8. DAPROT3 INDUCER TESTS

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Chapter 8

8. DAPROT3 INDUCER TESTS

8.1. RESULTS AND DISCUSSION FOR COLD TESTS

From Figure 8.1 to Figure 8.18 the results obtained for DAPROT3 inducer from the experimental campaign performed in cold flow condition are illustrated. Specifically, the phase and modulus of the normal and tangential components of the fluid-induced rotordynamic force are shown, along with the hydraulic efficiency. The experiments have been carried out in water at 20 °C, corresponding to a condition in which thermal effects can be neglected as previously shown in chapter 3.5. Experimental curves reported in Figure 8.1 to Figure 8.9 and in Figure 8.10 to Figure 8.18 present the comparisons of the results obtained at different flow coefficients with fixed cavitation number and, respectively, at different cavitation numbers with fixed flow coefficient. Experiments with both discrete and continuously varying whirl speed have been conducted. Excellent agreement between the two approaches has been observed, thus confirming the validity of continuous tests, simplifying and speeding up the experimental campaign and allowing for accurate characterization of the spectral minima and maxima, as required for the determination of the most dangerous regimes of operation of the machine.

8.1.1. INFLUENCE OF FLOW RATE AT FIXED

CAVITATION NUMBER

The diagrams in Figure 8.1 and Figure 8.2 show the effects of the flow coefficient at cold noncavitating conditions. It can be observed that the lower the flow coefficient the higher the peak of the rotordynamic force modulus. A shift at higher whirl frequency ratios of the minima and maxima can also be noted. This behavior can be observed at moderate and highly cavitating conditions too, as illustrated in Figure 8.4, 8.5, 8.7, and 8.8.

In general it is possible to recognize different trends of the fluid-induced rotordynamic force at negative and positive whirl ratios, in good agreement with the findings of previous experiments. The “classic” results, obtained for centrifugal pumps and explained by Brennen (see equation 4.20), where the spectrum of FN is parabolic whereas that of FT is quasi-linear, have been observed only at negative values of ω/Ω. A parabolic trend for FN at positive whirl-ratios has been obtained only when the flow

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rate is higher than ΦD. A deviation from these trends can be observed as the flow coefficient is lowered, where minima and maxima arise both for normal and tangential forces.

The stability of the rotordynamic force can be easily assessed from the phase diagrams where the radial and azimuthal components are analyzed.

From Figure 8.1, two different considerations can be made:

• If ω/Ω < 0 the normal force is destabilizing (thus tending to increase the impeller eccentricity) when ω/Ω is lower than -0.24 or -0.3 depending on the flow rate. A stable operational condition is present at low whirl frequency ratios. On the other hand the tangential force is always stable and decreases as the flow rate increases.

• If ω/Ω > 0 the stability of the normal and tangential forces highly depends on the flow rate.

At Φ = 0.065 the normal force component is stabilizing for ω/Ω < 0.5 whereas at Φ =

0.078 for ω/Ω < 0.4. At lower flow coefficients the stability condition is verified over a wider range of whirl speeds. In particular, for Φ = 0.052 the normal force is always stable for any investigated positive value of ω/Ω. On the other hand, for 0.6 < ω/Ω < 0.7 the tangential force is always stabilizing whatever the flow rate. For Φ = 0.078 it becomes destabilizing when ω/Ω < 0.55. When lowering the flow rate several minima and maxima of the tangential force spectra appear and their amplitudes increase. In this case a stable regime is present, which shifts towards higher whirl frequencies and becomes wider at lower flow rates. For Φ = 0.052 this stable region occurs in the range from ω/Ω = 0.08 to 0.37. Finally, for design flow rate, the tangential force is destabilizing from ω/Ω = 0.11 to 0.52.

The stabilizing/destabilizing nature of both the normal and tangential components can be simultaneously assessed from the phase diagrams of rotordynamic forces. The diagrams also indicate that when a local minima of the rotordynamic force modulus is reached a rapid variation of its phase takes place.

Similar considerations can be made for Figure 8.4, 8.5, 8.7, and 8.8, where the results for moderate and highly cavitation conditions are presented. In Figure 8.7 and Figure 8.8 it can be seen that for Φ = 0.078 the normal force displays a much larger stabilizing region for negative whirl frequency ratios in the -0.5 < ω/Ω < 0 range. A lower flow coefficient is usually associated with an increase in the stability region of both the normal and tangential rotordynamic force components.

