  Prior research has shown that round and planar buoyant jets "puff" at a
frequency that depends on the balance of momentum and buoyancy fluxes at the
inlet, as parametrized by the Richardson number. Experiments have revealed the
existence of scaling relations between the Strouhal number of the puffing and
the inlet Richardson number, but geometry-specific relations are required when
the characteristic length is taken to be the diameter (for round inlets) or
width (for planar inlets). In the present study, we show that when the
hydraulic radius of the inlet is instead used as the characteristic length, a
single Strouhal-Richardson scaling relation is obtained for a variety of inlet
geometries. In particular, we use adaptive mesh numerical simulations to
measure puffing Strouhal numbers for circular, rectangular (with three
different aspect ratios), triangular, and annular high-temperature buoyant jets
over a range of Richardson numbers. We then combine these results with prior
experimental data for round and planar buoyant jets to propose a new scaling
relation that accurately describes puffing Strouhal numbers for various inlet
shapes and for Richardson numbers spanning over four orders of magnitude.
