Research Article Surrogate Assisted Design Optimization of ...downloads.hindawi.com/journals/ijrm/2014/563483.pdf[ ]. e optimization of rotor blade sections of an impulse turbine was

Research ArticleSurrogate Assisted Design Optimization of an Air Turbine

Rameez Badhurshah and Abdus Samad

Department of Ocean Engineering Indian Institute of Technology Madras Chennai 600036 India

Correspondence should be addressed to Abdus Samad samadiitmacin

Received 30 May 2014 Revised 17 September 2014 Accepted 27 September 2014 Published 14 October 2014

Academic Editor Farid Bakir

Copyright copy 2014 R Badhurshah and A SamadThis is an open access article distributed under theCreativeCommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

Surrogates are cheaper to evaluate and assist in designing systems with lesser time On the other hand the surrogates are problemdependent and they need evaluation for each problem to find a suitable surrogateThe Kriging variants such as ordinary universaland blind along with commonly used response surface approximation (RSA) model were used in the present problem to optimizethe performance of an air impulse turbine used for ocean wave energy harvesting by CFD analysis A three-level full factorial designwas employed to find sample points in the design space for two design variables A Reynolds-averaged Navier Stokes solver wasused to evaluate the objective function responses and these responses along with the design variables were used to construct theKriging variants and RSA functions A hybrid genetic algorithm was used to find the optimal point in the design space It wasfound that the best optimal design was produced by the universal Kriging while the blind Kriging produced the worst The presentapproach is suggested for renewable energy application

1 Introduction

A computational fluid dynamics (CFD) based design requireslong time to evaluate objective functions of a problemThis type of analysis is called high-fidelity analysis and anyhigh-fidelity model requires many numerical simulations toevaluate the functions To optimize a CFD system physics-based low-fidelity models or surrogate models or surrogatesare employed and these help in reducing computationalburden A global optimization algorithm such as hybridgenetic algorithm (HGA) which mimics the evolutionaryprinciple assisted by sequential quadratic programming helpsin finding the optimal design [1]

The low-fidelitymodels depend on the nature of the prob-lem while the model-accuracy depends on several factorssuch as nature and distribution of sampling points type ofmodel optimizer capability and number of variables It wasfound that the Kriging (KRG) models were as competitiveas other surrogates [2] There are the surrogates such asresponse surface approximation (RSA) and artificial neuralnetwork (ANN) and these surrogates further have theirvariants Researchers are trying to increase the effectivenessand accuracy in constructing the surrogates to increase thenumber of variables to reduce the number of design pointsand so forth [3] Hence it is imperative to bring the researches

to application level and check whether particular surrogate orsurrogate variants can perform better than the others

There are ample articles describing surrogate models andtheir applicability to different problems [4ndash6] The modelsare problem dependent and selecting a propermodel requiresdesigner expertise [4] Peter andOnera [4] compared the sur-rogate models in an industrial context to design a stator bladein order to optimize the local pressure at the exit and showedthat universal Kriging (UKR) provided the better results interms of approximating the exact function In some otherapplication it did not perform well as compared to the othersurrogates [2] The KRG variants such as ordinary Kriging(OKR) UKR and blindKriging (BKR)which performedwellin several applications for optimization were compared foranalytical function based optimizations [2] BKR performedbetter in several applications [2] But there was no reportedapplication in CFD or turbomachinery application found inthe literatures regarding the applicability of BKR

One of the renewable energy systems is oscillating watercolumn (OWC) based systemwhich harvests energy from theocean waves OWC is a partially submerged hollow cylin-drical column consisting of a bidirectional flow turbine orsimply a bidirectional air turbine installed inside the column[7] The periodic wave pattern produces a reciprocating airflow over the turbine and thus it rotates the turbine in a

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2014 Article ID 563483 8 pageshttpdxdoiorg1011552014563483

2 International Journal of Rotating Machinery

Upstream GV

Rotor blades

Hub

Downstream GV

(a) 3D view (b) Periodic view

Figure 1 Impulse turbine

single directionThe popular bidirectional turbines are eitherreaction or impulse type The impulse turbine is better interms of having higher operating range The impulse turbinehas a symmetrical rotor sandwiched between two sets ofguide vanes (GVs) The GVs essentially deflect the flowthrough the inlet and helps increase the kinetic energy of flowAs a result the fluid particle hits the rotor blade (RB) andgives an ldquoimpulserdquo to the turbine [7] The earliest reportedsystematic optimization study was on reaction turbine airfoilblade shape modification for achieving multiple objectives[8] The optimization of rotor blade sections of an impulseturbine was carried by Gomes et al [9]

