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Implementation of Aeroacoustic Methods in Openfoam EXAMENSARBETE I TEKNISK MEKANIK 120 HP, AVANCERAD NIVÅ STOCKHOLM, SVERIGE 2016 Implementation of Aeroacoustic Methods in OpenFOAM ERIKA SJÖBERG KTH KUNGLIGA TEKNISKA HÖGSKOLAN SKOLAN FÖR TEKNIKVETENSKAP TRITA TRITA-AVE 2016:01 ISSN 1651-7660 www.kth.se Abstract A general method is established for external low Mach-number flows where aeroa- coustic analogies are used to decouple the sound generation from the sound prop- agation. The CFD solver OpenFOAM is used to compute the flow induced sound sources and Ffowcs-Williams and Hawkings acoustic analogy is implemented to calculate the propagation of sound. Incompressible and compressible source data is gathered for a test case and upon evaluation of the noise emission the assump- tion of incompressibility prove to be valid for a low Mach-number flow. Fur- thermore the advantage of non-reflecting boundary conditions in OpenFOAM is appraised and found to be effective. Lastly the method is tested on a more com- plicated test case in terms of a generic side mirror and results are found to agree well with previous studies. 3 Acknowledgments I want to extend my warmest thank Creo Dynamics for giving me the opportunity to do my master thesis at their company. I have felt like a part of Creo from day one and could not have wished for better colleges; your help and expertise have made this thesis possible. Moreover I want to extend a special thanks to Johan Hammar who has guided me through this process and always put time aside for me no matter how busy of a schedule he has had. I also want to thank my examinator Ciarán O’Reilly for his time and valuable input. Creo Dynamics, January 2016 Erika Sjöberg 5 Contents Notation 9 1 Introduction 1 1.1 Motivation . 1 1.2 Research Objective . 2 1.3 Outline . 2 2 Theory 3 2.1 Methodology . 3 2.2 CFD Analysis - predicting the flowfield . 4 2.2.1 Direct Simulation . 4 2.3 Turbulence Modelling . 6 2.3.1 Reynolds averaged Navier-Stokes Equation . 6 2.3.2 Large Eddy Simulations . 7 2.3.3 Detached Eddy Simulation . 7 2.3.4 Spalart Allmaras Turbulence Model . 8 2.3.5 Wall functions . 8 2.3.6 Turbulence Modelling . 9 2.3.7 Boussinesq Approximation . 9 2.4 Hybrid Methods . 10 2.4.1 Lighthill’s Acoustic Analogy . 10 2.4.2 Curle’s Analogy . 11 2.4.3 Ffowcs-Williams and Hawkings Analogy . 13 3 CFD Software 15 3.1 Spatial Discretization . 16 3.2 Temporal Discretization . 16 3.3 Pressure and Velocity Coupling . 17 3.3.1 SIMPLE Algorithm . 18 3.3.2 PISO Algorithm . 19 4 Validation Case 21 4.1 Cylinder Test Case . 21 7 8 Contents 4.2 Review of Flow around a Cylinder Test Cases . 23 4.3 Cylinder Setup . 23 4.4 Boundary Conditions . 24 4.5 Mesh . 25 4.6 Validation . 27 4.6.1 Flow Validation . 27 4.6.2 Acoustic Validation . 28 4.7 Results . 30 4.7.1 Incompressible Solution . 30 4.7.2 Compressible Solution . 31 4.8 Interim Conclusion . 36 5 Generic Side Mirror Case 37 5.1 Review of Flow around a Side Mirror Test Cases . 37 5.2 Side Mirror Setup . 38 5.3 Boundary Conditions . 39 5.4 Mesh . 40 5.5 Flow Results . 43 5.6 Acoustic Results . 46 5.7 Interim Conclusion . 50 6 Concluding Remarks 51 6.1 Future Work . 52 Bibliography 53 Notation Nomenclature Notation qi Heat flux eo Internal energy ρ density τij viscous stress tensor R ideal gas constant cv specific heat (constant volume) cp specific heat (constant pressure) µ molecular viscosity σ Prandtl number η Kolmogorov length scale Λ Kolmogorov large size eddies ui velocity Ui time averaged velocity u0 fluctuating velocity P time averaged pressure p0 fluctuating pressure p pressure xi coordinate position δij Kronecker delta e0 total internal energy e internal energy νt kinetic eddy viscosity K kinetic energy Sij mean strain rate tensor T temperature a speed of sound SPL sound pressure level f frequency fst strouhal frequency 9 10 Notation Nomenclature Notation τ retarded time r distance between source and observer Go Green’s free field function Tij Lighthill’s stress tensor H(f ) Heavyside step function Dimensionless quantities CD drag coefficient CL lift coefficient Re Reynolds number M Mach number St Strouhal number 1 Introduction 1.1 Motivation Aeroacoustics is the study of flow induced sound and was pioneered by James Lighthill back in the 1950’s. Flow induced sound can be created by turbulent wakes, detached boundary layers, vortex structures in the flow and flow interac- tion with solid walls [Y.Khalighi, 2010]. Flow-generated sound is today a well known problem in the transport industry, and according to a World Health Or- ganisation report side effects of noise can involve fatigue, stress, hearing loss and hormonal imbalance [Y.Khalighi, 2010]. Emphasis is today spent on noise control and to mitigate the aerodynamic noise a deeper understanding of the physics of the flow field and the sound field is necessary. Resolving both the sound and flow field presents an inherent scale problem where as Crighton [1993] so well described it ... in the 45 seconds of take-off roll