Momentum Theory Research Articles

Optimization and control strategy for wind turbine aerodynamic performance under uncertainties

Aerodynamic performance of wind turbine governs the overall energy efficiency, which has been an ever-lasting research focus in the field of wind power technology. Due to the coupling effect among the highly complex environmental and structural uncertainties, the practical aerodynamic performance may not be reliably predicted. To aggravate, this performance declines with time in service. It is of great significance to efficiently and reliably assess the impact of uncertain factors and reduce these influences on wind turbine aerodynamic performance. This paper establishes an uncertainty analysis and robustness optimization model of wind turbine aerodynamic performance considering wind speed and pitch angle error uncertainties. An approach combined the no-instrusive probabilistic collocation method is used, and the blade element momentum theory is applied to quantify influences of variable uncertainties on NREL 5 MW wind turbine aerodynamic performance. The optimization target is to reduce the sensitivity of wind turbine aerodynamic performance to uncertainties, as well as maintain capture power. The results show that the wind turbine aerodynamic and mechanical performance will be greatly affected with uncertain factors. By optimizing and adjusting wind turbine rotor speed and blade pitch angle, the wind turbine rotor power and thrust load variation can be reduced to 9.14% and 9.36%, respectively, which indeed reduces the uncertainty effects.

Technical Note: Analytical Estimate of Rotor Controls Required for a Propeller Wake Disturbance Rejection

During helicopter air-to-air refueling, the aircraft propeller's jet can engage with the helicopter rotor. The impact on the helicopter rotor thrust and aerodynamic hub moments is solved analytically for the first time, based on blade element momentum theory. The collective and cyclic blade pitch controls needed for disturbance rejection are computed for a typical air-to-air refueling scenario. A propeller jet affecting the retreating side of the rotor requires much more pilot controls to retrim than an impingement on the advancing side.

Comparative performance analysis of NACA 2414 and NACA 6409 airfoils for horizontal axis small wind turbine

While wind energy, which has an important place among renewable energy sources, is converted into electrical energy by means of wind turbines, the designs and aerodynamic behaviors of turbine blades gain importance in order to obtain optimal efficiency. The most important factor affecting the wind energy capture performance and aerodynamic behavior of the blade is the aerofil structure. In this study, the design and comparative performance analysis of NACA 2414 and NACA 6409 series airfoils under wind turbine conditions with 1x10^6 fixed reynolds number, 0-20^0 attack angles, constant air density and ambient conditions, 3kW nominal power and 2m blade length were carried out. The designs and analyzes for both airfoils were simulated using Q-Blade software version 2.0.5.2. While designing the blade, the propeller blade was divided into 20 equal parts so that there would be no aerodynamic interaction between the elements, and analyzes were made with a calculation method based on the Blade Element Momentum (BEM) theory. As a result, by comparing different features such as lift (Cl) and drag (Cd) coefficients, pressure distribution on the blades, power coefficients, it was seen that the NACA 6409 airfoil was more efficient than the NACA 2414 airfoil for small diameter wind turbines.

A Simplified Optimization Model for Hydrokinetic Blades with Diffuser and Swept Rotor

The use of a diffuser in hydrokinetic turbines can improve the power coefficient. However, the risk of cavitation in the rotor blades increases. Studies suggest that backward-curved blades can reduce the axial load on the rotor and therefore prevent cavitation. Therefore, this work develops an optimization procedure applied to backward-curved blades in hydrokinetic turbines with diffusers based on the Blade Element Momentum Theory. The main contribution is to consider both the sweep effect and the presence of a diffuser in the optimization in an innovative way. We use a radial transformation function that adjusts the radial position considering the curvature of the blade during optimization under the effect of the diffuser. The results showed that the increase in blade curvature resulted in greater chord distributions and twist angles, especially at the blade tips. The Prandtl’s loss factor was not sensitive to sweep, but the linked circulation increased at the blade tips, suggesting an increased risk of cavitation. Depending on the sweep angle, the optimized blades were able to mitigate or avoid cavitation. In particular, a sweep angle of 30∘ eliminated cavitation. This study indicated that the proposed optimization can effectively prevent cavitation, showing satisfactory results.

