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27th Symposium on Naval HydrodynamicsSeoul, Korea, 510 October 2008
Simulation of the Incompressible Viscous Flow aroundDucted Propellers with Rudders Using a RANSE Solver
A. SánchezCaja,1 J.V. Pylkkänen2 and Tuomas P. Sipilä1
(1,2VTT Technical Research Center of Finland, 2ret.)
ABSTRACT
Within EU Project SUPERPROP, fishing vessels havebeen studied. Usually their propulsion units consist ofducted propellers in order to provide large thrust intrawling. Rudders may significantly influence theperformance of ducted propellers especially if they arelocated at short distance from the duct. This papersummarizes some of the CFD calculations performedas the starting point for the development of a newpropeller design for a reference fishing boat. The basicdesign performance particulars were obtained from theanalysis of the existing conventional ducted propellerinstalled in the ship. The flow around the originalpropeller geometry and around one of the alternativedesigns is simulated using RANS code FINFLO. As apart of the project the rudder blockage effect has beeninvestigated using a quasisteady approach.
INTRODUCTION
Within EU Project SUPERPROP, fishing vessels havebeen studied to improve their operational costs.Generally, the operational profile of such vesselsincludes two distinct working conditions. In freerunning, they need a relatively high speed to reach thefisheries in a short time. In trawling, they operate atlow speed with the nets filled with fish and withpropellers heavily loaded. Ducted propellers aresuitable for meeting the latter condition efficiently.Usually the design point is selected as a compromisebetween the two situations.
During the lifetime of the vessel propellerefficiency deteriorates as a consequence of roughnessincrease on both propeller and hull. If operational costsare to be kept low, the propeller efficiency should beoptimized not only initially for the design operationpoint but also for the operational life of the propeller.Sometimes by remachining the blades, the propellercan be accommodated to the new operating conditions
with low costs. In other cases a new propeller designmay be the cheapest solution.
A reference fishing boat with an old ductedpropeller was selected as test case for hydrodynamicanalysis in the SUPERPROP project. The existingducted propeller installed in the ship was analyzed andwas found to be overpitched for the present situationafter several years of operation. A new design pointwas established with the agreement of the ship ownerand different alternatives were studied to adapt theexisting propeller to the actual working point. Theyincluded blade cutting and repitching of the propeller.Blade cutting was discarded as solution due to thealteration of the strength properties of the blade. Thedesign condition would be only reached by large cutsof the chord, which additionally would result in astrong reduction of the expanded blade area of thepropeller and consequently, in significant cavitationproblems. A new propeller design was considered amore appropriate solution. This paper presents thehydrodynamic numerical analysis for the existingducted propeller and rudder of the reference vessel.Additionally, several propeller designs were made andthe numerical analysis of an alternative ductedpropeller design is presented.
The interaction between the propeller and rudderhas been numerically investigated by severalresearchers. Moriyama (1981) developed an estimationmethod for the propellerrudder interaction by applyingthick wing theory and boundary layer theory to arudder with thickness. His calculation results includethe effects of rudder and propellerrudder gap on thepropeller performance coefficients. Suzuki, Toda, andSuzuki (1993) performed viscous flow computations ofpropellerrudder interaction. The steady flow field wascalculated by a viscous flow code coupled with a bodyforce distribution which represented the propeller. Hegives also the effect of the rudder on poweringperformance coefficients. Tamashima, Mori, Matsui,Yamazaki, and Yang (1993) use infinitely bladed
theory to simulate the propeller. A panel method wasapplied for the rudder. The friction forces on therudder were obtained by twodimensional boundarylayer theory. Li (1995) developed a linear method tomodel propellerrudder interaction. His samplecalculation results include ∆KT versus J for differentpropellerrudder gaps, ∆KT versus J for differentthickness/chord values, and open water results withand without rudder behind. Coupled potential methodsfor the analysis of propellerrudder interaction viacircumferential averaged flow are also found in Lee etal. (2003), Greco and Salvatore (2004), Kinnas et al.(2007). Han (2008) studied hull/propeller/rudderinteraction by coupling a RANS solver to either avortex lattice lifting surface or a lifting line propellermodel via body forces.
