Review of vortex methods for rotor aerodynamics and wake dynamics

Electric vertical take-off and landing(eVTOL)aircraft with multiple lifting rotors or prop-rotors have received significant attention in recent years due to their great potential for next-generation urban air mobility(UAM).Numerical models have been developed and validated as predictive tools to analyze rotor aerodynamics and wake dynamics.Among various numerical approaches,the vortex method is one of the most suitable because it can provide accurate solutions with an affordable computational cost and can represent vorticity fields downstream without numerical dissipation error.This paper presents a brief review of the progress of vortex methods,along with their principles,advantages,and shortcomings.Applications of the vortex methods for modeling the rotor aerodynamics and wake dynamics are also described.However,the vortex methods suffer from the problem that it cannot deal with the nonlinear aerodynamic characteristics associated with the viscous effects and the flow behaviors in the post-stall regime.To overcome the intrinsic drawbacks of the vortex methods,recent progress in a numerical method proposed by the authors is introduced,and model validation against experimental data is discussed in detail.The validation works show that nonlinear vortex lattice method(NVLM)coupled with vortex particle method(VPM)can predict the unsteady aerodynamic forces and complex evolution of the rotor wake.

AN IMPROVED MODEL OF CURVED VORTEX ELEMENT FOR ROTOR WAKE ANALYSIS

This paper describes an improved model of curved vortex element on the circular arc (CVEC) for rotor wake analysis.As the key of the paper,two approximate formulas are derived by the series of limited terms to replace the Legendre incomplete elliptical integrals from the Biot-Savart integration,and the analytical solution of the induced velocity for the CVEC is obtained, which is more efficient in the complex rotor free wake calculation. Furthermore,the approximate formulas with the chosen factors are selected to avoid sigularity and give finite result of the induced velocity on the Vortex line,and an equivalent viscous vortex core radius might be evaluated.As examples, the induced velocity calculations on the vortex ring and two turns of a skew vortex helix are performed, and the comparisons between the circular-arc vortex element and the conventional straightline vortex element (SLVE) are given.It is shown that this curved vortex element model is advantageous over the SLVE model and is suitable for the rotor wake analysis.

Investigation of Load Prediction on the Mexico Rotor Using the Technique of Determination of the Angle of Attack

Blade element moment（BEM） is a widely used technique for prediction of wind turbine aerodynamics performance,the reliability of airfoil data is an important factor to improve the prediction accuracy of aerodynamic loads and power using a BEM code.The method of determination of angle of attack on rotor blades developed by SHEN,et al is successfully used to extract airfoil data from experimental characteristics on the MEXICO（Model experiments in controlled conditions） rotor.Detailed surface pressure and particle image velocimetry（PIV） flow fields at different rotor azimuth positions are examined to determine the sectional airfoil data.The present technique uses simultaneously both PIV data and blade pressure data that include the actual flow conditions（for example,tunnel effects）,therefore it is more advantageous than other techniques which only use the blade loading（pressure data）.The extracted airfoil data are put into a BEM code,and the calculated axial and tangential forces are compared to both computations using BEM with Glauert＇s and SHEN＇s tip loss correction models and experimental data.The comparisons show that the present method of determination of angle of attack is correct,and the re-calculated forces have good agreements with the experiment.

NONLINEAR INVERSE SIMULATION FOR THE MANEUVERING FLIGHT OF COAXIAL ROTOR HELICOPTERS

The maneuvering flight governing equations for coaxial rotor helicopters are established. By introducing induced velocity interference factor analysis, the coaxial rotor aerodynamic interference can be taken into account. With the combination of coaxial rotor helicopter control features and nonlinear inverse solution technique, the governing equations for maneuvering flight can be solved so as to determine helicopter control input, control force and moment, and helicopter body attitudes which are needed for performing the defined maneuver. Finally, as an example of this methods engineering application, the calculated results with level turn, lateral jink maneuvers are presented and simply analyzed.

Combined Free Wake /CFD Methodology for Predicting Transonic Rotor Flow in Hover

A new combined wake /CFD methodology is used to include realistic wake effects in CFD solutions for the rotor flow in hover. The analytical method for predicting the hovering rotor wake is described to investigate the motion of the helical tip vortex. Beginning with the generalized wake model, a Semi Empirical Correction for the vortex core effect on the rotor wake is made. Then on the condition of circulation and wake geometry convergence, the free wake calculation is carried out. Finally, Euler equations are solved for transonic rotor flow employing Jameson’s finite volume explicit Runge Kutta time stepping scheme. The results are compared with the respective references and experimental data.

CALCULATION OF HELICOPTER ROTOR FLAPPING ANGLESAND COMPARISON WITH MEASURED DATA

Helicopter rotor flapping angles from hover to low speed forward flight are calculated and compared with the measured data in this paper. The analytical method is based on a second order lifting line/full span free wake model as well as a fully coupled rotor trim model. It is shown that, in order to accurately predict the lateral flapping angle at low advance ratio, it is necessary to use free wake analysis to account for the highly non uniform inflow induced by the distorted wake geometry at rotor disc plane.

Robust Navier-Stokes method for predicting unsteady flowfield and aerodynamic characteristics of helicopter rotor

A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes（RANS） equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method＂ and ‘‘minimum distance scheme of donor elements method＂ are established in this work. To improve the computational efficiency, Message Passing Interface（MPI） parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage（FAS） multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.

Experimental Analysis of the Aerodynamic Performance of an Innovative Low Pressure Turbine Rotor

In the present work the aerodynamic performances of an innovative rotor blade row have been experimentally investigated. Measurements have been carried out in a large scale low speed single stage cold flow facility at a Reynolds number typical of aeroengine cruise, under nominal and off-design conditions. The time-mean blade aerodynamic loadings have been measured at three radial positions along the blade height through a pressure transducer installed inside the hollow shaft, by delivering the signal to the stationary frame with a slip ring. The time mean aerodynamic flow fields upstream and downstream of the rotor have been measured by means of a five-hole probe to investigate the losses associated with the rotor. The investigations in the single stage research turbine allow the reproduction of both wake-boundary layer interaction as well as vortex-vortex interaction. The detail of the present results clearly highlights the strong dissipative effects induced by the blade tip vortex and by the momentum defect as well as the turbulence production, which is generated during the migration of the stator wake in the rotor passage. Phase-locked hot-wire investigations have been also performed to analyze the time-varying flow during the wake passing period. In particular the interaction between stator and rotor structures has been investigated also under off-design conditions to further explain the mechanisms contributing to the loss generation for the different conditions.