To predict the unsteady aerodynamic response of centrifugal compressor impeller blades to the potential eld generated by the downstream vaned diffuser, a small perturbation model is developed that considers the number of impeller blades and diffuser vanes, the impeller blade backsweep angle, the impeller rotational speed, and the mass ow rate. The unsteady ow is analyzed in the impeller exit region and the vaneless diffuser space between the impeller and the diffuser leading edge radius, where the unsteady ow generated by the diffuser vane potential eld is most signi cant. The unsteady ow perturbations are superimposed on an irrotational two-dimensional steady ow model, resulting in an analysis that is consistent with the small perturbation velocity potential equation. This model is then applied to a representative modern high speed impeller-vaned diffuser con guration.
NomenclatureA = speed of sound A 0i = stagnation speed of sound at in ow boundary G = impeller blade spacing vector k = reduced frequency k m d = tangential wave number at inlet boundary k m µ = tangential wave number for continuous analytic solution M r= stagnation pressure at the in ow boundary p = perturbation pressure r; µ ; t = cylindrical coordinate directions and time in rotating impeller frame r i = grid inlet radius r t = impeller tip radius r v = radius of diffuser vane leading edges (radius of grid exit) T oh = stagnation temperature at the in ow boundary V = velocity in the stationary frame of reference V r = radial velocity V rel = velocity in the rotating impeller frame V µ = tangential velocity in the stationary frame V µ rel = tangential velocity in the rotating frame v = perturbation velocity ® = impeller blade angle with respect to radial ® t = impeller blade angle at impeller exit 0 2 = 1 ¡ M 2 r 1C p = pressure coef cient differential across the impeller blade, 1p=. 1 2 ½ oi A 2 oh / ½ = perturbation density ½ 0i = stagnation density at in ow boundary ¾ = interblade phase angle Á = perturbation velocity potential