Lifting Surface Method Research Articles

Optimal hierarchical trimming method for multi-lift system with helicopters considering aerodynamic interference

It is difficult to accurately trim the multi-lift system with helicopters due to complex aerodynamic interference and troublesome manipulation redundancy. To solve this problem, a mid-fidelity method is utilized to simulate the aerodynamic interference of the system. Particularly, the lifting surface method is applied to calculate the unsteady air loads of the rotors, and the viscous vortex particle method is used to model the wake. Moreover, an optimal cable-force allocation strategy based on the equilibrium optimizer is proposed to deal with the manipulation redundancy. On the basis, the load-leading optimal hierarchical trimming method for the multi-lift system is obtained by introducing the improved delta trimming algorithm and the hierarchical theory simultaneously. The trimming results for the multi-lift system at different forward speeds verify the effectiveness of the trimming method and indicate that: the optimal force allocation strategy is beneficial to reduce coupling and there are different characteristics of helicopters in the multi-lift system.

Unsteady aerodynamic modelling for dual-rotor wind turbines with lifting surface method and free wake model

A time-marching aerodynamic model for dual-rotor wind turbines (DRWT) is presented with the lifting surface method and free wake model. The performance of a reference DRWT by two axial connected NREL 5MW wind turbines is calculated to verify the algorithm. The output converges with remarkable oscillation. Free wakes swell under the coupling effect. The accumulated power of DRWT outranges single-rotor wind turbine (SRWT) by a limited extent under certain operating conditions. The front rotor (FR) produces the major portion of the power, especially for low inflow velocity. The unsteadiness of performance and spanwise load is further investigated, and the result shows that the power output of the rear rotor (RR) undergoes greater fluctuation than FR. The rotor-rotor induction strengthens both the rotors’ performance before they align and weakens it when they rotate away. The additional disturbance caused by FR’s tip vortices acts negatively on RR’s torque by upwashing the blade tip.

Flight dynamics analysis of a small tandem helicopter considering aerodynamic interference

The interference calculation is essential to the flight dynamic analysis especially for multi-rotors configurations. To analyze the flight dynamic characteristics of a small tandem helicopter precisely, a vortex method is utilized to obtain the aerodynamic interaction between the tandem rotors and the fuselage. Specially, the unsteady air loads and the wake of the rotors are developed using a lifting surface method and the viscous vortex particle theory, respectively, and the fuselage is modeled by the panel method to simulate the blocking effect on the rotors. Then the aerodynamic interference of the small tandem helicopter is analyzed under the conditions of different vertical or horizontal distance between the rear and front rotors. Subsequently, to save calculation time during flight dynamic analysis, a hybrid optimization trimming method combining the equilibrium optimizer and the improved delta method is proposed. At last, the flight dynamic analysis for the small tandem helicopter with different configurations are carried out and the results indicate that configuration in which the rear rotor is located higher than the front rotor and the one with larger longitudinal distance between tandem rotors are beneficial to increase the stability in lateral and longitudinal directions, respectively.

Comparative Study of Lifting Surface and CFD Methods in the Simulation of Morphing Process of Folding Wing

A folding wing aircraft can autonomously change its configuration in flight to respond to different flying environments. Hinge moment during morphing process is an important basis for driving mechanism design and structural strength check, and its calculation depends on the simulation of the morphing process. Existing studies mostly use the simplified lifting surface method for aerodynamic modeling. In this paper, the CFD-based simulation method is studied, and the results are compared with those by the lifting surface method. First, the unsteady aerodynamic modeling method of the folding wing based on the CFD method is studied, an effective description method is given to define the wall mesh motion caused by wing folding and aileron deflection, and an unfolding–refolding strategy is proposed to improve the quality of the internal mesh in the case of large folding angles. Then, the CFD aerodynamic model is coupled through a developed coupling calculation program with the flexible multibody structure model for the simulation of a flight-morphing process. The comparison with the results of the lifting surface method shows that hinge moments obtained according to the two aerodynamic models are markedly different. Analysis of the difference shows that airfoil thickness considerably affects aerodynamic loading distributions and hinge moments of folding wing aircraft. The lifting surface method ignores airfoil thickness, which will cause large simulation errors in hinge moments.