The present work compares the Kriging variants alongwith RSA surrogate to enhance the efficiency of the turbineused for wave energy extraction Numbers of blade andguide vanes were modified to enhance the efficiency of theturbine Numerical analysis to validate the performance ofthe surrogates was implemented in this problem Detailednumerical approach and surrogate strategy along with resultshave been discussed in this paper

2 Problem Description andNumerical Procedure

21 Model Description and CFD Methodology Bidirectionalflow impulse turbine was chosen as the reference geometry[10] for studying the applicability of surrogate techniques toturbomachinery application Figure 1(a) shows the completegeometry The turbine has 30 rotor blades (119873rb = 30) and26 guide vanes (119873gv = 26) on either side of the rotor blade(RB) To reduce computational cost simulation was run oversingle RB rather considering all the blades Figure 1(b) showsthe flowdomainThemajor specifications are listed in Table 1To analyze the flow over the entire fluid domain (including allthe blades) a higher computational cost is required Hencethe walls of the domain where it faces the domain of otherblades are given as periodic conditions This has also beenreported in the literature [11]

Table 1 Design specifications of rotor and guide vane

Parameter Specifications

Rotor

Rotor blade profile Circular-ellipticalNumber of rotor blades (119873rb) 30

Rotor blade pitch 267mmHub diameter 210mmTip diameter 298mmTip clearance 1mm

Chord length (119897rb) 54mmBlade inlet angle 60∘

Guide vane

Guide vane profile Plate typeNumber of blades 26Stator blade pitch 308mmChord length (119897gv) 70mmTip clearance 1mmBlade thickness 05mm

Guide vane inlet angle 30∘

The flow was computed over the passage of the upstreamguide vane (GV) then over the RB Finally the flow leavesthrough the downstream GV Steady state flow with frozenrotor approach was used The turbulence model was 119896-120576 andthe turbine rotated at constant low speed of 600 rpm Inletvelocity (V) was varied to compute flow over different flowcoefficients and the exit pressure was set to 1 atm To achievethe uniform flow the flow domain was extended to 85 timesthe chord length [11] The Reynolds averaged Navier-Stoke(RANS) equations were solved for evaluating torque (119879) andtotal pressure drop (Δ119875) Rather than expressing torquepressure drop and velocity directly these were addressed indimensionless forms as torque coefficient (119862

119905) input power

coefficient (119862in) and flow coefficient (120593) respectively Flowcoefficient (120593) is the ratio of the inlet axial velocity to the

International Journal of Rotating Machinery 3

circumferential velocity The mathematical formulations ofthe parameters [10 12] are

Torque coefficient 119862119905=

2119879

120588 (V2 + 1198802) 119887119897rb119873rb119903 (1)

Input power coefficient 119862in =2Δ119875119876

120588 (V2 + 1198802) 119887119897rb119873rbV (2)

Efficiency 120578 =119879120596

Δ119875119876=

119862119905

120601 sdot 119862in (3)

Flow coefficient 120601 =V119880 (4)

The governing Navier-Stokes transport equations are asfollows

Mass

120597 (120588119906)

120597119909+

120597 (120588V)120597119910

+120597 (120588119908)

120597119911= 0 (5)

and momentum

minus120597 (119875)

120597119909+

120597 (120591119909119909)

120597119909+

120597 (120591119910119909)

120597119910+

120597 (120591119911119909)

120597119911= div (120588

119906119906)

minus120597 (119875)

120597119909+

120597 (120591119909119910)

120597119909+

120597 (120591119910119910)

120597119910+

120597 (120591119911119910)

120597119911= div (120588V119906)

minus120597 (119875)

120597119909+

120597 (120591119909119911)

120597119909+

120597 (120591119910119911)

120597119910+

120597 (120591119911119911)

120597119911= div (120588

119908119906)

(6)

Discretization of model was done in ICEM-CFD and themesh in the domain is shown in Figure 2 Unstructuredtetrahedral elements with finer meshing near the bladesurface and tip clearance regionwere employed ANSYS-CFXwas used as a RANS solver Twomixing planes one at each ofthe interfaces of the stator-rotor regions were used Table 2lists the initial and boundary conditions The domain wasdiscretized into number of cells and each cell represents afinite volumewith a central node at which the flowpropertieswere evaluatedThe tip clearance zonewasmodeledwith finermesh and it was assured that sufficient nodes should be therein radial direction

The simulations were run on 34GHz core i7-3370 pro-cessor with 8GB RAMThe average number of iterations forconverged results for a single simulation run was approxi-mately 1000 and average time was approximately 10 hours

