3-d Cfd Analysis on Effect of Hub-to-tip Ratio on Performance of Impulse Turbine for Wave Energy Conversion

Key words: wave energy, impulse turbine, computational fluid dynamics, hub-to-tip ratio


Introduction
The cur rent rate of world wide en ergy use is un sus tain able, mainly due to the depend ence on the use of fos sil fu els as the pri mary sources of avail able en ergy.Based on the cur rent us age trends of the fos sil fu els it is pre dicted that cur rent quan ti ties will be exhausted in ap prox i mately 200 years.The cur rent us age of avail able re sources is in di cating that in a mat ter of years, the world will face a pe riod of short ages, es ca lat ing prices and in creas ing in ter na tional ten sions, as de vel op ing coun tries de mand their share of a rap idly dwin dling re source.Through out the years, sev eral con cepts were de vel oped and in ves ti gated: the Salter Duck, Cockerell raft', the "SEA clam", and os cil lat ing wa ter column (OWC) de vices.These wave en ergy de vices are ei ther shore mounted or off shore.Shore-mounted de vices are fixed and eas ier to de sign but har ness less en ergy from shallow wa ters.Shore based con vert ers are gen er ally os cil lat ing wa ter col umn [1].Shore-mounted OWC con vert ers have been erected in Nor way, UK (Isle of Islay) and DOI:10.2298TSCI0704157T Por tu gal (Is land of Pico).Off shore con vert ers can be ei ther fixed sea bed or float ing and are meant for the height wave power den sity of the off shore sea.The var i ous off shore devices use dif fer ent en ergy con ver sion chains; the wave power can be cap tured by hy draulic sys tems, wa ter tur bines or air tur bines, via a wave to pneu matic con verter.These devices in clude the cir cu lar Clam, Salter's Duckt, and the float ing OWC.Ex am ples of the float ing OWC are the "whale" and the back ward bent duct buoy (BBDB), both orig i nating from Ja pan.One of the most prom is ing tech niques for har ness ing wave en ergy is the OWC.OWC based wave en ergy plants con vert en ergy into low-pres sure pneu matic power in the form of bidirectional air flow.Air tur bines which are ca pa ble of ro tat ing unidi rec tional in a bidirectional air flows, oth er wise also known as self-rec ti fy ing air turbines are used to ex tract me chan i cal shaft power, which is fur ther con verted into elec trical power by a gen er a tor.Dif fer ent type of im pulse tur bine have been pro posed over the year, but gen er ally their per for mance has no been in ves ti gated ex cept may in the case of McCormick tur bine whose ef fi ciency found to be rather low.The Wells tur bine, in troduced by Dr. A. A. Wells in 1976 was the first choice for all OWC based wave en ergy plants, which were built in Nor way, Ja pan, Scot land, In dia, and China.There are many re ports, which de scribed the per for mance of the Wells tur bine both at start ing and running con di tions [2][3][4].Ac cord ing to these re sults, the Wells tur bine has in her ent dis advan tage: nar row rang of flow rate at which it op er ates at use ful ef fi cien cies due to stall prob lem, poor start ing char ac ter is tics, high-speed op er a tion and con se quent noise and high ax ial trust.Setoguchi et al. [5][6][7][8][9][10][11][12] de vel oped an im pulse tur bine with self-pitch ing con trolled guide vanes and sub se quently with self-pitch ing linked guide vanes to overcome the draw backs of the Wells tur bine.Num bers of stud ies were con ducted on im pulse tur bine with self-pitch con trolled guide vanes over a pe riod of time.The tur bine has a rotor with im pulse blades.There two sets of guide vanes on ei ther side of the ro tor.The guide vanes are piv oted and are free to ro tate be tween two pre