Blade Element Method Research Articles

The influence of the rotor spacing distance and rotating speed ratio on the power production of dual rotor wind turbines using a modified two-way interaction blade element momentum method

The present study aims to develop an accurate and fast improved blade element method (BEM) with two-way rotor-rotor interaction model which can account for two-way rotor-rotor interaction and the influence of rotor spacing while most previous BEM models for co-axis dual rotor wind turbines (DRWT) ignore the rear to front rotor interaction effect. A modified BEM model distinct from computationally intensive Computation Fluids Dynamics (CFD) model, is proposed for DRWTs. Validation of the present model is conducted by comparing it with experimental data from referenced literature for both co- and counter-rotating configuration. In our case study, for both co- and counter-rotating configurations, the power coefficient (CP) maps exhibit a double-hump shape instead of a single peak on the power output -λ curve observed in a single rotor wind turbine system. This characteristic may lead the DRWT to a local CPmax condition rather than the global CPmax while pursing the optimum operational condition. Although the counter-rotating DRWT can achieve a higher CPmax for most rotor spacing ratio (S/R) cases, it exhibits inferior power output than the single rotor for the S/R = 0.1 case. The present model can serve as a rapid and accurate model for configuring and control strategy evaluating DRWTs.

Optimization of propellers under consideration of aeroacoustic and aerodynamic goals and installation effects

Advanced Air Mobility (AAM) vehicles like air taxis and cargo unmanned aerial vehicles (UAVs) operate close to urban areas. Therefore, it is necessary to keep the noise footprint of such aerial vehicles at a minimum to gain societal acceptance for AAM vehicle operations. Cargo UAVs are typically highly integrated in terms of functions leading to a high extent of aerodynamic interactions between propellers and the airframe. As a result of these installation effects, unsteady loading noise can become the dominant part of the aerial vehicle noise emissions which leads to a situation, where classical propeller noise reduction measures like blade tip Mach number reduction do not necessarily lead to a reduction in the overall noise emissions. Overcoming these uncertainties in propeller design necessitates propeller noise optimization on an aircraft configuration level. In this work, an existing propeller optimization framework for isolated propellers was extended accordingly: Consideration of propeller inflow velocity perturbations due to installation in the blade element momentum theory-based propeller performance prediction and utilization of a blade element method code (BEM) to consider the scattering of propeller noise on the airframe accounts for configuration noise aspects. Optimization results of a pusher propeller UAV configuration conclude this work.

Ceiling effect of flapping wing rotorcrafts to enable energy-efficient perching

Flapping wing rotorcrafts (FWRs) combine both the motion characteristics of flapping and rotary wings, exhibiting high aerodynamic efficiency at low Reynolds numbers. In this paper, the ceiling effect of FWRs has been studied through numerical and experimental methods to further investigate the aerodynamic performance of FWRs operating under a ceiling and to explore the feasibility of enhancing the flight efficiency of FWRs via ceiling-effect-based perching locomotion. Based on the momentum theory and blade element methods, a theoretical model is first established to predict the additional thrust generated by the FWR operating under the ceiling. Additionally, to uncover the detailed aerodynamic mechanisms of FWRs' ceiling effect, the computational fluid dynamics (CFD) simulations were conducted to analyze the changes in force production and flow field around the FWR at 75–115 mm distances from the ceiling. Furthermore, experimental methods were employed to validate the theoretical model and CFD simulation. The results demonstrate a continuous increase in the thrust from 19.18 to 22.15 gf as the ceiling distance decreases, while the total energy consumption remains relatively constant. Leveraging the ceiling effect, the tested FWR could achieve an additional lift force of up to 9.5% at 75 mm ceiling height with a 33 Hz flapping frequency. Finally, a ceiling perching demonstration was conducted to validate the feasibility of achieving FWRs' energy-efficient locomotion based on ceiling effects. Our study highlights the positive influence of ceiling effect on FWRs, showing a promising way to further improve the flight efficiency of FWRs.

