Nonlinear Computational Fluid Dynamics Research Articles

Non-Fourier computations of heat and mass transport in nanoscale solid-fluid interactions using the Galerkin finite element method

PurposeTo improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and development of models. The thermal performance of sample fluids is compared to determine which types of combination of nanoparticles are the best for an optimized enhancement in thermal performance of fluids. This article aims to: (i) investigate the impact of nanoparticles on thermal performance; and (ii) implement the Galerkin finite element method (GFEM) to thermal problems.Design/methodology/approachThe mathematical models are developed using novel non-Fourier heat flux theory, conservation laws of computational fluid dynamics (CFD) and no-slip thermal boundary conditions. The models are approximated using thermal boundary layer approximations, and transformed models are solved numerically using GFEM. A grid-sensitivity test is performed. The accuracy, correction and stability of solutions is ensured. The numerical method adopted for the calculations is validated with published data. Quantities of engineering interest, i.e. wall shear stress, wall mass flow rate and wall heat flux, are calculated and examined versus emerging rheological parameters and thermal relaxation time.FindingsThe thermal relaxation time measures the ability of a fluid to restore its original thermal state, called thermal equilibrium and therefore, simulations have shown that the thermal relaxation time associated with a mono nanofluid has the most substantial effect on the temperature of fluid, whereas a ternary nanofluid has the smallest thermal relaxation time. A ternary nanofluid has a wider thermal boundary thickness in comparison with base and di- and mono nanofluids. The wall heat flux (in the case of the ternary nanofluids) has the most significant value compared with the wall shear stresses for the mono and hybrid nanofluids. The wall heat and mass fluxes have the highest values for the case of non-Fourier heat and mass diffusion compared to the case of Fourier heat and mass transfer.Originality/valueAn extensive literature review reveals that no study has considered thermal and concentration memory effects on transport mechanisms in fluids of cross-rheological liquid using novel theory of heat and mass [presented by Cattaneo (Cattaneo, 1958) and Christov (Christov, 2009)] so far. Moreover, the finite element method for coupled and nonlinear CFD problems has not been implemented so far. To the best of the authors’ knowledge for the first time, the dynamics of wall heat flow rate and mass flow rate under simultaneous effects of thermal and solute relaxation times, Ohmic dissipation and first-order chemical reactions are studied.

Utilizing global-local neural networks for the analysis of non-linear aerodynamics

In addressing the computational challenges pervasive in engineering where time and cost limitations are key concerns, particularly within the Computational Fluid Dynamics (CFD) domain, Reduced Order Models (ROMs) have emerged as instrumental tools. Focused on reducing computational complexity without intrusively modifying the computational model, this study centres on the strategic application of aerodynamic ROMs, which provide efficient computation of distributed quantities and aerodynamic forces. This work presents ROMs for non-linear aerodynamic applications, integrating principal component analysis (PCA) with Global Local Neural Networks (GLNN). The effectiveness of the proposed methodology is demonstrated by leveraging dependency on the parameter space created with non-linear high-fidelity CFD data, incorporating viscous simulation for a comprehensive approach. Results are first presented for a two-dimensional airfoil case and then for a three-dimensional test case featuring a transonic wing-body-tail transport aircraft configuration (NASA Common Research Model). In transonic flows, the proposed ROMs demonstrate the ability to accurately capture both the location and strength of shocks, as well as forces and moments for unseen prediction points. This highlights the efficiency of the proposed method in navigating complex aerodynamic scenarios, achieving comparable accuracy to full-order modelling but at orders of magnitude less computational time, for unseen parameters outside the ROM training set within the parameter space.

Fully Parabolized Hypersonic Sonic Boom Prediction with Real Gas and Viscous Effects

We present a methodology to predict the aerodynamic near-field and sonic boom signature from slender bodies and waveriders using a fully parabolized approach. We solve the parabolized Navier–Stokes equations, which are integrated via spatial marching in the streamwise direction. We find that unique physics must be accounted for in the hypersonic regime relative to the supersonic, which includes viscous, nonequilibrium, and real gas effects. The near-field aerodynamic pressure is propagated through the atmosphere to the ground via the waveform parameter method. To illustrate the approach, three bodies are analyzed: the Sears–Haack geometry, the HIFiRE-5, and a power-law waverider. Ambient Mach numbers range from 4 through 15. The viscous stress tensor is essential for accurate hypersonic prediction. For example, viscous effects increase near-field and sonic boom overpressure by 15.7 and 8.49%, respectively, for the Sears–Haack geometry. The difference between viscous and inviscid predictions of the near-field is due to the hypersonic boundary layer. The computational cost for predicting the near-field is approximately 6.6% relative to fully nonlinear computational fluid dynamics.

