Narendra Thakur,Agnimitra Biswas*,Yogesh Kumar,Mithinga Basumatary

Mechanical Engg.Deptt.,NITSilchar,Silchar 788010,India

Keywords:Savonius w ater turbine CFD Impinging jet duct design Pow er coef fi cient Water power Flow physics

ABSTRACT The majority of research on water turbines focuses on design improvement of large-scale hydrokinetic turbines for power generation,which may have delayed the utilization of kinetic energy contained in riversand canals.The aim of this paper is to improve the ef fi ciency of a two bladed Savonius type cross-fl ow hydrokinetic turbine,which can be used as an energy converter to harness free-stream kinetic energy of w ater.An impinging jet duct design is presented for improving performance of the Savonius turbine in wind application as seen from literature.The performance of the modi fi ed turbine is evaluated using CFD software Fluent,and is compared with that of a simple two bladed Savonius water turbine and some of the prominent literature designs of the Savonius turbine.It is shown that the present design exhibits improved performance compared to the selected designs of the Savonius turbine.Further an insight of the improved performance of the modi fi ed turbine is also obtained from fl ow physics study.

1.Introduction

In thewakeof theresurgenceof research interest in renew ableenergy systems,harnessing w ater pow er from river stream current has gained considerable momentum.Cross-fl ow w ater turbines have some key advantagesover conventional w ith-head w ater turbines,likesimpli fi ed construction,omni-directionality,greater weight density of water,scope for installation in zero-head locations,low generator coupling costs,and less noisy due to reduced tip losses.Since no head w orks are required,such turbines can harness the abundant energy in free-fl ow ing w ater stream and convert into useful pow er.In the available literature,there are various cross-fl ow types of turbines using free-fl ow ing water stream to generate power[1],for e.g.Savonius turbine,helical Savonius turbine,H-Darrieus turbine,egg-beater Darrieus turbine,Gorlov helicoidal turbine,and Evapod turbine.Out of these turbines,Darrieus designs utilize lift force by using airfoil blades.In this w ork,the Savonius turbine is selected,for its simple blade constructions having semi-circular blades connected to a central shaft,omni-directional feature,self-starting,and self-regulating design compared to the other designs.

The Savonius turbine w as initially introduced as a vertical axis w ind turbine,but in the last decade,it has also been used as a vertical axis water turbine,w hich w orks on the same principle of its w ind counterpart.For better understanding of the performance of the Savonius water turbine,it is important to perform a literature survey of some of the important research w orks carried out so far.The performance is measured in terms of pow er coef fi cient(Cp),w hich is de fi ned as the ratio of turbine mechanical power to water power.This coef fi cient is directly in fl uenced by tip speed ratio(TSR)of the turbine,w hich is the ratio of blade tip speed to the w ater speed.Sarma et al.[1]carried out an experimental and computational investigation of a tw o-bladed Savonius w ater turbine w ith different w ater speeds ranging from 0.3 to 0.9 m·s-1in an open water channel.It wasreported that the hydrodynamic torque and the pow er increased w ith increase in free stream w ater speed,became maximum at w ater speed 0.9 m·s-1for an optimum TSR 0.77 and produced a maximum Cpof 0.39.Mabrouki et al.[2]experimentally evaluated the height effect on the performance of a Savonius turbine and reported a maximum Cpof 0.19 at a TSRof 3.02.

