Blade Element Theory Research Articles

Optimization of Quadcopter Propeller Aerodynamics Using Blade Element and Vortex Theory

The optimization of quadcopter propeller aerodynamics is crucial for enhancing the efficiency and stability of unmanned aerial vehicles (UAVs), especially in their increasing applications across various sectors, including humanitarian relief and delivery services. This study focuses on optimizing quadcopter propeller performance using Blade Element Theory and Glauert Vortex Theory to analyze the aerodynamic properties and predict thrust generation accurately. Experimental methods, including wind tunnel testing and static thrust measurements, were used to validate the theoretical models. The results indicate a close correlation between theoretical predictions and experimental data, providing insights into improving propeller efficiency and mitigating aerodynamic losses. By understanding the propeller characteristics, this research contributes to the development of advanced drone propulsion systems with enhanced thrust, reduced drag, and better overall flight performance. The findings also highlight the impact of environmental factors such as turbulence and blade geometry on quadcopter stability, pointing toward areas for further improvement in propeller design. This paper serves as a valuable resource for drone hobbyists, engineers, and researchers seeking to enhance UAV performance through optimized propeller aerodynamics.

Compensation Algorithm for Wind Turbine Main Shaft Loads Based on LSTM

Abstract For wind turbine development, load size is the core and critical factor. Currently, most companies employ Bladed software for load calculations, which enjoys widespread use in engineering applications due to its efficiency and ease of use. However, constrained by the limitations of blade element theory and momentum theory, there still exist discrepancies between the simulation results and actual conditions. This paper aims to combine simulation algorithms with the application of an LSTM (Long Short-Term Memory) neural network to develop a compensation algorithm for the main shaft loads of wind turbines. By doing so, it endeavors to realize real-time monitoring of the main shaft loads, thereby providing a foundation for achieving high-precision control in wind turbine systems.

A model-based design approach for low-pressure axial fan blades considering the air flow system characteristics

The paper puts forward a computer methodology for designing low-pressure axial fan blades for small-capacity refrigeration applications. Based on the blade element theory (BET), the airfoil efficiency of the airfoil, the principles of mass and momentum conservation together with empirical correlations for the flow irreversibilities, a mathematical model was devised for screening the blade geometric parameters (e.g., radial chord and pitch variation, and hub radius) by varying the induction coefficient distribution for a given fan diameter, motor speed, and airflow system characteristic curve. The best blade configuration is selected by means of a tailor-made optimization algorithm and undergoes a series of linear transformations for translating the fan parametrization into a CAD drawing. Two new fan blades were designed, one for maximum blade efficiency (MBE) and another for maximum airflow rate (MAR). In comparison with the free-swirl design approach, a standard procedure adopted in the open literature, the proposed blades showed an efficiency and an airflow by 20 % (MBE) and 14 % (MAR) higher than the reference. The airflow characteristics of the new designs were also assessed by means of wind-tunnel testing, which confirmed an increase of 11 % in the case of MBE design, while an enhancement of 10 % was observed in the case of MAR design.

Cooperative Drone Transportation of a Cable-Suspended Load: Dynamics and Control

The cooperative transportation of a cable-suspended load by two unmanned rotorcraft is analyzed. Initially, the equations describing a system composed of three point masses and two rigid cables are derived. The model is then linearized about the hovering condition, and analytical expressions are derived to describe the eigenstructure of the open-loop system. Thanks to the specific parameterization of the problem, the different dynamic modes are outlined and discussed within an analytical framework. A novel controller is designed to enable the UAVs in the formation to perform trajectory tracking, maintain formation geometry, and stabilize payload swing simultaneously. A preliminary investigation of closed-loop stability is conducted using a linear approach. Validation is performed in a realistic simulation scenario where two drones are modeled as rigid bodies under the effect of external disturbances and rotor-generated forces and moments, as obtained by Blade Element Theory. The proposed method demonstrates relative simplicity and significantly improves the flying qualities of delivery operations while minimizing hazardous payload oscillations and reducing energy demand.

Numerical Simulation Method for the Aeroelasticity of Flexible Wind Turbine Blades under Standstill Conditions

With the trend towards larger and lighter designs of wind turbines, blades are progressively being developed to have longer and more flexible configurations. Under standstill conditions, the separated flow induced by a wide range of incident flow angles can cause complex aerodynamic elastic phenomena on blades. However, classical momentum blade element theory methods show limited applicability at high angles of attack, leading to significant inaccuracies in wind turbine performance prediction. In this paper, the geometrically accurate beam theory and high-fidelity CFD method are combined to establish a bidirectional fluid–structure coupling model, which can be used for the prediction of the aeroelastic response of wind turbine blades and the analysis of fluid–structure coupling. Aeroelastic calculations are carried out for a single blade under different working conditions to analyze the influence of turbulence, gravity and other parameters on the aeroelastic response of the blade. The results show that the dominant frequency of the vibration deformation response in the edgewise direction is always the same as the first-order edgewise frequency of the blade when the incoming flow condition is changed. The loading of gravity will make the aeroelastic destabilization of the blade more significant, which indicates that the influence of gravity should be taken into account in the design of the aeroelasticity of the wind turbine. Increasing the turbulence intensity will change the dominant frequency of the vibration response in the edgewise direction, and at the same time, it will be beneficial to the stabilization of the aeroelasticity response.

