Hydrodynamic Design and Optimization of Hydro kinetic Turbines using a Robust Design Method

Transcription

1 Poceedings of the 1st Maine Enegy Technology Symposium METS13 Apil 10 11, 2013, Washington, D.C. Hydodynamic Design and Optimization of Hydo kinetic Tubines using a Robust Design Method Nitin Koleka 1 Zhen Hu 2 Aindam Banejee 1,a Xiaoping Du 2 1Depatment of Mechanical Engineeing & Mechanics, Lehigh Univesity, Bethlehem, PA Depatment of Mechanical and Aeospace Engineeing, Missoui S&T, Rolla, MO a Coesponding autho: ab612@lehigh.edu ABSTRACT Hydo kinetic Tubines (HKT), unlike conventional hydaulic tubines ae zeo head enegy convesion devices, which utilize the kinetic enegy of flowing wate fo powe geneation. The pefomance of these tubines depends on vaious paametes like numbe of blades, tip speed atio, type of aifoil, blade pitch, chod length & twist and its distibution along the blade span. The pesent wok aims at maximizing the pefomance of a hoizontal axis hydokinetic tubine though a coupled computational fluid dynamics blade element momentum (hydodynamic) analysis. Optimization is caied out using both obust and deteministic design optimization schemes and compaison is pesented. The cuent analysis is focused on constant chod blades due to low cost and ease of fabication. A hydodynamic analysis is caied out using blade element momentum (BEM) theoy to study effect of vaious opeating paametes on foces and toque developed by the tubine, theeby aiving at optimized design with maximum pefomance coefficient. BEM code is validated with expeimental data fom NREL phase III oto. BEM analysis is compaed with a detailed thee dimensional computational fluid dynamics (CFD) analysis. Finally, CFD analysis esults ae pesented fo optimized geomety. Nomenclatue: a = axial induction facto a = angula induction facto B = numbe of blades BEM (x) = BEM function fo optimization C d = actual dag coefficient (based on Re) C d, ef = dag coefficient based on Re ef c = chod length [m] C p = pefomance coefficient dq & dt = toque & thust developed on a blade element at adius [N & N.m] F Hub & F Tip = hub loss & tip loss coection factos m = optimization taget = mean value of pefomance coefficient m C oe,, = mean values of chod lengths TSR and blade pitch angles P = Tubine Powe p = vecto of andom paametes R = tubine adius [m] Re = flow Reynolds numbe Re ef = efeence Reynolds numbe fo hydodynamic data input R ( m x ) = obustness metics = adius of blade element [m] hub = hub adius [m] U = flow velocity [m/s] U = elative flow velocity in otating efeence fame [m/s] = standad deviation of C p s 2 Coe x d x = vecto of deteministic design vaiables = vecto of andom design vaiables p = pessue gadient acoss the tubine [N/m 2 ] 1

2 μ = dynamic viscosity of wate [Pa.s] = angula velocity of the wake [ad/s] Ω = tubine otational speed [ad/s] = angle of elative flow [ ] ρ = wate density [kg/m 3 ] σ = local blade solidity σ Cp = standad deviation of C p θ po = blade pitch angle [ ] 1.0 INTRODUCTION Renewable enegy esouces ae gaining global attention due to depleting fossil fuels and hamful envionmental effects associated with thei usage. Hydo, wind, sola, biomass and geothemal enegies fom the bulk of enewable enegy souces; among which hydo powe offes one of the most exciting and sustainable poposition. Taditionally, hydopowe has accounted fo the bulk of the enewable enegy poduction in the United States. The pimay enegy use in the U.S. in 2011 was 28,516 TWh/y of which only 9% came fom enewables[1]. Taditional hydoelectic o mico hydo facilities contibuted 35% of total enewable enegy poduction[1]. Howeve, gowth of conventional hydopowe plants ae limited due to limitations on the numbe of available natual sites, lage capital (initial) investment, pay back time and envionmental concens. In lieu of this, maine and hydokinetic (MHK) systems offe many advantages: these ae potable systems with small initial cost, no lage infastuctue and easy and quick deployment [2 5]. A study conducted by Electic Powe Reseach Institute (EPRI) fo US ives estimated hydokinetic powe