Unsteady flow in a cavitating axial inducer pump is analyzed with the help of a simple two-dimensional cascade model. This problem was motivated by a desire to study the effect of unsteady cavitation on the so-called POGO instability in the operation of liquid rocket engines. Here, an important feature is a closed loop coupling between several different modes of oscillation, one of which is due to the basic unsteady characterisitcs of the cavitation itself. The approaching and leaving flow velocities up- and downstream of the inducer oscillate, and the cavity-blade system participates dynamically with the basic pulsating flow. In the present work, attention is focused on finding a transfer matrix that relates the set of upstream variables to those downstream. This quantity, which is essentially equivalent to cavitation compliance in the quasistatic analyses, is found to be complex and frequency dependent. It represents the primary effect of the fluctuating cavity in the system. The analysis is based on a linearized free streamline theory