Stall Cell Prediction Using a Lifting-Surface Model

This paper investigates the use of a lifting surface method coupled with a nonlinear lift curve, the nonlinear vortex lattice method (NL-VLM), toward the study of stall cells on wings. First, Spalart’s spectral lifting line model is thoroughly investigated. It is found that the Gaussian filter leads to the existence of two different solutions, one directly interpolated in the lift polar and the other retrieved from the circulation distribution. Then the NL-VLM method is applied to the canonical cases of the infinite and the elliptic wing. In this model, the stall cells is represented as a sharp transition between stalled and prestalled wing section, meaning that no wing section effectively sees a negative slope of the lift against angle-of-attack relation. This sharp transition can be smoothed by introducing an artificial dissipation that also results in two separated solutions, without changing the underlying characteristics of the model. The effect of several parameters, like the grid spacing and the relaxation factor, is studied, with little effect on the wavelength of the predicted stall cells. The effect of specific parameters of the lift polar like the magnitude of the negative slope in the stall regime and the trend in the deep stall range is also investigated. It is observed that the slope of the lift versus angle of attack must not stay negative when the angle of attack goes to infinity for the system of equations to have a steady solution. The amplitude of the negative lift-curve slope has an effect on the wavelength of the cells explaining why the stall cells would not be observed for a leading-edge-type stall. Finally rectangular wings are studied for comparison to experimental data and higher-fidelity numerical simulations, showing the predictive capability of the proposed low-order model.

An investigation of scale effects on marine propeller under cavitating and non-cavitating conditions

ABSTRACT In this study, scale effects on the hydrodynamic performance of DTMB 4119 propeller have been investigated in uniform flow under non-cavitating and cavitating conditions by a simple practical method based on OpenFOAM. A potential based Lifting Surface Method has also been applied. A verification study of non-cavitating simulations has been carried out by Grid Convergence Index method at one scale ratio. Then the results have been validated with experiments. Schnerr-Sauer cavitation model of OpenFOAM has been used for the phase change between vapor and liquid. Cavitation simulations have been performed as a time-dependent with dynamic mesh while non-cavitating simulations have been carried out as a steady-state with static mesh. Effects of the scale ratio and cavitation simulations have been investigated and a simple fitting procedure on the thrust and torque values based on logarithm of Reynolds number have been applied. Results have also been compared with ITTC corrections.

Load control and unsteady aerodynamics for floating wind turbines

Unlike fixed-base offshore wind turbine, the soft floating platform introduces 6 more degrees of freedom of motions to the floating offshore wind turbine. This may cause much more complex inflow environment to the wind turbine rotors compared with fixed-base wind turbine. The wind seen locally on the blade changes due to the motions of the floating wind turbine platform which has a direct impact on the aerodynamic condition on the blade such as the angle of attack and the inflow velocity. Such unsteady aerodynamic effects may lead to high fluctuation of the loads and power output. The present work aims to study the high unsteady aerodynamic performance of the floating wind turbine under platform surge motion. The unsteady aerodynamic loads are predicted with a lifting surface method with a free wake model. A preview predict control algorithm is used as the pitch control strategy. A full scale U.S. Department of Energy’s National Renewable Energy Laboratory (NREL) 5 MW floating wind turbine is chosen as the subject of the present study. The unsteady aerodynamic performance and instabilities have been discussed in detail under prescribed platform surge motions with different control targets. Both minimizing the power output and rotor thrust fluctuation are set as the control objectives respectively. The theory analysis and the simulation results indicate that the blade pitch control can effectively alleviate the variation of the rotor thrust under platform surge motions. Larger amplitude of the variation of blade pitch is needed to alleviate the variation of the wind turbine power and this leads to high rotor thrust fluctuation. It is also shown that negative damping can be achieved during the blade pitch control process and may lead the floating platform wind turbine system into unstable condition.

