Numerical Analysis of the High Skew Propeller of an Underwater Vehicle Numerical Analysis of the High Skew Propeller of an Underwater Vehicle

Numerical Analysis of the High Skew Propeller of an Underwater Vehicle

  • 期刊名字:船舶与海洋工程学报
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  • 论文作者:Hassan Ghasseni,Parviz Ghadimi
  • 作者单位:Department of Marine Technology
  • 更新时间:2020-12-06
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J. Marine Sci. Appl. (2011) 10: 289-299DOL: 1.007511804-011-1071-4Numerical Analysis of the High Skew Propeller of anUnderwater VehicleHassan Ghasseni' and Parviz GhadimiDepartment of Marine Technology, Amirkabir University of Technology, Tehran 15875-4413. lranAbstract: A numerical analysis based on the boundary element method (BEM) was presented for thehydrodynamic performance of a high skew propeller (HSP) which is employed by an underwater vehicle (UV).Since UVs operate at two different working conditions (surface and submerged conditions), the design of sucha propeller is a cumbersome task. This is primarily due to the fact that the resistance forces as well as the vesselefficiency under these conditions are significantly different. Therefore, some factors are necessary for thedesign of the optimum propeller to utilize the power at the mentioned conditions. The design objectives of theoptimum propeller are to obtain the highest possible thrust, minimum torque, and efficiency. In the currentstudy, a 5-bladed HSP was chosen for running the UV. This propeller operated at the stem of the UV hull wherethe inflow velocity to the propeller was non-uniform. Some parameters of the propeller were predicted basedon the UV geometrical hull and operating conditions. The computed results include the pressure distributionand the hydrodynamic characteristics of the HSP in open water conditions, and comparison of these resultswith those of the experimental data indicates good agreement. The propeiler eficiency for both submerged andsurface conditions was found to be 67% and 64%, respectively, which compared to conventional propellers isasignificantly higher eficiency.Keywords: boundary element method (BEM); hydrodynamic analysis; high skew propeller; surface andsubmerged conditionsArticle ID: 1671-9433(2011)03-0289-111 Introductionhighly imperative. Prediction or calculation of theperformance of the marine propellers which operate in aPropellers operate at the stem of marine vehicles (such as non-uniform flow field is a very important matter forUVs) to generate thrust and drive them in the designedhydrodynamic specialists and designers because theseforward speed. The flow entering the propeller is .calculations and predictions play important roles innon-uniform and unsteady due to the existence ofachieving the favorable design speed of the vessels. Theboundary layer and the interaction of other devices such asmost important criteria for the propeller selection are thethe hull and the hydroplanes. The hydroplanes are installedmaximum required thrust and efficiency, minimum torque,at the hull's sterm and beside the propeller in the form of aand least negative pressure coefficient to avoid or mitigateplus mark (two vertical and two horizontal). The inflowcavitation (Breslin and Andersen, 1994; Carlton, 2006;wake into the propeller is influenced by the bhydroplanes.Burcher and Rydill, 1994).Therefore,the interaction of the propeller and thehydroplane is important and an integral part of the propellerBEM is an appropriate numerical scheme and a powerfuldesign. Here, two significant effects should be noted; onetool for hydrodynamic analysis of the propellers, and manybeing the choice of the propeller's blade number and theresearchers have thus far obtained acceptable results usingother is the sterm wake flow field of the vessel that mostlythis method. Hsin et al. (1991) employed a panel method fordepends on the hull form which mandates every vessel to the analysis of HSP. Kinnas and Hsin (1992) applied BEMadopt its own special wake flow. Another essentialfor the analysis of unsteady flow around the extremeparameter in the design of a UV propeller is the measure ofpropeller geometry. Kim et al. (2009), through the usage ofits capability in preventing or diminishing the cavitation andthe panel method and by refining the geometry of avibration in order to make the UV undetectable. One lastpropeller through modification of the blade sections, alignedparameter to be considered is the fact that the production ofwith surface streamlines and used this model to performthe high skew angle of the propeller is strongly affected bynumerical simulations and open water tests while reportingthe appropriateness of the design of a UV propeller. In viewan increase in propeller efficiency. On the other band,of all the cited key factors, to achieve a better hydrodynamicBenini (2004)中国煤化工tion.of theperformance, the efcient design of the propeller becomescombined mor, for light andmoderately loaYHCNMHGitsrelevanceto;Received date: 201 1-02-09.the design and analysis procedure.