An analytical linear two-dimensional actuator disc model and comparisons with computational fluid dynamics (CFD) simulations

Abstract. The continuous up-scaling of wind turbines enabled by more lightweight and flexible blades in combination with coning has challenged the assumptions of a plane disc in the commonly used blade element momentum (BEM)-type aerodynamic codes for the design and analysis of wind turbines. The objective with the present work is thus to take a step back relative to the integral 1-dimensional (1-D) momentum theory solution in the BEM model in order to study the actuator disc (AD) flow in more detail. We present an analytical, linear solution for a two-dimensional (2-D) AD flow with one equation for the axial velocity and one for the lateral velocity, respectively. Although it is a 2-D model, we show in the paper that there is a good correlation with axis-symmetric and three-dimensional (3-D) computational fluid dynamics (CFD) simulations on a circular disc. The 2-D model has thus the potential to form the basis for a simple and consistent rotor induction model. For a constant loading, the axial velocity distribution at the disc is uniform as in the case of the classical momentum theory for an AD. However, an important observation of the simulated flow field is that immediately downstream of the disc the axial velocity profiles change rapidly to a shape with increased induction towards the edges of the disc and less induction on the central part. This is typically what is seen at the disc in full non-linear CFD AD simulations, which is what we compare with in the paper. By a simple coordinate rotation the analytical solution is extended to a yawed disc with constant loading. Again, a comparison with CFD, now with a 3-D simulation on a circular disc in yaw, confirms a good performance of the analytical 2-D model for this more complicated flow. Finally, a further extension of the model to simulate a coned disc is obtained using a simple superposition of the solution of two yawed discs with opposite yaw angles and positioned so the two discs just touch each other. Now the validation of the model is performed with results from axis-symmetric CFD simulations of an AD with a coning of both 20 and −20∘. In particular, for the disc coned in the downwind direction there is a very good correlation between the simulated normal velocity to the disc, whereas some deviations are seen for the upwind coning. The promising correlation of the results for the 2-D model in comparison with 3-D simulations of a circular disc with CFD for complicated inflow like what occurs at yaw and coning indicates that the 2-D model could form the basis for a new, consistent rotor induction model. The model should be applied along diagonal lines on a rotor and coupled to an angular momentum model. This application is sketched in the outlook and is a subject for future research.

Active longitudinal motion control research of waterjet-propelled trimaran in random waves using direct CFD approach integrated with auto-control algorithm

The current numerical method for ship motion control primarily relies on mathematical ship models that require solving hydrodynamic derivatives. In this paper, a fully nonlinear viscous computational fluid dynamics (CFD) model integrated with motion control strategies on an appendage was proposed to directly investigate the longitudinal motion control problem in random waves. The longitudinal motion control model was established on a free-running waterjet-propelled trimaran CFD model by combining a speed controller on the propulsor and attitude motion controller on the stern flap appendage. Through direct CFD simulations in random waves, the motion control capability of the stern flap under different control strategies, including fixed, linear, and PID controllers, was evaluated. The results show that the PID controller is superior and achieves a mean trough reduction of the pitch and heave by 22.3% and 15.6%, respectively. Subsequently, the longitudinal motion control capability of the stern flap under different lengths, traveling speeds, and sea states was numerically researched. The results indicate that as the speed and sea state increase, the pitch control effects of the stern flap on the trimaran appear to be saturated and mainly affected by the limited motion control force and moment. Thus by using joint control with other appendages, better longitudinal motion stability could be achieved. The proposed model provides a direct evaluation method for controlling ship motion by appendages in waves and accounts for complex hull shapes, nonlinear environments, and real-time hydrodynamic feedback.

