Round Cavity Noise Simulations using Lattice-Boltzmann
Transcription
Round Cavity Noise Simulations using Lattice-Boltzmann
Round Cavity Noise Simulations using Lattice-Boltzmann Solver Christophe Coreixas∗ CERFACS, 42 Avenue G. Coriolis, 31507 Toulouse, France A new three-dimensional CFD solver, named LaBS, based on Lattice-Boltzmann Methods (LBM) has been developed within an academic and industrial consortium. In this paper, Wall-Modelled Large-Eddy Simulations (WMLES) of a grazing flow over a round cavity are performed. The latter features an aspect ratio depth-diameter H/D = 1 with a freestream Mach number M∞ = 0.20. A subgrid scale model belonging to the turbulent eddy-viscosity family is applied: the Shear-Improved Smagorinsky Model (SISM). No turbulence injection processes are employed here. Instead, an approximated Blasius laminar solution is used as an inlet condition, and the boundary layer is left free to develop. Aerodynamic and aeroacoustic results are directly computed from simulations and show good agreements with respect to experiments carried out during the AEROCAV project. Nomenclature Theory c Mesoscopic velocity f Velocity distribution function (VDF) f eq Equilibrium VDF τ Relaxation time ρ Macroscopic density ρu Macroscopic momentum θ Molecular agitation temperature r Perfect gas constant T Macroscopic temperature ∆t Time step I. Numerical Simulations H Cavity depth D Cavity diameter δ Boundary layer thickness x, y, z Cartesian coordinates u Longitudinal mean velocity p Pressure Subscript α Discrete velocity index ∞ Freestream condition Introduction Being an important part of noise radiation during approach and landing flight phases, airframe noise is an active research field in Aeronautics. Among the different contributions encountered, such as wing high-lift devices or landing gears, highly tonal noise can be emitted from cavities including anti-icing and kerosene over-pressure vents, tube openings or burst-disk cavities. For a long time, less attention has been paid to this component of airframe noise since its impact on acoustic radiation was not, or only bearly, noticeable on noise certification levels. Recent improvements, in reducing the other contributions, have forced aircraft manufacturers to seriously account for noise generated by flow grazing over round cavities. Over the past fifty years, acoustic noise radiated by cavities has been widely studied. It can be considered as a multi-faceted configuration. Indeed, cavity noise is the result of several phenomena such as turbulent boundary layer development into a shear layer, mixing layer impingement, complex recirculation and aeroacoustic feedback. Their coupling can be explained thanks to Vortex Sound Theory:1 1. Flow interactions with solid surfaces create vorticity which is self-sustained by the flow itself, vortex interactions or acoustic energy conversion into vortical structures. ∗ PhD Student, CFD Team, [email protected] 1 of 11 American Institute of Aeronautics and Astronautics 2. In turn, acoustic waves are generated through either the impact of the mixing layer with the leading edge of the cavity, or resonant cavity mode excitation. In order to estimate the influence of key geometrical and flow parameters, windtunnel experiments have been conducted and the acquired data have been studied, as part of a French research program named AEROCAV (AEROacoustics for cylindrical CAVities), by the French office ONERA2 and Ecole Centrale de Lyon.3 From these studies, two main configurations emerged as great candidates for numerical comparisons both including round cavities with H/D = 1 but with a freestream Mach number of M∞ = 0.20 and 0.26 respectively. Several numerical computations, aiming to identify underlying mecanisms of round cavity noise generation, have been recently published.4–7 None of them included direct measurement of far-field noise, instead integral formulations were used. The aim of the present work is to provide a first aeroacoustic validation, of the brand new solver LaBS, on