A 3D analytical model for orthogonal blade-vortex interaction noise Michael E. Quaglia a,n , Thomas Léonard a , Stéphane Moreau a , Michel Roger b a University of Sherbrooke, 2500 bd de l'université, J1K 2R1 Sherbrooke, QC, Canada b École Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Écully, France article info Article history: Received 16 November 2016 Received in revised form 21 March 2017 Accepted 23 March 2017 Handling Editor: A.V. Metrikine Available online 12 April 2017 Keywords: Counter-Rotating Open Rotor noise Blade-Vortex Interaction Tonal noise Turbomachinery Analytical method abstract A 3D analytical model of an Orthogonal Blade-Vortex Interaction (OBVI) for Counter-Ro- tating Open Rotor (CROR) tonal noise is investigated. The specific influence of two para- meters taking into account the three-dimensionality of both the vortex velocity and the convection velocity within the rotor-rotor volume is addressed. The first step is to extract the vortex parameters from a recent unsteady Reynolds-Averaged Navier-Stokes compu- tation and validate different vortex models. Lamb-Oseen and Scully vortices reproduce the behavior of the tip-vortex tangential velocity fairly well. Regarding the vortex axial ve- locity modeling, a Gaussian profile fits well with numerical results. On the one hand, the impact of the stream-tube contraction unbalances the lobes of the unsteady pressure with opposite phases produced by the OBVI event. This effect is larger than that of an equivalent blade sweep. On the other hand, adding the axial velocity deficit to the tan- gential one also unbalances the pressure lobes. Finally, from an acoustic point of view using Curle's acoustic analogy, both the stream-tube contraction and the axial velocity deficit have the same effect: they turn an acoustically-low efficient quadrupole into a strong dipole making these parameters fundamental for future CROR OBVI investigations. & 2017 Elsevier Ltd. All rights reserved. 1. Introduction Because of the weight and space limitations of nacelles for future Ultra High By-Pass Ratio (UHBR) turbofans, Counter- Rotating Open Rotor (CROR) design could be a viable alternative to classical turboengines for commercial airplane pro- pulsion. Since the beginning of CROR design with the preliminary work on the UnDucted Fan engine in the nineties [1–5], significant tonal noise reduction for this novel architecture has been achieved. Nowadays, 3D aerodynamic and aeroacoustic optimizations have yielded fully three-dimensional blade shapes and cropped aft rotor that have achieved substantial re- ductions in tonal noise without efficiency penalties at cruise conditions [6]. Yet, one of the main concerns regarding CROR noise, is to meet the community noise levels standards set by the International Civil Aviation Organization at take-off and approach conditions. At these regimes, it is particularly essential to take into account the three-dimensionality of the flow induced by unbalanced flow conditions within the CROR due to inflow incidence or streamtube contraction between the front and rear rotors. At these flow regimes, cropping the aft rotor might be insufficient to reduce the interaction noise due to the front-rotor tip vortex impingement as was recently shown by Soulat et al. [7]. In a typical uncropped CROR Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jsvi Journal of Sound and Vibration http://dx.doi.org/10.1016/j.jsv.2017.03.023 0022-460X/& 2017 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: michael.quaglia@usherbrooke.ca (M.E. Quaglia), thomas.leonard@usherbrooke.ca (T. Léonard), stephane.moreau@usherbrooke.ca (S. Moreau), michel.roger@ec-lyon.fr (M. Roger). Journal of Sound and Vibration 399 (2017) 104–123