Uncertainty Quantification of Compressor Map Using the Monte Carlo Approach Accelerated by an Adjoint-Based Nonlinear Method

Precise and inexpensive uncertainty quantification (UQ) is crucial for robust optimization of compressor blades and to control manufacturing tolerances. This study looks into the suitability of MC−adj−nonlinear, a nonlinear adjoint-based approach, to precisely and rapidly assess the performance discrepancies of a transonic compressor blade section, arising from geometric alterations, and building upon previous research. In order to assess the practicality and illustrate the benefits of the adjoint-based nonlinear approach, its proficiency and precision are gauged against two other methodologies, the adjoint-based linear approach (MC−adj−linear) and the high-fidelity nonlinear Computational Fluid Dynamics (MC−CFD) method. The MC−adj−nonlinear methodology exhibits impressive generalization capabilities. The MC−adj−nonlinear method offers a great balance between precision and time efficiency, since it is more precise than the MC−adj−linear method in both design and near-stall conditions, yet requires approximately a thirtieth of the time of the MC−CFD method. Finally, the MC−adj−nonlinear method was utilized to conduct fast UQ analyses of the section at four distinct speeds to quantify the performance uncertainty for the compressor map. It is found that aerodynamic performance is more sensitive to geometric deviations at high speeds than at low speeds. The impact of the geometric deviations is generally detrimental to the mean efficiency.

A Review of Solution Stabilization Techniques for RANS CFD Solvers

Nonlinear, time-linearized and adjoint Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solvers are widely used to assess and improve the aerodynamic and aeroelastic performance of aircrafts and turbomachines. While RANS CFD solver technologies are relatively mature for applications at design conditions where the flow is benign, their use in off-design conditions, featuring flow instabilities, such as separations and shock wave/boundary layer interactions, still faces many challenges, with tight residual convergence being a major difficulty. To cope with this, several solver stabilization techniques have been proposed. However, a systematic and comparative study of these techniques has not been reported, to some extent hindering the wide deployment of these methods for industrial applications. In this paper, we critically review the existing methods for solver convergence stabilization, with the main purpose of explaining the rationale behind the algorithms and providing a systematic view of the seemingly different methods. Specifically, mathematical formulations and implementation details of these methods, example applications, and the pros and cons of the methods are discussed in detail, along with suggestions for further improvements. This review is expected to give CFD method developers an overview of the various solution stabilization methods and application engineers an idea how to choose a suitable method for their respective applications.

Representative linearised models for a wave energy converter using various levels of force excitation

In guiding the progression, development, and operation of wave energy converters (WECs) in a more efficient way, mathematical analysis and understanding of the dynamic process is essential. Mathematical WEC models, obtained either by numerical analysis or physical modelling, form the basis of most (model-based) energy maximising control strategies available in the literature, where experimental design and system identification methodology directly impact the resulting model. This study, using an experimental-based WEC model (which can be used for linear control design), investigates the dynamic behaviour of a WEC by analysing the dominant poles of the system, generated using fully nonlinear computational fluid dynamics (CFD)-based numerical wave tank (NWT) experiments. The aim is to effectively track the dominant dynamics of the WEC, using different force-input amplitude levels in the NWT setup, and perform a comparison with the classical linear boundary-element-methods (BEM) equivalent methodology. Thus, the presented case studies are shown to agree with previously proposed model assessment of linear WEC models, based on a free-decay NWT setup. In addition, the representative WEC models determined as part of this study can be used for WEC controller design, either singly, or using a form of model/controller gain scheduling.

Multi-objective Bayesian hull form optimisation for high-speed craft

Simulation-based design plays an important role in many engineering fields enabled by advancements in computing resources, numerical algorithms and computer aided engineering software. In naval architecture, it opens new opportunities for improving hull form designs by reducing calm water resistance and hence minimising required propulsive energy. In this paper, we propose a low dimensional shape morphing tool suitable for designing novel and realistic hull forms for high-speed craft. We provide an efficient simulation-based design framework for optimising hull forms across multiple operating conditions by taking advantage of a multi-objective Bayesian optimisation method. We demonstrate the proposed framework for optimising the hull form of a conceptual high-speed catamaran at two speeds, corresponding to Froude numbers of Fr=0.35 and Fr=0.65. The results highlight the benefit of multi-objective optimisation for high-speed craft along with a nonlinear CFD (computational fluid dynamics) solver to evaluate design solutions. We show the proposed framework can design highly efficient hull forms along the multi-objective Pareto front that have a reduced total resistance when compared to a generic baseline hull by 31%–43% and 5.7%–8.2% at low and high Froude numbers, respectively.

Design and output power evaluation for a novel hybrid wave-wind energy converter

The performance of oscillating water column (OWC) wave energy converters (WEC) is highly affected by airflow rate. In this paper, a novel system is proposed that increases airflow rate and, therefore, output power through the integration of a mechanical structure known as a windcatcher with a conventional OWC. To investigate the hydrodynamic behaviour of the proposed system, a non-linear two-dimensional computational fluid dynamics (CFD) model is employed, along with the Reynolds Averaged Navier-Stokes (RANS) approach. The results of a comparison of the proposed OWC to a conventional type reveal a significant increase in airflow rate through the turbine blades, realizing an increase in converter output power. Moreover, the results show a power generation consistency in the proposed hybrid system, as the amplitude of the oscillatory part of the turbine airflow rate is diminished. Therefore, the proposed OWC converter not only generates significantly more power than a conventional type, it also has smoother power generation performance.

