1. Introduction
In recent years, an increasing number of households use dishwashers. Traditional dishwashers, which are mostly built-in cabinet-type models, cannot accommodate all user needs. In order to save space, a sink-style dishwasher was designed and integrated into the conventional kitchen sink. Li et al. [
1] compared the traditional dishwasher and a new sink-style dishwasher with an innovative pump, as shown in
Figure 1, and it was found to be an important part of sink-style dishwashers. Its working principle is driven by the rotating effect of the impeller; the water enters the volute and initiates powerful torque for the passive rotation of the twin-volute to complete the water transmission and spraying function.
Some studies have addressed this new type of dishwasher pump. A numerical simulation study on the interaction between the impeller and the twin-volute structure in the dishwasher pump was carried out by Ning et al. [
2]. Their results indicate that the hydraulic performance of the pump is slightly affected by the passive rotation of the twin-volute structure, which has a large effect on the flow field in the transition section located between the impeller and the volute. At the same time, a contrasting viewpoint on the vector distribution of the flow field was presented in this research paper. It was found that the shape of the vector distribution is the most regular for the 30 rpm scheme, which indicates that the stability of the pump is the highest. Zhu et al. [
3] carried out experiments on the pressure pulsation of a dishwasher pump using twin-volute and single-volute schemes with passive rotation, and the experimental data were compared with the data of a single volute. Zhu et al. [
4] analyzed the pressure pulsation characteristics of single-volute and twin-volute models in dishwasher pumps under stationary and rotating conditions. Both the experimental and numerical results showed that the pressure pulsation characteristics of the twin-volute scheme were better than those of the single volute and static volute. All the above studies guide innovation in the design of dishwasher pumps.
Numerous past researchers have investigated the volute since it is a crucial pump component for overcurrent conditions. By using experimental methods, Kaupert et al. [
5] investigated the effect of the volute on the pressure field of a centrifugal impeller with a high specific speed. The pressure pulsation induced by the rotor–stator interaction between the rotating impeller and the stationary volute, as indicated by Hodkiewicz et al. [
6] and CHU et al. [
7], is a significant factor affecting the pump’s performance. Numerous studies on pressure pulsation have been conducted [
8,
9,
10]. Hakan et al. studied the three-dimensional course of a curved spray arm and its projection onto the plane [
11]. This revolutionary curved design, which replaces the conventional spray arm, enhances the consumption of water and energy in dishwashers while enhancing their performance and reducing noise. Based on the stereoscopic light-curing molding technique, Dedoussis et al. [
12] rebuilt and improved the spray arms in dishwashers, with various geometric designs. Studies have revealed that the throat area and the clearance between the impeller and the volute are significant factors affecting the hydraulic performance of the pump, and Wu [
13] used CFD technology to analyze the effect of the geometry parameters of the volute on the performance of circulating hydraulic pumps, but the simulation was limited to those cases with few geometric models; thus, the study lacks research on the optimal design of the volute.