22 Objective Function and Design Variables Utilizingenergy from natural resources has to be carried out efficientlyso that the losses associated can be reduced Hence for thecurrent problem the turbine efficiency (120578) of the impulseturbine (3) was chosen to be the objective function Twodesign variables (DVs) namely number of the stator blades(119873gv) and the number of the rotor blades (119873rb) were selectedA feasible design space was formed by the lower and upperlimits of the variables as shown in Table 3 The variationin blade number changes its pitch thus depending on the

Shroud

Rotor

Hub

Figure 2 Mesh for rotor

Table 2 Initial and boundary conditions

Analysis Steady state analysisFluid Ideal gasTurbulence model 119896-120576Turbulence intensity Medium (5)Inlet boundary condition Inlet axial speedRotational speed 600 rpm (constant)Outlet boundary condition Static pressure (1 atm)Stage type Frozen rotorDomain Periodic boundary

number of blades the fluid domain changes and thus itaffects turbine performance More number of blades leaveslesser space for the fluid passage As the inlet flow velocityis constant the flow might get accelerated when it flowsover more number of blades This accelerated flow hits therotor blade with more impulse thus increasing the torquegenerated by the rotor On the other hand the same narrowpassage can give flow blockage and can reduce performance

23 Optimization Procedure Optimization is central themeto any problem involving decision-making that involveschoosing among alternatives The measure of goodness ofthe alternatives is represented by the objective functions orperformance indices [3] Optimization methodology dealswith the selection of the best alternative relative to the givendesigns

The procedure for optimization is shown in Figure 3Initially the design variables and the objectives are set upAs the surrogates cannot generate the initial population ahigh-fidelity analysis like the CFD is carried out The designvariables lower and upper bounds are defined At each of thecross combination of the DVrsquos CFD analysis is carried outThis being the initial data is fed to train the surrogate Aftertraining the surrogate the optimum point is searched usingan optimizer Once the convergence criteria are achieved thesurrogate predicted results are cross validated with CFD elsethe design space is further modified


CFD analysisReference CAD design Discretization Numerical

analysis (CFD) Validation

Selection of design variables and

objective function

Surrogate construction

Optimal point reached

Optimized model

Yes

No

Construct design space

Design optimization

Figure 3 Optimization procedure

Table 3 Design space

Variables LB UB119873rb 30 42119873gv 20 32

24 SurrogateModel Construction and Search Algorithm Thesurrogates such as KRG variants and RSA functions mimica high-fidelity response Kriging variants are approximationfunctions with multiple inputs and a single output The UKRis basically a data fitting or an interpolating technique thatuses a trend function or a regression function to capturelarge-scale variations and a systematic departure or stochasticprocess (119909) through the residuals to capture small-scale vari-ations Depending on the nature of the regression functionKriging variants have been organized with various names[13] Simple Kriging presumes the regression function to be aknown constant that is119891(119909) = 0 A popular category is OKRwhich imagines a constant but unknown regression function119891(119909) = 120583 The BKR deploys the linear regression functionas a trend function In another class UKR regards the trendfunction as a multivariate polynomial

Kriging is also considered as Gaussian process and asummary of the same is presented below [4 13 14] The ldquo119899rdquotraining points can be represented as 119909

1 1199092 119909

119899 and let

119891(119883) represent the response The Kriging interpolation isderived as

119891 (119909) = 119872120572 + 119903 (119909) sdot Ψminus1

sdot (119891 (119883) minus 119865120572) (7)

Here 119872 and 119865 represent the model matrices of the testpoint 119909 and the training set 119883 respectively The regressioncoefficient function120572 is determined bymethod of generalizedleast squares

120572 = (1198831015840

Ψminus1

119883)minus1

119883Ψminus1

119891 (119883) (8)

119903(x) = (120595(x x1) 120595(x x119899)) is an 1times119899 vector of correlationsbetween the data point 119909 and training set 119883 Ψ is 119899 times 119899

correlation matrix given as

Ψ = (

120595(x1 x1) sdot sdot sdot 120595 (x1 x119899) d

120595 (x119899 x1) sdot sdot sdot 120595 (x119899 x119899)

) (9)