The double‐tree method: An O(n) unsteady aerodynamic lifting surface method

SummaryTwo new methods for reducing the computational cost of the unsteady vortex lattice method are developed. These methods use agglomeration to construct time‐saving tree structures by approximating the effect of either a group of vortex rings or query points. A case study shows that combining the two new O(n·log n) tree methods together results in an O(n) method, called the double‐tree method. Other case studies show that the trade‐off between accuracy and speed can be easily and reliably controlled by the agglomeration cutoff distance. For a flat plate with 5 × 200 panels analyzed over 20 time steps, the double‐tree method is 7 times faster than the unsteady vortex lattice method with a <5% difference in the force distribution and total lift coefficient. The case studies suggest that the computational benefit will increase for the same level of accuracy if the size of the problem is increased, making the method beneficial for full‐aircraft analysis within optimization or dynamic load analysis, where the computational cost of the unsteady vortex lattice method can be large.

Numerical and experimental studies on the hydrodynamic damping of a zero-thrust propeller

Fluid added mass and damping are significant parameters when predicting the dynamic response of a submerged structure. The hydrodynamic damping of underwater rotating machinery is numerically and experimentally investigated by a zero-thrust propeller in this paper. The lifting surface method(LSM) combined with forced vibration was introduced as the numerical method to compute the corresponding unsteady thrust, while the experimental method of measuring added damping was accomplished by a propeller undergoing rotation combined heave motion. Results of the theoretical method are in good agreement with the experimental results before cavitation occurs, as cavitation is regarded to weaken the unsteady response of the propeller partly. The calculation results also show that both the frequency ratio(vibration frequency divided by rotation frequency) and the blade angle have a significant influence on the hydrodynamic damping. Therefore, the effect of blade angle on hydrodynamic damping should be considered during the design phase.

Inclination angle influence on noise of cavitating marine propeller

In this study, the effects of inclined shaft angle on the hydro-acoustic performance of cavitating marine propellers are investigated by a numerical method developed before and Brown\'s empirical formula. The cavitating blades are represented by source and vortex elements. The cavity characteristics of the blades such as cavitation form, cavity volume, cavity length etc., are computed at a given cavitation number and at a set advance coefficient. A lifting surface method is applied for these calculations. The numerical lifting surface method is validated with experimental results of DTMB 4119 model benchmark propeller. After calculation of hydrodynamic characteristics of the cavitating propeller, noise spectrum and overall sound pressure level (OASPL) are computed by Brown\'s equation. This empirical equation is also validated with another numerical results found in the literature. The effects of inclined shaft angle on thrust coefficient, torque coefficient, efficiency and OASPL values are examined by a parametric study. By modifying the inclination angles of propeller, the thrust, torque, efficiency and OASPL are computed and compared with each other. The influence of the inclined shaft angle on cavity patterns on the blades are also discussed.

Steady flow analysis of a slender wing by lifting surface method

In the paper hereby, steady flow around a thin-walled wing is analysed by means of the Lifting Surface Method. In order to carry out tests, the wing has been divided into a finite number of quadrilateral panels. All panel edges in turn are replaced by discrete straight vortex segments which induce velocities within the flow field. The problem boils down to working out velocity circulation distribution on the wing surface. For this purpose, numerical realization has been developed in C by Minimalist GNU for Windows compiler and Code::Blocks IDE. To work out a solution to the linear non-homogeneous algebraic system, the Gauss – Seidel stationary iterative method has been applied. The obtained results for various angle of attack values are depicted by means of ParaView.

Blade Section Profile Array Lifting Surface Design Method for Marine Screw Propeller Blade

Abstract The lifting surface model is widely used in screw propeller design and analysis applications. It serves as a reliable tool for determination of the propeller blade mean line and pitch distribution. The main idea of this application was to determine the blade shape that would satisfy the kinematic boundary condition on its surface with the prescribed bound circulation distribution over it. In this paper a simplified lifting surface method is presented – in which the 3D task for the entire blade is replaced by a set of 2D tasks for subsequent blade section profiles.

