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Linearized Navier-Stokes Solver for In-Duct Aeroacoustics

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Linearized Navier-Stokes Solver for In-Duct Aeroacoustics Linearized Navier-Stokes solver for in-duct aeroacoustics GUNILLA EFRAIMSSON Department of Aeronautical and Vehicle Engineering KTH, Stockholm, Sweden [email protected] Axel Kierkegaard, Wei Na, Mats Åbom, Ciarán O’Reilly, Susann Boij, Hans Bodén Outline • Tango-aspects • Linearized Navier-Stokes equations solver • Two tecases - Area expansion - Thick orifice • Conclusions and future work Tango setting Q˙ 0 Unsteady heat release Generation of sound waves Perturbation flow & flame Pressure Oscillation p0 Study the coupling sound , flow and heat release using linearized Navier-Stokes equations Generation and Propagation of Sound • Generation Fans, rotor-stator interaction, constrictions, jets, combustion - Acoustic analogies, direct methods - Transient phenomena è transient simulations (LES,, DES, uRANS) or scaling laws • Propagation Free air, pipes, influence of flow, influence of solid surfaces (shielding), coupling of sound and flow (whistling, damping of sound), duct terminations - Linear equations in time or frequency domain: Helmholtz equation, wave equation, linearized Euler equations etc Propagation of sound in ducts with constrictions Straight cylindrical duct with orifice plate Turbulent meanflow Incoming waves are partly reflected and partly transmitted Reflections from downstream obstacles (or boundary conditions) Zone I Zone III Zone IV Zone II x 0 1 = x2 = 0 Propagation of sound in ducts with constrictions Straight cylindrical duct with orifice plate Turbulent meanflow Incoming waves are partly reflected and partly transmitted Reflections from downstream obstacles (or boundary conditions) Zone I Zone III Zone IV Zone II x 0 1 = x2 = 0 Propagation of sound in ducts with constrictions Straight cylindrical duct with orifice plate Turbulent meanflow Incoming waves are partly reflected and partly transmitted Reflections from downstream obstacles (or boundary conditions) Zone I Zone III Zone IV Zone II x 0 1 = x2 = 0 Propagation of sound in ducts with constrictions Straight cylindrical duct with orifice plate Turbulent meanflow Incoming waves are partly reflected and partly transmitted Reflections from downstream obstacles (or boundary conditions) Zone I Zone III Zone IV Zone II x 0 1 = x2 = 0 Propagation of sound in ducts with constrictions Straight cylindrical duct with orifice plate Turbulent meanflow Incoming waves are partly reflected and partly transmitted Reflections from downstream obstacles (or boundary conditions) Zone I Zone III Zone IV Zone II x 0 1 = x2 = 0 Propagation of sound in ducts with constrictions Straight cylindrical duct with orifice plate Turbulent meanflow Incoming waves are partly reflected and partly transmitted Reflections from downstream obstacles (or boundary conditions) Zone I Zone III Zone IV Zone II x 0 1 = x2 = 0 Efficient simulation methodology The methodology should be efficient for • Confined flows • Mean flows effects • Dissipation due to acoustic-flow interaction Available simulation methods Linearized Navier-Stokes equations in frequency domain Assumptions • Linear acoustics • Frequency domain e-iωt • Isentropy. Temperature dependence via Sutherland’s formula and ideal gas law. • Solved using Comsol Multiphysics (FEM, direct solver) • Previous work on orifices and area expansions in 2D with good results. Now extended to 3D. Kierkegaard et al JASA 2010, JSV 2011, 2011 Inclusion of • Viscous effects e.g. acoustic boundary layers in the vicinity of edges Linearized Navier-Stokes equations in frequency domain Linearized Navier-Stokes equations in frequency domain Two stages 1. Calculate mean flow (using RANS) 2. Calculate perturbations around mean flow using linearized Navier-Stokes equations Frequency domain è One calculation for every frequency in a frequency sweep Case 1 Area expansion Experiment by Ronneberger (1987) Theory by Boij & Nilsson (2003). Step 1: Mean flow • Incompressible, steady-state, non-linear Reynolds Averaged Navier-Stokes (RANS). • Realizable k-ε turbulence model • Flow speed 14.5 m/s (Mach number = 0.08) Step 2: Linearized N-S eqns • Perturbations around mean flow. • Single frequency calculations. • Frequency sweep 100 < f < 3000 Hz, ∆f = 100 Hz. • Finite Element Method (FEM), COMSOL Multiphysics. Density perturbations • Frequency 1000 Hz • Both sound waves and vorticity • ρ’(x,t) = Re{ρ(x, ω)exp(-iωt)} Density perturbations • Frequency 500 Hz • Frequency 2500 Hz Side a Side b Scattering matrix (ω) • Relates outgoing waves to incident waves. • Every matrix element is a funtion of frequency. Scattering matrix, magnitude Experiments Simulations Analytical solution Scattering matrix, phase Experiments Simulations Analytical solution Case 2 Thick orifice Mean flow • M = 0.042, RANS k-ε Calulate perturbations • Density perturpations • f = 1800 Hz (maximum amplification) Scattering matrix (S) Solid black line: Simulations Dashed black: Experiments at KTH Solid grey: Experiments at Le Mans, France (Testud et al 2009) Whistling potentiality Amplicifaction or dissipation of sound Energy power balance è Sign of Eigenvalue of (1-SHS) Solid black line: Simulations Linearized Navier-Stokes equations Dashed black line: Simulations Linearized Euler equations Dotted black: Experiments at KTH Solid grey: Experiments at Le Mans, France (Testud et al 2009) Conclusions • Frequency domain linearized Navier-Stokes can predict acoustic scattering in ducts, such as area expansions, orifices, impedance tubes • Acoustic boundary layers needed in case of sound-vortex interaction • No special treatment at edges (eg Rutta conditions) • Fast compared to time domain in 2 space dimensions • Arbitrary geometries possible • Influence of mean flow different on different scattering matrix components, different flow field Present and future work • Inclusion of energy equations done • Include thermo-acoustic sources in process • Evaluation for higher order modes in process • Iterative solver Thank you for your attention .
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