high pressure pumps
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In actual practice, this assertion has been unequivocally confirmed by a statistical analysis of the measured efficiencies of high-quality, state-of the- art pumps. For example, the Europump ‘Efficiency’ working group, on which the TFA is represented, has elaborated and published a comparison of theoretical (i.e. calculated using ETAMAX) and actually achieved maximum efficiencies of single-stage volute casing pumps4. By way of an example from ref. 2, Figure 2 illustrates the theoretical upper limits for the internal efficiency of four-stage ring-section pumps similar to Type b
high pressure pumps
. The findings hold for profiled sealing gaps and, in particular, for hydraulically smooth surfaces. The maximum theoretically achievable overall efficiency (= internal efficiency x mechanical efficiency) can, however, be much lower than those shown in Figure 4, depending on the nature of the bearings and shaft seals.
Hub ratio
The so-called ‘hub ratio’ (DN/D1) in Figure 3 is another important geometric parameter, particularly with respect to multistage pumps
high pressure pumps
. For the findings shown in Figure 2, the hub ratio amounts to ν = DN/D1 = 0.3. According to the theoretical findings, increasing the hub ratio to, say, ν = 0.6 would cause a loss of efficiency amounting to some 1.5 to 4 percentage points (compare with figures shown in Figure 3, as taken from ref. 5), depending on the specific speed and nominal capacity.
Comparison of efficiencies
For the purposes of comparing the two types of high pressure pump for RO applications via ETAMAX, a representative nominal head and a constant speed of 50 Hz were postulated: thus H = 650 m and n = 2950 rpm.
The theoretically achievable efficiency was calculated for both types of pump assuming nominal volume flow rates of 400 to 2000 m3/h and stage numbers ranging from 2 to 5. Only design variants offering good efficiency (Figure 2) for specific speeds nq within the range 20–40 were considered. In order to account for the pumps’ normal production processes and operating environments:
  The roughness of the internal surfaces was assumed to be comparable to that of other good quality castings, but not hydraulically smooth, and
  The narrowest possible clearances were assumed for the sealing gaps around the impellers and stage casings.
As for the results illustrated in Figure 2, the Type b pumps were assumed to have a centralized balancing system with a piston and a volute casin