Wake Model Research Articles

Development and validation of a three-dimensional wind-turbine wake model based on high-order Gaussian function

Under natural conditions, the wake velocity distribution approximates top-hat shape in the near wake center, and a Gaussian shape in the far wake. To improve the prediction accuracy of the wake distribution, this paper proposes a three-dimensional high-order Gaussian linear entrainment wake model by modifying the wake velocity distribution with high-order Gaussian function. Field tests and wind tunnel tests are then conducted. The obtained results show that the proposed model can accurately describe the radial and vertical spatial distributions of the wake flow. Under different wind speeds, the maximum and minimum radial relative errors are respectively 7.29% and 1.4%, while the maximum and minimum vertical relative errors are respectively 7.64% and 3.87%. This demonstrates that the proposed model can accurately predict the velocity distribution in the whole wake region. The proposed model is simple, has low cost, and exhibits high accuracy. Thus, it can be used in wind farm layout optimization and wake control.

Possible application of quantum computing in the field of ocean engineering: optimization of an offshore wind farm layout with the Ising model

AbstractAs a possible application of quantum computing in the field of ocean engineering, an attempt is made to identify the optimum layout of an offshore wind farm with the quasi-quantum annealing method while assuming a wake model that conforms to the standard Jensen–Katic wake model but can be implemented in the Ising model. The optimum layouts obtained in the present study are compared with those identified with other conventional methods such as the genetic algorithm. It is confirmed that the quasi-quantum annealing method works as well as other methods in identifying the optimum layouts, while the optimum layout of an offshore wind farm composed of even more than 100 wind turbines can be identified with reasonable CPU time.

Combined wake control of aligned wind turbines for power optimization based on a 3D wake model considering secondary wake steering

The wake of the wind turbines leads to power losses in wind farms. The active wake control (AWC) method reduces the wake effect and increases the power output. This paper systematically studies the combined wake control (CWC) method, which simultaneously controls the yaw angles, rotor speeds, and pitch angles of turbines to enhance the power output of wind farms. The prediction of the spatial distribution of the wake velocity under different operating states of wind turbines is a key factor in AWC. This study proposes a novel three-dimensional wake model for yawed wind turbine, considering wind shear and secondary steering. This model is validated through comparisons with large eddy simulation. A database for the aerodynamic performances of the NREL 5 MW wind turbine is then established based on OpenFAST. The whale optimization algorithm is used to optimize the wake effects between wind turbines in order to maximize the overall power output of a wind farm consisting of five aligned NREL 5 MW turbines. The obtained results indicate that CWC effectively improves the power output of the wind farm, with better performance than the axial induce factor control and wake redirection control by leveraging more turbine degrees of freedom. Moreover, secondary steering effects allow some downstream turbines need only slight active yaw adjustments to deflect wake considerably. Variations in inflow wind speed, ambient turbulence intensity, and turbine streamwise spacing all influence CWC. Overall, the more serious the wake effects within the wind farm, the greater the power improvement offered by CWC.

A comparative study on energy extraction potential of an elastically mounted rigid cylinder and infinitely tensioned cable using the wake oscillator model

The present study compares the vortex-induced vibration (VIV) response of an elastically mounted rigid cylinder (EMRC) and an infinitely tensioned cable (ITC) with regard to energy transfer from the incoming fluid flow to the structure. The response of the EMRC and the ITC under uniform flow is predicted using the wake oscillator model (WOM) for different mass ratios. The study then probed into the energy extraction potential of an EMRC and an ITC having equivalent mass ratios using the instantaneous energy, which gives a comprehensive understanding of the energy transferred from the fluid to the structure during the course of interaction. The energy conveyed from fluid to structure is dependent on the vortex lift force coefficient on the structure and the velocity of the structure. It is found that EMRC performs superior to an ITC from the energy extraction point of view.

