Interaction of a Tunnel-like Acoustic Disturbance Field with a Blunt Cone Boundary Layer at Mach 8

Abstract

The existing measurements of laminar-to-turbulent transition over circular cones in conventional (i.e., "noisy'') hypersonic wind tunnels have established that the transition location moves downstream when the nose radius is increased from zero. However, this initially downstream movement slows down and ultimately reverses beyond a critical value of the nose radius, and may be related to external forcing in the form of freestream disturbances and/or surface roughness. To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, hypersonic boundary-layer receptivity to broadband freestream acoustic disturbances from the nozzle wall of a digital conventional wind tunnel is investigated by both direct numerical simulations (DNS) and modal and nonmodal stability analysis. A Mach $8$ flow over a 7 deg half-angle cone with a nose radius of $R_n = 5.2$ mm and freestream unit Reynolds number of $12.2\times10^6$ m\textsuperscript{-1} is considered. The results show that the broadband tunnel noise in the free stream of a convectional hypersonic wind tunnel (i.e., outside the nozzle-wall turbulent boundary layer) can be well represented by an acoustic model with an ansatz of slow plane acoustic waves. With successful calibration of the model parameters against the precursor tunnel DNS, such an acoustic ansatz can successfully reproduce both the frequency-wavenumber spectra and the temporal evolution of the broadband tunnel noise radiated from the nozzle wall. Additionally, the DNS of the Mach 8 blunt cone with tunnel-like acoustic input above the bow shock showed that the spectra of wall-pressure and heat-transfer fluctuations recover the signature of the axisymmetric waves predicted by the nonmodal analysis. Furthermore, the azimuthal wavenumber and frequency spectrum of the temperature fluctuations as a function of the wall-normal distance show higher amplitudes for three-dimensional waves above the boundary-layer edge. The numerical schlieren contours show the inclined structures commonly observed in blunt cone experiments, demonstrating that they correspond to three-dimensional structures due to freestream disturbances in the presence of an entropy layer.