2. Basic design approach of single-channel pump

The single-channel pump with an impeller and a volute for wastewater treatment is initially designed according to the Stepanoff theory [9]. The pump can then be modeled as a threedimensional shape, as shown in Figure 1 [10]. The three-dimensional model can be developed using commercial modeling software such as SOLIDWORKS and CATIA. Because the Stepanoff theory generally minimizes the flow loss due to flow speed differences by increasing the cross-sectional area of internal flow at a fixed rate according to the theta angle position, it is especially useful for designing a stationary volute. Nonetheless, the impeller of a singlechannel pump can be designed based on this concept because it has a free annulus passage State-of-the-Art Design Technique of a Single-Channel Pump for Wastewater Treatment http://dx.doi.org/10.5772/intechopen.75171 185

Figure 1. Three-dimensional shape of a single-channel pump [10].

driven perfectly along the flow path. Moreover, it has a complex structure, high cost, low capacity, and frequent replacement cycle. On the other hand, as a single-channel pump is a representative case of a flow-path-securing type, it has different mechanism features compared with general pumps pressurized by multiblades. A single-channel impeller has one free annulus passage and does not have multiple blades. Further, it is driven by the centrifugal force generated from the rotating annulus passage [1]. Therefore, a single-channel pump is very

Because of these advantages, the demand for single-channel pumps has increased rapidly in recent times in the field of wastewater treatment. Nevertheless, only a few studies have been published on the design of a single-channel pump [1–4]. To the best of the author's knowledge, the lack of studies can be attributed to the difficulties in establishing a theoretical design methodology, manufacturing, and especially, solving the balancing problem related to the fluid-induced vibration between the impeller and volute of a single-channel pump. In fact, because the mass distribution of a single-channel impeller is not rotationally symmetric, it is difficult to stabilize the fluid-induced vibration between the impeller and volute. Furthermore, unsteady radial forces, which rotate at a frequency generally determined by the rotating speed, are generated in the single-channel impeller [5]. These unsteady sources are generated by the interaction between the rotating impeller and volute, and these adversely affect the overall

performance of a single-channel pump, especially its life expectancy and durability.

2. Basic design approach of single-channel pump

design approach.

184 Wastewater and Water Quality

Over the past several years, there has been growing interest on the effects of unsteady dynamic radial forces due to impeller-volute interaction in centrifugal pumps [6–8]. However, no systematic studies on single-channel pumps have yet been attempted, except for several concepts and patents. To this end, this work presents a state-of-the-art design technique for a singlechannel pump for wastewater treatment based on a theoretical approach and threedimensional steady and unsteady numerical analyses. Moreover, advanced multidisciplinary numerical design optimization techniques are introduced and discussed in detail to simultaneously improve hydraulic efficiency and reduce the flow-induced vibration due to the impeller-volute interaction in a single-channel pump. The objective of this chapter is to provide practical guidelines for optimizing the design of a single-channel pump with the proposed

The single-channel pump with an impeller and a volute for wastewater treatment is initially designed according to the Stepanoff theory [9]. The pump can then be modeled as a threedimensional shape, as shown in Figure 1 [10]. The three-dimensional model can be developed using commercial modeling software such as SOLIDWORKS and CATIA. Because the Stepanoff theory generally minimizes the flow loss due to flow speed differences by increasing the cross-sectional area of internal flow at a fixed rate according to the theta angle position, it is especially useful for designing a stationary volute. Nonetheless, the impeller of a singlechannel pump can be designed based on this concept because it has a free annulus passage

robust, especially against failure and damage due to waste clogging.

Figure 2. Cross-sectional area distribution and definition of the impeller [10].

and does not contain multiple blades. Further, the impeller is driven by the centrifugal force generated from the rotating annulus passage. Thus, the internal flow distribution in the crosssectional area of the impeller and volute is changed proportionally with the theta angle position in order to maintain a constant flow velocity. Figures 2 and 3 show the distribution of internal flows in the cross-sectional area of the impeller and volute generated from the Stepanoff theory. In the authors' previous work, for example, the reference volume flow rate and total head at the design point were 1.42 m3 /min and 10 m, respectively, with a rotational speed of 1760 rpm [11].

When the distribution of internal flows in the cross-sectional area is determined according to the theta angle, the shape of the area should be defined. This shape is very important for deciding the hydraulic performance and size of solid matter in a single channel. In the previous work, the authors proposed a novel design method for defining the cross section of the

Figure 3. Cross-sectional area distribution and definition of the volute [10].

impeller and volute of a single-channel pump with high performance, as shown in Figures 2 and 3, respectively. The cross-sectional area is determined as follows:

The given total area (At) in the impeller part,

$$\mathbf{H}\_1 = 0.835 \times \mathbf{D}\_1 \tag{1}$$

At ¼ 2A4 þ A5 þ A6 (12)

State-of-the-Art Design Technique of a Single-Channel Pump for Wastewater Treatment

A5 ¼ R2 � L5 (15)

A6 ¼ At–2A4–A5 (16)

L7 ¼ A6=H2 ð Þ here; L7 > 0 (17)

� C2 (13)

http://dx.doi.org/10.5772/intechopen.75171

187

=4 (14)

R2 <sup>¼</sup> theta �

A4 ¼ πR2

The cross sections of the impeller and volute are defined as mentioned above. The threedimensional shape can then be modeled as shown in Figure 1. The more detailed explanation