Design and Analysis of Horizontal Axis Small Wind Turbine for Low Wind Velocity Using QBlade

Renewable energy systems are of high importance considering the present day energy requirement. In Wind energy systems design and analysis of wind turbines for enhanced efficiency at low at wind speed is studied in this paper. Aero foil shape is the one of the key aspects which determines the efficiency of the turbine. In this paper airfoil G4510, NACA 0018 and NACA 4412 are considered for the study with a blade length of 0.762 m. General Public Licensed Software QBlade is used for the simulation which uses Blade Element Method (BEM). Comparison of performance parameters for different aero foil is presented and blade is designed using G4510 airfoil nomenclature. Using these blades, a three bladed rotor is assembled and structural analysis is performed to know the pressure distribution on different areas of the blade. Finally, a tower is attached to the rotor assembly and simulation is carried on the small wind turbine. Graphical relationship between power, tip speed ratio, velocity and coefficient of pressure is obtained for analysis.

Extensive design and aerodynamic performance investigation of diffuser augmented wind turbine (DAWT) guided by generalized actuator disc theory

Shrouding a turbine boosts power, lowers cut-in speed, but raises installation costs, and limits adaptability to wind shifts. A compact, wide-angle DAWT with competitive capacity is crucial for practical installations. Small turbines, often in fluctuating wind sites, necessitate thorough off-design performance analysis. A relatively short, wide-angle GOE431 diffuser is optimized by an efficient response surface method. Inverse blade element method, combined with actuator disc DAWT CFD considering wake swirl, shapes 90 cm-diameter rotor blade with minimal iterations. Implications of Generalized Actuator Disc Theory on DAWT design and performance are addressed with three-dimensional CFD for the first time. This approach unveiled substantial room for improving DAWT efficiency and uncovered key factors causing deviations from ideal performance. Tip leakage and diffuser losses constituted 9.5% of overall energy losses, with wake rotation, blade efficiency, and blade drag at 9.2%. Tip-hub losses, finite blade number, rotor-diffuser interaction, suboptimal rotor, and turbulence contributed to 12.1% in three-bladed DAWT, reaching CP,max = 0.746, with tip losses about one-third of bare turbine. Six-bladed DAWT raised CP by 93%, from 0.417 to 0.805, achieving 75% of ideal DAWT. Finite blade number led to reduced attack angles, higher tip losses, and limited flow expansion, contributing significantly to energy losses. As blade number and design tip-speed-ratio increased, blade Reynolds number decreased, suggesting an optimal combination to minimize energy losses. At off-design, a strong connection existed between thrust coefficient, diffuser efficiency, and Cp increase in wide-angle diffuser DAWTs. Maintaining CT near CT,opt (0.786) at high tip-speed-ratio led to significant Cp rise.

Landing trajectory and control optimization for helicopter encountering different tail rotor pitch lockups