potential of 12,500 MW[6, 7]. This study was based on consevative assumption of tubine aay deployment fo ives with dischage ates geate than 113 m 3 /s and flow velocities geate than 1.3 m/s. A study conducted by EPRI evaluated many, but not all tidal enegy sites in U.S. and estimated 115 TWh/y of tidal enegy[6, 7]. These estimates show potential of MHK systems. Hydokinetic tubines (HKT) ae a class of low head enegy convesion devices which convet kinetic enegy of flowing wate into mechanical wok[8, 9]. Tidal and maine cuent tubines also falls into simila categoy of (lift dag) devices which utilize hydodynamic blade shapes to deive powe fom flowing fluid. Depending on the flow diection of wate elative to the axis of otation, HKT can be classified as hoizontal axis and vetical axis tubines. The pefomance of these tubines is govened by the thee non dimensional paametes defined below: (a) tip speed atio (TSR) that is defined as the atio of blade tip speed to fluid speed; (b) solidity (σ) that is defined as the atio of blade chod length times the numbe of blades to tubine cicumfeence; and, (c) Reynolds numbe. R TSR (1) U Bc (2) 2R Uc Re (3) Ove the last decade, the hydodynamics of HKT has been investigated using computational fluid dynamics (CFD) [10 12] and laboatoy scale expeiments [13 15]. Blade element momentum (BEM) analysis which foms the backbone of wind tubine oto design can be used fo HKT design [16]. Apat fom BEM, a seies of inexpensive CFD tools based on the solution of the Eule o Navie Stokes equations like panel method and votex lattice method can be used fo aeodynamic/hydodynamic analysis of these devices [17]. In addition, computationally expensive techniques that involve solving Reynolds aveaged Navie Stokes equations (RANS) with tubulence models has been successfully used fo hydodynamic analysis of HKT[10, 12, 18]. Consul et al.[10] pefomed a two dimensional CFD analysis to undestand the influence of numbe of blades on pefomance of coss flow tubines and found impoved pefomance with highe numbe of blades. Highe solidity tubine pefomed bette at low tip speed atios and low angles of attack[10]. Duquette and co wokes[12] pefomed expeiments and 2 D numeical analysis to study the effect of numbe of blades and solidity on the pefomance of hoizontal axis wind tubine. The numeical analysis was pefomed using BEM and lifting 2

3 line based wake theoy[12]. Thei analysis concluded that the ange of TSR fo maximum C p depends stongly on solidity and weakly on numbe of blades. This suggests that the chod length decides the optimum TSR ange of the tubine. Thei laboatoy expeiments with mico tubines with flat plate blades showed that lage blade pitch angles tend to decease the optimum TSR ange significantly with small change in maximum C p. Myes and Bahaj [13 15] expeimentally investigated the flow field and wake ecovey behind tidal tubine using mesh disk simulatos and found that ecovey depends on poximity to wate suface, sea bed oughness(which govens vetical velocity pofile and tubulent kinetic enegy of flow) and to a lesse extent on oto thust. Mukheji et al.[18] pefomed detailed thee dimensional CFD to undestand effect of TSR, solidity, blade pitch and numbe of blades on pefomance of HKT. They epoted a stong influence of TSR on pefomance coefficient fo vaious tubine geometies. Pefomance coefficient is a atio of tubine powe to the available powe in the flowing fluid passing though oto swept aea (Equation 4). C p = (4) Futhe, incease in tubine solidity and blade numbes wee epoted to maximize the C p with maximum C p obseved at lowe TSR. The knowledge base deived fom aeodynamic/hydodynamic analysis of wind/hydokinetic tubines can be used fo futhe design optimization study. Most of the optimization studies fo wind tubines[19 21] wee focused on maximizing coefficient of pefomance and annual enegy poduction (AEP). Selig and Covestone Caoll[19] used a genetic algoithm (GA) fo optimizing AEP and cost of enegy of low lift aifoils fo stall egulated wind tubines (wind tubines that have thei blades designed so that when fluid speeds