Viscous Vortex Particle Method Research Articles

An rVPM-Based Aerodynamic Hybrid Optimization Method for Coaxial Rotor with Differentiated Upper and Lower Blades in Both Hover and High-Speed Cruising States

To enhance the performance of rigid coaxial rotors across both hovering and high-speed cruising conditions, this study develops a novel aerodynamic optimization method that differentiates between the upper and lower rotors. Utilizing the lifting line and reformulated viscous vortex particle method (rVPM), this approach models the complex wake fields of coaxial rotors and accurately assesses the aerodynamic loads on the blades. The optimization of geometric properties such as planform configuration and nonlinear twist is conducted through an innovative solver that integrates simulated annealing with the Nelder–Mead algorithm, ensuring both rapid and comprehensive optimization results. Comparative analyses demonstrate that these tailored geometric adjustments significantly enhance efficiency in both operational states, surpassing traditional methods. This research provides a strategic framework for addressing the varied aerodynamic challenges presented by different flight states in coaxial rotor design.

Experimental and Computational Investigation of Rotor Noise in Hover

The noise magnitude and directivity of a four-bladed 1.108-m-radius rotor in hover were measured at a tip Mach number of 0.42, representative of an electric vertical takeoff and landing vehicle rotor. The tonal noise was filtered from the acoustic spectra, allowing for analysis of the separate contributions of tonal and broadband noise. Accompanying computations of the same rotor and operating conditions were performed using the rotorcraft comprehensive analysis system (RCAS) with a viscous vortex particle method (VVPM) for aerodynamic calculations and PSU-WOPWOP with the semi-empirical Brooks, Pope, and Marcolini (BPM) broadband model for predicting acoustics. Measured broadband and tonal noise contributed similar magnitudes to the overall sound pressure level, with broadband always several decibels greater. This is in contrast to conventional helicopter rotors, which are dominated by tonal noise. Simulated trends of tonal noise matched the measurements, though the higher harmonic components of the acoustic spectra were underpredicted by up to 30 dB. The broadband noise was underpredicted by 10 dB at moderate rotor collectives, as the measured noise contained noise from laminar and turbulent boundary layers, while the model predicted predominantly laminar boundary layer–vortex shedding noise. Comparing the time histories of the measured and simulated rotor thrust revealed that the RCAS-VVPM method does not capture the amplitude of the 4/rev component of the thrust and lacks the higher frequency content present in the measured thrust, indicating a possible source of discrepancy in the tonal acoustic predictions. The results of this study show that methods to predict rotor tonal and broadband noise without the use of lengthy computational fluid dynamics computations must be further developed.

Analysis of the Aeroacoustic Characteristics of a Rigid Coaxial Rotor in Forward Flight Based on the CFD/VVPM Hybrid Method

This study develops a hybrid solver with reversed overset assembly technology (ROAT), a viscous vortex particle method (VVPM), and a CFD program based on the URNS method, in order to study the aerodynamic and acoustic characteristics of coaxial rigid rotors. The aerodynamic load of the “AH-1G” helicopter rotor is first calculated based on the hybrid method and compared with available experimental data. The prediction of the linear noise of the OLS rotor is then performed and the obtained results are compared with available experimental data. These results allow the evaluation of the accuracy of the hybrid method for emulating rotor aerodynamics and acoustics. Afterwards, the hybrid and CFD methods are applied to obtain the aerodynamic and acoustic characteristics of the given coaxial rigid rotor model, while taking into account the trim of the collective pitch. The obtained results demonstrate that the hybrid method has high proficiency in capturing blade–vortex-interaction impulsive loads and high computational efficiency in predicting associated loading noise characteristics. Furthermore, the effect of the hybrid method on the noise characteristics of coaxial rigid rotors under a different advance ratio, blade tip speed, shaft angle, and other conditions, as well as the impact of the upper and lower rotors on the noise contribution of the coaxial rotor are analyzed. Finally, the impacts of the initial phase and the vertical spacing on the sound pressure level are studied.

