Investigating the Coupled Effects Between Rotor-Blade Aeroelasticity and Tip Vortex Stability

A hybrid Navier-Stokes/Free Wake methodology is applied to helicopter rotors in hover. Three tip planforms were analyzed: the S-76 rotor with a swept tip, a rectangular planform, and a swept tip with anhedral. The solidity of the three rotors was matched. A pitch sweep was conducted. Computed thrust, power, and figure of merit values have been compared with test data. Where available, comparisons with other calculations for these quantities and the near wake tip vortex trajectory have been done. The simulations are in reasonable agreement with published data for the thrust, power, and figure of merit. The simulations differ from full Navier-Stokes calculations in the predictions for tip vortex descent rate and contraction rate. The simulations correctly predicted the trends. The swept tapered anhedral tip had the highest figure of merit, followed by the swept tapered tip. The rectangular planform had the lowest figure of merit.

A procedure for the computation of transonic steady and unsteady flow around helicopter rotors is presented. The algorithm is based on the Euler equations and allows the computation of anisotropic rotational flow and thus an implicitly accurate calculation of shocks. In addition the capturing of the rotor wake and the tip vortex is provided for arbitrary tip shapes. The code for the computation of steady, fully 3-D rotor flow is derived from the EUFLEX procedure originated by A. Eberle, that has successfully been applied to a lot of fixed wing configurations up to now. A finite-volume scheme based on the method of characteristic flux averaging solves the Euler equations formulated in the conservation form. The discretizatlon of the flow field is carried out in two different manners concerning the grid topology and the size of the physical domain. Calculations are presented for a non-lifting case and for a helicopter rotor in hover. The comparisons of the method in its present stage show good agreement with experimental data.

High effective WENO scheme for transonic inviscid flow computation on a helicopter rotor in hover

In the present article, the authors are performing a comparison study between two vortex models for the rapid numerical computation of the static thrust of a helicopter rotor in hover. The aim of this study is to access the rapidity and accuracy of a vortex model, comprised of a series of vortex rings and a single semi-infinite vortex cylinder, compared to a helical wake model with straight-line segmentation. Studies are performed for the optimal number of vortex elements, as well as for their optimal positioning, in order to provide both fast computation and good agreement with the experimental data obtained from a wind tunnel test of a model rotor. The studied vortex model is shown to significantly reduce the amount of computational time required to evaluate the performance of the model rotor, when compared to the helical wake model, while offering a similar degree of accuracy.

Pressure-sensitive paint (PSP) has become an important technique for global pressure measurement on rotating surfaces such as helicopter rotor blades. Due to the temperature sensitivity of PSP, it is essential to apply accurate temperature correction method in PSP measurements. In previous studies, one-dimensional (1D) correction methods were generally adopted which only considered the radial temperature gradient on the blade. However, in the current study, it was found that the systematic error of this 1D assumption was non-negligible in large-scale experiments due to the growing chordwise temperature gradient. Accordingly, a two-dimensional (2D) temperature correction method considering both radial and chordwise temperature gradients was developed to improve the accuracy of PSP. In this method, a 2D temperature map was firstly generated based on the TSP results. Calibrations were then conducted under a series of temperature and pressure values to generate a calibration surface. According to the calibration results, the pressure and temperature fields on the rotor blade were solved directly. The proposed 2D method was validated through PSP measurements on a 2 m diameter BO-105 helicopter rotor in hover. Compared with 1D temperature correction, the results from the current method showed clearly improved agreement with the CFD results and reduced overall measurement error.

In this paper, the results of a correlation study using a new higher-order, free-wake method, applied to the problem of hovering rotors, are presented. The predictions of the free-wake method are compared with the experimental data from three different studies focusing on sectional force distributions, aggregate performance parameters such as figures of merit and downwash distributions. The correlations provide a good amount of confidence as to the ability of the new free-wake method in predicting the challenging aerodynamics of a helicopter rotor in hover.

This paper describes measurements of chordwise distributions of unsteady pressure at three radial locations on a stiff two-bladed teetering model helicopter rotor in hover, with the blades executing simple harmonic pitch oscillations about the quarter-chord pitch axis. The objective of the present work is to provide a data base to correlate the measured unsteady blade pressure distributions with dynamic inflow to establish the validity or deficiencies of available analytical methods for predictions of unsteady aerodynamic phenomena. The effect of dynamic inflow on rotor unsteady surface pressure has been

Generic wrap-around shape optimisation technology is presented, and is applied to a helicopter rotor in hover, using compressible CFD as the aerodynamic model. An efficient domain element shape parameterisation method is used as the surface control and deformation method, and is linked to a radial basis function global interpolation, to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh. This method is independent of mesh type and size, and optimisation independence from the flow solver is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference. The method is applied here to a two-bladed hovering rotor, with transonic tip speed, comparing the effects of global twist parameters and more local planform parameters. Significant torque reductions are achieved in both cases, and it is shown that using only three global twist parameters are extremely effective. Using 63 local and global parameters, large geometric changes are demonstrated, with both induced power and wave drag reduced.