8.1.2. INFLUENCE OF CAVITATION AT FIXED FLOW

RATE

From Figure 8.10 to Figure 8.18 the influence of the cavitation number at fixed flow rates (Φ = 0.065, 0.078, and 0.052, respectively) and low temperature (T = 20 °C) is shown. At design flow rate a high levels of cavitation tend to destabilize the tangential force over a wider range of whirl ratios, whereas the influence on the normal force is negligible. Cavitation increases the range at high values of ω/Ω where both the normal and tangential forces are destabilizing (red region in phase diagram). In this case there is also a significant increase of the minima and maxima of the rotordynamic force intensity at positive whirl ratios.

Conversely, moderate levels of cavitation appear to stabilize the tangential force at negative values of the whirl speed, whereas they have no effect at positive whirl ratios.

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Similar considerations also apply to the tangential force at Φ = 0.078, whereas a peculiar behavior of the normal force is manifest at ω/Ω < 0 when σN = 0.088. Indeed high levels of cavitation delay the destabilization of the normal force from ω/Ω = -0.3 to ω/Ω = -0.5 and affect the rotordynamic force modulus as shown in Figure 8.14. This phenomena does not occur at moderate cavitation levels.

Finally, at low flow rates the effect of cavitation is clearly negligible (Figure 8.16 and Figure 8.17), whereas a considerable influence can be observed for the other conditions.

8.1.3. INFLUENCE OF ROTORDYNAMIC FORCES ON

THE HYDRAULIC EFFICIENCY

The experimental campaign has included the assessment of the rotordynamic effects on the hydraulic efficiency of the test inducer. During the experiments the static pressure rise across the pump has been measured by means of a differential pressure transducer with a precision of 0.08% and the volumetric flow rate by means of an electromagnetic flowmeter with a precision of 0.5%. As illustrated in more detail in chapter 5.2121 two assumptions have been made for the characterization of the inducer pressure rise:

• _{that the static pressure at the exit of the inducer is equal to the static pressure measured in}

the discharge line, and

• that Carter’s rule can be used to evaluate the azimuthal velocity at the exit of the inducer. The hydraulic efficiency of the DAPRTO3 at T = 20 °C and Φ = ΦD = 0.065 at zero eccentricity conditions (2 mm blade tip clearance, corresponding to 7.7% of the mean blade height) is equal to 82% (chapter 6.1.1). The results obtained for noncavitating conditions as a function of the whirl frequency ratio at different flow rates are presented in Figure 8.3 and demonstrate that the presence of rotordynamic forces and moments may affect the hydraulic efficiency by 1.5 to 1.6 % both at design and off-design conditions.

At moderate cavitation conditions (Figure 8.6) a significant effect can be observed for hydraulic efficiency at low flow rate where a difference of 2% can be obtained, depending from the whirl speed, whereas at design conditions there may be a maximum difference of 1%.

Finally at highly cavitation conditions (Figure 8.9) the same observations can be done for lower and higher flow rates, whereas at Φ = ΦD a higher influence of rotordynamic forces can be seen. Indeed a difference of 1.8% can be observed between low and high positive whirl speed, where a linearly decreasing trend with increasing ω is present.

The effect of the cavitation phenomena on the hydraulic efficiency is shown in Figure 8.12, Figure 8.15, and Figure 8.18, where the results for Φ = ΦD, Φ = 1.2ΦD, and Φ = 0.8ΦD are respectively reported. From the experimental curves it is clear that the presence of cavitation tends to slightly decrease the efficiency of the machine, whereas the only significant effect manifest at design, where a highly cavitation condition may yield to a decrease in 1.5%, with respect to the moderate cavitation condition at high whirl ratios.

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8.1.4. ROTORDYNAMIC FORCE DIAGRAMS

Figure 8.1 Influence of the flow coefficient on the nondimensional normal force (top) and nondimensional tangential force (bottom) of the rotordynamic force with σN = 1.015 and T = 20 °C.

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Figure 8.2 Influence of the flow coefficient on the modulus (top) and phase(bottom) of the rotordynamic force with σN = 1.015 and T

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Figure 8.3 Influence of the rotordynamic effects on the hydraulic efficiency (top) with close-up view (bottom) at different flow coefficients when σN = 1.015 and T = 20 °C.