In this paper the RANS equations are solved forsimulating the flow around a ducted propeller andrudder. The actual geometry for both ducted propellerand rudder is modeled without any simplification. Inprinciple such computations may be made in threedifferent ways: full unsteady (SánchezCaja et al,1999), quasisteady and steadyaveraged (SánchezCaja et al, 2003). In the first case time effects are fullyaccounted for, but computational times are long forlarge meshes. In the second case the propeller block isrotating but fixed for the calculation at one angularposition. Here, memory (time) effects are not included,but lack of flow symmetry is present to some degree onthe propeller blades. In the third case the flowquantities are circumferentially averaged on anaxisymmetric surface (mixingplane) located midwaybetween the propeller and the rudder, and memoryeffects are not included. The advantage of the twolatter approaches is that they give an indication of theglobal performance for the propulsor unit within areasonable computational time. The computationspresented in this paper were made using a quasisteadyapproach. Some tests not reported in this paper weremade also following a steadyaverage approach.
NUMERICAL METHODS
The flow simulation in FINFLO is based on thesolution of the RANS equations by the pseudocompressibility method. FINFLO solves the RANSequations by a finite volume method. The solution isextended to the wall and is based on approximatelyfactorized timeintegration with local timestepping.The code uses either Roe's fluxdifference splitting orVan Leer's fluxvector splitting for compressible flowsand an upwindbased scheme for incompressible flows.In the latter case, the pressure is centerdifferenced anda damping term is added via a convective velocity. Amultigrid method is used for the acceleration ofconvergence. Solutions in coarse grid levels are used
as starting point for the calculation in order toaccelerate convergence. A detailed description of thenumerical method including discretization of thegoverning equations, solution algorithm, etc. can befound in SanchezCaja et al. (1999 and 2000). Chien’skepsilon turbulence model was used in the calculation.
Figure 1. Computational mesh on the propeller, ductand rudder surfaces. Original propeller
There are two ways to approximate unsteadyrotational flows. The first one is called a quasisteadyor multiple reference frame solution and the secondone a mixingplane approach. In both approaches therotating and nonrotating blocks are firstly connectedin an ordinary way. Since global Cartesian velocitycomponents are used no coordinate transformation isnecessary. In the mixingplane approach the flowquantities for both the rotating and nonrotating blocksare circumferentially averaged on both sides of thecommon face and then transferred to the ghost cells asboundary values. The flux calculation on the boundaryis done in an ordinary way. The procedureapproximates a situation, where the boundary valuesoscillate at a high frequency making the averagingsensible.
In the quasisteady approach the rotating and nonrotating blocks are connected without any averagingprocess. The solution approximates a situation, wherethe rotating block is frozen to a particular position. Asrotating and nonrotating blocks are connectedtogether, the flux calculation differs in those blocks. In
the rotating frame of reference, the rotational speedaffects the convective speed that is relative to a cellsurface. Furthermore in a rotating frame of referencethere is a source term in the momentum equation. As aresult the solution may exhibit special features, if theflow is not uniform (Sipilä, 2008). E.g. any flowdisturbance from for example an upstream nonrotatingblock will seem to rotate when traveling through thedownstream rotating one, or vice versa. In other words,although the absolute velocities will vary in a smoothcontinuous way through the interface, the flowdisturbances (wakes) will propagate changing directionat the interface. This means that the angular location ofa propeller blade in a quasisteady computation willnot correspond to the same location of the blade in atimeaccurate computation. This clearly differs fromthe quasisteady computations made in panel methodswhere such correspondence may be established. In themixingplane approach the averaging generates ahomogeneous boundary condition; hence theinterpretation of the solution from a physicalstandpoint is simpler than that resulting from a quasisteady approach.
In order to keep the numerical interactionbetween the rotating and nonrotating domains weakthe interface should be located far enough from solidsurfaces (i.e. propeller blades and rudder), being morecritical this remark for the downstream block.
