Forschung im HLRN-Verbund 2011

103Figure 1: Vorticity iso–surface (color) and acoustic pressure iso–surface (translucent, gray) of an under–expandedsupersonic and round jet including the complex geometry of the Laval nozzle (gray). Reynolds numberbased on the jet diameter: Re = 30000. Mach number at the exit of the jet: M = 1.55. Pressure ratio:p j /p ∞ = 2 (under–expanded). Approx. 33 million grid points solved on 256 cores in only 3000 CPUh.Due to the space-dependence of the design parameters,the number of parameters to control caneasily be in the order of several thousand. To handlethis amount of degrees of freedom in the optimizationalgorithm, adjoint methods will be used inan iterative design process to obtain the gradientinformation of the objective function (noise). Theadjoint equations are based on the full compressibleporous Navier–Stokes equations and are derivedin a continuous manner without any furthersimplifications. Since the control parameters areconstraint (0 < φ ≤ 1 and K < 0), due to theirphysical properties, a method based on slack variableswill be applied.To solve the supersonic aeroacoustic application,direct numerical methods will be used incombination with a high order finite difference approach.Based on the high Reynolds number(Re = 30000) approximately 0.5 · 10 9 points will beused to resolve the flow in the computational domain.Previous studies [2] showed that adjoint basedmethods, in combination with porous media, area promising and efficient method to minimize trailingedge noise. Beyond the aeroacoustic field, thistype of flow optimization may find application in avariety of disciplines and configurations where theoptimization of any objective by means of a modificationof the geometry and/or material is desired.More Information1. Schulze, J. and Sesterhenn, J. (2008). NumericalSimulation of Supersonic Jet–Noise. PAMMProc. Appl. Math. Mech. 8(1):10703–10704.2. Schulze, J. and Sesterhenn, J. (2010). Optimaldistribution of porous media to reduce trailingedge noise. EFMC8 Bad Reichenhall 2010.FundingGerman Research Foundation (DFG)Ingenieurwissenschaften