The regression function may be considered as mean of thegeometric progressionThe prediction which is far from datapoint will be reverted to the mean Initially the behaviorof the response is unknown hence a constant regressionfunction 120572 = 120583 is assigned this interpolation methodologydescribes ordinary Kriging (OKR) Also it is possible byapplying prior knowledge or any other technique to identifythe basis functions which could be used in the regressionfunction This enables extrapolating the points outside thesampled region If a quadratic polynomial is used theKriging technique is termed as universal Kriging (UKR)whereas when the Kriging is able to identify the best basisfunction on its own it is termed as blind Kriging (BKR) Theimportance of each basis function is determined using theBayesian variable ranking Further forward selection strategyis applied to enable inclusion of more basis functions in theBKR model The merit of using this method is that it satisfiesprinciples of effect hierarchy and effect heredity for examplelinear interactions are included before the quadratic effects

RSA is a methodology [14] of fitting a function fordiscrete responses obtained from numerical calculations Fora second-order polynomial RSA model the response can berepresented by

119865 (119909) = 120579119900+

119873DV

sum

119895=1

120579119895119909119895

+

119873DV

sum

119895=1

1205791198951198951199092

119895

+

119873DV

sum

119894=1

119873DV

sum

119895=1

119894 =119895

120579119894119895119909119894119909119895

(10)

where 119865(119909) represents the response of the function andterms 120579

119900 1205791 and so forth are the regression coefficients

The number of regression coefficients are found by relation


(119873DV + 1)119909(119873DV + 2)2 where119873DV is the number of designvariables and 119909 represents the selected design variable It isthe simplestmodel andmost commonly used in the surrogatebased optimization application

GA [15] a population-based algorithm is used for theglobal optimal search As GA is based on random numbergeneration each run produces a different result and actuallocal optima can be ignored Hence in order to reduce theproblem of GA sequential quadratic programming (SQP)which is a local search algorithm was used for fine-tuningSQP can be used directly to search optimally but it is depen-dent on initial guesses for the design variables as to where theglobal optimum can be located A highly nonlinear functioncan have several local optima and different guesses producedifferent designsOne option for alleviating that issue is to useseveral initial guesses run SQP several times and choose thebest objective function value among the predicted responsesAnother solution is using hybrid GA searching for a globaloptimum with GA and then fine-tuning with SQP

GA function in Matlab takes the following parameterssurrogate function to generate population number of initialpopulation boundary of the variables and stopping criteriaInitially 20 populations were generated and number of gener-ations was set to 50 Once the iteration is complete the opti-mal design variable values were obtained On the other handin SQP initial guess along with the boundary of the variableswas fed In this case the optimal design variable values wereused as initial guess of SQP Each run of GA produces dif-ferent result because it tries to find global optimal while withproper initial guess SQP finds a local optima or best design

3 Results and Discussions

Figure 4 validates the current CFD result with existingexperimental and CFD results for the objective function [1016] In the present simulations 14 million cell elements and0275 million nodes were generated Design points in thedesign space were selected through three-level full factorialdesign The objective function which is turbine efficiencywas evaluated at these points using the RANS solver Theevaluated objective function values are shown in Figure 5The computed efficiency values along with the design pointswere used for the surrogate construction Finally the HGAwas used to find optimal points from the surrogates Theoptimal design is solved again using the RANS solver to checkthe accuracy of surrogates

Table 4 shows the comparison of RANS and surrogatepredicted results of the objective function The optimizedresults show that the efficiency has increased to 4252whichwas around 1267 increment as compared to the referencedesign and it was obtained byUKRThe error in prediction ofUKR was minus031 which was lowest among all the surrogatesconsidered for the present evaluation The error was becauseof the noninteger prediction of the number of blades approx-imation in CFD computations and surrogate constructionThe table shows the optimal point in the design space and theoptimal numbers of RB and GV were 38 and 24 respectively

As the efficiency was highest by the UKR predicted resultfurther study to analyze the flow was done using the UKR

01

02

03

04

05

0 05 1 15 2 25

Experiment [Maeda et al 1999]CFD [current study]Numerical [Xiong and Liu 2011]

120578

120593

Figure 4 Validation for objective function

30

35

40

45

25 30 35 40 45Nrb

Ngv = 20

Ngv = 26

Ngv = 32

120578

Figure 5 Objective function values

predicted results only Figures 6ndash9 show the comparison ofRef andOpt designs For a wider range of flow coefficient theOpt design shows the overall improvement in the efficiency(Figure 6) The power produced is higher for the Opt designwhich contributes to higher torque (Figure 7) A turbineshould produce lesser pressure drop which gives higherefficiency and this can be clearly observed for the Opt designin Figure 8

Figure 9 shows the pressure distribution at a plane locatedat 50 span for the base and the optimal design It wasobserved that the pressure contour over the blade is lowerfor the optimized blade The pressure over the rotor is higherfor the reference design and is lower for the optimum designwhich results in lesser pressure drop across the optimumblade The lesser the pressure drop is the more it contributesto efficiency