set an gles de ter mined by me chan i cal stops.When ever the air flow change the di rec tion, the guide vanes flip un der the ac tion of aero dy namic mo ments act ing on them, and take up the right ori en ta tions (that is, up stream guide vanes act ing as noz zle cas cade and down stream guide vanes acting as a dif fuser cas cade) for ef fi cient op er a tion.Later im pulse tur bine with self-pinch ing guide vanes were pro posed, this type have the same de sign as the pre vi ous im pulse turbine with con trolled guide vanes ex cept that the ev ery vane on one side of the ro tor is con nected by a link out side of the ro tor.That is, any pair of vanes on ei ther side of the rotor is con strained to ro tate to gether.This de sign de liv ers use ful ef fi cien cies over a wide rang of flow rates, has very good start ing char ac ter is tics and low op er at ing speed.These char ac ter is tics have been put up with field trial.A 1.0-m di am e ter tur bine of this type was de signed, fab ri cated and is be ing op er ated by Na tional In sti tute of Ocean Tech nol ogy at Vizhinjam, a site near.Thiruvananthapuram which is a city on the west coast of In dia.Not with stand ing the su pe rior char ac ter is tics of the im pulse tur bine with self-pitch controlled guide vanes, cer tain dis ad van tages are im posed by such vari able ge om e try de sign.The guide vanes pitch at the wave fre quency call ing for a ro bust me chan i cal de sign to with stand a large num ber of os cil la tion cy cles per day.The mov ing parts lead to main tenance and op er at ing life prob lems and more cost.If a fixed guide vane were pro vided instead, it was felt that these prob lems would be mit i gated even though the per for mance may be poorer.With this in view, mode test were con ducted to de ter mine the char ac ter istics of fixed guide vane im pulse tur bine.The re sults were en cour ag ing and more test were con ducted to op ti mise var i ous pa ram e ters of the tur bine.There are few re ports pre sented on the nu mer i cal anal y sis on im pulse tur bine and Wells tur bine for wave en ergy con version ap pli ca tion.Kim et al. [13] have in ves ti gated an op ti mal in stal la tion an gle of the impulse tur bine by nu mer i cal anal y sis.In or der to achieve im prove ment in the per for mance of the im pulse tur bine, the ef fect of 3-D guide vanes has been in ves ti gated ex per i mentally by test ing a model un der un steady bidirectional flow con di tions [14] and found that the per for mance of the tur bine with 3-D guide vanes are su pe rior to those with 2-D guide vanes.The ef fect of tip clear ance on the per for mance of Wells tur bine has been in ves tigated ex per i men tally by few au thors [15][16][17] and found that the tur bine is very sen si tive to tip clear ance when com pared to a con ven tional tur bine.On the other hand the ef fect of tip clear ance on per for mance of im pulse tur bine with fixed guide vanes have been in vesti gated by Thakker et al. [18].
Based on the re-re view of the state-of-the-art of the wave en ergy tech nol ogy, it was found that there is a scope for en hanc ing the per for mance of im pulse tur bine with fixed guide vanes by con duct ing fur ther de sign anal y sis and de tailed flow in ves ti ga tion.The ob jec tive of this pa per is to pres ent the com puted ef fect of hub-to-tip ra tio (H/T) on per for mance of 0.6 m di am e ter im pulse tur bine with fixed guide vanes for wave en ergy con ver sion us ing 3-D com pu ta tional fluid dy nam ics (CFD) anal y sis as a tool un der steady flow con di tion.Aero dy namic stud ies have been made ex per i men tally and computationally to un der stand the pres sure losses in the ro tor and guide vanes.