GEOMETRY AND MESH
The propeller geometry was obtained by directmeasurements and transformed to IGES format. Thepropeller was a fourbladed one with 2.6 m diameterand about 0.96 pitch diameter ratio.
The computational mesh of the original propellerwas generated with the IGG grid program and an inhouse built program. The mesh was structured andcontinuous. The use of overlapping or nonmatchingblocks was avoided. Ctopology was selected aroundthe propeller blades, which allowed having cellsconcentrated on the propeller wake. Otopology wasused around the duct and H around the rudder.Computational cells were concentrated in the ductwake and propeller hub vortex zone.
The grids used in the present calculationsconsisted of 9.5 million cells distributed in 23 blocks.The calculation was made at model scale. Figure 1shows a view of the computational mesh on thepropeller, duct and rudder surfaces. The proximity ofthe rudder to the nozzle made it difficult theconstruction of the structured mesh. The mesh of thealternative propeller design was similar to that of theoriginal propeller, but Kaplan type blade shape was
used instead. Figures 2 and 3 show from a fore andback view respectively details of the grid construction.
Figure 2. Detail of grid construction on hub & blade.Fore view of propeller mesh for the alternative design.
Figure 3. Detail of grid construction on hub & rudder.Back view of propeller mesh for the alternative design.
BOUNDARY CONDITIONS
The boundary conditions were as follows. Thedownstream cap of the hub and surfaces of thepropeller blades are rotating solid walls with boundaryconditions enforcing the velocity field to match thepropeller rotational speed. The duct and ruddersurfaces are nonrotating solid walls. At thecomputational infinity the boundary conditions consistof uniform flow applied to the inlet and peripheralsurfaces, and zero streamwise gradients of the flowvariables as well as zero pressure difference at the
outlet. For the calculation without rudder the boundaryconditions were as those in the calculation with rudder,but cyclic boundary conditions were applied to benefitfrom the periodicity of the flow.
Figure 4. Convergence history of residuals for xmomentum in the second grid level (medium grid).
Figure 5. Convergence history of an overall dragcoefficient for the first grid level (fine grid).
CONVERGENCE AND ANALYSIS OF FORCES
Only one propeller position was analyzed in quasisteady flow. Even though the forces on each individualblade may vary significantly as the propeller rotates,the total force over all the blades do not vary so much.This makes the computations representative of theaverage performance to a resolution degree of the totalfluctuation amplitude.
The computations were performed on Xeon™with 8 or 9 3.0 GHz processors. In solving thedifferential equations the multigrid method was appliedwith two multigrid levels for acceleration ofconvergence. In some critical zones the multigrid levelwas one. Convergence was also accelerated by starting
the calculation with the solution on medium and coarsemeshes corresponding to the 2nd and 3rd grid levels.The coarse grid levels are obtained by removing everyother grid line in each direction from the mesh of theprevious grid level. Figure 4 shows the convergencehistory of residuals for xmomentum in the 2nd gridlevel corresponding to the calculation of one of theducted propellers with rudder. Figure 5 shows theconvergence of drag for the 1st grid level.
Computations were made first for the ductedpropeller without rudder in uniform flow at an advancenumber corresponding to the new design condition.The solution is timeindependent. The advance numberwas estimated from an average effective wake for theentire ducted propeller unit obtained with the help ofan actuator disk model coupled with RANS solverFINFLO (SánchezCaja et al. 2007). Model testmeasurements were available for the ducted propellerwithout rudder in open water. Table I comparescomputational results to measurements. The thrustcoefficient includes the duct thrust. The total thrust isoverpredicted by 1 percent and the torque is underpredicted by 6.6 percent.
Table I. Comparison between measured and calculatedperformance coefficients for the ducted propeller atJ=0.526 in percentages.
CalculatedMeasured1st level 2nd level
KTunit 100.0 101. 98.0KQ 100.0 93.4 93.6
Next, computations were made for the unsteadyflow around the ducted propeller with the rudderfollowing a quasisteady approach.