Some recent w orks have been reported on the performance improvement of the Savonius water turbine by various design modi fi cations.Khan et al.[3]experimentally studied the performance of three different types of Savoniusturbines in a wave tank.Single stage,double stage w ith 90°phase difference,and three stages w ith 60°phase difference Savonius turbines w ere designed and their performances w ere analyzed.It wasreported that the double stage rotor had the maximum Cphaving a peak value of 5%and remaining tw o had a peak value of 4%.Rosmin et al.[4]evaluated the ef fi ciency of a single-stage and a doublestage tw o bladed micro-sized Savonius turbine having aspect ratio 1.8 in a rain w ater harvesting system.The electrical pow er generated by the single stage and double stage turbines were compared.The single stage Savoniusturbine performed better than the double-stage Savonius turbine,generating almost double the pow er as that of the latter.Patel et al.[5]investigated the effect of overlap on the performance augmentation of a Savonius turbine and obtained highest hydrodynamic torque at overlap ratio 0.2.Damak et al.[6]improved the performance of a Savonius turbine with the help of overlap at the axis of the turbine for different fl ow conditions.Elbatran et al.[7]improved the performance using a duct design around the Savonius turbine,w hich reported a maximum Cpof 0.25 obtained at a TSR 0.73.

De fl ector plates have also aided the performance of the Savonius turbine.Golecha et al.[8]carried out an experimental investigation to study the in fl uence of eight different positions of a de fl ector plate on the performance of a single and multistage Savonius w ater turbine at Reynolds number 1.32×105and reported a maximum Cpof 0.21 for the single stage turbine at a TSRof 0.82.The optimal de fl ector position increased the pow er coef fi cient by 50%compared to w ithout de fl ector single stage Savonius turbine.As the number of stages increased,the percentage increase of Cpdecreased,producing 42%,31%and 17%for the tw o stage Savonius turbine w ith 0°phase shift,90°phase shift and the three stage Savonius turbine respectively.Thus single stage Savonius turbine w ith de fl ector plate performed better than the two stage and the three stage turbines w ith de fl ector.Basumatary and Biswas[9]also optimized the de fl ector position using CFDfor yielding maximum performance of the Savonius w ater turbine.

Different blade pro fi le modi fi cations such as blade tw ist,blade curvature and overall blade shape have also changed the performance of the Savonius turbine for the better.Hassan et al.[10]obtained a maximum pow er ef fi ciency of 12%for a 180°blade tw ist Savonius turbine w ithout overlap at a TSR of 0.8 and w ater speed of 1 m·s-1.Hassanzadeh et al.[11]compared the performance of a helical bladed Savonius turbine w ith a conventional Savonius turbine using CFD and reported improved performance of the former.Kumar and Saini[12]investigated the effect of twisted bladeson the performance of a modi fi ed Savonius turbine and reported an optimal tw ist angle of 12.5°for maximum performanceof theturbine.Again Kumar and Saini[13]improved theperformanceof a Savoniusturbineby modifying the blade curvature and the shape,w hich show ed even better performance than the earlier.

In this paper an attempt has been made to increase the ef fi ciency of the Savonius w ater turbine w ith an impinging jet duct design.The present work has been aimed to utilize the same duct design for a two bladed Savoniusw ater turbine and evaluateitsperformance at different w ater speeds ranging from 0.3 m·s-1to 0.9 m·s-1using Fluent CFD softw are,and also to compare w ith other designs of the Savonius w ater turbine.Moreover,performance insight of this duct design of the Savonius turbine is also obtained from fl ow physics of the turbine.The remaining sections have been organized in the follow ing manner—Section 2 discusses about the model geometry of the design and the computational modeling thereof,Section 3 describes the data reduction procedure,Section 4 elaborates the results w ith discussion,and fi nally conclusions are drawn in Section 5.

2.Selection of Model Geometry and Computational Modeling

Fig.1(a)show s the impinging jet duct design of the tw o bladed Savonius w ater turbine.The orientation of the turbine shaft is vertical.This design w as suggested by El-Askary et al.[14]in w ind application.Flow impingement on Savonius turbine blades to improve the turbine's performance w as tried before by El-Askary et al.[14]in w ind application.The returning blade of the conventional Savonius turbine has a lower thrust compared to the advancing blade because upstream fl ow impinges on to its convex face.Hence to enhance torque of the turbine,El-Askary et al.had attempted to increase thrust on the concave face of the returning blade by accelerating the fl ow on to it w ith the help of the impinging jet duct design.In this w ork,this concept has been applied in w ater application.Since the performance of the duct design w as benchmarked by El-Askary et al.,in this w ork the effect of a higher w eight density fl uid i.e.water on the turbine's performance has been studied using the same design features.Further,the contributions of pressure drag and shear drag on hydrodynamic torque production have also been ascertained.Hence in this study no attempt is made to investigate the effect of further design modi fi cation of nozzle or any part of the duct design and it is explored to investigate the effect of this duct design involving a higher w eight density fl uid,i.e.w ater,on the Savonius turbine performance for different water fl ow speeds.In addition performance insights of this improved design have also been derived for w ater application using CFD.

