Abstract
Through numerical simulations, this work analyzes the unsteady pressure pulsation characteristics in new type of dishwasher pump with double tongue volute and single tongue volute, under volute static and rotation conditions. Likewise, the performance tests were also carried out to verify the numerical results. Multiple monitoring points were set at the various positions of new type dishwasher pump to collect the pressure pulsation signals, and the relevant frequency signals were obtained via Fast Fourier Transform, to analyze the influence of volute tongue and its passive speed on the pump performance. The results reveal that when the double tongue volute is stationary, the pressure pulsation amplitudes increase from the impeller inlet to the impeller outlet. Under the influence of shedding vortex, the pressure pulsation in the lateral region of tongue becomes disorganized, and the main frequency of pressure pulsation changes from blade frequency to shaft frequency. In addition, compared with the static volute, double tongue volute can effectively guide the water flow out of the tongue during the rotation process, thus ensuring good periodicity for pressure pulsation in the tongue region. Accordingly, a volute reference scheme with passive rotation speed is proposed in this study, which can effectively improve the pressure pulsation at tongue position, and provides a new idea for rotor-stator interference to guide the innovation of dishwasher.
1. Introduction
Using a combination of volute and spray arm, new dishwasher pump realizes open cleaning without the pipeline, thereby indicating the following advantages: no pipeline dirt, short cleaning time, and labor and water saving. However, the innovative volute undergoes passive rotation under the combined action of impeller rotation and nozzle jet, and the internal complex flow in new dishwasher pump affects its performance, especially the new rotor-stator interference between compound impeller and double tongue volute with passive rotation speed. Similarly, the pressure pulsation produced under the rotor-stator interference reduces the system stability and the service life [1–3]. Moreover, the noise generated by pressure pulsation affects the user experience significantly, which is undesirable for a matured product.
Correspondingly, many researchers have addressed the pressure pulsation in the pump through experimental and simulation methods. For instance, Wang et al. [4] conducted an experimental study on the pressure pulsations in a mixed flow pump under different operating conditions. Acquired results suggested that the larger the flow rate was, the smaller the peak value of pressure pulsation was, and the frequency domain was dominated by blade passing frequency and multiple shaft frequency. Yang et al. [5] analyzed the pressure pulsation characteristics in a three-stage electrical submersible pump by experiments and numerical simulations. This research showed that the rotor-static interference between the impeller and the guide vane was a direct cause of pulsation. In another work, Zhang et al. [6] experimentally investigated the influence of different blade cutting angles on the pressure pulsation of centrifugal pump and highlighted the usefulness of cutting blade in reducing the pressure pulsation in the process of pump operation. Yang et al. [7] discussed the influence of water compressibility on pressure pulsation of centrifugal pump and indicated that the compressibility of water affects the amplitude of pressure pulsations at some discrete frequency. Feng et al. [8] studied the influence of tip clearance on pressure pulsations in an axial flow water pump via numerical simulations. It was found that the tip clearance had a great influence on the pressure pulsation in the impeller area; nevertheless, no influence was observed in the diffuser area. Tan et al. [9] performed a numerical analysis to investigate the influence of blade rotational angle on pressure pulsation and proved that the main frequency of pressure pulsation in impeller was dominated by shaft frequency or blade frequency. Furthermore, Zhang et al. [10] explored the relationship between fluid pressure pulsation and structural vibration characteristics of a vertical axial pump. It was confirmed that the rotating blades had similar frequency characteristics in both the fluid domain and the solid domain. In one related work, Pei et al. [11] introduced the pressure pulsation intensity coefficient and peak pressure coefficient, to provide a new way for evaluating the pressure pulsation. Similarly, Cao et al. [12] observed that the higher the amplitude of pressure pulsation, the larger the distribution range of frequency domain and the larger the frequency component in rotor-stator interaction zones. Shi et al. [13] noticed that the blade angle deviation led to an uneven pressure change in the impeller passage and substantially affected the safe and stable operation of axial flow pumps. In addition, Kc et al. [14] also analyzed the pressure pulsation of rotor-stator interaction in a Francis turbine. This study inferred that higher and lower dominant frequencies were determined by the impeller speed and the number of guide vanes, respectively.
