Summary: Derivation of the Viscous Moore-Greitzer
Equation for Aeroengine Flow
Keywords: Separation of scales, scaling, modeling, homogenization, two-scale conver-
gence, compressor, jet engine flow.
AMS classification numbers: 34D45, 34K15, 35B27, 35B40, 74Q15, 76M50
The viscous Moore-Greitzer equation modeling the airflow through the com-
pression system in turbomachines, such as a jet engine, is derived using a scaled
Navier-Stokes 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 rotor-stator 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 fast-time and local scale, describes this turbulent flow. The next
order equations, produce an axi-symmetric swirl and a flow-pattern analogous to
Rayleigh-BŽenard convection rolls in Rayleigh-BŽenard convection. On a much larger
spatial scale and a slower time scale, there exist modulations of the flow including