*Corresponding author Email: gasemi@aut.ac.ir◎Harbin Engincring University and Springer-Verlag Berlin Heidelberg 2011.29Hassan Ghasseni, et al. Numerical Analysis of the High Skew Propeller ofan Underwater VehicleIn this numerical scheme, in contrast with some other2 Mathematical formulationsmethods (finite difference, finite element, or finite volume),element generation is carried out at the boundary of theConsider the closed region V with boundary S and the unitbody which leads to the reduction of computing time andvector of n normal to S as depicted in Fig.1. Boundary Scosts. Application of this method is not limited to the fieldsof the flow region includes the surface of the body Sp , theof hydrodynamics and fluid mechanics, but it is also utilizedsurface of the wake Sw , and the outer control surface Soin other fields of engineering such as structural mechanics,that surround the surfaces of the body and the trailing vortexdynamics, and vibration. In recent years, this method hasbeen repeatedly used as a computational tool for thesurface.hydrodynamic analysis of the vessels and is quite capable ofperforming flow analysis around any shape of the body asseen in Felice et al. (2009), Andersen and Kappel (2009).BEM is also considered to be an acceptable and appropriate↑tool for the design and analysis of the lifting surfaces suchSwas hydrofoils and propellers. In the analysis of these bodies,wakethe Kutta boundary condition is very important. ThisS。boundary condition indicates that the pressure difference atthe suction and pressure surfaces of the trailing edge shouldbe zero.Fig.1 Demonstration of the Green's theorem on the bodyUsing the Green's theorem, the velocity potential at everypoint can be expressed as an integral equation at all parts ofBased on the assumption that the fluid in region V isthe boundary, and subsequently the potential field isincompressible, inviscid, and irotational, region V isdetermined at each point. Using this method, the surfaces ofsubjected to the inflow uniform velocity V at thehe propeller and the trailing vortex surface (helical for aupstream of the flow. With these assumptions, the flow fieldpropeller) are divided into hyperboloid-shaped elements. Byaround the body is characterized by the total velocityconsidering a dipole and a source at each element andpotential中and perturbation velocity potential φ whichsolving the resulting system of equations, the potential andsatisfies Laplace's equationspressure fields are determined. Furthermore, the thrust andtorque of the propeller are calculated.V2φ=0(1)v2φ=0Procedures and the main tasks involved in this methodIn Eq.(1), the total velocity potential is defined as follows:include the grid generation (element generation), calculationof the influence coefficient of the source and doubletφ=φ+φ(2)singularities at every element along with simultaneous=V,Xsolutions of the equations involving the singularity strength,The boundary value problem (BVP) is constructed bylocal velocities, total pressure, forces, and torques. In thisidentifying three boundary conditions on the boundary S, aspaper, hydrodynamic analysis and design of the propeller fordescribed below, Chang et al. (2007).a UV with a displacerment capacity of 120t is computedusing the boundary element method. Numerical computation1) Tangential conditionincludes the pressure distribution and the propellerThe kinetic boundary condition requires that the total flowhydrodynamic performance. Here, a parametric study wasvelocity perpendicular to the body surface Sg should beperformed to examine the impact of some factors that affectequal to zero.the propeller selection, and based on the achieved results, adφφproper propeller was selected and analyzed. This paper=0≈O=-V,n(3)consists of seven important sections. Following theintroduction in section one, section two describes thewhere n is the unit normal vector, pointing out of thegoveming equations and the boundary condition. Section 3boundary. The inflow velocity to the propeller can bedescribes the numerical implementation. Formulation of theexpressed as follows:propeller and surface mesh generation are explained inV,(X,Y,Z)=Vw(X,Y,Z)+ 0xr(X,Y,Z)(4)section four. Section five discusses the factors involved inwherehe propeller selection and its dimensions. Section sixpresents the hydrodynamic analysis, the implementation ofV中国煤化工the numerical scheme, and the discussion of thewhile Vs andTYHCNMH Gl's velocity andcomputational results. Finally, conclusions are highlightedwake factor, respectively.in section 6..Journal of Marine Science and Application (2011) 10: 289-299292) Conditions on the trailing vortex surfacecovering the blades and the hub is discretized into a finiteNo flow velocity jump occurs on the trailing vortex surfacenumber of elements over which the potential is solved atbut velocity potential jump does occur on this surface and isevery field point. Discretization of Eq.