The Efficacy of a Convex Corner at a Bend Inlet for the Control of Supercritical Oblique Waves

A novel method for the control of supercritical waves is introduced by the installation of a convex
corner at a bend inlet. In this method the negative waves emitted from the convex corner are
superimposed on the positive waves caused by the outer wall of the bend. Thereby, the heights of the
positive waves are decreased. In the first part of the article, the existing analytical relationships for the
supercritical flow in straight transitions and bends are reviewed and the interactions of waves in them
are examined. Then, using the Roe-TVD finite volume method, the supercritical flow in transitions
and bends is simulated numerically. The precision and accuracy of the numerical results in comparison
with analytical, numerical and experimental solutions of the other researchers are satisfactory. Next,
for the reduction of wave height at the outer wall of a curved channel, a small convex corner is located
at the inner wall of the bend inlet. The interaction of positive and negative waves transforms the
original single-hump wave at the outer wall to a smaller double-hump wave. The optimum expansion
angle of the convex corner (
) is a function of the offset breadth to the bend width, d/b, radius of
curvature to the bend width, rc/b, and the inlet Froude number, Fr0. The numerical studies carried out
for dimensionless widths (d/b=4%, 8%, 12%), in the range of 2.5<Fr0< 4.5 for three bends with (rc/b=
10, 15, 20) indicated that using an optimum convex corner the wave height may be decreased between
10 to 45%.