Experimental analysis
A sche matic lay out of the ex per i men tal set-up of Wave En ergy Re search Team at Uni ver sity of Lim er ick is shown in fig. 1.It con sists of a bell-mouth en try, test sec tion, drive and trans mis sion sec tion, a ple num cham ber with hon ey comb sec tion, a cal i brated noz zle, and a cen trif u gal fan.Air is drawn into the bell-mouth shaped open end; it passes through the tur bine and then en ters the ple num chamber.In the cham ber, the flow is con di tioned and all swirls/vorti ces are re moved prior to pass ing through a cal i brated noz zle and fi nally ex haust ing at the fan out let.A valve at fan exit con trols the flow rate.Details of the test rig cal i bra tion can be found in [19].The turbine test sec tion had an in ter - nal di am e ter of 600 mm and fab ri cated ro tor had a di am e ter of 598 mm, leav ing tip clearance of 1 mm.The hub di am e ter se lected as 358.8 mm, pro vid ing H/T of 0.6.The spec i fi ca tion of the tur bine is listed in tab. 1.The ge om e try has been ar rived based on the in ves ti ga tions by Setoguchi et al. [20], who con ducted large num ber of ex per i ments on im pulse tur bine with dif fer ent pitch chord ra tio, blade pro file and H/T of 0.7, 0.8, and 0.85.They also con cluded that the most fa vour able pitch chord ra tio is 0.5.The tur bine was mounted on a shaft in a cy lin dri cal an nu lar duct, with a blade tip clear ance of 1 mm.The shaft is cou pled to mo tor/gen er a tor via a torque me ter.The two rows of guide vanes (3-D) were mounted on the up stream and down stream hubs of the rig.The tur bine was tested by keep ing a con stant ax ial air ve loc ity of 8.49 m/s.Data was col lected by vary ing the ro ta tional speed of the tur bine from 1250 rpm to 125 rpm by load ing the gen er a tor, thus giv ing a flow co ef fi cient in the range of 0.27 to 2.7.The ap pa ra tus is fully equipped with in stru men ta tion for mea sur ing the es sen tial pa ram e ters like torque, speed, and pressure.A vibrometer torque trans ducer (Model TM 204-208) mea sures the torque and speed.The me chan i cal losses due to bear ing fric tion and wind age losses were tested before com mis sion ing the rig and a mean torque curve was de duced to cor rect the mea sured torque read ing.Mea sure ment of pres sure was made by means of pneu matic pres sure probes.A min ia tur ized five-hole probe was used for aero dy namic mea sure ments at 40 mm ahead of in let guide vane (IGV) in let, 10 mm be hind IGV, 10 mm be hind the tur bine, and 80 mm be hind down stream guide vane (DGV).The probe was mounted on tra verse mech a nism fixed to the tur bine outer cas ing of the test rig.Furness Con trol micro-manom e ter (Model FC012, Furness Con trols Ltd, UK) through a 60 chan nel scan ning box (Model FCS421, Furness Con trols Ltd, UK) with a least count of 0.01 mm of wa ter column were used to read the pres sure data.Pres sure mea sure ments were car ried out at 11 equi-spaced ra dial lo ca tions.The probe data ob tained was re duced us ing the cal i bra tion 160 charts to eval u ate all nec es sary pa ram e ters, in clud ing the flow rates.The Reynolds number based on the blade chord length was 0.74•10 5 at peak ef fi ciency.The over all per for mance of the tur bine was eval u ated by the tur bine an gu lar veloc ity w, torque gen er ated T, flow rate Q, and to tal pres sure drop dp across the ro tor.The re sults are ex pressed in the form of torque co ef fi cient C T , in put power co ef fi cient C A , and ef fi ciency h in terms of flow co ef fi cient f.The def i ni tions are: (1) (2)

