Research Article A Numerical Study on the Improvement of ...downloads.hindawi.com/journals/mpe/2014/269483.pdf · dimensional numerical analysis to design low speci c speed pump di

Research ArticleA Numerical Study on the Improvement of Suction Performanceand Hydraulic Efficiency for a Mixed-Flow Pump Impeller

Sung Kim, Kyoung-Yong Lee, Jin-Hyuk Kim, and Young-Seok Choi

Thermal & Fluid System R&BD Group, Korea Institute of Industrial Technology, 89 Yangdaegiro-gil, Ipjang-myeon, Seobuk-gu,Cheonan-si, Chungcheongnam-do 331-822, Republic of Korea

Correspondence should be addressed to Jin-Hyuk Kim; [email protected]

Received 28 April 2014; Revised 11 September 2014; Accepted 16 September 2014; Published 8 October 2014

Academic Editor: Shaofan Li

Copyright © 2014 Sung Kim et al.This is an open access article distributed under theCreativeCommonsAttributionLicense,whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper describes a numerical study on the improvement of suction performance and hydraulic efficiency of a mixed-flow pumpby impellers.The design of these impellers was optimized using a commercial CFD (computational fluid dynamics) code and DOE(design of experiments). The design variables of meridional plane and vane plane development were defined for impeller design.In DOE, variables of inlet part were selected as main design variables in meridional plane, and incidence angle was selected in vaneplane development. The verification of the experiment sets that were generated by 2𝑘 factorial was done by numerical analysis. Theobjective functions were defined as the NPSHre (net positive suction head required), total efficiency, and total head of the impellers.The importance of the geometric design variables was analyzed using 2𝑘 factorial designs.The interaction between the NPSHre andtotal efficiency, according to the meridional plane and incidence angle, was discussed by analyzing the 2𝑘 factorial design results.The performance of optimally designed model was verified by experiments and numerical analysis and the reliability of the modelwas retained by comparison of numerical analysis and comparative analysis with the reference model.

1. Introduction

Themixed-flow pump is a typical instrument of mass energyconsumption although it also has important roles in waterresource development and various industrial plants. Theimportance of design engineering of the mixed-flow pumpwith high total efficiency and suction performance andenergy saving as a consequence is increasing as oil priceincreases. The advanced enterprises in developed countrieslike the US, Germany, and Japan have competitivenessthrough their own technologies and know-how in pumpdesigning that has been accumulated formore than a hundredyears.

Specifically for the pumps that are used in highervalue added business such as desalination or extraction ofpetroleum, the total efficiency and suction performance are amain issue giving advanced enterprises possessing accumu-lated technologies absolute advantage. For that reason, therehave been researches going on regarding pumps includingmixed-flow pump and the results have been reported severaltimes by different companies and research agencies [1, 2].

When it comes to impeller designing of the mixed-flowpump, twomain objectives of the research, namely, high totalefficiency and improved suction performance, have conflict-ing directions of the design [3, 4]. The design technique thatcould improve suction performance maintaining high totalefficiency at the same time is very important but more designexperiences are required at this stage.

Suction performance correlate with cavitation. In casewhere the flow level changes by time when the pump isoperating, unusual phenomena such as cavitation happen asthe pressure of pump inlet part changes. Because of the natureof the fluid, the suction performance of a pump decreasescreating bubbles when the pressure is low. Thus, securingdesign technology for pump with high suction performanceis very important [5–7].

In order to improve total efficiency and suction perfor-mance of the impeller by selecting impeller shape variablesappropriately, an analysis that can determine the importanceof the design variables and the effect of chosen variables onpump performance is required. In order to perform the study,numerical analysis and bench marking via experiments were

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 269483, 17 pageshttp://dx.doi.org/10.1155/2014/269483

2 Mathematical Problems in Engineering

done on the reference model and the results of them wereused as criteria for the comparison.

Recently, the application of computational fluid dynamics(CFD) in the performance analysis of fluid machinery iscommon, and many studies have conducted for validatingits usefulness in predicting the performance of pumps. Forinstance, Goto and Zangeneh [8] applied their optimizationmethodology based on an inverse design method and three-dimensional numerical analysis to design low specific speedpump diffusers with high efficiency performance. Bing andCao [9] also improved the total hydraulic efficiency of amixed-flow pump impeller by a combined approach usingnumerical simulation, inverse design, and a genetic algo-rithm. J. H. Kim and K. Y. Kim [10] tried the single-objectivenumerical optimization to enhance the total efficiency of amixed-flow pump with two design variables related to vaneddiffuser geometry.

In design engineering, the importance of the mixed-flow pump with high total efficiency and suction perfor-mance has been increasing, which has made it necessaryto improve hydrodynamic design techniques in order todevelop a mixed-flow pump with high total efficiency andoptimal suction performance. Because the most importantcomponent of the pump is the impeller, its hydrodynamicdesign determines the pump design technique.

