Analysis of selected problems involving vortical flows

2008

Interactions between the blades and vortical structures within the wake of a helicopter rotor are a significant source of impulsive loading and noise, particularly in descending flight. Advances in the prediction and understanding of such blade vortex interactions have been aided in recent years by the extensive experimental dataset made available through the HART test programme. Brown's Vorticity Transport Model was used to predict the rotor blade loading, the resultant wake system and the acoustic noise radiation for the HART II rotor. The vorticity conserving properties of the Vorticity Transport Model allow the detailed wake features that are associated with blade vortex interactions to be resolved. The experimental airload data, in particular the higher harmonic loading associated with blade vortex interactions, is matched well by the computations. The computed vorticity distribution in the wake also shows good correlation with the experimentally measured vortex positions. Including a representation of the fuselage within the computation yields marked improvement in the prediction of the vortex positions compared to similar calculations with an isolated rotor. An accoustic analysis, based on a Ffowcs-Williams Hawkings approach, is able to predict accurately the locations of the sound pressure maxima and the upstream attenuation of the sound radiated by the rotor. The principal discrepancies in airload, vortex position and acoustic prediction are confined almost exclusively to the rear of the advancing side of the rotor and, if errors in measuring the blade deflection can be discounted, may be due to minor inaccuracies in modelling the roll-up of the wake.

A parametric study of the aerodynamics and the acoustics of parallel BVI has been carried out for different aerofoil shapes and vortex properties. Computing BVI using Computational Fluid Dynamics is challenging since the solution scheme tends to alter the characteristics of the vortex which must be preserved until the interaction. The present work uses the Compressible Vorticity Confinement Method (CVCM) for capturing the vortex characteristics, which is easier to implement and has minimal overhead in the performance of existing CFD solvers either in terms of CPU time or robustness during convergence. Apart from applying the CVCM method with an upwind solver, something not encountered in the literature, the present work couples CFD with Computational Aeroacoustics (CAA) and uses the strengths of both techniques in order to predict the nearfield and farfield noise. Results illustrate the importance of the aerofoil shape at transonic flow and show that the magnitude of the BVI noise depends strongly on the vortex strength and the miss-distance. The effect of the vortex core radius was also found to be important. Notation ε Confinement parameter Γ Normalised circulation µ Numerical viscosity, advance ratio ω Vorticity ρ Density Σ Surface S Source term ϑ Volume f b Body force term n Normalised vorticity gradient vector to the surface S V Velocity vector M tip Tip Mach number R Rotor radius r Distance from the vortex core, radial coordinates R c Non-dimensionalised core radius U ∞ Freestream velocity v θ Tangential velocity y 0 Miss-distance a Speed of the sound BVI Blade Vortex Interaction c Chord length CAA Computational Aeroacoustics CFD Computational Fluid Dynamics Cp Surface pressure coefficient CVCM Compressible Vorticity Confinement Method M Freestream Mach number NS Navier-Stokes

Aerospace Science and Technology, 2005

The computational method used at ONERA for the prediction of Blade-Vortex Interaction noise is presented in this paper. The five steps of the computational chain are first described. The calculations are then validated by comparison with two different databases. The first one was obtained in the HART program; in this case, it is shown that the influence of Higher Harmonic Control on wake geometry and radiated noise is well captured. The second one was obtained in the ERATO program, where a passive blade shape optimisation was done: in this case, the calculations succeed in predicting the relative difference in noise levels between the ERATO optimised blade compared to a reference blade, although the wake geometry of the ERATO rotor is not well captured. Finally, strategies to reduce the BVI noise for blades equipped with trailing-edge flaps are proposed.  2004 Elsevier SAS. All rights reserved.

2000

This paper presents a combined methodology consisting of rotor aerodynamic and aeroacoustic computation modules. Aerodynamic calculations utilise the Vortex Element Method for the description of free vortex wake, which determines the rotor flowfield. The mathematical model discretizes the wake into vortex elements. The induced velocity is calculated for the distorted wake geometry, by means of the Biot-Savart law, integrated in closed form over each of these elements. Bound circulation variations and unsteady blade airloading are computed as a result of the nonuniform induced downwash. Wake roll up process, vortex core modelling, vorticity dissipation, blade section boundary layer growth are incorporated in numerical modelling of aerodynamic computations. Computed blade loading variations are used as the basis of loading noise predictions. Aeroacoustic analysis concentrates on helicopter rotor noise prediction in time domain. The formulation is based on the Ffowcs-Williams and Hawki...

16th AIAA/CEAS Aeroacoustics Conference, 2010

Progress towards the computational prediction of the turbulent flow and broadband noise generated due to the interaction of rotor wakes and stator blades is presented. An inflow boundary treatment is developed which allows arbitrary incoming unsteady vortical flow disturbances to be imposed in a nonuniform mean flow while minimizing the generation of spurious acoustic signals. The boundary condition was implemented in a nonlinear Euler CAA code and validated on a series of 3D benchmark test cases. Validation results for these cases are shown.

