Trailing edge noise prediction for rotating serrated blades

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1 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 th AIAA/CEAS Aeroacoustics conference Atlanta, 20 June / 24

2 Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 2 / 24

3 Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 3 / 24

4 Introduction Motivation Wind turbines (Oerlemans et al 2007) Open rotors (Node-Langlois et al AIAA , Kingan et al AIAA ) 4 / 24

5 Introduction Motivation Wind turbines (Oerlemans et al 2007) Open rotors (Node-Langlois et al AIAA , Kingan et al AIAA ) Experiments Gruber et al (AIAA-2012) Moreau and Doolan (AIAA J. 2013) 4 / 24

6 Introduction Motivation Wind turbines (Oerlemans et al 2007) Open rotors (Node-Langlois et al AIAA , Kingan et al AIAA ) Experiments Gruber et al (AIAA-2012) Moreau and Doolan (AIAA J. 2013) Numerical Jones and Sandberg (JFM 2012) Sanjose et al (AIAA ) 4 / 24

7 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

8 Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 6 / 24

9 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

10 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

11 Edge spectra for serrated edges Rewriting of Howe (1991) & Azarpeyvand et al. (2013) Φ = ψ(k 1 δ) ψ(ρ) = ρ 2 [ρ ] ψ ρ 9 / 24

12 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 n = K n2 k 2 s ψ ρ 9 / 24

13 Edge spectra for serrated edges Modal amplitudes a n, K 1 h s = Straight Sawtooth Sinusoidal Slitted Sawtooth / 24

14 TEN for Rotating Airfoils Observer x α γ Ω θ z Flow y 11 / 24

15 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

16 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

17 Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 13 / 24

18 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 = M chord = / 24

19 Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re ] h/l s = Non-dimensional frequency kc 15 / 24

20 Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = Non-dimensional frequency kc 15 / 24

21 Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = 1 4h/l s = Non-dimensional frequency kc 15 / 24

22 Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = Non-dimensional frequency kc 15 / 24

23 Sawtooth serration design Effect of serration height Wide sawtooth l s = 2δ δ =0.5l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = 4 4h/l s = Non-dimensional frequency kc 15 / 24

24 Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re ] h/l s = Non-dimensional frequency kc 16 / 24

25 Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = Non-dimensional frequency kc 16 / 24

26 Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = 1 4h/l s = Non-dimensional frequency kc 16 / 24

27 Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = Non-dimensional frequency kc 16 / 24

28 Sawtooth serration design Effect of serration height Narrow sawtooth l s = δ/2 δ =2.0l s Sound Power Level (SPWL) [db re ] h/l s = 0 4h/l s = 1 4h/l s = 2 4h/l s = 4 4h/l s = Non-dimensional frequency kc 16 / 24

29 Effect of rotation on PSD Doppler factor CF Maximum Doppler factor (ω /ω) 2 (db) PCR 6.0 Pitch angle (deg) WT PTO Blade element Mach 0.0 WT: wind turbine PTO: propeller take-off CF: cooling fan PC: propeller cruise 17 / 24

30 Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 18 / 24

31 Generalized Amiet model for serrated edges Theory Inspired by Roger et al (AIAA ) 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 y 2 + 2ikM }. 2 y 1 19 / 24

32 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 / 24

33 Generalized Amiet model for serrated edges Results SPL (Straight Edge - Sawtooth) [db] order 0 order 1 Howe Non-dimensional frequency kc Isolated sawtooth blade, M = 0.1, l s /δ = 1, h s /l s = / 24

34 Outline 1 Introduction 2 Theory 3 Results 4 Generalized Amiet model for isolated serrated edges 5 Conclusions 22 / 24

35 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

36 Acknowledgements 24 / 24

37 Acknowledgements Further information 24 / 24

38 Acknowledgements Further information Thank you! 24 / 24

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