The presence of the rudder behind the propellerreduces the inflow at the propeller plane and thereforeinduces a physical blockage which can be expressedalso as an increment in propeller thrust coefficient. Inaddition the quasisteady (and the mixingplane)method causes a nonphysical change of the inflow atthe propeller plane, which will be manifested also inthe form of a thrust coefficient increase in the casewhen the propeller block is rotating in front of a nonrotating one with solid surfaces. Henceforth thisinteraction between blocks will be referred to asnumerical or computational blockage.
Three locations of the interface between therotating propeller block and nonrotating rudder blockwere analyzed. The aim was to investigate thenumerical blockage. The first location was very closeto the rudder, at an axial distance correspondingapproximately to the location of the duct trailing edge.
The second one was at the downstream edge of thehub. The third one was somewhere between the bladetrailing edge and the downstream edge of the hub.
0.04
0.05
0.06
0.07
0 0.05 0.1 0.15 0.2 0.25
x/D
Increm. Kt
Figure 6a. Influence of the interface location onpropeller thrust. Propeller TE at x/D=0; rudder LE atx/D=0.262.
0
0.01
0.02
0.03
0.04
0 0.05 0.1 0.15 0.2 0.25
x/D
Rudder drag
Figure 6b. Influence of the interface location onrudder drag. Propeller TE at x/D=0; rudder LE atx/D=0.262.
Figure 6a shows the influence of the location ofthe interface between the rotating and nonrotatingblocks on propeller thrust increase. The propellertrailing edge at the root is located at x/D=0 and therudder at x/D=0.262. As the interface moves fartherfrom the rudder (low x/D) the increment of thrust tendsto a constant value, which would ideally correspond toa value free of computational blockage. Figure 6bshows the variation of the rudder drag with theinterface distance and the same tendency is observed.
Similar trends were obtained for test computationsmade using the mixingplane approach. The latter testcalculations were made using a medium size grid (2nd
level).
Table II summarizes the results obtained fromcomputations made with the interface located atapproximately x/D=0.07. In principle the effect of theduct is to increase the physical flow blockage on thepropeller as compared to the physical blockageresulting from an open propeller. In a ducted propellerthe contraction of the flow is usually delayed to theduct trailing edge. An effective distance betweenpropeller and rudder could be defined for ductedpropellers taking as reference distance to the rudder theduct trailing edge instead of the propeller plane. Forthis particular case such distance is very small, whichpartially explain the large blockage effect. Additionallysome numerical blockage may still be present.
Table II. Calculated thrust and torque coefficients forthe old ducted propeller at J=0.526 (fine grid).
Withoutrudder
Withrudder
KT blades 0.145 0.200KT blades+duct 0.183 0.235KT blades+hub+duct+rudder 0.217KQ 0.0279 0.0356
FLOW ANALYSIS
Figures 7 and 8 show the pressure contours for theducted propeller without and with rudder respectively.Low pressure areas are displayed at the propellerleading edge and tip regions including the duct innersurface, which suggests that the propeller is overpitched for the new design condition. The excess ofpitch is noticeable at the outer radial stations. Lowpressure areas are also found on the rudder leadingedge caused by the propeller induced circumferentialflow. Such areas are visible on the lowerright andupperleft side of the rudder in Figures 8 and 9, and arenot so much extended and intense as those on the bladesuction side.
Figures 10 and 11 show the pressure contoursfrom a back view. Low pressure areas on the pressureside of the blades are displayed at the propeller trailingedge near the tip, which suggests that in the originalblade the trailing edge is somewhat bent in order toreduce the pitch. Figure 12 shows a detail view of theblade pressure side. A low pressure peak is seen at thetrailing edge.
