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Primary Cause of Rotor Self-Excitation
One of the greatest limitations of centrifugal compressors and pumps is that they prefer to operate at a specific revolution speed. Any move away from the best efficiency point (BEP) has a cost due to inefficiencies of a mismatch in the angles of incidence in the main flow, as well as limitations imposed by the growing imbalances in the secondary flows that potentially excite the rotor.
Leakage flowing through the impeller front and the back side cavities is referred to as secondary flow vs. the main flow through the impeller itself. Side cavities provide an alternate flow pathway (back to suction) through gaps at the impeller tip and eye/shaft seals. Ignoring flow reversals in the main flow, aggregate radial flow through the front cavity is always from periphery to eye seal. Aggregate flow through the back cavity can be in either direction, depending on operating conditions and whether it is a mid or final-stage of the machine. In any event, given the much larger pressure differential from periphery to hub in the front side cavity vs. the back, together with its associated higher leakage rate, forces acting on the rotor and generated in the front cavity are much more responsible for rotor self-excitation. Only front side cavity effects will be discussed further.
Self-excitation refers to the phenomenon where impeller rotation induces swirl in the front side cavity, and in turn, this energy (momentum) contained in the fluid (pre-swirl) drives self-excitation. The rotating shroud induces fluid rotation in the front side cavity. Bulk swirl velocity in a front side cavity having no leakage flow is steady at ~.45x. Swirl velocity of leakage flow entering through the impeller tip gap is ~1.0x. Therefore, the rate (and dynamic nature) of transit leakage flowing through the impeller front side cavity is responsible for the extent and dynamic nature of swirl velocity in the cavity. In turn, these changes in the leakage rate impact the magnitude of radial oscillations of the rotor and the level of axial thrust forces produced in the cavity.
The level of axial thrust generated in the front side cavity is a product of the bulk pressure in the cavity and the shroud area/ profile. In a front side cavity having no leakage flow, the rotating shroud centrifuges fluid, inducing a bulk fluid swirl velocity of ~.45x. A pressure decline toward the hub is established to recirculate the centrifuged fluid. Increasing the bulk swirl velocity reduces the pressure near the hub even more, reducing axial thrust forces generated in the cavity, therefore increasing residual axial thrust toward the thrust bearing at front. Leakage entering through the impeller tip gap has a high swirl component (~1.0x). Commonly during extreme operating conditions, the leakage rate increases dramatically and has a highly-variable/dynamic/chaotic character. This translates directly into the extent and dynamic nature of the level of axial thrust generated.
Radial displacement of the rotor is impacted by changes in the swirl velocity in the front side cavity in two ways. First, fluid in the front cavity imposes viscous drag forces on the rotating shroud, so the level of radial damping provided by the shroud is affected by the bulk swirl velocity in the cavity. These viscous damping effects on the shroud have been found to exceed those imposed at the eye seal by two times or more in high-pressure applications. Therefore, increasing swirl velocity via increased leakage will reduce damping, which increases the rotor orbit. Second, increasing bulk swirl velocity increases cross-coupled stiffness (k) at the eye seal and along rotating shroud, and increasing k increases the range of positive whirl where tangential forces are destabilizing. The result is a sub-synchronous resonance at whirl speed (inducing whirl, and potentially whip).
Leakage increases with eye seal wear or damage. As noted, increasing leakage reduces radial damping, increasing the rotor orbit. Also, increasing leakage increases the swirl velocity in the cavity, reducing pressure near the eye seal, and therefore increasing residual axial thrust toward the front. The thrust bearing must accommodate the full range of anticipated axial thrust forces generated in the cavity over the life of the eye seals. Seal wear is a major determinant regarding mean time-between-service intervals.
As revolution speed declines below BEP and the machine approaches stall, the leakage rate grows dramatically and becomes increasingly volatile and circumferentially non-uniform. Stall is characterized by partial to full flow reversals in the main flow, and these conditions migrate into the front cavity through the impeller tip gap and heavily impact pre-swirl in the front cavity. Given their linkage to the leakage rate, the radial orbit and axial thrust generation are directly affected. The forces generated can be violent and destructive, especially when compounded by increased leakage associated with worn or damaged eye seals. Given startups and shutdowns, operating within stall cannot be fully avoided.