A study on the strategic momentum of SMEs’ digital transformation: Evidence from China

The digital transformation of Chinese SMEs faces the reality of slow start-up and difficult deepening. Considering the multi-stage characteristics of SMEs' digital transformation, this article is drawn on the theory of strategic momentum and the TOE framework is improved to examine the process of Chinese SMEs' digital transformation from the dimensions of response speed and implementation depth. Data from 221SMEs is analyzed through the fsQCA to explore the complex interactions between digital technology, organization, environment and the initial and deepening stages of Chinese SMEs' digital transformation. Three key findings are revealed. Firstly, to effectively promote the initiation speed and implementation depth of SMEs' digital transformation, a collaborative effort is required by entrepreneurs, digital service companies, customers, and government. Secondly, external factors have a significant promoting effect on both the initial and deepening stage of SMEs' digital transformation. Of particular note is the usability of digital technology, which is indicated to be a crucial factor for both the initial and integration stage. This indicates that SMEs exhibit a heightened sensitivity to the complexity and future uncertainty of digital technologies. Thirdly, by promoting the digitalization of industrial clusters, the deepening stage can be facilitated effectively by governments.

Mitigation of In-Plane Vibrations in Large-Scale Wind Turbine Blades with a Track Tuned Mass Damper

To mitigate in-plane vibrations of wind turbine blades, a track tuned mass damper (TMD) is proposed and its performance for mitigating blade in-plane vibration is investigated considering various influence factors. Firstly, the organization and operational principles of the damping control device are explained. Then, the equations of motion of the individual TMD-equipped blade are then deduced from Euler–Lagrange. Secondly, blade’s wind loading is calculated by blade element momentum theory considering the blade rotation effect through the rotating sample spectrum. Thirdly, the dynamical response of the blade based on the MATLAB/SIMULINK tool is calculated. The peak maximum displacement and standard deviation of the blade tip are chosen as the estimation indicators to assess the TMD’s effectiveness of the device considering actually various argument including mass ratio μ , damping ratio ξ , and installation position x 0 / L . Based on the assumption that the mass block in the vibration reduction control device has no contact with the inside surface of the blade web in operation, the optimal relative values of mass ratio, damping ratio, and installation position of a single blade are determined as 0.03, 15%, and 0.55, respectively. As a result, the reduction of the peak value and the standard deviation can reach 52.78% and 53.75%, respectively. Therefore, with the optimal parameters, the designed vibration control device effectively not only reduces the blade tip displacement but also avoids the damage due to in-plane vibrations.

A Short Review on the Time-Domain Numerical Simulations for Structural Responses in Horizontal-Axis Offshore Wind Turbines

In addition to a carbon-neutral vision being recognized worldwide, the utilization of wind energies via horizontal-axis wind turbines, especially in offshore areas, has been intensively investigated from an academic perspective. Numerical simulations play a significant role in the design and optimization of offshore wind turbines. The current review focuses on studies concerning the numerical simulations of offshore wind turbine dynamics, including the modelling of the aerodynamic and hydrodynamic conditions of the environment and the reduced-order modelling of the wind turbine dynamic responses. In detail, the functions and mechanisms of each module in the numerical simulation of the wind turbine dynamics are articulated, which in turn demonstrates its importance for the design of offshore wind turbines, and hence the development of the offshore wind industry. Based on this review, it is argued that the vertical variations in wind velocities, the blade element momentum theory, the wave dynamic models, and the reduced-order model for structural dynamics are the major concerns for the numerical simulation of wind turbines. Consequently, such directions should be emphasized in future studies.

The Improvement of Blade Element Momentum Theory in Horizontal Axis Wind Turbine Performance Analysis

The present work uses the blade element momentum theory method for evaluating the performance of horizontal axis wind turbine. The wind turbine performances are described in term of the thrust coefficient CT, torque coefficient CQ and the power coefficient CP. The blade element momentum theory (BEMT) represents the wind turbine performance prediction method as result of combining two methods, namely the blade element theory (BET) and the momentum theory (MT). Both theories are able to formulate the axial forces and torques which work on the blade. Equating axial force and torque formulated by BET is equal axial force and torque by MT, makes one allows the axial induction factor and the angular induction factor a^’, the unknown quantities, can be defined and furthermore the wind turbine performances can be evaluated. The BEMT method used here is the combination of BEMT. The implementation this method as the tool for predicting the wind turbine performances are work well. However, for wind turbine configuration need a little adjustment, especially in setting the hub radius rh where the blade element momentum theory starts to make calculation from the inner blade to the tip. The high pitch angle and a relatively a large chord length at rh, make the BEMT fail to converge. In addition to the present work found that the three wind turbine performance coefficients are formulated by using the momentum theory is less accurate compared with BET formulation.