1990

Acoustic measurements from a model rotor wind-tunnel test are presented which show that the directionality of rotor blade-vortex interaction (BVI) noise is strongly dependent on the rotor advance ratio and disk attitude. A rotor free wake analysis is used to show that the general locus of interactions on the rotor disk is also strongly dependent on advance ratio and disk attitude. A comparison of the changing directionality of the B VI noise with changes in the interaction locations shows that the strongest noise radiation occurs in the direction of motion normal to the blade span at the time of interaction for both advancing and retreating side B VI. For advancing side interactions, the B VI radiation angle down from the tip-path plane appears relatively insensitive to rotor operating condition and is typically between 0 0 and 550 below the disk. However, the azimuthal radiation direction shows a clear trend with descent speed, moving toward the right of the flight path with increasing descent speed. The movement of the strongest radiation direction is attributed to the movement of the interaction locations on the rotor disk with increasing descent speed.

Comptes Rendus Physique, 2005

This paper is a review on the dynamics of vortices in fluids which get involved in aircraft wakes. Basic notions useful to appraise their dynamics are: inertial waves, 3D instabilities due to vortex interaction, vortex merging, vortex breakdown and turbulence. Each one of these topics is illustrated by means of experimental or numerical results. To cite this article: L. Jacquin et al., C. R. Physique 6 (2005).  2005 Académie des sciences. Published by Elsevier SAS. All rights reserved. Résumé Dynamique des sillages tourbillonnaires : instationnarité, instabilité et turbulence. On effectue une revue des propriétés dynamiques des tourbillons qui se forment dans les sillages d'ailes d'avions. Les notions importantes permettant d'appréhender ces écoulements sur un plan physique sont : les ondes d'inertie, les instabilités hydrodynamiques tridimensionnelles résultant des interactions entre tourbillons, la fusion de tourbillons, l'éclatement tourbillonnaire et la turbulence. Toutes ces notions sont discutées sur la base de résultats théoriques, expérimentaux ou numériques. Pour citer cet article : L. Jacquin et al., C. R. Physique 6 (2005).

Aeroacoustics Conference, 1996

An Euler code is used to model an isolated vortex interacting parallel with a rotor blade at transonic conditions in both forward flight and hover. A new field velocity approach is used to incorporate the effects of the vortex in the solution. Blade loading time histories and instantaneous pressure contours are examined to observe and explain the features of such transonic parallel blade-vortex interactions. A qualitative study is made of the transonic effects on the 3D blade vortex interaction. It is found that the strength and impulsiveness of the interaction for forward flight is greater than the interaction for the same rotor in hover at the same sectional Mach number. Furthermore, the investigation of disturbance pressure contours out past the tip of the rotor blade reveals some qualitative changes in the formation and initial propagation of blade-vortex interaction noise when strong transonic effects are present.

1984

Journal of The American Helicopter Society, 2009

Turbulence measurements were performed inside the vortical wake of a small hovering rotor, using stereoscopic, particle image velocimetry (PIV). An improved method of measurement correction based on the concept of helicity in the flow was used to separate the biasing effects of the inherent aperiodicity in the wake from the actual turbulence properties within the tip vortices. An analysis of the minimum number of PIV image pairs required to achieve statistical convergence for the turbulence quantities suggested at least 250 samples were needed for the first-order characteristics, and about 750 samples for the second-order characteristics. Significant turbulence activity was found up to two core radii from the tip vortex axis. The tip vortices were also shown to have asymmetric flow characteristics, with a pronounced anisotropic distribution of eddy viscosity, a typical characteristic of flows with high streamline curvature. The measurements should help to form a basis for developing improved turbulence models for vortex flows, as well as for validating existing computational fluid dynamics predictions. Nomenclature A velocity gradient tensor, s −1 C T rotor thrust coefficient, = T /ρπ 2 R 4 c blade chord, m F s field force per unit mass H z helicity, m s −2 i, j, k Cartesian direction vectors p pressure, N m −2 q determinant of matrix A, s −2 R radius of blade, m r, θ, z polar coordinate system, m, rad, m S trace of matrix A, s −1 TKE turbulent kinetic energy, = (u 2 + v 2 + w 2)/2, m 2 s −2 U instantaneous velocity, m s −1 U average velocity, m s −1 u, v, w velocities in Cartesian coordinates, m s −1 u , v , w normalized RMS velocities in PIV coordinates, m s −1 u v normalized Reynolds shear stress in X, Y plane, m 2 s −2 v w normalized Reynolds shear stress in Y, Z plane, m 2 s −2 u w normalized Reynolds shear stress in X, Z plane, m 2 s −2 V ax axial velocity of the tip vortex, m s −1 V r radial velocity of the tip vortex, m s −1

