Arungshu Das

International Journal of Mechanical Engineering and Computer Applications, Vol 1, Issue 5,Special Issue, October 2013, ISSN 2320-6349

All copyrights Reserved by eETECME-2013, Marathwada Mitra Mandal☂s polytechnique.Theragaon , Pune, India , Published by IJMCA (www.ijmca.org) Page 1

Design and Stress Analysis of a Mixed FlowPump Impeller

1Arunangsu Das, 2Apurba Kumar Roy, 2*Kaushik Kumar1Department of Mechanical Engineering, I.C.V. Polytechnic, Jhargram,(WB),India

2Department of Mechanical Engineering, Birla Institute of Technology, Mesra,Ranchi, [email protected], [email protected], [email protected]

Abstract: In order to avoid resonance of a mixed-flowpump impeller and to avoid blade failure due to excessivestress development, it is required to know the naturalfrequencies at different modes and one should have an ideaabout the Von Mises stress distribution in the impeller blades.In this present work design and FEM analysis has beencarried out on mixed flow pump impeller having differentblade positions on the meridional annulus. The naturalfrequencies at six different modes of the pump impeller wereobtained. The maximum Von Mises stress distribution wascompared among the impellers having different bladepositions. The mixed flow impeller having inlet inclined bladepositions on the meridional annulus experiences less amountof Von Mises stress as compared to impeller havingtrapezoidal blade positions on the meridional annulus. Thenatural frequencies of the impeller having inlet inclinedblade positions on the meridional annulus shows a highervalue as compared to compared to impeller havingtrapezoidal blade positions on the meridional annulus.

Index Terms♥ Mixed flow pump, Von Mises stress, FEManalysis, natural frequency

*Corresponding author

Nomenclature2C : tangential component of absolute velocity,

m/sec.C : actual chord ,mmC☂ : meridional chord, mmCL : coefficient of lift, dimensionlessCm : meridional velocity, m/sec.Cm1 : meridional velocity at inlet, m/sec.Cm2 : meridional velocity at outlet, m/sec.D1 : blade diameter at inlet, mmD2 : blade diameter at outlet, mmD1h : blade diameter at inlet at hub section, mmD1t : blade diameter at inlet at tip section, mm

D2h : blade diameter at outlet at hub section, mmD2t : blade diameter at outlet at tip section, mm

DL : Leiblein blade diffusion factor, dimensionlessDm : mean diameter, mm

e : diameter ratio, dimensionlessg : acceleration due to gravity, m/sec2.H : pressure head, mKu : velocity coefficient, dimensionlessl : blade span, mmN : rotational speed, rev./min.P : power, kWQ : volumetric discharge, m3/sec.r : radius, mmS : blade spacing, mmu1 : tangential velocity of blade at inlet, m/sec.u2 : tangential velocity of blade at outlet, m/sec.VS : slip velocity, mmサ1 : blade inlet angle, degreesサ2 : blade outlet angle, degreesサm : mean blade angle, degreesタ : blade stagger angle, degreesヅ : mass density of the fluid(water), kg/m3

ネ : angular velocity, ran/sec.キ : dimensionless specific speed, dimensionlessナ : semi-cone angle of the impeller, degrees

1. INTRODUCTION

The mixed flow pumps are extensively used inthermal power plants for cooling water duties. Theperformance of a mixed flow pump can be considerablyimproved by applying recent advances in understandingthe flow behavoiur of the pump and the blades. Thus,optimal blade position in the meridional annulus has animportant effect on loss and flow deflection. Theobjective of the blade design is to realize a given velocitytriangle with minimum losses as well as minimum stressdevelopment in the blade sections.

The industrial design methods are largely based onthe application of empirical and semi-empirical rulesalong with the use of available information in the form ofdifferent types of charts and graphs from the existingliterature. Impellers are mainly designed using profile



families which have been developed years ago. Theindustrial design method often ignores the actualhappening within the pump flow passage and isconsequently a poor guide when the question of a newdesign and development of pumps comes to picture. Inthe above design process the designer has less controlthan desirable over events. The lack of clear-cut rationalbasis also inhibits the correction of manufacturing ofshortfalls in expected performance. With the rapidadvancement of technology the complexity of theproblem is also increasing. This scenario demandsspeedy, efficient and optimal design of a mixed flowpump impeller.

