Description:
<jats:p>We use a numerical approach to study the receptivity of the boundary
layer flow over
a slender body with a leading edge of finite radius of curvature to small
streamwise
velocity fluctuations of a given frequency. The body of interest is a parabola
in order
to exclude jumps in curvature, which are known sites of receptivity and
which occur
on elliptic leading edges matched to finite-thickness at plates. The infinitesimally
thin flat plate is the limiting solution for the parabola as the nose radius
of curvature
goes to zero. The formulation of the problem allows the two-dimensional
unsteady
Navier–Stokes equations in stream function and vorticity form to
be converted to two
steady systems of equations describing the basic (nonlinear) flow and the
perturbation
(linear) flow. The results for the basic flow are in excellent agreement
with those in
the literature. As expected, the perturbation flow was found to be a combination
of
an unsteady Stokes flow and Orr–Sommerfeld modes. To separate these,
the unsteady
Stokes flow was solved separately and subtracted from the total perturbation
flow. We
found agreement with the streamwise wavelengths and locations of Branches
I and II
of the linear stability neutral growth curve for Tollmien–Schlichting
waves. The results
showed an increase in the leading-edge receptivity with decreasing nose
radius, with
the maximum occurring for an infinitely sharp flat plate. The receptivity
coefficient
was also found to increase with angle of attack. These results were in
qualitative
agreement with the asymptotic analysis of Hammerton & Kerschen (1992).
Good
quantitative agreement was also found with the recent numerical results
of Fuciarelli
(1997), and the experimental results of Saric, Wei & Rasmussen (1994).</jats:p>