Trailing edge noise prediction for rotating serrated blades Samuel Sinayoko 1 Mahdi Azarpeyvand 2 Benshuai Lyu 3 1 University of Southampton, UK 2 University of Bristol, UK 3 University of Cambridge, UK AVIATION 2014 20th AIAA/CEAS Aeroacoustics conference Atlanta, 20 June 2014 1 / 24
Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 2 / 24
Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 3 / 24
Introduction Motivation Wind turbines (Oerlemans et al 2007) Open rotors (Node-Langlois et al AIAA-2014-2610, Kingan et al AIAA-2014-2745) 4 / 24
Introduction Motivation Wind turbines (Oerlemans et al 2007) Open rotors (Node-Langlois et al AIAA-2014-2610, Kingan et al AIAA-2014-2745) Experiments Gruber et al (AIAA-2012) Moreau and Doolan (AIAA J. 2013) 4 / 24
Introduction Motivation Wind turbines (Oerlemans et al 2007) Open rotors (Node-Langlois et al AIAA-2014-2610, Kingan et al AIAA-2014-2745) Experiments Gruber et al (AIAA-2012) Moreau and Doolan (AIAA J. 2013) Numerical Jones and Sandberg (JFM 2012) Sanjose et al (AIAA-2014-2324) 4 / 24
Turbulent boundary layer trailing edge noise (TEN) A subtle process 1 Hydrodynamic gust convecting past the trailing edge 2 Scattered into acoustics at the trailing edge 3 Acoustic field induces a distribution of dipoles near the TE 4 The dipoles radiate efficiently (M 5 ) to the far field 5 / 24
Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 6 / 24
TEN modelling for isolated airfoils Howe s serrated edge model Howe (1991) & Azarpeyvand (2012) S pp = A D Φ Assumptions High frequency (kc > 1) Frozen turbulence Sharp edge Full Kutta condition ( P T E = 0) Low Mach number (M < 0.2) 7 / 24
TEN modelling for isolated airfoils Serration profiles x 1 l s U x 3 2h s l s l s 2h s h 2h s slit thickness d 8 / 24
Edge spectra for serrated edges Rewriting of Howe (1991) & Azarpeyvand et al. (2013) Φ = ψ(k 1 δ) ψ(ρ) = ρ 2 [ρ 2 + 1.33 2 ] 2 10 0 10-1 10-2 ψ 10-3 10-4 10 10-5 -2 10-1 10 0 10 1 10 2 ρ 9 / 24
Edge spectra for serrated edges Rewriting of Howe (1991) & Azarpeyvand et al. (2013) Φ = n a n(k 1 h) ψ(ρ n δ) ψ(ρ) = ρ 2 ρ [ρ 2 + 1.33 2 ] 2 n = K 2 1 + n2 k 2 s 10 0 10-1 10-2 ψ 10-3 10-4 10 10-5 -2 10-1 10 0 10 1 10 2 ρ 9 / 24
Edge spectra for serrated edges Modal amplitudes a n, K 1 h s = 25 1.0 Straight 0.8 0.6 0.4 0.2 0.0 30 20 10 0 10 20 30 0.25 Sawtooth 0.20 0.15 0.10 0.05 0.00 30 20 10 0 10 20 30 0.06 Sinusoidal 0.05 0.04 0.03 0.02 0.01 0.00 30 20 10 0 10 20 30 0.10 Slitted Sawtooth 0.08 0.06 0.04 0.02 0.00 30 20 10 0 10 20 30 10 / 24
TEN for Rotating Airfoils Observer x α γ Ω θ z Flow y 11 / 24
TEN for Rotating Airfoils Observer x α γ Ω θ z Flow y Time averaged PSD vs Instantaneous PSD S pp (ω) = 1 T T 0 S pp (ω, t)dt 11 / 24
Amiet s model for rotating airfoils Main steps: S pp (ω) = 1 T T 0 ( ω ω Ignore acceleration effects (ω Ω) ) 2 S pp(ω, τ)dτ Power conservation: S pp (ω, t) ω = S pp(ω, τ) ω Change of variable: t τ = ω ω Doppler shift: ω ω = ω S ω O = 1 M SO ê 1+M FO ê References: Schlinker and Amiet (1981) Sinayoko, Kingan and Agarwal (2013) 12 / 24
Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 13 / 24