Among the surrogates it was found that the UKRperformed well while the BKR performed badly The mostgeneral surrogate RSA somehow improved efficiency buterror was higher compared to UKR but lower than BKRSimilar confusing results were found by the authors [2 5 6]


Table 4 Optimal designs for efficiency

Model 119873gvopt 119873rbopt 119865Sur 119865CFD 119865Ref 119865Imp 119865Err BKR 25 37 4267 3754 3774 minus053 minus1367

OKR 24 36 4289 4207 3774 1147 minus195

UKR 24 38 4265 4252 3774 1267 minus031

RSA 20 37 4271 4109 3774 888 minus394

01

02

03

04

05

0 075 15 225

ReferenceUKR surrogate

120578

120593

Figure 6 Efficiency enhancement

0

100

200

300

400

500

00 03 05 08 10Q


Pw

Figure 7 Effect of flow rate on power

for the surrogates RSA OKR and neural network Hencea multiple surrogate approach is better for turbomachineryapplications as the same set of design points can producemultiple optimal and there is a greater chance to have betteroptimal design and less uncertainty in optimal design

4 Conclusion

An impulse turbine was numerically modeled and analyzedusing a RANS solver Different surrogate models includingKriging variants and RSA were used to find optimal designThe optimizer was hybrid genetic algorithm It was found

0

500

1000

1500

2000

00 03 05 08 10


ΔP

Q

Figure 8 Effect of flow rate on pressure drop

Reference OptimizedFlow

direction

GV downstream

Rotor

Rotational direction

GV upstream

100750

100975

101200

101425

101650

101875

102100

Pressure (Pa)

Figure 9 Pressure contour


that approximately 13 relative efficiency can be improvedthrough the optimization procedure The optimal numberof rotor and stator blades was 38 and 24 The increment inefficiency was significant over the entire flow coefficientsTheenhancement of efficiency was achieved because of change inpressure profile over the blade

Among the different surrogates universal Kriging per-formed better while blind Kriging failed to enhance theturbine performance Hence instead of single surrogatemultiple surrogate application is suggested to the readersTheCFDwith the surrogate coupled hybrid genetic algorithm canbe used for the ocean energy applications as this approach canreduce total design and simulation cost

Nomenclature

AbbreviationsBKR Blind KrigingCFD Computational fluid dynamicsDV Design variableGA Genetic algorithmGV Guide vaneKRG KrigingOKR Ordinary KrigingUKR Universal KrigingOpt OptimizedOWC Oscillating water columnRANS Reynolds averaged Navier-StokeRB Rotor bladeRef ReferenceRSA Response surface approximationSQP Sequential quadratic programming

Symbols

119862 Parameter coefficient119865 Objective functiongv Number of guide vane119897 Chord length119873 IntegerPw Power (Watts)119876 Flow rate (m3s)119903 Mean radius of rotor (m)rb Number of rotor blade119879 Torque (N sdotm)119880 Circumferential velocity at mean radius (ms)V Mean axial inlet flow velocity (ms)119909 VariableΔ119875 Total pressure drop (Pa)120578 Efficiency120579 Regression coefficient120588 Density of air (kgm3)120593 Flow coefficient120596 Angular velocity (rads)

Subscripts

cfd Computational fluid dynamicsDV Design variables

Err Errorgv Guide vaneimp Improvementin InputOpt OptimalRef Referencerb Rotor blade119904 Rotational speedSur Surrogate119905 Torque

Conflict of Interests

The authors do not have any conflict of interests

Acknowledgments

The authors gratefully acknowledge the financial support bythe Earth System Science Organization Ministry of EarthSciences Government of India to conduct the research

References

[1] T D Robinson Surrogate based optimization using multi-fidelity models with variable parameterization [PhD thesis]Massachusetts Institute of Technology Cambridge Mass USA2007

[2] A Samad K-Y Kim T Goel R T Haftka and W ShyyldquoMultiple surrogate modeling for axial compressor blade shapeoptimizationrdquo Journal of Propulsion and Power vol 24 no 2pp 302ndash310 2008

[3] F A C Viana T W Simpson V Balabanov and V ToropovldquoMetamodeling in multidisciplinary design optimization howfar have we really comerdquo AIAA Journal vol 52 no 4 pp 670ndash690 2014

[4] J Peter and M M Onera ldquoComparison of surrogate modelsfor turbomachinery designrdquo WSEAS Transactions on FluidDynamics vol 3 no 1 pp 10ndash17 2008

[5] A Samad Numerical optimization of turbomachinery bladeusing surrogate models [PhD thesis] School of MechanicalEngineering Inha University Incheon South Korea 2008