Fig.1.Savonius water turbine with radius R and impinging jet duct design[14].

There are two plates of the duct that lead w ater to strike the blades of the Savonius turbine.The inlet w ith the w idth of 5.7R collects w ater to strike the concave face of the advancing blade,and the right plate is used to avoid the w ater strike on the convex side of returning blade and direct it to strike the concave side of the returning blade in the form of an impinging jet.Thus,this structure shall increase the net positive torque of the rotor as the w ater strikes against the concave face of both the blades.The nozzle shape at the end of the curved duct plate accelerates the fl ow onto the concave side of the returning blade.The plate curvature has been properly maintained such that there is no separation from the inner w alls.The duct plates are fi xed and are not attached w ith the turbine blades,hence the tw o bladed Savonius w ater turbine is the only revolving part of this w hole design The Savonius w ater turbine consists of tw o semi-circular cylinder shaped blades with height 0.17 m,chord length 0.14 m and thickness 0.0015 m.The diameter of the central shaft is 0.014 m,and the overall diameter(D)of the turbine is 0.27 m.With regard to the overall radius(R)of the turbine,the various dimensionsof the duct design are show n in Fig.1.The thickness of the duct plates is 0.003 m.

In thecomputational modeling,arectangular computational domain has been created such that the upstream domain from the turbine axis is at 5D and the dow nstream domain is at 8D.The top and bottom domains are 5D each from the axis of the turbine.This enlarge computational domain has been created to minimize the w all boundary and the blockage effect that would otherwise affect the performance of the turbine and also to minimize the effect of uncertainties in the boundary conditions.Tw o-dimensional CFD simulations are conducted,for it is assumed that this turbine w ill be mounted in uniform stream having no gradient due to the presence of free surface or fl oor of the river,so that the results w ill not be changed by three-dimensionality effect.Moreover,the reason for tw o-dimensional computational modeling is because of the same blade pro fi le of the Savonius turbine along the depth direction.Similar modeling strategy w as also adopted by the researchers in[1,8,9,14,18].Then this domain is segmented into two sub-domains:exterior static zone(Fig.2a)and interior rotating zone(Fig.2b).The exterior cell zone is kept stationary w hereas the interior cell zone isallowed to rotate with respect to the turbineat a given rotational speed.The interior as w ell as exterior fl uid zones are discretized using triangular meshing.In the exterior region,course meshing is done and dense meshing is done in the interior region to capture blade-fl uid interactions in details.Further,a gradual transition of cell size across the boundary between the two regions is also ensured,as can be seen from Fig.2(a)and(b).For the inner circular cell zone,the cell size isΔi=0.8 mm,and for the outer static zone,the cell size is Δo=1.6 mm.The circular domain around the Savonius turbine is created to ensure local grid re fi nement near the turbine blades.Edge sizing is used to re fi ne mesh at the desired locations.The fi rst layer of grid points is carefully taken in the near w all mesh zone to keep y+value w ithin acceptable limit(maximum below 2).Overall face meshing is done in both the exterior and interior regions.ANSYSdesign modeler is used as the gridding softw are to generate the entire mesh.

The left boundary of the computational domain is assigned the velocity inlet condition,right boundary is assigned the pressure outlet condition,and symmetry condition is given to the upper and bottom boundaries.No slip condition is assigned on duct w alls as w ell as the turbine blades.Tw o computational domains,one for the simple Savoniusturbine and the other for the Savonius turbine with impinging jet duct design,have been formed follow ing the above procedure.