The two main objectives in designing the impeller ofthe mixed-flow pump, namely, high total efficiency andimproved suction performance, can be realized using con-trasting techniques. A design technique that could improvesuction performance andmaintain high total efficiency at thesame time is desirable but remains in the experimental stage.

In this study, the design variables of the impeller merid-ional plane and vane plane development were defined for theimprovement of suction performance. The design variableswere then rated in importance by systematically analyzingthem in relation to the response variables of the impeller.First, an impeller with high total efficiency, which satisfies thehead at the design flow rate, was designed by using database(𝐷/𝐵).

The impeller was designed using 𝐷/𝐵, 2𝑘 factorialdesigns, which were applied to analyze the effect on suctionperformance and total efficiency of the design variables. Thetendency to change performance according to each variationin shape was studied by numerical analysis. By applyingresponse optimization, themain design variables determinedby the 2𝑘 factorial design were used to create the optimalshape.

The performance of optimized impeller was verified bynumerical analysis and experiments. Numerical analysis andexperiment of the reference model were used to compare theoptimal impeller with the reference model.

2. Mixed-Flow Pump Impeller Design Method

2.1. Traditional DesignMethod. The traditional design for themeridional plane and the front plane of the impeller is doneeasily by applying pump theory. When design specificationsare given, the diameters of the inlet/outlet of the meridional

plane are determined by basic pump theory. The shroud andhub curve of the inlet/outlet of themeridional plane are easilyconnected by drawing an arc.

In designing the blade shape, the inlet/outlet angles ofthe blade are mainly determined by the flow angles of theinlet/outlet using the given meridional plane, according topump design theory.The sweep angle, which is relevant to theblade length, is determined by the inlet/outlet angles becauseit is designed such that it connects the inlet/outlet anglessmoothly when the angles are determined.

As shown in Figure 1, the shape of the impeller ispresented in the meridional and front planes; Figure 1(a)shows the meridional view of the blade shape and presentsinformation on the direction of axis and radius; Figure 1(b)shows the front plane representing the radius and rotationaldirection; and Figure 1(c) shows the vane plane developmentof the impeller. The vane plane development includes theblade angle distribution. Axis 𝑥 of the vane plane develop-ment indicates the total length of the arc at each radius fromthe front view. Axis 𝑦 indicates the total length of the bladein the meridional view. Hence, the distribution of the bladeangles is easily seen in the vane plane development and isusually achieved by the smooth connection of the inlet bladeangle and the outlet blade angle. The inlet and outlet anglesof the blade are mainly derived using pump design theory[11, 12].

The head can be satisfied by a traditionally designedimpeller but, in order to improve total efficiency and suctionperformance, a detailed definition of the design variables andsubsequent analysis of performance variations according todifferent impeller design variables are required.

The meridional plane shows the shape and size of blade.The impeller meridional shape was designed using our own𝐷/𝐵. Figure 2 shows the newly designed impeller shape. Asshown in Figure 2, consequentially, the axis direction of thenewly designed shape is approximate 24% shorter than thatof the reference model.

2.2. Design Variables in aMeridional Plane. The typical shapeof the meridional plane is shown in Figure 1(a), and thedesign variables for this meridional plane are defined inFigure 3. On the inlet of the impeller, 𝑅1ℎ is the hub, 𝑅1𝑠is the inlet radius of shroud, and Φ1 indicates the inclinedangle of the impeller’s leading edge. On the outlet of theimpeller, 𝑅2 is the outlet radius, 𝐵2 is the blade width ofthe impeller’s trailing edge, and Φ2 indicates the inclinedangle of the trailing edge. The outlet hub of the impellerand the straight line of the shroud are defined as %𝐿 ℎ and%𝐿 𝑠, respectively. Because it can express smooth curves, aBezier curve was used to connect the inlet to the outlet ofthe impeller. When using Bezier curves, two reference pointswith set inclination levels are connected smoothly using acontrol point, and the shape of the curve varies depending onthe location of the control point. When the control point isdetermined, the curve is connected smoothly in accordancewith the inlet/outlet angles. When the impeller hub curvemeets the horizontal and vertical lines, 𝜃1 ℎ and 𝜃2 ℎ indicatethe inlet angle and outlet angle, respectively. 𝜃1 𝑠 and 𝜃2 𝑠

Mathematical Problems in Engineering 3

Hub

Shroud

(a) Meridional plane

Hub

Shroud

R

(b) Front plane

Hub

Shroud

(c) Vane plane development

Figure 1: Traditional impeller design method.

Reference model

New design model

Figure 2: Comparison of meridional planes.

𝜃 s

%L s

%L h𝜃 h

Ztip

Φ2

𝛽2

𝜃2 s %CP2 s

𝜃1 s

%CP1 s

Φ1

R1h

𝜃1 h

%CP1 hR2

𝜃2 h

%CP1 s

R1s

Figure 3: Design variable of meridional plane [11, 12].


