4.1. Verification of Corrected Cavitation Model Reliability
NACA0015 hydrofoil is chosen to verify the reliability of the corrected cavitation model and its parameters are as follows: the chord length is 115 mm, the wingspan is 80 mm, the angle of attack is adjustable (4°, 5°, 6°, and 8°). During the experiment, three pressure taps are set evenly at 100 mm in front of the hydrofoil and at 140 mm in rear of the hydrofoil. Meanwhile, ten pressure taps were arranged on suction surface of NACA0015 hydrofoil, and two pressure taps were arranged on pressure surfaces of the hydrofoil, which are all shown in
Figure 3. Three-dimensional model of numerical simulation is shown in
Figure 4. Detailed description about the experiment is referred to reference [
9,
10].
The total mesh number reaches about 1.01 million, the whole meshes and the partial view of the head and tail of hydrofoil are shown in
Figure 5. The average
y+ value of mesh in suction surface of hydrofoil is 21.2 while in pressure surface is 18.5 as shown in
Figure 6. The boundary conditions are consistent with the experiment, which applied speed as the inlet boundary condition and used static pressure of mandatory outflow as outlet boundary condition. The suction surface and the pressure surface of the hydrofoil are set as slip-free solid wall, and both sides are symmetrical. Surface roughness of hydrofoil is ignored and the convergence precision is set as 10
−5.
The pressure distribution coefficient in hydrofoil surface is obtained through corrected cavitation model at 70 °C, and its default evaporation and condensation coefficients are 0.01 and 50 respectively. Besides, the value of pressure distribution coefficient in surface of hydrofoil is compared with the experimental values, which is shown in
Figure 7. As can be seen from the figure, the numerical data meets well with the experimental data in the rear of the hydrofoil, but large difference exists in the head of hydrofoil where the chord length ratio ranges from 0.1 to 0.4. Compared with the results in reference [
17] that applied the full cavitation model with the adjunction of energy equation, the corrected cavitation model in this paper is much more precise than that of cavitation model.
Considering the impact of evaporation and condensation coefficient, other two groups of coefficients are defined as 10, 0.002 and 1, 0.0002 based on experience. Diagram of the pressure distribution coefficients in hydrofoil surface are contrast when cavitation model is under three different evaporation and condensation coefficients at 70 °C, which is shown in
Figure 8. As can be seen in the figure, when the evaporation coefficient is 10 and condensation coefficient is 0.002, the numerical data is in best agreement with the experimental data. Along with the decrease of condensation and evaporation coefficient, pressure coefficient distribution curve tends to be smooth gradually. However, when evaporation coefficient is 1, several important turning points of chord ratio did not appear, the growth rate of bubbles was inhibited, the volume fraction of bubbles becomes lower, the shape of the bubble zone becomes flat. Therefore, the thermodynamic effect have been considered in the cavitation model of this study, and evaporation and condensation coefficient are respectively 0.002 and 10, which are set as the same in reference [
16].
4.3. Bubble Morphology in the Forming Process of Cavitation at 25 °C
The appearance of bubbles is the most intuitive cavitation phenomenon. The larger the bubble volume fraction is, the more serious the cavitation phenomenon is. Meanwhile, if bubbles flow to the high pressure zone it will collapse and cause cavitation damage, which can seriously damage the safe and stable operation of the pump.
Figure 10 shows cavitation formation processes and distributions in ECWP under different inlet pressures when the internal volume fraction of bubble is 0.1, the temperature is 25 °C, flow rate is 150 L/min with 3700 r/min rotation speed. When inlet absolute pressure is comparatively high, cavitation does not occur in impeller. With the reduction of inlet absolute pressure, bubbles firstly occur at the blade inlet side near the suction surface, which is called cavitation inception. Along with the further reduction of inlet absolute pressure, net positive suction head (
NPSH) decreases gradually while bubble distribution area expands, bubbles expand gradually from suction surface to pressure surface. During this process, cavitation gets developed. When the absolute pressure of pump inlet continues to decrease below the critical cavitation point, the quantity of bubbles will have a significant increase, the bubbles begin to clog the entire flow path of impeller, the bubbles will collapse when flowing to the high-pressure zone. The impeller will be shocked and eroded strongly when bubbles collapse, which will cause cavitation damage and significant decline in external characteristic of pump.
Impeller inlet parameters have signification impact on the internal impeller cavitation, and impeller cavitation area is mainly near the suction surface in the impeller inlet. In order to learn more details about cavitation bubbles, the distribution of bubbles in different cross-sections of impeller is researched in this study. The relative position of blade and tongue is shown in
Figure 11a. Three selected axial cross-sections (Planes 1–3) are shown in
Figure 11b.
The interphase mass conversion of different cross-sections, which obtained under 40 kPa inlet pressure condition, is shown in
Figure 12. As can be seen from the figure, in these three cross-sections, the areas where cavitation is generated are all near suction surface of blade inlet, bubbles flow to the suction surface near the mid and fore sections of blade (as is shown in red area) and condense in there. At the same time, due to the impacts of volute passage and tongue, the cavitation degrees of different blades along the circumferential direction are totally different. There is no bubble on the suction surface of two blades that have just passed through the volute tongue, and the cavitation on the blades far away from the tongue is more serious. Although bubble distribution in three kinds of blade cross-sections is similar, but the degree of cavitation in different cross-sections is different. From cross-section 1 to cross-section 3 (the diameter of inlet flow line becomes larger gradually), the region where cavitation occurs increases, the area of these region becomes larger, which indicates that the cavitation degree is more serious close to trailing edge, the cavitation is comparatively lighter on cross-section 1 where the inlet diameter of the impeller streamline is larger. On the other hand, it also implies that the inlet diameter of the impeller has a great impact on the cavitation performance, the better blade inlet environment means stronger anti-cavitation ability. Namely, the uniformity of the flow upstream of the impeller inlet is a significant method for reducing cavitation in vane pumps [
29,
30].
