Adjoint-based Trailing-Edge Noise Minimization via Porous Material

Transcription

1 Adjoint-based Trailing-Edge Noise Minimization via Porous Material Beckett Y. Zhou 1,2, Nicolas R. Gauger 1, Seong R. Koh 3, Matthias Meinke 3, Wolfgang Schröder 3 1 Chair for Scientific Computing, TU Kaiserslautern, Germany 2 Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Germany 3 Institute of Aerodynamics (AIA), RWTH Aachen University, Germany 19th Euro AD Workshop, Kaiserslautern April 7, 2016

2 Motivation Why do we need to perform aeroacoustic optimization? FAA forecast in 2012: Demand for air travel to DOUBLE over the next 20 years This situation is highly unsustainable as most major airports around the world are already saturated Long-term exposure to air traffic noise extremely hazardous to ground population near airports EU FLIGHTPATH 2050 goal: reduce perceived aircraft noise by 65% (from the 2000 level) by the year 2050 Aeroacoustic considerations must be included in the initial design phase of an aircraft to meet noise-specific challenges Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 2/ 24

3 Jet Noise Aircraft Noise Airframe Noise Slat Flap Boeing Landing Gear Trailing-edge noise Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 3/ 24

4 Jet Noise Aircraft Noise Airframe Noise Slat Flap Boeing Landing Gear Trailing-edge noise Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 3/ 24

5 Trailing-Edge Noise Generation and Propagation Computational Challenges: Fine grid & small time-steps required to resolve noise generating 3-D turbulent structure For low-speed flows, turbulence develops slowly and many thousands of time steps required to simulate one cycle (of shedding) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 4/ 24

6 Trailing-Edge Noise Generation and Propagation Computational Challenges: Fine grid & small time-steps required to resolve noise generating 3-D turbulent structure For low-speed flows, turbulence develops slowly and many thousands of time steps required to simulate one cycle (of shedding) Important ramifications on optimization Run-time Memory/storage overhead Accuracy and stability of adjoint solver Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 4/ 24

7 Trailing-Edge Noise Reduction Three Predominant Approaches Shape Optimization Adjoint-based [Rumpfkeil & Zingg, 2010; Economon & Alonso, 2012; Nilsen et al., 2015] Active Flow Control Injection of gas mixtures [Koh, Schröder & Meinke, 2011] Trailing-edge blowing for fan tonal noise [Enghardt et al., 2015] Suction and blowing for blunt airfoil trailing-edge [Ramirez & Wolf, 2015] Surface modification with porous material Experimental work: Geyer et al. 2010; Herr et al Airfoil with porous trailing-edge [Fassmann et al., 2015] Optimization of porous trailing-edge on a flat plate [Schulze & Sesterhenn, 2013] Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 5/ 24

8 Trailing-Edge Noise Reduction Three Predominant Approaches Shape Optimization Adjoint-based [Rumpfkeil & Zingg, 2010; Economon & Alonso, 2012; Nilsen et al., 2015] Active Flow Control Injection of gas mixtures [Koh, Schröder & Meinke, 2011] Trailing-edge blowing for fan tonal noise [Enghardt et al., 2015] Suction and blowing for blunt airfoil trailing-edge [Ramirez & Wolf, 2015] Surface modification with porous material Experimental work: Geyer et al. 2010; Herr et al Airfoil with porous trailing-edge [Fassmann et al., 2015] Optimization of porous trailing-edge on a flat plate [Schulze & Sesterhenn, 2013] Challenges: i) No clear design guidelines exist for ideal placement of porous media an uninformed choice may amplify noise ii) Noise reduction accompanied by a marked loss of lift (Herr et al.) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 5/ 24

9 Trailing-Edge Noise Reduction Three Predominant Approaches Shape Optimization Adjoint-based [Rumpfkeil & Zingg, 2010; Economon & Alonso, 2012; Nilsen et al., 2015] Active Flow Control Injection of gas mixtures [Koh, Schröder & Meinke, 2011] Trailing-edge blowing for fan tonal noise [Enghardt et al., 2015] Suction and blowing for blunt airfoil trailing-edge [Ramirez & Wolf, 2015] Surface modification with porous material Experimental work: Geyer et al. 2010; Herr et al Airfoil with porous trailing-edge [Fassmann et al., 2015] Optimization of porous trailing-edge on a flat plate [Schulze & Sesterhenn, 2013] Challenges: i) No clear design guidelines exist for ideal placement of porous media an uninformed choice may amplify noise ii) Noise reduction accompanied by a marked loss of lift (Herr et al.) Research Goal: Systematically search for optimal distribution of porous media via discrete adjoint optimization Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 5/ 24