Progress in Aerospace Sciences, 2008

This paper presents selected results from extensive experimental investigations on turbulent flow fields and unsteady surface pressures caused by leading-edge vortices, in particular, for vortex breakdown flow. Such turbulent flows may cause severe dynamic aeroelastic problems like wing and/or fin buffeting on fighter-type aircraft. The wind tunnel models used include a generic delta wing as well as a detailed aircraft configuration of canard-delta wing type. The turbulent flow structures are analyzed by root-mean-square and spectral distributions of velocity and pressure fluctuations. Downstream of bursting local maxima of velocity fluctuations occur in a limited radial range around the vortex center. The corresponding spectra exhibit significant peaks indicating that turbulent kinetic energy is channeled into a narrow band. These quasi-periodic velocity oscillations arise from a helical mode instability of the breakdown flow. Due to vortex bursting there is a characteristic increase in surface pressure fluctuations with increasing angle of attack, especially when the burst location moves closer to the apex. The pressure fluctuations also show dominant frequencies corresponding to those of the velocity fluctuations. Using the measured flow field data, scaling parameters are derived for design purposes. It is shown that a frequency parameter based on the local semi-span and the sinus of angle of attack can be used to estimate the frequencies of dynamic loads evoked by vortex bursting.

Propagation of acoustic waves originating from periodic vortices deforming in a nonuniform flow about a rigid body is examined numerically using a high-order compact finite-difference approximation. The governing equations are approximated by the linearized Euler equations in terms of disturbances. The aim of the study is to determine the sound directivity and strength as a result of the vortex street interaction with a solid body under subsonic base flow conditions. Both the vortex core diameter and vortex street spacing have a minor influence on the amplitude of the produced sound wave. When low-frequency vortex streets interact with a cylinder, the produced sound waves are very different from those that originated from high-frequency vortex streets. The interaction mechanism, sound generation, and propagation in a nonuniform flow are quite different for Taylor and Vatistas' vortex streets. In the case of a low-frequency Vatistas vortex street, the root-mean-square ͑RMS͒ value of the acoustic pressure has a well-defined sound directivity and amplitude. The former is greatly affected by the Mach number of the mean flow. For a high-frequency Vatistas vortex street, the RMS of acoustic pressure becomes highly nonmonotonic in the angular direction, while the mean flow Mach number has a moderate effect on the RMS angular profile. The striking differences in the sound amplitude and directivity for Taylor and Vatistas vortices are discussed in terms of their vorticity distribution.

17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), 2011

Direct numerical simulation of the dynamics and acoustics of 2D leapfrogging viscouscore vortex pairs is performed for the Reynolds number range Re=5000-10000. Compressible Navier-Stokes equations are solved in the conservation form on a Eulerian grid with the high-resolution CABARET method. Results for several grid resolutions are reported. Main integral characteristics of the problem such as the mean flow velocity and the vortex sleep-through period are compared with the analytical solution. Acoustic pressure signals on a far-field control surface are computed. For extending the model of two vortex pairs to flows that are periodic in the time domain, a linear acoustic model of periodic vortex roll-up and pairing is considered and its implications for jet noise modelling are discussed.

13th Applied Aerodynamics Conference, 1995

The present work explores prescribed pitching as a means of actively controlling the Blade Vortex Interaction (BVI) component of rotor noise. Distributed piezoceramic actuators would dynamically twist the helicopter rotor blades, resulting in a locally pitching motion. A 2-D Euler Navier-Stokes solver is used to analyse a simple 2-D model of a vortex interacting with a pitching airfoil. Two different formulations, based upon the calculated unsteady loadings are examined to calculate the required pitching motion of the airfoil about the quarterchord. It is demonstrated that the resulting far-field acoustic signature of the airfoil-vortex interaction can be reduced several-fold. Several implementation issues are examined and recommendations proposed for future work. Nomenclature a Angle of attack of the airfoil c i Time rate of change of a h Plunging Velocity Cl Coefficient of lift of the airfoil b Airfoil semichord c Airfoil chord w Frequency of oscillation Vm Free stream velocity k Reduced frequency (e) 'Copyright 0 1 9 9 4 by the American Institute of Aeronautics and Astronautics, Inc. All Rights Reserved.

2008

The aerodynamic operating environment of the helicopter is particularly complex and, to some extent, dominated by the vortices trailed from the main and tail rotors. These vortices not only determine the form of the induced flow field but also interact with each other and with elements of the physical structure of the flight vehicle. Such interactions can have implications in terms of structural vibration, noise generation and flight performance. In this paper, the interaction of main rotor vortices with the helicopter tail rotor is considered and, in particular, the limiting case of the orthogonal interaction. The significance of the topic is introduced by highlighting the operational issues for helicopters arising from tail rotor interactions. The basic phenomenon is then described before experimental studies of the interaction are presented. Progress in numerical modelling is then considered and, finally, the prospects for future