Design and flow simulation for a centrifugal pump with double suction impeller

Centrifugal pump is a hydraulic machine that is used to transport fluids by the conversion of rotational kinetic energy of impeller into the hydrodynamic energy of the fluid flow. The double-suction centrifugal pump are used for conveyance of a large quantity of water and have wide application due to its stable running, for the balance of axial thrust through by the double suction in impeller, and for a convenient maintenance. Because the design of the centrifugal pump impeller is not a universally standardized one and depends on designer's experience and its technical intuition, in this paper is presented a methodology of design and the fluid flow simulation throughout impeller.


Introduction
Generally a pump is a hydraulic machine which converts mechanical energy into hydraulic energy.The rotational energy typically comes from an electric motor, an engine or a steam turbine.The block diagram which shows the transformation of mechanical energy (torque M and angular velocity ω) into hydraulic energy (head H and flow Q) is shown in Figure1.A centrifugal pump with double suction is presented in the Figure 2. In the volute of the pump fluid enters axially through the eye of the impeller (low pressure area) which rotates at high speed.As the impeller and blades rotate, they transfer momentum to incoming fluid.The fluid accelerates radially outward from the pump chasing and a vacuum is created at the impellers eye that continuously draws more fluid into the pump [1,2,3].As the fluid's velocity increases obviously its kinetic energy increases and the fluid is forced out of the impeller [1,4,5].In the volute the fluid flows through a continuously increasing cross-sectional area, where the kinetic energy is converted into fluid pressure (according the Bernoulli's principle).The impeller blades are usually backward-curved.
1-shaft 2-bearing 3-double suction impeller 4-eye of impeller 5-casing The impeller is mounted on a shaft.Shaft is a mechanical component for transmitting torque from the drive source to the impeller.This study is structured on 5 sections and presents a methology of design and a computational fluid dynamics simulation for an impeller with double suction.Section 2 will present the design methodology of impeller.
In Section 3, will be shown the characteristics of CFD software and the model preparation for simulation.In section 4 will be analyzed the results of the simulation.Section 5 will present the conclusions of this study.

Design methodology of impeller
The impeller is the main component determining the pump performance.The impeller that is designed in this paper is for a double suction centrifugal pump that can provide a rate of 0,15 m 3 /s flow in the working conditions whose head is 20 m.The impeller dimensions are designed based on the head [6,7,8], flow rate and triangle of velocities (Figure 3).The absolute velocity at the inlet and outlet of impeller (c) is composed by tangential velocity (u) and the relative velocity (w) .
The following are the steps involved in designing a centrifugal impeller.From the head (H) and flow rate (Q), the kinematic specific speed (n s ) is calculated: From the head (H), flow rate (Q), specific weight of water (γ w ) and overall efficiency (η), the shaft power (N sh ) required is calculated: The shaft diameter (d sh ) is found using the formula: The hub diameter (d h ) is calculated from the empirical relation given below: The velocity (c 0 ) at the inlet is estimated using the relationship of below : With K cm1 the coefficient of velocity.
The inlet cross section area (A 0 ) is calculeted from the flow rate after accounting for volumetric efficiency (Q v ) with the relation: The inlet diameter (d 1 ) is calculated from the cross section area: Blade inlet angle (β 1 ) is calculated as: Breadth of the impeller (b 1 ) at the inlet is calculated with the relation: The outlet tangential velocity (u 2 ) can be calculated with an experimental velocity coefficient (K u2 ) as follows: The outlet diameter (d 2 ) is calculated with the relation: The breath of the impeller at the outlet is: Blade outlet angle (β 2 ) is assumed to lie within the limits of 15˚ to 35˚.The number of blades is calculeted by using the following equation: The Mathcad software was used to calculate the main impeller dimensions and the numerical values of these are shown in Table 1.With these dimensions, the 3D model of the rotor is built using the SolidWorks software.The impeller performance is significantly affected by the flow path geometry (vane profile).The vane profile for the impeller presented in figure 4 is developed by arc method.

CFD simulation for double suction impeller
The pressure and velocity distribution over the blade curvature of impeller was analyzed using a Computational Fluid Dynamics (CFD) package, more exactly the module Solid Works Flow Simulation.
Governing equation for SolidWorks flow simulation solves three-dimensional Navier-Stokes equation with the finite volume method [8][9][10][11][12].The first step in CFD simulation is preprocessing.At this step modeling and mesh is generated.Input data for flow analysis is the assigning of computational domain, boundary condition and rotating region.In this phase the boundary conditions are set (Figure 5) and then the simulation is running.

Results of simulation
The results of simulation for velocity and pressure distributions can be see in Figure 6 and Figure 7 respectively.The pressure distribution is increasing from impeller inlet to outlet as it is shown in Figure 7.At the eye pressure is negative.https://doi.org/10.1051/matecconf/201817805018IManE&E 2018 Fig. 7.The flow pressure distribution over the impeller.

Conclusions
The double suction impeller (3D model) was generated with SolidWorks and analyse in the same software with flow simulation module.The shape of blades for the impeller is created with arc method.
From the speed distribution analysis in the rotor we find that the velocity has decreased in the exit area of the rotor.
The maximum value of the velocity through impeller is 32.6 m/s, and the velocity distribution can be see in Figure 6.
The velocity distribution is non-uniform because the circulating motion through the impeller.
After the study of pressure distribution, it was observed that is a low pressure at the suction of impeller and the maximum of pressure is after the outlet of impeller.
The results obtained by simulation is comparable with theoretical results which confirms the design methodology.

Fig. 1 .
Fig. 1.Block diagram of the energy transformation in a pump.

Fig. 2 .
Fig. 2. Overview of main components for a centrifugal pump with double suction impeller.

Table 1 .
The geometric characteristics of impeller.