Fig.2(c)showstheresult of grid independencestudy wherein thevariation of drag coef fi cient(Cd)is plotted against the re fi nement level for the simple Savoniusturbine.The considered re fi nement levelsand corresponding drag coef fi cient values are shown in Table 1.The expression of Cdisgiven in Eq.(1),w here Fdisthe drag force,Atisthe turbine projected area to the fl ow,w hich is tw ice its radius,and U is the incoming w ater speed.Here Cdis taken to grid independent level since the Savonius turbine's performance is largely affected by the drag force.The hydrodynamic torque of the Savonius w ater turbine is generated by the pressure and viscous drag force difference across the inner and outer blade surfaces.Thus,calculation of Cdneedsto be unaffected by thegrid resolution;hence with respect to Cd,grid independence study is considered.As the re fi nement levelincreases,Cdincreasesto match with theforcedifferenceacross the blades corresponding to the spatial resolution.A common sense in numerical simulation is that when increasing grid resolution,the numerical results will tend tow ards identical and become a constant.For achieving this,iterations are continued till all scaled residuals drop below 1×10-5.Fig.2(c)shows that after the sixth re fi nement level,Cdvaluesalmost reach to aconstant level thereby reaching thegrid independence limit.This re fi nement level corresponds to 127312 numbers of nodes and 243578 numbers of triangular cells or elements.This mesh con fi guration is fi nally considered in the CFD simulation of the turbine performance.In addition,Fig.2(d)show s the result of the grid independence study involving the variation of moment coef fi cient(Cm)with different re fi nement levels.The expression for Cmis shown in Eq.(2).Cmis de fi ned as the ratio of aerodynamic torque produced by the turbine to the angular momentum of the incoming fl ow.It also shows that at the sixth re fi nement level,the value of Cmhas almost become grid independent.

Table 1 Details of mesh re fi nement levels

Fig.2.(a)Computational mesh of outer static fl uid zone,(b)computational mesh of inner rotating fl uid zone,(c)variation of drag coef fi cient with re fi nement level,(d)variation of moment coef fi cient w ith re fi nement level.

where Atis the turbine projected area,which is 5.7Ri.e.0.77.

Different inlet w ater velocities such as 0.3 m·s-1,0.65 m·s-1,and 0.9 m·s-1have been chosen to simulate the performance of both the turbines(i.e.w ith and w ithout impinging jet duct design).The continuity and N-Sequations are integrated over the control volume and then discretized using fi nite volume technique to obtain a set of governing equations.The resulting set of algebraic equationsissolved using Fluent CFDsoftware in an iterative manner after applying the above boundary conditions.Semi-Implicit Pressure Linked Equations(SIMPLE)algorithm is used to couple the pressure and velocity terms of the pressure correction equations.The spatial discretization is enforced using a least squares cell based gradient w ith second order discretization for the pressure and momentum.First order upw ind discretization is adopted for turbulent kinetic energy and speci fi c dissipation rate.The convergence criterion is based on the residual value of 1×10-5for the calculated variables,i.e.,mass,velocity components,and k and omega terms.SST k-ωturbulence closure model is considered for the present turbines as this model is the most suitable turbulence model for vertical axis turbines for w ind or w ater application[15,16].The two transport equations for k andωare as shown below

In these equations,ui=(u,v)are velocity components in the directions of xi=(x y z),k represents the turbulence kinetic energy,ω represents speci fi c turbulence dissipation,Гkand Гωare the effective diffusivity for k andω,Gkrepresents the generation of turbulence kinetic energy due to mean velocity gradients,and Gωrepresents the generation ofω.Ykand Yωrepresent the dissipation of k andωdue to turbulence,and Dωis the cross-section diffusion term.The tip speed ratio(TSR)is an operating parameter w hich is the ratio of blade tip speed to the w ater speed and an important input parameter.For any w ater speed,blade speed is varied to obtain different input TSRvalues at w hich performance of the turbines is tested.

