Momentum Theory Research Articles

Distributed Hybrid Electric Propulsion Aircraft Design Based on Convex Optimized Power Allocation Management

In order to ensure that aircraft have medium and long-range flights, enhanced aerodynamic performance, and reduced fuel consumption, this paper presents an original Distributed Hybrid Electric Propulsion Aircraft (DHEPA) design scheme and proposes a novel power allocation management method based on convex optimization. Firstly, by taking the Tecnam P2006T general-purpose aircraft as a reference, key components of DHEPA are selected and modeled. Then, a power allocation management method for DHEPA is proposed on the basis of convex optimization, which takes the minimum fuel consumption as the performance index to realize the reasonable power allocation of the battery and engine, while avoiding sliding into the local optimum of allocation. Finally, momentum theory and numerical simulation methods are used to analyze the aerodynamic enhancement effect of the propeller on the wing in the DHEPA, and a dynamics method is utilized to calculate the dynamics performance of the aircraft at several important stages. The results show that, compared with the reference aircraft, the lift of the DHEPA is increased by 46%. Under typical sectors, the DHEPA has a higher rate of climb and maximum leveling off speed at cruise, and a significantly lower fuel consumption.

Vertical-Axis Tidal Turbines: Model Development and Farm Layout Design

In this paper, we propose a new 3D model for vertical-axis tidal turbines (VATTs) embedded in the shallow-water code SHYFEM. The turbine model is based on the Blade-Element∖Momentum (BEM) theory and, therefore, is able to predict turbine performance based on the local flow conditions and the geometric characteristics of the turbine. It is particularly suitable for studying turbine arrays, as it can capture the interactions between the turbines. For this reason, the model is used to test a tidal farm of 21 devices with fluid dynamic simulations. In particular, we deploy the farm at Portland Bill, which is a marine site characterised by a wide spread in the direction of the tidal currents during a flood-ebb tide cycle. We optimised the lateral and longitudinal spacing of the turbines in a fence using computational fluid dynamics simulations and then performed a sensitivity analysis by changing the distance between the fences. The results show that the greater the distance between the fences, the higher the power output. The increase in power generation is around 16%, but this implies a huge increase in the horizontal extent of the farm. Further assessments should be carried out, as the expansion of a marine area dedicated to energy exploitation may conflict with other stakeholder interests.

Going beyond BEM with BEM: an insight into dynamic inflow effects on floating wind turbines

Abstract. Blade element momentum (BEM) theory is the backbone of many industry-standard wind turbine aerodynamic models. To be applied to a broader set of engineering problems, BEM models have been extended since their inception and now include several empirical corrections. These models have benefitted from decades of development and refinement and have been extensively used and validated, proving their adequacy in predicting aerodynamic forces of horizontal-axis wind turbine rotors in most scenarios. However, the analysis of floating offshore wind turbines (FOWTs) introduces new sets of challenges, especially if new-generation large and flexible machines are considered. In fact, due to the combined action of wind and waves and their interaction with the turbine structure and control system, these machines are subject to unsteady motion and thus unsteady inflow on the wind turbine's blades, which could put BEM models to the test. Consensus has not been reached on the accuracy limits of BEM in these conditions. This study contributes to the ongoing research on the topic by systematically comparing four different aerodynamic models, ranging from BEM to computational fluid dynamics, in an attempt to shed light on the unsteady aerodynamic phenomena that are at stake in FOWTs and whether BEM is able to model them appropriately. Simulations are performed on the UNAFLOW 1:75 scale rotor during imposed harmonic surge and pitch motion. Experimental results are available for these conditions and are used for baseline validation. The rotor is analyzed in both rated operating conditions and low wind speeds, where unsteady aerodynamic effects are expected to be more pronounced. Results show that BEM, despite its simplicity, can adequately model the aerodynamics of FOWTs in most conditions if augmented with a dynamic inflow model.