Review of Data-Driven Models in Wind Energy: Demonstration of Blade Twist Optimization Based on Aerodynamic Loads

With the increasing use of data-driven modeling methods, new approaches to complex problems in the field of wind energy can be addressed. Topics reviewed through the literature include wake modeling, performance monitoring and controls applications, condition monitoring and fault detection, and other data-driven research. The literature shows the advantages of data-driven methods: a reduction in computational expense or complexity, particularly in the cases of wake modeling and controls, as well as various data-driven methodologies’ aptitudes for predictive modeling and classification, as in the cases of fault detection and diagnosis. Significant work exists for fault detection, while less work is found for controls applications. A methodology for creating data-driven wind turbine models for arbitrary performance parameters is proposed. Results are presented utilizing the methodology to create wind turbine models relating active adaptive twist to steady-state rotor thrust as a performance parameter of interest. Resulting models are evaluated by comparing root-mean-square-error (RMSE) on both the training and validation datasets, with Gaussian process regression (GPR), deemed an accurate model for this application. The resulting model undergoes particle swarm optimization to determine the optimal aerostructure twist shape at a given wind speed with respect to the modeled performance parameter, aerodynamic thrust load. The optimization process shows an improvement of 3.15% in thrust loading for the 10 MW reference turbine, and 2.66% for the 15 MW reference turbine.

Numerical study on the effectiveness of two dampers on high-order vortex-induced vibration and low-order rain-wind-induced vibration of stay cables

In recent years, high-order vortex-induced vibrations (VIVs) of ultra-long stay cables have been frequently observed on real bridges. However, additional dampers or aerodynamic measures were often designed to suppress wind-rain induced vibrations (RWIVs) of stay cables, which is mainly for the vibrations of low-order modes. This brings new challenges to the vibration reduction of stay cables. In this study, the theoretical models are used to investigate VIV and RWIV characteristics of ultra-long stay cables and verify the validity of installing two viscous dampers at the lower end of stay cables to suppress low-order RWIV and high-order VIV simultaneously. First, an empirical model, the wake oscillator model, is introduced to study VIV characteristics of stay cables subjected to different wind profiles, damping ratio and wind velocity, and the linear wake-structure coupling resonance is also introduced to investigate VIV mechanism of the stay cable. Second, the characteristics of RWIV of ultra-long stay cables based on the existing RWIV model is investigated. Finally, the optimizing parameters of the cable-dampers system is conducted for simultaneous control of RWIV and VIV, and the multimode damping is investigated. Finally, the study compares and analyzes the control effect of the multimode vibration with different measures.

A study on the wake model of floating wind turbine with swaying motions based on an improved actuator disk method

Offshore floating wind turbines may undergo swaying motions, resulting in significant changes in the wake wind field characteristics of the wind turbine, which can seriously affect the applicability and accuracy of existing wake models. This paper systematically investigates the turbulent wake flows of floating wind turbine with swaying motion based on an improved actuator disk method (ADM). The improved ADM is introduced to reproduce the wake flows of wind turbines, and the characteristics of the turbulent wind fields (i.e., mean wind velocity, turbulence intensity and Reynolds stress) are verified by wind tunnel tests. Furthermore, the wind fields of a floating wind turbine with different swaying amplitudes under turbulent atmospheric boundary layer are simulated, and the mean wind fields and turbulent statistics are analyzed. The performance of various existing wake models (i.e., Jensen model, modified Jensen model and Gaussian model) are compared, and a Gaussian-Shear wake model is proposed for floating wind turbines, which can account for non-uniform inflow and accommodate different swaying amplitudes. The results indicate that the proposed Gaussian-Shear wake model outperforms the other three models in describing the wake flows of floating wind turbines with swaying motions, which can be used for layout optimization and yaw control of offshore floating wind turbines.