Flight dynamics modeling and analysis for a Mars helicopter

Flight dynamics modeling for the Mars helicopter faces great challenges. Aerodynamic modeling of coaxial rotor with high confidence and high computational efficiency is a major difficulty for the field. This paper builds an aerodynamic model of coaxial rotor in the extremely thin Martian atmosphere using the viscous vortex particle method. The aerodynamic forces and flow characteristics of rigid coaxial rotor are computed and analyzed. Meanwhile, a high fidelity aerodynamic surrogate model is built to improve the computational efficiency of the flight dynamics model. Results in this paper reveal that rigid coaxial rotor can bring the Mars helicopter sufficient controllability but result in obvious instability and control couplings in forward flight. This highlights the great differences in flight dynamics characteristics compared with conventional helicopters on Earth.

Variations in Thrust Sharing for Torque-balanced Lift-offset Coaxial Rotors

This paper presents numerical calculations, on coaxial rotor systems, that show the variations of rotor thrust share with lift offset, system thrust, and advance ratio. The calculations are based on a coupled analysis between the U. S. Army's Rotorcraft Comprehensive Analysis System (RCAS) and a viscous vortex particle method. The level of agreement between calculations and experimental data is good in hover and mixed in edgewise flight. In hover and zero lift offset–a condition in which the upper rotor typically produces more thrust than the lower rotor–changing system thrust does not significantly alter the rotor thrust share. For advance ratios up to approximately 0.25, independently increasing lift offset increases the lower rotor thrust; this is an aeroelastic phenomenon that is eliminated with rigid blades. Independently increasing advance ratio leads to three distinct regions with different thrust sharing behaviors; these behaviors are governed by changes to the longitudinal skew of the upper rotor wake and its proximity to the lower rotor.

Nonharmonic Control of the Blade-Vortex Interaction Noise of Electrically Controlled Rotor

Electrically controlled rotor, also known as swashplateless rotor, represents an active rotor system that, due to the use of a trailing edge flap system instead of a swashplate, not only enables primary control but also conveniently reduces the blade-vortex interaction (BVI) noise of the rotors through active control. The effect of nonharmonic inputs on the control of the BVI noise of electrically controlled rotors based on their unique trailing edge flap systems has been investigated in this paper. To this end, an analytical model for the vortex interaction-induced load and noise of electrically controlled rotor is first established based on the viscous vortex particle method, the Weissinger-L blade model, and the Ffowcs Williams-Hawkings (FW-H) equation. On this basis, a simulation study of flap nonharmonic control for BVI noise reduction in electrically controlled rotors is carried out. According to the mechanism of the BVI in electrically controlled rotors, the second quadrant flap nonharmonic control is used to reduce the advancing side BVI noise, and the effects of different control waveforms and amplitudes on the peak value and directivity of the BVI noise of the sample electrically controlled rotors are analyzed to reveal the noise reduction mechanism of flap nonharmonic control. Subsequently, the effect of the third quadrant flap nonharmonic control on BVI noise on the retreating side of the sample electrically controlled rotors is investigated. The results show that flap nonharmonic control has little effect on miss distance and that it controls BVI noise mainly by reducing the wake vortex strength on the advancing and retreating sides, which may lead to an increase in rotor noise in other regions; the noise reduction effect of flap nonharmonic control for different blade preindex angles indicates that suitable preindex angles coupled with flap nonharmonic control help optimally reduce noise.

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.

Accelerated method of helicopter brownout with particle-particle collisions

A novel background mapping-splitting method is proposed and coupled with an analysis method of helicopter brownout based on a viscous vortex particle method and a discrete element method to improve the efficiency of brownout simulations. In this work, particle-particle collisions are considered and a background mapping method where sand particles are mapped into structured background grids is established to accelerate the simulation. Furthermore, a background splitting method where a structured background grid is divided into several zones is developed to reaccelerate the simulation. The method is then demonstrated for the US Army EH-60L in brownout. The results show that the predicted behavior of brownout agrees well with observations from flight tests of the EH-60L. The CPU time of a direct method in the brownout simulation increases as a parabola, while the CPU time of the present method is a linear growth. Compared with the direct method, the efficiency of the present method is significantly improved, and the computational time is reduced by 70.29% compared with the background mapping method for a 10 million particles case.