: An experimental study of the tip vortex behind a NACA 0015 rectangular wing of aspect ratio 4 was carried out to understand the structure and evolution of the vortex in the near-wake region. The results of these experimental studies are presented in this report. These measurements were made nonintrusively using three-component laser-Doppler velocimetry (LDV). The experiments were carried out at a Reynolds number of about 180,000 in a low- speed wind tunnel. Two cases were studied, namely, (1) stationary wing and (2) wing oscillating in pitch sinusoidally about its quarter-chord axis. The flow properties measured were the three components of the instantaneous velocity. These data were processed to obtain time-mean and phase-locked flow properties such as velocity, vorticity and turbulence. The data were obtained at several locations at 0.15 - 3.0 chord lengths downstream from the trailing edge. The typical distributions of mean velocity, vorticity, circulation and turbulent intensity in the near wake are presented and discussed for the stationary wing. In the case of the oscillating wing, the phase-locked velocity, vorticity and turbulence data show details of the evolution of the unsteady tip vortex downstream from the trailing edge. The results also show that the flow is strongly non-quasi-steady at the oscillation frequency studied. The results are fully archived on tape and are available to any interested reader. These can be used as database in the development of wake models for the finite wing, and in studies of three-dimensional wing aerodynamics.

The wake produced by a model wind turbine is investigated using proper orthogonal decomposition (POD) of numerical data obtained by large eddy simulations at a diameter‐based Reynolds number . The blades are modeled employing the actuator line method and an immersed boundary method is used to simulate tower and nacelle. Two simulations are performed: one accounts only for the blades effect; the other includes also tower and nacelle. The two simulations are analyzed and compared in terms of mean flow fields and POD modes that mainly characterize the wake dynamics. In the rotor‐only case, the most energetic modes in the near wake are composed of high‐frequency tip and root vortices, whereas in the far wake, low‐frequency modes accounting for mutual inductance instability of tip vortices are found. When tower and nacelle are included, low‐frequency POD modes are present already in the near wake, linked to the von Karman vortices shed by the tower. These modes interact nonlinearly with the tip vortices in the far wake, generating new low‐frequency POD modes, some of them lying in the frequency range of wake meandering. An analysis of the mean kinetic energy (MKE) entrainment of each POD mode shows that tip vortices sustain the wake mean shear, whereas low‐frequency modes contribute to wake recovery. This explains why tower and nacelle induce a faster wake recovery.

In this work, the wing tip vortex structure behind a NACA 0015 airfoil with and without small flaps was studied using a Partical Image Velocimetry (PIV) system. The experiment was carried out in a low speed wind tunnel with a test section of 0.5 m × 0.5 m. The Reynolds number (Re), defined by the chord length of the wing (C), was 8.1×104. The angle of attack was fixed at 10°. The PIV measurements were made from 0 to 2C, measured from the trailing edge of the model. The dihedral angle of three flaps was −15°, 0° and 15°, respectively. Compared with the clean airfoil, the one with three flaps significantly changed the wing tip vortex structure, the vorticity and the core of the wing tip vortex. The occurrence of three flaps decreased the gradient of pressure on the two sides of the wing tip, which depressed wing tip vortex formation to some extent. Vortices shed from three flaps influence the evolution of the wingtip vortex generated by the base airfoil. The interaction of those vortices resulted in a weakening of the wing tip vortex.

Large-eddy simulations of a propeller operating upstream of a hydrofoil at incidence were conducted on a cylindrical grid consisting of almost 4 × 109 points. This manuscript, focused on the interaction between the tip and hub vortices shed by the propeller with the downstream hydrofoil, is part of a broader study, including the analysis of the boundary layer on the hydrofoil [A. Posa and R. Broglia, “Flow over a hydrofoil at incidence immersed within the wake of a propeller,” Phys. Fluids 33, 125108 (2021)] and the downstream development of the wake of the overall system [A. Posa and R. Broglia, “Development of the wake shed by a system composed of a propeller and a rudder at incidence,” Int. J. Heat Fluid Flow 94, 108919 (2022)]. The results demonstrate a substantial influence by the orientation of the hydrofoil on the propeller wake. The pressure and suction side branches of the tip vortices experience outward and inward spanwise shifts across the hydrofoil, respectively. However, these shifts are affected significantly by the angle of incidence. As a result, the propeller wake undergoes an overall contraction on the suction side of the hydrofoil, promoting higher levels of shear and turbulence and a faster growth of the boundary layer thickness. The opposite occurs on the pressure side of the hydrofoil, producing eventually a strong asymmetry of the overall wake. Also the evolution of the hub vortex is substantially affected. It splits into two branches, shifting across the span of the hydrofoil in the direction opposite to the tip vortices. As the incidence angle of the hydrofoil grows, the branch of the hub vortex populating its pressure side becomes larger than the one on its suction side, developing a higher shear with the hydrofoil boundary layer and the suction side branches of the tip vortices.