To keep pace with the development and ensure betteroutput from the mixed flow pump, one has to formulate arational basis for the designing of impellers starting frombasic principles, such that the use of empirical co-relations is minimized. Such a design from the basicprinciples has advantages that the designer will havemore control over the outcome of his design, whilekeeping the physical principle constantly in view andenables him to rectify any faults in the performance of thepump.

In this present work, design of a mixed flow pumpimpeller was carried out for three different bladepositioning in the meridional annulus based on basicprinciples of fluid mechanics and turbo machinery. Theabove three models ware compared on the basis of finiteelement method (FEM) analysis to select the best amongthem and for design acceptability.

2. LITERATURE REVIEWThe research and development on mixed flow pump

have not gone to an extent as compared to conventionalcentrifugal and axial flow pumps. The flow through themixed flow pump is quite complex. The design of themixed flow pump impeller is much complex because ofits complex geometry and large number of flow variablesplay a very important role in its optimum design. In 1965,Wislicensus [1] initiated the design of a mixed flowpump impeller.

The modification of mixed flow pump impeller wascarried out by Myles [2]. In 1928, Busemann☂s [3]developed a formula for slip velocity for a mixed flowpump. Senoo and Nakase [4], and later on Inoue et al. [5]developed a design method by calculating the meridionalstream line. A.J. Stepanoff [6] gave a design procedurefor mixed flow pump impeller. Neumann☂s [7] and,Gahlot and Nyiri [8] suggested the step-by-step designprocedure for designing mixed flow pumps. YumikoTakayama and Hiroyoshi Watanabe [9] presented amulti-objective optimization strategy of mixed-flowpump design by means of Three Dimensional InverseDesign Approach. Jin- Hyuk Kim & Kwang-Yong Kim[10] developed an optimization procedure for highefficiency design of mixed-flow pumps. In 2013, Hao et

al. [11] studied the effects of meridional flow passageshape on hydraulic performance of mixed-flow pumpimpellers.

In 1981, K. Sham Sunder [12] presented a three-dimensional method of stress analysis using finiteelement techniques for determining the stress distributionin centrifugal impellers. Later on many researchers e.g.Ramamurti and Balasubramanian [13], Jonker and VanEssen [14], Samir Lemeｻ and Nermina Zaimovi@-Uzunovi@ [15], Bhope and Padole [16], Hao et al. [11]and Mehta and Patel [17] contributed much on the stressanalysis for highly complex blades of various pumps.

Although, a number of excellent literatures areavailable on the flow analysis through mixed flowpumps, but study on design and structural analysis ofmixed flow pump impellers are scanty. Therefore, thepresent work is devoted to design and stress analysis ofmixed flow pump impeller having different bladepositions on the meridional annulus.

3. DESIGN METHODOLOGY

Here the design of the mixed flow pump impeller isbased on free vortex theory. The stream surfaces throughthe meridional annulus are kept parallel to hub andcasing, whereas, the hub and casing are parallel to oneanother. It is also assumes that the meridional velocitydistribution remains uniform across the annulus [2]. Inthe present case a mixed flow pump impeller has beendesigned for discharge (Q) =0.125 m3/sec., headdeveloped (H) = 5 m, speed of rotation (N) = 1000rev/min.

3.1 Design procedure

Calculation of non-dimensional specific speed (キ)

using the relation, キ = 4/3)(gHQ

------- (1)which results in キ = 1.998 rad./sec.The inlet diameter (D1) of the impeller has been

calculated using the relation

H =2

12 .2

1e

NDgKu

---------- (2)

Where, e =2

1DD ---------- (3)

Ku = gHu2

2 ---------- (4)

The value of e and Ku for a given specific speed hasbeen used from A.J.Stepanoff work. [6].



The ideal power requirement is calculated using therelation P = kWgHQ

1000 ---------- (5)

which results in P = 15 kW.

The choice of cone angle of the mixed flow pupimpeller is chosen as suggested in [2], which must be inbetween 450 to 600. In the present case the cone angle hasbeen chosen 600 for the design and a preliminary layout isprepared as shown in fig. 1.

Fig. 1 Preliminary layout of the blade profile

From the fig. 1, the inlet diameters (D1h, D1t) andoutlet diameters (D2h, D2t) of the impeller were measured.Then the meridional velocity at inlet (Cm1) and outlet(Cm2) were calculated using the relation Cm = rl

Q2 . For

a proper design, Cm2/ Cm1 should be in between 1.2 to1.22 [2]. So, to keep the value of Cm2 / Cm1 within thespecified limit, the rectangular position of the blade in themeridional annulus has been modified, resulting in threedifferent blade positioning in the meridional annulus asshown in fig.2.The inlet and out let diameters of theimpeller blades are shown in Table 1 .