(9) leads to a linearequal to the circulation r around the blade. Mathematicalsystem of algebraic equations for the unknown valuesof中equations of these two conditions (i.e. the flow velocity andas follows:velocity potential) are expressed as follows:(0)onSw =φ°-o°=r(6)2na==兰D,(C)+^ts,(映and(10)(聚)。 =(照阳-(架v°=0(7)兰(兰1(04), 12..where B and F indicate the back and face of the propeller.where Si and Wy1 ,Dj are the dipole and sourcecofficients for element j that acts on the control point of3) Kutta condition at the trailig edge (TE)element i. These cofficients are expressed as inThis condition is one of the most important conditions usedfor the lifting surfaces. The Kutta condition theory indicatesthat the velocity would remain limited along the sharp .0.喝的局它心trailing edge. As another equivalent form, it can beunderstood that the pressures at both back and face sides ofd1the blade, are identical. This Kutta condition of equalWy=Iswan,(R-)ds;(11)pressure is used for determining the unknowns Oφ of thedipole strength for a trailing vortex surface. It is defined asQP=0 at TE8)(5。LasUsing Green's theorem, the perturbation velocity potential atFor obtaining the above coefficients which are actually theeach point of the field can be expressed as an integralevaluation of the integrals, a combination of Morino'sequation corresponding to the distribution of the source andformulae (1974) and a special Gauss Quadrature scheme,dipole. Therefore, for a field pointp in region V, we have(Ghassemi and Kohansal, 2009), has been used. By(Kinnas and Hsin, 1992):calculation of these coefficients and development of thesystem of equations, the value of φ is obtained. This2np(p)= Is (q)=an R(p.q)system of equations can be expressed in matrix form ass。od,isls,o0(q);alds(9)Dφ=S+WOφ(12)ISg amg R(P,9)Ong R(p,q)where D the matrix of the dipole coefficients on the bodywhere R(p,q) is the distance between the singular pointsurface,S the matrix of the source coefficients on thep(x,y,z) and the point q(u,v, w). The itrinsic coordinatebody surface, W the matrix of the dipole coefficients(u,v,wW) is defined for the q where the integral isinfluence on the trailing vortex surface, and中,0中arecalculated. The right hand of the Eq.(9) has three terms. Theunknown perturbation potentials and unknown potentialfirst two terms are the dipole and source on the body whilejump (or discontinuity) at the blades' trailing edge.the third term is the dipole on the trailing vortex wakesurface (defined only for lifting bodies). This equation canIn numerical calculations, construction of matrices D,Sbe considered as an illustration of the velocity potentialand W would basically require the evaluation of Si andcorresponding to the distribution of a dipole strengthof φWyu,Dy matrices and is a very time consuming process.)n the surface of the body Sg, the distribution of theD isa large matrix and the solution of Eq.(12) and findingsource strength dφ/n on Sg, and the distribution oit would require great effort. Since huge time and storage isdipole strength of Oφ on the trailing vortex surface Sw .required for obtaining D, when the number of mesh is veryAt this point, the only remaining unknown is the dipolelarge, a direct method for solution of the system is avoidedstrength φ which is obtained by simultaneous solution ofand instead an iterative Gauss Seidel method has beenEqs.(8) and (9). The term dφ/an in Eq.(9) is obtained fomadopted.boundary condition 1) in Eq.(3) (Kinnas and Hsin, 1992).Once the dip中国煤化工element is3 Numerical implementationdetermined, vel:MYHCNMH Gtions can becalculated directly via Bernoulll 's equation:For a propeller with Z number of blades, the surface.Hassan Ghasseni; e1 al. Numerical Analysis of the High Skew Propeller of an Undenwater Vehicle[" =VqSubsequently, the coordinates of a point on the surface of the :(13)kth blade at both the back and face sides can be expressed in|R=05.p(2y,-.)the following equations:The pressure coefficient can be expressed asXB.r= rtanγ+(S(r)+ L())sinBr -YB.F cosB&Cn-只(14)YB,F =rcos(7B.F +8)(19)0.5pU2EB.F =rsin(nB.F +0k)where ρ is the density of the fluid.whereThrust and total torque of the propeller with twonB,r =[(S(r)+ [(>)cos,, +Yg.; sinBc]1rcomponents of pressure and friction are expressed ask =2r(k-1)/Zk-=2,2...