Design of 0.6 m impulse turbine
Cal cu la tions were made to de fine the en tire blade and guide vane ge om e try param e ters.A worksheet was cre ated in Microsoft Ex cel to de fine the com plete blade and guide vane ge om e try pro file data for 0.6 m im pulse tur bine by giv ing, the re quired ini tial de sign con strains, such as ro tor di am e ter, H/T, guide vane in let and out let an gles, num ber of blades and guide vanes, all the other pa ram e ters are cal cu lated au to mat i cally.2-D draw ing of tur bine blade and guide vanes were pro duced us ing AutoCAD to val i date this de sign data.Fol low ing this val i da tion, a 3-D solid model was gen er ated us ing CAD pack age Pro-En gi neer v2.0.

Numerical method and calculation
GAMBIT 2.0 and FLUENT V6 were used for mesh ing and an a lyzing the prob lem, re spec tively.The com pu ta tional grid is vi su al ized in fig.2, where only the grid lines attached to the sur faces are shown.Here, the res o lu tion of all the bound -Figure 2. Computational grid ary lay ers is vis i ble.The grids are clus tered near the hub, cas ing, and tip to give ap pro priate y + val ues.Also the mat ter of grid in de pend ence has been taken a se ri ous con sid er ation in the pres ents CFD anal y sis.By em ploy ing fi nite num ber of grid points dis trib uted over the flow filed the nu mer i cal re sults will be ef fected by the grid pa ram e ters, grid struc ture, grid dis tri bu tion, and num ber of grid.In or der to ex am ine the grid de pend ency on nu meri cal ac cu racy a grid in de pend ence test has been car ried out on the com pu ta tional do main.The per for mance tests of the tur bine for var i ous cases are shown in fig.3a-c.A to tal number of 400,000, 500,000, and 600,000 grid cells are used for 0.5, 0.55, and 0.6 H/T, respec tively.It was nec es sary to set up three fluid zones us ing mix ing plane tech nique.Three zones are the up stream guide vane, the ro tor and the down stream guide vane.The fluid at ro tor is de fined as a mov ing ref er ence frame with the an gu lar speed equiv a lent to that of the blade.In flow is set as mass flow in let, out flow is set as pres sure out let and pe riodic walls are set as tran si tional to al low cas cade ef fect on blade and guide vane to be sim u lated.The es sen tial idea be hind the mix ing plane con cept is that each fluid zone is solved as a steady-state prob lem.At some pre scribed it er a tion in ter val, the flow data at the mix ing plane in ter face are av er aged in the cir cumfer ential di rec tion on both the stator out let and the ro tor in let bound aries FLUENT man ual [21].The code im ple men ta tion uses area-weighted av er ages.By per form ing cir cumfer ential av er ages at spec i fied ra dial or ax ial sta tions, "pro files" of flow prop er ties can be de fined.These pro files, which will be func tions of ax ial co or di nate, are then used to up date bound ary con di tions along the two zones of the mix ing plane in ter face.The flow is set as fully tur bu lent.

Validation of numerical procedure
In or der to val i date the pres ent nu mer i cal model, the com puted and mea sured val ues of in put co ef fi cient, torque co ef fi cient and ef fi ciency have been com pared at var ious flow co ef fi cients.From the in put co ef fi cient pre dic tion in fig.4a, the com puted value gives higher in put co ef fi cient at high flow co ef fi cient but gen er ally the same shape as the ex per i men tal mea sured val ues.A good agree ment be tween com puted and ex per i men tal mea sured torque co ef fi cient val ues are shown in fig.4b, these in di cate the 3-D flow and torque de liv ered by the tur bine is cor rectly pre dicted by the CFD.From fig. 4c, the ef ficiency pre dicted by CFD is in ex cel lent agree ment with the ex per i men tal mea sured results, for the en tire flow co ef fi cient ex cept at very low co ef fi cients.

Measured guide vane losses on performance of 0.6 m impulse turbine
Ex per i ments have been con ducted to in ves ti gate ro tor and guide vanes losses on per for mance of the im pulse tur bine [14].Also, aero dy namic mea sure ments have been  made at var i ous ra dius ra tios, R (R = r/r t ), where r is the ra dius where mea sure ment has been made and r t is the tip ra dius) to an a lyze the flow and to mea sure the losses at var i ous sta tions like out let of in let guide vane, be hind ro tor, and be hind down stream guide vane.Fig ures 5a-e, show the vari a tion of pres sure loss co ef fi cient at var i ous sta tions from hub--to-tip re gion for the flow co ef fi cients f = 0.45, 0.67, 1.00, 1.35, and 1.68, re spec tively.The to tal pres sure loss co ef fi cient has been de fined as: where P is the pressure and the subscripts i, o, and s denotes inlet conditions, total conditions, and static conditions, respectively.The pressure drop due to inlet guide vanes is almost negligible and uniform from hub-to-tip in all the flow coefficients, as the flow is steady and two-dimensional.From the figs.5a-c, it can be seen that the pressure drop across the turbine is nearly uniform from hub-to-tip and its mean value seems very high at f = 0. From the above discussion, it is clear that the DGV plays important role for considerable reduction in efficiency of the turbine and hence the guide vanes have been designed according to free vortex theory.Computational analysis has been made to calculate the advantage of using twisted guide vanes on performance of the turbine and also to understand the change in flow behaviour due to effect of twisted guide vanes, and the results are presented in the next section.The values of C Pt at various stations are averaged circumferentially from hub-to-tip for various flow coefficients and plotted in fig.6.The figure shows that the total pressure drops about 40% in the DGV at lower flow coefficients and about 10% at higher flow coefficients.It can also be observed that there is a straight correlation between pressure loss coefficients in the rotor and the DGV rather than IGV.It expounds the need of improvement in aerodynamic design of DGV to enhance the performance of turbine for wide range of flow coefficient.7a, shows the im prove ment in torque de vel oped by the tur bine with 0.5 H/T for the full range of flow co ef fi cient as com pared to 0.55 and 0.6 H/T tur bine.In par tic u lar the improve ment is well no ticed above the flow co ef fi cient of 1.0.At the same time, while consid er ing the pres sure drop across the tur bine, the drop in pres sure due to 0.5 H/T tur bine is slightly higher when com pared to 0.55 and 0.6 H/T tur bine.Also for 0.5 H/T tur bine, higher torque gen er ated, thus re sult ing into higher ef fi ciency for full rang of flow co ef ficient.The ef fi ciency of the tur bine with 0.5, 0.55, and 0.6 H/T is shown in fig.7c.The fig ure shows the tur bine ef fi ciency has im proved con sid er ably due to 0.5 H/T through out the range of flow co ef fi cients.The max i mum im prove ment in ef fi ciency about 7.1% is ob served at the de signed con di tion of flow co ef fi cient 1.0.Fur ther more, in the off-de sign con di tions, the tur bine ef fi ciency of 0.5 H/T is greater than that of 0.55 and 0.6 H/T.