of “terrifyingly loud ”Boeing 707, the total energy radiated as sound is only about enough to cook one egg. Due to the scale difficulties severe limitations are put on computational re- sources and the aeroacoustic field have been heavily dependent upon experimen- tal methods. With the advance of technology and computational power acoustic analogies have proven to be an effective tool. Lighthill established aeroacoustics when he developed an equation for the propagation of sound waves for a turbulent flow. Since then many researches have followed in his footsteps and made extensions to Lighthill’s original theory. Some of the more renowned are Curle’s analogy that takes into account the pres- ence of solid boundaries, and Ffowcs-Williams and Hawkings equation that also includes surfaces in motion. 1 2 1 Introduction Due to the limitation of computational resources aeroacoustic analogies are a very useful tool since it drasticly reduces the computational power needed when solving for sound propagation. Acoustic analogies reduces the computational domain to the near field where high resolution is required and the sources are computed. All non-linear effects are prescribed to the near field and a linear wave operator propagates the sound in the acoustic domain. 1.2 Research Objective The objective of the present thesis is to establish a method in OpenFOAM to calcu- late the sound field using aeroacoustic analogies. The results should be compared to previous studies done using commercial available software. To achieve the objectives this work is broken down into several sub-goals: • Build a good test case. The test case should be simple enough that one can focus on the essential flow features but still capture the unsteady von Kármán vortex shedding. • Evaluate both the aerodynamic (CFD) part as well as the acoustic field cal- culated using the Ffowcs-Williams and Hawkings analogy. • Test the methodology on a more demanding case. Other aims behind the research is to evaluate the existing boundary condi- tions in OpenFOAM with the goal of minimizing reflections at the boundaries. 1.3 Outline The following structure will be used in the report. • Chapter 2 will cover the general theory and governing equations behind the flow and aeroacoustic field. • Chapter 3 briefly explains the OpenFOAM software, user settings, and dis- cretization schemes. • Chapter 4 and 5 presents the Validation case and a study of a Generic Side Mirror respectively. • Conclusions and future work is found in chapter 6. 2 Theory 2.1 Methodology Utilizing the continuity, momentum and energy equations in combination with initial and boundary conditions the flow field as well as the acoustic part can be found. Focusing on the sound generation and its propagation various methods can be used varying in computational effort and accuracy. Two main numerical Computational Aero Acoustic (CAA) approaches can be distinguished; 1. Direct Methods: A transient solution is calculated where the source and its propagation is resolved out to the far field. This method requires a very fine grid for the spatial and temporal resolution which places stringent demands on computational resources. X. Gloerfelt [2003] writes that direct methods can only predict good acoustic results for simple configurations at moderate Re numbers. 2. Hybrid methods: The source field is computed using CFD analysis and the propagation is predicted using a transport method. Hybrid methods significantly reduces the computational demand since only the nearfield needs to be spatially and temporally resolved. Fig. 2.1 shows a schematic layout of the various CAA methods available [C. Wag- ner, 2007]. 3 4 2 Theory Figure 2.1: Various CAA Methods A distinction will be made between calculating the flow field (1) and using the data from the flow field to predict the sound field (2). Sec 2.2 will present various methods available to solve for the flow field and sec 2.4 will focus on the implementation of acoustic analogies to calculate the sound radiation. 2.2 CFD Analysis - predicting the flowfield 2.2.1 Direct Simulation Direct methods is the most exact and perhaps also the most straightforward methodology in CAA. In Direct Simulation (DS) the governing equations are solved without using physical simplifications therein resolving the physical phe- nomena without modelling. The governing equations used are the fundamental equations of fluid dynamics: the continuity, momentum and the energy equation. They are here written in conservative form for a compressible fluid using the in- dex notation and Einstein convention. The continuity equation, @ρ @(ρu ) + i = 0 (2.1) @t @xi The momentum equation, @(ρu ) @(ρui uj ) @ p @τij i + = + (2.2) @t @xj −@xi @xj 2.2 CFD Analysis - predicting the flowfield 5 And the energy equation, @(ρe ) @(ρe0uj + puj ) @(τij ui qj ) 0 + = − (2.3) @t @xj @xj Where the energy e0 is the total internal energy, 1 e = e + u u (2.4) 0 2 i i Further equations to close the system of equations are needed.
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