Studies focusing on the optimization process have extensively investigated the optimization of the characteristics of pump operation. Donno et al. designed centrifugal pump settings using genetic algorithms based on sophisticated surrogate optimization techniques and parameterized these settings using Bezier surfaces and Scilab scripts [
14,
15,
16]. Finally, ERCOFTAC centrifugal pumps were used to verify the viability and efficacy of such optimization procedures. Thakkar et al. [
17] optimized the clean centrifugal pump by using the response surface method and a multi-objective optimization algorithm. Their results showed that, in comparison to the original model, the head and efficiency of the optimization model at the design point increased by 9.154% and 10.15%, respectively. Lu et al. [
18] used a radial basis function (RBF) neural network, the optimal Latin hypercube (OLH) sampling method, and the multi-island genetic algorithm to optimize mixed-flow pumps. Their CFD results revealed a 5.1% increase in efficiency. According to Zhao et al. [
19], the performance of centrifugal pumps can be predicted by considering impeller characteristics using a non-parametric machine learning technique called Gaussian process regression (GPR). The outcomes demonstrated that the SE kernel function-equipped GPR model had a greater level of accuracy and resilience. Wang et al. [
20] used the Latin hypercube sampling method (LHS) and a genetic algorithm (GA) to optimize the impeller in waste-heat discharge pumps, and they compared the precision of three additional models for pump performance prediction: the response surface model (RSM), the Kriging model (KRG), and the radial basis neural network (RBNN). Zhang et al. [
21] studied the impact of rational pump blade shapes on pump hydraulic performance using proper orthogonal decomposition (POD); specifically, they applied the sum calculation method of NSGA-II and RBF to optimize its hydraulic performance, obtaining the Pareto optimal solution. An adaptive proper orthogonal decomposition (APOD) alternative model was put forth by Chen et al. [
22]. The model was capable of making quick and precise predictions about the impeller’s flow field. The forecast time was less than 1/360 of the time needed with CFD, and the prediction accuracy was noticeably better than that of the FPOD approach.
Although a few studies exist on this new type of volute structure, compared with the traditional volute, the influence of this special twin-volute structure on the hydraulic performance of the pump and its optimal design remains to be studied. Thus, in this paper, an optimization method is proposed that combines the RSM and MOGA for improving the hydraulic performance optimization of the new type of dishwasher pump. The RSM is applied to select the design parameter interval for the optimization. The head and efficiency of the new type of dishwasher pump are set as the optimization objectives. The best combination of design parameters is achieved by using the MOGA for the approximate model.
2. Numerical Simulation and Experimental Validation
2.1. Pump Model
Figure 2 depicts the original geometric model of the new type of dishwashing pump. It is designed to deliver flow at a volumetric flow rate of 55 L/min, a head of 2 m, and a rotational speed of 3000 r/min. The geometrical parameters of the dishwasher pump are listed in
Table 1.
Notably, the numerical twin-volute model is simplified compared with the real machine volute, and the two-dimensional profile of the numerical model is determined by six radii of curvature.
As shown in
Figure 3, six curves with various curvature radii primarily regulate the twin-volute. Correspondingly, the outer curve of the twin-volute structure’s cross-section consists of two curves with different radii of curvature, which are defined as the parameters “DS_1” and “DS_2”, respectively; the inner curve of the cross-section is composed of three curves with various radii of curvature, and they are defined as “DS_3”, “DS_4”, and “DS_5”; the external profile of the first to the fourth section of the worm shell is defined as “DS_6”.
2.2. Mesh Independence
The whole computational domain is composed of the inlet pipe, the impeller, and the twin volute. All the parts except for the inlet pipe were generated with an unstructured mesh using ANSYS Meshing software, and
Figure 4 depicts these grids in more detail.
To determine the most logical number of grids, grid independence was carried out. By altering the grid size while ensuring the grid quality, the dishwasher pump head with five groups of different grid numbers was calculated.
Table 2 shows that, compared with Mesh 4, the change rate for the pump head using Mesh 5 was 0.18%. The head of Mesh 4 was found to have considerable accuracy, and the simulation changed a little even if the number of grids increased. Consequently, Mesh 4 was selected for numerical simulation throughout the optimization.
2.3. Turbulence Model
ANSYS Fluent was used to simulate the incompressible flow for the dishwasher pump. The continuity equation was solved using the SST
k–
ω published by Menter [
23] because of its accurate predictions of the inception and quantum of flow separation under various pressure gradients. The governing equations can be expressed as follows:
where
k is the turbulent kinetic energy;
ω is the unit dissipation rate;
ui is the average velocity component;
Gk and
Gω are the generations of the turbulence variables
k and
ω; Γ
k and Γ
ω are the effective diffusivities of
k and
ω, respectively;
Dω is the orthogonal divergence term;
Sk and
Sω are the custom item; and
Yk and
Yω are the dissipative terms of
k and
ω, respectively.
