Aeroacoustic Analogy for the Computation of Aeroacoustic Fields in Partially Closed Domains

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1 INSTITUT FÜR MECHANIK UND MECHATRONIK Messtechnik und Aktorik Aeroacoustic Analogy for the Computation of Aeroacoustic Fields in Partially Closed Domains A. Hüppe 1, M. Kaltenbacher 1, A. Reppenhagen 2, F. Zenger 3, S. Becker 3 1 Vienna University of Technology 2 Virtual Vehicle Research Center, Graz 3 Lehrstuhl für Prozessmaschinen und, FAU Erlangen Nürnberg Friedrich Alexander University of Erlangen Nuremberg

2 Axial Fan Setup Mounted in ridged wall tube Speed 1500 RPM Max. radial velocity m/s Mass flow inlet Real measurement setup Full volume coupling CFD computation with OpenFOAM, Finite Volumes Acoustic computation with CFS++, Finite Elements Investigations Application of aeroacoustic analogy, separating flow and acoustics Application of data transfer algorithms for hybrid grid method Rotating domains in fluid flow and acoustics Evaluation of aeroacoustic source terms Computation of acoustic wave propagation 2

3 Aeroacoustic Analogy Perturbation ansatz, additive splitting of field variables Acoustic Perturbation Equations for incompressible, isentropic flow (APE-2) 1 Clean separation of acoustic and hydrodynamic quantities High computational effort for volume discretization schemes (4 variables per node or cell) Further simplification necessary and possible 1 R. Ewert W. Schröoder: Acoustic perturbation equations based on flow decomposition via source filtering, Journal of Computational Physics

4 Aeroacoustic Analogy By using elimination of third equation Introducing the acoustic velocity potential Substitution into mass conservation results in a Perturbed Convective Wave Equation (PCWE) Only one unknown, well suited for using finite element schemes Just first order derivatives on the right hand side (less numerical noise) Mean flow effects on wave propagation included 4

5 Avoiding refractions due to grid rotations Rigid body rotation of interior grid may not affect wave propagation Inclusion of grid rotation in substantial time derivative 5

6 Determination of acoustic modes Artificial source at blade tip of single blade Recording of acoustic pressure at the measurement microphone position 100Hz Mic 90 Mic 66 Mic 33 Mic 0 350Hz Transfer function of acoustic pressure 450Hz 6

7 CFD Setup Straight blades Mounts and gear with complex geometry 29.8 million cells 1500RPM Quantities for export Pressure Pressure gradient Mean flow at last time step Mass flow inlet 1.3 m³/s Grid rotation of fan using OpenFOAM AMI (Arbitrary Mesh Interface) Source term including u mean and u rot 7

8 Computational Setup - Acoustics Absorbing boundary conditions Time Domain Perfectly Matched Layer Rotating domain coincide with CFD Sound hard wall Geometry resolving mesh according to CFD Grid Propagation domain to include microphone positions (+0.1m) Propagation: FRONT PML Propagation : BACK Rotating domain 8

9 Acoustic Grid Finite Element Grid elements on interface 1.9 million nodes 3.36 million unknowns (incl. PML) Ca. 60 FGMRES iterations per time step 9

10 Interpolation via Cell Intersection Assumption: Source Term is constant over CFD cell 1) Find two intersecting cells 2) Compute intersection polygon, its volume V c and Center X c CAA CFD V c, X c CAA CFD 3) Compute weighted sum for CAA nodes 4) Resulting source field 10

11 Time step Algorithm 1. Import source terms on CFD grid 2. Interpolate source terms from CFD to CAA Grid (Initial state) 3. Rotate CAA grid to align with CFD Time loop 4. Compute Grid intersection between rotating and quiescent domain Ω 1 Ω 2 5. Update and solve algebraic system of equations 6. Perform post process, store solution 11

12 Data transfer Acoustic and Flow grid resolve geometry Similar element sizes in some regions Application of novel Cut-Cell conservative interpolation Accumulated volume error in domain of 1% CFD Grid with contours of flow pressure Source terms on CAA grid CFD Grid and outline of CAA grid (white) 12

13 Source terms in rotating domain Source term in rotating domain 10 2 BPF 254Hz dp/dt (Pa/s) Frequency (Hz) 1004Hz 13

14 Comparison to measurements 2 Measurement (0.1s) Measurement (10s) OpenFoam CFS (0.1s) 4 Measurement (0.1s) Measurement (10s) OpenFoam CFS (0.1s) 0,04 s = one complete turn 1 Measurement (0.1s) Measurement (10s) OpenFoam CFS (0.1s) 3 Measurement (0.1s) Measurement (10s) OpenFoam CFS (0.1s) 14

15 Conclusions Wave equation scheme PCWE Propagation for rotating domains Separation of flow and acoustics Computational scheme allows the computation of the acoustic pressure inside the flow region CFD is computed independently of CAA CAA computation can take into account acoustic scattering Source term investigation allows determination of acoustic sources Good agreement of spectra to measurement data Outlook Towards Compressible CFD Interpolation scheme Computational efficiency 15

16 Acknowledgement The authors would like to acknowledge the financial support of the "COMET K2 Competence Centres for Excellent Technologies Programme" of the Austrian Federal Ministry for Transport, Innovation and Technology (bmvit), the Austrian Federal Ministry of Science, Research and Economy (bmwfw), the Austrian Research Promotion Agency (FFG), the Province of Styria and the Styrian Business Promotion Agency (SFG). We would furthermore like to express our thanks to our supporting industrial and scientific project partners and to the Graz University of Technology. 16

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