Study of Stresses Developed on the Impeller of Centrifugal Pump at Different Speed using Ansys

Study of Stresses Developed on the Impeller of Centrifugal Pump at Different Speed using Ansys

Mr. Satish M. Rajmane

Research Scholar, WIT Research Centre,

Solapur University, Solapur, India

Dr. S. P. Kallurkar

Principal,

Atharva College of Engineering, Malad(w),Mumbai, India

Abstract Pump is a mechanical device generally used for raising liquids from a lower level to a higher one. Centrifugal Pumps are the machines, which employ centrifugal force to lift water from a lower level to a higher level by developing pressure. Computational fluid dynamics (CFD) analysis is being increasingly applied in the design of Centrifugal Pumps. CFD is an important tool for pump designers. This paper is mainly focused on design development of pump from customer requirement at initial design phase and FEA analysis of Centrifugal Pump using ANSYS for checking stresses and deformation from point of safe design. The rotating device i.e. Impeller has basic issues of failure at different speed and forces. As a case study, pilot project with research methodology in the preliminary stage of design of Centrifugal Pump is considered. The Pump dimensions are calculated according to the customer requirements of input parameters like head, discharge, and speed. Stress analysis of Impeller of Centrifugal Pump at different speed is done randomly to test design is safe or not.

Keywords Stress analysis, CFD, FEA, ANSYS, Centrifugal Pump.

1. INTRODUCTION

   Computational fluid dynamics (CFD) is the analysis of the system involving fluid flow, heat transfer and associated phenomena such as chemical reactions by means of computer based simulation. With the aid of the CFD approach, the complex internal flows in the impellers, which are not fully understood yet, can be well predicted; to speed up the pump design procedure.The prediction of behavior in a given physical situation consists of the values of the relevant variables governing the processes of interest. To obtain an

2. PROBLEM DESCRIPTION

   Impeller is very important part of Centrifugal Pump and it is experiencing various loads like fluid pressure, inertia, unbalanced forces, and vibrations during rotation. Excessive stresses may lead to development of cracks in the impeller and ultimately failure of impeller. Hence it is essential to analyze the stresses developed in the impeller.

3. SCOPE OF WORK

   ANSYS Workbench which is a Finite Element Analysis (FEA) software used in the numerical simulation of the centrifugal impeller with the finite element method. The equivalent stress distribution of the impeller, which caused by the centrifugal load, the coupling effect of centrifugal load and aerodynamic load, is analysed. Based on the fluid components transport theory, the distribution of the flow field inside the impeller is analysed, and discussed the influence of the stress distribution. Analytical design &CFD analysis of Pump at 1800 rpm and validation of an impeller design using stress analysis at various speed such as 1050 rpm, 1250 rpm, 1450 rpm is analysed. Post processing shows the stress and deformation results at each node. This is analysed to check whether the results are in safe limit or not.

4. DESIGN OF CENTRIFUGAL PUMP

1. Customers requirement for Pump specification

   Head (H ) = 13.8 m, Flow rate (Q) = 16 lit /s ,Speed (n) = 1800 rpm, Fluid=water, Pump type =Radial

2. General dimensions of impeller are calculated as below

   1. Specific speed ns= nx Q

3

H4

approximate solution numerically, we have to use a discretization method which approximates the differential equations by a system of algebraic equations, which can then be solved on a computer. The approximations are applied to small domains in space and/or time so the numerical solution provides results at discrete locations in space and time. Much as the accuracy of experimental data depends on the quality of the tools used, the accuracy of numerical solutions is dependent on the quality of discretization used. CFD is used in pump design industry to analyze the effect of various forces, vibrations, fluid pressure and its effect. Optimization in the existing design of pump can produce large savings in material costing of pump with increase of head & efficiency.

3/4

=1800x 0.016

13.8

= 31.79 rpm 2.Nominal diameter D1

= 4.5 x 103 x3 Q.016

1800

= 93.1 mm

= 4.5 x 103x 3Q

n

2

1. Hydraulic efficiency, h = 1 0.42

   (log D10.172)

   = 87%

   1

   Cm1 = K1 x Cmo

   = 1.4 x 2.26

   = 3.164 m/s

2. Volumetric efficiency ,v = 2

   3.14D1n

   =93.72%

   1+0.68(ns) /3

   5.u1 = 60

3. Assuming mechanical efficiency ,m= 0.96 6.Overall efficiency, = h x v x m

= 78.27%

1. Output Power, No = QH / const.

   = (9.81 x 1000 x0.016 x 13.8 ) / 1000

   = 2.17 KW( 2.91hp )

2. Input power, Ni =NO

   = 2.7468 KW( 3.68hp )

3. Assuming an overload of 15% , input power (Ni) = 2.74 x 1.15

= 8.5 m/s

6.Inlet blade angle (1)will be calculated as, 1= tan1(Cm1 / u1 ) = tan1(3.164/8.5)

= 20.420(taken as 250)

D. Outlet dimensions are calculated as below

1. Manometric head(Hm) ,

   Hm = H

   h

   = 17.23 m

2. First approximation of u2 taking, Cu2 = 0.5 First approximation of u2,

= 3.15 KW(4.22 hp)

1. Torque, T =Ni= 3.15 x 60

   u2= gHm

   2 x 3.14 x 1800

   = 0.0167 KN-m

   Cu2

   = 9.81 17.23/0.5

2. Taking the shaft material as EN8, Ultimate stress ( fm) as 35 N/mm2,and taking factor safety ( FS ) as 2 for uniform speed of rotation.