Aerodynamic and Structural Design Procedures Supported by Fabrication and Flight Testing of a Small Unmanned Helicopter

In this work, typical design, production, and testing procedures for a small unmanned helicopter are explained and performed. In doing so, preliminary sizing of the helicopter and three main disciplines are conducted: aerodynamic analytical and numerical simulations, power calculations, and structure analysis assessment. First, a thorough survey is implemented to obtain the trends for the maximum take-off weight versus some design constraints such as rotor diameter, motor power, payload, and empty weight. Performance calculation results are obtained to figure out all aspects that correspond to the specified mission. The designed rotor geometry along with the aerodynamic characteristics and flight performance variables is then validated using the blade element theory and numerical simulations. Second, based on the power curves obtained for different flight regimes, an electric brushless motor is selected. The numerical simulations (Computational Fluid Dynamics) analysis is used to enhance the selection which implies that the motor power should be greater than 5.4 kW to overcome the drag forces. The motor power selection corresponds to a maximum rotor pitch angle of 15∘ and a maximum rotor speed of 1450 RPM. Then, the aerodynamic loads are used as an input for the structural analysis using one-way coupling of fluid–structure interaction (FSI) and consequently designing the internal structure of the blade. Eventually, the internal structure manufactured using carbon fiber-reinforced polymer (CFRP) by applying a combined technique between wet layup and compression molding. The blade is statically tested compared with numerical finite element model results. The fuselage structure along with hub and tail units is manufactured and assembled with the existing on-shelf components to examine the helicopter lift capability with different payloads up to 9 kg. The results show that the detailed design process is significant for manufacturing such blades and the helicopter is capable of lifting off the ground with various payloads depending on the rotor pitch angles (8∘, 12∘, and 15∘) at a constant rotor speed of 1450 RPM.

Effects of motion parameters on the propulsion characteristics of flexible pectoral fins in bio-manta robots

Manta rays have emerged as excellent bionic objects due to their efficient and flexible propulsion. A thorough understanding of the propulsion characteristics of manta ray robot pectoral fins is highly important for optimizing pectoral fin design and guidance strategies. Based on the silhouette and kinematics of the manta ray, we designed flexible pectoral fins and a 2DoF bionic mechanism that couples the flapping and pitching movements. Blade element theory was used to conduct a dynamic analysis of the bio-manta pectoral fins. The Strouhal number is used as a key dimensionless number that affects the hydrodynamic characteristics of a bio-manta robot during periodic flapping, as well as the flexibility of the pectoral fins and the angle of attack. We describe a series of hydrodynamic experiments conducted to analyze the single and interactive effects of the motion parameters of pectoral fin propulsion and regression analysis. The results show that when St is [0.2,0.4], the CT (thrust coefficient) of the flexible pectoral fin increases rapidly. When St increased beyond 0.4, the growth trend slows and remains essentially unchanged after 0.8. The CT reaches its peak, the propulsion efficiency is highest when St is between [0.4,0.6]. The angle of attack and the CT show a negative inverse quadratic trend, reaching a peak at 6.5°, and their influence is weaker than that of the frequency. The flexibility and CT showed a cubic trend, and the influence of flexibility was more significant when swimming at medium and low speeds. When swimming slowly, flexibility has a significant interactive effect on the frequency and angle of attack. However, these interactive effects reduce at high speeds. When the bio-manta robot starts at 0 speed, it should maneuver at high frequency and large amplitude while ensuring sufficient structural strength. After reaching a certain speed, the device maintains a large amplitude and low-frequency flapping operation to continuously drive propulsion.

Facilitating aerospace engineering senior design: Integrating lab curriculum redesign with student project and new technologies

AbstractThis study addresses a gap in existing literature by exploring the impact of an aerodynamics laboratory course on students' readiness for senior design projects in Aerospace Engineering at North Carolina State University. The redesigned curriculum focuses on propellers, aligning with the increasing popularity of senior design projects involving fixed‐wing aircraft and multi‐rotor systems in the Mechanical and Aerospace Engineering Department. The updated course incorporates Additive Manufacturing (AM) and an anechoic chamber for the first time, outlining its structure, objectives, and pivotal concepts. The use of data acquisition codes streamlines experimentation while integrating AM accelerates practical applications of blade element theory (BET). Through an assessment of lab report grades, this initiative significantly enhances students' grasp of propeller concepts, marking a pivotal step in their preparation for senior design projects.

