Leading-Edge Receptivity to Acoustic Waves for
High-Speed Flows over a Blunt Wedge
Adriano Cerminara, Neil D. Sandham
Aerodynamics and Flight Mechanics Research Group
University of Southampton, Southampton, Hampshire, SO17 1BJ, United Kingdom
The leading-edge receptivity to acoustic disturbances of supersonic/hypersonic boundary layers
on a cylinder-wedge of 20º half-wedge angle and 0.1 mm nose radius is numerically investigated
for a set of six different cases with Mach number ranging from 3.0 to 7.3, through direct numerical
simulation (DNS) of the two-dimensional (2D) Navier-Stokes equations. Two angles of attack
(0º, 10º), and two inclination angles of the acoustic waves (0º, 10º) are considered among the
different numerical cases. For the Mach 3.0 case both fast and slow planar acoustic waves with
multiple frequencies are inserted into the flowfield of the steady state solution in order to carry
out unsteady computations, while for the remaining cases the unsteady computations are
performed only for fast waves in the freestream. The results show that the response along the wall
is stable in the nose region, up to 400 nose radii downstream, and that at Mach 3.0 there is a higher
amplitude for the fast mode than for the slow mode, as shown in Figure 1, where the density
fluctuation fields for fast and slow freestream acoustic waves are compared. For the case of fast
acoustic waves, a frequency-dependent oscillatory behaviour is shown by the wall pressure
perturbations (Figure 2), which is due to a modulation of the internal mode F with the external
forcing mode and other internal waves. The wall pressure perturbation spectra at three different
distances from the leading-edge (corresponding to the transducer locations in experiments carried
out at DLR) for the Mach 3 case (Figure 3) show that the receptivity to fast acoustic waves is
higher than to slow acoustic waves, and that for the slow mode the maximum amplitude is reached
at the lowest frequency. Increasing the angle of incidence of the acoustic waves seems to slightly
increase the amplitude of the response on the top (lee) side of the body at the higher frequencies,
and to produce a flatter response on the same side for the lower frequencies. Including an angle
of attack decreases the receptivity along the top side, as the shock is weaker here, and amplifies
the response on the windward side. These results serve to quantify the relationship between the
disturbances measured by sensors near the leading-edge of a measurement probe and the
freestream disturbances in hypersonic wind tunnels.
Figure 1. Density fluctuation fields for fast (a) and slow (b) freestream acoustic waves (Mach 3).
Figure 2. Pressure fluctuation amplitude distribution along the wall at different frequencies of the fast acoustic waves
(Mach 3).
Figure 3. Pressure fluctuation frequency spectra at different distances on the wall from the leading edge (transducer
points), for fast (a) and slow (b) freestream acoustic waves (Mach 3).