An approach to calculate Franck-Condon factors involving anharmonic potentials using harmonic oscillator bases

In this contribution a discrete variable representation (DVR) approach to calculate Franck-Condon factors (FCFs) is presented. The method is illustrated using a harmonic oscillator basis. The advantage of this approach is that it is possible to calculate FCFs associated with general potentials based on the knowledge of the harmonic oscillator theory. First the coordinate and momentum representations are introduced. Based on this concept, the DVR is proposed, which allows the Franck-Condon factors to be calculated in a simple form. This method takes advantage of the momentum as generator of translations to include the displacement of the potentials. The calculation of the FCFs is exemplified for transitions involving the ground state X1Σg+ and the excited state a 1Π g of the diatomic molecule 14N2 both modelled with Morse potentials.

Numerical Calculation of 1P Aerodynamic Loads on Aviation Propellers

To accurately predict the 1P aerodynamic loads of aviation propellers, this paper established a mathematical model of aviation propeller 1P aerodynamic loads based on the coupling method of blade element theory and momentum theory. Correction methods such as the Prandtl tip correction method and the propeller root correction method were implemented to further improve calculation accuracy. A 1P aerodynamic load calculation procedure was developed based on the mathematical model by using the Matlab software. 1P aerodynamic loads of a three-blade propeller were predicted for three different angles including 3 °, 9 °, and 12°. The numerical calculation results show that the calculated aerodynamic characteristic parameters of individual propeller blades obtained based on the propeller 1P aerodynamic load mathematical model deviate less than 6% from the CFD simulation results, and regular periodic pulsations are observed. The numerical calculations in this paper show that the propeller 1P aerodynamic load calculation procedure developed based on this model can accurately predict the propeller 1P aerodynamic load, which can provide some reference for the study of aviation propeller aerodynamic characteristics.

Tidal turbine blade design optimization based on coupled deep learning and blade element momentum theory

The practical design optimization of blade structures is crucial for enhancing the power capture capability of tidal turbines. However, the significant computational costs required for directly optimizing turbine blades through numerical simulations limit the practical application of blade structure optimization. This paper proposes a framework for tidal turbine blade design optimization based on deep learning (DL) and blade element momentum (BEM). This framework employs control points to parameterize the three-dimensional geometric shape of the blades, uses convolutional neural networks to predict the hydrodynamic performance of each hydrofoil section, and couples BEM to forecast the performance of tidal turbine blades. The multi-objective non-dominated sorting genetic algorithm II is employed to optimize the geometric parameters of turbine blades to maximize the power coefficient and minimize the thrust coefficient, aiming to obtain the optimal trade-off solution. The results indicate that the prediction of the DL-BEM model agrees well with experimental data, significantly improving optimization efficiency. The optimized tidal turbine blades exhibit excellent power coefficients and reduced thrust coefficients, achieving a more balanced structural solution. The proposed optimization framework based on DL accurately and rapidly predicts the performance of tidal turbines, facilitating the design optimization of high-performance tidal turbine blades.

Computing Education Interventions to Increase Gender Equity from 2000 to 2020: A Systematic Literature Review

Although gender parity has been achieved in some STEM fields, gender disparities persist in computing, one of the fastest-growing and highest-earning career fields. In this systematic literature review, we expand upon academic momentum theory to categorize computing interventions intended to make computing environments more inclusive to girls and women and consider how those characteristics vary by the success of the intervention. Particular attention is given to the efficacy of broadening participation and success for women in computer science, information technology, and related fields. After scrutinizing 168 relevant studies, 48 met the inclusion criteria and were included. We introduce a framework for gender equity in computing, expanding on existing research on academic and STEM momentum to encompass new domains representing social and structural momentum. Our analysis reveals the complex roles of intervention domains, strategies, goals, levels, and duration in shaping their efficacy. Implications for theory, research, and practice are discussed.

Research on the Calculation Method of Propeller 1P Loads Based on the Blade Element Momentum Theory