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.

Electric Motor Chain Modeling Using Artificial Neural Networks and Semi-Empirical Methods

The methodology presented in this paper is dedicated to a user who wants to design a power chain of an electric unmanned aerial vehicle. The power chain includes a brushless direct current (BLDC) motor, a propeller, and a battery. Three models are presented to predict the thrust, electrical consumption, mechanical torque, and rotational speed provided by each component of an electrical power chain. Only public data were used to design these models. The research was developed in order to be used by all people who want to buy electrical power chain components and therefore to model their properties. Neural networks set with MATLAB parameters were used to design BLDC motor output (rotational speed and mechanical torque) models. Empirical methods such as blade element theory (BET) and disk area were used to model propeller thrust. A battery discharge model was designed based on public datasheets. Very good prediction results were obtained for the rotational speed (0.20% of error) and torque (0.45% of error). Small thrust modeling errors of 1.06% were found with the BET method. Models presented in this research could be designed using a wide type of data, such as public data (provided on manufacturer websites) or real test bench measurements.

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.

The engine mission simulation system: coupled simulation of aircraft and engine in the mission

AbstractWhen designing future aircraft, the entire system including airframe, propulsion system, energy management and mission control must be considered in a coupled approach at an early design stage. To model and study this complex interaction, the Engine Mission Simulation System (EMSS) environment was created in cooperation with the Bundeswehr Technical Center for Aircraft and Aircraft Equipment. EMSS is intended to serve as a digital, flying test bed at the Institute of Jet Propulsion for the rapid and low-cost evaluation of new concepts for propulsion and power supply systems for new and legacy aircraft designs. This tool chain allows a detailed engine simulation under consideration of its flight condition while using an external propulsion and power control system. First, the software architecture of EMSS is discussed, which involves a propulsion simulation in NPSS® coupled with the X-Plane 11 flight simulator via MATLAB®/Simulink®. The aircraft itself is modeled as a six degrees of freedom simulation using the blade element theory, allowing both complex flight maneuvers and unusual aircraft to be easily simulated. The EMSS achieves real-time capability and enables user-friendly pre-design as well as quick trend detection through the ability to perform focused parametric studies. To evaluate the accuracy of the system’s results, the engine model used is validated against experimental data. Subsequently, the aerodynamic characteristics of the aircraft model are verified with a CFD simulation. Finally, a parametric study is used to demonstrate the mission as well as propulsion evaluation capabilities of the Engine Mission Simulation System.

Dynamic responses analysis of crane-blade coupling system for the single blade installation of offshore wind turbine considering the wind effect

The single blade installation method for large-scale offshore wind turbine has the advantage of reduced deck and crane requirements on the installation vessel. Accurately simulating the coupled dynamic responses of the system throughout the entire hoisting process is crucial to avoid spatial interference with surrounding structures. Additionally, the aerodynamic loads, particularly the turbulent wind with spatiotemporal non-uniformity, further aggravate the uncertainty of the dynamic responses. Therefore, a numerical model capable of comprehensive analysis of mechanical-hydrodynamic-aerodynamic-control is urgently needed. However, it is challenging for the commercial software to achieve the coupling analysis. In this paper, the hoisting process is investigated by jack-up installation vessel, so the influence of wave loads on the structure is not considered. The aerodynamic loads are firstly calculated by the blade element theory, and then the numerical model is established by the Lagrangian method, finally the analysis program is developed in MATLAB. The accuracy of the program is verified by code-to-code, and the interaction between the ship-mounted crane and aerodynamic loads during the hoisting process are analyzed. The results show that the aerodynamic loads should be considered during the hoisting of the blade, and the established program could determine the trajectory of the blade inputting the sea state, which can avoid the possible collisions with the surrounding structures.

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.

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.

Aerodynamic Analysis of Mathematically Modelled Propeller for Small UAV Using CFD in Different Temperature Conditions

Unmanned aerial vehicle (UAV) usage has witnessed a significant rise owing to its cost-effectiveness and versatile applications. However, the design techniques for UAV propellers, encompassing aerodynamic and structural analysis, have received limited attention from researchers. A well-designed propeller can effectively reduce battery consumption and enhance overall efficiency. This study focuses on mathematically designed propellers and compares them with advanced precision composite (APC) Slow Flyer propeller blades in terms of thrust coefficients, power coefficients, and efficiency. The investigation includes the utilization of tetrahedron meshing in simulations, employing the standard k–ω (k–omega) model. To evaluate the accuracy of the blade element theory (BET) in predicting thrust, the simulation data is compared with BET results. Furthermore, the study encompasses experimental testing to validate the simulation findings. The findings demonstrate that the mathematically modelled propeller outperforms the APC Slow Flyer propeller across all ranges of revolutions per minute (rpm). When comparing the results of both methods, BET exhibits an error difference of 10 % in higher rpm ranges, but this error diminishes as the rpm decreases. This study contributes a novel design technique for modelling propellers using mathematical formulas and provides a comprehensive comparison of their aerodynamic properties with existing propellers, utilizing both BET and computational fluid dynamics (CFD) methods, along with experimental validation.