4.5. Unsteady Cavitation Evolution in ECWP
As can be seen from the above, temperature plays a catalytic role in the cavitation effect of ECWP. Cavitation is most significant at 70 °C when the inlet pressure is 40 kPa, and the vortex in the pump is also very chaotic. At the same time, the daily working temperature of ECWP is about 70 °C, so the modified cavitation model is used to calculate the unsteady simulation of ECWP at 70 °C, to explore the transient process of cavitation and the impact on the performance characteristics of the pump.
Figure 17 shows the transient pulsation process of dimensionless head at 70 °C and explores the unsteady relationship between cavitation and performance characteristics.
Figure 17a shows the transient pulsation process in the time range of 0~90
t*, where
t* represents the time required for impeller to rotate for one circle, and
Figure 16a shows the head fluctuation process of impeller rotating for 90 circles.
Figure 16b shows the local pulsation characteristic curve of 5
t*~10
t*.
As can be seen from the figure, the head waves with time with irregular pulsation characteristics at 70 °C. In the range of 0~10
t*, the amplitude of head pulsation is very large, and the characteristics of head pulsation show obvious periodicity. The time length of large-scale wave is about 4.35
t*, and cavitation plays a leading role in the performance of ECWP. However, in the range of 12
t*~27
t*, the amplitude of head pulsation weakens and shows stable pulsation. Therefore, the cavitation effect in ECWP is weakened and the distribution of volume fraction changes steadily. Then the cavitation effect increases gradually, and the head shows large-scale pulsation. At 50
t*~65
t*, the cavitation effect weakens to the extreme again, showing the same pulsation as that of 12
t*~27
t*. Then, with the increasing cavitation effect, a large-scale wave with the time range about 4.35
t* appears again. Then, the pulsation process of head is accompanied by the weakening, stability, and enhancement of cavitation. Meanwhile, as can be seen from
Figure 17b, in each impeller rotation cycle
t*, there are seven peaks and troughs in the head fluctuation curve, corresponding to seven blades of the impeller. Therefore, when cavitation affects the head of ECWP, the circumferential rotation effect of impeller also plays a corresponding role in head pulsation.
In a single large-scale wave, namely the single vapor developing period (5
t*~10
t*), take seven different times from a to g, the variation law of vapor volume fraction in single vapor developing period is calculated, shown in
Figure 18. In a single large-scale wave, bubble appears the process of periodic collapse, birth, development, and collapse. Therefore, the volume fraction of vapor has a periodic oscillation relationship, which is inversely proportional to the head.
To analyze the frequency characteristic of pressure fluctuation, time domain data is transferred to frequency domain using fast Fourier transform (FFT) [
32,
33,
34].
Figure 19a shows the frequency spectrum of head fluctuation in impeller,
Figure 19b shows the local frequency spectrum, the range is 0~100 Hz. As the sampling frequency is 3700 Hz, the shaft frequency
fs is 61.67 Hz, and the blade passing frequency
fb is 431.69 Hz.
As can be seen from the figure, the main frequency is composed of two parts under the cavitation condition of ECWP at 70 °C, including low frequency below 100 Hz and blade passing frequency (fb = 431.69 Hz). The low frequency part is the uneven pulsation caused by the periodic initiation, development and collapse of cavitation. Through further analysis of the low-frequency components, it is found that the main low frequency consists of the two components, Where f1 = 0.65 Hz, f2 = 14.2 Hz. It can be seen from the above that the propagation period of large-scale wave is 4.35t*. Therefore, the frequency of f2 corresponds to the large-scale wave, f2 is the cavitation frequency.
As FFT cannot reflect the change process of frequency with time, wavelet transform is used to explore the unsteady process of cavitation frequency amplitude with time, shown in
Figure 20. As can be seen from the figure, the cavitation frequency
f2 and blade passing frequency
fb alternate into dominant frequency in the time range of 0~90
t*.The main frequency components after wavelet transform are consistent with the above, namely
fb and
f2, and the lower frequency
f1 is not captured due to the insufficient data. It can be seen from the figure that the frequency of
f2 does not change with time as the impeller rotates in the circumferential direction, and keeps a fixed value. With the impeller rotating, the main frequency which affects the head pulsation of ECWP is changing alternately. Especially in 15
t*~30
t*, with the decrease of cavitation effect, the rotor and stator interference effect is enhanced,
fb replace
f2 as the dominant frequency. Then, the influence of cavitation process on the head pulsation becomes more and more serious, while the rotor and stator interference effect decays after maintaining stability for a period of time, and
f2 replaces
fb as the dominant frequency. From
Figure 20b, we can more clearly observe the unsteady process of cavitation effect. It is not only the initiation, development and collapse of bubble in a single large-scale wave (like 5
t*~10
t*), the cavitation effect is also in the process of strengthening, stabilizing, and weakening. The period of cavitation effect is much longer than that of bubble developing period, constitutes an extremely low frequency as low as 0.65 Hz.