ae high, the otational speed o the toque, and thus the powe poduction, deceases with inceasing fluid speed above a cetain value that is usually not the same as the ated speed). Belesis[20] pesented GA fo constained optimization of stall egulated wind tubine and found it to be supeio to classical optimization methods. Fuglsang and Madsen[21] pefomed multi disciplinay optimization on stall egulated hoizontal axis wind tubine consideing fatigue, maximum load and AEP. Most of these studies wee based on BEM analysis and did not conside thee dimensional flow dynamics which is inheent to wind tubines and hydokinetic tubines. The pesent wok focuses on maximizing the pefomance of a stall egulated, fixed pitch, constant chod, hoizontal axis hydokinetic tubine opeating in a cavitation fee envionment that is sufficiently away fom the fee suface by using a combination of BEM and thee dimensional CFD analysis. As a stating point, a hydodynamic analysis is caied out using BEM theoy; the objective being to study the effect of vaious opeating paametes on toque developed by the tubine. BEM(lowe ode analytical model = less physics) esults ae compaed with a detailed thee dimensional CFD analysis (highe ode model = moe physics) to test the fidelity of BEM analysis. Aeodynamic data fo BEM paametic study is obtained fom Xfoil[22]. Results of paametic study wee used as a guideline fo setting up bounds on decision vaiables (TSR, c, θ po ) duing optimization pocess. Optimization was pefomed using obust design appoach to handle uncetainties in nondeteministic vaiables: ive velocity, angle of attack of ive flow, and otational speed of tubine. Also, the obust design esults ae compaed with deteministic design appoach. The optimized geomety is then modeled in ANSYS CFX and a thee dimensional computational fluid dynamics (CFD) analysis is pefomed to calculate the fluid foces and toque developed by tubine. This povides validation fo ou BEM based optimization appoach. 2.0 THEORY AND APPROACH: BEM theoy, oiginally attibuted to Betz and Glauet[16] is a combination of blade element theoy and momentum theoy. Accoding to blade element theoy, foces on tubine blade can be obtained by dividing blade into numbe of aeodynamically (o hydodynamically) independent elements. 3

4 Aeodynamic foces on these elements ae calculated based on local flow conditions using two dimensional lift dag data. Foces ae then summed togethe to find total foce on tubine blade. Momentum theoy, the othe half of BEM assumes that the wok done by the flow on tubine blade ceates pessue (o momentum) loss acoss the oto plane. Induced velocities in axial and tangential diection can be calculated fom this momentum loss. These induced velocities affect the foces on tubine blade. BEM combines blade element and momentum theoy and solves coupled equations in iteative manne to detemine fluid foces (thust and toque) and induced velocities nea oto[23]. The oiginal BEM theoy of Betz and Glauet was modified fo ou HKT analysis to take into account effect of hub, tip and Reynolds numbe dependence fo aeodynamic/hydodynamic data coection. Pandtl s tip loss coection facto was incopoated in the algoithm to account fo losses due to fluid flow fom pessue side to suction side at blade tip as: 2 B( R) F cos exp (5) 1 Tip 2 sin( ) The hub loss coection facto was also incopoated to account fo losses caused by swiling flow due to pesence of hub as: 2 1 B( ) (6) F Hub cos exp 2 hub sin( ) hub The effects of coection factos fo tip and hub losses ae combined into single facto F that is defined as: F F Tip F Hub (7) The tip and hub loss coection facto is used to detemine net thust and toque fom tubine: dt F U 2 4a(1 a) d 3 dq 4 Fa (1 a ) U d (8) The axial induction facto (a) is defined as factional decease in wate velocity between the fee steam and the oto plane. The angula induction facto (a ) is defined as one half the atio of the angula velocity of the wake to the angula velocity of the oto (a = /2). Lift and dag coefficients fo SG6043 hydofoil that wee adopted fo ou HKT blades ae obtained fom Xfoil[22]. Xfoil