Prediction of steady hydrodynamic performance of pump jet propulsion based on free wake vortex model

Due to mutual interference between various components, the transitional motion of fluid particles in the flow field of pump jet propulsion becomes more complex and variable. Additionally, the vortex structure at the wake can undergo severe contraction and deformation. To further improve the accuracy of predicting the hydrodynamic performance of pump jet propulsion, this paper proposes a time-varying, space-varying, and induced velocity-varying free wake numerical calculation model based on potential flow theory. A set of hydrodynamic performance prediction methods that consider the interference of the free wake model is also established. Furthermore, a velocity smoothing model based on time reversal is constructed based on the distribution pattern of numerical singularity points during the induced velocity calculation process, which enhances the robustness of the calculation program. By comparing and analyzing the numerical calculation results with experimental results, including pressure, circulation distribution, and hydrodynamic performance, the accuracy of the free wake model proposed in this paper is verified. The results also demonstrate that the free wake model proposed in this paper can effectively improve the prediction accuracy of the hydrodynamic performance of the pump jet propulsion.

Dynamic wake steering control for maximizing wind farm power based on a physics-guided neural network dynamic wake model

Wake effect is a significant factor contributing to power loss in wind farms. Studies have shown that wake steering control can mitigate this power loss. Currently, wind farm wake control strategies primarily utilize fixed yaw control due to limitations in the accuracy and efficiency of dynamic wake models. However, fixed yaw control fails to fully exploit the power improvement potential of wake steering control. Therefore, in this study, we first propose a dynamic wake model for wind farms based on the physics-guided neural network (PGNN) approach. This model can predict the dynamic wake flow field within wind farms in real time using instantaneous inflow wind speed and turbine operational states. Then, by employing the PGNN dynamic wake model as the predictive model, a wind farm dynamic wake control strategy based on the model predictive control method is proposed. To quantify the advantages of the proposed control strategy, both fixed yaw control and dynamic yaw control are tested on a wind farm with a 3 × 2 layout. Results from large eddy simulations demonstrate that the proposed dynamic wake control strategy increases the power output of the wind farm by 11.51% compared to a 6.56% increase achieved with fixed yaw control.

An Untethered Heart Rhythm Monitoring System with Automated AI‐Based Arrhythmia Detection for Closed‐Loop Experimental Application

AbstractThe heart produces bioelectrical signals, which can be measured as an electrocardiogram (ECG) for the detection of rhythm disturbances. Rapid and precise detection of these arrhythmias is crucial for their termination by closed‐looped therapeutic interventions to counteract detrimental effects. However, there is a current lack of such systems tailored for experimental cardiovascular applications. This hampers not only in‐depth mechanistic studies but also translational testing of new therapeutic strategies, especially in an untethered manner in awake animal models. To break new ground, recent advances to develop a non‐invasive AI‐supported heart rhythm monitoring system for untethered automated arrhythmia detection in a continuous manner is combined. This system is housed in a lightweight jacket for mobile use and includes an on‐skin ECG sensor, a low‐power microprocessor unit, a massive data storage unit, and a power‐management system. By implementing a novel hybrid algorithm based on so‐called heart rate (R‐R) variability and a case‐specific AI model, 100% sensitivity and 95% specificity is achieved in detecting atrial arrhythmias within 2 s upon initiation in adult rats. Thereby, the novel system sets the stage for advanced mechanistic studies and therapeutic testing, including closed‐loop applications aiming for the termination of a broad range of atrial arrhythmias.

Coordinated voltage control for large-scale wind farms with ESS and SVG based on MPC considering wake effect

The wake effect reduces the wind speed at downstream wind turbines (WTs), making it necessary for the central controller to collect wind power generation data from each WT. However, wind farms (WFs) face a more complex problem in maintaining the voltage stability at the WT terminal while following the transmission system operator (TSO) instructions due to the information collection as well as the possible data loss during transmission. Therefore, this study proposes a coordinated control method for WTs and multiple power sources based on model predictive control under wake disturbance conditions, aiming to reduce the average voltage deviation in WT terminals and go close to the rated voltage and ensure effective compliance with TSO commands in large-scale WFs. Accordingly, the Jensen wake model was utilized to accurately calculate the available active and reactive power limits for each WT. Energy storage systems and static Var generators were modeled to coordinate and maintain the voltage in all WT terminals within the feasible range, providing peak shaving and valley filling support to reduce wind energy waste and shortfall, thereby enhancing the economic and operational reliability of WF. Further, the effectiveness of the proposed method was validated in MATLAB/Simulink.

