Numerical simulation of compressible flows with application to noise control

Spatial direct numerical simulations of compressible plane jets exhausting into parallel streams are examined. The inviscid mathematical model captures the most dynamically important, large-scale mixing events, such as vortex roll-up and pairings. Two-dimensional simulations employ the fully explicit (2-4) method, while three-dimensional simulations use implicit spatial compact differencing with Runge-Kutta time-advancement. All simulations utilize characteristic-based boundary conditions. Shear layer linear instability computations validate the numerical methods. Time averages over long streamwise jet domains capture the mean field and turbulence structure. The convective Mach number {dollar}Msb{lcub}c{rcub}{dollar} is varied to assess compressibility effects on the nearly self-similar region.; The two-dimensional simulations demonstrate that the model is capable of capturing the correct jet spreading and decay. Mean streamwise excess velocity profiles are unaffected by compressibility, but normal entrainment velocity is essentially shut off at low-to-moderate compressibility {dollar}(Msb{lcub}c{rcub} le 0.4).{dollar} Two-dimensional computations are unable to capture the turbulence structure of the jet due to their artificial vortex organization in the fully developed region.; The three-dimensional computations examine one identical case, {dollar}Msb{lcub}c{rcub} = 0.4,{dollar} to assess the validity of the two-dimensional computations. Additionally, the three-dimensional model allows extension to a higher compressibility, {dollar}Msb{lcub}c{rcub} = 0.7,{dollar} at which smaller three-dimensional structures dominate. Excess velocity profiles are again the same, but entrainment velocity is not completely eliminated like in two dimensions. The three-dimensional inviscid model adequately captures the turbulence structure. Good qualitative agreement is obtained between the computed turbulent statistics and available (incompressible) experimental data. Two-point correlations in the normal direction provide insight into the spatial evolution of organized structures.; The (2-4) scheme and characteristic boundary conditions are also employed to compute acoustic wave propagation in an acoustically lined duct. The motivation is to assess the effect on sound attenuation of bias flow passed through the liner for application to noise suppression in jet engine nacelles. The mathematical model lumps the liner presence into a continuous empirical momentum equation source term which mimics the liner's acoustic impedance behavior. This source term deter- mines the time-domain effects of the nonlinear impedance of the liner's component porous sheets. The source term constants are matched to complex impedance data via a one-dimensional numerical impedance tube simulation. Sound pressure levels and axially transmitted power in a two-dimensional duct are computed to examine attenuation with different bias flows and frequencies. A final case considers noise propagation in the presence of a complicated hydrodynamic field, computed using the two-dimensional jet code.