- 1. Flow and Noise Simulation of the NASA Tandem Cylinder Experiment using OpenFOAM Con Doolan School of Mechanical Engineering University of Adelaide Adelaide, South Australia 5005 con.doolan@adelaide.edu.au May 11, 2009 C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 1 / 40
- 2. Overview Introduction Numerical Method Aerodynamic Simulation Code:OpenFOAM Computational Details Acoustic Simulation Aerodynamic Results Mean Flow Unsteady Flow Acoustic Results Summary and Conclusions C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 2 / 40
- 3. Introduction Aerodynamic Noise: Aircraft Landing Gear Khorrami et al. PRELIMINARY ANALYSIS OF ACOUSTIC MEASUREMENTS FROM THE NASA-GULFSTREAM AIRFRAME NOISE FLIGHT TEST. 14th AIAA/CEAS Aeroacoustics Conference (2008) AIAA-2008-2814-922 C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 3 / 40
- 4. Introduction Previous Work: Vortex Wake G/D = 1 G/D = 3 Power Ratio C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 4 / 40
- 5. Introduction Aims of this work 1. To present a 2D URANS ﬂow simulation of the NASA tandem cylinder experiment using OpenFOAM and compare the ﬂow results with published experimental data. 2. To present a statistical noise calculation method, use it to predict tandem cylinder noise and assess its performance against published experimental data. C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 5 / 40
- 6. Introduction NASA Tandem Cylinder Experiment Tandem Cylinder Experiment, NASA QFF, Re = 166, 000, M = 0.1274, L/D = 3.7 Jenkins et al., 36th AIAA Fluid Dynamics Conference (2006) Baseline experimental data for CAA validation, focus of future CAA validation workshops (a) Layout (b) Installation in QFF C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 6 / 40
- 7. Numerical Method Aerodynamic Simulation OpenFOAM OpenFOAM = (Open Field Operation and Manipulation) CFD Toolbox Open source ﬁnite volume CFD solver Written in C++ Supplied with numerous pre-conﬁgured solvers, utilities and libraries, or can write your own! 3D unstructured mesh as standard (2D, orthogonal treated as subset) Robust, implicit, pressure-velocity, iterative solution framework Parallel running is easy See: http://www.opencfd.co.uk/openfoam/ C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 7 / 40
- 8. Numerical Method Aerodynamic Simulation Computational Details Unsteady Reynolds Averaged Navier Stokes (URANS), second order. C-Mesh, orthogonal mesh of diameter 16d clearance all about objects, 205,508 nodes 30 ≤ y + ≤ 40, k − turbulence model using a wall function (a) Full domain (b) Detail about cylinders C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 8 / 40
- 9. Numerical Method Aerodynamic Simulation Convergence Table: Summary of average results from three computational grids and comparison with experiment. Case Nodes C D,up CL,up C D,down CL,down Grid 1 101,902 0.271 0.075 0.237 0.393 Grid 2 146,406 0.305 0.082 0.240 0.438 Grid 3 205,508 0.338 0.086 0.245 0.487 Experiment1 - 0.49-0.52 - 0.24-0.35 - 1 Jenkins et al., 36th AIAA Fluid Dynamics Conference (2006) C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 9 / 40
- 10. Numerical Method Acoustic Simulation Noise Generation: Theory of Curle Sound generated by ﬂuctating pressures on a rigid, non-moving object: ∂ lj 4πc2 (ρ(˜, t) − ρ0 ) = 0 x [pδij ] dS(˜) y (1) ∂xi S r c0 : speed of sound ρ0 : the ﬂuid density in the medium at rest y : point on the rigid surface ˜ x: observer point ˜ r = |˜ − y | x ˜ li are the components of the unit vector that is normal to the surface p: pressure ρ: density The square brackets denote a value taken at the retarded time t − r/c0 . C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 10 / 40
- 11. Numerical Method Acoustic Simulation Noise Generation: Compact Theory of Curle ∂ Fi 1 xi ∂Fi 4πc2 (ρ(˜, t) − ρ0 ) = − 0 x = (2) ∂xi r c0 r2 ∂t where Fi are the three vector components of the resulting force applied on the ﬂuid. C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 11 / 40
- 12. Numerical Method Acoustic Simulation Compact Limits When λ/d > 1, can consider acoustically compact. fd 1 1 St = = (3) U0 M (λ/d) Experiment: M = 0.1274 Therefore, frequency “limit” for compactness to hold, St < 7.84 In this work: 0.1 ≤ St ≤ 2 Hence compact assumption valid. C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 12 / 40