Aeromechanics and Aeroelastic Stability of Coaxial Rotors

Coaxial rotor aeroelasticity is complex due to the counter-rotating wake system, rotor lift offset, periodic blade passage loads, unsteady rotor wake interactions, reduced rotor speed, and stiff hingeless blades. In this study, the aeroelastic stability of a coaxial rotor is examined in hover and forward flight. The rotor wake is modeled with the viscous vortex particle method, a grid-free approach for calculating vortex interactions over long distances. The spanwise blade aerodynamic loading is calculated using a computational-fluid-dynamics-based reduced-order model in attached flow, and the ONERA dynamic stall model in separated flow. Two propulsive trim procedures are developed: one with the propulsor not operating, and the other with the vehicle at level attitude. An aeroelastic stability analysis based on Floquet theory is applied to the periodic system. A novel graphical method is developed to identify coupling between blade modes of the two rotors. The effects of lift offset and advance ratio on the hub loads, inflow distribution, and aeroelastic stability are examined to provide an improved physical understanding of the aeroelastic interactions. Results indicate that the blade passage effect is caused by the bound-circulation-induced inflow. The first and second lag modes are the least stable modes in hover and forward flight.

Experimental and computational investigation of stacked rotor performance in hover

Experiments were performed on a 1.108 m diameter coaxial, co-rotating rotor, also called a stacked rotor, in hover. The performance of the stacked rotor was measured at various azimuthal and axial spacings. The performance of the rotor was also analyzed using the Rotorcraft Comprehensive Analysis System (RCAS) employing the viscous vortex particle method (VVPM) as well as computational fluid dynamics (CFD). Both the experimental results and the simulations showed that as the azimuthal spacing changed from negative angles (lower blades leading) to positive angles (upper blades leading), the thrust on the upper rotor increased by ∼50% and the thrust on the lower rotor decreased by a similar amount. The total thrust decreases by as much as 10% as the index angle reached zero. These changes in individual and total rotor thrust are explained by the interference velocity due to the bound circulation of the lifting blades. This property, combined with advances in electric motor control technology, can be useful as a novel method of aircraft control by in-flight adjustments of the azimuthal spacing. A 17.1% change in total thrust was observed with an azimuthal spacing change of 22.5∘ at constant collective. While RCAS and CFD predicted the rate of change with azimuthal angle well, the total change in thrust was underpredicted (11.6% change in thrust predicted by CFD and 6.3% predicted by VVPM). Configurations were determined which improved rotor efficiency, measured by CT/CP, by 11.6% compared to a single, four-bladed rotor. VVPM and CFD simulations were used to understand the physical mechanisms responsible for changes in thrust and efficiency including the blades proximity to tip vorticies.

On the Influence of Inflow Model Selection for Time-Domain Tiltrotor Aeroelastic Analysis

The methods of using the viscous vortex particle method, dynamic inflow, and uniform inflow to conduct whirl-flutter stability analysis are evaluated on a four-bladed, soft-inplane tiltrotor model using the Rotorcraft Comprehensive Analysis System. For the first time, coupled transient simulations between comprehensive analysis and a vortex particle method inflow model are used to predict whirl-flutter stability. Resolution studies are performed for both spatial and temporal resolution in the transient solution. Stability in transient analysis is noted to be influenced by both. As the particle resolution is refined, a reduction in simulation time-step size must also be performed. An azimuthal time step size of 0.3 deg is used to consider a range of particle resolutions to understand the influence on whirl-flutter stability predictions. Comparisons are made between uniform inflow, dynamic inflow, and the vortex particle method with respect to prediction capabilities when compared to wing beam-bending frequency and damping experimental data. Challenges in assessing the most accurate inflow model are noted due to uncertainty in experimental data; however, a consistent trend of increasing damping with additional levels of fidelity in the inflow model is observed. Excellent correlation is observed between the dynamic inflow predictions and the vortex particle method predictions in which the wing is not part of the inflow model, indicating that the dynamic inflow model is adequate for capturing damping due to the induced velocity on the rotor disk. Additional damping is noted in the full vortex particle method model, with the wing included, which is attributed to either an interactional aerodynamic effect between the rotor and the wing or a more accurate representation of the unsteady loading on the wing due to induced velocities.