10 Flow through Porous Media Navier-Stokes equations for flow through porous media: [Liu & Vasilyev, 2007] ρ t ρu i t e t = ρu j ( 1 x j ε 1)χ ρu j x j = x j (ρu i u j ) p x i + 1 Re a τ ij x j χ K v (u i U oi ) = [(e + p)u j ] x j + 1 Re a u i τ ij x j + 1 (µ T ) χ (T T o) Re apr(γ 1) x j x j K t Allows to model flow inside permeable media and external flow monolithically (χ = 1: porous; χ = 0: external) Porosity ε = (fluid volume)/(total material volume) (ε 0: solid) Viscous K v and thermal K t permeabilities: flow conductance at a given porosity (K v, K t 0: impermeable solid) Parameters can be transformed to pore sizes Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 6/ 24

11 Objective Function: J = Optimization Framework 1 Nt N tn p j Np i ˆ J 2 (t j, x i ), ˆ J : instantaneous measure of turbulence intensity/noise N p : user-defined observation points. N t : number of time steps. Design Variables: spatially varying ε, K v and K t Optimization Algorithm: Gradient-based Quasi-Newton BFGS algorithm with line search and box constraints for design variables to prevent singularity Design Gradient: Computed using algorithmic differentiation (AD) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 7/ 24

12 AD-based Discrete Adjoint Framework Algorithmic Differentiation (AD) View a complex solver as sequence of elementary operations Successive application of chain-rule for derivatives Forward (tangent) mode: exact but one evaluation per gradient component Reverse (adjoint) mode: exact AND entire gradient vector in one stroke. High memory requirement tackled by checkpointing Techniques: Operator overloading Source-code transformation Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 8/ 24

13 AD-based Discrete Adjoint Framework Algorithmic Differentiation (AD) View a complex solver as sequence of elementary operations Successive application of chain-rule for derivatives Forward (tangent) mode: exact but one evaluation per gradient component Reverse (adjoint) mode: exact AND entire gradient vector in one stroke. High memory requirement tackled by checkpointing Techniques: Operator overloading Source-code transformation Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 8/ 24

14 AD-based Discrete Adjoint Framework Algorithmic Differentiation (AD) View a complex solver as sequence of elementary operations Successive application of chain-rule for derivatives Forward (tangent) mode: exact but one evaluation per gradient component Reverse (adjoint) mode: exact AND entire gradient vector in one stroke. High memory requirement tackled by checkpointing Techniques: Operator overloading Source-code transformation Advantages of AD-based Adjoint Algorithmically differentiates through entire solver (LES filtering, turbulence models, flux limiter, dynamic grid movement, etc.) Adjoint solver inherits convergence properties of the primal solver Flexibility in defining objective function w/o special interface treatment Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 8/ 24

15 Minimization of Trailing Edge Pressure Fluctuation Configuration: y x z c s d h Flat plate with a finite thickness (c = 33h) Noise characterized by a strong tonal component due to periodic vortex shedding (δ 2.5h) Spanwise porous strips in last 12% chord (d = 0.12c) M = 0.20, Re c = million elements in x-y plane, solved with LES with RK-5 time-marching scheme (1) ε i, K i v, Ki t (1). Implementation details on the LES solver can be found in: S. Koh, M. Meinke and W. Schröder, Impact of Wall Permeability on Trailing-Edge Noise at High Reynolds Number, AIAA Paper Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 9/ 24

16 Minimization of Trailing Edge Pressure Fluctuation y/c Observer Location 1 Observer Location 2 Observer Location 3 ε i, K i v, Ki t 0.06c 0.06c d = 0.12c x/c 5h h Reduce pressure fluctuation (p ) near the T.E. directly: J = f (p ) p measured at 3 observer locations situated 5h above porous T.E. along plate centerline Design variables: ε, K v & K t in each segment 30 DV s Constraints: ε [0.3, 0.5] K t [0.0005, 0.1] K v [0.005, 0.1] Baseline: ε i = 0.40, K i v = 0.001, K i t = 0.05 for all segments ( hardplate ) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 10/ 24