Aircraft propellers produce relatively large in-plane loads, called propeller 1P loads, during maneuvers such as turning, diving, and lifting, and these loads can negatively affect the flight and control of the aircraft. In order to study the change rule of 1P aerodynamic loads, in this paper, a mathematical model of the propeller 1P aerodynamic loads has been developed based on the blade element momentum theory. This mathematical model was then corrected using the Pitt–Peters incoming flow correction method, the Prandtl tip correction method, and the propeller root flow correction method. Based on this mathematical model, a calculation procedure for the propeller 1P aerodynamic loads was developed using MATLAB software, and the accuracy of the procedure was verified by comparing the results with CFD simulation results. Numerical simulations show that the results calculated based on the proposed mathematical model for the coefficients of thrust, power, bending moment, and the tangential force of the propeller have an error of less than ±6.00% compared to the CFD simulation results. For a small inflow angle, the coefficients of bending moment and tangential force of the whole propeller fluctuate in a small range. But, as the inflow angle increases, the fluctuation range of the aerodynamic characteristic parameters of the propeller increases and the fluctuation becomes more complicated. Through numerical calculations, it has been shown that the mathematical model presented herein is reliable and accurate. In addition, it greatly shortens the calculation time and improves the calculation efficiency. It is expected that the proposed model can provide a certain help for the strength design of the propeller structure and the study of the aerodynamic performance of the whole aircraft.

Acceleration neglect in trend extrapolations.

Many decisions rely on intuitive predictions based on time series data showing a trend. For instance, the current upward trend in global temperatures might lead to specific predictions about the extent to which global temperatures will rise in the future, and these predictions might be used to inform judgments about the urgency with which climate change must be addressed. However, those predictions often need to be revised to incorporate the effects of unexpected events that might accelerate a trend (i.e., increase its rate of change), such as an unanticipated increase in CO₂ emissions, or decelerate a trend (i.e., decrease its rate of change), such as an unanticipated reduction in CO₂ emissions. In this work, we uncover a new cognitive bias by which people neglect how much a trend can accelerate (vs. decelerate) due to unexpected events. We explain this bias in terms of momentum theory and a naive understanding of physics. These findings have important implications for businesses and policymakers seeking to communicate information about topics such as climate change, stock market prices, or disease prevention. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Deep learning enhanced fluid-structure interaction analysis for composite tidal turbine blades

A precise and cost-effective prediction tool for fluid-structure interaction (FSI) analysis is crucial for optimizing the structural design of tidal turbine blades. However, the high computational costs associated with fluid dynamic analysis pose a significant challenge, as the current lack of efficient FSI prediction methods hinders the advancement of cutting-edge tidal turbine designs. To address this issue, this paper proposes a novel consolidated framework that integrates deep learning convolutional neural networks (CNN) with blade element momentum (BEM) theory and finite element method (FEM) to perform deformation analysis of turbine blade structures. The proposed CNN-BEM-FEM integrated framework efficiently identifies the geometric features and predicts the hydrodynamic parameters of turbine blades and thus, achieving accurate assessments of the structural behavior of tidal turbines. The study applies two-step verification procedures to validate the prediction accuracy of the CNN-BEM-FEM framework and the result demonstrates excellent agreement with experimental tests for hydrodynamic performance and blade deformation. When compared with the static one-way FSI calculated by Ansys Workbench software, the computational efficiency of CNN-BEM-FEM framework increases by more than 18 times, with discrepancies in blade deformation and equivalent stress calculations generally less than 5 %. By applying the proposed method to predict the FSI performance of tidal turbine blades with various shear web structures, the practical applicability for composite turbine blade design is successfully demonstrated. The results underscore the potential of the CNN-BEM-FEM framework as an efficient and accurate prediction tool for optimizing the structural design of tidal turbine blades.

Wind Tunnel Investigation of Transient Propeller Loads for Non-Axial Inflow Conditions

Recent developments in electrical Vertical Take-off and Landing (eVTOL) vehicles show the need for a better understanding of transient aero-mechanical propeller loads for non-axial inflow conditions. The variety of vehicle configurations conceptualized with different propellers in terms of blade geometry, number of blades, and their general integration concept results in aerodynamic loads on the propellers which are different from those on conventional fixed-wing aircraft propellers or helicopter rotors. Such varying aerodynamic loads have to be considered in the vehicle design as a whole and also in the detailed design of their respective electric propulsion systems. Therefore, an experimental approach is conducted on two different propeller blade geometries and a varying number of blades with the objective to explore the characteristics at non-axial inflow conditions. Experimental data are compared with calculated results of a low-fidelity Blade Element Momentum Theory (BEMT) approach. Average thrust and side force coefficients are shown to increase with inflow angle, and this trend is captured by the implemented numerical method. Measured thrust and in-plane forces are shown to oscillate at the blade passing frequency and its harmonics, with higher amplitudes at higher angles of inflow or lower number of blades.