High-Fidelity Modeling of Multirotor Aerodynamic Interactions for Aircraft Design

Electric aircraft technology has enabled the use of multiple rotors in novel concepts for urban air mobility. However, multirotor configurations introduce strong aerodynamic and aeroacoustic interactions that are not captured through conventional aircraft design tools. This paper explores the capability of the viscous vortex particle method (VPM) to model multirotor aerodynamic interactions at a computational cost suitable for conceptual design. A VPM-based rotor model is introduced along with recommendations for numerical stability and computational efficiency. Validation of the individual rotor is presented in both hovering and forward-flight configurations at low, moderate, and high Reynolds numbers. Hovering multirotor predictions are compared with experimental measurements, evidencing the suitability of the proposed model to capture the thrust drop and unsteady loading produced by rotor-on-rotor interactions.

Finite State Inflow Flow Model for Coaxial Rotor Configuration

An analytical coaxial rotor inflow model has been developed from potential flow theory using the pressure potential superposition approach. The coaxial rotor pressure potential superposition inflow model (PPSIM) is formulated in statespace form with structure similar to the Peters–He model, except that additional off-diagonal blocks are included in the apparent mass (M-matrix) and influence coefficient matrices (L-matrix). These off-diagonal blocks take into account mutual interference effects present in a coaxial rotor system by relating the rotor's inflows due to other rotor's pressure loadings. Induced inflow distributions on both upper and lower rotors are computed using PPSIM for comparison against predictions from high-fidelity models such as GT-Hybrid and the viscous vortex particle method (VVPM). Good agreement between PPSIM-induced inflow results and GT-hybrid as well as VVPM data has been shown for hover flight condition. At low advance ratio, there are differences in fore-to-aft inflow states between PPSIM and the high-fidelity models. This is because PPSIM assumed rigid, skewed cylindrical wake geometries for both upper and lower rotors during forward flight. But in GT-Hybrid and VVPM, wake structures are allowed to move freely in space and are mainly affected by rotor-induced velocities at low advance ratios. Owing to the close proximity between upper and lower rotors, mutual interference-induced velocities significantly distorted the rotors' wake geometries. The rigid rotor wake geometry assumptions in PPSIM and the distortion captured in higher fidelity models are the reasons behind differences in rotor-induced inflows. At higher advance ratios, wake distortion effects are less prominent since free-stream inflows are significantly larger than rotorinduced velocities. Hence, smaller differences between PPSIM inflow states and those extracted from GT-Hybrid as well as VVPM are observed at high advance ratios.

Finite State Coaxial Rotor Inflow Model Enhancements Using VVPM-Extracted Influence Coefficients

An analytical coaxial rotor inflow model has been developed in the literature by combining pressure fields of individual rotors. In such a pressure potential superposition inflow model (PPSIM), real flow phenomena such as viscous effects, flow swirls, and wake distortions are neglected. To capture real flow effects, inflow distribution predictions from the viscous vortex particle method (VVPM) are used to correct PPSIM influence coefficients (L-matrix). It is found that cosine–sine coupling is significant during hover and low advance ratios, especially on the lower rotor. Most correction terms are found to be insensitive to the thrust coefficient ratio between the upper and lower rotors. For ease of implementation, the curve-fitted correlation of each L-matrix correction element and wake skew function is found. Inflow states computed from PPSIM with curve-fitted L-matrix corrections are close to VVPM results, with an average difference of 6%.