Σ(R d𝜃)

ΣdM

R2 d𝜃 (h, s)

%𝛽2

𝛽2

%𝛽1 𝛽1

(h, m, s)

(h, m, s)

(h, m, s)

(h,m

,s)

(h,m,

s)

(h, m, s)

Figure 4: Design variable of vane plane development [13, 14].

indicate those of the shroud. 𝜃 ℎ and 𝜃 𝑠 indicate the angles ofthe outlet hub and the shroud, respectively, when %𝐿 ℎ and%𝐿 𝑠 of the straight lines meet the vertical axis. The controlpoints of the hub inlet and outlet are shown as %CP1 ℎ and%CP2 ℎ, respectively, and%CP1 𝑠 and%CP2 𝑠 indicate thoseof the shroud. 𝑍tip indicates the length of the axial directionfrom inlet/outlet parts of the shroud [11, 12].

2.3. Design Variables in a Vane Plane Development. A typicalshape of vane plane development is shown in Figure 1(c),and the design variables for this vane plane developmentare defined in Figure 4. In the diagram, “ℎ” means hub, “𝑚”means midspan, and “𝑠” means shroud. Σ(𝑅 𝑑𝜃) (ℎ,𝑚, 𝑠)indicates the total length of the arc at each radius fromthe front view. Σ𝑑𝑀 (ℎ,𝑚, 𝑠) represents the total valuesof blade length in the meridional view; %𝛽1 (ℎ,𝑚, 𝑠) and%𝛽2 (ℎ,𝑚, 𝑠) show the portion of the blade having the sameblade angle at the leading edge and trailing edge, respectively,and they are presented as a percentage of the whole lengthof the 𝑦-axis. 𝛽1 (ℎ,𝑚, 𝑠) is the inlet angle of the blade fromthe impeller, and 𝛽2 (ℎ,𝑚, 𝑠) is the outlet angle of the bladefrom the impeller. 𝑅2 𝑑𝜃 (ℎ, 𝑠) shows the inclination leveltoward the circumference from the hub and shroud at theoutlet of the impeller. The inlet and outlet sections are con-nected by a smooth curved line, the angle of which changedlinearly. Figure 5 shows the three-dimensional geometry ofthe impeller using the variables of the meridional plane andthe vane plane development [13, 14].

3. Numerical Analysis Methods

The three-dimensional shape of the impeller was generatedusing the ANSYS CFX-BladeGen program. The structuredgrid system was generated using ANSYS CFX-TurboGrid, aprogram that generates a fluid machinery grid [15].

Although the impeller has five blades, we carried out thenumerical analysis on only one blade passage using a periodiccondition. Figure 6 shows the boundary conditions for theimpeller calculation.Waterwith ambient temperature of 25∘Cwas specified as the working fluid. We set the atmosphericpressure of 1 atm with the turbulence intensity of 5% on theinlet section of the impeller and gave the mass flow rate of

Figure 5: Three-dimensional geometry of the impeller.

Inlet: total pressure

Outlet: mass flow rate

Computational domain:1 passage region

(using periodic condition)

Rotational speed

(1 atm)

Figure 6: Boundary conditions for the impeller calculation.

665.33 kg/s of one blade passage at the design point on theexit section as a boundary condition.The solid surfaces in thecomputational domain were considered to be hydraulicallysmooth with adiabatic and no-slip conditions. The rotationalspeed of the impeller was 580 r/min. When the numericalanalysis was performed for the impeller only, the inlet wassimplified as a straight pipe and the outlet was expressed asthe same meridional shape without the diffuser vane.

A structured grid system was constructed in the compu-tational domain, with O-type grids near the main blade andvane surfaces and H-type grids in the other regions. Figure 7shows the results of the grid dependency test for the total headand total efficiency of the reference impeller model. The totalhead and total efficiency values of the reference impeller didnot change as the grid size was varied from approximately90,000 to 110,000. Thus, about 90,000 grid points were usedto define the computational domain encompassing the main


Selected pointTo

tal h

ead

(m)

Number of nodes

60

58

56

54

52

50

100

98

96

94

92

90To

tal e

ffici

ency

(%)

Reference modelReference model total efficiency

5 6 7 8 9 10 11

× 104

Ht

Figure 7: Results of the grid dependency test.

impeller passage. Figure 8 shows a typical example of the gridsystem used for the mixed-flow pump impeller in this work.

The ANSYS CFX-11, which is a commercial compu-tational fluid dynamics (CFD) code, was used for thenumerical analysis. A three-dimensional Reynolds averageNavier-Stokes equation was used to analyze incompressibleturbulence flow inside the pump.The governing equationwasdiscretized using a finite volume method. A high-resolutionscheme, which has more than a second degree of accuracy,was used to solve the convection-diffusion equations. For theturbulent model, the shear stress transport 𝑘-𝜔 model [16–19], which is appropriate for the prediction of flow separation,was used to analyze turbulent flow through the impeller.