(20)follows:Bc=tan'(5)T=Z之Pn,/As,-Tr=|(15)Q=Z艺P(ny,=-n":);)SS;+Qp4.1 Description of the propeller meshing procedureFor obtaining a numerical solution for the integral equation,where the frictional coefficient Cp for the frictionalthe surfaces of the propeller blades, hub and trailing vortexcomponent of thrust Tr and torque Qr of the propeller can beare divided into small elements. In the usual applications ofexpressed by Schlichting and Gersten (2000)the boundary element methods for the analysis of the(1+ Imx()]_ 0.455propeller, quadrilateral plane elements are used for surfaceC,()=|(gRe)28(16)approximation. However, due to the non-planner nature ofthe helical surfaces of the propeller blades, plane elementsHere, Re is the Reynolds number and is calculated fromcause a gap at the corner of each element and consequentlyRe= VyU).CU)(17)produce significant numerical errors. In order to obtain aclosed surface and avoid numerical errors, hyperboloidalFinally, the hydrodynamic cofficients of the propeller areelements have been used. Generally, selection of elementdetermined as follows:type and the generation of smooth elements are importantTparts of this method as is in all other numerical methods inJ=AKτ=ρn2D4which the choices may affect the results directly. ThisQ1 Kr(18)implies that the solver may operate properly while theρn2D°2π Kegeneration of an improper grid may generate numericalerrors in the computed results.4 Propeller formulationsElement generation is divided into the following parts:●Generation of blade elementsThe propeller is considered to rotate counterclockwise with an●Generation of hub elementsangular velocity of 0 in an inviscid, incompressible, andirrotational fluid with uniform or non-uniform axial velocity●Generation of elements on the trailing vortex surface.VA at the upstream. The Cartesian coordinate system 0-xJzGeneration of non-distorted elements and smooth planes iswas fixed at the center of the blade. The x axis is consideredenormously important in the boundary element method andalong the propeller axis with a positive downstream direction.influences the results. Accordingly, the surface should beThe z-axis which is considered to be positive in upwardsmooth accompanied by accurate interpolation for thedirection and situated on the generator line of the propeller'spropeller dimensions. Accordingly, surfaces of the propellerkey blade and the )-axis which completes this right-handand the trailing vortex surface should be divided into severalsystem 0xZ are ilustratled in Fig2.small quadrilateral hyperboloidal elements.2↑Meshing of the propeller's hub and the location of isintersection with the blades is very complicated. In order tomesh the hub, three parts are considered: the downstreamregion (tailing vortex flow located downstream), the bladeregion, and中国煤化工hull located inrupstream). AFhub operates as acylinder orMYHCNMHGr'shubandthelocation of its intersection with blades are considered to beFig.2 Coordinate system of the propellerellipsoidal. The blade region is spaced into the same stripsJournal of Marine Science and Application (2011) 10: 289-299293 .which are located at the surrounding angle between the17blades'roots. This type of spacing establishes helical1口2界elements on the hub. At the intersection zone, the grid1-50includes only one strip of elements which is in harmony子8-40主with the other elements on the blade.心6t4.2 Vessel hull element generation-1Table 1 indicates the relative dimensions of the UV. The0节2345678910市72shape of the main body in the longitudinal direction and inV/knreal scale was measured repeatedly and introduced to ourFig.4 Computed total resistance and efective power of thecomputational software as entry data. Subsequently, theUV in fully immersed condition (H> >D)main body is longitudinally meshed by our software usingspline interpolation. In this software. all of the meshing190process is done using math functions and spline-80-70interpolation, and the position of each element is accuratelycomputed (Hsin et al, 1991). The generated surface50主elements for the UV and its propeller assembly are40illustrated in Fig.3.30~20Table 1 Relative data of the UV02345678910 i9ParameterValueV!knLength-diameter ratio6.14Fig.5 Computed total resistance and effective power of theSpan- chord ratio of hydroplaneUV in fully surface condition (H=D)Hydroplane sectionNACA0010Displacement in fully submerged condition/t125.1 Influence of the blade numberGenerally, the number of the propeller blades of a marinevehicle ranges from 3 to 7(3≤Z≤7). The number of thepropeller blades in an underwater vehicle which possesses 4hydroplanes (2 vertical and 2 horizontal) is restricted to anodd number because this has been proven to produce theleast reaction. A 4-bladed propeller may not be selectedbecause in each rotational cycle, each of the 4 blades isexposed to the hydroplane's wake flow simultaneously andas a result the oscillation of the generated thrust would beseverely high. Accordingly, the blade number could beselected from 3, 5, or 7 blades. The propeller with 7 bladesFig3 