Propeller influence on the aeroelastic stability of High Altitude Long Endurance aircraft

AbstractThis work investigates the propeller’s influence on the stability of High Altitude Long Endurance aircraft, incorporating all resultant loads at the propeller hub, propeller slipstream, and gyroscopic loads. Such effects are usually neglected in the aeroelastic simulation of HALE aircraft. For that goal, a previously developed framework, which couples a geometrically nonlinear structural solver with an Unsteady Vortex Lattice method (uVLM) for lifting surfaces and a Viscous Vortex Particle (VVP) method for propeller slipstream, was employed to generate time-data series. Also, a method, based on a combination of Proper Orthogonal Decomposition and system identification, to extract dynamic information (frequencies, damping, and modes) of the aircraft from a time-series signal is proposed and successfully tested for a purely structural case, for which reference data is available. The method is then applied to investigate the stability of aeroelastic cases. The results demonstrate that the presence of propellers can influence the aeroelastic stability of a Very Flexible Aircraft.

Aerodynamic characteristics analysis of electrically controlled rotor based on viscous vortex particle method

An electrically controlled rotor (ECR), also called as swashplateless rotor, replaces a swashplate with a trailing edge flap system to implement primary rotor control. To investigate the aerodynamic characteristics of the ECR, an analysis model based on the viscous vortex particle method, ECR blade pitch equation and Weissinger-L lifting surface model is established. In this model, the ECR wake flow field vorticity is discretized as multiple vortex particles, and the vorticity-velocity form Navier-Stokes equation is solved to simulate the transport diffusion of the vorticity. The impact of flap deflection on the blade bound vortex circulation is calculated via the equivalent incidence angle. The flap deflection induced blade pitch movement is obtained by solving the ECR blade pitch movement equation via the Runge-Kutta fourth-order method. On this basis, to address the low computing efficiency of the viscous vortex wake model, a “relaxation difference”-based trim strategy is developed to reduce the calculation times of the viscous vortex wake model during trim iteration. Based on this model, the aerodynamic characteristics of a sample ECR in hovering and forward flight conditions are analysed. The results show that in hovering and forward flight conditions, when the rotor trim requires large flap deflection, in the rotor wake vorticity field, apart from blade tip vortex, there are intense vortices at both ends of the flap. This additional intense vortex results in an ECR wake vorticity distribution that is more complex than that of a conventional rotor, significantly impacting the distribution of the rotor disc inflow and load. Additionally, in the forward flight condition, the ECR flap collective deflection results in cyclic blade pitch movement, while flap cyclic deflection results in a significant portion of the 2Ω harmonic component in the blade pitch movement when the advance ratio is high.

Rotorcraft Comprehensive Analysis Calculations of a Coaxial Rotor with Lift Offset

This paper presents comparisons of rotor performance, blade pitch, rotor hub loads, and blade clearance between two sets of rotorcraft comprehensive analysis calculations and experimentally measured test data for a coaxial rotor system in forward flight conditions. The calculations are from the U.S. Army’s Rotorcraft Comprehensive Analysis System (RCAS) with one set calculated using a prescribed vortex wake model and another set calculated by coupling RCAS to a viscous vortex particle method. For rotor performance and blade pitch, the calculations and test data are presented as functions of lift offset for four different advance ratios and for two different test upper rotor collective pitch settings. Rotor hub loads and blade clearance are compared on a time-varying basis for test points that form a lift offset sweep, an advance ratio sweep, and a rotor-to-rotor phase sweep. The main conclusion is that both sets of calculations generally reflect the same trends as the test data, which provides confidence in the ability of RCAS at calculating the aeromechanics behaviors of lift-offset coaxial rotors.

