Nonlinear small-disturbance equations for three-dimensional transonic flow through a compressor blade row

A derivation is given of the nonlinear, small-disturbance equations governing three-dimensional transonic flow through a fan or compressor rotor. These equations represent the counterpart, for turbomachinery flows, of the small-disturbance equations appropriate to an isolated airfoil. Thus, they facilitate the application to turbomachinery flows of the many numerical solution methods developed in recent years for isolated-airfoil problems. Boundary conditions for design and off-design conditions are formulated, at a level of approximation consistent with the small-disturbance field equations. An order-of-magnitude analysis is presented, which reveals the transonic similarity parameters for flow in blade rows of low and high solidity. The validity of a rectilinear transonic shear flow as a representation of the flow through a fan or rotor is also discussed.