Broadband Noise Predictions Based on a New Aeroacoustic Formulation

Transcription

1 Boadband Noise Pedictions Based on a New Aeoacoustic Fomulation J. Caspe and F. Faassat NASA Langley Reseach Cente Hampton, Viginia AIAA Pape -8 Aifame Noise Session 4 th AIAA Aeospace Sciences Meeting and Ehibit Reno, Nevada Januay 16, 1

2 Outline Intoduction / Motivation Acoustic Fomulation Model Poblems Suface Pessue fom Thin Aifoil Theoy Velocity Scaling Popeties, Diectivity Boadband Noise Pediction Incident Tubulence Noise Compaison with Epeiment Pateson and Amiet, 1976

3 Intoduction / Motivation Boadband Noise Pediction Tools Aifame noise, ducted fan noise Incident tubulence, TE noise Time Domain Appoach Acoustic Analogy Ffowcs Williams Hawkings equation Decouples aeodynamics fom acoustics Input fom CFD o epeiment V pt FW-H Equation Acoustic Pessue db f 3

4 Acoustic Fomulation 1,, 3 f% : suface geomety ˆ ν geodesic nomal obseve position y souce position y cos eˆ 3 V θ f > e 3 e 3 y y 1, y, 3 f f > 1 ν The only estiction on the velocity vecto is that it lie in the same plane as the suface. 4

5 5 1 θ y 1, y, 1,, 3 V 3 y ν e 3 e 3 f > f > f f Ffowcs Williams - Hawkings Equation [ ],, ˆ f H t p f p n H p t p c δ δ Solution: Acoustic Fomulation Loading Noise Dipole τ δ τ δ π d d y y f H y y p g t p t R,,, Fee-space Geen s function:, 4 c t g g + τ π δ

6 Fomulation 1B p/ τ V p/ scos 4 π p, t c 1 M f% > p cos M pcos ν + ds 1 M 1 f% M > f% et Given p y, t on the suface, this fomula yields the loading noise at an obseve at time t. Fo M << 1, >> λ, the fist integal dominates the signal. The contou integal vanishes at the tailing edge if the Kutta condition is satisfied. This fomulation is valid fo a otating suface. et ds et dl 6

7 Fomulation 1B Test Cases Velocity Scaling Popeties Diectivity Analytic Suface Pessue Thin Aifoil Theoy Amiet, Peiodic Gust Constant Fequency Flat Plate in Unifom Rectilinea Motion 7

8 Analytic Suface Pessue Rectangula Suface at Constant Velocity 1 LC, b b T V [ U,,] 1,, 3 3 Upwash ik 1 w, t we 1 Ut V 1 b Suface pessue P, t ρ Uwg, ke 1 1 ikut L C k ω / U constant, g, k fom thin aifoil theoy 1 8

9 Diectivity L C b M U.5 m. m m/s V 3 ψ 1 w.5 U b Test Cases 1 L C :, ψ, 3m, ψ π f 1 khz, f khz 9

10 Diectivity 1 O 9 O 6 O f 1 khz f khz scaled 15 O 3 O p ma, Pa 1

11 Incident Tubulence Noise Epeiment: Pateson and Amiet 1976 NACA 1 Aifoil Chod.3 m Span.53 m α degees Micophone:.5 m, θ 9 degees Sceen shea laye nozzle U 11

12 Upwash,, ˆ, D Peiodic Gust [ ] ik1 1 Ut+ k w t w k k e dk dk Suface pessue,, ˆ,,, i kut 1 k P t ρ U wk k g k k e dkdk Amiet 1975 Skewed gusts contibute little to the sound eceived by an obseve in the plane mid-span, i.e. k is the only spanwise wave numbe to conside. 1

13 Boadband Suface Pessue N P, t ρ U A gk,, e n, 1 1, n N n Ut+Φ i k 1, n n A n, S k, k k 1 ww 1, n 1 1/ S k, k powe spectal density of w ww Φ n andom phase angle on [, π ] Without eplicit spanwise integation, this fomulation can be epected to equie amplitude scaling in the fa field, but the spectal shape of the noise will be unaffected. 13

14 Tubulence PSD -Component von Kaman Fomula S ww 4 kˆ 1 1 7/3 9π k ˆ ˆ e 1 + k1 + k k, k u + kˆ ˆ ki ki, ke k e π Γ5/ 6 L Γ1/ 3 1 L 1 and u detemined by epeimental measuement S ww k, Fequency, Hz 14

15 Boadband Pediction in Time Suface pessue input to Fomulation 1B Five tunnel speeds: U 4, 6, 9, 1, 165 m/s Diectivity and amplitude coected fo efaction though shea laye Acoustic pessue Fouie analyzed to convet to spectal density p, Pa Pedicted Signal U 165 m/s time, seconds 15

16 Fa Field Noise Spectum 9 8 Pedictions SPL, db Epeiment 4 m/s 6 m/s 9 m/s 1 m/s 165 m/s Fequency, Hz 16

17 Concluding Remaks A new solution to the FW-H equation povides a useful fomulation fo loading noise pedictions. Although simple in fom, Fomulation 1B is applicable to otating sufaces. A boadband noise pediction was shown to agee well with epeimental measuement. The fomulation s simplicity lends itself well to statistical analysis of boadband noise. Futue eseach will include the application of the statistical fomulation to tailing edge noise. 17