a configuration including complex noise radiation phenomena. Thus, to accurately judge the capability of the software to provide realistic cavity noise generation and propagation, it has been chosen to not apply any kind of integral formulation. Instead, pressure fluctuations in the far-field region will be directly simulated through Wall-Modelled Large-Eddy-Simulations (WMLES) based on Lattice-Boltzmann Methods (LBM). This paper is organized as follows: the numerical approach is briefly recalled in section II. Then, the investigated configuration and numerical setup are adressed in section III. The computational results are presented and analysed in section IV. II. II.A. Numerical approach Lattice-Boltzmann Method Lattice Boltzmann Methods (LBM) originate from Kinetic Theory of Gas. They consider the spatiotemporal evolution of the velocity distribution function f (x, c, t), the number of fictitious particles at point (x, t) travelling at speed c, through Boltzmann equation Eq. (1). From the macroscopic point of view, collisions can be associated to a relaxation process that makes f tend to its thermodynamic equilibrium f eq . Then, the RHS of Eq. (1) can be substituted by the Bhatnagar-Gross-Krook (BGK8 ) collision operator, which leads to Eq. (2): ∂f ∂f ∂f + ci = (1) ∂t ∂xi ∂t coll 2 f − f eq =− τ with f eq − ρ = e 3/2 (2πθ) (c-u) 2θ (2) where τ is the relaxation time after which f is supposed to have recovered thermodynamic equilibrium f eq , u the macroscopic velocity and θ = rT the molecular agitation temperature. An efficient way to solve this equation is to consider a discrete set of speeds (cα )α instead of all possible particle speeds in R3 . Using only 19 speeds for velocity space discretization in the three dimensional case (D3Q19 model), isothermal Navier-Stokes set of equations can be recovered in the hydrodynamic (Kn 1) and weakly compressible (M 1) limits.9 Further spatial/temporal discretization of derivatives eventually leads to the famous second-order explicit scheme defined by: fα (x + cα ∆t, t + ∆t) = fα (x, t) − ∆t [fα (x, t) − fαeq (x, t)] τg (3) with τg = τ + ∆t/2. Then, in order to recover macroscopic behaviors of the flow, it is necessary to compute stochastic moments of f with respect to mesoscopic velocity c: Z X ρ(x, t) = f (x, c, t) dc = fα (x, t) 3 α ZR X (4) ρ(x, t)u(x, t) = cf (x, c, t) dc = cα fα (x, t) 3 R α θ(x, t) = θ0 2 of 11 American Institute of Aeronautics and Astronautics This numerical scheme yields several advantages for Computational Fluid Dynamics (CFD). Among them, low-dissipation10 and intrinsic parallelizable properties make LBM serious candidates for aeroacoustic computations, where density fluctuation waves orginating from turbulence need to be perfectly convected over long distances with respect to grid cell size. II.B. Numerical Method In the present work, the newly developed Lattice-Boltzmann Solver (LaBS) is used to directly compute aerodynamic (density ρ, momentum ρu) and aeroacoustic (pressure p) properties of the flow. This code has been developed within a consortium of industrial companies (Renault, Airbus, CS), academic laboratories (UPMC, ENS Lyon) and strong partnerships with other entities (Onera, Gantha, Paris Sud University, Alstom, Matelys) from 2010 to 2014. The discretization of the velocity space is based on a D3Q19 lattice and a Two-Relaxation-Time (TRT) collision operator.11 The latter adds a regularizion step of pre-collision distribution functions, allowing better stability/accuracy properties of the numerical scheme through rotational invariance recovery.12, 13 Furthermore, to properly recover the behaviors of turbulent flow without solving all vortical structures down to Kolmogorov scale, a subgrid scale model based on turbulent eddy-viscosity is used. Thus, LES are performed using a Shear-Improved Smagorinsky Model (SISM).14 Due to high-Reynolds characteristics of the flow encountered, wall-resolved meshes are hardly achievable within industry perspectives. Consequently, a wall model including