- 13. Numerical Method Acoustic Simulation Unsteady Surface Pressures φ1 = +90◦ φ2 = −90◦ φ = φ1 − φ2 Re = 2 × 104 Random, low frequency beating 4 Data: Norberg. Fluctuating lift on a circular cylinder: review and new measurements. Journal of Fluids and Structures (2003) C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 13 / 40
- 14. Numerical Method Acoustic Simulation Temporal Phase Dispersion Model True signal y(t) is convolved with the simulated (URANS) signal x(t) over a signal of time length T using an impulse response function h(t) T y(t) = h(τ )x(t − τ ) dτ (4) 0 h(t) = e−iφτ (5) The true signal can be considered as a sum of a number of original simulated signals, each with a randomly dispersed phase diﬀerence φτ = φτ (τ ). C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 14 / 40
- 15. Numerical Method Acoustic Simulation Temporal Phase Dispersion Model Assume correlation coeﬃcient can be distributed according to Laplacian statistics ρτ (τt ) = exp (−wτ (τt )) (6) Use a linear distribution of variance over 0 ≤ τt ≤ 1 wτ (τt ) = wτ,max τt (7) Gaussian statistics could also be assumed. C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 15 / 40
- 16. Numerical Method Acoustic Simulation Temporal Phase Dispersion Model Retarded time modulated using: φτ d Θτ = Θ + (8) 2π U0 100 URANS signals, each with a randomly dispersed phase, are used to create a single temporally decorrelated signal. Assumed that disturbances occur at about every Nτ = 60 vortex shedding periods. Assuming this is equal to the standard deviation, −2 2πNτ 1/wτ,max ∼ St0 ∼ 10−6 . This is a crude estimate of the variance, however, as shown, it produces reasonable results. C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 16 / 40
- 17. Numerical Method Acoustic Simulation Spatial Phase Dispersion Model Sound recombines at microphone from each cylinder segment with constructive/destructive interference Sound Flow Sound Cylinder with N segments, each with an aerodynamic force that has different phase C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 17 / 40
- 18. Numerical Method Acoustic Simulation Spatial Phase Dispersion Model After temporally decorrelating the signal, spanwise decorrelation eﬀects are taken into account. The model developed by Casalino and Jacob, JSV, (2003) was used with 30-100 spanwise segments. Laplacian statistics: |η| ρ(η) = exp − (9) Ll wmax = 1/Ll (10) φη d Θη = Θ + (11) 2π U0 C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 18 / 40
- 19. Aerodynamic Results Sources of Experimental Data Aerodynamic Data: Jenkins et al. Measurements of Unsteady Wake Interference Between Tandem Cylinders. 36 th AIAA Fluid Dynamics Conference and Exhibit AIAA Paper 2006-3202 (2006) PIV and Aerodynamic Data: Khorrami et al. Unsteady Flowﬁeld Around Tandem Cylinders as Prototype Component Interaction in Airframe Noise. AIAA Journal (2007) vol. 45 (8) pp. 1930-1941 Acoustic and Aerodynamic Data: Lockard et al. Tandem Cylinder Noise Predictions. 13 th AIAA/CEAS Aeroacoustics Conference AIAA Paper 2007-3450 (2007) C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 19 / 40
- 20. Aerodynamic Results Mean Flow Mean streamwise velocity: URANS 1.5 1.2 1 1 0.5 0.8 0.6 y/d 0 0.4 −0.5 0.2 −1 0 −1.5 −0.2 −1 0 1 2 3 4 5 6 x/d C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 20 / 40
- 21. Aerodynamic Results Mean Flow Mean streamwise velocity: NASA PIV C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 21 / 40
- 22. Aerodynamic Results Mean Flow Mean streamwise velocity between cylinders, y = 0 0.6 0.5 0.4 0.3 0.2 U/U0 0.1 0 Experiment BART URANS −0.1 −0.2 −0.3 1 1.5 2 2.5 3 3.5 4 x/d C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 22 / 40
- 23. Aerodynamic Results Mean Flow Streamlines <8-+quot;FL~|{kU]X =:.AD'KNmg Z 0 BEHOzTe Y > ,#!J }Qj h [ 1 C&I PoV 2 *(G upia ? $ Mw b 3 % vqd @) ;6 45 /9 7 yc xW tr f R_ s` lS^ n Computed Experiment C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 23 / 40
- 24. Aerodynamic Results Mean Flow Mean vertical velocity: URANS 1.5 0.3 1 0.2 0.5 0.1 y/d 0 0 −0.5 −0.1 −1 −0.2 −1.5 −0.3 −1 0 1 2 3 4 5 6 x/d C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 24 / 40
- 25. Aerodynamic Results Mean Flow Mean vertical velocity: NASA PIV C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 25 / 40