calculates lift and dag foces on a given hydofoil by combining a linea voticity steam function panel method and a viscous solution method (fo bounday laye and wake). The entie viscous solution is stongly inteacted with the incompessible potential flow via the suface tanspiation model. Aeodynamic data obtained fom Xfoil is coected accoding to Equation 9 suggested by Henandez and Cespo[24] as: 0.2 ReRef C d C d,re (9) Ref Re that suggests that the dag coefficient scales invesely with Reynolds numbe but the lift coefficient emains elatively unchanged. Eq. 9 should be used with exteme caution as it is based on small wind tubines ove a Reynolds no. ange of 10 5 to 10 7 and epesents a vey simplistic appoach. Estimation of the dag coefficients at low values of Reynolds numbe can be vey complex. 2.1 Computational Fluid Dynamics analysis: A thee dimensional CFD analysis was pefomed whee Reynolds Aveaged Navie Stokes equations (RANS) wee solved in ANSYS CFX using a multiple efeence fames technique [25]. A otating efeence fame was incopoated to take into account the effect of tubine otation by tansfoming an unsteady flow in an inetial (stationay) fame to a steady flow in a non inetial (moving) fame using equations below: U 0 (10) ( U ) ( U U ) (2 U ) p t (11) whee U is the elative velocity viewed fom otating efeence fame, is the otational speed of the tubine, ( 2 U ) is the Coiolis foce, ( ) is the centifugal foce, is viscous stess tenso, p is the pessue gadient acoss the tubine. The fluid domain consists of inne otating domain with tubine and oute stationay domain as shown in Figue 1. A gid independence study was caied out to study effect of numbe of elements on the CFD analysis. Mesh size was vaied fom a coase mesh of 3.5 million to a fine mesh of 10 million elements and flow vaiables wee monitoed. 4

5 based on aveage ive flow data[30, 31] and chod length is tuncated at six sigma level to account fo manufactuing toleances. Equation 12 pesents the obust design model used fo the optimization study. min ; =,,, ; 2 12 ; 0 18 (12) Figue 1 Computation domain and mesh used fo CFD analysis A mesh with 7.8 million elements was found to be optimal, as inceasing mesh size beyond this point did not cause appeciable change in toque and foces on tubine. Mesh was locally efined with pism elements on tubine wall fo accuate bounday laye pediction to attain a y+ value <100. A y+ value is a non dimensional paamete elated to mesh size which defines distance of fist mesh node fom the tubine wall whee a noslip bounday condition is imposed. Lowe the y+, bette the bounday laye flow esolved nea the wall[26]. Convegence citeia fo continuity and momentum equations wee set to 10 6 absolute and highe ode numeics wee used fo tubulence modeling. A k ω SST (Shea Stess Tanspot) tubulence model was chosen due to its accuacy fo advese pessue gadient flows as the cuent case [27 29]. 2.2 Robust Design Optimization: To account fo uncetainties inheent in the woking envionment of HKT, optimization is caied out using both deteministic and obust design appoaches. The consideed uncetainties include vaiation in ive velocity, chod length, pitch angle and TSR. Table 1 summaizes paametes and design vaiables used fo optimization. Out of eight input paametes, fou ae deteministic paametes (tubine adius, hub adius, numbe of blades and numbe of blade elements), wate velocity is a andom paamete, and the othe thee ae andom design vaiables (pitch angle, TSR, and chod length). The mean values of andom design vaiables ae expected to be optimized to maximize the powe coefficient. Wate velocity is tuncated at [0.8, 3.7] m/s whee, R ( m ) is the obustness metics, x BEM (x) is the BEM function with inputs of p d, p, x d, and x, p d =[R, hub, B, N] is the vecto of deteministic paametes, p =[U] is the vecto of andom paametes, x d =[ ] is the vecto of deteministic design vaiables, and x =[θ po, TSR, c] is the vecto of andom design vaiables whose mean values need to be optimized. The obustness matix used fo the cuent study is given by R = w ( m - ) 2 + s 2, + = 1 1 C m w 2 C w 1 w (13) 2 