Highenergy Pumps

Over the past few decades, there has been a trend toward pumping machinery that concentrates more power within a given volume. This trend is driven by cost and technology improvements. The basic energy transfer relationships show that smaller size demands higher rotative speed. Thus, over the same time period, speeds of high-power pumps have been increasing. Moreover, the number of stages in multistage pumps has been decreasing. There have been spikes in these trends; the resulting pumps suffering from excessive vibration, rotor and hydraulic instabilities, component failure, and cavitation damage57. The term "high energy" has been applied to these machines, and this label can be quantified in terms of the stresses arising in critical pump components and the likelihood of an adverse mechanical response that such stress levels imply. Research has led to technical solutions for effectively controlling rotordynamic behavior and reducing unsteady hydraulic thrust and surge as well as cavitation erosion63,68,69. The resulting pump reliability improvements and life extension should enable the previous trends to continue. Being aware of the energy level enables the pump user to assess whether operation and maintenance difficulties are likely to occur after the pump is installed and running, and it enables the designer to take the appropriate measures to ensure the technical integrity of the product.

Pressure Pulsations Measured at the inlet or outlet port, the amplitude of the pressure pulsations can be a significant fraction of the pressure rise of the pump—especially at flow rates well below that of the BEP for the speed involved. Sources are a) the interaction of the pressure fields of the impeller and diffuser or volute, b) unsteady separated and reversed flows at impeller inlet and discharge and in the diffuser, c) cavitating flows, and d) combinations of these phenomena. Pressure pulsations presumed to exist at the impeller OD from the interaction of impeller blade-to-blade and diffuser vane-to-vane variations of pressure have been calculated by inviscid flow analysis to have a peak-to-peak amplitude that is of the same order as the static pressure rise of the impeller60. Moreover, the viscous, thicker wakes existing at lower-than-BEP flow rates (here called "low flows") and separated recirculating fluid from both impeller and diffuser that participate in these interactions can be expected to increase the pressure pulsation amplitude at such conditions.

Figure 31 confirms these ideas, showing a bronze impeller that operated extensively at low flow. Cavitation pitting can be observed near the OD of the impeller, which means that the rarefactions of the pressure waves were below the vapor pressure of the liquid—these pressure minima therefore being below the inlet pressure to the impeller. Moreover, the bulged-out shrouds can be assumed to be the result of the repeated occurrence of the associated pressure spikes (that is, the maxima of the pressure waves) within the radial gap ("Gap B") between the impeller blades and the diffuser vanes, the sidewall pressures on the outsides of the shrouds remaining comparatively constant. At greater values of design pressure rise than was the case for this impeller, this phenomenon creates correspondingly greater forces that have led to actual breakage of the impeller shrouds and diffuser vanes61. The cavitation seen in Figure 31, can also be observed on the leading edges of diffuser vanes, as in Figure 21 of Section 9.5, and this raises the possibility of diffuser vane breakage.

Energy Level: Stage Pressure Rise Even in the absence of the weakening effect of cavitation erosion, the leading edge of a diffuser vane or volute tongue is a representative, highly stressed zone within a pump that is subject to failure if the magnitude of the pressure pulsations arising from the impeller-diffuser interactions just described is sufficiently large. Thus, the hydraulically induced stresses in these vanes can be the basis for quantifying the energy level of a pump stage. In Table 12, this concept is developed into an expression for the stress in terms of the fluctuating pressure magnitude Sp that is assumed to act across the vane leading edge as illustrated in the table. The width b of the vane is close enough to b2 of the impeller exit to utilize the relationships for C and fi of Figure 12 to relate b/D to specific speed in Eq. (c) of the table. For similar velocity fields, the pressure pulsation magnitude Sp is a constant multiplied by the stage pressure rise APstg. Thus, for a limiting value of stress, the concept of a limiting stage pressure rise

FIGURE 31 Damage to impeller from low-flow operation (Source: E. Makay in Power)

emerges in Eq. (e). The constant K is chosen from experience, which leads to the resulting Eq. (f). This relationship is plotted in Figure 32. [It will be observed that this choice for K corresponds to a limiting stress s from Eq. (d) of 6,600 psi (45.5 MPa) that would exist if Sp were equal to APstg—with t/D = 0.01 and e = 0.85 as in the example.] The inverse variation with specific speed is a consequence of the greater b/D of higher-Hs pumps (as developed in Table 12), the wider vane introducing more stress at the juncture with the sidewalls for the same pressure loading and so imposing a lower stage pressure-rise limit. Conversely, lower-Hs pumps should have higher limits for APstg.