We used water as a working fluid. Disk friction losses,mechanical losses, leakage losses, and the tip clearance effectwere not included in this calculation. The specific speed(r/min, m3/min, m) of the pump was 380, the flow rate was12,000m3/hr, and the total head was 60m.

4. Design of Experiments

The experiments design was based on the modern analysisof statistics, which helps select the main cause of abnormalfluctuations from many possible causes. In this study, 2𝑘factorial designs of the design of experiment (DOE) wereused as numerical optimizationmethods [21–23]. Minitab 14,a commercial program, was used for the analysis of DOE.

Figure 9 shows the flow chart of this study. The per-formance of the reference model with same specific speedwas analyzed and drawbacks that reduce pump performancecould be identified based on the result of the analysis.Impeller design variables for the improvement of pumpperformance were defined using 𝐷/𝐵. Response variables

Zoom in

Figure 8: Grid system for numerical analysis of the impeller.

Design variables selection

Analysis of CFD results

Response variables selectionReference model selection

Comparison analysis of response variables

DOE (2k factorial design)

Figure 9: Optimization process flowchart.

were defined as total head, total efficiency, and suctionperformance. Tendencies of the response variables accordingto the identified design variables were analyzed by using 2𝑘factorial.The response variables of experiment sets generatedby 2𝑘 factorial were verified by using numerical analysis.Impeller shape was deduced by response optimization withthe result of 2𝑘 factorial. The performance of the optimizedmodel was compared to that of the reference model usingcomparative analysis.

In DOE, a response variable should be defined in orderto analyze the performance of the impeller according to thedesign variables. The actual response variables are defined inthe total head curve, the total efficiency curve, and the NPSHcurve, as shown in Figures 10 and 11. The design flow-rate isconsidered ideal if the flow rate at maximum total efficiencycorresponds to the required flow rate.

In the case where the flow level changes over timewhen the pump is operating, unusual phenomena, such ascavitation, happen as the pressure of the pump inlet changes.Because of the nature of the fluid, the suction performanceof the pump decreases, creating bubbles when the pressureis low. Thus, securing a design technology for a pump withhigh suction performance is very important.The graph of theresults shows that net positive suction head (NPSH) value,which is represented as the 𝑥-axis, is determined by the set


Table 1: Design target (real), design specifications, and CFD results of the reference model.

Design target (real) Design specifications Reference modelCFD

𝑄 (m3/hr) 12,000 12,000 12,000Total head (m) 60 More than 63m 57.48Total efficiency (%) To be maximized To be maximized 96.84NPSHre (m) To be minimized To be minimized 6.7

Design flow rate0

Total efficiency curve

Total head curveMaximum efficiency

Q

Ht,

tota

l effi

cien

cy

Hd

Figure 10: Total head and total efficiency curve.

decreases by 3%

NPSHre

Decreasing inlet pressure

Onset of cavitation

NPSH (m)

A spot where total head

Ht (m)

Figure 11: NPSH curve.

inlet pressure (𝑃in) and saturation vapor pressure (𝑃v), and itis calculated by the following equation:

NPSH =𝑃in − 𝑃v𝜌𝑔

. (1)

Different NPSH values are generated as the inlet pressuredecreases and NPSH required (NPSHre) represents an areawith more than 3% of loss in the total head [24–26].

5. Optimal Mixed-Flow Pump Impeller Design

Table 1 shows the real design target and the modified designspecifications for the CFD cases and the CFD results forthe reference model. The specific speed (r/min, m3/min, m)of the pump is 380, the flow rate is 12,000m3/hr, the totalhead is 60m, the total efficiency should be maximized, and

the NPSHre should be minimized at the design flow-rate.According to the numerical analysis of the reference model,however, the numerical analyses for the impeller do notsatisfy 60m. As a result, a new design model that satisfies thespecifications is needed.

Because of the simplified flow domain, without includingtip clearance and roughness, the results of the numericalanalysis are expected to be higher than those of the designtarget. Thus, we modified the design specifications for theCFD results. Design specifications for the numerical analysisare shown in Table 1. The total head was defined to be higherthan 63m from the impeller. The total efficiency should bemaximized and the NPSHre should be minimized at thedesign flow rate.

5.1. 2𝑘 Factorial Designs. 2𝑘 factorial designs are usuallyrepresented as 𝑛𝑘. In this DOE, the number of factors is 𝑘and the number of levels is 𝑛.The experiments are performedin every possible combination of all factors. The numberof performed experiments should be at least 𝑛𝑘, withoutrepetition. The advantage of factorial designs is that we canassume the main effect (the sole effect of the factor) andinteraction effect (the effect between factors) of all factors.This convenient screening method can be used to find thecore factor when there are many factors involved at thebeginning of the experiment. In this study, considering thenumber of factors involved and the number of possibleexperiments, in addition to cost and time, we used fractionalfactorial designs in which the number of experiments isreduced by deleting less meaningful interactions.

