induced pseudomagnetic field. The valley polarization of the edge pseudomagnetoplasmon can occur in a specific valley, depending on the pseudomagnetic field and the electron density in equilibrium. A full valley polarization is achieved at the edge of the graphene sheet for a pseudomagnetic field of tens of Tesla, which is a realistic value in current experimental technologies.

Computational Fluid Dynamics simulations of the Late Pleistocene Lake Bonneville Flood

At approximately 18.0 ka, pluvial Lake Bonneville reached its maximum level. At its northeastern extent it was impounded by alluvium of the Marsh Creek Fan, which breached at some point north of Red Rock Pass (Idaho), leading to one of the largest floods on Earth. About 5320 km3 of water was discharged into the Snake River drainage and ultimately into the Columbia River. We use a 0D model and a 2D non-linear depth-averaged hydrodynamic model to aid understanding of outflow dynamics, specifically evaluating controls on the amount of water exiting the Lake Bonneville basin exerted by the Red Rock Pass outlet lithology and geometry as well as those imposed by the internal lake geometry of the Bonneville basin. These models are based on field evidence of prominent lake levels, hypsometry and terrain elevations corrected for post-flood isostatic deformation of the lake basin, as well as reconstructions of the topography at the outlet for both the initial and final stages of the flood. Internal flow dynamics in the northern Lake Bonneville basin during the flood were affected by the narrow passages separating the Cache Valley from the main body of Lake Bonneville. This constriction imposed a water-level drop of up to 2.7 m at the time of peak-flow conditions and likely reduced the peak discharge at the lake outlet by about 6%. The modeled peak outlet flow is 0.85·106 m3 s−1. Energy balance calculations give an estimate for the erodibility coefficient for the alluvial Marsh Creek divide of ∼0.005 m y−1 Pa−1.5, at least two orders of magnitude greater than for the underlying bedrock at the outlet. Computing quasi steady-state water flows, water elevations, water currents and shear stresses as a function of the water-level drop in the lake and for the sequential stages of erosion in the outlet gives estimates of the incision rates and an estimate of the outflow hydrograph during the Bonneville Flood: About 18 days would have been required for the outflow to grow from 10% to 100% of its peak value. At the time of peak flow, about 10% of the lake volume would have already exited; eroding about 1 km3 of alluvium from the outlet, and the lake level would have dropped by about 10.6 m.

Plasmonic modes in nanowire dimers: A study based on the hydrodynamic Drude model including nonlocal and nonlinear effects

A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a Discontinuous Galerkin Time-Domain approach and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, second-harmonic generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interprete the physical mechanisms that lead to corresponding field distributions, the associated linear quasi-electrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes, both in the linear and the nonlinear regime. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nano-antenna systems.

Influences of the separation distance, ship speed and channel dimension on ship maneuverability in a confined waterway

Ship maneuvering in the confined inland waterway is investigated using the system-based method, where a nonlinear transient hydrodynamic model is adopted and confinement models are implemented to account for the influence of the channel bank and bottom. The maneuvering model is validated using the turning circle test, and the confinement model is validated using the experimental data. The separation distance, ship speed, and channel width are then varied to investigate their influences on ship maneuverability. With smaller separation distances and higher speeds near the bank, the ship's trajectory deviates more from the original course and the bow is repelled with a larger yaw angle, which increase the difficulty of maneuvering. Smaller channel widths induce higher advancing resistances on the ship. The minimum distance to the bank are extracted and studied. It is suggested to navigate the ship in the middle of the channel and with a reasonable speed in the restricted waterway.