  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. Finally, the predictions of the model are compared to
axisymmetric Reynolds Averaged Navier-Stokes (RANS) simulations of a compound
nozzle. 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.