To address the negative consequences of high or variable swirl velocity in the front side cavity, the primary tool has been circumferential protrusions/ fins affixed to the casing that oppose tangential flow, destroying the swirling flow structure. They are often employed near the eye seal entrance (so-called swirl breaks) to improve entrance conditions to increase damping and reduce cross coupling.
In higher-pressure applications where self-excitation is of greater concern, protruding fins are sometimes employed in the periphery of the cavity (thrust breaks). They reduce bulk swirl velocity in the cavity to reduce residual axial thrust, to increase damping and to mute excitation sources. Thrust breaks are avoided whenever possible because of their not small efficiency penalty. They waste the energy contained in swirl; and eddy structures formed in the wake of thrust breaks evolve with rotating speed, making their performance not as uniform/ predictable as would be desired along the full radial length of the shroud and at the eye seal entrance. Their benefits plateau at high revolution speeds.
To summarize, transit leakage through the front side cavity is the greatest contributor to the self-excitation phenomenon in centrifugal compressors and pumps, having a significant impact on both radial displacement and residual axial thrust generation.
PERIPHERAL DIFFUSER WITH RETURN CHANNEL
One possible solution is a peripheral diffuser and return channel for secondary flow in the front side cavity. The front cavity is enlarged, and an annular disc with de-swirl vanes (on the casing side) is attached to the casing wall. A ring is press fit into the periphery of the front side cavity (see diagram on previous page).
Fluid circulates radially around an annular disc, and flow is circumferentially diffused at the periphery. Fluid is centrifuged out by the rotating shroud and flows into peripheral diffuser. Leakage enters through impeller tip gap and flows into peripheral diffuser. The peripheral diffuser promotes circumferential equalization of fluid. Fluid exits the peripheral diffuser at its inner radius, flowing into a side cavity adjacent to casing having de-swirl vanes that efficiently remove swirl and redirects flow to eye seal. The swirl velocity of the fluid at the exit of the vanes near the eye seal is circumferentially uniform, as is pressure, which is slightly above impeller tip pressure. Its design and function are similar to part of the main flow in a mid-stage section (an open diffuser, 180° bend and return channel to hub).
This front side cavity design creates a tortuous pathway to protect areas most susceptible to excitation (eye seal entrance and along rotating front shroud) from the primary excitation source (impeller tip leakage). It provides near-optimal conditions at the eye seal entrance (no swirl and circumferentially uniform in pressure) as well as along the rotating shroud (no swirl, circumferentially uniform in pressure, and an outward-only radial flow (inward transit leakage flow is shunted to the hub separately). Changes in the leakage rate are now de-linked from affecting the radial orbit of rotor or the level of axial thrust forces generated in the front cavity. In effect, there is no potential for self-excitation due to forces generated in the front side cavity.
By eliminating the potential for self-excitation, a number of rotordynamic limitations are removed, expanding the operating envelope. Rotordynamic imbalances occurring during stall and surge are caused primarily by the effects of leakage flowing through the front side cavity. Now that leakage is shunted away and conditioned separate from areas susceptible to excitation, it is likely that the instability thresholds encountered on either side of BEP will be pushed out if not eliminated. Given that swirl velocity in the front cavity is de-linked from leakage rate changes, there is no potential for whirl or whip, so these operating regions need not be avoided. Additionally, as the flow pattern in the side cavity with rotating shroud is similar to that of a pressurized spindle bearing (circumferentially-uniform pressurized fluid fed at hub, and outward-only radial flow with no pre-swirl), significantly higher revolution speeds may be attainable.
Compared to thrust breaks, this design provides a better solution to pre-swirl in the cavity and self-excitation, including the potential for higher revolution speeds. Importantly, the efficiency penalty is much less than with thrust breaks, if any at all. ■