Noise prediction for serrated trailing-edges

Transcription

1 Noise prediction for serrated trailing-edges Benshuai Lyu 1 Mahdi Azarpeyvand 2 Samuel Sinayoko 3 1 Department of Engineering, University of Cambridge 2 Department of Mechanical Engineering, University of Bristol 3 Institute of Sound and Vibration Research, University of Southampton June 22, 2015

2 Outline Motivation Why is TE noise important? Introduction to TE noise generation and control TE noise generation TE noise control Inaccurate existing model Analytical formulation The mathematical model Fourier transformation and iterative-solving procedure Far-field sound Results FEM validation Model results Comparison with Howe s model Noise reduction mechanisms Conclusion

3 TE noise problems are important Figure 1: Applications where TE noise is important Fig(a): sitesgooglecom/site/flightdeckathome/liveatc 2 Fig(b): blogjournalscambridgeorg/2013/01/wind-turbine-syndrome-fact-or-fiction 3 Fig(c): wwwaliexpresscom/promotion/electronic_computer-fan-noise-promotionhtml

4 TE noise problems are important TE noise of an approaching aircraft (a) An approaching aircraft Figure 1: Applications where TE noise is important Fig(a): sitesgooglecom/site/flightdeckathome/liveatc 2 Fig(b): blogjournalscambridgeorg/2013/01/wind-turbine-syndrome-fact-or-fiction 3 Fig(c): wwwaliexpresscom/promotion/electronic_computer-fan-noise-promotionhtml

5 TE noise problems are important TE noise of an approaching aircraft TE noise of wind turbines (a) An approaching aircraft (b) Wind turbines Figure 1: Applications where TE noise is important Fig(a): sitesgooglecom/site/flightdeckathome/liveatc 2 Fig(b): blogjournalscambridgeorg/2013/01/wind-turbine-syndrome-fact-or-fiction 3 Fig(c): wwwaliexpresscom/promotion/electronic_computer-fan-noise-promotionhtml

6 TE noise problems are important TE noise of an approaching aircraft TE noise of wind turbines TE noise of rotating fans (a) An approaching aircraft (b) Wind turbines (c) A rotating fan Figure 1: Applications where TE noise is important Fig(a): sitesgooglecom/site/flightdeckathome/liveatc 2 Fig(b): blogjournalscambridgeorg/2013/01/wind-turbine-syndrome-fact-or-fiction 3 Fig(c): wwwaliexpresscom/promotion/electronic_computer-fan-noise-promotionhtml

7 Outline Motivation Why is TE noise important? Introduction to TE noise generation and control TE noise generation TE noise control Inaccurate existing model Analytical formulation The mathematical model Fourier transformation and iterative-solving procedure Far-field sound Results FEM validation Model results Comparison with Howe s model Noise reduction mechanisms Conclusion

8 TE noise generation Focus on the turbulent-boundary-layer TE noise, which will be referred to as TE noise

9 TE noise generation Focus on the turbulent-boundary-layer TE noise, which will be referred to as TE noise When the turbulent boundary layer convects past the TE, the non-radiating pressure fluctuation is scattered into sound capable of propagating to the far-field Turbulent boudary layer Sound radiation Airfoil Wake Figure 2: TE noise generation by edge-scattering

10 TE noise reduction techniques Figure 3: TE noise reduction techniques Fig(a): TGeyer et al Fig(b): Michaela Herr et al Fig(c): Gruber s PhD thesis Theory: (a) and (b) Jaworski and Peake 2013, Lorlna Ayton (c) Howe 1991

11 TE noise reduction techniques Porous airfoil (a) Porous airfoil Figure 3: TE noise reduction techniques Fig(a): TGeyer et al Fig(b): Michaela Herr et al Fig(c): Gruber s PhD thesis Theory: (a) and (b) Jaworski and Peake 2013, Lorlna Ayton (c) Howe 1991

12 TE noise reduction techniques Porous airfoil Brush-type TE (a) Porous airfoil Figure 3: (b) Brush-type TE TE noise reduction techniques Fig(a): TGeyer et al Fig(b): Michaela Herr et al Fig(c): Gruber s PhD thesis Theory: (a) and (b) Jaworski and Peake 2013, Lorlna Ayton (c) Howe 1991

13 TE noise reduction techniques Porous airfoil Brush-type TE Serrated TEs (a) Porous airfoil Figure 3: (b) Brush-type TE TE noise reduction techniques (c) Serrated TEs Fig(a): TGeyer et al Fig(b): Michaela Herr et al Fig(c): Gruber s PhD thesis Theory: (a) and (b) Jaworski and Peake 2013, Lorlna Ayton (c) Howe 1991

14 Howe s model Howe s model significantly overpredictes the noise reduction capability of serrated TEs Figure 4: Comparison of experiment and Howe s model 8 8 Fig4: Gruber s PhD thesis 2012

15 Howe s model Howe s model significantly overpredictes the noise reduction capability of serrated TEs Figure 4: Comparison of experiment and Howe s model 8 8 Fig4: Gruber s PhD thesis 2012

16 Outline Motivation Why is TE noise important? Introduction to TE noise generation and control TE noise generation TE noise control Inaccurate existing model Analytical formulation The mathematical model Fourier transformation and iterative-solving procedure Far-field sound Results FEM validation Model results Comparison with Howe s model Noise reduction mechanisms Conclusion