Assessment of Reynolds-Averaged Navier–Stokes/Blade Element Theory Body Force Method for Propeller Modeling

This work presents an actuator disk-like body force method designed for propeller modeling, which is based on a full coupling between computational fluid dynamics (CFD) and blade element theory (BET). An analysis is conducted on the model to identify best practices for source term distribution. It is found that the source term volume shape has no impact on propeller loads and flowfield and that the velocities used for the BET analysis at each radial section should be evaluated exactly where half the source terms have been distributed in the CFD domain. Four tip-loss corrections, including two from literature, are also analyzed and compared to lifting-line and Reynolds-averaged Navier–Stokes (RANS) blade-resolved computations. The best practices and the most effective tip-loss correction lead to a final model that is compared to lifting-line, RANS, and unsteady RANS computations for different pitch angles and incidence angles, on the ONERA HAD-1 three-bladed light propeller. The RANS/BET body force model predicts thrust within 3% for axial flow and 8% for cases with incidence. The same accuracy is obtained for wake prediction.

Construction of Simulation Model of 'Lushijia No.1' under Wind and Wave Integration

Based on the new ' Lu Shijia No.1 ' platform, the project team has customized a set of force and motion response theory system for it. The existing model is extended, and the basic coordinate system of eight frames is proposed for the new platform, which simplifies the analysis process. By considering the design parameters of the platform, the linear potential flow theory, Stokes wave theory and blade element theory are used to analyze the force and motion response of the platform, and the numerical calculation standards of various forces are defined. At the same time, the H ∞ controller of the optimized fan is integrated to improve the overall control system of the fan. Based on the full coupling integration of wind turbine and platform, the project team uses AQWA hydrodynamic analysis software to simulate and analyze the platform in frequency domain. With the help of FAST-matlab, the time domain full coupling analysis of the platform is carried out. The simulation results show that the new ' Lu Shijia No.1 ' achieves the expected effect of ' reducing response and increasing power '. On the basis of simulation, the project team constructed a scaled down ' Lu Shijia No.1 ' model. Through the final launching test of the solid model, the feasibility of the theoretical design was proved.

An Improved Method for Swing State Estimation in Multirotor Slung Load Applications

A method is proposed to estimate the swing state of a suspended payload in multirotor drone delivery scenarios. Starting from the equations of motion of the coupled slung load system, defined by two point masses interconnected by a rigid link, a recursive algorithm is developed to estimate cable swing angle and rate from acceleration measurements available from an onboard Inertial Measurement Unit, without the need for extra sensors. The estimation problem is addressed according to the Extended Kalman Filter structure. With respect to the classical linear formulation, the proposed approach allows for improved estimation accuracy in both stationary and maneuvering flight. As an additional contribution, filter performance is enhanced by accounting for aerodynamic disturbance force, which largely affects the estimation accuracy in windy flight conditions. The validity of the proposed methodology is demonstrated as follows. First, it is applied to an octarotor platform where propellers are modeled according to blade element theory and the load is suspended by an elastic cable. Numerical simulations show that estimated swing angle and rate represent suitable feedback variables for payload stabilization, with benefits on flying qualities and energy demand. The algorithm is finally implemented on a small-scale quadrotor and is investigated through an outdoor experimental campaign, thus proving the effectiveness of the approach in a real application scenario.

Experimental investigation of UAV rotor aeroacoustics and aerodynamics with computational cross-validation

The study provided a base of comparison of known computational techniques with different fidelity levels for performance and noise prediction of a single, fixed-pitch UAV rotor operating with varying flight parameters. The range of aerodynamic tools included blade element theory, potential flow methods (UPM, RAMSYS), lifting-line method (PUMA) and Navier–Stokes solver (FLOWer). Obtained loading distributions served as input for aeroacoustic codes delivering noise estimation for the blade passing frequency on a plane below the rotor. The resulting forces and noise levels showed satisfactory agreement with experimental data; however, differences in accuracy could be noticed depending on the computational method applied. The wake influence on the results was estimated based on vortex trajectories from simulations and those visible in background-oriented schlieren (BOS) pictures. The analysis of scattering effects showed that influence of ground and rotor platform on aeroacoustic results was observable even for low frequencies.