Experimental investigation of the wake replenishment mechanisms of paired counter-rotating vertical-axis wind turbines

The understanding of wake recovery mechanisms is crucial for the design of efficient wind farm layouts and the development of accurate wake models. Recently, placing two vertical-axis wind turbines (VAWTs) in close proximity has demonstrated potential for increased power output. In this study, wind tunnel experiments were conducted to investigate the wake replenishment mechanisms behind paired VAWTs. The experimental campaign included testing an isolated VAWT and paired counter-rotating VAWTs. By combining qualitative observations of key flow field variables with a quantitative analysis based on momentum conservation, this study aims to enhance our understanding of the mixing mechanisms supporting the reintroduction of streamwise momentum into the wake of paired VAWTs. This research also involves a comparison of these mechanisms with those observed in the wake of a standalone VAWT. The results show that the differences between isolated and paired VAWTs in overall wake characteristics are minimal. The increased lateral advection within the wake of the isolated VAWT is offset by the enhanced vertical advection in the paired configuration, as a result of the change in the direction of cross-stream velocity within the gap between the paired VAWTs, which promotes a shift towards vertical flow rather than lateral flow.

An efficient solution for large offshore wind farm power optimization with the Porté-Agel wake model: Optimality and efficiency

The wake effects may cause significant energy loss in the large offshore wind farm without proper coordination. Therefore, cooperative yaw and induction control is needed to mitigate wake effects and increase power output. This study reveals that conventional methods to solve the power optimization problem may trap into local optimum and have slow computation speed for large offshore wind farm. In this paper, the Porté-Agel wake model is adopted to precisely capture the dynamics and a data-driven method is proposed to calibrate its parameters only using measurements. Then, we propose a distributed hybrid search-BFGS(DHSB) algorithm to solve the power optimization problem. In this algorithm, firstly the yaw angles of some specific turbines are searched coarsely and distributionally to provide a good initial point and escape from the local optimum. Then, a distributed BFGS is developed to solve the optimization problem with very high efficiency, in which the gradient and objective value are updated in distributed manner. Simulation results show that our proposed DHSB can always achieve global optimum with much high efficiency compared to traditional gradient-based methods.

Automatic grouping of wind turbine types via multi-objective formulation for nonuniform wind farm layout optimization using an analytical wake model

This study introduces a novel methodology that aims to minimize the number of different wind turbine types used in nonuniform wind farms. This approach involves a trade-off to tackle the logistical challenges associated with installing, operating, and maintaining such wind farms. To accomplish this, a Gaussian analytical wake model is used in conjunction with evolutionary algorithms (NSGA-II and SMS-EMOA) for multi-objective optimization. A multi-objective problem is formulated, regarding wind farm capacity factor (CF) and levelized cost of energy (LCOE), and addressed using two distinct approaches. In the first approach, proposed here, the number of different wind turbine types is limited and treated as an additional objective. In contrast, the second approach allows for flexibility in choosing any number of different turbine types. Comparing the results obtained, it was observed that the methodology presented here yielded a reduced number of different turbine types without compromising CF and LCOE objectives. A multi-criteria decision maker was applied to extract the final non-dominated solutions from the obtained Pareto set. Finally, economic indicators show the profitability of these solutions.