3.Data Reduction

The performance of the Savonius water turbine with and without impinging jet duct design is evaluated w ith the help of hydrodynamic torque,pow er and pow er coef fi cient.For deducinghydrodynamic torque,pow er and power coef fi cient,the necessary formulae[17]can be represented as in Eqs.(4)-(7).The hydrodynamic torque is calculated by measuring the pressure and shear force signature on both concave and convex faces of the advancing and returning blades.The required distributions of pressure and shear force are obtained from the postprocessing results of Fluent CFD simulation.The hydrodynamic torque(T)is calculated using Eq.(4)as given in[17]for the Savonius turbines:

w here Ffpressureand Ffshearare the pressure and shear force acting on the face area Afand l is a local torque arm vector from the rotation axis about which the moment is taken.Thus,pow er extracted by the turbine can be represented as

w hereωis circular frequency of the turbine.

The maximum pow er available in the free-fl ow ing stream of w ater can be represented as

In thisexpression of maximum power,turbine projected area(At)is 5.7R.Thew ater iscollected through the collection areacorresponding to 5.7R to strike the turbine blades.

Thus,the pow er coef fi cient(Cp)can be expressed as

4.Results and Discussions

Firstly,the computational model of the simple Savonius turbine has been validated with the available literature result[9].Fig.3 shows the comparison of the variation of Cpw ith respect to TSRbetw een the experimental and computational results.Both the trends match qualitatively w ith the maximum error between the two inside±6%,thereby validating the computational model.

Fig.3.Validation of computational C p with respect to experimental C p for simple Savonius turbine.

Fig.4.(a)Torque vs.velocity,(b)power vs.velocity,and(c)C p vs.TSR.

Fig.4 show s the comparison graph betw een the simple Savonius water turbine and Savoniuswater turbine with impinging jet duct design.Fig.4(a),(b),and(c)respectively shows the variation of torque w ith respect to free stream velocity,turbine pow er with respect to free stream velocity,and pow er coef fi cient(Cp)with respect to tip speed ratio(TSR).In the simulation process,TSRisconsidered as an input parameter,which isto becontrolled by amechanical brakew hen in operation so that Cpcan be varied over the selected TSR.By observing the graphs it can be noted that w ith the increase of free stream w ater speed from 0.3 m·s-1to 1.5 m·s-1,the torque generated and the power extracted by the turbines monotonically increase.As w ater speed increases,w ater power also increases;hence the turbines have the opportunity of extracting more torque and pow er from the water stream.The torque or power extracted by the Savonius w ater turbine w ith impinging jet duct design is higher than the simple Savonius w ater turbine at any w ater speed(Fig.4a and b),w hich is due to increased local speed at the exit of the lower duct plate nozzle and then onto the concave face of the returning blade of the former turbine.Further,guided fl ow onto the concave face of the advancing blade by the left plate also aids in the improved performance of the former turbine(Fig.1).The maximum power generated by the Savonius w ater turbine w ith impinging jet duct design is 31.02 W at free stream water speed 1.5 m·s-1w hereasthe maximum power generated by the simple Savonius w ater turbine is 17.5 W at the same water speed.Due to higher mechanical pow er of the former turbine,Cpof the same is higher at any TSRcompared w ith the latter turbine(Fig.4c).Fig.4(c)shows that Cpincreases w ith TSRup to a certain limit,and then decreases w ith further increase of TSR.This is because every turbomachinery has its rated performance corresponding to a certain operating TSRcondition,which also dependson thecross-sectional areaand solidity of the machine.If TSRis increased beyond its optimum limit,the turbine w ill not be able to hold on to its rated performance as that w ill be restricted by the size of it.The maximum Cpof the simple Savonius water turbine is 0.35 at a TSRof 0.64 w hereas the maximum Cpof the modi fi ed design is 0.50 at a TSRof 0.61.The present design uses more w ater(5.7R/2Ri.e.almost 3-fold).Therefore,although output Cpincreases by 43%,w ater energy utilization ef fi ciency is decreased since the modi fi ed design uses more w ater to increase Cpby that percentage amount compared with the simple Savonius w ater turbine.In the calculation of maximum Cpof both the designs,the turbineprojected areaisthesame i.e.2R.Although the modi fi ed design occupies a larger w ater collection area(5.7R),more w ater strikes the same projected area of the turbine in both the designs.Fig.4(c)also includes performance comparison of the present design w ith tw o literature results.And the higher performance of this design can clearly be seen in the fi gure.