pressure gradient contribution15 is used to correctly recover flow behaviors (friction coefficient and velocity profile) at the first fluid node above walls. III. III.A. Investigated Configuration and Simulation Setup Configuration of Interest As a highly resonant case, the configuration including a round cavity with an aspect ratio H/D = 1 and a free-stream velocity of u∞ = 70 m/s (M∞ = 0.20 at ISA conditions) is considered. For this particular configuration, experiments conducted at Ecole Centrale de Lyon provide measurements of mean/rms velocity profiles, steady/unsteady wall pressure and far-field noise. Data are obtained via Laser-Doppler-Anemometry (LDA), pressure taps and a revolvable arc of microphones respectively.16 III.B. III.B.1. Mesh Strategy & Boundary Conditions Grid Generation In this paper, aeroacoustic radiations emitted from the cavity will be computed directly: acoustic analogy formulations are not employed here. Thus, a 25D × 25D × 15D multi-block mesh is built, with the cavity diameter D = 10 cm . The revolvable arc of microphones, where pressure data are compiled, is located 1m above the cavity center and is directly simulated in the present paper. Besides, 2.5-meter thick sponge layers, based on Perfectly Match Layer formulations,17 have been added to all boundary conditions but flat plate. Ultimately, octree-based18 grid refinements are used to: • Allow a realistic development of the boundary layer from the inlet to the cavity. • Capture phenomena occuring above (shear layer formation / impingement) and inside (strong recirculation) the cavity. The global view of the computational domain and a longitudinal cut of Medium case mesh are illustrated in Fig. 1. III.B.2. Boundary Conditions No turbulence injection process is used in this study. Consequently, there is no need to introduce a turbulent mean velocity profile at the fluid domain inlet since its slope is directly linked to molecular 3 of 11 American Institute of Aeronautics and Astronautics (a) (b) Figure 1. Mesh strategy: Simulation domain (a) and Y=0 m mesh cut (b). The cavity center is the origin of the reference frame. viscosity, which is itself reinforced by turbulent mecanisms. Instead, a laminar mean velocity profile is applied as inflow condition, and the boundary layer is left free to develop in order to provide a realistic behavior of the flow. The polynomial approximated solution of Blasius problem enables the introduction of a laminar boundary layer with a thickness δ for various orders (see Fig. 2). Being the most accurate, the 6th-order approximated solution of Blasius, defined by Eq. (5), is then chosen as inflow condition. z 5 z 6 z 4 u z +6 −2 =2 −5 u∞ δ δ δ δ (5) where u is the longitudinal mean velocity, and z is the coordinate normal to the flat plate. Regarding the outlet and the upperside of the simulation domain, Dirichlet pressure conditions are applied. Finally, periodicity conditions are employed for both lateral sides. Figure 2. Longitudinal mean velocity profile u, with δ = 15 mm et u∞ = 70 m.s−1 . Black: Blasius solution, blue: 4th order polynomial approximation, green: 6th order polynomial approximation (from Desvigne5 ). III.C. Simulation Matrix The mesh convergence has been analysed through two successive grid refinements of Coarse case. This methodology allows a statistical convergence of aerodynamic and aeroacoustic variables. All computations, including geometrical and physical parameters of interest, are summarized in Tab. 1. 