In recent years, tail rotor failure has been a significant factor in helicopter accidents, contributing to around 30 % of all incidents. Among these failures, tail rotor pitch lockup accounts for nearly 2/3. However, there is currently a lack of research on the landing trajectory and control optimization for piloted helicopters facing tail rotor pitch lockup. Therefore, this paper aims to study the landing trajectory and pilot control strategy optimization during helicopter tail rotor pitch lockup. The findings of this research are expected to provide valuable insights and serve as a reference for subsequent real-time pilot-in-the-loop simulations and final flight tests. In this paper, we utilize the UH-60A helicopter as a prototype to establish a flight dynamics model and a pilot model. The aerodynamic forces and induced velocity of the main rotor are calculated using the blade element method and Pitt-Peters model. The rotor flap motion is simplified to a first-order harmonic quantity. We then formulate the problem of safe landing and control optimization as a nonlinear optimal control problem, with the cost function designed to reflect safety and feasibility during the flight and touchdown process. To solve the optimal control problem numerically, we use direct multiple shooting and sequential quadratic programming algorithms. Flight test data for the UH-60A, encompassing steady-state flight, dynamic response, and autorotation landing, are utilized to validate the accuracy of the flight dynamics model and the effectiveness of the optimal control algorithm. Finally, the paper investigates the safe landing trajectories and control strategies for the sample helicopter when encountering high tail rotor pitch lockup and low tail rotor pitch lockup, respectively. Simulation results demonstrate that when the tail rotor is stuck at a high pitch, it is advisable for pilots to execute a high-power state landing by maintaining the engine at high power while reducing forward speed and descent rate. Conversely, when the tail rotor is stuck at a low pitch, flying at an economical speed (in a low-power state) is advantageous, but it does not facilitate a safe landing thereafter. If the pilot attempts a conventional landing, the yaw rate at touchdown would be very high and potentially dangerous. In contrast, if an autorotation landing is executed, the landing will be safer with a much lower yaw rate at touchdown. The optimal landing trajectory and control process align with the recommendations from actual helicopter flight tests. The proposed method provides feasible pilot control strategies for safe landing when helicopters encounter various tail rotor pitch lockup situations. This research can serve as a reference for pilots before conducting actual flight tests.

Effects of the spacing between two hydrokinetic turbines on the bedforms by numerical simulations

Accelerating hydrokinetic renewable energy development towards endurance requires investigating interactions between the hydrokinetic turbine and its surrounding physical environment. Interactions between hydrokinetic turbines (HT) and mobile sediment bed are considered as a critical area of assessment, however limited research studies have been published to address this issue. Hill et al. (2015) have shown experimentally that the presence of either single or multiple turbines and the rotation of the blades affect the bed morphology. Musa et al. (2019) have investigated experimentally the local effect of streamwise aligned turbines on the bedload, they found as a result that the geomorphic effects are stronger with increasing shear stress due to the presence of the rotors, inducing an alternating scour-deposition phenomenon. Chen et al. (2017) have investigated the influence of rotor blade tip clearance (distance between blades and seabed) on the scour rate of pile-supported horizontal axis current turbine. The results suggest that the decrease in tip clearance increases the scour depth, hence more sediment transport. Recently, Khaled et al. (2021) have studied the impact of hydrokinetic turbine on erodible sand banks, they showed numerically a significant interaction between the confinement of the turbine and its impact on the near bottom.
 
 In the present issue, we study the impact of two interacted turbines on the near bedform morphology. A modelling framework is derived to predict the significant transport induced by the turbines, such as the Euler-Euler (EE) multiphase model for sediment transport and the Blade Element Method (BEM) to model the forces generated by the turbines, using the open source platform OpenFOAM and the library SedFoam (Chauchat et al. 2017). A phase of validation is presented for the combined model (EE and BEM) using experimental results of Hill et al. (2015). The present study consists in considering one sediment class, sand of diameter of 0.25 mm, and two horizontal axis turbines with an axial flow direction corresponding to the riverine case. The approach is configured with four different axial inter-turbines distances. The wake distribution behind the second turbine is altered by the wake of the upstream turbine in all configurations (fig. 2). This interaction promotes the erosion under the turbines and the deposition along the axis of the turbines in the wake due to relation between the dynamics of ripples generation and the wake effects of turbines (fig. 3).

