A Navier-Stokes solver for simulating unsteady viscous e uid e ow in turbomachinery components has been developed and used to study e uid dynamic phenomena that lead to instabilities in centrifugal compressors. These studies indicate that large e ow incidence angles, at reduced e ow rates, can cause boundary-layer separation near the blade leading edge. High-pressure jets upstream of the compressor face are studied as a means of controlling compressor instabilities. Steady jets are found to alter the leading-edge e ow pattern and effectively suppress compressorinstabilities.Itisalsoobservedthatyawedjetsaremoreeffectivethanparalleljetsandthatanoptimum yaw angle exists for each compression system. Pulsed jets can yield additional performance enhancements and lead to a reduction in external air requirements for operating the jets. Jets pulsed at higher frequencies perform better than low-frequency jets. HE stable operating regime of current generation centrifugal compressors is limited at reduced mass e ow rates by two e uid dynamic phenomena: rotating stall and surge. The occurrence of these phenomena dee nes the surge limit, also referred to as stall line. When operating a compression system under these conditions, stronge uctuationsandlimitcycleoscillationscancauselargevibra- tions, leading to fatigue and damage of the entire compression unit. Unsteady e uctuations, caused by rotating stall or surge, may lead to excessive heating of the impeller blades and can produce additional periodicloadson theimpeller,resultinginincreasedoperating noise levels. If the e uctuations are left unchecked, even a complete e ow re- versal is possible, a situation that a compressor cannot tolerate. Because of the severity of these hazardous conditions, centrifugal compressors are conservatively designed to operate well below the peak pressure rise point. A safety margin of 10 -20% is generally introduced between the surge line and the design operating condi- tion. Most compressor control systems currently used in industry are based on this strategy, called avoidance control. Signie cant progress has been made in the past several years to develop reliable compressor control schemes. These schemes em- ploy fast-response-stall-detection devices, in most cases circumfer- entially distributed over thecasing walls thatmeasure e owe eld data and send e ltered signals to a controller unit. When a compressor approaches a stall-like condition, the presence of growing insta- bilities, sometimes called stall precursor waves, is measured and signaled back to the controller unit before the actual stall process begins. The control mechanism is then activated by a direct link be- tween the controller and a set of high-bandwidth actuation devices. The type of control system is often categorized by the choice of a particular actuator.