Numerical simulation of multi-dimensional acoustic propagation in air including the effects of molecular relaxation

by 1979- Wochner, Mark

A computational acoustic propagation model based upon the Navier-Stokes equations is created that is able to simulate the effects of absorption and dispersion due to shear viscosity, bulk viscosity, thermal conductivity and molecular relaxation of nitrogen and oxygen in one or two dimensions. The model uses a fully nonlinear constitutive equation set that is closed using a thermodynamic entropy relation and a van der Waals equation of state. The use of the total variables in the equations rather than the perturbed (acoustical) variables allow for the extension of the model to include wind, temperature profiles, and other frequency independent conditions. The method of including sources in the model also allow for the incorporation of multiple spatially and temporally complex sources. Two numerical methods are used for the solution of the constitutive equations: a dispersion relation preserving scheme, which is shown to be efficient and accurate but unsuitable for shock propagation; and a weighted essentially non-oscillatory scheme which is shown to be able to stably propagate shocks but at considerable computational cost. Both of these algorithms are utilized in this investigation because their individual strengths are appropriate for different situations. It is shown that these models are able to accurately recreate many acoustical phenomena. Wave steepening in a lossless and thermoviscous medium is compared to the Fubini solution and Mendousse’s solution to the Burgers equation, respectively, and the Fourier component amplitudes of the first harmonics is shown to differ from these solutions by at most 0.21 %. Nonlinear amplification factors upon rigid boundaries for high incident pressures and its comparisons to the Pfriem solution is shown to differ by at most 0.015 %. Modified classical absorption, nitrogen relaxation absorption, and oxygen relaxation absorption is shown to differ from the analytical solutions by at most 1 %. Finally, the dispersion due to nitrogen relaxation and oxygen relaxation are also shown to differ from the analytical soiii lutions by at most 1 %. It is believed that higher resolution grids would decrease the error in all of these simulations. A number of simulations that do not have explicit analytical solutions are then discussed. To demonstrate the model’s ability to propagate multi-dimensional shocks in two dimensions, the formation of a Mach stem is simulated. The amplification factors determined in the test demonstrate a qualitative similarity with discussions in the literature and explosion data. The ability of the algorithm to propagate jet noise is then investigated using full scale jet noise as the input into the algorithm. The waveforms predicted by the model are compared to a Burgers equation algorithm and using a weak shock theory analysis of the shock propagation speeds, an under-prediction of shock coalescence is noted in the Burgers equation algorithm. To establish if the under-prediction of shock coalescence by the Burgers equation algorithm is the cause of the discrepancy between its predictions and recently measured scale model data, the WENO scheme is also used to propagate the scale model jet noise. The predictions by the two models agree very well for both cold and heat simulated jet cases which is due in part to the relatively small amplitudes and propagation distances. The two models, however, do not agree very well with the experimental data and it is concluded that more work is needed to determine the precise reasons for this discrepancy. iv