Direct numerical simulation of pressure fluctuations induced by supersonic turbulent boundary layers

Direct Numerical Simulations are used to generate a database of high-speed zero-pressure-gradient turbulent boundary layers developing spatially over a flat plate with nominal freestream Mach number ranging from 2:5 to 14 and wall-to-recovery temperature ranging from 0:18 to 1:0. The flow conditions of the DNS are representative of the operational conditions of the Purdue Mach 6 quiet tunnel, the Sandia Hypersonic Wind Tunnel at Mach 8, and the AEDC Hypervelocity Tunnel No. 9 at Mach 14. The DNS database is used to gauge the performance of compressibility transformations, including the classical Morkovin\u27s scaling and strong Reynolds analogy as well as the newly proposed mean velocity and temperature scalings that explicitly account for wall heat flux, examine the pressure fluctuations generated by the turbulent boundary layers. The unsteady pressure field is analyzed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. The simulations show that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder wall case. The pressure structures propagate with similar speeds for both wall temperatures. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers. Precomputed flow statistics, including Reynolds stresses and their budgets, are available at the website of the NASA Langley Turbulence Modeling Resource --Abstract, page iv