We investigate the influence of rotational and vibrational energy
relaxation on the
stability of laminar boundary layers in supersonic flows by numerically
solving the
linearized equations of motion for a flow in thermal non-equilibrium. We
model air
as a mixture of nitrogen, oxygen and carbon dioxide, and derive accurate
models
for the relaxation rates from published experimental data in the field
of physical
chemistry. The influence of rotational relaxation is to dampen high-frequency
instabilities, consistent with the well known damping effect of rotational
relaxation on
acoustical waves. The influence of rotational relaxation can be modelled
with acceptable
accuracy through the use of the bulk-viscosity approximation when the bulk
viscosity is computed with a formula described herein. Vibrational relaxation
affects
the growth of disturbances by changing the characteristics of the laminar
mean flow.
The influence is strongest when the flow field contains a region at, or
near, stagnation
conditions, followed by a rapid expansion, such as inside wind tunnels
and around
bodies with a blunt leading edge, whereby the rapid expansion causes the
internal
energy to freeze in a distribution out of equilibrium. For flows at Mach
4.5 and
stagnation temperature of 1000 K, the total amplification exhibited by
boundary-layer
disturbances over a sharp flat plate in wind-tunnel flows can reach a value
that is fifty
times as high as the value computed under the assumption of thermal equilibrium.
The difference in amplification can be twice as high in the case of a blunt
flat plate
at atmospheric flight conditions.
