Numerical Study of Pressure Fluctuations Due to High-Speed Turbulent Boundary Layers

Abstract

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by fully developed turbulence in supersonic turbulent boundary layers with an emphasis on both pressure fluctuations at the wall and the acoustic fluctuations radiated into the freestream. The wall and freestream pressure fields are first analyzed for a zero pressure gradient boundary layer with Mach 2.5 and Reynolds number based on momentum thickness of approximately 2835. The single and multi-point statistics reported include the wall pressure fluctuation intensities, frequency spectra, space-time correlations, and convection velocities. Single and multi-point statistics of surface pressure fluctuations show good agreement with measured data and previously published simulations of turbulent boundary layers under similar flow conditions. Spectral analysis shows that the acoustic fluctuations outside the boundary layer region have much lower energy content within the high-frequency region. The space-time correlations reflect the convective nature of the pressure field both at the wall and in the freestream, which is characterized by the downstream propagation of pressure-carrying eddies. Relative to those at the wall, the pressure-carrying eddies associated with the freestream signal are larger and convect at a significantly lower speed. The preliminary DNS results of a Mach 6 boundary layer show that the pressure rms in the freestream region is significantly higher than that of the lower Mach number case.

Numerical Study of Pressure Fluctuations due to a Mach 6 Turbulent Boundary Layer

“…The successful application of DNS for capturing the freestream acoustic pressure fluctuations has been demonstrated by the current authors in the context of a simulation of a Mach 2.5 supersonic turbulent boundary layer, in which many single and multi-point statistics of the pressure field, including the pressure intensities, frequency spectra, space-time correlations, and convection speeds, were described. 21 The current study extends that previous study into the hypersonic Mach number regime (where even the properties of surface pressure fluctuations have not been quantified as yet) to highlight the variation of acoustic characteristics with Mach number as well as to provide additional validation of simulations against experimentally measured trends.…”

“…Figure 4a shows that the wall pressure rms normalized by the local wall shear for the Mach 6 case is about 2.8, which is close to the corresponding value of approximately 2.6 at Mach 2.5. 21 The normalized value is also close to the value p (Fig. 5).…”

“…Figure 1 shows the general computational set-up for the DNS in the present work, which parallels the setup in Duan et al 21 for the Mach 2.5 simulation, wherein the effects of domain size and grid resolution were also assessed. The choice of grid parameters for the present study is based on lessons learned from Duan et al, 21 allowing a single simulation to be used to assess the effects of Mach number. The domain size for the present computation is (58.7δ i , 15.7δ i , 39.7δ i ) in the stream-wise, span-wise, and wall-normal directions, respectively.…”

“…A similar variation of convection speed with the wall-normal distance is observed in the Mach 2.5 case. 21 In addition, Fig. 10b further compares the convection speeds at the wall and in the freestream between the Mach 6 and Mach 2.5 cases.…”

“…21 Therefore, only a cursory description is given here. The full three-dimensional compressible Navier-Stokes equations in conservation form are solved in generalized curvilinear coordinates.…”