Influence of drift angle on the propulsive efficiency of a fully appended container ship (KCS) using Computational Fluid Dynamics

To estimate the powering and manoeuvring performance of the ship in a real seaway, it is essential to accurately determine forces acting on the hull, propeller, rudder and their interaction effects when operating at an angle of drift. The rotating propeller alters the fluid flow around the upstream hull and the downstream rudder. Likewise, when a non-zero drift or rudder angle is applied, significant crossflow is generated across the propeller plane, changing the wakefield and the actual performance of the propeller. A study is conducted to analyse the hull–propeller–rudder interaction of the benchmark KRISO Container Ship (KCS) in calm water using Computational Fluid Dynamics (CFD). The KCS is studied at drift angles of −10°, 0°and ＋10°, combined with a series of rudder angles (−35°to ＋35°), which can represent quasi-static phases of an actual ship manoeuvre. The propeller is modelled using two body force models, Blade Element Momentum Theory and the Yamazaki model. Good agreement is found between experimental and numerical results when predicting hull forces and wave patterns at drift, providing a good reference for experimental measurement of the hull and its appendage forces at drift and future validation of actual dynamic manoeuvring simulations.

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.

Scattering of a wave packet by the Pöschl-Teller potential well

We investigate the scattering of a wave packet by the Pöschl-Teller potential in momentum representation. The scattering dynamics of the wave packet for a long-time evolution is feasible in this representation. With the wave function in momentum space, we can construct the time-dependent phase space Wigner function. The corresponding density function in coordinate space is then calculated through the Wigner function. The reflectionless wave packet for integer ν and partially reflected for non-integer ν are demonstrated by analyzing the Wigner function.

The inverted U-shaped relationship between performance appraisal interval and proactive work behavior: The dual time frame effect

In consideration of how to promote employees' work proactivity in the time frame of performance appraisals, we focused on a time-related construct called the performance appraisal interval (PAI). Drawing from psychological momentum theory, we constructed a model of the dual effect of the PAI on employees' proactive work behavior. A cross-level analysis of 561 employees from 55 groups indicated that PAI was positively related to delayed gratification, but the effect decreased gradually as time passed. Delayed gratification was positively related to proactive work behavior and mediated the relationship between PAI and proactive work behavior. Second, PAI was positively related to perceived uncertainty and the effect gradually increased over time. Perceived uncertainty was negatively related to proactive work behavior and mediated the relationship between PAI and proactive work behavior. In this study we found a compatible explanatory mechanism to integrate the positive and negative effects of a given PAI, which provides a new explanatory mechanism for stimulating proactive work behavior.

Analytical model for the power production of a yaw-misaligned wind turbine

Wake steering has proven to be effective in enhancing the power output of a wind farm. However, this approach still highly relies on empirical formulas to predict the power production of yawed turbines, limiting its potential in practical applications. In this study, an analytical model is proposed to predict the power production of a yaw-misaligned turbine under uniform inflow conditions. The model is based on the combination of the blade element theory and the momentum theory, with a modification in the latter to account for the disturbance on the spanwise velocity caused by the yawed turbine. A series of large eddy simulations were performed using a utility-scale wind turbine operating at yaw angles |γ|≤30° and tip-speed ratios λ=5–8. The validity of the proposed model is confirmed by the good agreement between the theoretical predictions and the simulation data. Furthermore, the well-known cosine model is shown to describe well the power production of the yawed turbine within the studied parameter range. However, the power-yaw loss exponent is not a constant, but rather a function of the tip-speed ratio. These findings may be useful in yaw optimization and control strategies in wind farms.

Application of an Open-Source OpenFoam for Fluid-Structure Interaction Analysis of the Horizontal-Axis Wind Turbine Blade

This study investigates numerical simulation for fluid-structure interaction in wind turbine blades, emphasizing the influence of dimensionless numbers. Utilizing OpenFoam, the Navier-Stokes equation is accurately solved with the PISO algorithm, ensuring proper interface conditions. The icoFsiFoam solver is validated through dynamic testing, demonstrating its effectiveness. In contrast to the widely adopted Blade Element Momentum Theory (BEMT), our approach focuses on analyzing blade deformation and resonance phenomena, capturing intricate deformations and stress concentrations. Our investigation explores the impact of reduced velocity on blade behavior across a range of 0.105 to 0.145, while consistently maintaining crucial dimensionless numbers such as Reynolds number (Re = 10⁶), Froude number (Fr = 4.93), and Cauchy number ( Cy = 10-5). The outcomes of this study significantly contribute to the understanding of fluid-structure interaction in wind turbine blades. By examining the oscillatory behavior of the blades, we observe trends similar to those predicted by BEMT. However, our approach surpasses BEMT by providing additional insights into stress concentrations and deformation modes. This advancement enables superior performance optimization and facilitates advanced blade analysis. The implications of our research are paramount for optimizing blade design and performance under varying reduced velocities. By incorporating the findings of this study, blade designers can make well-informed decisions to enhance the efficiency and durability of wind turbine technologies. The presented methodology and results provide a comprehensive investigation into the fluid-structure interaction of wind turbine blades, highlighting the importance of dimensionless numbers and their influence on blade behavior. Overall, this study offers valuable insights for improving wind turbine design and performance.