The structure and parameters of the volute, an important part of the pump, play a key role in the pressure pulsation [15]. Chalghoum et al. [16] proved that the pressure pulsation was periodic due to the relative position of impeller blade to volute tongue, and the period of pressure pulsation in time domain was the same as the number of blades. Chalghoum et al. [17] also studied the influence of different volute shapes on pressure pulsation in the centrifugal pumps. The results revealed that the pressure pulsation amplitude of tangential diffuser was larger than that of radial diffuser. Shim et al. [18] carried out a multiobjective optimization for double volute centrifugal pump with diaphragm, where the pressure pulsation for the optimized model was reduced, significantly.
However, only a few research studies discuss the pressure pulsation caused by the interaction between special double tongue volute (formed by 180° array of a single tongue volute) and compound impeller (combined with axial flow blade and centrifugal blade). At present, most of the research on pressure pulsation in the pump is based on the static condition of volute, while the literature on pressure pulsation under the rotating condition of volute is scarce, which initiates an urge to carry out required relevant research.
2. Numerical Simulation Methods
2.1. Computational Domain
The fluidic domains of physical model are given in Figure 1, which are mainly composed of inlet, water guide ring, double tongue volute, and compound impeller. The bottom end of compound impeller is a forward-curved axial flow blade, while the top is a radial centrifugal blade, and there are no obvious front and back shrouds. Besides, the fluid flows axially through the bottom of composite impeller, flows radially from the top, and enters the double tongue volute. Driven by the rotational effect, the fluid flows into the volute and generates a speed torque, to drive the volute rotation. The volute turns the same as the impeller, while its speed is much lower than the impeller. Subsequently, the fluid moves centrifugally in the volute and then sprays in different directions through the nozzle on the volute, to achieve an all-round cleaning effect.
Figure 2 shows the plane design of double tongue volute chamber, constructed by a 180° array of a single tongue volute. Compared with the traditional single tongue volute, the double tongue volute has only four sections for design. Section VIII of single tongue volute is the same as section IV of double tongue volute, and the relationship between the areas of two sections is as follows:
Once the VIII section area (F8) of a single tongue volute and the IV section area (F4∗) of a double tongue volute are known, another arbitrary section area (Fφ) can be obtained according to the law of equal velocity. The specific relationship is as follows:
In order to ensure the full development of fluid, the volute outlet is smoothly transitional, where two symmetrical jet outlets are arranged on the left and right sides of double tongue volute.
In this study, water is used as the working fluid. Therefore, an Euler equation for noncompressible and nonviscous flow without considering the effect of viscosity in the Navier-Stokes equation is adopted [19]. The governing equation can be expressed as follows:where ρ is the density of fluid, t is time, U is rotational velocity, and p is pressure.
2.2. Mesh Generation and Independence Analysis
ICEM software was used in this work to divide the grid of computational domain. As shown in Figure 3, the computing domain for volute adopts an unstructured grid, while a hexahedral grid structure was adopted for other computing domains. To obtain the most suitable mesh number, a mesh independence analysis was carried out. Likewise, the head and efficiency of single tongue volute mesh were calculated by changing the mesh size. As evident from Figure 4, when the mesh number of single tongue volute is 1533305, the pump head and efficiency tend to be stable. Compared with the mesh number of 2792928 for single tongue volute, the change rates for pump head and pump efficiency at mesh number 1533305 are 0.308% and 0.855%, respectively; i.e., the change rates for both are less than 1%. Hence, it can be considered that the further increase in number of grids (beyond 1533305) has only a little influence on the simulation results, and the results have sufficient accuracy when the number of grids is 1533305. Therefore, considering the independent test and computer capability [20–22], the grid number of 1533305 was selected as an optimal scheme for numerical study. The y + criteria of simulation were considered, where the maximum value is 62, which can be seen in Figure 5.
2.3. Numerical Simulation
In this paper, the commercial CFD software ANSYS fluent 2020 R1 was used to simulate the three-dimensional incompressible flow in the pump. The inlet boundary was set as the mass flow inlet, with the flow rate of 55 L/min. The two outlets were set as pressure outlet, and its static pressure value was set to atmospheric pressure. The rotational speed of the impeller was fixed at 3000 r/min, and k-ω turbulence model was adopted as the turbulence model. Additionally, the Time Step Size of transient calculation was set as 0.000222 s, which was equivalent to 4° of impeller rotation. Furthermore, the MRF (multiple reference frame) approach was employed in this study, and the frame motion was exerted on volute and impeller, to simulate the rotating motion. Moreover, the interface between impeller and volute was set to moving wall-rotational. In order to ensure the accuracy of calculation results, the Max Iterations/Time Step was set to 40 times. Besides, the simulation results of steady calculation were taken as the original conditions of transient calculation to obtain satisfactory convergence. Simple algorithm was used in the calculation, while second-order upwind scheme was used in the discrete process. Lastly, the convergence accuracy was set to 10−4.