Generated surface element of the UV with propellerhas high costs and a high possibility of torque generation;also, for a 3-blade propeller the possibility of cavitationoccurrence is high. Therefore the best selection is a propeller5 Propeller selection parameterswith 5 blades which can provide desirable hydrodynamicThe first step of the propeller design is the calculation of theperformance conditions.required thrust for overcoming the resistance force at adesigned speed. Here, by virtue of an empirical method5.2 Influence of skew angle(Burcher and Rydill, 1994), the vessel resistance wasIn recent years, the skew propeller has been widelycalculated and was subsequently used for computation of theexploited in UVs, and appropriate results have beentotal resistance force and total effective power. This wasobserved. The skew angle is like the sweep angle in thedone at different velocities ranging from 1 to 10 kn and forhydrofoils which is basically the angle that the UV makesboth the submerged and surface conditions. Results arewith the flow direction so that the entry flow would beshown in Figs.4 and 5. Subsequently, for the determinationgradually imposed on the propeller blade while reducing theand optimization of the propeller's parameters, a parametricpossibility of the cavitation phenomenon. In other words,study was performed in order lo examine their effecls. Thesethe effective center pf the hudrndvnamic forces movesparameters included the number of blades, main diameter,closer to the roo中国煤化工。examples ofpitch ratio, expanded area ratio, skew angle and bladethe 3 and 5-bladeMHCNMHGprofile, and cross-section.The advantages of the skew angle include the elimination of.94Hassan Ghasseni, et al. Numerical Analysis of the High Skew Propeller of an Underwater Vehiclethe cavitation and prevention of the pressure oscillation andV, =(V,+vy)+(wxr-vn)(21)a sudden dynamic load on the blade, conduction of entryflow toward the leading edge, reduction of the fatigue stresswhere vA and VR are the axial and tangential inducedwhile increasing the propeller time endurance (life time),velocities, respectively. Fig.9 depicted the velocity diagramand generation of the non-oscillating uniform axial forcefor the element of dr at radius r. Geometric pitch angleand torque. Considering these advantages, the skew angle isBc = tan(Pc 12xr) is the summation of the incidence angleenormously important for the UV propellers. Based on thecriteria given by Carlton (2006), and Breslin and Andersena and the hydrodynamic pitch angle β. It is clear that(1994), and the authors of this paper, the ideal skew angle isa is related to the pitch. If the propeller pitch increases, thebelieved to be approximately 50 degrees. On the other hand,incidence angle will increase. Consequently, thrust anhigh skew angle could also reduce efficiency. In this paper, atorque would be increased and cavitation could occur, Thus,highly skewed propeller is noted as HSP-5.propeller's pitch should be optimized in such a way thatadequate thrust is produced while preventing cavitation. Forthe targeted UV, a mean pitch-diameter ratio of 0.6 can be asuitable choice which brings about a moderate pressuredistribution on the propeller blade; however, the bladecross-section and profile (thickness and camber of blade)strongly influence the pressure distribution. Propeller pitchis considered variant so that the pitch value is small at theblade tip and is highest at the blade midpoint (at the radiusfor which chord length is the highest). This is done mainlyFig.6 Highly skew propeller with BMAXR=0.249 (with 3because the lowest load must be exerted on the blade tip toand 5 blades)prevent cavitation while pitch must be considered high inthe mid-part of the blade so that the generated load is5.3 Chord-diameter ratiodistributed on an expanded area. It should be noted that theThis parameter actually shows the blade area which means itradius r=(0.4- -0.7)R has the maximum pitch. At thishas a direct relationship with the blade expanded area ratioradius, the corresponding maximum pitch-diameter ratio is(EAR). This ratio is shown as (CMax ID= BMAXR)0.72. In the meantime, at the tip of the propeller, the pitch isFigs.6 and 7 indicate the effects of this parameter on the 3at the minimum value of 0.37.and 5-bladed propller. As BMAXR increases, the propeller士Skew anglegets wider and an increase in the propeller area is observed.120 量MfLO0OChrdlDiaerxBMAXR) 17The effect of BMAXR on the hydrodynamic performance is100significant. It diminishes the possility of cavitation with anincrease of the BMAXR. On the other hand, it causes the60}reduction of efficiency due to higher frictional drag and40torque. Fig.8 shows the variation of the geometrical of theblade at each radius. This figure demonstrates the thickness0totratio and chord length ratio