Because the whirl frequency is already a built-in parameter in the zeroth-order flow problem, it takes only a lateral eccentricity of the rotor axis for complete whirl excitation to materialize. It is important to understand the physical aspects of the flow field under such disturbance.

Consider the case where an observer is “attached” to the origin of the whirling frame of reference (see Figure 16.8) and is whirling with it. To this observer, the distortion of the flow domain is the result of an upward displacement of the housing (and not the rotor) surface. To the same observer, all nodal points in the original finite element discretization model will undergo varied amounts of upward displacement, except for nodes on the rotor surface which will remain undisplaced. As a result, varied amounts of geometric deformations will be experienced by the entire assembly of finite-elements in the rotor-to-housing flow passage (see Figure 16.8). Finally, the observer, whose rotation is at the rate of the whirl frequency Ω, will register a “relative” linear velocity of the housing surface whose magnitude is Ωrh, where rh is the local radius of the housing inner surface at this particular axial location, as shown in Figure 16.8.

With no lack of generality, consider the rotor position in Figure 16.13, where the nodes of the typical element (e) have been displaced by different amounts. The nodal displacements, as shown in the figure, depend on the original ycoordinate of each individual node.