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Figure 8.10 Influence of the cavitation number on the nondimensional normal force (top) and nondimensional tangential force (bottom) of the rotordynamic force with Φ = ΦD = 0.065 and T = 20 °C.

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Figure 8.11 Influence of the cavitation number on the modulus (top) and phase(bottom) of the rotordynamic force with Φ = ΦD =

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Figure 8.12 Influence of the rotordynamic effects on the hydraulic efficiency (top) with close-up view (bottom) at different cavitating conditions when Φ = 0.065 and T = 20 °C.

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Figure 8.13 Influence of the cavitation number on the nondimensional normal force (top) and nondimensional tangential force (bottom) of the rotordynamic force with Φ = 0.078 and T = 20 °C.

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Figure 8.14 Influence of the cavitation number on the modulus (top) and phase(bottom) of the rotordynamic force with Φ = 0.078 and T = 20 °C.

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8.2. OVERALL DIAGRAMS

A new kind of diagrams have been developed with the aim of summarize all the informations of rotordynamic forces in a single experimental curve. This new approach is based on the principle of Figure 4.6 where the normal and tangential stabilizing/destabilizing behavior can be represented on the whirl orbit. Since in this schematical representation the nondimensional rotordynamic force vector is reported at a specific whirl frequency ratio with the only information of its sign, the vector will be represented as a single point instead of its arrow and the variation of the whirl speed will be represented by a gradient of its color as shown in Figure 8.19.

Figure 8.19 Color gradient for whirl frequency ratio in overall diagrams.

Conversely two diagrams are necessary for this representation: one for positive whirl speed and one for negative. This separation is needed due to the different stabilizing/destabilizing regions of the tangential force which are symmetrically reflected with respect to vertical axis. As reported in the diagram legend four colors will define the stabilizing regions in the following way:

• green: stabilizing normal and tangential forces,

• yellow: stabilizing tangential force and destabilizing normal force, • orange: destabilizing tangential force and stabilizing normal force, • red: destabilizing tangential and normal forces.

Moreover the points are separated between each other by a gap of 0.01 of the whirl frequency ratio. This allows to understand the speed of transition between specific regions and a rapidly phase change can be observed by the scatter of the points.

Since in the present thesis the classic diagrams have been taken into account as a universally recognized approach, in the following Figure 8.20, Figure 8.21, Figure 8.22, and Figure 8.23, only the most significant results are reported. In the former figure, the nondimensional force vector diagram is shown for noncavitating condition, at design flow coefficient, and low temperature (T = 20 °C), whereas in Figure 8.21 the results at low flow rate (Φ = 0.052) are presented.

A different behavior between positive and negative whirl ratios can be observed. Indeed in the latter case a quasi-linear relation can be found between normal and tangential forces whereas an undefined relation is present for ω/Ω > 0. By a comparison of the results at different operating conditions in terms of flow rate and inlet pressure, as shown in Figure 8.22 and Figure 8.23 respectively, it is possible to confirm the linear trend at ω/Ω < 0 and it is also clear that the straight line shape tends to shift to the left both for decreasing cavitation number and flow rate.

The negative side effect of this kind of representation is the difficulty of showing a comparison between different operating conditions especially at positive whirl ratios.

In Appendix A.3 the matlab code exploited for the development of the overall diagrams is reported, as a part of the graphic_plot GUI.

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Figure 8.20 Overall diagrams of nonimensional rotordynamic force vector for positive (top) and negative (bottom) whirl frequency ratios for DAPROT3, at design flow coefficient and noncavitating condition (T = 20 °C).

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Figure 8.21 Overall diagrams of nonimensional rotordynamic force vector for positive (top) and negative (bottom) whirl frequency ratios for DAPROT3, at low flow coefficient (Φ=0.052) and noncavitating condition (T = 20 °C).

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Figure 8.22 Overall diagrams of nonimensional rotordynamic force vector for positive (top) and negative (bottom) whirl frequency ratios for DAPROT3, at noncavitating condition and different flow coefficients (T = 20 °C).

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Figure 8.23 Overall diagrams of nonimensional rotordynamic force vector for positive (top) and negative (bottom) whirl frequency ratios for DAPROT3, at various cavitation conditions and at Φ = 0.078 (T = 20 °C).