Fig.5 show s the variation of starting hydrodynamic torque of the Savonius turbine w ith impinging jet duct design w ith respect to azimuthal angle for different water speeds in the range 0.3-1.5 m·s-1.There are tw o peaks,one each for the advancing and returning blades during one complete turbine rotation.As w ater speed increases,the starting torque also increases.The maximum starting torque obtained for w ater speeds 0.3 to 1.5 m·s-1lies betw een 0.21 N·m-1and 4.6 N·m-1.The turbine at 135°and 330°azimuthal positions show maximum starting torque because of maximum exposed area of both concave sides of the advancing and returning blades of the turbine.At 0°,180°and 360°azimuthal positions,the starting torque obtained is less because of less blade exposed area to the w ater jet.

To obtain performanceinsight of the modi fi ed Savoniuswater turbine w ith impinging jet duct design,static pressure and velocity magnitude contour plots are analyzed from the fl ow physics aspect.The static pressure contour incorporates the effect of both the pressure drag and shear force drag on hydrodynamic performance of the turbine.These two contributing forcesare not analyzed separately in thiswork.Here,the objective is to see how the static pressure and velocity distributions across the blades contribute to hydrodynamic torque generation.Fig.6(a)and(b)showsthestatic pressureplotsat 45°and 135°turbineazimuthal position for water speed 0.9 m·s-1.Fig.7(a)and(b)show sthevelocity magnitude plots at 45°and 135°turbine azimuthal positions for the same w ater speed condition.The static pressure contour show s a decrease in static pressure from the upstream to the dow nstream side of the tw o bladed Savonius turbine,w hich results in useful hydrodynamic torque and hence pow er extraction by the turbine.This difference of static pressure across the turbine is more at 135°position.Because of the increase of thewater volumein theupstream narrow region of theturbine(bounded by the upper duct plate),the region showsmore uniform pressure increment.Further,the static pressure distribution at 135°azimuthal angle generates maximum torque due to maximum exposed frontal area of both the concave sides of the advancing and returning blades,w hich w ill belessat 0°,180°or 360°azimuthal position becauseof minimum exposed area of the turbine blades.Fig.6(b)shows that the returning blade exposed area to the impinging jet at 135°is more than at 45°angle.Similarly advancing blade exposed area bounded by the upper duct plate isalso more.At 45°angle,a stagnation vortex is created on the top face of the left plate and at 135°angle;another stagnation vortex is created on the bottom face of the right plate,which do not interfere with the fl ow in the turbine interior.These stagnation points are created as the upper and bottom plates are stationary.

Fig.5.Variation of starting hydrodynamic torque with turbine azimuthal angle for different water speeds.