defined by AA and BB..2 0.4 0.60.Fig.8 Skew angle, chord length and maximum thickness ofthe HSP-5 PropellerFig.7 Non-skew propeller with BMAXR=0.369 (with 3 and 5blades)5.4 Pitch and its influencePropeller pitch is like the angle of attack in a foil. Fig.9中国煤化工shows the velocity diagram on the radial blade section.4TYHCNMHGConsidering the induced velocities, the resultant inflowFig.9 Velocity diagram on the element dr of the propellervelocity to the blade at radius r is expressed asJournal of Marine Science and Apication (201) 10: 289-2992955.5 Profile of the blade sectionTable 2 Main dimensions of the propeller HSP-5Criteria for the design of blade sections may be selected toParameterValueinclude minimum thickness and chord, sufficient camber toPropeller typeHSP-5generate the design lift, distribution of thickness and camberDiameter D/m1.45to avoid boundarylayer separation as well as prevent orExpanded area ratio (EAR)0.63mitigate cavitation, having strength requirements againstPitch-diameter ratio P/DVariabledynamic forces with an adequate safety factor (Carlton,Hub radius to propeller radius0.182006).Blade maximum chord ratio MBAXR0.32Number of blades ZSince the propeller blade at each radius has diferent chordRake angl/(°)10.0length, pich, skew., and inflow velocity. it is very dificult to .Skew angle(°)define the profile section. The HSP-5 (with blade sectionBlade sectionHSP-SRI-BHSP-SRI-B) profile section is used for the present propelleras shown in Fig.10. Considering the effects of all these 5.6 Non-uniform wake effectparameters, the appropriate propeller designed for theThe viscous nature of the water, the boundary layertargeted UV is shown in Fig11. When the propeller rotatesdevelopment, and also the shape and form of the hull (mainwith constant ;peed, the trailing vortex surface is produceddiameter of the main hull, hydroplanes,. and cone tail angle)at downstream of the propeller. Fig. 12 shows the elements are the parameters which are effective in the development ofof the propeller along with the helical trailing vortex surface. the wake. Every hull shape has a different wake. For theBased on the discussed parameters, the chosen dimensionspresent UV, the flow near the sterm is approximately uniformof the HSP-5 propeller are demonstrated in Table 2.with the exception of conditions such as trim andmaneuvering in which case there would be a complex wake0.8flow. Figs.I3 and 14 show the wake flow beside the0.7-propeller at the speed of 4 and 8 kn.060.02两临N00.1--0.4-03-0.2-0.100.1 0.2 0.30.4 0.5 0.6-0.6Chord drctionFig10 Profiles of blade sections at various radius of the-0.8 -0.6 -0.4-0.2 00.20.4 0.6 0.8Fig.13 Predicted axial velocity of the stern onto the propelerv24kn,两=0.35, V.=2.6kn0.8 r.6-).4 t.2不0.2↓Fig,11 Element arrangement of the HSP-5-0.4)中国煤化工0.08HCNMH GFig.12 Modeling of the trailing vortex surface of the HSP-5Fig.14 Predicted aXxa velocty o1 me stern onto the propellerV,-8km,雨=0.35, Va=5.2kn96Hassan Ghasseni, et al. Numerical Analysis of the High Skew Propeller of an Undenwater Vehicle5.7 Computation flow chartby Ukon et al. (1991). The mentioned comparison showsA flow chart for boundary element computation in theexcellent agreement with the experiments for velocityanalysis of the propeller of a UV vessel is ilustrated inratios of 0.5 and 0.6 while relative agreements has beenFig.15. In this flow chart, the main dimensions of the UVdemonstrated for velocity ratio of 0.9. The authors believeare introduced according to the given data. Subsequently, thethat this is attributed to the fact that the propeller isvessel resistance is calculated at two different conditions atoperating at a light condition which implies that thethe surface and submerged, using an empirical formula.possibility of cavitation occurrence is minimal. PressureNext, the three -dimensional propeller modeling is donedistributions under four different velocity conditionsusing the geometric characteristics of the propeller (e.g.indicate that the possibility of cavitation occurrencediameter, pitch, thickness, camber, etc.). Later, the solverincreases because the negative pressure coefficient at theperforms a hydrodynamic analysis for the propeller usingsuction side is higher. Comparison of the hydrodynamicBEM. Needless to say, at this stage, an iterative method iscoefficients at open water condition with the experimentalused for solving the resulting system of equation. Thevalues has been demonstrated (shown in Fig.17) and goodcomputed results include pressure distribution, thrust, torque, agreement has been displayed.and efficiency of the propeller.-2r十Preent Method+ Present Methodhoput 中heaople dnetuo。A Exp.》 Exp.-1h。Cacltnon of unereser ehsle reusance * desgnseeBlake manber Popeler dameterMam de ofiletucies ol he blade meach .ndus Pichrmolantal gess for routuan seed oftheBounday chement merthod00..40.8.1.0peien bued on he geer's(a) rlR-0.7, J=0.5Uung bountary deree rechnd lo demmon ehyhodynamc coe2厂- Present Method。