5.2. Effect of Impeller Design Variables. To analyze the influ-ence of the impeller design variables on the performance ofthe mixed-flow pump, the 2𝑘 factorial designs were appliedafter defining the design variables of the meridional planeand the vane plane development.We therefore generated nineexperimental conditions for the numerical analysis, includinga center point using four design variables. As the variousimpeller design variables, the selected design variables for the2𝑘 factorial designs are i𝛽1 ℎ and i𝛽

1𝑠, which are related to

the incidence angle of the design variables of the vane planedevelopment, and 𝑅1𝑠 and 𝑍tip, which are the meridionalplane design variables. Here, the i𝛽

1ℎ, and i𝛽

1𝑠 are the

incidence angles at the leading edge of the blade on the huband shroud, respectively. The incidence angles are the designvariables showing the difference between flow angle and theinlet angle.


64.50

64.25

64.00

63.75

63.50

64.50

64.25

64.00

63.75

63.50

64.50

64.25

64.00

63.75

63.50

64.50

64.25

64.00

63.75

63.50

0.0 5.0 0.0 7.2

3 6 9 2 5Point type Point type

Corner

Center

2.5 3.6

Corner

Center

−1

R1s Ztip

i𝛽1 h i𝛽1 s

Mea

n of

Ht

Mea

n of

Ht

Mea

n of

Ht

Mea

n of

Ht

Main effects plot (data means) for Ht Main effects plot (data means) for Ht

Main effects plot (data means) for Ht Main effects plot (data means) for Ht

Figure 12: Main effects plot for total head.

Table 2: 2𝑘 factorial designs set.

Set 𝐴 𝐵 𝐶𝐷

(𝐴×𝐵×𝐶)1 − − − −

2 + − − +3 − + − +4 + + − −

5 − − + +6 + − + −

7 − + + −

8 + + + +Center 0 0 0 0

Table 2 shows the set arrangement of 2𝑘 factorial designsfor nine experimental conditions. Here, the symbols of “+”and “−” mean the maximum and minimum levels of eachdesign variable, respectively. In Table 2, the variables of 𝐴, 𝐵,

and𝐶 are defined by the orthogonal design and the𝐷 variableis decided by the combination of 𝐴 × 𝐵 × 𝐶.

The base model applied in 2𝑘 factorial designs was theshape used in a previous study, and it satisfiedmaximum totalefficiency at the design flow rate. Variation ranges of i𝛽

1ℎ and

i𝛽1𝑠 are±3∘, and those of𝑅1𝑠 and𝑍tip were±2.5% and±3.6%,

respectively.The rest of the design variables of themeridionalplane and vane plane development were fixed as base designvalue. Table 3 shows the numerical analysis sets of 2𝑘 factorialdesigns.

Figures 12 and 13 show plots of the main effects and aPareto chart of the total head, respectively. In the main effectsplot, the tendency to increase the total head can be identifiedas increases in 𝑅1𝑠, i𝛽1 ℎ, and i𝛽1 𝑠. In Pareto chart, the totalhead is influenced by i𝛽1 𝑠,𝑅1𝑠, and i𝛽1 ℎ in the order ofmostto least.

Figures 14 and 15 show plots of the main effects andPareto chart of total efficiency, respectively. In the maineffects plot, total efficiency tends to increase as 𝑅1𝑠 and𝑍tip decrease, but i𝛽

1ℎ and i𝛽

1𝑠 increase. It is clear that

the tendency of the meridional plane design variables is


Term

Standardized effect0 1 2 3 4

Pareto chart of the standardized effects(response is Ht)

R1s

Ztip

i𝛽1 h

i𝛽1 s

Figure 13: Pareto chart for total head.

0.0 5.0 0.0 7.2

3 6 9 5

2.5 3.6

97.50

97.25

97.00

96.75

96.50

Mea

n of

tota

l effi

cien

cy

97.50

97.25

97.00

96.75

96.50

Mea

n of

tota

l effi

cien

cy

97.50

97.25

97.00

96.75

96.50

Mea

n of

tota

l effi

cien

cy

97.50

97.25

97.00

96.75

96.50

Mea

n of

tota

l effi

cien

cy

2−1

Point type

Main effects plot (data means) for total efficiency Main effects plot (data means) for total efficiency

Main effects plot (data means) for total efficiency Main effects plot (data means) for total efficiency

Point typeCorner

CenterCorner

Center

R1s Ztip

i𝛽1 h i𝛽1 s

Figure 14: Main effects plot for total efficiency.


Term

Standardized effect0.0 0.5 1.0 1.5 2.0

Pareto chart of the standardized effects(response is total efficiency)

R1s

Ztip

i𝛽1 h

i𝛽1 s

Figure 15: Pareto chart for total efficiency.

Table 3: Numerical analysis set of 2𝑘 factorial designs for the impeller design.