Velocity contour plot corroboratesthe fi nding of the pressure contour plots.The fl ow is accelerated below the left plate towards the concave face of the advancing blade,which results in higher fl ow static pressureand shear forceon theadvancingblade.Dueto thiseffect,thehydrodynamic torque is augmented as also reported previously.This effect is more in case of 135°azimuthal position due to more exposed area of the upstream blade facing the fl ow(Fig.7a).An acceleration of fl ow through the nozzle of the lower duct plate can also be seen from the velocity contour,w hich is again more for 135°azimuthal position(Fig.7b).Thus,the role of the right plate is to create an accelerating jet to impinge on the concave face of the returning blade,which will augment performance of the returning blade.Rotating vortices are also generated in the vicinity of the concave side of the returning blade(both Fig.7a and b)due to the jet strike and the water de fl ection from the back of the advancing blade.Sharp separating stream lines can be seen at the edges of the plates as the plates are stationary,w hich do not affect the interior fl uid zone.Thus accelerated fl ow through the nozzle of the low er duct plate onto the returning blade and the guided fl ow below the top duct plate onto the advancing blade,contribute towards performance augmentation of thepresent design,which ismore effective at 135°azimuthal position.The fl ow region wider than 5.7R is affected by thetwo platesascan beseen from Fig.6.For theleft plate,fl ow exterior to it fi ndsadivergingpassagefor w hich aseparation zoneiscreated tow ards the end of the plate.Another stagnation zone is created below the right plate.Similar phenomenon was also observed by the researchers in[14]for w ind application.Thus the turbine performance is not affected by the outer zone as the turbine'szone of operation isbounded between the plates only.These plates are guiding the fl ow and are not in contact w ith the turbine blades.However,as can be seen from Fig.6(a),from inlet to turbine downstream,the static pressure is much lower in the area beside the turbine fl ow.Thishappensasthe gap between the left plate and tip of the turbine blade increases due to turbine rotation thereby making some amount of w ater bypassthrough thisgap.Thishappensfor azimuthal position from 0°to 90°in the fi rst quarter of therotation.In Fig.7 for velocity magnitude contours,the outer fl ow is affected by the separating streamlines from the extreme edges of the plate,w hich again do not change the performance of the turbine.The separated vortices(blue color)are far dow nstream the turbine blades,thus not affecting the turbine rotation.

Fig.6.Static pressure(in Pa)contour plot at(a)45°azimuthal angle and(b)135°azimuthal angle.

Fig.7.Velocity magnitude(in m·s-1)contour plot at(a)45°azimuthal angle and(b)135°azimuthal angle.

Fig.8(a)showsthe distribution of pressure force on blade 1 and blade 2 w ith respect to blade curve length and Fig.8(b)show s the distribution of shear force on blade 1 and blade 2 w ith respect to blade curve length,which are draw n for w ater speed 0.6 m·s-1.The curve length signi fi es the blade circumference covering its concave and convex sides.Fig.8(a)&(b)shows pressure and shear force differential across the two surfaces adjoining each blade surface.The pressure force distributions on blade 1 and blade 2 are quite comparable to each other.The returning blade producesnear the same amount of positive thrust asthe advancing blade,w hich is attributed by the impinging jet.It can be also seen that thrust is negative over some portions of the curve lengths of the blades.These locations correspond to the convex surfaces of the blades.Furthermore,the negative thrust on blade 2 does no longer exist compared to blade 1.This is caused as the fl ow is directed through the channel device to strike the concave surface of blade 2,for w hich the concentration of fl ow on the convex surface has decreased.From Fig.8(b),it can be seen that shear force differential acrossblade2 ismorethan blade 1,for the effect of impinging jet.However,values of shear force are lower than the pressure force.This is due to the fact that the Savonius turbine utilizes thepressuredifferential acrossitssidesfor thrust generation,w hoseeffect is more than that obtained from shear force differential.

Fig.9(a)and(b)shows the variations of hydrodynamic torque contributed by the pressure and shear forces respectively w ith regard to the curve length for both blade 1(advancing blade)and blade 2(returning blade),which are also drawn for w ater speed 0.6 m·s-1.The variations of torque follow the trends of force variations.Positive torque band by the contribution of shear force of blade 1 is smaller in size compared to blade 2.Further,blade 1 has negative torques on its convex surface,w hereas the negative torque band of blade 2 is almost negligible due to the impinging jet duct design.Similar to previous case,contribution of hydrodynamic torque by share force islessthan the same by pressure force.Thus,it may be con fi rmed that the Savonius w ater turbine is pre-dominantly a pressure drag-driven device.