Mutual Effect Between Swept-and-Leaned Vanes and Acoustic Liners on Fan Interaction-Noise Reduction

The swept-and-leaned vanes and acoustic liners can both be used to reduce the turbofan noise. In this work, an analytical model was proposed under an idealized condition, in which an annular stator cascade and a locally reacting liner exist in an infinite duct at the same time, to study the mutual effect between these two techniques. Based on the transfer element method, the system matrix of multi-elements can be established based on the continuity of disturbance pressure and velocity at the interfaces. The acoustic elements for a stator and a liner were established, respectively, by employing the three-dimensional lifting-surface method and the equivalent surface source method, which are both the so-called methods of singularity. The interface matching pattern between adjacent elements was improved in this paper with more physics included, which can also be combined with the numerical methods easier. Because the technologies for fan-noise reduction, which are the swept-and-leaned vanes and acoustic liners in this paper, are both closely related to the modal acoustic field in the duct, the coupling effect can be strong in some conditions. The results showed that the noise reduction gained by these two techniques cannot be superposed simply. They should not be considered isolatedly. Further discussions on the transmission and reflection between different kinds of acoustic elements should be made to achieve the system optimization in the nacelle.

The unsteady aerodynamics of floating wind turbine under platform pitch motion

The aerodynamic performance of floating platform wind turbines is much more complex than fixed-base wind turbines because of the flexibility of the floating platform. Due to the extra six degrees-of-freedom of the floating platform, the inflow of the wind turbine rotors is highly influenced by the motions of the floating platform. It is therefore of interest to study the unsteady aerodynamics of the wind turbine rotors involved with the interaction of the floating platform induced motions. In the present work, a lifting surface method with a free wake model is developed for analysis of the unsteady aerodynamics of wind turbines. The aerodynamic performance of the NREL 5 MW floating wind turbine under the prescribed floating platform pitch motion is studied. The unsteady aerodynamic loads, the transient of wind turbine states, and the instability of the wind turbine wakes are discussed in detail.

Study of the unsteady aerodynamics of floating wind turbines

The aerodynamic performance and instabilities of floating platform wind turbines are much more complex than fixed based wind turbines because of the flexibility of the floating platform. Due to the extra six degree-of-freedom of the floating platform, the inflow of the wind turbine rotors is highly influenced by the motions of the floating platform. In the present study, an unsteady lifting surface method with a free wake model is developed for the analysis of the wind turbine unsteady performance under the floating platform surge motion conditions. The full scale NREL 5 MW floating wind turbine is chosen as the subject of the present study. The unsteady aerodynamic performance and instabilities have been discussed in detailed. It is believed that under certain platform surge motion, the wind turbine may gain more aerodynamic power output than under steady state condition. The flow separation on the surface of the blade and the pitch control may have the potential of leading the floating wind turbine into unstable conditions during certain platform surge motion.

Gemi Pervanelerinde Kavitasyon Kaynaklı Gürültü ve Farklı İz Alanlarının Pervane Performansına Etkisinin İncelenmesi

The fact that the inflow to the marine propeller is not uniform and cavitation phenomenon which is likely to develop on propeller blades may lead to undesirable effects (performance loss, erosion, vibration, and noise) with respect to hydrodynamic performance. Particularly, periodically changing of the sheet cavitation size on the propeller blades leads to unsteady propeller force, vibration, underwater radiated noise as well as noise in the ship. In this study, prediction of sheet cavitation induced noise of a marine propeller whose geometry and wake distribution are known, were examined. Cavitation was present in all given operating conditions. Further investigations were carried out for the target propeller to observe the effect of five different wake distributions on propeller performance, thrust values on the propeller blade for one rotation, and changing of propeller induced pressure pulse at a point on the hull. By changing skew value (two different skew angle), which is one of the geometric characteristics of original propeller, the effect on the cavitation induced noise was analyzed parametrically. The current study includes a discussion for only the original propeller in terms of performance (thrust, torque and efficiency). A numerical approach, based on Brown’s method and lifting surface method, was used to predict noise calculations. Noise levels obtained from calculations were compared to the other noise predictions in literature. It can be seen that skew has an effect in cases where the inflow is non-uniform. It can be concluded that vibration and noise levels can be reduced significantly by increasing the skew value of the propeller in these operating conditions