Set 𝑅1𝑠 (m) 𝑍tip (m) i𝛽 ℎ (∘) i𝛽 ℎ (∘) Total head (m) Total efficiency (%) NPSHre (m)

1 0 0 3 −1 63.24 96.65 6.362 5 0 3 5 64.92 97.21 5.233 0 7.2 3 5 64.07 97.61 5.644 5 7.2 3 −1 63.25 95.47 8.095 0 0 9 5 64.18 97.55 6.156 5 0 9 −1 63.86 97.19 5.287 0 7.2 9 −1 63.83 97.18 5.748 5 7.2 9 5 64.55 97.04 5.28Center 2.5 3.6 6 2 64.10 97.54 5.48

opposite to that of the vane plane development. In thePareto chart, i𝛽

1𝑠, 𝑅1𝑠, and i𝛽1 ℎ are variables affecting total

efficiency; i𝛽1𝑠 shows themost influence and i𝛽

1ℎ shows the

least.Figures 16 and 17 show plots of the main effects and a

Pareto chart of NPSHre. In the main effects plot, NPSHretends to increase as 𝑍tip decreases, but i𝛽

1ℎ and i𝛽

1𝑠

increase. Compared to other design variables, 𝑅1𝑠 does nothave a significant effect onNPSHre. Apart from𝑅1𝑠, it is clearthat the tendency of the meridional plane design variablesis opposite to that of the vane plane development. In thePareto chart, i𝛽

1𝑠, i𝛽1ℎ, and𝑍tip are variables affecting total

efficiency; i𝛽1𝑠 shows the most influence and 𝑍tip shows the

least.To summarize the 2𝑘 factorial designs, it was identified

that the tendencies of total efficiency and NPSHre wereopposite, depending on the design variables. The analysis ofthe tendencies of the response variables was important inorder to draw a shape with improved NPSHre in high totalefficiency, depending on the changing design variables. Inorder to create an impeller shape with improved NPSHrein high total efficiency, a response optimization method was

applied. In Table 3, most of the 2𝑘 factorial sets satisfy 63mof total head. Thus, the response variables were defined toimprove total efficiency and NPSHre at the design flow rate,except for the total head as the objective function.

Response optimization was performed by regressionanalysis. Regression analysis is assuming mathematicalmodel based on data in order to investigate the relevanceamong variables. Generally, the estimated model is used tomake necessary prediction or statistical inference. Multipleregression analysis is a type of regression analysis where therelation between two or more predictors and one dependentvariable is estimated linearly on straight line. Estimationequation for multiple regression analysis is as follows:

�̂� = 𝛽0 + 𝛽1 × 𝑋1 + 𝛽2 × 𝑋2 + ⋅ ⋅ ⋅ + 𝛽𝑛 × 𝑋𝑛, (2)

where 𝑋 indicates the design variables from 2𝑘 factorial. �̂�and 𝛽 are established by regression analysis. The regressionmodel with consideration of multiple regression models is as(3) and (4).


6.50

6.25

6.00

5.75

5.50

Mea

n of

NPS

Hre

0.0 5.0 0.0 7.2

3 6 9 5

2.5 3.6

6.50

6.25

6.00

5.75

5.50

Mea

n of

NPS

Hre

6.50

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Mea

n of

NPS

Hre

6.50

6.25

6.00

5.75

5.50

Mea

n of

NPS

Hre

Main effects plot (date means) for NPSHre Main effects plot (date means) for NPSHre

Main effects plot (date means) for NPSHre Main effects plot (date means) for NPSHre

2−1

Point type Point typeCorner

CenterCorner

Center

R1s Ztip

i𝛽1 h i𝛽1 s

Figure 16: Main effects plot for NPSHre.

Standardized effect0.0 0.2 0.6 0.8 1.2

Pareto chart of the standardized effects(response is NPSHre)

1.00.4

Term

R1s

Ztip

i𝛽1 h

i𝛽1 s

Figure 17: Pareto chart for NPSHre.


HiCurLo

NewD

0.79

Total efficiencyMaximum

NPSHreMinimum

9.0[9.0]3.0

5.0[5.0]

5.0[0.0]0.0

7.2[7.2]0.0 −1.0

d = 0.77

d = 0.81

Y = 97.77

Y = 5.38

R1s Ztip i𝛽1 h i𝛽1 s

Figure 18: Plot for response optimization.

(a) Reference model (b) Optimum model

Figure 19: Comparison of three-dimensional geometry impeller.

The regression equations for total efficiency and NPSHreare as follows, respectively:

Total efficiency = 96.7 − 0.104 × 𝑅1𝑠 − 0.0447 × 𝑍tip

+ 0.0839 × i𝛽1ℎ + 0.121 × i𝛽

1𝑠,

(3)

NPSHre = 6.68 − 0.000 × 𝑅1𝑠 + 0.0604 × 𝑍tip

− 0.119 × i𝛽1ℎ − 0.132 × i𝛽

1𝑠.

