Direct Numerical Simulation of Acoustic Disturbances in a Hypersonic Two-Dimensional Nozzle Configuration

Abstract

Direct numerical simulations (DNS) are performed to study acoustic radiation in a quasi-two-dimensional nozzle with two independent spatially evolving turbulent boundary layers with an edge Mach number of 6. The emphasis of this work is to compare the radiated pressure fluctuations in a geometrically confined environment with those radiated from a single wall in an unconfined setting. The boundary-layer profile of the rms pressure fluctuation scaled by the mean shear stress at the wall is found to be in good agreement with prior flat-plate calculations at similar conditions. However, the normalized rms pressure fluctuation within the freestream region is significantly higher than that in the unconfined case, by a factor that is approximately equal to . The application of two different compressibility transformations to the computed mean velocity profiles indicates that, in comparison with the van Driest transformation, the Trettel and Larsson transformation provides a better collapse with flat-plate simulations over a broad range of Mach numbers. The DNS data also reveal that, in spite of displaying a strongly non-Gaussian behavior inside the boundary layer, the radiated acoustic fluctuations in all thermodynamic variables have a skewness of approximately 0.3, indicating a minor deviation with respect to Gaussian behavior. Surface pressure fluctuations along the nozzle walls are not significantly impacted by the acoustic waves radiating from the opposite wall.