Three-dimensional analysis of vane sweep effects on fan interaction noise

The lifting surface method is an efficient solution for fully three-dimensional aerodynamic response of an annular cascade to the unsteady disturbances. Based on this response function, a prediction model for fan tonal and broadband interaction noise has been established. Three dimensional effects, including primarily the annular geometry and the radial non-uniformity of the upwash, can be fully taken into account. In this paper, a thorough analysis of vanes sweep effects is carried out by particularly considering the great dependence of the annular cascade aerodynamic response and modal acoustic field upon the radial phase profiles of incident disturbances. For fan tonal noise, different control behaviors of the forward and backward swept vanes are observed when the radial non-uniformity in the incident gust is introduced. The argument suggests that sweep should be selected so as to increase the wake intersections per vane, until it is larger than the number of cut-on radial acoustic modes. For fan broadband noise, the backward sweep succeeds in reducing the sound power level for a wide range of frequencies. Due to the statistical average effect, the efficiency relies much on the shape of the turbulence spectrum. And the sweep angle should be large enough to guarantee a preferable reduction to the fan broadband noise.

Aerodynamic shape optimization of non-straight small wind turbine blades

Small wind turbines usually operate in sub-optimal wind conditions in order to satisfy the demand where it is needed. The aerodynamic performance of small horizontal axis wind turbines highly depends on the geometry. In the present study, the geometry of wind turbine blades are optimized not only in terms of the distribution of the chord and twist angle but also with 3-dimensional stacking line. As the blade with 3-dimensional stacking line is given sweep in the plan of rotation and dihedral in the plan containing the blade and rotor axis, the common used blade element momentum method can no longer provide accurate aerodynamic performance solution. A lifting surface method with free wake model is used as the aerodynamic model in the present work. The annual energy production and the starting performance are selected as optimization objective. The starting performance is evaluated based on blade element method. The optimization of the geometry of the non-straight wind turbine blades is carried out by using a micro-genetic algorithm. Results show that the wind turbine blades with properly designed 3-dimensional stacking line can increase the annual energy production and have a better starting behavior compared with 2-dimensional-optimized blade geometries.

Predictions of Fan Broadband Noise Using Lifting Surface Method

This paper adopts the three-dimensional lifting surface method as a new cascade-response function to predict fan broadband interaction noise. The stator is modeled as an annular cascade, and the vanes are assumed to be zero-thickness plates with no stagger angle. The unsteady loading spectrum on the stator vanes is considered under a fully three-dimensional condition rather than calculated by the strip theories that are widely used in the existing analytical broadband fan noise models. The sound power spectrum is calculated in an annular duct using numerical integration weighted by statistical turbulence spectrum. The present theory is verified by calculating the category 4 benchmark problem of the Third Computational Aeroacoustics Workshop for the response function and by comparing the predictions of a benchmark test for the broadband formulations of the sound power spectra. Then, the predictions of the inlet and exhaust sound power spectra for the NASA source diagnostic test are presented, which both show good agreement with the experimental results. The discrepancies indicate the importance of further corrections for stagger and swirling mean flow effects in realistic predictions. In the end, the variation trend of the sound power with different vane numbers is well captured, which indicates that this effect mainly refers to the propagation of cut-on acoustic modes in an annular duct. This model has the capability for further studies on the vane swept or lean effects.

Multi-objective optimization of wind turbine blades using lifting surface method

This paper describes a multi-objective optimization method for the design of horizontal axis wind turbines using the lifting surface method as the performance prediction model. The aerodynamic code for the design method is based on the lifting surface method with a prescribed wake model for the description of the wake. A multi-objective optimization algorithm approach is employed for the optimization of wind turbine blades with 3D stacking line (swept leaned blades). The (NSGA II) Non-dominated sorting genetic algorithm II is used to facilitate the multi-objective optimization and to find the global optima of high-dimensional problems. The scope of the optimization method is to achieve the best trade off of the following objectives: maximum of annual energy production and minimum of blade loads including thrust and blade rood flap-wise moment. To illustrate how the optimization of the blade is carried out the procedure is applied to NREL Phase VI rotor. The result shows the optimization models can provide more efficient designs.