(4)

The regression models in (2) and (3) were producedconsidering each design variable and thereby applicable asreliable optimization and predictive models. In responseoptimization, the objective function was defined as max-imum total efficiency and minimum NPSHre. The totalhead was excluded because it showed little change as thedesign variables changed. Figure 18 shows the plot of responseoptimization. As shown in Figure 18, the optimummodel thatsatisfies the objective value can be drawn when 𝑅1𝑠 is 0%,𝑍tip is 7.2%, i𝛽

1𝑠 is 9∘, and i𝛽

1ℎ is 5∘. Figure 19 shows the

three-dimensional geometry impeller of referencemodel andoptimummodel.

6. Analyses of Numerical Analysis andExperiment Results

The selected optimummodel was verified by numerical anal-ysis. Figure 20 shows total head and total efficiency curvesaccording to the result of numerical analysis. Figure 20(a)shows total head curves of the reference and optimum mod-els. The tendencies of total head curves from the referenceand optimum models are same but total head curve ofoptimum model has higher value than that of referencemodel. Especially, the total head at design flow rate from thereference model is expected to be under 60m not meetingthe requirement of design specification. Optimummodel wasdesigned to have total head higher than 60m which is designspecification considering disk friction losses, mechanicallosses, leakage losses, tip clearance effect, machine loss,roughness loss, and diffuser loss. Figure 20(b) shows the total


Tota

l hea

d (m

)

Reference modelOptimum model

80

75

65

55

50

400.7

70

60

45

0.8 0.9 1 1.1 1.2 1.3

Q/Qd

(a) Total head curve


Tota

l effi

cien

cy (%

)

100

98

96

94

900.7

92

0.8 0.9 1 1.1 1.2 1.3

Q/Qd

(b) Total efficiency curve

Figure 20: Comparison of total head and total efficiency curve.


Figure 21: Comparison of streamline at design flow rate.

efficiency curves of the reference and optimum models. InFigure 20(b), the total efficiency of optimummodel is highernot only from the design flow rate but also from low and highflow rates than that of the reference model.

Figure 21 shows the comparison between reference andoptimum models regarding streamline at impeller blades. InFigure 21(a), there is a section side with flow separation atinlet shroud of the referencemodel.The total efficiency seemsto decrease as a result of this flow separation at impellerblades. In Figure 21(b), the streamline is stabilized at inletshroud of the optimum model increasing total efficiencycompared to reference model.

The NPSH curves for the reference and optimummodelsare shown in Figure 22. In Figure 22, the NPSHres for thereference and optimum models are 6.7m and 5.7m, respec-tively. Consequently, the optimum model was improved as1m compared to the reference model. On the other hand,Figures 23 and 24 show the isosurfaces of vapor pressuresof −20 kPa and −40 kPa at the NPSH = 8.0m (design flowrate) and NPSH = 5.9m, respectively. It seems that thequantity of vapor in both the models is similar as shownin Figure 23. In Figure 24, the dramatic decrease of thevapor in the optimum model is observed at the NPSH =5.9m in comparison with the reference model. It is thought


Tota

l hea

d (m

)


NPSH (m)

65

60

55

452

50

4 5 6 8 9 1073

Figure 22: Comparison of NPSH curve at design flow rate.


Figure 23: Comparison of isosurface of vapor pressure at NPSH = 8.0m.

that the suction performance of the optimum model isimproved by the considerable decrease of vapor in the suctionside.

Figure 25 shows the NPSHre curves for the referenceand optimum models. In Figure 25, it is apparent that thesuction performance of the optimum model is improvedin the entire flow rate, compared to the reference model.Table 4 shows the numerical results of the efficiency andNPSHre for the reference and optimummodels at the designflow rate. According to the result of numerical analysis inTable 4, total head of optimum model is improved by theapproximate 6m than that of reference model. Moreover,it has shown 1m and 0.81% improvements in the NPSHreand total efficiency, respectively, compared to the reference

Table 4: Comparison of total head, total efficiency, and NPSHre(CFD results).

Total head(m)

Totalefficiency (%) NPSHre (m)

Reference model 57.48 96.84 6.7Optimum model 64.25 97.65 5.7

model. Therefore, the optimum design produced mostlystable flows in the impeller passage.

The overall experimental apparatus used in the per-formance test is illustrated in Figure 26, which shows theinstallation of the test pump [20].The test pump is connected



Figure 24: Comparison of isosurface of vapor pressure at NPSH = 5.9m.

NPS

Hre

(m)


10

9

7

5

20.7

3

0.8 0.9 1 1.1 1.2 1.3

8

6

4

Q/Qd

Figure 25: Comparison of NPSHre curve.

to the electric motor which is controlled by an inverterand a data acquisition system. As shown in Figure 26, themain component devices for the experimental apparatusconsist of the flow meter, control valve, heat exchanger,booster pump, thermometer, damping valve, and pres-sure gauge. The measuring instruments and their uncer-tainties used for the performance test are tabulated inTable 5.

The numerical and experimental results for the totalhead, total efficiency, and NPSHre of the optimummodel arecompared in Figure 27. As shown in Figures 27(a) and 27(b),although the numerical and experimental results are differentin terms of quantitative value, they are similar in tendency.