Effect of Turbulent Wind Conditions on the Dynamic Characteristics of a Herringbone Planetary Gear System of a Wind Turbine

Due to complex environmental factors, the gear transmission systems of wind turbines are continuously affected by large torque load excitation with periodic and random properties. This paper shares the load-sharing and dynamic characteristics of a herringbone planetary gear system applied in a wind turbine. The gear dynamic model is established using a typical lumped parameter method, in which the nonlinear transmission errors of the gear pairs and left and right-side coupling stiffness of the herringbone gears are included. With the help of the blade element momentum theory, the precise calculation of the hub load of the wind turbine, which is the external excitation of the gear system, is implemented, in which the wind shear, tower shadow, turbulent effect, and tip loss correction are taken into consideration. The nonlinear dynamic characteristics of the system are obtained using the Runge-Kutta method and then discussed. The results show that the turbulent effect plays a major role in the impact on the load-sharing characteristics, and a reasonable set of the support stiffness of rotational components can improve the load-sharing characteristics of the system. The purpose of this research is to provide some useful references in numerical modelling and methods for designers and researchers of wind turbine transmission systems.

An improved B-L model for dynamic stall prediction of rough-surface airfoils

The Beddoes-Leishman (B-L) semi-empirical model is a classical method for predicting the dynamic stall of wind turbine airfoils. However, the model performs poorly for rough-surface airfoils due to the premature entry of turbulence and stall condition under the roughness effect. In this study, an improved dynamic stall model is developed for rough-surface airfoils. Two corrections are involved in the modifications. First, the calculation of flow separation points is corrected considering the difference between the normal and tangential separation points, and then an attenuation coefficient is introduced for the effective angle of attack to account for the rough-surface effect. Subsequently, the proposed model is extensively verified by experimental data of S-series airfoils with rough surfaces. Results show that the proposed model can well predict the dynamic stall characteristics of rough-surface airfoils with a higher accuracy than that of the original B-L model under various mean angle of attacks, oscillating amplitudes and reduced frequencies. At last, the model is utilized to predict the operating loads of a wind turbine using the Blade-Element Momentum theory. Significant difference between the dynamic loads predicted by smooth and rough models is observed. This indicates that the roughness effect on the dynamic stall model as well as the prediction of the operating loads on wind turbines cannot be ignored.

A Comprehensive Investigation of Linear and Nonlinear Beam Models on Flexible Wind Turbine Blade Load Calculations

This study was performed to investigate the effects of structural nonlinearity and large deformations on the aeroelastic loads of flexible wind turbine blades. First, a blade structural analysis model was established using the geometrically exact beam (GEB) theory. Subsequently, the blade element momentum (BEM) theory was corrected using the geometrically exact method leading to the development of a geometrically exact blade element momentum (GE-BEM) model. The results from the GE-BEM model indicated that flapwise deformations always reduce blade fatigue loads, while torsional deformations decrease fatigue loads under low wind speeds but increase them under high wind speeds. Finally, the linear Euler–Bernoulli beam and the GEB were compared to explore the influence of geometric nonlinearity on the blade aeroelastic loads, which revealed that the Euler beam model underestimates the blade loads. The simulations that used the GEB model produced torsional root twist fatigue loads that were 57.49% greater than those generated when the Euler beam model was used. Furthermore, the flapwise bending moment fatigue loads at the root were 8.24% greater than those obtained by the Euler beam model. The smallest discrepancy between the results of the two models was 7.26%, and it corresponded to the edgewise fatigue load.

Performance analysis of an idealized Darrieus–Savonius combined vertical axis wind turbine

AbstractTo investigate the effect of force distributions of each turbine component on the power performance of the Darrieus–Savonius combined vertical axis wind turbine (hybrid VAWT), the hybrid VAWT is modeled as idealized turbine under various force distributions. The goal of idealization is to simplify the intricate interactions between the Savonius and Darrieus components. The simulation actuator surfaces with uniform force distributions lead to a cost‐effective way to identify the optimal force distribution of each turbine component. The numerical model was validated against momentum theory. The results demonstrated that the numerical and theoretical results yield similar predictions in the low‐thrust cases but show differences in the high‐thrust cases. The maximum power coefficient of an idealized hybrid VAWT with given thrust coefficient is lower than that of a single actuator. This is a consequence of the nonoptimal loading on the actuator. The results indicate that an idealized hybrid VAWT does not show a significant power increase compared with an optimal single Darrieus rotor. Therefore, the presence of a Savonius rotor inside a Darrieus rotor leads to a lower power output in any circumstance. The hybrid configuration is primarily advantageous for the start‐up performance of the combined rotor, which is not explored in this study.