17 The mathematical model d c z y φ θ Observer (x1, x2, x3) x Wall pressure gust P iae i(ωt k1x k2y ) λ 2h Figure 5: The schematic of a flat plate with a serrated TE The following wave equation needs to be solved (Roger and Moreau 2013) ( β 2 + H 2 (y) ) 2 P x P y P z 2 2H (y) 2 P x y + ( 2iM0 k H (y) ) P x + k2 P = 0, (1)

18 Fourier transformation Making use of Fourier transformation P (x, y, z) = P n (x, z)e ik 2ny, (2) where, k 2n = k 2 + 2nπ/λ,

19 Fourier transformation Making use of Fourier transformation P (x, y, z) = P n (x, z)e ik2ny, (2) where, k 2n = k 2 + 2nπ/λ, the wave equation reduces to where, DP = AP + B P x, (3) { (β D = 2 + σ 2) 2 } x z 2 + 2ikM 0 (4) x

20 The iterative-solving procedure P (0) is obtained by solving DP = AP (5)

21 The iterative-solving procedure P (0) is obtained by solving DP = AP (5) Then P (1) is evaluated by solving DP = AP + B P(0) x (6)

22 The iterative-solving procedure P (0) is obtained by solving DP = AP (5) Then P (1) is evaluated by solving DP = AP + B P(0) x (6) Continuing this process, P (2) is found by solving DP = AP + B P(1) x (7)

23 The iterative-solving procedure P (0) is obtained by solving Then P (1) is evaluated by solving DP = AP (5) DP = AP + B P(0) x (6) Continuing this process, P (2) is found by solving A solution sequence DP = AP + B P(1) x (7) P (0), P (1), P (2), P (3)

24 Far-field sound The far-field sound is obtained by evaluating the surface integral based on the theories of Kirchoff and Curle p f (x, ω) = iωx 3 4πc 0 S0 2 P (x, y )e ikr d x d y, (8) s where S0 2 = x2 1 + β2 (x x2 3 ), and R takes the following form: R = M 0(x 1 x ) S 0 β 2 + x 1x + x 2 y β 2 β 2 S 0, (9) where, P denotes the pressure jump across the flat plate

25 Outline Motivation Why is TE noise important? Introduction to TE noise generation and control TE noise generation TE noise control Inaccurate existing model Analytical formulation The mathematical model Fourier transformation and iterative-solving procedure Far-field sound Results FEM validation Model results Comparison with Howe s model Noise reduction mechanisms Conclusion

26 FEM validation For wide serrations log 10 p f (db) Baseline theory 40 Baseline FEM Serrated theory Serrated FEM kc (a) M 0 = 01 20log 10 p f (db) Baseline theory 40 Baseline FEM Serrated theory Serrated FEM kc (b) M 0 = 02 Figure 6: SPL at 90 above the trailing-edge in the mid-span plane with x 3 = 1 due to a wall pressure gust of frequency ω with k 2 = 0, parameters of the serrations are λ/h = 6, h/c = 0025

27 FEM validation cont For narrow serrations, log 10 p f (db) Baseline theory 40 Baseline FEM Serrated theory Serrated FEM kc (a) λ/h = 3 20log 10 p f (db) Baseline theory 40 Baseline FEM Serrated theory Serrated FEM kc (b) λ/h = 1 Figure 7: SPL at 90 above the trailing-edge in the mid-span plane with x 3 = 1 due to a wall pressure gust of frequency ω with k 2 = 0, parameters of the serrations are h/c = 005 with M 0 = 01

28 Model results For wide serrations, log 10 Ψ (db) Baseline Serrated kc (a) λ/h = 8 10log 10 Ψ (db) Baseline Serrated kc (b) λ/h = 4 Figure 8: The normalized spectrum for straight and serrated trailing-edges, h/c = 0025, M 0 = 01, the observer is at 90 above the trailing-edge in the mid-span plane with x 3 = 1λ/h = 8, λ/h = 4

29 Model results cont For narrow serrations, log 10 Ψ (db) Baseline Serrated kc (a) λ/h = 04 10log 10 Ψ (db) Baseline Serrated kc (b) λ/h = 02 Figure 9: The normalized spectrum for straight and serrated trailing-edges, h/c = 005, M 0 = 01, the observer is at 90 above the trailing-edge in the mid-span plane with x 3 = 1

30 Comparison with Howe s model 40 (a) (b) 10log 10 Ψ (db) Howe Baseline Howe Serrated New Model Baseline New Model Serrated kc kc Figure 10: The normalized spectrum of Howe s model and the new model, h/c = 005, M 0 = 01, the observer is at 90 above the trailing-edge in the mid-span plane with x 3 = 1 (a)λ/h = 04, h/c = 005, M 0 = 01 (b) λ/h = 02, h/c = 005, M 0 = 01

31 Noise reduction mechanism σ = 5 (a) kλ = π/10, (b) kλ = π/5, (c) kλ = π/2, (d) kλ = π (a) (b) x /λ (c) (d) x /λ y /l y y /l y

32 Outline Motivation Why is TE noise important? Introduction to TE noise generation and control TE noise generation TE noise control Inaccurate existing model Analytical formulation The mathematical model Fourier transformation and iterative-solving procedure Far-field sound Results FEM validation Model results Comparison with Howe s model Noise reduction mechanisms Conclusion

33 Conclusion 1 Compared to Howe s model, the presented model includes the convection effect of the mean flow, and can better agrees with experiments 2 It is found that the destructive interference of the scattered pressure is the cause of sound reduction 3 The approach used in this model can be used for other serrations Future work on optimizing the serration profiles can be done

34 Thank You!