The paper presents part of the experimental activities carried out in the GARTEUR Action Group RC/AG-26 to study the acoustic and aerodynamic characteristics of small rotor configurations, including the influence of the rotor-rotor interactions. Two rotors, equipped with two-bladed propellers of a diameter of D=330.2 mm, were operated at two rotating speeds of 8025 RPM and 10120 RPM and arranged in different configurations. Isolated rotor and two different coaxial configurations in hover conditions were assessed. The aerodynamic loads and the rotor slipstream characterisation, in terms of flow field velocity, tip vortex characterization as well as acoustics emissions, were performed using a six-component load cell, Particle Image Velocimetry and microphone measurements. The isolated pusher rotor presented better aerodynamic performance with respect to the puller one. The coaxial configurations result in a loss of thrust and an increase in torque compared to the isolated rotors. The upper rotor is barely affected by the presence of the lower one, while the lower rotor experiences a thrust loss ranging from 17 to 19%. The configuration with the larger rotor distance experiences greater performance loss. The mean velocity fields of the isolated rotors are measured and compared with the coaxial configurations for assessing the roto-rotor interaction, the results support the aerodynamic behaviour. The isolated rotor slipstream characterisation was carried out by phase-locked measurements covering the full rotor azimuth angle range from 0° to 350° with an increment of 30°. Tip vortex paths are followed up to a vortex age of 3.5 rotor revolutions. The 3D reconstruction of the tip vortices is conducted to gain insight into the slipstream behaviour and enhance the occurring vortex roll-up during the second revolution. The tip vortex jitter is investigated and the anisotropic distribution is confirmed along the slipstream. Furthermore, the noise emission intensifies in magnitude for the coaxial configuration with increasing relative gap between the rotors. The turbulent kinetic energy and the meandering of the blade tip vortices support the findings of the acoustics results.

A simple analytical method has been developed to predict the induced velocities at the tip vortex in the wake of a hovering helicopter rotor. The wake model in the analysis includes the blade bound vortex as well as a tip vortex and vortex sheet trailed from each blade. Standard, prescribed wake models were used to describe the geometry of the tip vortex and the vortex sheet. Curved vortex elements were used to model the tip vortices and the vortex sheets. The analysis was used to study the contribution from each wake component to the axial-induced velocity of the tip vortex. Results show a highly variable induced velocity at the tip vortex both before and after the first blade passage. However, the prescribed tip vortex models require a constant axial velocity of the tip vortex. This inconsistency between the prescribed axial velocity of the tip vortex and the velocity that the wake geometry induces on the tip vortex points to a limitation of the current prescribed tip vortex geometry models.

Wingtip vortices are an important phenomenon in fluid dynamics due to their complex and negative impacts. Despite numerous studies, the current understanding of the inner vortex is very limited; thus, a basis for the design of effective wingtip geometry and vortex manipulation is narrow. This work examines the structure of the trailing vortex shed from a swept-tapered wing, analogous to a commercial aircraft topology. Stereoscopic particle imaging velocimetry has been utilized to compare the vortex structure and development through several angles of attack at various downstream stations for a fixed Reynolds number (Re = 1.5 × 106). After correcting for vortex meander through helicity-based spatial localization of the vortex core, relationships between the vortex core velocity/vorticity fields, core shape, and turbulent properties have been examined. Subsequently, the vortex is found to exhibit a layered structure with slow linear rates of dissipation indicative of laminar diffusion mechanisms, despite being a turbulent vortex. The turbulent kinetic energy distribution in the vortex signals that relaminarization of the inner core occurs. Consideration of the streamline curvature around the core, via examination of the local Richardson number, indicated that a laminar core structure had formed within which large-scale turbulent eddies could not contribute to the turbulent diffusion of vorticity away from the core. The normalized circulation within the vortex core has been shown to exhibit self-similar behavior typical of the fully developed axisymmetric vortices.