A hybrid numerical framework of potential and viscous flows for simulations of free running surface ship maneuvering in waves

This study presents a hybrid numerical framework for the accurate and efficient simulation of free-running surface ship maneuvering in waves. The proposed hybrid framework combines the MOUM (Modified Osaka University Method) body-force method to model the propeller and a hybrid approach of potential and viscous flows for wave-ship interactions. The MOUM body-force method, based on BEMT (Blade Element Momentum Theory), considers the three-dimensional viscous effects of propellers. The hybrid approach of potential and viscous flows decomposes the total physical field into the incident field and the complementary field, where the incident wave is solved by the potential flow theory to ensure the accuracy of wave propagation with coarse grids, and viscous and nonlinear effects are incorporated through the adapted URANS (Unsteady Reynolds Averaged Navier-Stokes) with refined grids. The 6DOF (Degrees of Freedom) motion equations of the rigid body and the dynamic structured grid with the overset technology are adopted to simulate the 6DOF motions of ship maneuvering in waves. Firstly, the applicability of the computational domain, domain-moving strategy, and ship motion-solving method for effectively simulating ship maneuvering in wave conditions are thoroughly examined. Then the reliability of present hybrid approach is validated using turning benchmark model tests of KCS model in regular waves. Simulations of turning circle and zig-zag maneuvers in regular waves are carried out by the traditional viscous CFD (Computational Fluid Dynamics) based on the boundary wave-generation approach and the proposed hybrid framework. The trajectories, motions and forces of ship maneuvering in waves predicted by both methods, as well as the computational efficiency, are compared. Numerical results indicated that the proposed method offers high accuracy and efficiency for predicting ship maneuvering in waves and could serve as a highly credible alternative to existing methods.

Rotor Performance Predictions for Urban Air Mobility: Single vs. Coaxial Rigid Rotors

This work details the development and validation of a methodology for high-resolution rotor models used in hybrid Blade Element Momentum Theory Unsteady Reynolds Averaged Navier–Stokes (BEMT-URANS) CFD. The methodology is shown to accurately predict single and coaxial rotor performance in a fraction of the time required by conventional CFD methods. The methodology has three key features: (1) a high-resolution BEMT rotor model enabling large reductions in grid size, (2) a discretized set of momentum sources to interface between the BEMT rotor model and the structured URANS flow solver, and (3) leveraging of the first two features to enable highly parallelized GPU-accelerated multirotor CFD simulations. The hybrid approach retains high-fidelity rotor inflow, wake propagation, and rotor–rotor interactional effects at a several orders of magnitude lower computational cost compared to conventional blade-resolved CFD while retaining high accuracy on steady rotor performance metrics. Rotor performance predictions of thrust and torque for both single and coaxial rotor configurations are compared to test the data that the authors obtained at the NASA Langley 14- by 22-ft. Subsonic Tunnel Facility. Simulations were run with both fully turbulent and free-transition airfoil performance tables to quantify the associated uncertainty. Single rotor thrust and torque were predicted on average within 4%. Coaxial thrust and power were predicted within an average of 5%. A vortex ring state (VRS) shielding phenomenon for coaxial rotor systems is also presented and discussed. The results support that this hybrid BEMT-URANS CFD methodology can be highly parallelized on GPU machines to obtain accurate rotor performance predictions across the full spectrum of possible UAM flight conditions in a fraction of the time required by conventional higher-fidelity methods. This strategy can be used to rapidly create look-up tables with hundreds to thousands of flight conditions using a three-dimensional multirotor CFD for UAM.