Optimisation of Air turbines for OWC Wave Energy Converters: Sensitivity of Realistic Wave Climates

Wave Energy, Oscillating Water Column, Air turbines, Optimisation, Genetic Algorithms, Wave climates.
 Among all the Wave Energy Converter (WEC) technologies suggested in the last decades, the Oscillating Water Column (OWC) technology seems to be the most robust and reliable technology. Different are currently in operation, such as the Mutriku Wave Power Plant installed in a harbour, or are being developed, such as the MARMOK floating OWC device developed by IDOM and tested for over a year in the Biscay Marine Energy Platform (BIMEP). One of the key elements of the OWC technologies is the power take-off (PTO) system that converts the pneumatic energy trapped in the chamber into electrical energy. Such PTO system consists of an air turbine coupled to an electric generator, and has been the object of several studies, including numerical and experimental works that cover a wide range of different air turbine configurations, and some of the proposed research lines even reaching to combine both approaches. The most common turbine, mainly due to its relative simplicity both on the conceptual andmechanical aspects, is the Wells monoplane turbine, including variations such as the biplane and the counter-rotating configurations. However, other configurations such as the impulse turbine or the more recent bi-radial turbine have also been analysed.
 The preliminary design of these turbines usually relies on analytical models based on the blade element method, using dimensionless parameters for representing the behavioural charts of the different configurations. In fact, in order to better represent the behaviour of air turbines in realistic conditions with polychromatic waves, it is usual to consider the stochastic version of these dimensionless parameters so that they provide an overall indicator of their sea-state-related behaviour. However, the air turbines, regardless of their configuration, include a large number of different geometrical parameters, which complicates the optimisation procedure and leads to a decision-making process that relies on an expertise-based intuition. In this sense, suggests an optimisation method based on a Genetic Algorithm (GA) that enables the articulation of all the relevant parameters. This GA-based optimisation method articulates the information about the hydrodynamic behaviour of the WEC and the pneumatic conversion within the chamber. Hence, the optimisation is sensitive to the characteristics of the wave climate and, thus, the behaviour of the WEC in that specific wave climate.
 However, in order to make wave energy economically viable, mass production of the WECs, including their PTO systems, is a crucial point. As a consequence, standard WEC floaters and PTO system elements may need to be used in the different locations under different resource conditions. In order to evaluate the sensitivity of the optimal air turbine designs to the characteristics of specific wave climates, the present study will define optimal air turbines for different locations worldwide, comparing the characteristics of the different designs.

Numerical investigation of the local impact of hydrokinetic turbine on sediment transport—Comparison between two actuator models

Hydrokinetic turbines interact with the dynamics of the sedimentary bottom at small and large scale. Despite the interest that the study of these interactions deserves, little research has been published in the field. In this paper, we investigate by numerical simulation the interaction between modeled hydrokinetic turbines and bed load under clear-water scour conditions. The mixture of water and sediment is accounted for by an Eulerian multiphase model developed in the open source platform OpenFOAM. The turbine blades are parameterized by two models: the Blade Element Method (BEM) and the Actuator Disc Theory (AD). A good agreement with measurements is obtained in the near wake. The effects of the two different turbine models on the bedload sediment transport and on the wake characteristics are then examined. The local impact of the turbine modeled by BEM is more pronounced on the bed than the one modeled by the AD. So, the BEM modeling is preferable to the AD one for local studies of the impact of a turbine on the bed morphology. However, combining BEM with the two-phase fluid-sediment is time consuming and make difficult the use of this method to study a farm of several stream turbines. In such a case the use of AD is still remains recommended for now. Moreover, more studies must be done at real scale as the turbine rotational speed is relatively low and could induced less impact of the swirl on the bottom shear stress.

Research of the array spacing effect on wake interaction of tidal stream turbines

Understanding the wake interactions among turbines is important for developing efficient tidal farm configurations. The present study compares the power and wake generated by a 2-row by 1-column array separated at three lateral spacings with those of a single tidal stream turbine. According to the results, power fluctuations increase with the tip speed ratio, with mean values corresponding to the inverse-u shape prediction of the blade element methods. For a single turbine, the cloud diagram of the lateral velocity deficit follows a half-elliptical contour with its center at the hub and initial covertices at the tip. The twin turbines largely exhibit these symmetric transversal distributions; however, they are doubled, with wake fusion occurring at the mid-width and closer with turbines approximation. The superposition of Gaussian-type velocity distributions matches the experimental bimodal functions with horizontally decreasing heights only after x > 6D. Vertically, the TIx in all conditions displays two strong areas, just above and below the turbine, owing to the interaction of the tip with tower vortices and the free and bed surface. In the two-unit arrangement, the blockage effect and the velocity of the mid-passage flow increase with the lateral separation of the turbines. This has a direct effect on wake combination, width, and recovery.