2.4. Research Case for Simulation
As shown in Figure 6, three different cases were considered for the volute model. The pump operates at a design flow rate of 55 L/min, with a head of about 2 m. In order to facilitate the construction of test bench, the original model is simplified. The static condition of the double tongue volute is used for testing, thus avoiding the difficulties of pressure test in volute rotation case. The simulation was carried out using the conditions of volute case shown in model 1. The simulation results were then compared with the test results, to ensure the correctness of simulation. After validating the simulation when the double tongue volute is static, as shown in model 2, the rotating speed of double tongue volute is set to 60 rpm, to simulate the working condition of the pump under the real condition. To explore the difference between double tongue volute and traditional single tongue volute, a single tongue spiral case (model 3) was designed, where the inlet flow rate was set to 27.5 L/min. The specific design parameters of the three models and the detailed design parameters of the pump are shown in Table 1.
2.5. Pressure Pulsation Monitoring Points Setting
In order to explore the characteristics of pressure pulsation for various cases in detail, pressure pulsation monitoring points were set, as presented in Figure 7. Along the center line of impeller flow passage, three pressure pulsation monitoring points were, respectively, set at each inlet of compound impeller, outlet of compound impeller, and junction of centrifugal impeller and axial flow impeller. To study the influence of tongue on the rotor-stator interference, pressure pulsation monitoring points G1∼G5 were set near the tongue. Additionally, six pressure pulsation monitoring points V1∼V6 were set between the impeller and the volute in the same circle.
To normalize pressure pulsation data, the pressure coefficient Cp was introduced to describe the pressure pulsation [23–25], which is defined aswhere p is the instantaneous pressure at monitoring points; p is the average of instantaneous pressures at different times; ρ is the density of fluid; u2 is the circumferential velocity of impeller outlet.
3. Experimental Validation
Figure 8 shows a test bed for the pump model, which was fabricated from plexiglass as a whole. The performance test is based on the static condition of volute, and the volute is passively rotated as the dishwasher operates. In addition, multiple nozzles are set on the spray arm of dishwasher in reality, whereas the test is simplified by considering one on both sides. This facilitates the measurement of flow under different working conditions during the experiment, as well as the measurement of inlet and outlet pressures. The test bed mainly includes a model pump, pipeline, a water storage tank, two turbine flowmeters, two solenoid valves, and a pressure sensor, etc. Three pressure sensors are located at one inlet and two outlet positions of the pump, where the measuring accuracy of pressure sensors is 0.2%. Moreover, the turbine flowmeters and solenoid valves are placed symmetrically on both sides of the outlet pipelines. The turbine flowmeter is powered by a lithium battery and has an accuracy of 0.1%. It allows flow readings to be displayed directly on a LCD screen under different conditions. In order to adjust the opening of solenoid valve accurately, the electric actuator inputs a current in the range of 4–20 mA, to control the 0–1 opening of solenoid valve. The test was repeated for 10 times at room temperature, and the uncertainty of the test was analyzed. According to the calculation of experimental data, the experimental uncertainty is ±0.1%. The motor speed controller changes the speed of brushless DC motor by changing the input current, and the impeller at different flow of 3000 rpm, 2500 rpm, 2000 rpm, 1500 rpm, and 1000 rpm was measured. Accordingly, the performance curves for the pump at different impeller speeds were obtained.
The characteristics of the pump form an important basis to judge the pump performance. The relationship between the pump head, efficiency, and flow rate can be intuitively seen through the pump characteristic curve, which provides a guidance for the optimization of pump. According to the pump similarity law, if a point A1(H1, Q1) with rotation speed n1 is known on the characteristic curve, the parameters of working point A2(H2, Q2) with rotation speed n2 are related to the point A1, through following relationship:
When the speed is ni, the parameters of working point Ai(Hi, Qi), which is similar to the point A1, are
The head H1 and flow rate Q1 at the impeller speed of 3000 r/min were measured in the test. At this stage, the flow rate Qi at different speeds is known, and the theoretical head at different impeller speeds can be obtained using equation (6). Figure 9 displays a comparison between the test head and the theoretical head of impeller at various speeds. The experimental results show that the head curves of pump at different speeds are lower than the theoretical results, which is due to the energy loss in experimental process. In addition, the comparison results indicate that the new dishwasher pump composed of compound impeller and double tongue volute conforms to the similarity law of traditional pump, which validates the accuracy of test.