   = 18.45 m/s

3. Working stress(fs )=fm

FS

3. D2 1st approximation,

Outside diameter(D2),

= 17.5 N/mm2

D2 =

60u2

s

1. Shaft diameter, d = 3 16T

   3.14fs

   = 0.01687 m= 17 mm

   Taking fatigue stress (bending and shear) into account, minimum shaft diameter (ds)is taken as 25 mm, ds = 25 mm

2. Hub diameter, dh = 1.25 ds = 1.25 x 25 = 30 mm.

C. Inlet dimensions are calculated as below

1. Theoretical discharge, Qth = Q / v

   = 0.016 / 0.9372 = 0.0170 m3/s

2. Eye diameter of impeller (Do)is taken as 76.4mm , the axial velocity at an impeller eye (Co ) is

4Qth

3.14n

= 196 mm

4.Taking, Cm3 = 0.8 x Cmo= 0.8 x 2.26 = 1.81 m/s

5.Taking K2 = 1.2 and w1 / w2 = 1.18 Sin 2= Sin 1 K2w1Cm3 = 0.3419

K1w2Cm0

Outlet blade angle, 2=200

6.Outlet flow velocity(Cm2), Cm2 = 0.687 x Cm1

= 0.687 x 3.164

Co = 2

3.14 ds

= 3.7 m/s

3.The diameter of the inlet edge of impeller blade (D1)is taken as 90 mm

Inlet breadth (B1 ) = Qth

3.14D1Cm1

= 25.8 mm (Considered as 26 mm) 4.Taking K1 = 1.4 ,

= 2.18 m/s

7.No of blades , Z = 6.5 x D2+D1 x sin 1+2

D2D1 2

= 6.01,Z is taken as 6 8.Assuming p as 0.2915

Ho= ( 1 + p ) Hm = (1+0.2915 ) 17.23 = 22.26 mm

1. Second approximation of u2,

   Outlet blade velocity, u2

   = 18.07 mm/s

   = Cm2

   2tan2

   + Cm2 +gHm

   2tan2

   Table 1. assumptions made in FEA

   Parameters	Values
   Fluid-	Water
   Material	Mild Steel
   Youngs Modulus	1.1e+005MPa
   Poissons Ratio	0.28
   Structural Density	7.2e-006 Kg/3
   Thermal Expansion	1.1e-005 1/ °C
   Tensile Yield Strength	240 MPa
   Ultimate Tensile Strength	840 MPa
   Specific Heat	875J/Kg °C
   Thermal conductivity	5.2e-002 W/mm °C

2. D2 2nd approximation,

60u2

Outside diameter (D2) = 3.14n

= 0.192m

D2 1st approximation (D21st = 196 mm ) and D2 2nd approximation (D2 2nd = 192mm),closely agrees. Final value of outer diameter D2 is taken as 200 mm

11.Cm3 =Cm2 = 1.82 m/s

K2

1. Outlet breadth, B2 = Qth

   3.14D2Cm3

   = 15mm

   1. Geometry of Impeller Model

1. Verification of flow coefficients are calculated as below

   The model of impeller and casing is made in CATIA and imported in ANSYS for deformation and stress analysis.

   1.K1=1/(1- Z1

   3.14D1Sin1

   2.K2=1/(1- Z2

   3.14D2Sin2

   ) = 1.414

   ) = 1.195

   3. W1 = Cm1 = 7.49 m/s

   sin1

   4.W2= Cm3 = 6.37 m/s

   sin2

   5.1 =1.18

   2

2. Volute Casing design steps are as below

   1. Inlet width of volute, B3 = 1.8 B2= 1.8 x 17= 30.6 mm 2.Outlet width of volute, D3 = 1.15 D2

= 1.15 x 0.192= 220.8 mm

3.Rv =D2+D3 = 0.10

4

4.Width at X distance Bx = B3 +2RvD2 = 30.60 mm

1.73

G. Dimensions of pump according to customer requirements are calculated and listed below

Specific Speed (Ns) =31.79 rpm, Pump type=Radial Torque 0.0167 KN-m, Hydraulic efficiency =87 % ,

Volumetric efficiency =93.72 % ,Overall efficiency =78.27 % , Input power 3.15 KW(4.22hp) ,Output power 2.17 KW

Shaft diameter (ds)=17 mm, Hub diameter= 30 mm

Eye diameter (Do) =76.4 mm, Inlet diameter (D1) =90 mm Outlet diameter (D2)= 192 mm ,Number of blades (z)= 6 Inlet breadth (B1)= 26 mm, Outlet Breadth (B2) =15 mm

1. Mesh Model

   Fig. 1 Model of Casing

   Fig. 2 Model of Impeller

   Blade velocity (u1) =8.5 m/s, Blade velocity (u2) =18.45 m/s Blade angle (1) =250 ,Blade angle (2) =200

   V DETAILS OF FEA

   The FEA analysis is carried out randomly at different speed of 1050 rpm,1250 rpm and 1450 rpm for testing whether theoretical design calculation of pump dimension are safe or not. The assumptions made in FEA are given in below Table 1.

