Direct Numerical Simulations of Acoustic Disturbances in Various Rectangular Nozzle Configurations

We perform Direct Numerical Simulations (DNS) to study the acoustic freestream disturbances radiating from the turbulent boundary layers along the contoured nozzle walls of a hypersonic wind tunnel with a rectangular test section. To begin with, the effects of the spanwise end walls are suppressed by confining the spanwise computational domain to a finite segment of the overall nozzle cross section and by imposing periodic boundary conditions across that spanwise domain. Besides providing a building-block configuration to reveal par- tial effects of the enclosed acoustic environment within the wind tunnel, these computations serve as a stepping stone toward the goal of fully-3D computations including the nozzle end walls. Building upon the earlier simulations of Deegan et al. (2018), we show that the computed acoustic characteristics in the spanwise periodic simulations are insensitive to changes in the grid resolution parameters (e.g., x+ and z+). This is relative to the previous simulations that involved a coarser resolution in the streamwise and wall-normal directions, especially up- stream of the test section. Furthermore, we outline a comparison of the pressure fluctuations induced by the turbulent boundary layers over the contoured nozzle walls and several other calculations involving boundary layers over a single flat plate at nearly the same value of the edge Mach number. We also show the impact of having only one turbulent boundary layer instead of two within the computational setup. Various flow statistics, including the first and second moments of the unsteady flow field, are computed for the different flow configurations. Good comparisons of the statistics of the nozzle-wall boundary-layer turbulence and of the freestream acoustic disturbances between the simulations of coarser and finer grids confirms DNS procedure, but also the insensitivity of noise characteristics t section to the inflow turbulence generation technique.