Dynamic Stall Modeling Using Viscous Vortex Particle Method for Coaxial Rotors

Dynamic stall is an important source of vibrations on a rotor at high advance ratios. The periodic flow separation and reattachment during dynamic stall generates large unsteady loads. In this study, the flow separation is modeled as the shedding of concentrated vorticity from the leading edge of the airfoil. The viscous vortex particle method is used to calculate the evolution of the rotor wake. Blade loads are calculated using a reduced order model obtained from computational fluid dynamics, and dynamic stall loads are calculated using the ONERA dynamic stall model. Results are presented for single main rotor and coaxial rotors at advance ratios of μ = 0.3–0.4. The separated wake modifies the angle of attack distribution on the rotor and hence impacts the hub loads. The results indicate that the separated wake modifies the vibratory hub loads by 5–10% for a single main rotor at μ = 0.3. The vibratory hub loads for the coaxial rotor are modified by 10–20% at μ = 0.4 with the inclusion of the separated wake. The upper and lower rotor tip path planes are tilted such that the blade and wake interaction is greater on the retreating side of the upper rotor and decreased on the advancing side.

Electrically Controlled Rotor Blade Vortex Interaction Airloads and Noise Analysis Using Viscous Vortex Particle Method

An electrically controlled rotor (ECR), also called a swashplateless rotor, replaces a swashplate with a trailing‐edge flap system to implement primary rotor control. To investigate the aerodynamic characteristics of an ECR in blade‐vortex interaction (BVI) condition, an analysis model based on the viscous vortex particle method, ECR blade pitch equation, and the Weissinger‐L lifting surface model is established. In this model, the ECR wake flow field vorticity is discretized as multiple vortex particles, and the vorticity‐velocity form of the Navier‐Stokes equation is solved to simulate the transport diffusion of the vorticity. The flap motion‐inducing blade‐pitch movement is obtained by solving the ECR blade‐pitch movement equation via the Runge–Kutta fourth‐order method. On the basis, BVI noise radiation of an ECR is evaluated using the Ffowcs Williams and Hawkings (FW‐H) equation. Based on the present prediction model, the aerodynamic and acoustic characteristics of a sample ECR in BVI condition are analyzed. The results show that since the BVI event of the ECR on the advancing side is mainly caused by the interaction between the flap tip vortex and the blade, the blade spanwise range of ECR BVI occurrence on the advancing side is smaller than that of the conventional rotor. In addition, the magnitude of the maximum sound pressure level on the advancing side as well as on the retreating side of the ECR is also different from that of the conventional rotor, which is consistent with the difference in the airloads between the ECR and conventional rotor. Furthermore, a study was performed to examine the effect of the pre‐index angle on the BVI‐induced airloads and noise. The amplitude of the impulsive airloads of the ECR on the advancing side is increased with the increase in pre‐index angle, while the amplitude of the impulsive airloads of the ECR on the retreating side is decreased. Indeed, when the pre‐index angle of the sample ECR is 8 degrees, the retreating‐side noise radiation lobe is almost disappeared. In addition, the different intensity of wake vorticity is the main reason for the differences of the BVI‐induced airloads and noise among the ECR with different pre‐index angles.

New Approach for Aerodynamic and Aeroacoustic Analysis of Actively Controlled Flaps Rotor

A new approach for aerodynamic and aeroacoustic analysis of actively controlled flaps (ACF) rotor is established to predict airloads and noise reduction. The approach is divided into three parts. The first is an unsteady aerodynamic model of the ACF described through a panel method, and the unsteady pressure under interaction of rotor tip vortex and ACF trailing-edge vortex, which are depicted through a viscous vortex particle method, are taken into account. The second is the influence of the ACF on trajectory of the wake and ACF trailing-edge vortex, which is carried out by a new imaged vortex model to capture blade-vortex interaction (BVI). The third is an aeroacoustic model coupled into the aerodynamic model by transmitting the unsteady pressure to Ffowcs Williams and Hawkings (FW-H) equation. The present approach is applied to AH-1G rotor, and the results show that the predicted unsteady airloads, high-speed impulsive (HSI), and BVI noise are compared favorably with experiment and Reynolds-averaged Navier–Stokes (RANS)/FW-H results. Finally, the variation of airload and noise reduction of ONERA Active Blade Concept rotor (ABC) is predicted and compared with experiment. It is shown that the present approach predicts the airload and noise reduction of the ACF with different phases and flap locations with good accuracy.