Nonlinear stiffness enhancement of submerged wave energy device in high fidelity model

A three degree of freedom submerged wave energy converter with a nonlinear stiffness mechanism was modelled using both linear and nonlinear hydrodynamics. The linear hydrodynamics scenario used linear potential flow methods to predict the fluid–structure interaction, while the nonlinear hydrodynamic scenario use computational fluid dynamics (OpenFOAM). The potential energy of the nonlinear stiffness mechanism was varied relative to the potential energy of the incident wave. The wave energy converter was excited using regular and irregular waves. The nonlinear stiffness scenarios were compared to scenarios with optimised linear control parameters. When compared to optimal conditions, models using linear hydrodynamics to emulate both regular and irregular waves showed no improvement in power generation. In the regular wave nonlinear hydrodynamic scenarios, the nonlinear stiffness showed inconsistent improvements to power production and significant detuning at different levels of nonlinearity. The irregular wave scenario using nonlinear hydrodynamic methods demonstrated a small improvement compared to optimised linear control parameters when the nonlinear stiffness potential energy peak was less than half the potential energy of the incident wave. The nonlinear stiffness improved the robustness of the wave energy converter, and was an effective method for detuning the system, depending on the degree of nonlinearity.

Analysis of computational fluid dynamics (CFD) on fiber reinforced self-compacting concrete

An experimental and CFD analysis of self-compacting concrete uses quarry dust and various partial flea ash substitutes, silica fumes, and both flea ash and silica fume combinations to construct a finely-structured polypropylene reinforced concrete beam. Using three different fractions of fiber volume, this article investigates the influence of polypropylene fibers on self-compacting concrete beams (2.0 percent, 2.5 percent and 3.0 percent). The M30 grade was taken into consideration. This study employed a computational fluid dynamics tool to model the experimental beam and failure scenarios. The three-dimensional CFD technique method used to model concrete beams has proven to be a reliable predictive tool for concrete beam analysis. However, when performing non-linear CFD analysis, it is critical to select appropriate finite elements and the correct mesh density in order to obtain a satisfactory solution to the problem. Furthermore, it has been discovered that linear regression may provide a good forecast of first crack load, deflection at first crack load, yield load, deflection at yield load, ultimate load, deflection at ultimate load, and ultimate load, deflection at ultimate load. There is a high level of agreement between the forecast and the test findings.

Investigation of Oil–Air Flow and Temperature for High-Speed Ball Bearings by Combining Nonlinear Dynamic and Computational Fluid Dynamics Models

Abstract An improved nonlinear dynamic model of high-speed ball bearings with elastohydrodynamic lubrication is adopted to predict the movements of balls and power loss of ball bearings for defining the boundary conditions of a computational fluid dynamics (CFD) model. Then, this method of combining nonlinear dynamic and CFD models is validated through the experimental verification. Subsequently, oil–air flow and temperature distribution inside the bearing chamber are studied at low and high speeds and light and heavy loads. The effect of nozzle’s position on the formation of oil film and heat dissipation is revealed under combined loads. The research results provide a theoretical basis for engineering application of high-speed rolling bearings.

Hydrodynamic Analysis of a Multibody Wave Energy Converter in Regular Waves

A performance assessment of wave power absorption characteristics of isolated and multiple wave energy converter (WEC) rotors was presented in this study for various wave-heading angles and wave frequencies. Numerical hydrodynamic analysis of the WEC was carried out using the three-dimensional linear boundary element method (BEM) and nonlinear computational fluid dynamics (CFD). Experimental results were used to validate the adopted numerical models. Influence with and without power take-off (PTO) was estimated on both isolated and multiple WEC rotors. Furthermore, to investigate the interaction effect among WECs, a q-factor was used. Incorporation of viscous and PTO damping into the linear BEM solution shows the maximum reduction focused around peak frequency but demonstrated an insignificant effect elsewhere. The q-factor showed both constructive and destructive interactions with the increase of the wave-heading angle and wave frequencies. Further investigation based on the prototype WEC rotor was carried, and calculated results of the linear BEM and the nonlinear CFD were compared. The pitch response and q-factor of the chosen wave frequencies demonstrated satisfactory consistency between the linear BEM and nonlinear CFD results, except for some wave frequencies. Estimated optimal time-averaged power using linear BEM show that the maximum extracted power close to the zero wave-heading angle around the resonance frequency decreases as the wave-heading angle increases. Overall, the linear BEM on the extracted power is overestimated compared with the nonlinear CFD results.