Here, case-me (inlet inclined), case-II (trapezoidal)and case-III (outlet inclined) blade positioning in themeridional annulus were used for further processing. Themeridional annulus along the blade span was divided intoten numbers of equal sections parallel to hub and casing.

Fig. 2 Final layout of the blade profile

Table 1 Blade diameters in mm.Case-I(Inlet

inclined)

Case-II(Trapezoidal)

Case-III(outlet

inclined)D1t 269.46 294.46 319.46D1h 169.00 169.00 169.00D2t 294.46 319.46 344.46D2h 244.00 244.00 244.00Calculation of blade angles are carried out using thefollowing relations,

u1 = 601ND m/sec ------ (6)

u2 = 602 ND m/sec. ------ (7)

tan サ1= 1

1

mCu

------ (8)

tan サ2 = Sm

VCCu2

22 ---- (9)

where, VS= Z

u sincos 22--- (10)

mean blade angle,

tan サm = 2tantan 21 -- (11)

pitch, S = ZDm ------ (12)

and Dm = 221 DD ------ (13)

actual chord, C = cos'C ------ (14)

The blade stagger angle シ has been calculated usingCarters correlation.

The blade angles calculated for each section along theblade span using above relations have to be verified to

H u b

T ip1

2

C m 1

C m 2

H u b

T ip M id sp a n

In le tin c lin ed

T ra p izo id a l B a c k w a rdin c lin ed



satisfy Leiblein blade diffusion factor DL to avoidseparation of boundary layer from the blade surfaces. TheLeiblein blade diffusion factor

DL = 6.0tantan2cos

coscos1 21

1

2

1CS --

(15)

If the blade angles fail to satisfy the blade diffusionfactor, the shifting of the blade positioning along the hubon the meridional annulus has to be made and all thecalculation of blade angles to be repeated till all thedesired conditions (サ1<サ2) and DL<0.6 are satisfied. Here,NACA 10C4 blade profile is used for the impeller bladesas suggested in [5].

3.2 Construction of 3D model of the impeller andFEM analysis

Once the blade angles were calculated, the straighttwo-dimensional cascade was transformed into thecorresponding conical cascade using conformaltransformation method. The blade sections were stagedone over another by maintaining proper stagger angle.Finally, using surface revolution method, 3D model ofthe mixed flow pump impeller has been prepared. In thiswork three different blade positioning are selected asshown in fig.2 and corresponding 3D models of themixed flow pump impeller were prepared. To find out thedevelopment of stresses in the above impellers and alsoto know the natural frequencies, finite element analysis(FEM) analysis has been carried out.

In this present work, the FEM analysis has beencarried out using CATIA V5 software to find thedevelopment of Von Mises stress, natural frequencies ofthe mixed flow pump impeller having different bladepositioning on the meridional annulus.

4. RESULTS AND DISCUSSIONThe design parameters such as blade angles, camber

angles, stagger angles, chord dimension were calculatedat different sections along the blade span for the threedifferent blade positioning in the meridional annulus.During the process of design calculations, it is observedthat the case-III failed to meet the basic design criteria(サ1>サ2) so, designing of the case-III was discarded.Therefore, further designing of case-I and case-II wereundertaken. The span wise variation of blade inlet angle(サ1), blade outlet angle (サ2), blade stagger angle (シ) forcase-I and case-II are shown in fig. 3 and fig.4respectively.

Fig. 3 Span wise variation of blade angles for inletinclined blade position (case-I) on meridional annulus

Fig. 4 Span wise variation of blade angles fortrapezoidal blade position (case-II) on meridional annulus

The blade solidity which is blade spacing by bladechord length (S/C) plays a very important role on theoverall performance a turbo machine. So to vary thisparameter one needs to vary blade spacing, pitch andchord length for optimal design. In this present work theoptimal number of blade was found to be eight. The bladesolidity (S/C) is related to coefficient of lift (CL) for anaerofoil/hydrofoil blade which is given by

CL = 2( CS ) (tan サ1- tan サ2) cos サm ------- (16)

Where, サm is the mean blade angle as given astan サm = (2

1 tan サ1 + tan サ2) --------- (17)The variations of blade solidity along blade span (hub

to tip) for case-I and case-II are shown in Fig. 5.