4 of 11 American Institute of Aeronautics and Astronautics Mesh SGS Coarse Medium Fine SISM SISM SISM Voxels Points/D 6 5 · 10 40 · 106 140 · 106 100 200 300 ∆xmin (m) −3 1.0 · 10 5.0 · 10−4 3.3 · 10−4 ∆tmin (s) Mean z + TS (s) TCP U (h) 200 100 75 0.22 0.22 0.22 1.25 · 103 4.34 · 104 5.26 · 104 −6 1.68 · 10 8.4 · 10−7 5.6 · 10−7 Table 1. Computations and numerical/physical parameters review. The minimal time step is computed through the unity sound-based CFL condition inherent in conventional LBM. IV. Results Before analysing the simulation results, two main discrepancies with respect to the experimental setup are to be pointed out. Indeed, numerical computations were done assuming a cylindrical cavity over an infinite flat plate and the windtunnel geometry is, for conveniency, not included into the simulation. Thus, 3D installation effects are not taking into account here. IV.A. IV.A.1. Aerodynamic Results Velocity Profiles Mean and rms velocity profiles have been obtained through LDA measurements at several locations (see Fig. 3). In the present work, computation results are compared to these experimental data for Y = 0 m, and only longitudinal velocity is investigated. Comparisons are plotted in Fig. 4 and show satisfactory agreement for longitudinal mean velocity profiles. Regarding the longitudinal velocity fluctuations, good results are obtained even if a lack of turbulent structures is observed in the upstream boundary layer. Nevertheless, it is worth noting that recovering a boundary layer with specific thickness, mean and rms velocity profiles at a given location, remains a tedious issue in CFD. Above all, when a transition from laminar to turbulent flow is expected. Figure 3. Sketch of experimental measurement locations (from Desvigne5 ). IV.A.2. Cavity Wall Pressure After developping above the round cavity, the shear layer originated from the upstream boundary layer impacts the dowstream corner of the cavity. This leads to a strong recirculation which can be divided into three phenomena: (i) part of the mixing layer enters inside the cavity, (ii) inflow attains the cavity bottom, (iii) it goes up and interacts with the shear layer at the upstream corner (see sketches of Figs 5, 6 and 7 respectively). 5 of 11 American Institute of Aeronautics and Astronautics Figure 4. Longitudinal velocity profile evolution at Y = 0 m: mean (up) u1 and rms (down) urms . Fine case results (green) are compared with LDA measurements (· · · ) at locations : x = −55, x = −45, x = −35, x = 0, x = 35, x = 50, x = 55 et x = 90 mm. 6 of 11 American Institute of Aeronautics and Astronautics (a) Sketch of some measurement locations. (b) P1 : (x, y, z) = (D/2, 0, −D/10) (c) P2 : (x, y, z) = (D/2, 0, −D/4) (d) P3 : (x, y, z) = (D/2, 0, −D/2) (e) P4 : (x, y, z) = (D/2, 0, −3D/4) (f) P5 : (x, y, z) = (3D/8, 0, −D) Figure 5. Configuration sketch (a) and cavity wall pressure fluctuations at P1 (b), P2 (c), P3 (d), P4 (e), P5 (f ): Experimental measurement (black cross), Coarse case (green), Medium case (blue) and Fine case (red). 7 of 11 American Institute of Aeronautics and Astronautics (a) Sketch of some measurement locations. (c) (e) (b) P7 : (x, y, z) = (D/8, 0, −D) (d) P9 : (x, y, z) = (−D/8, 0, −D) (f) P6 : (x, y, z) = (D/4, 0, −D) P8 : (x, y, z) = (0, 0, −D) P10 : (x, y, z) = (−D/4, 0, −D) Figure 6. Configuration sketch (a) and cavity wall pressure fluctuations at P6 (b), P7 (c), P8 (d), P9 (e), P10 (f ): Experimental measurement (black cross), Coarse case (green), Medium case (blue) and Fine case (red). 8 of 11 American Institute of Aeronautics and Astronautics (a) Sketch of some measurement locations. (b) P11 : (x, y, z) = (−3D/8, 0, −D) (c) P12 : (x, y, z) = (−D/2, 0, −3D/4) (d) P13 : (x, y, z) = (−D/2, 0, −D/2) (e) P14 : (x, y, z) = (−D/2, 0, −D/4) (f) P15 : (x, y, z) = (−D/2, 0, −D/10) Figure 7. Configuration sketch (a) and cavity wall pressure fluctuations at P11 (b), P12 (c), P13 (d), P14 (e), P15 (f ): Experimental measurement (black cross), Coarse case (green), Medium case (blue) and Fine case (red). 