Numerical investigation of aerodynamically efficient wing tip-mounted propeller configuration using coupled RANS–BEM approach

Purpose Recent interest in electric aircraft has opened avenues for exploring innovative concepts and designs. Because of its potential to increase wing aerodynamic efficiency, the idea of wing tip-mounted propellers is becoming more popular in the context of electric aircraft. This paper aims to address the question of which configuration, tractor or pusher at wing tip is more beneficial. Design/methodology/approach The interactions between the wing and tip-mounted propellers in tractor and pusher configurations have been studied computationally. In this study, the propeller is modeled as a disk, and the blade element method (BEM) coupled with the computational fluid dynamics (CFD)–Reynolds-averaged Navier–Stokes (RANS) solver is used to calculate propeller blade loading recursively. A direct comparison between the wing with tip-mounted propellers in tractor and pusher configurations is made by varying the direction of rotation and thrust. Findings Wing with tip-mounted propellers having inboard-up rotation is found to offer less drag in tractor and pusher configurations than those without propeller cases. Wing tip-mounted propeller in tractor configuration with inboard-up rotation offers higher wing aerodynamic efficiency than the other configurations. In tractor and pusher configurations with inboard-up rotating propellers, wing tip vortex attenuation is seen, whereas with outboard-up rotating propellers, the wing tip vortex amplification is observed. Originality/value SU2, an open-source CFD tool, is used in this study and BEM is coupled to perform RANS–BEM simulations. Both qualitative and quantitative comparisons were made between the tractor and pusher configurations, which may find its value when a question arises about the aerodynamically best propeller configuration at wing tips.

Predicting the aerodynamic noise of counter-rotating coaxial rotors

This work presents an aerodynamic noise prediction model for counter-rotating coaxial rotors. The aerodynamic interactions due to the flow accelerations and wake flow properties are considered in an efficient blade element and momentum theory method to compute the mean flow variables. Then, the sectional aerodynamic lifts are represented as an array of point vortexes. Using the potential flow theory, the induced flow speeds, which vary with time due to the rotational motion, can cause unsteady forces acting on the blade surfaces. The computed aerodynamic variables are then incorporated into the noise prediction model. The computed acoustic spectra and directivities for coaxial rotors with identical rotating speeds are compared with experiments, and fairly good agreements are obtained. Notably, the unsteady loading due to the interaction of potential flows surrounding the blades can lead to significant tonal noise at high-order harmonics of the blade passing frequency. The dependence of the noise radiation on rotation speed is also explored, showing different scaling laws from the isolated rotors.

Characterization of Aerodynamics of Small Wind Turbine Blade for Enhanced Performance and Low Cost of Energy

During a turbine’s lifetime, minimizing the cost of power production should be the primary aim in addition to attaining high technical efficiency. Thus, this paper was aimed at enhancing the aerodynamic efficiency of a site-specific small wind turbine considering the cost of energy as one of the design parameters. The wind distribution of a specific site was employed to characterize the wind using the Weibull distribution method. The aerodynamics of a typical 5 kW wind turbine blade were investigated by implementing a blade element method (BEM) using a MATLAB code that applied the advancements and improvements with different modifications and which was validated by engaging computational fluid dynamics (Ansys-Fluent). The optimal pitch angle was then employed to further promote the performance characteristics of the blade. The cost of energy was reformulated in terms of rated power considering a cost variation of the main components that deviates with the rated power. Accordingly, the performance parameters were investigated against a varying rated power and the relative cost of energy, achieving a maximum power coefficient of 55.37% at a lower cost of energy. Moreover, annual energy production of approximately 18 MWh with a corresponding capacity factor of approximately 41% was achieved at a lower cost of energy. These findings demonstrate that the selected modelling, analysis procedures, and modifications enhance the aerodynamic performance characteristics and lower the cost of energy of the small wind turbine blade, which promotes the affordability and energy harnessing capability of small wind turbines.