2.4. Simulation Settings
With a flow rate of 55 L/min, the inlet boundary was set as the mass flow inlet. The static pressure value was set to atmospheric pressure, the wall condition was non-slip, and the two outlets were configured as pressure outlets. The impeller rotated at 3000 rpm. The unsteady calculation was carried out based on the results of the steady simulation, and the rotation field was set as “mesh motion”. The time step for the transient calculation was set to 2.22 × 10−4, which is equal to 1/90 T, according to the rotating period T of the impeller.
The volute and the impeller were also subjected to frame motion using the multiple reference frame (MRF) approach to simulate rotational motion. Additionally, the second-order upwind difference scheme was used during the discretization process, and the SIMPLE algorithm was utilized throughout the computation. The convergence residual was set to 10−4.
2.5. Experimental Validation
Figure 5 depicts the hydraulic performance test bench for the new type of dishwasher pump. It included a tank, a pump, an outlet pipeline, and an intake pipeline. The instrument location and the pipes leading from the outlet to the water tank were symmetrically placed, and the diameter of the volute outlet was 40 mm. Intelligent pressure sensors with an accuracy of 0.2% FS were used to measure the inlet and outlet pressure of the dishwasher pump, and the measuring range of pressure sensors was −20 kPa~20 kPa at the inlet and 0 kPa~30 kPa at the outlet.
The flow rate was determined using an electromagnetic flowmeter with a 40 mm pipe diameter, 0.5% FS measurement accuracy, and a measuring range of 0.5 m3/h to 20 m3/h. By manipulating the electromagnetic valve, the pump could be adjusted to a desirable operating condition, at which point the hydraulic characteristic curve of the dishwasher pump could be determined. An external electric actuator regulated the valve opening to guarantee the correctness of the regulation. The 0 to 1 opening of the solenoid valve was controlled with an electric actuator 0 to 100 with a flange connection. The measuring range of the torsiograph was 0 to 0.5 Nm with a 0.2% FS accuracy.
The head curve and efficiency curve of the original pump were obtained and are shown in
Figure 4. According to the test results, as shown in
Figure 6, the simulated curves revealed essentially compatible results with the experimental results. Under the design point, the error between the simulated efficiency and the experimental one was 8.3%, and the error between the simulated head and experimental value was 3.2%. The simulated head value under the low-flow scenario was higher than the test value, whereas the simulated efficiency value was lower than the test value, which fell within the error range of the numerical calculation.
5. Conclusions
An automatic numerical optimization method that combined the RSM and MOGA was proposed to improve the efficiency of the new type of dishwasher pump. The numerical simulation results with SST k–ω turbulence models were evaluated and verified through experiments. The database of the twin-volute structure controlled by six radii of curvature was generated with LHS. The response surface optimization method (RSM) was crucial in choosing the parameter interval for the optimization, and the MOGA allowed for choosing a more effective hydraulic model. By comparing and analyzing the numerical simulation results of the model before and after optimization, the following conclusions can be drawn:
(1) The “DS_6” parameter representing the external profile of the first to the fourth section of the worm shell had the most significant effect on the pump head and efficiency, which provided the basis for the selection of the interval size in the optimization, and the results of the response surface optimization provided a solution for the selection of the parameter interval range in the optimization;
(2) The head flow curves did not significantly change before and after optimization. By contrast, the optimal efficiency significantly changed, with a 2.7% increase in the efficiency at the design point;
(3) Compared with the original model, the impeller of the optimal model pump had a lower overall distribution of turbulent kinetic energy and higher overall pressure in its flow channels. The optimal model efficiently reduced the vorticity in the twin-volute inlet area and increased the pressure in the flow channel. All the above findings confirmed that the optimal model had better hydraulic performance than the original model;
(4) The combination of the RSM and MOGA can effectively solve the problem of optimization for new types of dishwashers and provides a reference for the development of subsequent hydraulic models.