3. Steady and unsteady numerical analyses

impeller and volute of a single-channel pump with high performance, as shown in Figures 2

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

¼ 0:013 � D1

¼ 0:38 � D1

H1 ¼ 0:835 � D1 (1)

L1 ¼ At=H1 (3)

At ¼ 2A1 þ A2 þ A3 (5)

A2 ¼ R1 � L2 (8)

A3 ¼ At–A2–2A1 (9)

L3 ¼ A3=H1 ð Þ here; L3 > 0 (10)

<sup>2</sup> (2)

<sup>2</sup> (4)

< theta � ≤ 360 �

=4 (7)

(6)

(11)

and 3, respectively. The cross-sectional area is determined as follows:

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

At @0 � � <sup>70</sup> �

At @360 �

–70 value of fixed area angle ð Þ � C1 here; <sup>70</sup>�

A1 ¼ πR1

H2 <sup>¼</sup> <sup>0</sup>:<sup>01</sup> � At @<sup>360</sup> �

2

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

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

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

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

of the impeller.

186 Wastewater and Water Quality

R1 <sup>¼</sup> theta �

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 CFX-Post, respectively.

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

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

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

CP3, CP4, and CP5) of both the impeller and volute are selected as design variables to obtain

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

The aim of the current optimization problem is to simultaneously improve the hydraulic efficiency (η) and reduce the radial force sources considering the impeller-volute interaction in the single-channel pump. Here, one of the three objective functions, that is, the hydraulic

<sup>η</sup> <sup>¼</sup> <sup>r</sup>gHQ

where r, g, H, Q, τ, and ω denote the density, acceleration of gravity, total head, volume flow

τω (18)

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

189

the most sensitive results for the variation in curve among the control points [17].

efficiency, is defined as follows.

arte, torque, and angular velocity, respectively.

Figure 5. Definition of the design variables. (a) Impeller part (b) Volute part.

Figure 6. Definition of objective functions related to the radial force sources [10].

Figure 4. Computational domain and grids.

adiabatic and no-slip conditions. The stage average and transient-rotor-stator methods are respectively applied to connect the interface between the rotating impeller and volute domains in the steady and unsteady analyses.

The convergence criteria in a steady computation consist of the root-mean-square (RMS) values of the residuals of the governing equations, which are set to less than 10<sup>5</sup> for all equations. The physical time scale was set to 1/ω, where ω is the angular velocity of the impeller. The computations are carried out using an Intel Xeon CPU with a clock speed of 2.70 GHz, and the converged solutions are obtained after 1000 iterations with a computational time of approximately 4 h.

The results of the steady RANS analysis are used in the unsteady RANS analysis to obtain the characteristics of the radial force sources in the region of the exit surface of the impeller according to the impeller-volute interaction in the single-channel pump. In an unsteady simulation, the time step and coefficient loop for the time scale control are set to 0.000947 s and three times, respectively. The solutions are obtained after 180 iterations with an unsteady total time duration of 0.170478 s (five revolutions), and the computational time for the unsteady calculation was approximately 8 h.
