Impeller Design

ISSN 1 746-7233, England, UK
World Journal of Modelling and Simulation
Vol. 10 (2014) No. 2, pp. 152-160
Design and analysis of pump impeller using SWFS
R. Ragoth Singh1∗
, M. Nataraj2
1
Mechanical Engineering, Karpagam College of Engineering, Coimbatore, India
2
Mechanical Engineering, Government College of Technology, Coimbatore, India
(Received June 27 2013, Accepted January 11 2014)
Abstract. In this study, Computational Fluid Dynamics (CFD) approach was suggested to investigate the flow
in the centrifugal pump impeller using the SolidWorks Flow Simulation (SWFS). Impeller is designed for the
head (H) 24 m; discharge (Q) 1.583 L/sec; and speed (N) 2880 rpm. Impeller vane profile was generated
by circular arc method and point by point method and CFD analysis was performed for the impeller vane
profile. Further the impeller was analyzed for both forward and backward curved vane. The simulation on
vane profile was solved by Navier-Stokes equations with modified K- turbulence model in the impeller.
Velocity and pressure distribution were analyzed for the modified impellers. Further a mixed flow impeller
was analyzed for multiphase flow in future to improve the performance using SWFS.
Keywords: CFD, impeller,pump, turbulence model, vane profile
1 Introduction
Centrifugal pumps are very common equipment used in residence, agriculture and industrial applications.
It is essential for a pump manufactured at low cost and consuming less power with high efficiency. The overall
performance is based on the impeller parameters and it is essential to identify the optimized design parameter
of the impeller. CFD helps the designer to identify the optimal parameters of the impeller by numerical flow
simulation. The impeller is virtually analyzed using CFD software package SWFS. The aim of the present
paper is to investigate the performance of impeller by developing the vane profile by circular arc method
and point by point method and perform CFD analysis of the impeller vane profile for forward and backward
curved vane shown in Fig. 1. Impeller vane profile was developed and analysis was performed using SWFS by
Ragoth Singh, Nataraj, Surendar and Siva[12]. A investigation of internal flow in a centrifugal pump impeller
using CFD and RSM were done by Nataraj and Ragothsingh[7]. A numerical approach was performed by
Ji-fengwang, Januszpiechna[4] and norbert mller[1] using CFD to examine the characteristics of static torque
and extracted power of turbine in a free stream with various hydrodynamic flow conditions. Numerical inves-
tigation using k-ε turbulence model in the water turbine as discussed Jifeng Wang, Blake gower and Norbert
Muller[3]. The performance of the pump was numerically optimized on a two-dimensional centrifugal pump
impeller to find the impeller geometry for maximizing the pump efficiency by varying the design variables
of blade angles at the leading and the trailing edge by John Anagnostopoulos[5]. A methodology for opti-
mizing the impeller geometry using CFD and Response Surface Method were discussedby Ragothsingh and
Nataraj[10] Raúl Barrio, Jorge Parrondo and Eduardo Blanco[2] were performed CFD analysis on the unsteady
flow behavior near the tongue region of a centrifugal pump for three-dimensional unsteady flow regarding grid
size, time step size and turbulence model. Shojaeefard, Tahani, Ehghaghi, Fallahian and Beglari[11] carried out
experimental study for performance improvement of centrifugal pump by modifying the geometric character-
istics using CFD for viscous fluid. Computational investigation of water turbine based on three-dimensional
∗
Corresponding author. E-mail address: ragothsingh@rediffmail.com.
Published by World Academic Press, World Academic Union