Towards a Computational Fluid Dynamics implementation of the critical wave groups method

The prediction of extreme ship responses continues to be an important and longstanding topic in ship hydrodynamics with a significant focus on developing probabilistic methods based on simple descriptions of the hydrodynamics that mainly provide qualitative observations. While simple nonlinear hydrodynamic formulations provide insight into extreme events, their underlying assumptions can prevent accurate quantitative representations of the mechanisms that are ultimately responsible for the extreme responses.Thus, research must strive to utilize increasingly more accurate hydrodynamic formulations to provide quantitative evaluations of extreme events. The present work aims to integrate extreme event probabilistic research based on the critical wave groups (CWG) method and fully nonlinear Computational Fluid Dynamics (CFD) to achieve a high fidelity representation of extreme events. This aim is achieved by embedding deterministic wave groups into irregular wave trains with known responses to produce different states at the moment of wave group encounter. The new framework is demonstrated by predicting the probability of exceedence of roll with a 2-D midship section of the Office of Naval Research Tumblehome hull in Sea State 7. The framework showcases how CFD and CWG can together reduce the computational burden of predicting extreme ship responses.

An adaptive and energy-maximizing control optimization of wave energy converters using an extremum-seeking approach

In this paper, we systematically investigate the feasibility of different extremum-seeking (ES) control and optimization schemes to improve the conversion efficiency of wave energy converters (WECs). Continuous-time and model-free ES schemes based on the sliding mode, relay, least-squares gradient, self-driving, and perturbation-based methods are used to improve the mean extracted power of a heaving point absorber subject to regular and irregular waves. This objective is achieved by optimizing the resistive and reactive coefficients of the power take-off (PTO) mechanism using the ES approach. The optimization results are verified against analytical solutions and the extremum of reference-to-output maps. The numerical results demonstrate that except for the self-driving ES algorithm, the other four ES schemes reliably converge for the two-parameter optimization problem, whereas the former is more suitable for optimizing a single parameter. The results also show that for an irregular sea state, the sliding mode and perturbation-based ES schemes have better convergence to the optimum in comparison to other ES schemes considered here. The convergence of PTO coefficients toward the performance-optimal values is tested for widely different initial values in order to avoid bias toward the extremum. We also demonstrate the adaptive capability of ES control by considering a case in which the ES controller adapts to the new extremum automatically amid changes in the simulated wave conditions. Moreover, no explicit knowledge of (future) wave excitation forces is required in the algorithm, which implies that the model-free ES can be used as a causal controller for WECs. Our results demonstrate that the continuous-time and model-free ES method achieves the optimum within a single simulation, which is in contrast to evolution-based optimization strategies that typically require a large number of (possibly expensive) function evaluations. This makes ES control optimization schemes suitable for nonlinear computational fluid dynamics simulations, where typically evolutionary strategies are used for performing black-box optimization.

Prediction of nonlinear vertical bending moment using measured pressure distribution on ship hull

Accurate prediction of wave loads on ships and floating structures is paramount in the structural design stage. Use of a segmented ship model is a common method to quantify the wave loads. Nevertheless, the value could be measured only at segmented sections. To obtain the wave loads at any longitudinal position and to account for nonlinear features in the wave loads more precisely, local quantities of the pressure on the whole ship-hull surface need to be measured along with ship motions in waves. In this paper, an unprecedented experiment using a bulk carrier model has been carried out to measure the spatial distribution of wave-induced unsteady pressure by means of a large number of Fiber Bragg Gratings (FBG) pressure sensors affixed on the whole ship-hull surface, and at the same time the wave-induced ship motions and ship-side wave profile have been measured. In order to see hydrodynamic characteristics in nonlinear and forward-speed effects on measured and analyzed results, some computations with the linear frequency-domain Rankine Panel Method (RPM) and the nonlinear Computational Fluid Dynamics (CFD) method solving the Reynolds-Averaged Navier-Stokes (RANS) equations are made. Favorable agreement is found for the pressure distribution and resulting vertical bending moment between the results of the experiment and corresponding numerical computations. Validation of the measured pressure distribution has also been made through a comparison of the wave-exciting force and moment between the two independent results obtained by integration of the measured pressure over the entire wetted surface of a ship and by direct measurement using a dynamometer. Very good agreement is confirmed in this case, too. As another validation for the wave loads, a comparative study is made with the benchmark test data of a 6750-TEU container ship used for the ITTC-ISSC joint workshop in 2014; which also demonstrates remarkable agreement. The present study may provide a new research technique, especially in the experiment, for predicting the wave-load distribution and for studying local hydrodynamic features in wave-related unsteady phenomena.

