## 11

The significant values of "m" are 0, 1 and 2. The lower the order of either the impeller blades or the diffuser vanes, the stronger is the interaction. The responses that occur for these "m" values are as follows:

• m = 0 - strong pressure pulsations and fluctuating axial loads and torsional forces.

• m = 2 - small pressure pulsations and a chance of resonance of the impeller about the two nodal diameters - at a frequency equal to the value of q x Zd times the rotational frequency (rpm or rps)

In this example, m = 1 in the second order of the impeller blades (i.e.. p=2); thus, the frequency of the resulting disturbances will be twice that of blade passing frequency p x Zj x rpm or 2 x 7 x rpm cycles per minute or 2 x 7 x rpm/60 Hertz. This is therefore a poor vane combination and should be avoided - especially for such low orders of vane number; i.e., for such small values of p and q, (Here, p=2 and q=l.) In general, m = 0 and 1 should be avoided altogether, and m = 2 should be avoided in the lower orders.

m = 1 occurs only in the highest orders of both and should therefore be of little consequence. Checking whether 10 or 11 vanes would be better yields m = 1 in the third order of impeller blades and second order of diffuser vanes, which is probably less desirable than m = 2 in the first orders. Therefore, Figure 33 shows a value of "Gap B" that is 12 percent of the impeller radius, which should provide adequate protection from pressure pulsations and excitations of resonance. (The gaps at the impeller OD will be discussed further on.)

Recirculation Separation and stall of the fluid flowing in the passages of impellers and diffusers occurs at low flow because of the incidence and large reduction in the one-dimensional velocity relative to the passage that happens at low flow. This and the con sequent recirculation patterns in the impeller were discussed and illustrated in Figure 6. Fischer and Thoma66 visually observed and recorded the flow patterns, finding that as flow rate is reduced, wakes on the suction side of all blades thicken until they occupy half the passage width at half the BEP flow rate. At lesser flow rates, the wakes continue to thicken but become irregular, stalling in one passage and not the others—the stall pattern moving into and out of adjacent passages and so rotating relative to the impeller. As shut-off is approached, this rotating pattern is accompanied by reversed flow emerging from the inlet of the stalled passage. Fraser, working with typical impeller geometries, formulated rules for computing the flow QSR at which this reversal occurs as Q is reduced at constant speed67. His expressions, found further on, include the effect of impeller eye size on QSR. As one might expect, a pump with an eye diameter approaching that of the impeller OD will have QSR approaching QBEP. At Q < QSR, the impeller flow patterns are highly unsteady—as is usually the case with massively separated flows—creating non-synchronous, low-frequency or random pressure pulsations, the resulting shear layers between the reverse-flowing and in-flowing fluid having vortices with locally low pressures so cavitation can also exist. Fraser also quantified the flow rate QDR below which impeller discharge recirculation exists. Forces from such motion can cause fatigue failure of the impeller blades, diffuser vanes or volute tongue, cavitation erosion also playing a part as in Figure 31. In Section 2.3.2, Fraser describes the identification and consequences of recirculation in detail, the more general designation QR referring to either QSR or QDR, depending on whether Q is between or below both.

The ability for pumps to operate with any form of separation; stall; or, worse, flow reversal (recirculation) depends on the energy level. This can be approximately quantified, as outlined under the subject of Minimum Flow Limit, further on, which include consideration of accompanying cavitation activity.

Axial Thrust Response to Recirculation Discharge recirculation usually involves backflow from the diffuser, itself containing oscillating flow patterns and rotating stall. Fluid emerging from the diffuser will be spinning opposite to the direction of rotation, such fluid having a major effect on the sidewall gap flows as it joins the leakage flows described under Predicting Axial Thrust. As this fluid invades the sidewall gaps, it can slow or virtually cancel the usual positive swirling of the gap fluid. Iino, Sato, and Miyashiro experimentally observed and recorded this behavior, which was exaggerated by shifting the impeller axially and by changing the ring clearances68.

An added, not unexpected effect is that as Q is reduced below QDR, the invading flow from the diffuser can favor the front or back side of the impeller and then switch sides upon further reduction of Q. This effect is clearly seen in the experimental thrust-versus-Q plots of Figure 34, the impellers having been shifted as just described. Depicted there is the resulting net load on the axial thrust bearing of an eight-stage, 3600-rpm diffuser pump that had a cylindrical balancing drum (not a self-compensating balancing disk). The drum was sized so as not to completely eliminate the thrust—in order to avoid thrust reversals. The solid lines are the predicted net thrust according to the methods outlined in Table 4 for three axial positions of the impeller. The large excursions in net thrust were eliminated by restricting the entry of the invading diffuser backflow into the sidewall gaps —through a tightening of the gap between the shrouds of impeller and diffuser (Gap "A") in Figure 35. Gap "A" is not effective unless the "overlap" of the two mating shrouds is from four to six times the gap dimension61. Moreover, if Gap "A" is minimized, this can exaggerate the blade-vane interactions, making it necessary to open up Gap "B" more than would be necessary were Gap "A" not minimized69.

A further possibility that has been observed in a single-stage double-suction pump is the unsteadiness of impeller discharge recirculation and, most likely, of the diffuser or volute backflow. The side-to-side switching just mentioned appears in Figure 36 to be happening as a function of time as well as of flow rate Q, as evidenced by the axial motion, which is accompanied by discharge pressure pulsations. The "fix" mentioned in the figure was, again, mainly minimizing Gap "A."

Closing Gap "A" and opening Gap "B" are procedures that have been widely and successfully applied in high-energy pumps, which usually work well at BEP but run into difficulties at low flow69. The procedures have proven to cure the thrust and pressure lbf 20,000 16,000 12,000 8,000 4,000 0

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