University:
Boston University
Course:
ENG ME 302 | Engineering Mechanics II
Academic year:

2023
Views:

191

Pages:

16
Author:

Kolten Khan

Some more CAA applications in the literature DNS examples Gloerfelt, Bailly, Juve (JSV 266:119-146, 2003) - subsonic cavity Use DRP to discretize equations Use non-reflecting boundary conditions + absorbing layer Couple to an integral approach Colonius, Freund, Lele (AIAA J, 38:2023, 2000) - supersonic jet Use Pade methods for discretization Use non-reflecting boundary conditions LES examples Bogey, Bailly, Juve (Theor. Comp. Fluid Dyn, 16:273-297,2003) - jet Use DRP to discretize equations Use non-reflecting boundary conditions Uzun, Lynrinztis, Blaisdell (AIAA Paper No. 2004-0517) - jet Use DRP to discretize equations Use non-reflecting boundary conditions Couple to an integral approach Sheen, Meecham (ASME Fluids Div, Sum. Mtg, 2:651-657, 2003) - jet Coupled to an integral approach Oberai et.al. (AIAA J., 40(11):2206-2216, 2002) - incompressible airfoil Use finite element incompressible LES Use non-reflecting boundary conditions Coupled to an integral approach Euler, examples Main applications found in literature -- rotor type simulations where flow disturbance is periodic and dominant in the creation of sound. Lee, et al (JSV 207(4):453-464, 1997) - rotor noise Lockard, Morris (AIAA J 36(6):907-914, 1998) - airfoil/gust Coupled to integral approach allowed for viscosity in some calcs Hixon (AIAA Paper No. 2003-3205), Golubev - cascade,airfoil/gust Different approach, no time marching, space time mapping LEE, examples Florea, Hall (AIAA J, 39(6):1047-1056,2001) - cascade/gust Low-order discretization, finite volume Bailly, Juve (AIAA J, 38(1):22-29,2000) - apps. DRP scheme Longatte, et al (AIAA J, 38(3):389-394,2000) - sheared ducted flow Lim, et al (JSV, 268(2):385-401,2003) - diffraction from impedance barriers High order discretization Ozyorok, et al (JSV, 270(4-5):933-950,2004) - turbofan noise Chen, et al (JSV, 270(3):573-586,2004) - sound from unflanged duct Mankbadi et al (AIAA J, 36(2):140-147, 1998) - jet Splitting (LEE-based) (Atassi, Grzedzinski, JFM 209:385-403) This new unsteady velocity splitting appears as The vortical part of the velocity still satisfies exactly as it did in the original splitting, but the boundary conditions are now defined so that there is no singularity The potential function is now governed by • the boundary condition along the surface is • the jump of the potential velocity in a wake must be 0 • far upstream: Splitting, examples 9 The vortical part is first solved analytically or numerically, and then the potential part is found numerically. 9 Most often these problems are computed in the frequency domain. 9 As shown on last slide, valid for subsonic, nonswirling flows Scott, Patrick/Grace, Atassi, (JCP 119(1):75-93, 1995, AIAA J. 31(1):12-19, 1993) - airfoil/gust Low order-finite difference Coupled to an integral approach Fang, Atassi, (JFE 115:573-579, 1993) - cascade/gust Low order-finite difference Novel non-reflecting boundary conditions Verdon, Hall (AIAA J. 29(9):1463-1471, 1991)- cascade/gust Peake et al. - (JFM 463(25):25-52, 2002) cascade/gust Golubev, Atassi (AIAA J 38(7):1142-1158,2000) - cascades/swirling flow Vortical velocity is no longer the solution to a homogeneous equation Summary We’ve consider the main features of computational aeroacoustic methods Governing equations - hierarchy of approximations Discretization schemes DRP, Padé--spatial, LDDRK--time, methods for damping not described Boundary conditions Acoustic propagation methods for coupling near/far fields Many choices are problem dependent -- makes it difficult to incorporate good acoustic calculations in general CFD type codes If one is implementing these methods, it is good to use the CAA benchmark problems as preliminary method checks. Thanks: Atassi, Tam, Bogey/Bailly, AME Dept., NCAD, Sondak The End More questions? LES Two - dimensional governing equations in conservative form Cartesian co-ordinate system for a perfect gas Spatially filtered (overbar), Favre (or density weighted) average (tilde) Smagorinksy turbulence model ρ - density p - pressure u - velocity vector eT - total energy τ - viscous stress tensor T - temperature R - gas constant γ - ratio of specific heats q - thermal conduction μt - turbulent viscosity T - subgrid scale stress tensor Cs - Smagorinsky constant DES Bisseseur et. al. (Aerospace Science Mtg. Proc. pg. 1673-1685, 2004) Use high-order compact difference scheme Couple to an integral approach CFD, examples Turbulence is modelled, usually high level of dispersion in discretization Kim, et al (AIAA Pap. 2003-3202) - general apps FLUENT for near-field Coupled to an integral approach Hendriana, et al (AIAA Pap. 2003-01-1361) - sideview mirror FLUENT for near-field Coupled to an integral approach Grace, Curtis (ASME, IMECE, NCAD 26:103-108, 1999) - cavity FLUENT (URANS) for near-field Coupled to solution of wave equation Splitting Technique (Goldstein, JFM 89(3):433-468) Ideally (uniform mean flow) the unsteady velocity can be split into solenoidal (vortical/entropic) and irrotational (potential) parts with separate governing equations. The components are linked through boundary conditions. For realistic flows (no shocks or swirl), the velocity components cannot be split as such. •Potential governed by a single inhomogeneous, non-constant coefficients, convective wave equation forced by the solenoidal component •Vortical part governed by homogeneous, non-constant coeffeicient, convective wave equation •Entropic part governed by energy equation. Used when the disturbance is vortical or entropic not acoustic. Upstream where flow is uniform: So entropy and velocity upstream are the boundary conditions imposed on the flow. Splitting cont. Equations for the split variables are derived from the nonconservative form of the governing equations with the energy equation expressed in terms of entropy. One can show that the solution to this set of equations can be written as: where The components of the argument are Lagrangian coordinates of the steady flow fluid particles. The components of X are defined as independent integrals of Lighthill drift function, time for particles to travel along a streamline Splitting cont. Solenoidal part of flow is defined and then the single equation: must be solved, subject to the boundary condition on the surface: and far upstream: This splitting above leads to singular behavior of the solenoidal part along the solid boundary. Time discretization Consider the time discretization: 3 b’s chosen so that the Taylor’s series are satisfied to 3rd order. Leaving one free parameter b0 to minimize dispersion error. Transform the discretized equation b0 chosen to minimize E1. allows one to adjust the degree of emphasis placed on wave propagation (real part) or damping characteristics (imaginary part). Tam uses a value of 0.36