Figure 32, therefore, illustrates this concept of a limiting stage pressure rise as a measure of the energy level of centrifugal pumps, the basis being a limiting stress level in a critical component of the pump. Starting with stress at other locations in the pump leads to similar results. To provide perspective, specific examples of pumps that by this definition are in the high-energy domain are plotted on the figure. These data points are taken from Table 13, which contains information for several well-known liquid rocket engine turbo pumps62,63,64 and for some representative high-energy electric utility boiler feed pumps53,57.

The last column in Table 13 is another, more general way of comparing the energy level of these machines; namely, the torque per unit volume, which also has the dimensions of stress. For fixed ratios of stage width, casing OD, and other dimensions to impeller radius r (= r2), torque per unit volume differs from the listed values of torque/r3 by a factor. The actual torque per unit volume therefore ranges from one-half to one-sixth of the tabulated

2.1 CENTRIFUGAL PUMP THEORY TABLE 12 Hydraulically induced stress levels

torque/r3, depending on the casing or barrel thickness, and so on. However, as has been demonstrated, the critical stresses are more closely associated with the impeller OD, which makes comparison of the tabulated values more relevant. Thus, a pump with high torque/r3 can be expected to have correspondingly high local internal stresses. The maximum values listed, namely for the high-pressure propellant pumps on the RD-170 (Russian) and SSME (U.S. Space Shuttle) engines, tend to explain the high level of research and development that was necessary to successfully deploy these machines. Illustrations of some of these rocket engine pumps can be found in Section 9.19.2. Similarly, Section 9.5

1000 2000 3000

FIGURE 32 Pump energy level defined in terms of stage pressure rise provides examples of high-energy boiler feed pumps: the massive, barrel-type construction of these machines is illustrated in Figure 18. Specifically, the first boiler feed pump listed in Table 13 is the sole feed pump supplying the steam generator of a super-critical 1300 MW electric generating unit and consumes nearly 50 MW of shaft power. It can be seen in Figures 7 and 20 of Section 9.5.

For pumps in the low-energy domain of Figure 32, normal design and manufacturing practices result in a more benign mechanical response to the abnormal fluid phenomena discussed here. However, for locations other than the diffuser entrance, which was the basis for the development of the figure, limiting stresses could be reached at considerably lower values of stage pressure rise. For this reason, the dashed line is offered as the upper limit of the low-energy domain; however, a thorough analysis of the stresses in any given application is the ultimate determinant of all the limits suggested in Figure 32 and of the acceptability of the design. It can now be seen that the design example treated earlier in this section is of the low-energy variety; therefore, the special design problems treated here and further on are of relatively little concern in such pumps. On the other hand, if the curve in Figure 32 were extended to much higher specific speeds, it would be found that many existing, large, high-Hs, low-head pumps are high-energy machines by this stress-related definition. It is therefore not surprising that such pumps generally require full stress and modal analyses to identify possible destructive resonances and stresses.

Fluid/Structure Interactions With the dimensions of pump energy level identified, the next step is to continue the examination of the problems mentioned previously and the methods that have become available for solving them. Attention is focused on hydraulic phenomena because, as the previous discussion of pressure pulsations implies, most of the adverse mechanical behavior exhibited by pumps originates from the behavior of the internal flow field. Excessive measured vibrations, material erosion, and component failures are often the external symptoms of fluid/structure interaction phenomena that are fundamentally explained from a hydraulics perspective. In addition to the hydraulically

TABLE 13 Data on high-energy pumps*

Pump

No. of stages

(m)

("s)

Torque/r3 psi (MPa)

Liquid Rocket

Propellant

Turbopumps

Saturn V Booster -Fl Engine: Oxygen

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