In the computation domain generated from the basic design approach, the internal flow field is analyzed by solving three-dimensional steady and unsteady incompressible Reynoldsaveraged Navier–Stokes (RANS) equations with a k-ω-based shear stress transport (SST) turbulence model by using a finite volume solver. In this work, the commercial computational fluid dynamics (CFD) code ANSYS CFX 14.5 is used, and ICEM CFD is applied to generate computational meshes for the impeller and volute. The numerical analysis is carried out with boundary conditions, solved, and post-processed using ANSYS CFX-Pre, CFX-Solver, and

For the turbulence closure model, the k-ω-based SST model [14] is employed to accurately predict flow separation under an adverse pressure gradient. In this model, the k-ω and k-ε models are applied in the near-wall region and bulk domain, respectively, and a blending function ensures smooth transitions between these two models. The accuracy of the numerical analyses of turbulent flows significantly depends on treating the wall shear stress. In this chapter, the near-wall grid resolution is adjusted to maintain y + ≤ 2 to accurately capture the

A tetrahedral grid system is constructed in the computational domain with a prism mesh near the surfaces, as shown in Figure 4 [15]. The rotating single-channel impeller and the volute domains are each constructed using approximately 1,300,000 and 1,200,000 grid points. Hence, the optimum grid system selected using the grid independency test has approximately

For the boundary condition, water is considered as the working fluid, and the total pressure and designed mass flow rate are set to the inlet and outlet of the computational domain, respectively. The solid surfaces in the computational domain are considered to be hydraulically smooth under

wall shear stress and to implement a low-Reynolds-number SST model.

2,500,000 grid points, as previously reported [15, 16].

2

where C2 = 0.1 � H2/89.5 is the expansion coefficient.

can be found in the previous works of the authors [12, 13].

3. Steady and unsteady numerical analyses

CFX-Post, respectively.

where the impeller height (H1) is fixed along theta angle and D1 represents the inlet diameter of the impeller.

$$\mathbf{A}\_t \left( \otimes \mathbf{0}^\circ \sim \text{70}^\circ \right) = 0.013 \times \text{D}\_1^{\cdot 2} \tag{2}$$

$$\mathbf{L}\_1 = \mathbf{A}\_t / \mathbf{H}\_1 \tag{3}$$

$$\mathbf{A}\_{\mathrm{f}} \left( \mathbb{t} \mathbb{3} \boldsymbol{\Theta} \mathbf{0}^{\circ} \right) = \mathbf{0}.38 \times \mathbf{D}\_{\mathrm{l}}^{\circ 2} \tag{4}$$

$$\mathbf{A}\_{\mathbf{t}} = 2\mathbf{A}\_{1} + \mathbf{A}\_{2} + \mathbf{A}\_{3} \tag{5}$$

R1 <sup>¼</sup> theta � –70 value of fixed area angle ð Þ � C1 here; <sup>70</sup>� < theta � ≤ 360 � (6)

where C1 = 0.1 � H1/83.5 is the expansion coefficient.

$$\mathbf{A}\_1 = \pi \mathbf{R}\_1^2 / 4 \tag{7}$$

$$\mathbf{A}\_2 = \mathbf{R}\_1 \times \mathbf{L}\_2 \tag{8}$$

$$\mathbf{A}\_3 = \mathbf{A}\_t \mathbf{-A}\_2 \mathbf{-2} \mathbf{A}\_1 \tag{9}$$

$$\mathbf{L}\_3 = \mathbf{A}\_3 / \mathbf{H}\_1 \text{ (here,} \mathbf{L}\_3 > 0) \tag{10}$$

The given total area (At) in the volute part,

$$\mathbf{H}\_2 = \mathbf{0}.01 \times \mathbf{A}\_t \text{(@§60^\circ)}\tag{11}$$

where the volute height (H2) in fixed along theta angle.

State-of-the-Art Design Technique of a Single-Channel Pump for Wastewater Treatment http://dx.doi.org/10.5772/intechopen.75171 187

$$\mathbf{A}\_{\mathbf{t}} = \mathbf{2}\mathbf{A}\_{\mathbf{4}} + \mathbf{A}\_{\mathbf{5}} + \mathbf{A}\_{\mathbf{6}} \tag{12}$$

$$\mathbf{R}\_2 = \text{theta} \mathbf{t} \mathbf{a} \mathbf{(}^\circ) \times \mathbf{C}\_2 \tag{13}$$

where C2 = 0.1 � H2/89.5 is the expansion coefficient.

$$\mathbf{A}\_4 = \pi \mathbf{R}\_2^{\,2} / 4 \tag{14}$$

$$\mathbf{A}\_5 = \mathbf{R}\_2 \times \mathbf{L}\_5 \tag{15}$$

$$\mathbf{A}\_6 = \mathbf{A}\_t \mathbf{-2} \mathbf{A}\_4 \mathbf{-A}\_5 \tag{16}$$

$$\mathbf{L}\_7 = \mathbf{A}\_6 / \mathbf{H}\_2 \text{ (here, } \mathbf{L}\_7 > 0\text{)}\tag{17}$$

The cross sections of the impeller and volute are defined as mentioned above. The threedimensional shape can then be modeled as shown in Figure 1. The more detailed explanation can be found in the previous works of the authors [12, 13].