A CFD Study on High‐Thrust Corrections for Blade Element Momentum Models

ABSTRACTThis paper presents a reanalysis of four axial‐flow rotor simulation datasets to study the relationship between thrust and axial induction factor. We concentrate on high‐thrust conditions and study variations in induction factor and loads across the span of the different rotor blades. The datasets consist of three different axial‐flow rotors operating at different tip‐speed ratios and, for one dataset, also at different blockage ratios. The reanalysis shows differences between the blade‐resolved CFD results and a widespread empirical turbulent wake model (TWM) used within blade element momentum (BEM) turbine models. These differences result in BEM models underestimating thrust and especially power for axial‐flow rotors operating in high‐thrust regimes. The accuracy of BEM model predictions are improved substantially by correcting this empirical TWM, producing better agreement with blade‐resolved CFD simulations for thrust and torque across most of the span of the blades of the three rotors. Additionally, the paper highlights deficiencies in tiploss modelling in common BEM implementations and highlights the impact of blockage on the relationship between thrust and axial induction factors.

Low-intensity transcranial focused ultrasound suppresses pain by modulating pain-processing brain circuits

AbstractThere is an urgent and unmet clinical need to develop nonpharmacological interventions for chronic pain management because of the critical side effects of opioids. Low-intensity transcranial focused ultrasound (tFUS) is an emerging noninvasive neuromodulation technology with high spatial specificity and deep brain penetration. Here, we developed a tightly focused 128-element ultrasound transducer to specifically target small mouse brains using dynamic focus steering. We demonstrate that tFUS stimulation at pain-processing brain circuits can significantly alter pain-associated behaviors in mouse models in vivo. Our findings indicate that a single-session focused ultrasound stimulation to the primary somatosensory cortex (S1) significantly attenuates heat pain sensitivity in wild-type mice and modulates heat and mechanical hyperalgesia in a humanized mouse model of chronic pain in sickle cell disease. Results further revealed a sustained behavioral change associated with heat hypersensitivity by targeting deeper cortical structures (eg, insula) and multisession focused ultrasound stimulation to S1 and insula. Analyses of brain electrical rhythms through electroencephalography demonstrated a significant change in noxious heat hypersensitivity-related and chronic hyperalgesia–associated neural signals after focused ultrasound treatment. Validation of efficacy was carried out through control experiments, tuning ultrasound parameters, adjusting interexperiment intervals, and investigating effects on age, sex, and genotype in a head-fixed awake model. Importantly, tFUS was found to be safe, causing no adverse effects on motor function or the brain’s neuropathology. In conclusion, the validated proof-of-principle experimental evidence demonstrates the translational potential of novel focused ultrasound neuromodulation for next-generation pain treatment without adverse effects.

A Two-Step Grid–Coordinate Optimization Method for a Wind Farm with a Regular Layout Using a Genetic Algorithm

Currently, most studies on the optimization of wind farm layouts on flat terrain employ a discrete grid-based arrangement method and result in irregular layouts that may damage the visual appeal of wind farms. To meet the practical requirements of wind farms, a two-step optimization method called “grid–coordinate” based on a genetic algorithm is proposed in this paper. The core idea is to initially determine the number of wind turbines and their initial positions using a grid-based approach, followed by a fine-tuning of the wind farm layout by moving the turbines in a row/column manner. This two-step process not only achieves an aesthetically pleasing arrangement but also maximizes power generation. This algorithm is conducted to optimize a 2 km × 2 km wind farm under three classic wind conditions, one improved wind condition, and a real wind condition employing both the Jensen and Gaussian wake models. To validate the effectiveness of the proposed method, the optimization of configurations based on different wake models was conducted, yielding results including the efficiency, total power output, number of wind turbines, and unit cost of electricity generation. These results were compared and analyzed against the classical literature. The findings indicate that the unit cost of electricity generation using the two-step optimization approach with the Gaussian wake model is higher than that of the initial grid optimization method. Additionally, varying the number of wind turbines can lead to instances of high power generation coupled with low efficiency. This phenomenon should be carefully considered in the wind farm layout optimization process.