0 10 20 30 40 50 606062646668707274767880

Inlet inclined(case-I)

Blade

angle

s(in d

egree

s)

Spanwise distance from Hub to Tip(mm)

0 10 20 30 40 50 606062646668707274767880

Trapizoidal(cas-II)

Blad

e ang

les(in

degre

es)




Fig. 5 Span wise variation of blade solidity for bothinlet inclined blade position (case-I) and trapezoidal blade

position (case-II) on meridional annulus.From the fig.3 and fig. 4, it is observed that variation

of blade angles from hub to tip are more for case-II ascompared to case-I. More the twisting, the more isloading on the blades so, more is the stress developmentin the blades. This contributes to the more blade loadingfor the case-II as compared to case-I. From the fig. 5, it isalso observed that the variation of blade solidity(S/C)along the blade span is quite smooth and linear in naturefor case-I as compared to case-II. This contributes to thebetter lift coefficient (CL) for case-I and hence, betterhydraulic performance. As stated earlier that in this workNACA 10C4 blade profile was used. The cross section ofthe blades at hub and tip section of case-I and case-II areshown in fig. 6 and fig. 7 respectively.

Once the design of the impeller blades wascompleted, 3-D model of the impeller was prepared usingCATIA V5 solid modeling software. The 3-D model forthe case-I and case-II are shown in fig. 8 and fig. 9respectively.

The structural analysis of the above two models werefurther carried out for Von Mises stress and naturalfrequency.

Fig. 6 Cross section of the blades at hub and tipfor inlet inclined blade position on meridional annulus

(case-I)

Fig. 7 Cross section of the blades at hub and tipfor trapezoidal blade position on meridional annulus

(case-II)

Fig. 8 3-D Model of the impeller for inlet inclinedblade position on meridional annulus (case-I)

Fig. 9 3-D Model of the impeller for trapezoidal bladeposition on meridional annulus (case-II)

Before proceeding to FEM analysis on the pumpimpellers, validation of the finite element formulationwas checked and grid independency test was carried outto choose the optimum element size for FEM analysis. Todo so, a rectangular shaped cantilever beam having thelength equivalent to the span of the blade, the width,equivalent to the average width of the blade and thethickness, equivalent to the average thickness of the bladewere taken. A normal force equivalent to maximumpressure force, which the impeller blades are supposed toexperience, was applied on one side of the cantileverbeam. Here, it is assumed that the pressure force is actingon the blades as uniformly distributed load(UDL).Calculation was made for the analytical solutionfor the Von Mises stress. Using CATIA V5 software,numerical analysis for the same has been carried out

0 10 20 30 40 50 60

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Blad

e soli

dity(S

/C)


Trapiziodal(case-II) Inlet inclined(case-I)

0 25 50 75 100 125 150 175 200-50

-25

0

25

50

HUB SECTION

TIP SECTIONInlet inclined blade position

Blad

e thic

knes

s(t),m

m

Chord length(C),mm

0 25 50 75 100 125 150 175 200-50

-25

0

25

50

TIP SECTION

HUB SECTION

Trapizoidal blade position

Blad

e thic

knes

s(t),m

m

Chord length(C),mm



using seven different sizes of the tetrahedral elementnamely 3, 3.5, 4, 4.5, 5, 5.5 and 6mm. Among the variouselement sizes, 4, 4.5 and 5 mm elements showed anexcellent agreement between the analytical result and thenumerical result. So, 5 mm tetrahedral element waschosen for the FEM analysis for the impellers. The resultsof the grid independency test are shown in fig. 10. TheVon Mises stress distribution for the case-I and case-IIare shown in fig. 11 and fig. 12 respectively. From thefigs. 11 & 12, it is observed that case-I is experiencingless Von Mises stress as compared to case-II.

Fig. 10 Grid independency test for Von Mises stressdistribution calculations

Fig. 11 Von Mises stress distribution of the impellerfor inlet inclined blade position on meridional annulus

(case-I)

Fig. 12 Von Mises stress distribution of the impellerfor trapezoidal blade position on meridional annulus

(case-II)

Here an attempt has also made to find out naturalfrequencies of the impeller at first six modes. The naturalfrequencies of the impeller having two different bladepositions, case-I and case-II are tabulated and shown inTable 2. From the natural frequency analysis it isobserved that the value of the natural frequencies for thecase-I is little higher than that of case-II.