Quantifying the impact of modeling fidelity on different substructure concepts for floating offshore wind turbines – Part 1: Validation of the hydrodynamic module QBlade-Ocean

Abstract. To realize the projected increase in worldwide demand for floating offshore wind, numerical simulation tools must capture the relevant physics with a high level of detail while being numerically efficient. This allows engineers to have better designs based on more accurate predictions of the design driving loads, potentially enabling an economic breakthrough. The existing generation of offshore wind turbines is reaching a juncture, where traditional approaches, such as the blade element momentum theory, are becoming inadequate due to the increasing occurrence of substantial blade deflections. QBlade is a tool that includes a higher-fidelity aerodynamic model based on lifting-line theory, capable of accurately modeling such scenarios. In order to enable the simulation of offshore conditions in QBlade and to make use of this aerodynamic capability for novel offshore wind turbine designs, a hydrodynamic module called QBlade-Ocean was developed. In the present work, this module is validated and verified with two experimental campaigns and two state-of-the-art simulation frameworks on three distinct floating offshore wind turbine concepts. The results confirm the implementation work and fully verify QBlade as a tool to be applied in offshore wind turbine simulations. Moreover, a method aimed to improve the prediction of non-linear motions and loads under irregular wave excitation is analyzed in various conditions. This method results in a significant improvement in the surge and pitch degrees of freedom in irregular wave cases. Once wind loads are included, the method remains accurate in the pitch degree of freedom, while the improvements in the surge degree of freedom are reduced. A code-to-code comparison with the industry-designed Hexafloat concept highlights the coupled interactions on floating turbines that can lead to large differences in motion and load responses in otherwise identically behaving simulation frameworks.

Comparative study on dynamic responses of integrated installation process of a 5-MW and a 15-MW offshore wind turbine considering a pre-installed foundation

The integrated installation method for offshore wind turbines has the characteristics of high efficiency and low economic cost due to the small amount of construction work. However, the complexity of the entire system is exacerbated by environmental loads and mechanical couplings. Hence, it is urgent to investigate the dynamic response of OWTs during integrated installation procedures. This work compares the dynamic responses between NREL 5 MW and IEA 15 MW OWT installation systems. The hydrodynamics are calculated using the potential flow theory and the Morison equation, while the aerodynamics under wind turbine parked conditions are computed using the blade element momentum theory. Time domain simulations, considering various wind and wave conditions, are conducted via SIMA. This paper discusses the effects of wind and wave loads on the motion responses of catamaran installation vessel and spar, the relative motion at the mating point, and the sliding gripper forces, respectively. The results reveal that both the surge motions of the catamaran and the spar and the pitch motion of the spar exhibit sensitivity to wind loads. During installation, the motion response of the IEA 15 MW model is more dramatic than that of the NREL 5 MW system. Under wave-only conditions, the radial distances of the mating points for both NREL 5 MW and IEA 15 MW systems reach 1.65 m and 2.51 m, respectively. However, the influences of wind loads and wave incident angle are limited.

An Investigation of Tidal Stream Turbine Wake Development Using Modified BEM–AD Model

Tidal stream turbines (TST) are a promising option for electricity generation to meet the ever-increasing demand for energy. The actuator disk (AD) method is often employed to represent a TST, to evaluate the TST operating in a tidal flow. While this method can effectively reduce the computational cost and provide accurate prediction of far-wake flow conditions, it falls short of fully characterising critical hydrodynamics elements. To address this limitation, a hybrid method is implemented by coupling AD with the blade element momentum (BEM) theory, using detailed performance data, such as thrust, to enhance the prediction of the wake effects. This work focuses on the development of a hybrid BEM–AD method using Reynolds-Averaged Navier–Stokes (RANS) turbulence models within computational fluid dynamics (CFD). Two variations and a hybrid modification of an AD model are presented in this paper. The first modified variation is a velocity variation that takes into account velocity profile inflow into the disk’s configuration. The second modified variation is a radial variation that integrates the blade element theory into the disk’s configuration. The hybrid modified model combines both the velocity profiles influenced and blade element theory in the design and analysis of the actuator disk. Several key investigations on some of the pre-solver parameters are also investigated in this research such as the effect of changing velocity and radial distance on the porosity and loss coefficient of the actuator disk performance. Importantly, this work provides an improved method to evaluate the key wake effects from a TST array which is crucial to determine the power performance of the TST array.