Research on three-dimensional wake model of horizontal axis wind turbine based on Weibull function

In wind turbine wake models, Gaussian models depend on multidimensional integration to ascertain the distribution of wake velocity deficits. These integrations, which often involve complex boundary conditions, significantly enhance the complexity of mathematical computations. Due to the difficulty of obtaining analytical solutions, numerical integration methods such as Monte Carlo or other numerical integration techniques are commonly employed. This study presents a three-dimensional wake model (3DJW) for horizontal axis wind turbines, utilizing the Weibull function to simplify wake deficit characterization instead of traditional Gaussian distribution methods. The 3DJW model considers wind shear effects and mass conservation laws to enhance predictions of vertical wake velocities. By integrating incoming wind conditions and turbine parameters, the model efficiently computes downstream wake velocities, improving computational efficiency. To enhance predictions in the ultra-far wake region, an improved three-dimensional Weibull wake model is proposed using the exponential fitting method. Validation through wind tunnel experiments and wind farm data demonstrates the model's accuracy in predicting wake deficits at the hub height, with relative errors in horizontal and vertical profiles mostly within 5% and 3%, respectively. The proposed model enables accurate and rapid calculation of wake velocities at any spatial location downstream, facilitating enhanced energy utilization and reduced costs.

Floating offshore wind potential for Mediterranean countries

Floating offshore wind is a promising renewable energy source for several Mediterranean Countries. The exploitation of this resource will contribute to reducing carbon dependence and support the clean energy transition towards a climate neutral Europe. This work presents a novel methodology for estimating spatially-resolved Levelised Cost of Energy and offshore wind energy potential to provide optimal design of floating offshore wind farms in the Mediterranean Sea. For the first time, each site is optimised based on electrical grid cable design and wind farm layout optimisation using the Jensen wake model. The largest technical capacity potentials are obtained in Libya, Tunisia, Italy and Greece, accounting for 72.2 % of the total Mediterranean potential with a total installed capacity of 782 GW. The average LCOE is 93.4 €/MWh and the average capacity factor is 31.8 %, while 67.5 % of the technical potential has LCOE below 90 €/MWh which demonstrates that floating offshore wind in the Mediterranean could become soon competitive with other renewable energies. Optimal floating wind farm design parameters show the prevalence of a wind farm array of 10x10 wind turbines with a preferred rated power of 15 MW and the HVDC export cable connection. Among the selected floating platforms, Hywind outperforms WindFloat and GICON-SOF in 59.2 % of the suitable areas due to the lower structure material. Policymakers and stakeholders will primarily benefit from this study, which provides them with important information for careful marine spatial planning and the development of floating offshore wind farms in the Mediterranean.

RMSE POWER COEFFICIENT OF WIND TURBINES WITH INVERSE TOQUE-SPEED CONTROL

The Blade Element Momentum (BEM) method stands out among various turbine modelling techniques due to its integration of airfoil aerodynamics with momentum theory, allowing detailed force calculations on blade elements. While traditional methods like BEM and Wake Models are efficient for initial turbine design, advancements in computational power have enabled the use of Computational Fluid Dynamics (CFD) for more accurate simulations. Although these models are precise, they are computationally intensive, leading to the continued use of simpler empirical methods, such as the static power coefficient approach, in power system studies. Future research aims to validate and implement dynamic estimation models to account for wind variability and turbine control dynamics. Traditional constant torque-speed control strategies maintain a constant generator speed by using a fixed electromagnetic torque command and adjusting the pitch angle when wind speed exceeds the rated value. However, if the pitch control does not respond quickly enough, rotor acceleration can occur, leading to increased power beyond the generator’s rating. To mitigate this, the pitch control mechanism must react promptly to adjust the turbine's torque profile, ensuring convergence to the rated operating point and avoiding prolonged generator overload. To reduce the burden on the pitch-control system, an inverse torque-speed control approach is proposed, where the electromagnetic torque is dynamically adjusted based on real-time rotor speed data. This method aims to achieve rated power operation with improved responsiveness and reduced stress on the pitch-control mechanism.