World Journal of Modelling and Simulation, Vol. 10 (2014) No. 2, pp. 152-160 153
numerical flow were calculated and analyzed for a specific flow speed discussed by Wang ji-feng, Piechna-
janusz, and Mller Norbert[1].
Figure 1: Methodology
Specification of Pump
Design calculation
Vane profile development
Modeling using Solid Works
Flow simulation using CFD
Result and Discussion
Fig. 1. Methodology
2 Design and analysis
2.1 Impeller design
The impeller was designed for the operational condition of head (H) = 24m; flow rate (Q) =
1.58m3/sec; and speed (N) = 2880rpm. The design parameters of the impeller were calculated using the
empirical equations found Srinivasan [13]. The impeller design procedures are shown in Eq. ( 1 - 19).
Specific Speed (NS) :
NS =
3.65 × N
√
Q
H0.75
, (1)
Nominal Diameter (D1):
D1 = 4.5 × 103
×
s Q
N
mm, (2)
Hydraulic Efficiency (ηH):
ηH = 1 −
0.42
(log D1 − 0.172)2
%, (3)
Volumetric Efficiency (ηV ):
ηv =
1
1 + 0.68(NS)
−Z
S
%, (4)
Mechanical Efficiency (ηm):
Assume η to be as86%, (5)
Overall Efficiency (ηO):
ηO = ηH × ηv × ηm%, (6)
Output Power (PO):
WJMS email for subscription: info@wjms.org.uk

154 R. Singh & M. Nataraj: Design and analysis of pump impeller
Output power assumed as 1hp, (7)
Input Power to motor (PI):
PI =
ηO
O
hp(Power input to pump), (8)
Shaft Diameter (dS):
dS = s 16 × T
π × fS
, (9)
Torque (T):
T =
Pi
ω
Working stress(fs)
fs =
fm
FOS
; Ultimate stress(fm) and FOS, (10)
Theoretical Discharge (Qth):
Qth =
Q
v
m3
/s, (11)
Inlet Velocity (U1):
U1 =
π × Ds × N
60
m/s, (12)
Inlet Blade Angle (β1):
β1 = tan−1 Cm1
U1
Cm1 = K1 × Cmom/s (13)
K1 value is to be assumed as 1.05m/s,
Out Blade Angle (β2):
sin β1 ×
K2
K1
×
w1
w2
×
Cm3
Cm0
K2 = assumed to be 1.2, (14)
Manometric Head (Hm):
Hm =
H
ηH
m, (15)
Outlet Velocity (U2):
U2 =
g × H
Cu2
m/s, (16)
Impeller Outer Diameter (Dd):
Dd =
60 × U2
π × N
mm, (17)
Outlet Flow Velocity (Cm2):
Cm2 = 0.687 × Cm1m/s, (18)
No. of Blades/Vanes (Z):
Z = 6.5 ×
Dd + Ds
Dd − Ds
× sin
β1 + β2
2
. (19)
WJMS email for contribution: submit@wjms.org.uk

2.2 Vane profile
The methods of constructing vane profile are Circular arc method, point by point method and confor-
mal representation method. In this paper, two methods (circular arc method and point by point method) are
considered for developing the vane profile. Tab. 1 lists the main geometric parameters to model vane profile.
Table 1. Parameters of impeller
Parameter Dimension
Head 24 m
Discharge 1.583 L/sec
Speed 2000 rpm
2.3 Circular arc method
The impeller is arbitrarily divided into a number of concentric rings between r1 and r2. The radius of
arc ρ, between any two rings rband rais obtained from the Eq.(20). The computations of the values of ρ for
various rings and the radii of ar of the vane are shown in Fig. 2.
ρ =
rb
2 − ra
2
2(rb cos βb − ra cos βa)
. (20)
Figure 2: Vane profile – Circular arc method
Fig. 2. Vane profile - Circular arc method
2.4 Point by point method
The co-ordinates for developing the vane profile together with the inlet and outlet angle depends on the
radius (r). Tabular integration method is used for obtaining the co-ordinates. The radiuses with respect to angle
are obtained from the Eq.(22). The values of the vane profile coordinates and the vane profile are shown in
Fig.3.
r.dθ =
dr
tan β
, (21)
θ =
180
r
ra
rb
dr
r. tan β
. (22)