Exp.Setnstying th truttorce nd denshingFanshFig.15 Calculation flowchart for propeller design0.20.40.6 0.81.0s/C6 Numerical results()r/R=0.7,J=0.66.1 Open-water conditionThe most important part of hydrodynamic analysis of apropeller is finding the pressure distribution on its surface2r+ - Present Methodr Present Methodin an open water condition, the inflow velocity onto thepropeller is uniform and all the blades operate in the same。gExp.manner. Accordingly, a propeller with one blade of-14。x(2NxM) elements is considered. Here, M is the numberof divisions in a radial direction while N is the number ofdivisions in a chordwise direction. Fig.16 shows thecomparison of the computed pressure distribution and thatof experimental data (Ghassemi and Kohansal, 2009) at a中国煤化工08 1.oradius ratio of r/R=0.7 and for different advanced velocityYHCNMHGratios of J=0.5, 0.6, 0.7, 0.9. These experimental results are" (C)r/K-U.I,JAU.1related to the open water condition and have been reportedJourmal of Marine Science andpplication (2011) 10: 289-29929- Present MethodFig.18 ilustrates the pressure distribution of HSP-5 behind aPresent MethodUV during one cycle rotation at J=0.6. These pressuredistributions are shown for the different point at face andback sides of the blade. The fluctuation in pressure is due tonon-uniform wake.Computation of the propeller performance is done for allspeeds ranging from I to 10 kn with an incremental step of1kn. Fig.19 presents the computational results obtained as0.2.40.0.8 1.0part of the hydrodynamic performance of the propeller insubmerged condition.(d) r/R=0.7,J=0.90.7,+Thrust士TorqueFig.16 Comparison of the pressure distribution of HSP-5 atopen water condition30 合0.:25十K, (computed) -一10K。(computed)”(computed) 。K-(Exp.)0.4 t200.7。 10K。(Exp)15.6-5 0.5& 0.3↑370340310280250 220 190 160 130.22RPM.1 t(a) The forces+K,0.3 0.4 0..80.90.7士η 甘-RPM]350Fig.17 Comparison of open water characteristics of the HSP-50.63006.2 Actual operating condition behind the UVThe propeller operates at the UV stern where the inflow isnon-uniform due to the wake generated by the hull and the查0.3150hydroplanes. At this condition, all the blades should bek 0.2100considered in the computation. For the propeller with Knumber of blades and M and N divisions in the radial as well5Is chordwise directions, respectively, the total number ofequations is equal to (2NxMxK) . As such, 1820 .0.25 0.350.45 0.55 0.65 0.7elements are generated for a five -bladed propeller and 400(b) The cofficientselements are generated on the hub, thus a total of 2220Fig.19 Hydrodynamic performance of the HSP-5 propellerelements are generated for the whole body.at speed of 8 kn in submerged condition-1.2 |+ BS-0.25←BS-0.40 士BS-0.60Here, an attempt is made to show how the optimized speed女FS-0.25 -毋FS-0.40 + FS-0.60-1.0nd efficiency of the propeller are determined when the-0.8propeller performance is known at the surface and submergedconditions. Using the resistance force (drag) and the total、-0.power at the surface (D=T) and submerged conditions(H>>D), and also by the aid of the propeller hydrodynamicperformance, the optimized vessel speed van be obtained.-0.2As an example, a UV speed of 8 kn is considered in whichcase the resistan中国煤化工7kN for the0.2560120 180 240 300 360submerged corYHCNMH G。the surfaceProp. rotating angle 0/°)condition. ReqFig.18 Pressure distribution of HSP-5 behind the UV during speed of 8kn in submerged condition is found to beone cycle rotation at J=0.6(assumed at t=0.15):.98Hassan Ghasseni, et al. Numerical Analysis of the High Skew Propeller of an Underwater Vehicler_R__ 8.77= 10.3178kN22)Table 5 Propulsion performance at UV speed=8 knParameterSubmerged/kW Surfaced/kWEffective power/kW36.1242.56The values of rotational speed and the propeller efficiencyDelivered powerkW42.1249.33can be determined in a way that they can provide theBrake power/kW46.9855.72required thrust of the vessel. The following calculatedProp. efic. behind of hull0.670.64results have been obtained for the surface and submergedHydrodynamic efficiency0.8750.862conditions.Submerged condition:7 ConclusionsT =10.3178 kNIn this article, the boundary element method was applied toRPM =227For Fully Immersedevaluate the hydrodynamic performance of the HSP of annp =0.67(H>> Dyou)underwater vehicle. Based on the numerical findings, theSurfaced condition:following conclusions can be drawn:T=12.120kN1) Comparisons of the computed pressure distribution andhydrodynamic characteristics of the 5-bladed skewedRPM = 240For Surfacedpropeller in open water conditions with the experimentalng =0.64(H = Dqau)data indicate that the current method has high capability.The propeller efficiency