Computed flow behaviour due to effect of guide vane shape
In or der to in ves ti gate the ef fect of H/T in the flow field, ve loc ity con tours have been plot ted at var i ous blade heights hub-mid-span-tip for the cases of 0.5 and 0.55 H/T tur bine at the de signed con di tion of flow co ef fi cients of 1.0 and ro ta tional speed of 350 rpm is shown in fig.8a-f, re spec tively.The flow co ef fi cients have been cho sen to in ves ti gate the flow in de sign (f = 1.0) con di tion.From the fig.8d-f, it is ob served that the flow en ter ing in to the down stream guide vane is be ing sep a rated by lead ing edge of down stream guide vanes, caus ing large recirculation zone for the case of 0.55 H/T tur bine.But, by us ing the 0.5 H/T tur bine, fig.8a-c, the recirculation has re duced slightly from hub to med re gion,

Conclusions
The pres ent com pu ta tional model has been val i dated with ex per i men tal re sults with rea son able ac cu racy and found well suit able for fur ther de sign anal y sis.It is found that k-e tur bu lence model can pre dict the per for mance of tur bine well in the low ro ta tional 167  speed of tur bine.The per for mance curves of the im pulse tur bine with var i ous H/T have been ar rived nu mer i cally.It is ev i dent that the down stream guide vanes are caus ing the flow sep ara tion; hence, the shape of the up stream and down stream should be in ves ti gated.The CFD anal y sis shows that the tur bine with 0.5 H/T has better per for mance com pared to 0.55 and 0.6 H/T tur bine.

Figure 1 .
Figure 1.Schematic diagram of the test rig at University of Limerick

) 164 THERMALFigure 5 .
Figure 5. Variations of total pressure loss coefficient at various stations for various flow coefficients 45 and reducing drastically up to f = 1.0.Beyond the value of f = 1.0, fig.5d-e, rotor pressure losses are more in the tip region from R = 0.8 to 1.0 due to wake effects and tip clearance leakage vortex.It is very clearly seen from the figure that the pressure drop due to downstream guide vanes is very high with reference to the pressure drop curve of rotor, especially at the flow coefficients f = 0.45, 0.67, and 1.0, figs.5a-c.It can also be noted that the pressure drop at DGV follows the same trend of rotor-loss-curve above f = 1.0.

Fig
Fig ures 7a-c shows the vari a tions of C T , C A , and ef fi ciency of 0.6 m im pulse turbine with 0.5, 0.55, and 0.6 H/T, re spec tively, with re spect to flow co ef fi cients.Fig ure

Figure 6 .
Figure 6.Variation of percentage of total pressure loss coefficient with flow coefficient