Volume 8, Number 3, Fall 2000
THE INITIAL FLOW PAST A UNIFORMLY
ACCELERATING INCLINED ELLIPTIC CYLINDER
S.J.D. D'ALESSIO AND F.W. CHAPMAN
Abstract. This paper solves the problem of determining
the initial twodimensional motion of a viscous incompressible
fluid past an inclined elliptic cylinder which is uniformly
accelerated from rest. This motion is calculated using two
types of methods. The first takes the form of a double
series solution where an expansion is carried out in powers
of the time, t, and in powers of λ = √8t/R where R is the
Reynolds number. This approximate analytical solution is
valid for small times following the start of the motion and
for large Reynolds numbers. The second method involves a
spectralfinite difference procedure for numerically integrating
the full NavierStokes equations expressed in terms of a stream
function and vorticity. Our results demonstrate that for small
times and moderately large R the two methods of solution
are in good agreement. Results are presented for the cases
R = 100 and R = 1, 000 for an ellipse inclined at 45º to the
free stream and having an aspect ratio of 0.5.
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