Aerodynamic analysis for a bat-like robot with a deformable flexible wing

AbstractDue to the efficient and flexible flight ability of bats, bat-like robots have become the focus of research in the field of bionic robots. Aerodynamic calculation is an important part of the research field of bat-like robot, which is the basis of the structure design and flight controller design of bat-like robot. However, due to the complex flight mechanism of bats, there is no mature theoretical method to calculate the flight aerodynamic force of bat-like robots. To solve this problem, this paper takes the membrane of a bat-like robot as the research object and analyzes in detail the effects of wing folding and unfolding and flexible deformation of the membrane on the chord length, passive torsion angle and relative velocity. Based on quasi-steady state model and blade element method, a set of aerodynamic calculation method for flexible deformed wing is established. In order to verify the effectiveness of the proposed method, the theoretical calculation results and the results of the fluid-structure interaction simulation are compared and analyzed under various working conditions. The two results are in good agreement under each working condition, and the errors are all within reasonable range, which proves the effectiveness of the method. This study can provide a theoretical basis for rational structure design and precise flight control of bat-like robot.

Aerodynamic Modeling and Performance Analysis of Variable-Speed Coaxial Helicopter

In this paper, the variable-speed coaxial helicopter is modelled by the blade element method, non-uniform inflow method and empirical function method, and the aerodynamic performance analysis method is proposed. To ensure the accuracy of this method, a flight test of the verification aircraft has been performed, and the rotor speed and required power under different forward flight speeds have been obtained. By comparing the experimental results with the calculation results, it is ascertained that the rotor speed trim error of this method is less than 6%, and the required power calculation error is less than 5%, which demonstrates the accuracy of this method. Finally, when the rotor diameter, hovering collective pitch and hovering rotor speed are equal, the required power of variable-speed coaxial helicopter and variable collective-pitch coaxial helicopter is compared through this method. The comparison results show that the variable-speed coaxial helicopter has low required power when it is less than the forward flight speed corresponding to the hovering rotor speed. When the forward speed is higher than that corresponding to the hovering rotor speed, the variable-pitch coaxial helicopter has lower required power.

Vorticity Confinement Technique and Blade Element Method for Accurate Propeller Modelling

Traditional CFD techniques are not effective in preserving wakes and vortices over larger distances and for longer times. Vorticity Confinement (VC) technique helps counter the numerical diffusion to preserve wakes and vortices. In the current study, VC was used to accurately model the propeller flow using two different propeller modelling techniques after being implemented into SU2, an open-source CFD solver. One resolves flow past the propeller by solving RANS equations in a rotating reference frame. Another is a simplified propeller modelling technique in which the propeller needs to be modelled as a disk, and the propeller loading is determined using the blade element method. In the first case, VC enabled tip and hub vortices to convect over larger distances from the propeller, along with an improved resolution of gradients in the tip vortex. With the latter technique, VC helped conserve the tangential velocities for longer distances.

