A Three-Dimensional Actuator Disk Model for Fan Response to Inlet Distortion: Part I - Formulation

Abstract This paper describes a semi-analytical approach to investigate the response of a fan stage of arbitrary hub-tip ratio subjected to inlet distortion. The flow is taken to be incompressible and inviscid and the length scale of the imposed distortion is assumed to be sufficiently large that the blade rows can be treated as actuator disks. Work addition by the rotor is taken to be radially nonuniform, in general. Under conditions representative of contemporary fans, the background flow is shown to be well represented by the radial equilibrium approximation. On the further assumption that the imposed distortion is a small perturbation about this background flow, semi-analytical forms are derived for the flow fields upstream and downstream of the fan stage. The upstream perturbations are comprised of decaying potential modes and convected vortical modes. The nonuniform downstream flow does not permit a straightforward decomposition of this type. Instead, the perturbations are found to be comprised of decaying modal-type disturbances and convected disturbances that grow algebraically downstream. By matching the upstream and downstream disturbances across the actuator disks using the conservation laws, the overall perturbation field can be determined. The numerical procedure for accomplishing this is very efficient, permitting the present method to be employed in trade studies during early design phases.