Semi-empirical model for supersonic flow separation in
rocket
nozzles

Abstract: The commercial potential of space flight can be described as a quotient of
system performance and system weight. The system costs are primarily
dependent on this quotient. To increase the quotient focus has been on
reducing the system weight. After exploiting numerous ways of reducing the
system weight and finally reaching the limit of mechanical load capacities,
the current aim is to increase the thrust-to-weight ratio of the rocket
nozzle. This is achieved by reducing the divergent length and increase the
specific momentum of the nozzle, i.e. increasing the expansion ratio.
However, this may causes the nozzle to be overexpanded at sea level and
thus
provokes the flow to separate from the nozzle wall. The unsteady and
asymmetric flow separation generates lateral forces on the nozzle wall, so
called side loads, which can be of dimensioning size for the nozzle and the
rocket structure and not at least for the payload.

Extensive studies have been made through the years to understand the flow
separation phenomena in overexpanded rocket nozzles. A better understanding
could lead to better prevention or even control of flow separation. In
addition, a reliable separation model is needed for accurate prediction of
the side-loads experienced during start up and shut down of the engine. The
aim of this thesis was to examine current separation models and try to
develop a new semi-empirical model for hot gases. Focus was on the
recirculation region where the flow is separated from the nozzle wall.

A new model was developed to determine the pressure- and flow distribution
in the recirculation region. The model includes various parameters of the
jet- and ambient gas and can therefore be used for hot gases. Several steps
of the model were validated with good agreement with experimental data and
numerical results found in the literature. The complete model on the other
hand showed poor agreement with experiment and further work must therefore
be made before the model can be useful.