Figure 10 shows the comparison between test and simulated results of head curve. The results highlight that the measured head decreases with an increase in flow rate, and the values of simulated Q-H curve are slightly higher than the experimental results. When the inlet flow of pump is 18 L/min, the deviation between the simulated head value and the experimental head value is 6.8%, which satisfies the calculation accuracy requirements for current low head pump; hence the simulation strategy for the pump model meets the calculation requirements.
4. Result and Discussion
4.1. Comparative Analysis of Different Locations in Static Double Tongue Volute
Through unsteady state calculation, the instantaneous pressure values for each monitoring point of the double tongue volute under the static state were obtained, as shown in Figure 11. Next, FFT transformation was carried out on the pressure pulsation data in time domain, to extract the frequency domain curve for pressure pulsation.
(a)
(b)
(c)
As seen from the time domain diagram, eight wave troughs and eight wave peaks appear during one blade rotational period of 0.02 s, which is consistent with the number of blades [26–28]. Moreover, the secondary peak occurs at each main peak, due to suction surface and pressure surface of the blade during impeller rotation. Overall, the pressure pulsation in impeller domain is primarily determined by the interaction between impeller and volute.
According to the frequency domain figure, the first main frequency of pressure pulsation at Y1–Y9 is the blade frequency fBPF (400 Hz), which is eight (blade number) times the shaft frequency fn (50 Hz), and the secondary frequency of pressure pulsation is 2fBPF. The pressure pulsation amplitudes increase from the impeller inlet to the impeller outlet. In addition, closer to the impeller outlet, the secondary harmonic frequency of pressure pulsation is added. It is shown as a pressure fluctuation with large amplitude corresponding to a frequency that is an integral multiple of the blade frequency. Essentially, the closer the flow to the volute, the stronger the squeezing effect of the flow in impeller, which makes the flow field unstable and the flow pattern more complex, thus increasing the secondary flow vortex.
In the impeller inlet domain, the pulsation amplitudes increase along the radius from blade hub to tip (Y1 < Y2 < Y3). Furthermore, in the junction domain of centrifugal impeller and axial flow impeller, the pulsation amplitudes decrease along the radius from blade hub to tip (Y4 > Y5 > Y6). Whether this phenomenon is caused by the impeller combination remains a topic to be studied further.
Progressively, Figure 12 shows the pressure pulsation analysis for measure points G1–G5 at the tongue position. As the monitoring point changes from G1 in the inner part of tongue to G5 in the outer part of tongue, the periodicity of pressure pulsation time domain curve gradually becomes less obvious. Particularly, it can be seen that monitoring point G1 has 8 peaks and 8 troughs of pressure pulsation within one rotation of the impeller, while this feature is not obvious at monitoring points G4 and G5, and the relevant pressure fluctuation range is large. This is because when the blade sweeps over the volute tongue, the interference between the vortex at blade outlet and the volute tongue is more complex and unstable.
From the frequency domain of pressure pulsation, it can be seen that the pulsation amplitudes decrease from the inner part of tongue to the lateral septum of volute (G5 > G4 > G3 > G2 > G1). The main frequency of pressure pulsation at G5, G4, and G3 is 50 Hz (fn), while at G2, the dominant pressure frequency is 150 Hz (3fn), and lastly, the main frequency at G1 is 400 Hz (fBPF). This behavior can be interpreted by the fact that secondary flow characteristics in the volute tongue domain are very unsteady and complex.
Figure 13 shows the time domain and frequency domain diagrams of pressure pulsation at 6 monitoring points between impeller and volute. From the time domain diagram, the pressure amplitudes reduce steadily from V1 to V6. The maximum pressure amplitude is at V1, which is closer to the volute, compared to other monitoring points. This clearly demonstrates that the rotor-stator interference between the rotating impeller and the stationary volute is the root cause for pressure pulsation. For the monitoring points closer to the middle position of two tongues, the pressure pulsation is affected by the two symmetrical tongues of double tongue volute. As shown in the fluctuation curves of V5 and V6, the secondary peak appears on the main peak.
Similarly, from the frequency domain diagrams of pressure pulsation, it can be seen that the main frequency of pressure pulsation at points V6 and V5 is three times the shaft frequency (3fn), while the pressure frequency for other monitoring points is dominant at 400 Hz (fBPF). Such change of main frequency is due to the interaction between two volute tongues, where the unstable swirl occurs easily in the region between two volute tongues.