17 Minimization of Trailing Edge Pressure Fluctuation p/ρoa 2 o Pressure History at Observer Location Optimization Window tuo/h Minimize root-mean-square of the pressure fluctuation at all 3 observer locations J = 1 Nt N tn p j Np i [(p ) j i ]2, where (p ) j i = p j i p i Optimized over 3 periods of shedding Computation re-started from freestream at each design stage until optimization window J and G re-evaluated 5 design updates performed Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 11/ 24

18 Optimal Porosity & Permeability Distributions Baseline Optimized Constraint Porosity (ε) Baseline Optimized Constraint Viscous Permeability (Kv) Streamwise Strip Number Streamwise Strip Number Baseline Optimized Constraint Thermal Permeability (Kt) Streamwise Strip Number Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 12/ 24

19 Optimal Porosity & Permeability Distributions Baseline Optimized Constraint Porosity (ε) Baseline Optimized Constraint Viscous Permeability (Kv) Streamwise Strip Number Streamwise Strip Number Baseline Optimized Constraint Thermal Permeability (Kt) ε Kv Kt Magnitude of Gradient Component Streamwise Strip Number Streamwise Strip Number Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 12/ 24

20 Pressure Fluctuation Pressure Fluctuation at 3 Observer Locations c 0.06c Baseline Optimized Obs. Loc. #1 y/c h 0 h d = 0.12c p /ρoa 2 o Optimization Window Obs. Loc. #2 Obs. Loc. # x/c Observer Location Noise Reduction (db) tu o/h RMS of p reduced by 82% over 3 observer locations Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 13/ 24

21 Vorticity Magnitude Baseline Optimized Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 14/ 24

22 Pressure Fluctuation Field Baseline Optimized Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 15/ 24

23 Minimization of Trailing Edge Pressure Fluctuation Overall Sound Pressure Level (OASPL) dB Baseline Optimized θ 12dB reduction in normal direction (where the observer locations are situated) Noise reduction achieved in all directions. Up to 18dB in upstream direction 180 OASPL (db) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 16/ 24

24 Minimization of Trailing Edge Pressure Fluctuation Overall Sound Pressure Level (OASPL) dB Baseline Optimized High K v & K t 0 OASPL (db) θ 12dB reduction in normal direction (where the observer locations are situated) Noise reduction achieved in all directions. Up to 18dB in upstream direction Uniformly high permeability does not lead to further noise reduction Advantage of adjoint-based optimization: achieves significant noise reduction without resorting to unnecessarily porous/permeable surfaces. Critical when considering practical aerodynamic constraints such as lift Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 17/ 24

25 Transitioning to a Hybrid Noise Prediction Strategy Ω 1 (CFD) Γ p x r Ω 2 (CAA) Observer To obtain the same accuracy of acoustic signals at a given offbody position, the grid resolution for a direct DNS/LES noise prediction is M 3 times higher than that is necessary to resolve the acoustic field ( λ l t M 1 ). A hybrid two-step approach more favourable Allows for more efficient noise predictions due to the separation of hydrodynamic and acoustic computations Many hybrid CFD-CAA frameworks exist (URANS-FWH, LES-FWH, URANS-Kirchoff...) Near-body turbulent flow field resolved using LES Noise source propagated to near-far field using Acoustic Perturbation Equations (APE) (Ewert & Schröder, 2003) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 18/ 24

26 Acoustic Perturbation Equations (APE-4) Re-arranging Navier-Stokes equations, dropping viscous and nonlinear fluctuating terms: p t + c2 o (ρ o u p ) + u o co 2 = c2 o ρ o Ds c p Dt u t + ( u o u ) ( ) p + = ( ω u) + T s s T ρ o An acoustic analogy in which sound is generated by vorticity and entropy inhomogeneities Dominant vortex sound source (fluctuating Lamb vector): L = ( ω u) Spatial discretization: 6-th order FD scheme using summation-by-parts operator Temporal discretization: alternating 5-6 stage low-dispersion and low-dissipation Runge-Kutta scheme Mean flow/source quantities ( ) o based on an offline sampling stage Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 19/ 24

27 Acoustic Perturbation Equations (APE-4) Re-arranging Navier-Stokes equations, dropping viscous and nonlinear fluctuating terms: 0 p t + c2 o (ρ o u p ) + u o co 2 = c2 o ρ o Ds c p Dt u t + ( u o u ) ( ) p + = ( ω u) + T s s 0 T 0 ρ o An acoustic analogy in which sound is generated by vorticity and entropy inhomogeneities Dominant vortex sound source (fluctuating Lamb vector): L = ( ω u) Spatial discretization: 6-th order FD scheme using summation-by-parts operator Temporal discretization: alternating 5-6 stage low-dispersion and low-dissipation Runge-Kutta scheme Mean flow/source quantities ( ) o based on an offline sampling stage Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 19/ 24