Impact of spatially varying flow conditions on the prediction of fatigue loads of a tidal turbine

Site development for tidal turbines relies upon a good understanding of the onset flow conditions, with disk averaged velocity typically used as a reference to define turbine power and mean loading. This work investigates the variation of onset flow conditions which occur for the same disk averaged velocity. Analysis builds upon data previously acquired during the measurement campaign conducted for the ReDAPT project using bed mounted ADCPs \cite{Sellar2018}. These measurements define the turbulence characteristics and vertical shear profiles over the rotor plane which are incorporated into an efficient blade element method for prediction of unsteady blade loads. This method allows efficient calculation of blade loading for multiple onset shear and turbulence profiles, each with the same disk average velocity, to determine the cyclic loading which contributes towards fatigue. Predictions of fatigue loads from measured profiles are compared with predictions from profiles predicted for the same location with a MIKE3 model \cite{Gunn2014}. Within the water depth two vertical positions are analysed, with vertical shear profiles from measurements and a multi-parameter model used to define the onset. For a near-bed location, use of the averaged predicted velocity profiles neglecting variation of turbulence intensity with flow-speed provides fatigue loads to within 1\% of predictions obtained using all measured profiles of velocity and corresponding turbulence intensity. For the near-surface location, the same approach under predicts fatigue loads by 16-19\%. This is partly due to the occurrence of a wider range of turbulence intensities. Since this is nearly constant with flow-speed a scaling factor is applied to load cycles from predicted profiles to estimate the aggregated fatigue load obtained using all measured conditions, providing confidence that accumulated fatigue loads can be predicted efficiently from velocity profiles obtained from shallow water models.

마이크로 수력 발전을 위한 프로펠러형 림구동 축류 터빈 설계

A design method for a propeller type rim-driven axial-flow turbine for a micro-hydropower system is presented. The turbine consists of pre-stator, impeller and post-stator, where the pre-stator plays a role as a guide vane to provide circumferential velocity to the on-coming flow, and the impeller as a rotational power generator by absorbing angular momentum of the flow. BEM(Blade Element Method), which is based on the turbine Euler equation, is employed to design the pre-stator and impeller blades. NACA 66 thickness form and a=0.8 mean camber line, which is widely accepted as a marine propeller blade section, is used for the pre-stator and turbine blade section. A CFD method, derived from the discretization of the RANS equations, is applied for the analysis of the designed turbine system. The design conditions of the turbine is confirmed by the CFD calculation. Turbine characteristic curve is calculated by the CFD method, in order to provide the performance characteristics at off-design operation conditions. The proposed procedures for the design of a propeller type rim-driven axial-flow turbine are established and confirmed by the CFD analysis.

A comparison of wind turbine blade parametrization schemes for planform design optimization

This work compares nodal, spline and interpolation parametrization schemes for wind turbine blade planform design. The comparison is done on a power coefficient maximization problem, where the aerodynamic properties of the blade are computed using the Blade Element Method. The problem is solved using a gradient-based interior-point method with analytic gradients. We show the variation in planform design for each parametrization scheme when the degrees of freedom of the parametrization varies. We compare how the power coefficient converges with increasing degrees of freedom for each scheme. Our results shows that the B´ezier spline, the Piecewise Cubic Hermite Interpolation Polynomial (PCHIP) and Lagrange interpolation schemes present the best grid convergence out of all studied schemes.

Comparison and evaluation of blade element methods against RANS simulations and test data

This paper compares several blade element theory (BET) method-based propeller simulation tools, including an evaluation against static propeller ground tests and high-fidelity Reynolds-Average Navier Stokes (RANS) simulations. Two proprietary propeller geometries for paraglider applications are analysed in static and flight conditions. The RANS simulations are validated with the static test data and used as a reference for comparing the BET in flight conditions. The comparison includes the analysis of varying 2D aerodynamic airfoil parameters and different induced velocity calculation methods. The evaluation of the BET propeller simulation tools shows the strength of the BET tools compared to RANS simulations. The RANS simulations underpredict static experimental data within 10% relative error, while appropriate BET tools overpredict the RANS results by 15–20% relative error. A variation in 2D aerodynamic data depicts the need for highly accurate 2D data for accurate BET results. The nonlinear BET coupled with XFOIL for the 2D aerodynamic data matches best with RANS in static operation and flight conditions. The novel BET tool PropCODE combines both approaches and offers further correction models for highly accurate static and flight condition results.