Blade optimization for hydrodynamic performance improvement of a horizontal axis tidal current turbine

This paper proposes an innovative methodology applied to blade optimization for hydrodynamic performance improvement of a horizontal axial tidal current turbine (HATCT) considering the effect of Reynolds number. Axial induction factor, tangential induction factor and angle of attack are employed for identifying the accuracy and applicability of modified Blade Element Momentum (BEM) theory. Combined with the XFoil software, the hydrofoil shape function is represented by trigonometric functions through Theodorsen method. The hydrodynamic characteristics of the hydrofoil are employed as the optimization targets, and the particle swarm optimization algorithm is used to optimize the original hydrofoil. Based on the modified BEM theory and the optimized hydrofoil, the tidal current turbine power coefficient at different tip speed ratio (TSR) is optimized according to the MATLAB function. The optimized tidal current turbine shows better performance compared with the original tidal current turbine.

Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation

Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation

The universal one-loop effective action with gravity

We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

Hadronic Isospin Helicity and the Consequent SU(4) Gauge Theory

A new approach to the Dirac equation and the associated hadronic symmetries is proposed. In this approach, we linearize the second Casimir operator of the Lorentz Group, which is defined by the energy–momentum four-vector and the fermion spin, thereby using the spinor-helicity representation instead of the three-vector representation of the particle momentum and spin vector. We then expand the so-obtained standard Dirac equation by employing an inner abstract “hadronic” isospin, initially describing a SU(2) fermion doublet. Application of the spin-helicity representation of that isospin leads to the occurrence of a quadruplet of inner states, revealing the SU(4) symmetry via the isospin helicity operator. This further leads to two independent fermion state spaces, specifically, singlet and triplet states, which we interpret as U(1) symmetry of the leptons and SU(3) symmetry of the three quarks, respectively. These results indicate the genuinely very different physical nature of the strong SU(4) symmetry in comparison to the chiral SU(2) symmetry. While our approach does not require the a priori concept of grand unification, such a notion arises naturally from the formulation with the isospin helicity. We then apply the powerful procedures developed for the electroweak interactions in the SM, in order to break the SU(4) symmetry by means of the Higgs mechanism involving a scalar Higgs field as an SU(4) quadruplet. Its finite vacuum creates the masses of the three vector bosons involved, which can change the three quarks into a lepton and vice versa. Finally, we consider a toy model for calculation of the strong coupling constant of a Yukawa potential.

The Aerodynamic Performance of a Novel Overlapping Octocopter Considering Horizontal Wind

This paper investigates the aerodynamic performance of an overlapping octocopter with the effect of horizontal wind ranging from 0 to 4 m/s using both low-speed wind tunnel tests and numerical simulations. The hovering efficiency and the potential control strategies of the octocopter under the effect of horizontal wind are also validated using blade element momentum theory. The velocity distribution, rotor pressure and vortex of the downwash flow with the horizontal wind are presented using the Computational Fluid Dynamics (CFD) method. Finally, wind tunnel tests were performed to obtain the thrust and power consumption with the rotor speed ranging from 1500 to 2200 rpm for horizontal winds at 0 m/s, 2.5 m/s and 4 m/s. The results showed that horizontal wind decreased the flight efficiency of the planar octocopter and had little effect on the coaxial octocopter. It is also interesting to note that horizontal wind is beneficial for thrust increments at a higher rotor speed and power decrements at a lower rotor speed for the overlapping octocopter. Specifically, the horizontal wind of 2.5 m/s for a lower rpm is presented with a power decrement with proper aerodynamic interference between the rotor blades. Additionally, the overlapping octocopter obtains a higher hover efficiency at 4 m/s compared to traditional octocopters, which is more suitable for flying in a cross wind with a more compact structure.

Investigation of tidal turbine array performance using computational fluid dynamics in the presence of waves

Tidal turbine arrays have undergone extensive research to determine the optimal spacing for efficient performance and reduced wake generation. Small-scale laboratory tests are typically conducted to analyze wake structures prior to deployment. These tests often result in conditions of extreme blockage due to channel narrowing in comparison to turbine size. The primary objective of this study is to investigate flow behavior around turbines under blockage conditions and their performance close to the free surface, both in current-only and wave-and-current scenarios. The methodology employed a combination of blade element momentum theory and computational fluid dynamics (CFD) integrating a virtual blade model (VBM) code. The findings of this study indicate potential enhancements in tidal turbine array performance of up to 7% in lateral arrangements and 11% in streamwise arrangements under blockage conditions. The wake is significantly influenced by surface waves, which also contribute to increased downstream turbine performance.