28 Coupled CFD-CAA Framework Mean Flow Field Q o = [ρ o, u o, p o ] T ε ρ, u, p ρ x = K v, u, p LES APE K t J = (p ) 2 Mean Source Term Lo = ( ω u) o Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 20/ 24

29 Coupled CFD-CAA Framework Mean Flow Field Q o = [ρ o, u o, p o ] T ε ρ, u, p ρ x = K v, u, p LES APE K t J = (p ) 2 Mean Source Term Lo = ( ω u) o Full chain algorithmically differentiated for dj d x Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 20/ 24

30 Coupled CFD-CAA Framework Mean Flow Field Q o = [ρ o, u o, p o ] T ε ρ, u, p ρ x = K v, u, p LES APE K t J = (p ) 2 Mean Source Term Lo = ( ω u) o Full chain algorithmically differentiated for dj d x Mean source term ( L o ) and flow field ( Q o ) recomputed from free-stream after each design update Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 20/ 24

31 Acoustic Pressure in Near-Far Field Acoustic Pressure at 3 Observer Locations c 0.06c Baseline Optimized Obs. Loc. #1 y/c c=33h 0 h p /ρoa 2 o Optimization Window Obs. Loc. #2 Obs. Loc. #3 d = 0.12c x/c Observer Location Noise Reduction (db) tu o/h RMS of p reduced by 87% over 3 observer locations Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 21/ 24

32 Conclusion Conclusion and Future Work First work in noise-minimization to couple discrete adjoint with a high-fidelity LES and LES-APE solver Significant noise reduction achieved by minimizing the pressure fluctuation at off-body observation points 12dB in the normal direction and up to 18dB in the upstream directions. Preliminary result on coupled LES-APE solver also shows effective suppression of acoustic pressure fluctuation in the near far-field observer points via optimal distribution of porous material in the trailing edge Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 22/ 24

33 Conclusion Conclusion and Future Work First work in noise-minimization to couple discrete adjoint with a high-fidelity LES and LES-APE solver Significant noise reduction achieved by minimizing the pressure fluctuation at off-body observation points 12dB in the normal direction and up to 18dB in the upstream directions. Preliminary result on coupled LES-APE solver also shows effective suppression of acoustic pressure fluctuation in the near far-field observer points via optimal distribution of porous material in the trailing edge Take-away Messages Adjoint-based method allows for exploration of large design spaces Non-intuitive designs possible without unnecessarily penalizing other performance metrics Algorithmic differentiation leads to accurate & stable adjoint information over long integration times particularly well-suited for design problems in aeroacoustics Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 22/ 24

34 Conclusion and Future Work Future Work Perform optimizations on a full 3D turbulent case at increased spanwise resolution Allow variations of porosity/permeability parameters in the spanwise direction (Stay tuned and join us at the 22nd AIAA Aeroacoustics Conference in Lyon, France: Session AA-14, May 30) Apply methodology to aerodynamic shapes airfoil or wing with porous trailing edge Incorporate practical design constraints lift-constrained noise minimization Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 23/ 24

35 Acknowledgements Financial support from German Research Foundation (DFG) and Canadian Postgraduate Scholarship (NSERC-PGS-D) Computing resources provided by the Alliance of High Performance Computing Rheinland-Pfalz (AHRP), via the Elwetritsch Cluster at the TU Kaiserslautern Thank you for your attention Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

36 Optimal Porosity & Permeability Distributions (LES) Baseline Optimized Constraint Porosity (ε) Baseline Optimized Constraint Viscous Permeability (Kv) Streamwise Strip Number Streamwise Strip Number Baseline Optimized Constraint Thermal Permeability (Kt) Streamwise Strip Number Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

37 Optimal Porosity & Permeability Distributions (LES-APE) Porosity (ε) 0.54 Baseline 0.52 Optimized Constraint Streamwise Strip Number Baseline Optimized Constraint Viscous Permeability (Kv) Streamwise Strip Number Baseline Optimized Constraint Thermal Permeability (Kt) Streamwise Strip Number Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

