Pressure fluctuations induced by a hypersonic turbulent boundary layer

Abstract

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analysed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean-velocity profiles and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows 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 wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from Taylor’s hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The free-stream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the free-stream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Effect of wall cooling on boundary-layer-induced pressure fluctuations at Mach 6

“…The objective of the current paper is to investigate the dependence of boundarylayer-induced pressure fluctuations on wall temperature for hypersonic Mach numbers. In a previous paper by the present authors (Duan et al 2016), the successful application of DNS in capturing the global fluctuating pressure field has been demonstrated for a spatially developing flat-plate nominally Mach 6 turbulent boundary layer with a wall-to-recovery temperature ratio of T w /T r = 0.76. A new DNS dataset at Mach 6 with a different wall temperature (T w /T r = 0.25) from the previous Mach 6 data (Duan et al 2016) is introduced for the study of wall-temperature effects.…”

“…In a previous paper by the present authors (Duan et al 2016), the successful application of DNS in capturing the global fluctuating pressure field has been demonstrated for a spatially developing flat-plate nominally Mach 6 turbulent boundary layer with a wall-to-recovery temperature ratio of T w /T r = 0.76. A new DNS dataset at Mach 6 with a different wall temperature (T w /T r = 0.25) from the previous Mach 6 data (Duan et al 2016) is introduced for the study of wall-temperature effects. The effect of wall temperature on single-and multi-point statistics of the computed pressure fluctuations at multiple wall-normal locations (including the inner layer, the log layer, the outer layer and the free stream) is reported, including the intensity, frequency spectra, space-time correlations and propagation velocities.…”

“…Experimental measurements consist largely of those at the wall using surface-mounted pressure transducers (Kistler & Chen 1963;Fernholz et al 1989;Beresh et al 2011). Previous DNS studies of pressure fluctuations induced by high-speed turbulent boundary layers have focused on boundary layers with adiabatic or nearly adiabatic walls Di Marco et al 2013;Duan, Choudhari & Wu 2014;Duan, Choudhari & Zhang 2016). To the best of the knowledge of the authors, no existing studies have been conducted in the high-Mach-number cold-wall regime that provide the off-wall fluctuating pressure field including the free-stream acoustic pressure fluctuations.…”

Direct Numerical Simulation of Acoustic Noise Generation from the Nozzle Wall of a Hypersonic Wind Tunnel

“…Numerical schlieren images of the radiated acoustic field are shown in Figure 9. The wave fronts exhibit a preferred orientation of θ ≈ 31 • with respect to the nozzle centerline within the streamwise-radial plane (Figure 9c), a little larger than that seen for the flat plate turbulent boundary layer (Figure 9d), [6][7][8]28 where θ ≈ 26 • . The acoustic field within the core of the nozzle clearly shows the simultaneous presence of waves propagating in both upward and downward directions within the streamwise-radial plane.…”

“…15 The details of the DNS methodology have been documented in our previous simulations of acoustic radiation from turbulent boundary layers. 6,7,9 The DNS solver has been previously shown to be suitable for computing transitional and fully turbulent flows, including hypersonic turbulent boundary layers, 16,17 the propagation of linear instability waves in 2D high-speed boundary layers, and secondary instability and laminar breakdown of swept-wing boundary layers. 18,19…”