Table 5: Specifications of a measurement device.

Measurement device Uncertainty (%)Torque meter ±2Flow meter ±2Rotational sensor ±0.3Absolute pressure transducer ±2Differential pressure transducer ±2Thermocouple ±2

In Figure 27(c), they are also similar in tendencies in theNPSHre curves but show the bigger difference at especially


Discharge control valve

Discharge

Booster pump

Flow meter

Control valve

Thermometer

Dampening valve and

pressure gauge

Pump on test

Dampening valve and

pressure gauge

Flow meter

Heat exchanger H

Figure 26: Schematic diagram of experimental apparatus for a mixed-flow pump [20].

the high flow rate. This is probably explained by the factthat bell mouth of inlet part, disk friction losses, mechanicallosses, leakage losses, tip clearance effect, machine loss,roughness loss, and diffuser loss were not considered for thenumerical analysis. First of all, the main effect on a relativelylarge error between the CFD and experiment results is due tono consideration of the tip clearance. These results illustratethe enhancement of the pump impeller’s performances as aresult of the optimization.

7. Conclusion

A numerical optimization on the improvement of suctionperformance and hydraulic efficiency of a mixed-flow pumpimpeller was conducted in this work. The main conclusionsof this work are summarized as follows.

(1) In this work, the impeller’s meridional plane andvane plane development were employed as the designvariables to improve the suction performance andtotal efficiency of the mixed-flow pump. According tothe result of 2𝑘 factorial, it showed that the suctionperformance and total efficiency had an oppositetrend with the selected design variables.

(2) In the analyses of the main effects plot and Paretochart, the i𝛽

1𝑠 was more sensitive than other vari-

ables in terms of the NPSHre and total efficiency. Onthe other hand, the 𝑅1𝑠 affected considerably to totalefficiency, whereas it did not affected absolutely to theNPSHre.

(3) As a result of the optimization, the total head of theoptimum model was numerically improved by theapproximate 6m, and moreover its numerical resultshowed 1m and 0.81% improvements in the NPSHreand total efficiency, respectively, in comparison withthe reference model.

(4) The numerical and experimental results for thetotal head, total efficiency, and NPSHre of theoptimum model were compared. Although thenumerical and experimental results for the totalhead, total efficiency, and NPSHre were differentin terms of quantitative value, they were similar intendency. Therefore, the numerical optimizationmethod based on the impeller’s meridional plane andvane plane development can be effectively used forimproving hydraulic performance of the mixed-flowpump.

Nomenclature

CFD: Computational fluid dynamicsDOE: Design of experimentsℎ: Hub𝐻d: Designed total head (m)𝐻t: Total head (m)𝑀: Meridional length (m)𝑁: Rotational speed (r/min)NPSH: Net positive suction head (m)NPSHre: Net positive suction head required (m)𝑁s: Specific speed (r/min, m3/min, m)𝑃in: Inlet pressure (pa)𝑃v: Vapor pressure (pa)𝑄: Flow rate (m3/hr)𝑄d: Design flow rate (m3/hr)𝑅1: Radius of inlet part (m)𝑅2: Radius of outlet part (m)𝑠: Shroud𝑍tip: Axial direction from inlet/outlet parts of

the shroud (m)Φ1: Inclined angle of the leading edge (∘)Φ2: Inclined angle of the trailing edge (∘)


Tota

l hea

d (m

)80

70

50

30

00

10

0.2 0.4 0.8 1 1.2 1.4

60

40

20

0.6

Reference model CFDOptimum model CFD

Reference model ExpOptimum model Exp

Q/Qd

(a) Performance evaluation of the total head

Tota

l effi

cien

cy (%

)

100

60

40

00 0.2 1 1.2 1.4

80

20

0.4 0.80.6



Q/Qd

(b) Performance evaluation of the total efficiency

NPS

Hre

(m)

20

10

0

15

5

1 1.2 1.40.4 0.80.6



Q/Qd

(c) Performance evaluation of the NPSHre

Figure 27: Comparative analysis of the performance evaluation (experimental versus numerical analysis).

𝛽1: Inlet angle of the impeller (∘)i𝛽1: Incidence angle (∘)

𝜃1: Inlet angle from meridional curve (∘)𝜃2: Outlet angle from meridional curve (∘)%𝐿: Straight line from outlet part (%)

%CP1: Control points of inlet part (%)%CP2: Control points of outlet part (%)%𝛽1: Portion of same inlet blade angle (%)

%𝛽2: Portion of same outlet blade angle (%)𝜔: Angular velocity (m/s).


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by a grant (no. 10044860) fromthe Korea Institute of Industrial Technology Evaluation andPlanning (ITEP) that is funded by the Ministry of Science,ICT and Future Planning.

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Research Article A Numerical Study on the Improvement of ...downloads.hindawi.com/journals/mpe/2014/269483.pdf · dimensional numerical analysis to design low speci c speed pump di