38 Validation of AD Gradients (LES Case) i Finite Difference Forward AD Reverse AD Table: Comparison between the gradients computed using 2nd order finite difference (δ = 10 6 ), forward-mode and reverse-mode of AD, over 100 time steps *generated using AD tool TAPENADE Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

39 Validation of AD Gradients (LES Case) i Finite Difference Forward AD Reverse AD Table: Comparison between the gradients computed using 2nd order finite difference (δ = 10 6 ), forward-mode and reverse-mode of AD, over 100 time steps *generated using AD tool TAPENADE Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

40 Validation of AD Gradients (LES-APE Case) i Finite Difference Forward AD Reverse AD E E E E E E E E E E E E E E E-7 Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

41 Pressure Fluctuation Field Baseline Optimized Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

42 AD-based Unsteady Discrete Adjoint Framework Consider a system of semi-discretized PDEs as follows: du dt + R(U) = 0 U: spatially discretized state vector R(U): is the discrete spatial residual vector. Second-order backward difference is used for time discretization: R (U n 3 ) = 2 t Un + R(U n ) 2 t Un t Un 2 = 0, n = 1,..., N Dual-time stepping method converges R (U n ) to a steady state solution at each time level n through a pseudo time τ: du n dτ + R (U n ) = 0 Implicit Euler method is used to time march the above equation to steady state: U n p+1 U n p + τr (U n p+1) = 0, p = 1,..., M Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

43 AD-based Unsteady Discrete Adjoint Framework The resultant nonlinear system can be linearized around Up n to solve for the state Up+1: n [ ] Up+1 n Up n + τ R (Up n ) + R n U (Up+1 n Up n ) = 0, p = 1,..., M This can be written in the form of a fixed-point iteration: p U n p+1 = G n (U n p, U n 1, U n 2 ), p = 1,..., M, n = 1,..., N G n : an iteration of the pseudo time stepping U n 1 : converged state vector at time level n 1 U n 2 : converged state vectors at time level n 2 The fixed point iteration converges to the numerical solution U n : U n = G n (U n, U n 1, U n 2 ), n = 1,..., N Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

44 AD-based Unsteady Discrete Adjoint Framework The discretized unsteady optimization problem over N time levels: min J = 1 N J(U ˆ n, β) β N n=1 subject to U n = G n (U n, U n 1, U n 2, β), n = 1,..., N β: vector of design variables. One can express the Lagrangian associated with the above constrained optimization problem as follows: L = 1 N N [ J(U ˆ n (Ūn, β) ) ( T U n G n (U n, U n 1, U n 2, β))] N n=1 n=1 Ū n : adjoint state vector at time level n. KKT : L Ūn = 0, n = 1,..., N (State equations) L U n = 0, n = 1,..., N (Adjoint equations) L β = 0, (Control equation) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

45 AD-based Unsteady Discrete Adjoint Framework The unsteady discrete adjoint equations can be derived in the fixed point form as: ( ) Ūi+1 n G n T ( ) G n+1 T ( ) G n+2 T ( = Ūn U n i + U Ūn+1 + n U Ūn ˆ ) T J n, n = N,..., 1 n N U n Ū n+1 : converged adjoint state vector at time level n + 1 Ū n+2 : converged adjoint state vector at time level n + 2 The unsteady adjoint equations above are solved backward in time. The sensitivity gradient can be computed from the adjoint solutions: N ( ) dl dβ = 1 Jˆ n N β + (Ūn ) T G n β n=1 High-lighted terms computed using AD in reverse mode Reverse accumulation used at each time level to tape the computational graph for AD Adjoint iterator inherits the same convergence properties as primal iterator G includes: turbulence model, grid movement, limiters, etc Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

46 Run-time and Memory Usage 3.5 million cells Primal solution: 10GB, constant at all time steps Reverse-mode AD: 42GB per time step, scales with number of time steps Slow-down factor: 15 (primal vs. black-box reverse mode AD) Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24

47 Minimization of Trailing Edge Turbulence Intensity Viscous Permeability (K v ) Strip Viscous Permeabilities baseline optimized Strip Number Optimizer makes the last strip almost an impermeable solid (constraint active) Unclear a priori why this permeability distribution is optimal Highlights the power of combining high-fidelity simulation with numerical optimization opportunity to explore non-intuitive and unconventional designs Beckett Y. Zhou et al. Adjoint-based Noise Minimization via Porous Material 24/ 24