**1. Introduction**

The pumps are classified as general machinery with varied applications [1–5]. Blade slotting was first used in the aviation industry to improve the separation of airflow over the wings [6]. Blade slotting technologies work by allowing the pressure difference to be adjusted between two sides of an airfoil so that gas on the high-pressure side flows through the slot, thus forming a jet upon reaching the low-pressure side. This jet effectively delays the separation of the boundary layer of the airfoil surface and increases the airfoil head coefficient to improve overall airfoil properties [7–9]. The effects of various slot parameters on the performance of blade centrifugal pump represent significant information for engineers.

Many scholars have investigated the effects of slotting technology on the mechanical performance of impellers. Tang et al. [10], for example, carried out a numerical simulation using the three-dimensional (3D) uncompressible Navier–Stokes equation to determine the influence of the slot position and slot width on the centrifugal fan performance. They found that the efficiency and total pressure of the slotted impeller improved under the design conditions; noise was also reduced as the performance under non-design conditions improved. Huang et al. [11] optimized slotting long and short blade impeller parameters based 3D, incompressible Navier–Stokes equations and a *k*- turbulence model followed by a prototype test; they concluded that the slotting technique improves blower performance. Wang et al. [12] used the RNG *k*-<sup>ε</sup> model to simulate the multiphase flow in a centrifugal pump with a slotted blade structure. They found that an opening near the blade inlet improves the cavitation performance of the medium-low specific speed centrifugal pump. Ye [13] studied the effects of slotted

blades on the centrifugal e fficiency, head, and internal flow field of a pump; the blade slot was found to increase the head and flow of the pump under high flow conditions. Gao et al. [14] determined the loss of pressure and coe fficient of heat transfer in the slotted turbine blade of a trailing edge by numerical simulation and experimental verification; they also analyzed the e ffects of slotting on the flow and heat transfer characteristics of the surface. Xing [15] studied the e ffects of long and short blades on the internal flow field and impeller performance of pumps using the numerical simulation method. Yuan [16] found that the use of splitter blades e ffectively improves the performance of low specific speed centrifugal pumps. Kergourlay et al. [17] used the unsteady Reynolds average Navier–Stokes (URANS) method to study the e ffect of blade slotting on the flow field in a centrifugal pump. An impeller with a slotted structure was found to make the circumferential speed and pressure distribution more uniform while slightly improving the pump performance. Gölcü et al. [18] found that a slotted-blade impeller is less loaded than the impeller without a slotted blade.

There has been a grea<sup>t</sup> deal of research on slotting the blades of low specific speed centrifugal pumps [12,13,19], but previously published techniques have certain limitations due to the sole analysis of a single condition. In an e ffort to systematically explore the e ffects of slotted blades on the performance of centrifugal pumps, the present study was conducted to test four parameters: slotted blade position, slotting width, slotting angle, and slotting depth. The e ffects of various combinations of di fferent parameters on the performance of medium specific speed centrifugal pumps were explored accordingly via orthogonal design.

#### **2. Numerical Simulation Method**

#### *2.1. Computation Model*

A medium specific speed centrifugal pump with a speed ratio of *n*s = 85 was selected to study the effects of blade slotting on the pump performance. The specific speed is formulated as follows:

$$n\_s = \frac{3.65n\sqrt{Q}}{H^{3/4}}\tag{1}$$

where, *n* is the rotating speed (r/min), *Q* is the rated point flow rate (m<sup>3</sup>/s), and *H* is the rated point head (m).

The main design parameters of the pump are shown in Table 1.


**Table 1.** Main design parameters of centrifugal pump.

The total flow field was computed to consider the e ffects of ring clearance leakage on the pump's performance. As shown in Figure 1, the computational domains in this case include the inlet section, impeller, pump cavity, volute, and outlet section, wherein the pump cavity portion includes the front and ring cavities. The extension lengths of the inlet and outlet sections in the computational domain were set to four times the diameters of the inlet and outlet pipes, respectively, to ensure a sufficient flow development.

**Figure 1.** Simulation pump model. 1. Inlet section; 2. pump cavity; 3. impeller; 4. volute; 5. outlet section; 6. front cavity and 7. rear cavity.