   The impeller blade and casing model is meshed and hexa mesh is obtained by giving body sizing and edge sizing.

   Fig. 3 Meshing of Pump

   Fig. 4 Meshing of Impeller

   Fig. 5 Pressure distribution

   Fig. 6 Velocity distribution

2. Boundary Conditions

Using the following boundary conditions static structural analysis is performed.

Case 1- Boundary Condition With 1050 rpm-

As per static structural analysis the Rotational velocity is applied to all bodies is 1050 RPM , Fixing condition is applied as Remote displacement that is Rotation in X direction is free and other Degree of freedom is fixed. The other end of the shaft is fixed. This remote displacement support is applied on the circumference of the one end of the shaft.

• Rotational Velocity-

  Fig. 7 Rotational velocity at 1050 rpm

• Pressure at suction side 9.45 x 10-2 MPa

  Fig. 8 Pressure at suction side at 1050 rpm

• Pressure outer side 6.66 x 10-2 MPa

Fig. 9 Pressure at discharge side at 1050 rpm

• Pressure on top side 0.15 MPa

  Fig. 10 Pressure at top side at 1050 rpm

• Remote Displacement

  Fig. 11 Remote displacement at 1050 rpm

• Standard Earth Gravity for self-weight

  Fig. 12 Standard Earth Gravity at 1050 rpm

  Results

• Total Deformation-

  Fig. 13Total deformation at 1050 rpm

• Equivalent Von-Misses Stress

  Fig. 14Von-Mises stress at 1050 rpm

  Observations-

  • The maximum total deformation of 0.005 mm is within safe limit and can be considered safe.

  • The maximum Von Misses stress value of 10.65 MPa is less than the allowable limit and hence the impeller can be considered as safe.

    Case 2- Boundary Condition With 1250 rpm-

    For case 2 all the boundary conditions are similar as case 1 except the rotational velocity which is 1250 rpm.

• Rotational Velocity- 1250 rpm

• Equivalent Von-Misses Stress

  Observations-

  Fig. 17Von-Misesstress at 1250 rpm

  • The maximum total deformation of 0.0059 mm is within safe limit and can be considered safe.

  • The maximum Von Misses stress value of 13.052 MPa is less than the allowable limit and hence the impeller can be considered as safe.

• Results

  Fig. 15 Rotational Velocity at 1250 rpm

  Case 3. Boundary Condition With 1450 rpm-

  For case 3 all the boundary conditions are similar as case 1 except the rotational velocity which is 1450 rpm.

• Rotational Velocity at 1450 rpm-

  Total Deformation

  Results-

  Fig. 18 Rotational Velocity at 1450 rpm

  Fig. 16 Total deformation at 1250 rpm

• Total Deformation-

  Fig. 19 Total deformation at 1450 rpm

  Observations-

  • The maximum total deformation of 0.0069 mm is within safe limit and can be considered safe.

  • The maximum Von Misses stress value of 15.864 MPa is less than the allowable limit and hence the impeller can be considered as safe.

    VI CONCLUSIONS

    Stress analysis of impeller is done at different speeds. It is found that the impeller blade is safe under rotational velocity of 1050 rpm, 1250 rpm and 1450 rpm .The results show that stresses increases with speed, but are still under safe limit.

• Equivalent Von-Misses Stress

Fig. 20 Von-Misesstress at 1450 rpm

REFERENCES

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2. Qing Zhang, Hai Zhou, Qingpeng Gao, etc alAnalysis Of Effects Of Impeller Inlet Width On The Performance Of Centrifugal Pump, Journal of Chemical and Pharmaceutical Research , 2014,6 (5) :2078-2081.

3. S .Yedidiah,Present Knowledge Of The Effects Of The Impeller Geometry On The Developed Head , Proc Instn Mech Engrs Vol 210, 1996

4. W.Huang, T Caderetc al, Two Phase Flow Structure At The Impeller-Volute Interface,Proceedings of The 2ndInternational Conference On Multiphase Flow, Kyoto Japan April 3-7,1995

5. Cader, T., Masbernet, O., etc al, Two-Phase Velocity Distributions and Overall Performance of a Centrifugal Slurry Pump,ASMEJ.Fluids Engineering Conf., Washington DC, 116, pp. 176186,1994