Rotordynamic Effects of Compressor Rotor-Tip Clearance Asymmetry

Abstract

Rotordynamic effects caused by nonaxisymmetric rotor-tip clearance in an axial compressor stage have been analyzed. Two coupled actuator disc analyses are carried out at blade (meridional plane) and radius (radial plane) scales. Continuity, axial, and tangential momentum equations are used to connect upstream and downstream ows across the compressor stage, and a small perturbation analysis is used to obtain ow eld nonuniformities. Predictions indicate the following. Relative to the passage ow, the ow associated with the rotor-tip clearance is axially retarded and tangentially underturned. Furthermore, the compressor blades near the smaller tip gap are more highly loaded. Thus, the tangential force asymmetry promotes a backward whirl. However, the pressure asymmetry caused by azimuthal ow redistribution induces a forward whirl. The net result is a backward-whirling force whose magnitude is much smaller than that of the forward-whirling force found in turbines. Nomenclature= magnitude of rotor offset F x = lateral force in the direction of the offset F y = lateral force perpendicularto the direction of the offset f y = tangential force per azimuthal length H = annulus height H b = rotor blade span h = enthalpy L = rotor thickness P m = mass ux P = pressure Q = strength of the shear layer q = nondimensional vorticity strength; local mass ux R = mean compressor radius; turbine reaction s = blade pitch t = radial tip clearance U = turbine rotational speed at the mean radius, ! R W = relative velocity X = direction along the rotor offset x = axial direction Y = direction perpendicular to rotor offset y = tangential direction z = radial direction ® = absolute ow angle, eigenvalue ® x = direct excitation force coef cient ® y = cross excitation force coef cient = relative ow angle; angle between tip jet ow and passage ow 1 = thickness of underturned layer downstream of actuator disc 8 = turbine ow coef cient, C x =U µ = azimuthal angle measured in the direction of rotation from the minimum gap location; angle between the underturned stream and the bladed stream = nondimensional mass fraction of underturned ow ½ = density 9 = meridional stream function; work coef cient ! = angular velocity of rotor shaft rotation; vorticity Subscripts D = design value m = mean t = stagnation condition 0 = far upstream of actuator disc in the blade scale analysis 0¡ = near upstream of the actuator disc in the radius scale analysis 0C = near downstream of the actuator disc in the radius scale analysis 1 = rotor inlet in the blade scale analysis 2 = stator inlet in the blade scale analysis 3 = stator outlet in the blade scale analysis 4 = far downstream of stator in the blade scale analysis ? = meridional component Superscripts ¡ = the part of ow downstream that has crossed the bladed part of turbine ow C = the part of ow downstream that was underturned due to the rotor tip gap '= nonaxisymmetric perturbation = azimuthal mean, or axisymmetric valuê = complex amplitude

Numerical Investigation on Flow Field Distribution of Eccentric Compressors Based on Steady and Unsteady CFD Methods

“…Then Song [11] combined the continuity equation, axial and circumferential momentum equations with two shock disk models to analyze the effect of non-uniform tip clearance on compressor blade load. After 2000, with the introduction of active control and stall warning, more and more researchers have conducted experiments to investigate the relationship between non-uniform tip clearances and stall signals.…”