Sawtooth serration design Wind turbine blade element Wind turbine blade element: Pitch angle: 10 deg Chord: 2m Span: 7.25m Rotational speed Ω = 2.6rad/s (RPM=25) Angle of attack: 0 deg M blade = 0.165 M chord = 0.167 14 / 24
Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 10 10 0 10 1 10 2 Non-dimensional frequency kc 15 / 24
Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 10 10 0 10 1 10 2 Non-dimensional frequency kc 15 / 24
Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 4h/l s = 2 10 10 0 10 1 10 2 Non-dimensional frequency kc 15 / 24
Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = 4 10 10 0 10 1 10 2 Non-dimensional frequency kc 15 / 24
Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = 4 4h/l s = 8 10 10 0 10 1 10 2 Non-dimensional frequency kc 15 / 24
Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 10 10 0 10 1 10 2 Non-dimensional frequency kc 16 / 24
Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 10 10 0 10 1 10 2 Non-dimensional frequency kc 16 / 24
Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 4h/l s = 2 10 10 0 10 1 10 2 Non-dimensional frequency kc 16 / 24
Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = 4 10 10 0 10 1 10 2 Non-dimensional frequency kc 16 / 24
Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re 1 10 12 ] 50 45 40 35 30 25 20 15 4h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = 4 4h/l s = 8 10 10 0 10 1 10 2 Non-dimensional frequency kc 16 / 24
Effect of rotation on PSD Doppler factor 40 35 CF Maximum Doppler factor (ω /ω) 2 (db) PCR 6.0 Pitch angle (deg) 30 25 20 15 10 WT PTO 4.8 3.6 2.4 1.2 5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Blade element Mach 0.0 WT: wind turbine PTO: propeller take-off CF: cooling fan PC: propeller cruise 17 / 24
Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 18 / 24
Generalized Amiet model for serrated edges Theory Inspired by Roger et al (AIAA-2013-2108) Fourier series in spanwise direction. Pressure formulation and scattering approach Discretize the solution using n Fourier modes LP = DP + C P y 1 { (β L = 2 + σ 2) 2 y 2 1 + 2 y 2 + 2ikM }. 2 y 1 19 / 24
Generalized Amiet model for serrated edges Iterative solution 1 Refine the solution iteratively P = 2 Decoupled solution (order 0) lim n + P n 3 Coupled solution (order 1) LP 0 = DP 0 LP 1 = DP 1 + C P 0 y 1. 20 / 24
Generalized Amiet model for serrated edges Results SPL (Straight Edge - Sawtooth) [db] 30 25 20 15 10 5 0 order 0 order 1 Howe 5 10 0 10 1 Non-dimensional frequency kc Isolated sawtooth blade, M = 0.1, l s /δ = 1, h s /l s = 3.75. 21 / 24
Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 22 / 24
Conclusions 1 Rotation effect can be incorporated easily using Amiet s approach 2 Rotation has little effect (< 1dB) for low speed fans 3 Rotation has significant effect (up to 5dB) on high speed fans 4 Preliminary results for new model improves significantly on Howe s theory 23 / 24
Acknowledgements 24 / 24
Acknowledgements Further information http://www.sinayoko.com http://bitbucket.org/sinayoko s.sinayoko@soton.ac.uk @sinayoko 24 / 24
Acknowledgements Further information http://www.sinayoko.com http://bitbucket.org/sinayoko s.sinayoko@soton.ac.uk @sinayoko Thank you! 24 / 24