An extension of the compound flow theory with friction between the streams and at the wall

TL;DR

This paper extends the compound flow theory by incorporating friction effects, providing a 1D model that accurately predicts the upstream and downstream displacement of the sonic section in compressible parallel streams.

Contribution

It introduces a novel 1D model including friction between streams and walls, explaining sonic section displacement directions in compound flows.

Findings

Friction causes upstream displacement of the sonic section.

The model matches RANS simulation results across various conditions.

Friction is identified as the main factor influencing sonic section movement.

Abstract

Compound flows consist of two or more parallel compressible streams in a duct and their theoretical treatment has gained attention for the analysis and modelling of ejectors. Recent works have shown that these flows can experience choking upstream of the geometric throat. While it is well known that friction can push the sonic section downstream the throat, no mechanism has been identified yet to explain its displacement in the opposite direction. This study extends the existing compound flow theory and proposes a 1D model, including friction between the streams and the duct walls. The model captures the upstream and downstream displacements of the sonic section. Through an analytical investigation of the singularity at the sonic section, it is demonstrated that friction between the streams is the primary driver of upstream displacement. The 1D formulation is validated against axisymmetric Reynolds Averaged Navier-Stokes (RANS) simulations of a compound nozzle for various inlet pressure and geometries. The effect of friction is investigated using an inviscid simulation for the isentropic case and viscous simulations with both slip and no-slip conditions at the wall. The proposed extension accurately captures the displacement of the sonic section, offering a new tool for in-depth analysis and modeling of internal compound flows.