Figures 13 and 14 show respectively a top andbottom view of the ducted propeller unit with therudder. The limiting streamlines are shown on the solidsurfaces. Flow detachment is illustrated on the outer
Figure 7. Pressure distribution on the ducted propellerwithout rudder. J=0.526
Figure 8. Pressure distribution on the ductedpropeller and rudder surfaces. J=0.526
Figure 9. Pressure distribution on the ductedpropeller and rudder surfaces. Starboard side.J=0.526
Figure 10. Pressure distribution on the ductedpropeller without rudder. Back view. J=0.526
Figure 11. Pressure distribution on the ductedpropeller and rudder surfaces. Back view. J=0.526(The rudder is not shown to facilitate the illustration)
Figure 12. Detail of pressure distribution on thepropeller trailing edge on the pressure side of theblade. J=0.526
Figure 13. Limiting streamlines on the duct and ruddersurfaces. Top view. J=0.526
Figure 14. Limiting streamlines on the duct and ruddersurfaces. Bottom view. J=0.526
Figure 15. Arrows indicating the flow direction on aplane perpendicular to the rudder symmetry plane atan axial location near the midchord of the rudderprofile. Front view. Arrow tips in red. J=0.526
surface of the duct both at the leading edge area and atthe trailing edge in front of the rudder. This situation isexpected to be less severe at full scale.
Two vortical structures can be identified on therudder surfaces in Figures 13 and 14 as a concentrationof streamlines near the trailing edge. They arevisualized in Figure 15 where arrow vectors show theflow direction on a plane perpendicular to the ruddersymmetry plane at an axial location near the midchordof the rudder profile. They result from the impinging ofthe rotating flow on the rudder surfaces. The delayedcontraction of the flow is apparent from the directionof the flow at the periphery of the picture.
ALTERNATIVE DESIGN
A set of alternative ducted propeller designs wereprepared. This section describes one of them.
Figure 16. Pressure distribution on the ductedpropeller and rudder surfaces. Alternative design. Portside. J=0.526.
Full scale measurements provided input data forthe calculations made to estimate the pitch reductionrequired to meet the new engine conditions. A radialchord and skew distribution of Kaplan type was chosenfor the blade. The rake for the new design was that ofthe existing propeller. In this way the relative locationof the propeller inside the duct remains unchanged.The design shown in this section was made usingNACA a=0.8 camber line with NACA 16 thicknessform. The maximum thickness at each section was thatof the existing propeller. A vortex lattice lifting surfaceapproach was used for the final adjustment of the newpropeller geometry particulars.
Figure 17. Pressure distribution on the ductedpropeller and rudder surfaces. Alternative design.Starboard side. J=0.526.
Figure 18. Pressure distribution on the ductedpropeller. Alternative design. Back view. J=0.526.(The rudder is not shown to facilitate the illustration.)
Figures 16 and 17 show the pressure contoursfrom a port and starboard view, respectively for thenew design propeller. The low pressure areas at theleading edge of the old propeller are shifted towardsthe midchord in the new design and the low pressurepeak is reduced. Low pressure areas on the rudderleading edge caused by the propeller inducedcircumferential flow are smaller for the new design dueto the reduced propeller loading. Such areas are visibleon the upperleft and lowerright side of the rudder.
Figure 18 shows the pressure contours from aback view for the new design propellers. Irregularities
on the pressure distribution such as a low pressurepeak at the trailing edge and tip in the existing oldpropeller have been now corrected. Figure 19 showsthe blade pressure side in a detail view. A smootherpressure distribution is apparent in the new design.
Figure 19. Detail of pressure distribution on thepropeller trailing edge on the pressure side of theblade. Alternative design. J=0.526.
Figure 20 is indicative of the behavior from thecavitation standpoint of the existing propeller withoutand with rudder and of the new design. Areas belowthe vapor pressure are shown in white. The rudderincreases somewhat the cavitation at the blade tip dueto the decrease of the effective advance number at thepropeller plane. Contrary to the existing propeller, thenew design is displayed almost free of cavitation at thedesign condition.
