  The compression driver, the standard sound source for midrange acoustic
horns, contains a cylindrical compression chamber connected to the horn throat
through a system of channels known as a phase plug. The main challenge in the
design of the phase plug is to avoid resonance and interference phenomena. The
complexity of these phenomena makes it difficult to carry out this design task
manually, particularly when the phase-plug channels are radially oriented.
Therefore, we employ an algorithmic technique that combines numerical solutions
of the governing equations with a gradient-based optimization algorithm that
can deform the walls of the phase plug. A particular modeling challenge here is
that viscothermal losses cannot be ignored, due to narrow chambers and slits in
the device. Fortunately, a recently developed, accurate, but computationally
inexpensive boundary-layer model is applicable. We use this model, a level-set
geometry description, and the Cut Finite Element technique to avoid mesh
changes when the geometry is modified by the optimization algorithm. Moreover,
the shape calculus needed to compute derivatives for the optimization algorithm
is carried out in the fully discrete case. Applying these techniques, the
algorithm was able to successfully design the shape of a set of
radially-directed phase plugs so that the final frequency response surprisingly
closely matches the ideal response, derived by a lumped circuit model where
wave interference effects are not accounted for. This result may serve to
resuscitate the radial phase plug design, rarely used in today's commercial
compression drivers.
