 
Summary: Derivation of the Viscous MooreGreitzer
Equation for Aeroengine Flow
Bjšorn Birnir
Songming Hou
Niklas Wellander
Keywords: Separation of scales, scaling, modeling, homogenization, twoscale conver
gence, compressor, jet engine flow.
AMS classification numbers: 34D45, 34K15, 35B27, 35B40, 74Q15, 76M50
Abstract
The viscous MooreGreitzer equation modeling the airflow through the com
pression system in turbomachines, such as a jet engine, is derived using a scaled
NavierStokes equation. The method utilizes a separation of scales argument, based
on the different spatial scales in the engine and the different time scales in the flow.
The pitch and size of the rotorstator pair of blades provides a small parameter,
which is the size of the local cell. The motion of the stator and rotor blades in the
compressor produces a very turbulent flow on a fast time scale. The leading order
equation, for the fasttime and local scale, describes this turbulent flow. The next
order equations, produce an axisymmetric swirl and a flowpattern analogous to
RayleighBŽenard convection rolls in RayleighBŽenard convection. On a much larger
spatial scale and a slower time scale, there exist modulations of the flow including