9 of 11 American Institute of Aeronautics and Astronautics Wall pressure fluctuations, corresponding to each part of the recirculation, are compared with experimental data in Figs 5, 6 and 7. Agreement between curves increases when recirculation strength decreases. This is essentially due to very scattered hydrodynamic pressure fluctuations. In addition, these discrepancies seem to be unchanged even with finer grids. The remaining differences between experiments and numerical computations are also pointed out in several other simulations5, 7, 19, 20 and are still not well understood. Nevertheless, one possible explanation could lie in the fact that hydrodynamic pressure fluctuations are in the range of 100−1000 Pa, whereas an overestimation of 10 dB leads to an overprediction of about 1 to 20 Pa (for decibel ranges encountered). Thus, achieving a reasonnable fitting between experiments and numerical simulations is, a priori, out of reach for WMLES. Finally, the pressure fluctuation peaks at f ' 650 Hz (resulting from the coupling between the second shear layer mode and the first depth mode of the cavity5 ) and higher frequencies (attributable to cavity modes5 ) are properly recovered. IV.B. Aeroacoustic Results: Far-Field As a reminder, far-field noise measurements are taken through a revolvable arc of microphones located one meter above the cavity center (see Fig. 8 (a)). Moreover, without taking into account windtunnel geometry, installation effects have been ignored whereas they does have an impact on far-field noise measurements.4 Consequently, only data obtained exactly one meter above the cavity center (microphone 4) are compared to experiments (see Fig. 8 (b)). Simulations show good agreement for frequencies higher than 400 Hz, and noise generated by the aeroacoustic feedback is well recovered. It must be noted that acoustic radiations at low frequencies are directly linked to the windtunnel background noise.4 Thus, it is a priori very unlikely to recover, at this range of frequencies, good pressure fluctuations without including installation geometries. Regarding frequencies higher than 1500 Hz, it seems that parasitic noise is generated inside the simulation domain. It induces an emitted noise overstatement of less than 10 dB at high frequencies. Origins of this parasitic noise are still under investigation. (a) Experimental sketch (b) Data comparison at microphone 4 Figure 8. Far-field noise measurements.16 Experimental (black cross) and numerical results are compared: Coarse case (green), Medium case (blue) and Fine case (red). V. Conclusion A new three-dimensional CFD solver, LaBS, based on Lattice-Boltzmann Methods (LBM) has been developed in the framework of an university and industry consortium. For the first time, direct noise radiations of a grazing flow over a round cavity, with an aspect ratio depth-diameter H/D = 1 and a freestream Mach number M∞ = 0.20, have been computed using this solver. Whereas a simple laminar mean velocity profile was imposed as inflow conditions and led to an underestimation of the turbulence intensity inside the upstream boundary layer, satisfactory aerodynamic results 10 of 11 American Institute of Aeronautics and Astronautics have been obtained inside and above the cavity. Regarding wall pressure fluctuations, uncertainties remain although aeroacoustic feedback and cavity modes are well recovered. Finally, installation effects coverage is found to be crucial to properly predict far-field noise propagation in the low frequency range. Although parasitic noise leads to an overestimation of high frequency cavity acoustic radiation, the aeroacoustic feedback is well simulated. Similar conclusions can be found in Sengissen et al .21 Though young, LaBS software has provided promising aerodynamic and aeroacoustic results that are a first step towards further improvements. Acknowledgments The author wants to thank J.-C. Jouhaud & J.-F Boussuge from CERFACS and N. Gourdain from ISAE for their useful pieces of advice. A. Sengissen from Airbus Operations SAS, J.-C. Giret & R. Cuidard from CS and D. Ricot from Renault are gratefully acknowledged for their technical and theoretical support on Lattice Boltzmann Solver: LaBS. All numerical simulations have been conducted on Airbus’ HPC resources. References 1 M. S. Howe. Theory of Vortex Sound. Cambridge University Press, 2002. Cambridge Books Online. Mincu, I. Mary, S. Redonnet, L. Larchevêque, and J.-P. Dussauge. Numerical Simulations of the Unsteady Flow and Radiated Noise Over a Cylindrical Cavity. In Aeroacoustics Conferences. American Institute of Aeronautics and Astronautics, May 2008. 