1. Conformal mapping
2. Provided that the unsteady compressible flow-field measured in the stationary reference frame of an axial-flow compressor can be approximated by an incompressible solution in a rotating frame, conformal mapping techniques can be used to provide information regarding compressor flow-field physics. Conformal mappings are useful, as they transform the flow-field around a simple geometry to that of a more complex one, by applying stretching, and/or rotation, between coordinate planes. Ig In such transformations, the C-plane is typically denoted as the simple geometry plane, and is defined by the complex coordinates < = < + iv. Conversely, the z-plane is often denoted as the physical plane, or solution plane, and is de&red by the complex coordinates E = x + ~Y.~O Figure 4: Flow about circular cylinder.
3. AI AA 2000-0229 is shown in Fig. 6, where the mean fre+stream velocity, U, has been subtracted from the computed total velocity. Figure 6 clearly shows areas of higher velocities above, and lower velocities below, the free-stream airfoil (the airfoil is located along v = 0), as dictated by suction-surface acceleration and pressuresurface deceleration.