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8.3. RESULTS AND DISCUSSION FOR HOT TESTS

Figure 8.24-Figure 8.35 show the results of the experiments that have been carried out in water at 70 °C, corresponding to moderate thermal cavitation conditions. The influence of flow rate can be observed in Figure 8.24-Figure 8.29 whereas the effect of cavitation is shown in Figure 8.30-Figure 8.35. From the results it is clear that the peculiar behaviors observed in previous chapter for cold tests is verified also at T = 70 °C.

Indeed maxima and minima of rotordynamic force tends to shift towards higher whirl ratios for decreasing flow rate and at the same time an increase in the intensity is observed. Also in hot tests the deviation from the classic trend typically obtained for centrifugal impellers is present for flow coefficients equal or lower than design conditions. Conversely the parabolic and quasi-linear trend, for normal and tangential forces respectively, are verified for the highest flow rate corresponding to Φ = 0.078. On the other hand, these behaviors are respected at ω/Ω < 0 in any cavitation or flow rate conditions.

Figure 8.24 shows that the normal force becomes destabilizing for ω/Ω < -0.26 at all flow rates. A similar range is obtained for the other cavitating conditions. The lowest flow coefficient is generally associated to a more stabilizing behavior of normal and tangential forces, both at positive and negative whirl speed. The influence of the flow coefficient is generally confirmed also at moderate and highly cavitating conditions as illustrated in Figure 8.26, Figure 8.27, Figure 8.28, and Figure 8.29.

In Figure 8.26 a particular behavior can be observed for negative whirl speed since the range over which the normal force is stabilizing is wider for Φ = 0.078 as the destabilizing region shifts from ω/Ω < -0.23 to ω/Ω < -0.43. In previous chapter (see Figure 8.7), thus for cold tests, a similar trend has been observed in highly cavitating conditions, at the same value of flow coefficient. This would suggests the presence of some concomitant effects on the rotordynamic force as a consequence of the thermal cavitation phenomena since the higher temperature shifted the experimental diagram deviation from a highly to a moderate cavitating condition.

Figure 8.30-Figure 8.35 show the influence of the cavitation number at fixed flow rate (Φ = ΦD = 0.065, Φ = 0.078, and Φ = 0.052, respectively) for hot flow condition. For the lowest flow rate the effect of cavitation is clearly negligible and so for the highest, apart from the phenomena just explained for what concern the moderate level of cavitation. On the other hand, for flow coefficient at design, the presence of high cavitation tends to increase the peak of rotordynamic force intensity at positive whirl ratios.

A direct comparison between cold and hot tests, as reported in Figure 8.36 and Figure 8.37, show that the higher fluid temperature is associated with an increase in the normal force only at higher values of |ω/Ω|. Conversely, the effect on the tangential force can be considered as negligible.

Finally, for what concern the hydraulic efficiency, no differences can be observed from the statements made for cold tests since the only effect of the temperature is to shift the experimental diagrams of almost the same quantity independently from the whirl ratio. Indeed, a comparison between T = 20 °C and T = 70 °C is reported from Figure 8.38 to Figure 8.40 where the results for different cavitating conditions at design flow coefficient are shown. Moreover, in Figure 8.41 and Figure 8.42, the results at noncavitating conditions for Φ = 0.078 and Φ = 0.052 are presented.

It is clear that the loss in hydraulic efficiency is always higher for hot flow condition and it can be observed that these losses tend to increase with inlet pressure since the effect of higher temperature is to inhibit the collapsing bubble phenomena as previously seen in chapter 3.5. Hence the effect of

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cavitation on hydraulic efficiency is totally negligible at high temperatures, as verified also in Figure 8.43 by comparing it to Figure 8.12.

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Figure 8.36 Influence of the temperature on the nondimensional normal force (top) and nondimensional tangential force (bottom) of the rotordynamic force with Φ = 0.065 andσN = 1.015.

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Figure 8.37 Influence of the temperature on the modulus (top) and phase(bottom) of the rotordynamic force with Φ = 0.065 andσN =

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Figure 8.38 Influence of the rotordynamic effects on the hydraulic efficiency for different flow temperatures at Φ = 0.065 and σN =

1.015.

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0.088.

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1.015.

Figure 8.43 Influence of the rotordynamic effects on the hydraulic efficiency at different cavitating conditions when Φ = 0.065 and T = 70 °C.