for both submerged and surfaceFurthermore, computations were continued until theconditions were found to be 67% and 64%,respectively,bydrodynamic efficiency, nB, at the back of the vehiclewhich compared to conventional propellers have muchand the rotational velocities were found for all speeds. Notehigher efficiency.that the wake factor (w) and the thrust deduction factor ()are assumed to be axial in both conditions. This assumption2) In order to satisfy the Kutta condition, a special iterativeis acceptable because at both conditions, the propeller isscheme is required in numerical calculations, which hasubmerged and the wake factor and the thrust deductionbeen implemented in this paper.factor are independent of submergence height. Having thevalues of the required thrust and hydrodynamic efficiency of3) In the suggested method, the criteria for the design andthe propeller at the back of vessels, values of the deliveryselection of some parameters such as number of blades, thepower and the engine power have been determined.skew and rake angles, pitch ratio, and expanded area ratioMechanical efficiency of the system is given in Table 3. Inhas been determined using related literature, the authors'experience, or trial and error computations.submerged conditions at speeds of 4 and 8 kn are presented,respectively. Note that the hull efficiency and the totaAcknowledgementhydrodynamic efficiency of the propeller can be calculatedby the following equations:The authors wish to thank to the Marine Research Center of1-1Amirkabir University of Technology for financial support ofHull eficiency ny=1wthis research.Total bhydrodynamic eficiency np =ηp]7H(23)Total mechanical eficiency力M = nceB7s IMisceReferencesAndersen P, Kappel JJ, Spangenberg E (2009). Aspects of propellerTable 3 Mechanical efficiency of the systemdevelopments for an underwater vehicle. First InternationalValueSymposium on Marine Propulsor, Trondheim, Norway, WB2-2.Hull fficiency1.307Benini E (2004). Significance of blade element theory inShaft fficiency0.97performance prediction of marine propellers. OceanGearbox efficiency0.95Engineering, 31, 957-974.Miscellaneous effic.0.96Beslin JP, Andersen P (1994). Hydrodynamics of ship propellers.Mechanical efficiency0.89University Press, Cambridge, UK.Burcher R, Rydill L (1994). Concepts in underwater vehicle design.Department of Mechanical Engineering, University ColegeTable 4 Propulsion performance at UV speed=4 knSubmergedkW Surfaced/kW~Carlton J (2006), Marine propeller and propulsion.4.57545.3464Delivered power/kW5.5046.190 .Butterwort中国煤化工uo Chunyu (2007).Chang Xin, 26.3126.490InfluenceTYHCNMH Gince of a variable0.620.61vector propeller of different rules of pitch angle change.0.8340.813Joumal of Marine Science and Application, 6(4), 32-36..Journal of Marine Science and Application (2011) 10: 289-299299elice FD, Felli M, Liefvendahl M, Svennberg U (2009).Schlichting H, Gersten K (2000). Boundary-layer theory. 8Numerical and experimental analysis of the wake behavior of arevised edition, Springer-Verlag, Berlin.generic underwater vehicle propeller. First InternationalUkon Y, Kudo T, Yuasa H, Kamiirisa H (1991). Measurement ofSymposium on Marine Propulsors, Trondheim, Norway,pressure distribution on full scale propellers. Proceedings of theWB2-2.proepllers/Shgfing '9I Symposium, Virginia Beach, Virginia,Ghassemi H (2009). Effect of the wake flow and skew angle ontoUSA, 11-123.the hydrodynamic performance of ship propeller. Journal ofScience and Technology (Scientia lranica), 16(2), 149-158.Hassan Ghassemni is an associate professor ofGhassemi H, Kohansal AR (2009). Numerical evaluation of variousAmirkabir University of Technology (AUT). Hiscurrent research interests include marine propulsorlevels of singular integrals, arising in BEM and its applicationdesign, high-speed crafts, and hydrodynamiein hydrofoil analysis. Applied Mathematics and Computation,numerical methods such as BEM and CFD.ynamc213(2), 277-289.Hsin CY, Kerwin JE, Kinnas SA (1991). A panel method for theanalysis of the flow around highly skewed propellers.Proceedinthe Propllers/Shafing '9I Symposium, VirginiaBeach, Virginia, 1-13.Kinnas SA, Hsin CY (1992). Boundary element method for theParviz Chadimi is an associateprofessor ofanalysis of the unsteady flow around extreme propellergeometry. AIAA Journal, 30(3), 688 696.current research interests includecomputationalfluid dynamics, advanced engineeringKim YC, Kim TW, Pyo s, Suh JC (2009). Design of propellermathematics, and analytical calculations.geometry using streamline-adapted blade sections. Journal ofMarine Science and Technology, 14, 161-170.Morino L, Kuo CC (1974). Subsonic potential aerodynamics forcomplex configuration: a general theory. AIAA Journal, 12(2),191-197.中国煤化工MHCNMH G.

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