DISCUSSION OF RESULTS
The flow around a ducted propeller with rudder isbasically unsteady. Some simplifications can be madeto reduce the computational times in a flow simulation,namely using either a quasisteady (multiple referenceframe) or a mixingplane approach. In principle aquasisteady RANS calculations differ in manyrespects from quasisteady calculations based on panelmethods. In quasisteady RANS methods an additionalprovision should be made, not present in panelmethods, for minimizing possible numerical blockageeffects induced by the interface between rotating andnon rotating blocks. This effect will be stronger whenthe interface is located too close to solid boundaries.Solid boundaries in downstream blocks seem to bemore sensitive to blockage than those in upstream
Figure 20. Comparison of low pressure areas for theexisting propeller without rudder (above), with rudder(middle) and new design with rudder (below). J=0.526.
blocks. Such numerical blockage is also present in themixingplane approach.
Additionally the quasisteady approach presentsnonphysical features. E.g. any flow disturbance froman upstream nonrotating block seems to rotate whentraveling through the downstream rotating one. Thismeans that if a propeller is calculated in the presenceof a nonhomogeneous inflow by a quasisteadyapproach, the axial location of the interface betweenthe rotating and nonrotating part will determine theangular position at which the nonhomogeneity willmeet the propeller blade. An additional remark is thatthe simplified numerical approaches cannot be used inoblique flow. Therefore they should be used carefully,being aware of their application limits.
Speaking now about physical blockage, the effectof the duct in principle is to increase the flow blockageon the propeller as compared to the blockage resultingfrom an open propeller. In a ducted propeller workingat moderate advance numbers the contraction of theflow is delayed to the duct trailing edge. Usually thephysical blockage produced by a rudder is expressed asa function of the distance of the rudder leading edge tothe propeller. For ducted propellers an effectivedistance between propeller and rudder could be definedtaking as reference distance to the rudder the ducttrailing edge instead of the propeller plane. For thisparticular case such distance is very small, whichpartially explain the large blockage effect present inthe calculations. Additionally some numerical blockagemay still be present.
The steady state calculations of the ductedpropeller without rudder show good correlation of thetotal thrust coefficient, however the torque coefficientis underpredicted in about 6.5 percent. This trend issimilar to that presented in SánchezCaja et al (2000)for a ducted propeller at the design advance number,where the correlation of torque was somewhat better.
Two vortical structures typical in propellers withrudders were identified using the quasisteady method.They result from the impingement of the propellerinduced rotating flow on the rudder surfaces and aremanifested as a concentration of streamlines near therudder trailing edge on each side of the rudder surface.They are similar to those observed in measurementsusing PIV technique. Flow detachment was visible onthe outer surface of the duct.
Changes in pressure distributions between thecomputations made without and with rudder are morevisible on the propeller pressure side. However, ablockage effect on cavitation is apparent in thecalculations. The low pressure area is larger for theducted propeller with rudder due to the larger flowangle of attack at the tip region caused by the rudderblockage.
CONCLUSIONS
The flow around an existing old propeller of areference fishing boat has been analyzed using RANScode FINFLO. The analysis provided enough insight toidentify the major issues to be accounted for in thedevelopment of the new propeller design. In particular,low pressure areas of interest from the standpoint ofcavitation, areas of flow detachment and vorticalstructures were identified. An alternative design basedon NACA sections was made to correct irregularities inthe shape of the old propeller and meet the new designcondition. The new design was derived from existingfull scale measurement on the old propeller and RANScalculations were used to check the quality of the newgeometry.
The calculations revealed the appearance of aphysical blockage effect at the propeller plane due tothe presence of the rudder. The presence of the ductseems to increase the blockage effect from that existingin a conventional propeller. Additionally a nonphysical blockage in quasisteady and mixingplaneapproaches was identified as a function of theproximity of the interface between rotating and nonrotating blocks to solid boundaries. In order tominimize the latter blockage the interface should belocated far from solid boundaries. Several locations ofthe interface between rotating and nonrotating blockswere investigated.
ACKNOWLEDGEMENTS
This work has been made within the European UnionSUPERPROP project. The authors wish to thank thepartners in the SUPERPROP consortium. Specialthanks are given to PESCANOVA for providing thegeometries subject to investigation.
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