Fig.10(a)and(b)show sthevelocity vector distributionsinvolvingthe turbine design for w ater speed 0.3 m·s-1and 0.6 m·s-1respectively.In these plots,the turbine azimuthal position is90°,at which the maximum blade area is projected onto the fl ow.Velocity vectors can be seen on the concave and convex faces of the advancing and returning blades.After hitting against the concave face of the advancing blade,these vectors migrate through the gap between the bladesand then arrive on the concave sideof thereturning blade.Thevectorscloseto theconcavesurfacefollow thebladecurvature,which isa shear dominated fl ow[19].Away from the blade surface,the fl ow vectorsare normal to the plane of the blade to signify pressure drag dominated fl ow.The combined shear and pressure drag contributes to the hydrodynamic torque as seen from Fig.9.The concentrations of these vectors and their size increase w ith the increase of w ater speed from 0.3 m·s-1to 0.6 m·s-1.At water speed 0.3 m·s-1,the velocity vectors on the returning blade deviate away from the blade surface and migrate downstream.How ever,at water speed 0.6 m·s-1,not all the vectors migrate,rather some of them strike the concave face of the returning blade.Moreover,concentration of vectors at the nozzle exit also increases w ith increase of w ater speed.Hence due to this phenomenon,thrust on the returning blade(as w ell as on the advancing blade)increases at this higher water speed.This is caused due to increased momentum of the fl ow and the pressure force exerted on the blades.

Fig.9.Contribution of the blades to hydrodynamic torque by virtue of(a)pressure force and(b)shear force at a same w ater speed of 0.6 m·s-1.

Fig.10.(a)Velocity vector plots involving the turbine design for(a)w ater speed 0.3 m·s-1 and(b)for w ater speed 0.6 m·s-1.

5.Conclusions

In this paper the performance of a tw o bladed Savonius w ater turbine w ith impinging jet duct design and de fl ector w as evaluated using Fluent CFD softw are and compared w ith that of a simple tw o bladed Savonius w ater turbine.Moreover an insight of the improved performance of the impinging jet duct design w as also obtained from the fl ow physics study of the turbine.The follow ing conclusions have been drawn from the study:

·With the increase of free stream w ater speed from 0.3 m·s-1to 1.5 m·s-1,the torque generated and the pow er extracted by the turbines monotonically increase.The maximum pow er generated by the simple Savonius w ater turbine is 17 W at free stream velocity 1.5 m·s-1whereas the maximum power extracted by the Savonius water turbine w ith impinging jet duct design is 31.02 W at the same water speed.

·The higher pow er is caused by the fl ow acceleration through the bottom channel of the duct design by virtue of its converging shape.And it is also affected by the fl ow directly converging on the concave face of the advancing blade below the left plate.

·The maximum Cpof a simple Savonius w ater turbine is 0.35 at a tip speed ratio of 0.64,w hereas the maximum Cpof the modi fi ed design is 0.50 at a tip speed ratio of 0.61.The present design has Cphigher than some of the prominent designs of the Savonius w ater turbine.The higher Cpis attributed to the fact that the fl ow width of the modifi ed design(i.e.5.7R)is almost three times the normal fl ow w idth(2R)of the basic design of the Savonius turbine.

·As the water speed increases,the hydrodynamic torque also increases.The maximum hydrodynamic torque obtained for water speeds 0.3 to 1.5 m·s-1lies betw een 0.21 N·m-1and 4.6 N·m-1.The turbine at 135°and 330°azimuthal positions produce maximum hydrodynamic torque.Major contribution behind improved torque is from the pressure drag rather than the shear drag.

·Several velocity vector plots have been used to signify the improved performance of the Savonius turbine by using the impinging jet duct design.

·Thus the present research showsthe importance of impinging jet duct design for improving the performance of the Savonius w ater turbine.How ever if the developed turbine design is to be used in rivers or canals,then the river/channel bed and free water surface might modify the performance of the turbine.This w ill particularly happen if the turbine is mounted in shallow w ater depths or w hen the w ater depth is variable.Thus,future study entails consideration of this aspect on the performance of the present turbine design,w hich is then to be solved using a three-dimensional analysis.