4.2. Comparative Analysis of Static Volute and Rotate Volute
Figure 14 compares the head and efficiency of the model pump under rotating and static volute. The head coefficient of the dishwasher pump is improved by using rotating volute, when compared with the case of static volute.
With the small flow rate of 3 L/min, the head coefficient of rotating volute increases by 0.18, compared with the static volute. On the other hand, under a large flow rate of 55 L/min, the head coefficient of rotate volute increases by 0.13. This is because in the simulation process, the volute passively accepts the speed of 60 rpm, allowing the rotate volute to produce power, and finally, this part of work is converted to head. The efficiency of dishwasher pump with static volute is similar to that with rotate volute under different flow rates, where the maximum variation is 0.09.
Figure 15 illustrates the time domain variation of pressure pulsation at monitoring points G1–G5, with static volute and rotate volute. In the case of static volute, a significant change in the pressure pulsation appears just outside the tongue in one cycle; however, with the revolution speed given to volute, the variations in pressure pulsation are obviously reduced, compared with the case of static volute. Furthermore, the time domain curve of pressure pulsation is periodic during one blade rotational period of 0.02 s, under the rotate volute condition. However, when the double tongue volute is static, the periodic law of pressure pulsation is not obvious, especially at monitoring points G2–G5. This is because the flow can perform a better transition from the position of tongue, under the condition of rotating volute. Adversely, the water flow is blocked at the position of tongue under static volute condition, which makes the flow more complicated and causes a disorder in pressure curve. This observation is consistent with the reduction in vorticity under rotating condition shown in Figure 16.
4.3. Comparative Analysis of Single Tongue Volute and Double Tongue Volute
Figure 17 compares the head and efficiency of the model pump under double and single tongue volutes. Under the same flow rate, the outlet area of double tongue volute is twice as large as that of single tongue volute, which indicates that the velocity of outlet for double tongue volute is also twice in size. Hence, with the increase in flow rate, the decline rate of head coefficient is faster than that of dishwasher pump by using double tongue volute. The high efficiency area of the dishwasher pump with single tongue volute is concentrated at 27.5 L/min, which is consistent with the design flow rate. Alternatively, the high efficiency area of the dishwasher pump with double tongue volute is 40 L/min, which is less than the design flow rate of 55 L/min.
As indicated in Figure 18, at monitoring points V1, V2, V3, and V4, time domain pressure distributions for double tongue volute and single tongue volute are similar to each other. At monitoring points V5 and V6, the pressure pulsation distributions are relatively uniform for single tongue volute. However, as the monitoring points get closer to the middle of two tongues, the interaction between the two tongues becomes obvious, thus causing a disorder in the pressure pulsation curve of double tongue volute.
5. Conclusion
In this paper, the accuracy of simulations is verified via experiments, and the pressure pulsation characteristics in the dishwasher pump with double tongue volute are studied by numerical calculation method. Accordingly, the following important conclusions are reached:(1)The compound impeller composed of centrifugal blade and axial flow blade satisfies the pump similarity theory, and the test head and the theoretical head are consistent under five different impeller speeds.(2)When the double tongue volute is static, the pressure pulsation amplitudes increase from the impeller inlet to impeller outlet. The domain frequency for the monitoring points that are in upper tongue region is the blade frequency, i.e., 400 Hz, and for the points that are in lower tongue region it is 150 Hz. The main frequency of pressure pulsation is 50 Hz, when the monitoring points are located in the middle area between two tongues.(3)Compared with static double tongue volute, the head coefficient of dishwasher pump is lager by using rotate volute with 60 rpm. The time domain curve of pressure pulsation is periodic, and the variations in pressure pulsation are evidently reduced by using the rotating volute.(4)Compared with the double tongue volute, the decline rate of head coefficient is faster when using a single tongue volute. The high efficiency areas of the dishwasher pump with single tongue volute and double tongue volute are concentrated at 27.5 L/min and 40 L/min, respectively. Moreover, the time domain curve of pressure pulsation distributions is relatively uniform with single tongue volute.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the Natural Science Foundation of Jiangsu Province (no. BK20180871), the project of National Natural Science Foundation of China (no. 51809120), the Project Funded by China Postdoctoral Science Foundation (no. 2018M640462), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no. 18KJB470005), the Key Research and Development Plan Project of Jiangsu Province (no. BE2019009), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).