Investigation of a ship resonance through numerical simulation

Understanding dynamic stability of a ship at a resonance frequency is important because comparatively smaller external forces and moments generate larger motions. The roll motion is most susceptible because of smaller restoring moments. Most studies related to the failure modes such as parametric roll and dead ship condition, identified by second generation of intact stability criteria (SGISC) are performed at a resonance frequency. However, the nature of resonance, where the model experiences an incremental roll motion, has not been well understood. In this study, nonlinear unsteady computational fluid dynamics (CFD) simulations were conducted to investigate the resonance phenomenon using a containership under a sinusoidal roll exciting moment. To capture the complexity of the phenomenon, simulations were conducted over a range of frequencies to cover the resonance frequency including lower and higher amplitudes. In addition to the resonance frequency, the phase shift between roll exciting moment and roll angle, as well as the phase difference between acceleration and roll angle, were found to have significant effects on the occurrence of resonance.

Numerical Calculation Method of Model Predictive Control for Integrated Vehicle Thermal Management Based on Underhood Coupling Thermal Transmission

The nonlinear model predictive control (NMPC) controller is designed for an engine cooling system and aims to control the pump speed and fan speed according to the thermal load, vehicle speed, and ambient temperature in real time with respect to the coolant temperature and comprehensive energy consumption of the system, which serve as the targets. The system control model is connected to the underhood computational fluid dynamics (CFD) model by the coupling thermal transmission equation. For the intricate thermal management process predictive control and system control performance analysis, a coupling multi-thermodynamic system nonlinear model for integrated vehicle thermal management was established. The concept of coupling factor was proposed to provide the boundary conditions considering the thermal transmission interaction of multiple heat exchangers for the radiator module. Using the coupling factor, the thermal flow influence of the structural characteristics in the engine compartment was described with the lumped parameter method, thereby simplifying the space geometric feature numerical calculation. In this way, the coupling between the multiple thermodynamic systems mathematical model and multidimensional nonlinear CFD model was realized, thereby achieving the simulation and analysis of the integrated thermal management multilevel cooperative control process based on the underhood structure design. The research results indicated an excellent capability of the method for integrated control analysis, which contributed to solving the design, analysis, and optimization problems for vehicle thermal management. Compared to the traditional engine cooling mode, the NMPC thermal management scheme clearly behaved the better temperature controlling effects and the lower system energy consumption. The controller could further improve efficiency with reasonable coordination of the convective thermal transfer intensity between the liquid and air sides. In addition, the thermal transfer structures in the engine compartment could also be optimized.

Adaptive Control of a Wave Energy Converter

Energy maximizing controllers (EMCs), for wave energy converters (WECs), based on linear models, are attractive in terms of simplicity and computation. However, such (Cummins equation) models are normally built around the still water level as an equilibrium point and assume small movement, leading to poor model validity for realistic WEC motions, especially for the large amplitude motions obtained by a well-controlled WEC. The method proposed here is to use an adaptive algorithm to estimate the control model online, whereby system identification techniques are employed to identify a linear model that is most representative of the actual controlled WEC behavior. Using exponential forgetting, the linear model can be regularly adapted to remain representative in changing operational conditions. To that end, this paper presents a novel adaptive controller based on a receding horizon pseudospectral formulation. A case study is presented, providing an preliminary evaluation of the adaptive receding horizon pseudospectral control (ARHPC), using simulations based on both linear hydrodynamic modeling and computational fluid dynamics (CFD). The parameter adaptation is shown to behave as expected in both different simulation environments. The ARHPC is observed to perform well in irregular sea states, absorbing more power than its nonadaptive counterpart. The optimal trajectory calculated by the adaptive model is seen to have a smaller motion and power take-off (PTO) forces, compared to those calculated by the nonadaptive linear control model, due to the increased amount of hydrodynamic resistance estimated by the adaptive model, as identified from the nonlinear viscous CFD simulation.