Figure 3: Vane profile – point by point method.
Fig. 3. Vane profile - point by point method
3 Flow simulation using CFD
CFD approach was carried out to analyze the behavior of flow field in the impeller using the SWFS soft-
ware. SWFS software is a powerful CFD tool that enables designers to quickly and easily simulate fluid flow
for the success of designs. Design cycles are expensive and time-consuming. CFD analysis is able to help the
designers to optimize the designs by simulating several concepts and scenarios to make absolute assessment.
SWFS solves time-dependent three-dimensional Reynolds-averaged Navier-Stokes equations using the k - ε
turbulence model with the Finite Volume Method (FVM)Technical paper [8].
3.1 Modeling and meshing
The first step in CFD simulation is preprocessing. In preprocessing modeling and mesh is generated.The
CAD model and mesh was carried out using Octree - based mesh technology, combined with a unique im-
mersed boundary approach embedded with mesh from Technical paper [9]. Two-Scale Wall Functions ap-
proach automatic mesh generation with automatic detection of initial mesh settings resolves the governing
equations. Automatic meshing tools allowed creating mesh for any arbitrary 3D model. Meshing subdivides
the model and the fluid volume into several tiny pieces called cells. The multi block multi grid approach
(structured mesh) was used to approximate the solid fluid boundary.
3.2 Governing equations
The principles of conservation law governed by fluid dynamics are:
Mass Continuity:
αρ
αt
+ .(ρu) = 0, (23)
Navier-Stkes:
ρ
αu
αt
+ u. u = − p + T + f, (24)
Energy:
ρ
De
Dt
= −ρ u + .(k T) + Φ. (25)

3.3 The modified k − ε turbulence model
The two-equation modified k − ε turbulence model was used to evaluate the impeller flow simulation in
this study. SWFS software has been bench marked against a wide range of CFD turbulence cases based on the
physical nature of the problem, quality of the result and computing power. The two-equation modified k − ε
turbulence model leads to good predictions for spatial laminar, turbulent and transitional flows over a range
of compressible and anisotropic flows with its unique Two-Scale Wall Functions approach and immersed
boundary Cartesian meshes Technical paper [9].
∂
∂t
(ρk) +
∂
∂xi
(ρkui) =
∂
∂xi
µ +
µt
σk
∂k
∂xi
+ τR
ij − ρε + µtPB, (26)
∂
∂t
(ρε) +
∂
∂xi
(ρεui) =
∂
∂xi
µ +
µt
σε
∂ε
∂xi
+ Cε1
ε
K
f1τR
ij
∂ui
∂xj
+ CBµtPB − f2Cs2
ρε2
K
. (27)
Where, τR
ij = µSij; τR
ij = µSij − 2
3 ρkδij; Sij = ∂ui
∂xj
+
∂uj
∂xi
− 2
3 δij
∂uk
∂xk
; PB = − gi
σB
1
ρ
∂P
∂xi
; the default
values for the constants in the above equations are Cµ = 0.09; Cε1 = 1.44; Cε2 = 1.92; σk = 1.0; σε =
1.3; σB = 0.9; CB = 1 if PB > 0; CB = 0 if PB < 0,The turbulent viscosity is determined from;
µt = fµ
Cµρk2
ε
(28)
Damping function fµ is determined from Lam and Bremhorst [6];
fµ = (1 − e−0.025Ry
)2
· (1 +
20.5
Rt
). (29)
Where, Ry = ρ
√
ky
µ ; Rt = ρk2
µε y is the distance from point to the wall and Lam and Bremhorst’s damping
function f1 and f2 are determined from:
f1 = 1 +
0.05
fµ
3
; f2 = 1 − eR2
t . (30)
Lam and Bremhorst’s damping function f, f1, f1 decrease turbulent viscosity and turbulence energy
and increase the turbulence dissipation rate when the Reynolds number Ry based on the average velocity of
fluctuations and distance from wall becomes too small, when fµ = 1, f1 = 1 and f1 = 1 the approach
obtaines the original k − ε model.
3.4 Two scale wall function
The modified k−ε turbulence model always uses wall functions.SWFS uses the dimensionless value y+.
Since the computational mesh used in SWFS is always immersive boundary non-body-fitted Cartesian mesh,
y+ of some near-wall cells could be very small.
y+
=
√
ρτwy
µ
(31)
3.5 Boundary condition
The fluid is permitted to arrive at the impeller eye which turns the flow centrifugally outwards through the
blades. The boundary conditions for the impeller are inlet, outlet, and impeller rotation. The inlet volume flow
at the entrance of the impeller was given as inlet; the outlet was set as static pressure equal to the environmental
pressure; and relative velocity of the impeller was set as global rotating frame as shown in Fig. 4. Since the
working fluid is water, the simulations were performed based on the assumptions: incompressible flow; no-slip
boundary conditions have been imposed over the impeller vanes and walls, and gravity effects are negligible.