oe oe whee, m is the taget of optimization, m C oe is the mean value of pefomance coefficient, s 2 is the standad deviation of Coe pefomance coefficient, w 1 and w 2 ae weights fo optimization. The mean value and standad deviation of pefomance coefficient is obtained fom Monte Calo Simulation (MCS) fo cuent study. The values of weights, w 1 and w 2, epesent the decision make's pefeence to the mean value and vaiance. Fo example, if the mean value is moe impotant than the vaiance to the decision make, then a lage value is assigned to the weight w 1. On the othe hand, if the vaiance is moe impotant, a lage value is then assigned to w 2. A Paeto cuve epesents the points of mean value and vaiance unde diffeent combinations of w 1 and w 2. Fom the Paeto cuve, if designes pefe a lage mean value, they will then sacifice the vaiance; and vice vesa if they pefe a lage vaiance value. 2.3 Validation of BEM with Expeimental data: Due to absence of expeimental data fo ou HKT design, BEM code was validated with NREL phase III combined expeimental oto (CER) esults[32]. NREL CER oto is a 5.03m adius, thee bladed wind tubine having 5

6 vaying chod, twisted blades. This tubine uses S809 aifoil fom blade oot to blade tip. BEM analysis was caied out ove a ange of blade pitch angles (0 to 7 ) and TSR (0 to 8). Figue 2a c compaes esults of BEM with NREL data, which shows a good match up to TSR values of 5. At high TSR values, BEM analysis deviates fom expeiments which can be attibuted to non unifom blade loading[33] and acceleated span wise flow, which ae not taken into account in BEM analysis. Table 1. Paametes and design vaiables used fo the optimization study Paamete Type Mean Value Standad deviation Tubine adius (R) Deteministic 1m 0 Hub adius (hub) Deteministic 0.1m 0 # of blades (B) Deteministic 3 0 # of blade elements (N) Deteministic 20 0 Wate velocity (U) Tuncated Gaussian 2m/s 0.4 m/s Blade pitch angle (θpo) Unifom 1, 1 TSR Unifom 0.2, 0.2 Chod length (c) Tuncated Gaussian m c Figue 2 Validation of BEM with NREL expeiments: (a) 0 blade pitch, (b) 4 blade pitch, (c) 7 blade pitch Figue 3 Effect of TSR and blade pitch angle on tubine pefomance at vaious chod lengths: (a) 0.03m chod, (b) 0.06m chod, (c) 0.12m chod 3.0 RESULTS AND DISCUSSION: a. BEM paametic study: A validated BEM code was used fo hydodynamic analysis of a model theebladed constant chod tubine of adius 1m. This tubine uses SG6043 aifoil fom oot to tip as it gives a high C L /C d value ove the cuent opeating ange of Reynolds numbe (110 5 <Re<510 5 ) [12, 34, 35]. BEM analysis is pefomed to undestand effect of chod length, blade pitch and TSR on the tubine pefomance. The tubine blade was divided into 20 elements and BEM analysis was pefomed to estimate thust foces and 6

7 toque developed on the tubine blades. The wate velocity used fo analysis was 2 m/s which is consideed aveage ive wate velocity in the U.S. [30]. The design space selected fo cuent study is such that TSR is vaied fom 2 to 12, blade pitch angle fom 0 to 18 and chod length fom to 0.18m. The expeience gained fom wind tubine industy is used to specify TSR ange fo paametic study. Fo a wind tubine, which is a lift dag device simila to HKT, the TSR fo maximum C p anges fom 6 to 10. The SG6043 aifoil used fo cuent study, depending on flow Reynolds numbe, has stall angle aound Hence the design paamete space of [0, 18 ] is expected to cove all possible opeating blade pitch angles fo optimizing C p. The lowe limit on chod length is based on manufactuing feasibility and uppe limit of 0.18m was specified to estict R/c to 0.56(σ=0.086). Highe the chod length, lage the blade aea undegoing thust loading which is detimental to tubine life. Futhe, incease in chod length does not impove the pefomance significantly but only shifts C p vs TSR cuve towads oigin[12, 18]. The esults of the paametic study ae pesented in Figue 3a c showing the effect of blade pitch and TSR on tubine pefomance coefficient fo blades with chod lengths of 0.03m, 0.06m, and 0.12m espectively. As the chod length is inceased fom 0.03 (Figue 3a) to 