Table 2 Comparison of natural frequencies for both inletinclined blade position (case-I) and trapezoidal blade position

(case-II) on meridional annulusMode Inlet inclined

blade position (case-I)(Hz)

Trapezoidal bladeposition (case-II)

(Hz)1 132.655 131.7162 132.692 131.8183 249.244 246.8164 314.003 315.4675 1323.26 1324.546 1323.29 1324.46

5. CONCLUSIONA mixed flow pump impeller of non dimensional

specific speed of 1.998 rad/sec has been designed foruse in large cooling water duties of thermal powerplants. From the analysis, it is found that the mixedflow pump impeller having inlet inclined bladeposition on the meridional annulus (case-I)experiences less Von Mises stress as compared totrapezoidal blade position on meridionalannulus(case-II). From the natural frequency analysisit is also found that the value of the naturalfrequencies for the inlet inclined blade position onmeridional annulus (case-I) is more than that in thecase of trapezoidal blade position on meridionalannulus (case-II). The blade solidity along the spanfor the inlet inclined blades shows bettercharacteristics than that of the trapezoidal bladeposition on meridional annulus. Therefore, from thispresent work, it can be concluded that the mixed flowpump impeller having inlet inclined blade position onmeridional annulus can be a better choice for use.

REFERENCES

[1] Wislicensus, G. F., The Design of mixed flowpumps. Proceedings of the symposium held at theN.E.L.Glasgow, 1965.[2] Myles, D.J., A design method for mixed flowfans and pumps, Report No. 117, National Engg.Laboratory, 1965.[3] Busemann, A., The pump head ratio of radialcentrifugal pumps with logarithmic spiral blades (InGerman), Z. Angew. Math. Mech. March 1928, 8 (5),pp.372-384.[4] Senoo, Y. and Nakase, Y., An analysis of flowfor Power, 1972, Paper No. 71-GT-2, pp43-72.



[5] Inoue, M., Ikui, T., Kamada, Y. and Tashidaro,M., A quasi three dimensional design of diagonal flowimpellers by use of cascade data. IAHR, 10thSymposium, Tokyo., 1980, pp. 403-414.[6] Stepanoff, A.J., Centrifugal and Axial flowpumps, 1957, John Wiley and sons 2nd Edition, NewYork.[7] Neumann, B., The interaction BetweenGeometry and Performance of a centrifugal Pump, 1991,Mechanical Engineering Publications, London.[8] Gahlot V.K. and Nyiri A., Impeller Pumps,Theory and Design, 1993, M.A.C.T., Bhopal.[9] Yumiko Takayama and Hiroyoshi Watanabe,Multi-Objective Design Optimization of a Mixed flowimpeller. ASME 2009, Fluids Engineering Division,Summer Meeting. Colorado USA.[10] Jin-Hyuk Kim and Kwang-Yong Kim,Optimization of Vane Diffuser in a Mixed-Flow Pump forHigh Efficiency Design. International Journal of FluidMachinery and Systems Vol. 4, No. 1, January-March2011.[11] Bing, H. C., Shuliang, T. L. and Zhu, B., Effectsof meridional flow passage shape on hydraulicperformance of mixed-flow pump impellers. ChineseJournal of Mechanical Engineering, 2013, Volume 26,Issue 3, pp.469-475.[12] Sham Sunder, K, Finite Element Analysis ofCentrifugal Impellers, Ph.D. Thesis, School ofMechanical Engineering, Cranfield Institute ofTechnology, 1981.[13] Ramamurti, V. and Balasubramanian, P., Steadystate stress analysis of centrifugal fan impellers,Computers & Structures, 1987, 25 (1). pp. 129-135.[14] Jonker, J. B. and Van Essen, T. G., A finiteelement perturbation method for computing fluid-induced forces on a centrifugal impeller, rotating andwhirling in a volute casing, International Journal forNumerical Methods in Engineering, 1997, Vol. 40, pp.269-294.[15] Samir Lemeｻ and Nermina Zaimovi@-Uzunovi@,Mode shapes of centrifugal pump impeller, 6thInternational Research/Expert Conference on Trends inthe Development of Machinery and AssociatedTechnology, TMT 2002, Neum, B&H, 18-22 September,2002.[16] Bhope D.V. and Padole P.M., Experimentaland theoretical analysis of stresses, noise and flow incentrifugal fan impeller, Mechanism and MachineTheory, 2004, Volume 39, Issue 12, pp.1257-1271.[17] Mehta, M.P. and Patel, P.M., Performance

analysis and optimization of mixed flow pump.International Journal of Emerging Trends in Engineeringand Development, 2013, Issue 3, Vol.1, pp 647 ♠ 661.

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Arungshu Das