Aeroacoustic optimisation by means of adjoint sensitivity maps
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1 Aeroacoustic optimisation by means of adjoint sensitivity maps CHRISTOS KAPELLOS GOFUN
2 AGENDA Continuous adjoint method for external aerodynamics Physical mechanisms of sound propagation to the interior OpenFOAM-based process for interior noise prediction Computing the adjoint aeroacoustic sensitivity maps Conclusions & future steps ACKNOWLEDGEMENTS Dr. Michael Hartmann Nikolaos Magoulas Alexander Kabat vel Job 2
3 THE CONTINUOUS ADJOINT METHOD FORMULATION FOR NS-EQUATIONS Optimization problem: minimize the objective function: JJ = JJ vv, pp, bb subject to: RR vv, pp, bb = 0 Flow (primal) Equations RR vv = vv RR vv, pp, bb = RR pp = vv = 0 + vv vv ττ + = 0 Augmented objective function: LL = JJ + qq RR pp dd + δδ vv,pp = 00 uu RR vv dd Variation: δδll = δδ vv,pp JJ + qq RR pp dd + uu RR vv dd + δδ bb JJ + qq RR pp dd + uu RR vv dd RR uu, qq = Adjoint Equations RR qq = uu = 0 RR uu = uu + vv uu uu vv ττaa + qq = 0 Sensitivity Derivatives: δδδδ δδδδ = SS uu νν vv + dddd 3
4 THE CONTINUOUS ADJOINT METHOD FORMULATION FOR NS-EQUATIONS Optimization problem: minimize the objective function: JJ = JJ vv, pp, bb subject to: RR vv, pp, bb = 0 Flow (primal) Equations RR vv = vv RR vv, pp, bb = RR pp = vv = 0 + vv vv ττ + = 0 Augmented objective function: LL = JJ + qq RR pp dd + δδ vv,pp = 00 uu RR vv dd Variation: δδll = δδ vv,pp JJ + qq RR pp dd + uu RR vv dd + δδ bb JJ + qq RR pp dd + uu RR vv dd RR uu, qq = Adjoint Equations RR qq = uu = 0 RR uu = uu + vv uu uu vv ττaa + qq = 0 Sensitivity Derivatives: δδδδ δδδδ = SS uu νν vv + dddd 4
5 PHYSICAL MECHANISMS OF SOUND PROPAGATION TO THE INTERIOR 1. Noise creation 2. Sound propagation to window 3. Structural vibration 4. Noise radiation in the interior Transmitted sound waves Stochastic noise Bending waves Turbulence Sound field 5
6 PROCESS FOR INTERIOR NOISE PREDICTION 1. Noise creation (time resolved CFD) OpenFOAM IDDES Spalart Allmaras SnappyHexMesh for meshing RR vv = vv RR pp = vv = 0 + vv vv ττ + = 0 Hydrodynamic pressure pp on the mirror 2. Noise radiation (Kirchhoff-Integral) OpenFOAM Fully parallelised pp = mmiiiiiiiiii 1 1 rr nn pp + rr3 ccrr 2 pp rr nn tt dddd 3. Structure vibration (Bending waves) OpenFOAM 1.6-ext Using finitearea solver RR ww = 2 ww tt 2 + ηη 1 DD mmm 4 ww + ηη 2 + ηη 3 DD mmm 2 ww pp mm = 0 4. Sound propagation (Wave equation) OpenFOAM 1.6-ext Castellated mesh in vehicle interior RR ppaa = 2 pp aa tt pp aa = 0 BC on the window: pp aa ρρ 2 ww tt 2 = 0 6
7 WIND NOISE PREDICTION 1. Turbulent Flow 2. Sound Radiation 3. Structural Vibration 4. Cabin Noise experiment SPL, db simulation with 1mm mesh valid up to 5 khz Frequency, Hz 7
8 ADJOINT PROCESS FOR SENSITIVITIES COMPUTATION 1. Noise creation (time resolved CFD) Primal simulation time 2. Noise radiation (Kirchhoff-Integral) 3. Structure vibration (Bending waves) Each time step has an effect on the following time steps 4. Sound propagation (Wave equation) Adjoint simulation What is the sensitivity of each time step? time The information of this sensitivity has to travel backwards in time 8
9 ADJOINT PROCESS FOR SENSITIVITIES COMPUTATION RR qq = uu = 0 RR uu = uu + vv uu uu vv ττaa + qq = 0 BC on the mirror: uunn = qqq 4. Adjoint Navier-Stokes (uu, qq) OpenFOAM Adjoint solver provided by ENGYS + in house modifications Checkpointing technique to save primal fields 3. Adjoint Kirchhoff-Integral (qq ) OpenFOAM Fully parallelised RR zz = 2 zz tt 2 + ηη 1 qq = wwwwwwwwwwww DD mmm 4 zz ηη 2 ηη 3 ff(zz xx, tt, xx )dddd DD mmm 2 zz cc 2 ρρ 2 qq tt 2 = 0 2. Adjoint Bending waves (zz) OpenFOAM 1.6-ext Using finitearea solver RR qqaa = 2 qq tt qq aa + δδjj δδqq aa = 0 1. Adjoint Wave equation (qq aa ) OpenFOAM 1.6-ext 9
10 ADJOINT PROCESS FOR SENSITIVITIES COMPUTATION 1. Noise creation (time resolved CFD) Adjoint aeroacoustic sensitivities on the vehicle mirror 2. Noise radiation (Kirchhoff-Integral) 3. Structure vibration (Bending waves) 4. Sound propagation (Wave equation) 4. Adjoint Navier-Stokes (uu, qq) 3. Adjoint Kirchhoff-Integral (qq ) 2. Adjoint Bending waves (zz) 1. Adjoint Wave equation (qq aa ) 10
11 ADJOINT AEROACOUSTIC SENSITIVITIES Simulation of the adjoint aeroacoustic chain Red: push in to reduce interior noise Blue: pull out to reduce interior noise 11
12 ADJOINT AEROACOUSTIC SENSITIVITIES Local Morphing 88 % reduction Red: push in to reduce interior noise Blue: pull out to reduce interior noise 12
13 CONCLUSIONS & FUTURE STEPS Continuous adjoint method for interior noise prediction developed and implemented in OpenFOAM including all steps of noise propagation from the flow to the interior One-step optimisation performed as proof of concept Solutions for the bottlenecks of data handling and computational cost are under consideration A complete optimization process will be performed in the future 13
A CONTINUOUS ADJOINT APPROACH FOR VEHICLE INTERIOR NOISE REDUCTION
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