0.12m (Figue 3c), the bell shaped C p vs TSR cuve shifts towads the oigin; which implies that highe the chod length, lowe is the TSR fo maximum pefomance. In addition, highe the chod length, highe the blade pitch angle fo maximum pefomance. Futhemoe, fo a given chod length, lowe the TSR, highe the blade pitch fo maximum pefomance. In geneal, hydodynamic analysis suggests that, lowe values of blade chod lengths maximize the coefficient of pefomance. b. Optimized esults: Taking a cue fom paametic study, optimization was caied out using deteministic design and obust design appoaches to maximize the pefomance of model HKT. Figue 4 illustates the Paeto cuve of obust design optimization of hydokinetic tubine blades. Figue 4 shows that the standad deviation of C p will incease with the mean value of C p. A lage C p coesponds to a lage standad deviation. Thus, designe can make a decision to achieve a tadeoff between mean and standad deviation. The optimized design vaiables and tubine blade pefomance fom deteministic design and obust design ae given in Table 2. In this pape, we use w 1 =0.78 and w 2 =0.22. The taget fo optimization, m is assigned a value of 0.6. Figue 4 Paeto cuve of obust design. The esults illustate that the deteministic design method can achieve a maximum C p of 0.52, but its mean value is a smalle than that of obust design and its standad deviation is about two times of that of obust design. The obust design has a smalle TSR than the deteministic design. The compaison of PDFs of C p unde deteministic design and obust design is shown in Figue 5. PDF Robust design Deteministic design Two level of obust design Two level of deteministic design C p Figue 5 Compaison of Pobability Density Functions (PDFs) fom deteministic design and obust design 7

8 The two sigma level and mean value of the two PDFs ae also indicated in Figue 5. The figue demonstates that design fom obust design method has a smalle standad deviation and lage mean value. Hence, the obust design method is less sensitive to the uncetainties in woking envionment than the deteministic design. The two sigma level of PDF unde deteministic design is much lage than that of obust design as shown in Figue 5. [Note: m C, p,max P Method Table 2. Optimized esults of deteministic design and obust design C and s C P ae mean, maximum and standad deviation of pefomance coefficient] θpo TSR c m C P s C P C p,max Deteministic Design Robust Design c. CFD analysis: This section summaizes esults of theedimensional CFD analysis pefomed in ANSYS CFX using a otating efeence fame technique [18]. CFD analysis was pefomed to test the fidelity of BEM based optimization technique. The tubine geometies with diffeent blade configuations (blade pitch angle and chod lengths) wee modeled in SolidWoks and meshing was caied out in ANSYS. A hybid mesh with 7.8 million elements having pism layes on tubine wall was used fo CFD analysis. The esults of CFD analysis ae summaized and compaed with BEM analysis in Table 3. Table 3 Compaison of BEM with CFD analysis Vaiables CFD BEM Blade Pitch ( ) Chod (m) TSR Thust (N) C p Thust (N) C p tailing edge and blade oot. These votices affect the flow field aound tubine and hence the pefomance of tubine. The CFD esults fo obust optimized geomety ae compaed with BEM analysis in Table 4. The coefficient of pefomance and thust foce on tubine obtained fom CFD ae compaable to those obtained fom BEM validating the esults of ou optimization. The tip votices, centifugal and Coiolis foces acting along the blade affect the flow field and pefomance of the tubine. CFD analysis takes into account all these effects which ae not modeled in BEM analysis. Table 4 Compaison of CFD with BEM analysis [Note: All paametes ae in SI units.] Blade BEM CFD Chod TSR pitch C p Foce C p Foce The CFD esults agee in pinciple with values obtained fom BEM analysis. The discepancy in thust and C p values can be attibuted to simplified assumptions of BEM theoy which states that the foces acting on blade element ae essentially twodimensional (calculated based on aeodynamic data). Moeove, BEM does not take into account hydodynamic inteaction between adjacent blade elements and the effect of votices geneated at blade tip, blade Figue 6 Total pessue contous on tubine blade on: (a) Pessue side, (b) Suction side, (c) Zoomed in view of leading edge. 8