[6] A Samad and K-Y Kim ldquoShape optimization of an axial com-pressor blade bymulti-objective genetic algorithmrdquo Proceedingsof the Institution of Mechanical Engineers Part A Journal ofPower and Energy vol 222 no 6 pp 599ndash611 2008

[7] A F D O Falcao ldquoWave energy utilization a review of thetechnologiesrdquo Renewable and Sustainable Energy Reviews vol14 no 3 pp 899ndash918 2010

[8] M H Mohamed G Janiga E Pap and D Thevenin ldquoMulti-objective optimization of the airfoil shape ofWells turbine usedfor wave energy conversionrdquo Energy vol 36 no 1 pp 438ndash4462011

[9] R P F Gomes J C C Henriques L M C Gato and A FO Falcao ldquoMulti-point aerodynamic optimization of the rotorblade sections of an axial-flow impulse air turbine for waveenergy conversionrdquo Energy vol 45 no 1 pp 570ndash580 2012

[10] H Maeda S Santhakumar T Setoguchi M Takao Y Kinoueand K Kaneko ldquoPerformance of an impulse turbine with fixedguide vanes for wave power conversionrdquo Renewable Energy vol17 no 4 pp 533ndash547 1999


[11] A Thakker and T S Dhanasekaran ldquoExperimental and com-putational analysis on guide vane losses of impulse turbine forwave energy conversionrdquo Renewable Energy vol 30 no 9 pp1359ndash1372 2005

[12] T Setoguchi S Santhakumar H Maeda M Takao and KKaneko ldquoA review of impulse turbines for wave energy conver-sionrdquo Renewable Energy vol 23 no 2 pp 261ndash292 2001

[13] I Couckuyt A Forrester DGorissen F DeTurck andTDhae-ne ldquoBlind Kriging implementation and performance analysisrdquoAdvances in Engineering Software vol 49 no 1 pp 1ndash13 2012

[14] R H Myers and D C Montgomery Response Surface Method-ology-Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 1995

[15] D-KHe F-LWang andZ-ZMao ldquoHybrid genetic algorithmfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 78 no 4 pp 626ndash633 2008

[16] C Xiong and Z Liu ldquoNumerical analysis on impulse turbinefor OWC wave energy conversionrdquo in Proceedings of the Asia-Pacific Power and Energy Engineering Conference (APPEEC rsquo11)Wuhan China March 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Upstream GV

Rotor blades

Hub

Downstream GV

(a) 3D view (b) Periodic view

Figure 1 Impulse turbine

single directionThe popular bidirectional turbines are eitherreaction or impulse type The impulse turbine is better interms of having higher operating range The impulse turbinehas a symmetrical rotor sandwiched between two sets ofguide vanes (GVs) The GVs essentially deflect the flowthrough the inlet and helps increase the kinetic energy of flowAs a result the fluid particle hits the rotor blade (RB) andgives an ldquoimpulserdquo to the turbine [7] The earliest reportedsystematic optimization study was on reaction turbine airfoilblade shape modification for achieving multiple objectives[8] The optimization of rotor blade sections of an impulseturbine was carried by Gomes et al [9]

The present work compares the Kriging variants alongwith RSA surrogate to enhance the efficiency of the turbineused for wave energy extraction Numbers of blade andguide vanes were modified to enhance the efficiency of theturbine Numerical analysis to validate the performance ofthe surrogates was implemented in this problem Detailednumerical approach and surrogate strategy along with resultshave been discussed in this paper

2 Problem Description andNumerical Procedure

21 Model Description and CFD Methodology Bidirectionalflow impulse turbine was chosen as the reference geometry[10] for studying the applicability of surrogate techniques toturbomachinery application Figure 1(a) shows the completegeometry The turbine has 30 rotor blades (119873rb = 30) and26 guide vanes (119873gv = 26) on either side of the rotor blade(RB) To reduce computational cost simulation was run oversingle RB rather considering all the blades Figure 1(b) showsthe flowdomainThemajor specifications are listed in Table 1To analyze the flow over the entire fluid domain (including allthe blades) a higher computational cost is required Hencethe walls of the domain where it faces the domain of otherblades are given as periodic conditions This has also beenreported in the literature [11]

Table 1 Design specifications of rotor and guide vane

Parameter Specifications

Rotor

Rotor blade profile Circular-ellipticalNumber of rotor blades (119873rb) 30

Rotor blade pitch 267mmHub diameter 210mmTip diameter 298mmTip clearance 1mm

Chord length (119897rb) 54mmBlade inlet angle 60∘

Guide vane

Guide vane profile Plate typeNumber of blades 26Stator blade pitch 308mmChord length (119897gv) 70mmTip clearance 1mmBlade thickness 05mm

