Numerical study of acoustic radiation due to a supersonic turbulent boundary layer

Abstract

Direct numerical simulations are used to examine the pressure fluctuations generated by fully developed turbulence in a Mach 2.5 turbulent boundary layer, with an emphasis on the acoustic fluctuations radiated into the free stream. Single-and multi-point statistics of computed surface pressure fluctuations show good agreement with measurements and numerical simulations at similar flow conditions. Consistent with spark shadowgraphs obtained in free flight, the quasi-homogeneous acoustic near field in the free-stream region consists of randomly spaced wavepackets with a finite spatial coherence. The free-stream pressure fluctuations exhibit important differences from the surface pressure fluctuations in amplitude, frequency content and convection speeds. Such information can be applied towards improved modelling of boundary layer receptivity in conventional supersonic facilities and, hence, enable a better utilization of transition data acquired in such wind tunnels. The predicted acoustic characteristics are compared with the limited available measurements. Finally, the numerical database is used to understand the acoustic source mechanisms, with the finding that the supersonically convecting eddies that can directly radiate to the free stream are confined to the buffer zone within the boundary layer.

Stationary Crossflow Breakdown due to Mixed Mode Spectra of Secondary Instabilities

“…The DNS code has been previously shown to be suitable for computing fully turbulent flows. 20,21 In additional unpublished work, further validation of this code was performed in the context of the propagation of linear instability waves in a 2D, high-speed boundary layer. Convergence studies showed that the 7 th -order WENO performs well at a resolution of 10 points per wavelength or higher, depending on the streamwise extent of the computational domain.…”

High-resolution PIV measurements of a transitional shock wave–boundary layer interaction

“…To further investigate the nature of the freestream disturbances, the shape of the spectrum of the pressure fluctuations has been compared to the spectra measured in the works of Laufer (1964) and Duan et al (2014) (see Fig. 1).…”

High-resolution PIV measurements of a transitional shock wave-boundary layer interaction

“…Following the approach of Laufer (1964), it then follows that the RMS level of the pressure fluctuations equals 1.9 × 10 −2 p ∞ . To further investigate the nature of the freestream disturbances, the shape of the spectrum of the pressure fluctuations has been compared to the spectra measured in the works of Laufer (1964) and Duan et al (2014) (see Fig. 1).…”

“…1). Duan et al (2014) performed DNS simulations on a supersonic (M = 2.5) turbulent boundary layer and analysed the radiated acoustic pressure field. Laufer (1964) performed hot-wire measurements in the freestream of a M = 2 supersonic wind tunnel and converted the measured mass flux fluctuations to pressure fluctuations.…”

“…Figure 1 presents the normalized power spectral density. The data of Laufer (1964) and Duan et al (2014) are not available for ωδ/U ∞ < 0.2. Therefore, to allow a fair comparison with the current data set, the spectrum normalization is performed such that the integral over the frequency range ωδ/U ∞ > 0.2 equals unity for all three cases.…”