# Scaling of the Puffing Strouhal Number for Buoyant Jets

## TL;DR

This study demonstrates that using the hydraulic radius as the characteristic length yields a universal scaling relation for puffing Strouhal numbers across various buoyant jet geometries and Richardson numbers, supported by simulations and prior experiments.

## Contribution

It introduces a unified scaling relation for puffing frequency in buoyant jets based on hydraulic radius, applicable across multiple geometries and a wide range of Richardson numbers.

## Key findings

- A single Strouhal-Richardson relation fits diverse geometries.
- Numerical simulations validate the scaling across different inlet shapes.
- The relation spans over four orders of magnitude in Richardson number.

## Abstract

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.