The Similarity of Ducted Jets With Low and High Pressure Gradients

Abstract

The objective of the present work is to study what type of effects the dimensionless jet parameters really consider. To do it, three classical dimensionless jet parameters are redeveloped using an unified methodology. This methodology is based on the integral balances of mass and momentum. The momentum balance terms are classified as inertial or pressure terms and as flux or source terms. This redevelopment enlighten the meaning of the dimensionless jet parameters and allows the definition of a new set of parameters. A scaling methodology is presented to compare the dimensionless jet parameters adequacy in scaling center line jet velocity and jet width at different operational conditions. Two regimes are distinguished: low pressure gradient and high pressure gradient. The scaling for low pressure gradient is based on two criteria: the diffusivity ratio proportionality and the linear expansion rate of the jet. The diffusivity is modelled using the Prandtl’s mixing length model and a dimensional analysis based only on inertial momentum terms. The scaling for high pressure gradient is based on jet velocities and widths scaled simultaneously by pressure and inertial momentum terms. The application of this methodology to jet literature data shows jet similarity for low and high pressure gradients. However, some drawbacks are identified in scaling the jet width at high pressure gradients.