Guide vane inlet angle 30∘

The flow was computed over the passage of the upstreamguide vane (GV) then over the RB Finally the flow leavesthrough the downstream GV Steady state flow with frozenrotor approach was used The turbulence model was 119896-120576 andthe turbine rotated at constant low speed of 600 rpm Inletvelocity (V) was varied to compute flow over different flowcoefficients and the exit pressure was set to 1 atm To achievethe uniform flow the flow domain was extended to 85 timesthe chord length [11] The Reynolds averaged Navier-Stoke(RANS) equations were solved for evaluating torque (119879) andtotal pressure drop (Δ119875) Rather than expressing torquepressure drop and velocity directly these were addressed indimensionless forms as torque coefficient (119862

119905) input power

coefficient (119862in) and flow coefficient (120593) respectively Flowcoefficient (120593) is the ratio of the inlet axial velocity to the




2119879

120588 (V2 + 1198802) 119887119897rb119873rb119903 (1)


120588 (V2 + 1198802) 119887119897rb119873rbV (2)

Efficiency 120578 =119879120596

Δ119875119876=

119862119905

120601 sdot 119862in (3)



Mass

120597 (120588119906)

120597119909+

120597 (120588V)120597119910

+120597 (120588119908)

120597119911= 0 (5)

and momentum

minus120597 (119875)

120597119909+

120597 (120591119909119909)

120597119909+

120597 (120591119910119909)

120597119910+

120597 (120591119911119909)

120597119911= div (120588

119906119906)

minus120597 (119875)

120597119909+

120597 (120591119909119910)

120597119909+

120597 (120591119910119910)

120597119910+

120597 (120591119911119910)

120597119911= div (120588V119906)

minus120597 (119875)

120597119909+

120597 (120591119909119911)

120597119909+

120597 (120591119910119911)

120597119910+

120597 (120591119911119911)

120597119911= div (120588

119908119906)

(6)




Shroud

Rotor

Hub











objective function



Optimized model

Yes

No


Design optimization






1 1199092 119909

119899 and let


119891 (119909) = 119872120572 + 119903 (119909) sdot Ψminus1

sdot (119891 (119883) minus 119865120572) (7)


120572 = (1198831015840

Ψminus1

119883)minus1

119883Ψminus1

119891 (119883) (8)



Ψ = (



) (9)



119865 (119909) = 120579119900+

119873DV

sum

119895=1

120579119895119909119895

+

119873DV

sum

119895=1

1205791198951198951199092

119895

+

119873DV

sum

119894=1

119873DV

sum

119895=1

119894 =119895

120579119894119895119909119894119909119895

(10)












01

02

03

04

05

0 05 1 15 2 25


120578

120593


30

35

40

45

25 30 35 40 45Nrb

Ngv = 20

Ngv = 26

Ngv = 32

120578








OKR 24 36 4289 4207 3774 1147 minus195

UKR 24 38 4265 4252 3774 1267 minus031

RSA 20 37 4271 4109 3774 888 minus394

01

02

03

04

05

0 075 15 225


120578

120593


0

100

200

300

400

500

00 03 05 08 10Q


Pw



4 Conclusion


0

500

1000

1500

2000

00 03 05 08 10


ΔP

Q



direction

GV downstream

Rotor


GV upstream

100750

100975

101200

101425

101650

101875

102100

Pressure (Pa)





Nomenclature


Symbols


Subscripts





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












2119879

120588 (V2 + 1198802) 119887119897rb119873rb119903 (1)


120588 (V2 + 1198802) 119887119897rb119873rbV (2)

Efficiency 120578 =119879120596

Δ119875119876=

119862119905

120601 sdot 119862in (3)



Mass

120597 (120588119906)

120597119909+

120597 (120588V)120597119910

+120597 (120588119908)

120597119911= 0 (5)

and momentum

minus120597 (119875)

120597119909+

120597 (120591119909119909)

120597119909+

120597 (120591119910119909)

120597119910+

120597 (120591119911119909)

120597119911= div (120588

119906119906)

minus120597 (119875)

120597119909+

120597 (120591119909119910)

120597119909+

120597 (120591119910119910)

120597119910+

120597 (120591119911119910)

120597119911= div (120588V119906)

minus120597 (119875)

120597119909+

120597 (120591119909119911)

120597119909+

120597 (120591119910119911)

120597119910+

120597 (120591119911119911)