3 O. Marsden, C. Bailly, C. Bogey, and E. Jondeau. Investigation of flow features and acoustic radiation of a round cavity. Journal of Sound and Vibration, 331(15):3521 – 3543, 2012. 4 D. Mincu, I. Mary, E. Manoha, L. Larchevêque, and S. Redonnet. Numerical Simulations of the Sound Generation by Flow over Surface Mounted Cylindrical Cavities Including Wind Tunnel Installation Effects. In Aeroacoustics Conferences. American Institute of Aeronautics and Astronautics, May 2009. 5 D. Desvigne. Bruit rayonné par un écoulement subsonique affleurant une cavité cylindrique : caractérisation expérimentale et simulation numérique par une approche multidomaine d’ordre élevé. Theses, Ecole Centrale de Lyon, December 2010. 6 O. Marsden, C. Bogey, and C. Bailly. Investigation of flow features around shallow round cavities subject to subsonic grazing flow. Physics of Fluids (1994-present), 24(12):–, 2012. 7 A. Hazir, D. Casalino, R. Denis, and A. F. Ribeiro. Lattice-Boltzmann Simulations of the Aeroacoustics Properties of Round Cavities. In AIAA Aviation. American Institute of Aeronautics and Astronautics, June 2014. 8 P. Bhatnagar, E. Gross, and M. Krook. A Model for Collision Processes in Gases. i. Small Amplitude Processes in Charged and Neutral One-Component Systems. Phys. Rev., 94:511–525, May 1954. 9 X. Shan, X.-F Yyan, and H. Chen. Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation. Journal of Fluid Mechanics, 550:413–441, 3 2006. 10 S. Marié, D. Ricot, and P. Sagaut. Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics. Journal of Computational Physics, 228(4):1056 – 1070, 2009. 11 I. Ginzburg, D. dHumières, and A. Kuzmin. Optimal Stability of Advection-Diffusion Lattice Boltzmann Models with Two Relaxation Times forPositive/Negative Equilibrium. Journal of Statistical Physics, 139(6):1090–1143, 2010. 12 J. Latt and B. Chopard. Lattice Boltzmann Method with Regularized Pre-collision Distribution Functions. Math. Comput. Simul., 72(2-6):165–168, September 2006. 13 H. Chen, R. Zhang, I. Staroselsky, and M. Jhon. Recovery of full rotational invariance in lattice Boltzmann formulations for high Knudsen number flows. Physica A: Statistical Mechanics and its Applications, 362(1):125 – 131, 2006. Proceedings of the 13th International Conference on Discrete Simulation of Fluid Dynamics. 14 E. Lévêque, F. Toschi, L. Shao, and J.-P. Bertoglio. Shear-Improved Smagorinsky Model for Large-Eddy Simulation of Wall-Bounded Turbulent Flows. Journal of Fluid Mechanics, 570:491–502, 1 2007. 15 N. Afzal. Wake Layer in a Turbulent Boundary Layer With Pressure Gradient: A New Approach. In IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers, pages 95–118. Bochum, Germany, 1996. 16 P. Souchotte and E. Jondeau. Projet AEROCAV: Rapport d’essais. Technical report, Ecole Centrale de Lyon, LMFA, December 2007. 17 H. Xu and P. Sagaut. Analysis of the absorbing layers for the weakly-compressible lattice Boltzmann methods. Journal of Computational Physics, 245(0):14 – 42, 2013. 18 H. Touil, D. Ricot, and E Lévêque. Direct and large-eddy simulation of turbulent flows on composite multi-resolution grids by the lattice Boltzmann method. Journal of Computational Physics, 256(0):220 – 233, 2014. 19 J. Chicheportiche and X. Gloerfelt. Direct Noise Computation of the Flow over Cylindrical Cavities. In Aeroacoustics Conferences. American Institute of Aeronautics and Astronautics, June 2010. 20 J. Chicheportiche and X. Gloerfelt. Effect of a turbulent incoming boundary layer on noise radiation by the flow over cylindrical cavities. In Aeroacoustics Conferences. American Institute of Aeronautics and Astronautics, June 2011. 21 A. Sengissen, C. Coreixas, J.-C. Giret, and J.-F. Boussuge. Simulations of LAGOON landing-gear noise using Lattice Boltzmann solver. In Aeroacoustics Conferences. American Institute of Aeronautics and Astronautics, June 2015. 2 C. 11 of 11 American Institute of Aeronautics and Astronautics