Figure 4: Boundary Conditions
Fig. 4. Boundary Conditions
4 Result and discussion
Four impellers CAFC, CABC, PPFC and PPBC were analyzed using SWFS. The analyses were made
for the circular arc method and point by point method with forward and backward curved vanes. The results
of the flow field investigation are presented in terms of velocity and pressure distribution of the impeller
passages. Fig.5 shows the velocity distributions and pressure distributions on the vane-to-vane for impeller
A, B, C and D, respectively. Noting the fact that flow distributions in the backward curved vane have high
efficiency compared with forward curved vane. Hence it is evident from Fig. 5 the backward curved vanes
have better flow distribution than the forward curved vane. The pressure increases normally on the pressure
surface than on the suction surface on each plane. Impeller B has gradual pressure distribution in the stream
wise direction than other impellers as shown in Fig. 5. The maximum efficiency of the impeller was obtained
for the backward curved vane profile. However, the maximum efficiency is 58.53% for the backward curved
circular arc method. Based on the simulation a mixed flow impeller was designed and analyzed using SWFS
and the pressure contour was shown in Fig. 6. Using the methodology adopted in this investigation the mixed
flow impeller is analyzed for multiphase (oil and water) flow by varying the mixture of oil and water in future.
Figure 5: Pressure and Velocity contour of impellers (A, B, C and D).
Fig. 5. Pressure and Velocity contour of impellers (A, B, C and D)

Figure 6: Pressure contour of mixed flow impeller.Fig. 6. Pressure contour of mixed flow impeller
5 Conclusion
Numerical investigations were carried out to analyze the flow field in the pump impeller using SWFS.
To design a centrifugal pump impeller a procedure is proposed. The design procedure leads to good results
in a lesser time. The effect of the forward curved vane and backward curved vane were analyzed. From the
numerical results the backward curved vanes have better performance than the forward curved vane. The vane
profile was developed by two methods viz. circular arc method and point by point method. The efficiency of
the circular arc method was 58.53% and point by point method was 57.31%. The circular arc method have
higher efficiency than point by point method. Since the variation was minimum, the impeller vane design may
be selected based on the easiest manufacturing process method.
6 Future work
The mixed flow impeller will be analyzed for multi-phase flow (oil and water) by varying the mixture of
oil and water in future using SWFS.
Nomenclature
Q, m3/s Volume flow rate
H, m Head
N, rpm Speed
ω , rps Angular velocity
PT , Pa Total pressure
ρ fluid density
k turbulence energy
ε dissipation rate of turbulence energy
µ fluid viscosity
µt fluid turbulent viscosity
τij ij-th component of the laminar stress tensor
ui i-th component of the fluid velocity vector
τR
ij ij-th component of the Reynolds stress tensor
xi i-th component of the Cartesian coordinate system

ni i-th component of the normal-to-the-wall in the fluid region
y distance from the wall along the normal to it
y+ dimensionless distance from the wall along the normal to it
δ boundary layer thickness calculated by the integral method
τw Wall shear stress
Cm, m/s Meridional component of absolute velocity
Cu, m/s Peripheral component of absolute velocity
Km2 Capacity constant at point, Cm√
2gH
Subscripts
1, 2 Inlet and outlet
i,j,k directions of the Cartesian coordinate system
w at the wall
References
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