9 The contous of total pessue(in stationay fame) on pessue side(upwind) and suction side(downwind) of the blade ae shown in Figue 6. On the pessue side(figue 6a), the pat of blade nea the tip expeience highe pessue compaed to est of the span. Similaly, on suction side(figue 6b) lowe pessue is obseved nea the blade tip compaed to the pat of the blade nea the hub. Thus the pessue gadient acoss the blade is highe at egions away fom the blade oot. The blade egion away fom the hub is subjected to successively highe elative wate velocity and highe angle of elative flow. This indicates that the pat of blade away fom oot contibutes moe towads hydodynamic foces and has significant ole in thust and toque development. Figue 6c shows zoomed in view of total pessue contou nea leading edge of blade which shows the pesence of stagnation zone nea the leading edge and not fa into the pessue side of blade. This indicates that the angle of elative flow (sum of angle of attack and blade pitch angle) is still below stall point. The CFD analysis demonstates possibilities of futhe impovement in hydodynamic pefomance. The contibution of nea hub blade egion can be impoved by poviding highe pitch angles nea the blade oot. A twisted blade with successively deceasing section pitch angles fom blade oot to tip will not only impove Cp, but will help achieving unifom loading on blade. While the cuent wok focused on a constant chod blade HKT, the futue wok will taget hydo stuctual optimization based on coupled BEM CFD FE (finite element) analysis. 4.0 CONCLUSION: A hydodynamic analysis and optimization based on obust design methodology shows that the pefomance of hydokinetic tubine can be maximized by choosing the ight combination of design vaiables. Coefficient of pefomance as high as 0.52 was achieved with a constant chod blade tubine in a non cavitating envionment at depths sufficiently away fom the fee suface. Results of BEM ae in easonable ageement with thee dimensional steady state CFD analysis. Robust design method yielded a design configuation which is less susceptible to uncetainties in design vaiables than the deteministic design. ACKNOWLEDGEMENT: The authos gatefully acknowledge the suppot fom the Office of Naval Reseach though contact ONR N REFERENCES: 1. Annual Enegy Review, in Office of Enegy Statistics, U.S. Enegy Infomation Administation. 2011: Washington, DC Hall, D.G., et al., Wate Enegy Resouces of the United States with Emphasis on Low Head/Low Powe Resouces, I.N.E. Laboatoy and Envionmental, Editos. 2004, U.S. Depatment of Enegy. 3. Hall, D.G., et al., Wind and Hydopowe Technologies, Feasibility Assessment of the Wate Enegy Resouces of the United States fo New Low Powe and Small Hydo Classes of Hydoelectic plants, Tech epot DOE ID 11263, in U.S. Depatment of Enegy, Enegy Efficiency and Renewable Enegy. 2006, Idaho National Laboatoy. 4. Date, A. and A. Akbazadeh, Design and Cost Analysis of Low Head Simple Reaction Hydo Tubine fo Remote Aea Powe Supply. Renewable Enegy, : p Guney, M.S. and K. Kaygusuz, Hydokinetic Enegy Convesion Systems: A Technology Status Review. Renewable and Sustainable Enegy Reviews, (9): p Bedad, R., Oveview of U.S. Ocean Wave and Cuent Enegy: Resouce, Technology, Envionmental and Business Issues and Baies. 2007: Electic Powe Reseach Institute. 7. Bedad, R., Pioitized Reseach, Development, Deployment and Demonstation Needs: Maine and Othe Hydokinetic Renewable Enegy. 2008, Electic Powe Reseach Institute. 8. Khan, M.J., M.T. Iqbal, and J.E. Quaicoe, Rive Cuent Enegy Convesion Systems: Pogess, Pospects and Challenges. Renewable and Sustainable Enegy Reviews, : p Schwatz, S.S., Poceedings of the Hydokinetic and Wave Enegy Technologies Technical and Envionmental Issues Wokshop, ed. I. 9

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