120597119911= div (120588

119908119906)

(6)




Shroud

Rotor

Hub











objective function



Optimized model

Yes

No


Design optimization






1 1199092 119909

119899 and let


119891 (119909) = 119872120572 + 119903 (119909) sdot Ψminus1

sdot (119891 (119883) minus 119865120572) (7)


120572 = (1198831015840

Ψminus1

119883)minus1

119883Ψminus1

119891 (119883) (8)



Ψ = (



) (9)



119865 (119909) = 120579119900+

119873DV

sum

119895=1

120579119895119909119895

+

119873DV

sum

119895=1

1205791198951198951199092

119895

+

119873DV

sum

119894=1

119873DV

sum

119895=1

119894 =119895

120579119894119895119909119894119909119895

(10)












01

02

03

04

05

0 05 1 15 2 25


120578

120593


30

35

40

45

25 30 35 40 45Nrb

Ngv = 20

Ngv = 26

Ngv = 32

120578








OKR 24 36 4289 4207 3774 1147 minus195

UKR 24 38 4265 4252 3774 1267 minus031

RSA 20 37 4271 4109 3774 888 minus394

01

02

03

04

05

0 075 15 225


120578

120593


0

100

200

300

400

500

00 03 05 08 10Q


Pw



4 Conclusion


0

500

1000

1500

2000

00 03 05 08 10


ΔP

Q



direction

GV downstream

Rotor


GV upstream

100750

100975

101200

101425

101650

101875

102100

Pressure (Pa)





Nomenclature


Symbols


Subscripts





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













objective function



Optimized model

Yes

No


Design optimization






1 1199092 119909

119899 and let


119891 (119909) = 119872120572 + 119903 (119909) sdot Ψminus1

sdot (119891 (119883) minus 119865120572) (7)


120572 = (1198831015840

Ψminus1

119883)minus1

119883Ψminus1

119891 (119883) (8)



Ψ = (



) (9)



119865 (119909) = 120579119900+

119873DV

sum

119895=1

120579119895119909119895

+

119873DV

sum

119895=1

1205791198951198951199092

119895

+

119873DV

sum

119894=1

119873DV

sum

119895=1

119894 =119895

120579119894119895119909119894119909119895

(10)












01

02

03

04

05

0 05 1 15 2 25


120578

120593


30

35

40

45

25 30 35 40 45Nrb

Ngv = 20

Ngv = 26

Ngv = 32

120578








OKR 24 36 4289 4207 3774 1147 minus195

UKR 24 38 4265 4252 3774 1267 minus031

RSA 20 37 4271 4109 3774 888 minus394

01

02

03

04

05

0 075 15 225


120578

120593


0

100

200

300

400

500

00 03 05 08 10Q


Pw



4 Conclusion


0

500

1000

1500

2000

00 03 05 08 10


ΔP

Q



direction

GV downstream

Rotor


GV upstream

100750

100975

101200

101425

101650

101875

102100

Pressure (Pa)





Nomenclature


Symbols


Subscripts





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















01

02

03

04

05

0 05 1 15 2 25


120578

120593


30

35

40

45

25 30 35 40 45Nrb

Ngv = 20

Ngv = 26

Ngv = 32

120578








OKR 24 36 4289 4207 3774 1147 minus195

UKR 24 38 4265 4252 3774 1267 minus031

RSA 20 37 4271 4109 3774 888 minus394

01

02

03

04

05

0 075 15 225


120578

120593


0

100

200

300

400

500

00 03 05 08 10Q


Pw



4 Conclusion


0

500

1000

1500

2000

00 03 05 08 10


ΔP

Q



direction

GV downstream

Rotor


GV upstream

100750

100975

101200

101425

101650

101875

102100

Pressure (Pa)





Nomenclature


Symbols


Subscripts





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












OKR 24 36 4289 4207 3774 1147 minus195

UKR 24 38 4265 4252 3774 1267 minus031

RSA 20 37 4271 4109 3774 888 minus394

01

02

03

04

05

0 075 15 225


120578

120593


0

100

200

300

400

500

00 03 05 08 10Q


Pw



4 Conclusion


0

500

1000

1500

2000

00 03 05 08 10


ΔP

Q



direction

GV downstream

Rotor


GV upstream

100750

100975

101200

101425

101650

101875

102100

Pressure (Pa)





Nomenclature


Symbols


Subscripts





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Nomenclature


Symbols


Subscripts





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Surrogate Assisted Design Optimization of ...downloads.hindawi.com/journals/ijrm/2014/563483.pdf[ ]. e optimization of rotor blade sections of an impulse turbine was