- 26. Aerodynamic Results Mean Flow Time averaged streamwise velocity ﬂuctuation: URANS 1.5 0.25 1 0.2 0.5 0.15 y/d 0 0.1 −0.5 0.05 −1 −1.5 −1 0 1 2 3 4 5 6 x/d C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 26 / 40
- 27. Aerodynamic Results Mean Flow Time averaged streamwise velocity ﬂuctuation: NASA PIV C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 27 / 40
- 28. Aerodynamic Results Mean Flow Instantaneous spanwise vorticity: URANS 1.5 15 1 10 0.5 5 y/d 0 0 −0.5 −5 −1 −10 −1.5 −15 −1 0 1 2 3 4 5 6 x/d C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 28 / 40
- 29. Aerodynamic Results Mean Flow Instantaneous spanwise vorticity: NASA PIV C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 29 / 40
- 30. Aerodynamic Results Mean Flow Mean Surface Pressure 1.5 1.5 Experiment BART Experiment BART 1 1 Experiment QFF Experiment QFF 0.5 URANS 0.5 URANS 0 0 Cp Cp −0.5 −0.5 −1 −1 −1.5 −1.5 −2 −2 −2.5 −2.5 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 θ (degrees) θ (degrees) (a) Upstream cylinder (b) Downstream cylinder C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 30 / 40
- 31. Aerodynamic Results Unsteady Flow RMS Pressure: URANS Visualisation 1.5 1 0.25 0.5 0.2 y/d 0 0.15 −0.5 0.1 −1 0.05 −1.5 0 −1 0 1 2 3 4 5 6 x/d C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 31 / 40
- 32. Aerodynamic Results Unsteady Flow Unsteady Surface Pressure 0.2 1 Experiment BART Experiment BART Experiment QFF Experiment QFF 0.8 0.15 URANS URANS 0.6 C′p,rms p,rms 0.1 C′ 0.4 0.05 0.2 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 θ (degrees) θ (degrees) (a) Surface pressure: upstream cylin- (b) Surface pressure: downstream der cylinder C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 32 / 40
- 33. Aerodynamic Results Unsteady Flow Simulated unsteady lift and drag coeﬃcients 1.5 1.5 C C L L 1 C 1 C D D 0.5 0.5 CL or CD D C or C 0 0 L −0.5 −0.5 −1 −1 −1.5 −1.5 0 10 20 30 40 50 0 10 20 30 40 50 tU0/D tU0/D (a) Upstream cylinder (b) Downstream cylinder C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 33 / 40
- 34. Acoustic Results Spanwise Correlation - Fitted Model 1.5 1.5 Experiment BART Experiment BART Experiment QFF Experiment QFF Model Ll = 0.25 Model Ll = 0.35 1 Model L = 0.17 1 Model L = 0.17 Correlation Correlation l l Model Ll = 0.1 Model L = 0.1 l 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 z/Lz z/Lz (a) Upstream cylinder (b) Downstream cylinder Experiment: Lockard et al 13 th AIAA/CEAS Aeroacoustics Conference (2007) C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 34 / 40
- 35. Acoustic Results Microphone Locations Microphones B C A r/d = 33.74 r/d = 38.45 r/d = 29.03 Name x/d y/d Microphone A -8.33 27.817 Microphone B 9.11 32.49 Microphone C 26.55 27.815 Cylinders C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 35 / 40
- 36. Acoustic Results Simulated acoustic pressure at Microphone B −3 x 10 8 6 4 p /(ρU0) 2 2 0 ′ −2 −4 −6 0 50 100 150 200 250 tU /D 0 C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 36 / 40
- 37. Acoustic Results Acoustics at Microphone A, r/d = 29.03 120 URANS + Statistics 110 2D URANS 100 Experiment (NASA QFF) 90 PSD [dB/Hz] 80 70 60 50 40 0.1 0.2 0.4 0.8 1 1.4 2 St Experiment: Lockard et al 13 th AIAA/CEAS Aeroacoustics Conference (2007) C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 37 / 40
- 38. Acoustic Results Acoustics at Microphone B, r/d = 33.74 120 URANS + Statistics 110 2D URANS 100 Experiment (NASA QFF) 90 PSD [dB/Hz] 80 70 60 50 40 0.1 0.2 0.4 0.8 1 1.4 2 St Experiment: Lockard et al 13 th AIAA/CEAS Aeroacoustics Conference (2007) C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 38 / 40
- 39. Acoustic Results Acoustics at Microphone C, r/d = 38.45 120 URANS + Statistics 110 2D URANS 100 Experiment (NASA QFF) 90 PSD [dB/Hz] 80 70 60 50 40 0.1 0.2 0.4 0.8 1 1.4 2 St Experiment: Lockard et al 13 th AIAA/CEAS Aeroacoustics Conference (2007) C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 39 / 40
- 40. Summary and Conclusions Summary and Conclusions OpenFOAM can provide accurate noise source data for low Mach number bluﬀ body aeroacoustic ﬂows. Using a statistical approach in the time domain, the eﬀects of spanwise phase dislocation can be simulated. 2D URANS ﬂow results can therefore be used to recreate 3D acoustics, hence signiﬁcantly reducing simulation requirements. Questions? C. Doolan (University of Adelaide) 15th AIAA/CEAS Aeroacoustics Conference May 11-13, 2009 40 / 40