Proceedings of the Sixth International Conference on Numerical Ship Hydrodynamics (1994) / Chapter Skim
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Session 14- Lifting-Surface Flow: Propeller/Rudder Interactions, and Others
Session 14- Lifting-Surface Flow: Propeller/Rudder Interactions, and Others
Pages 739-798
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From page 741... ...
Qualitative agreement is obtained between the calculations and the mean-flow data. Although the details of the flow field is different because of the laminar flow computation and numerical treatment, the computational results show the essential feature such as upward movement of propeller slipstream in port side vise versa in starboard side.
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From page 742... ...
For the better understanding and improvement of the performance of such devices, it is advisable to develop the calculation model which can express the phenomena which is observed in experiments. On the other hand, with respect to the time-averaged flow of the propeller slipstream, it is reported that the computed propeller-hull interaction flow field by the method that propeller effect is represented by the body force distribution in the computation code of Navier-Stokes equation shows good agreement with the experimental result in propeller slipstreamed.
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From page 743... ...
3 COMPUTATION 3.1 Governing Equations and Computational Method In this paper, the computation was carried out for the zero thickness flat plate rudder which had same profile as the rudder used in experiment and the time averaged flow using time averaged body force distribution following Stern et al.9. The computation was carried out for steady laminar flow ease because the turbulence model in the slipstream was not elear, the present approach ean not treat the eomplieated unsteady phenomena in the slipstream sueh as blade wake and so on and the grid number was limited due to the memory size of the computer.
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From page 744... ...
Although the computation was carried out for both with and without rudder condition and the loading conditions were a little bit different in experiment, the loading condition for without-rudder condition was used for both condition because the zero thickness plate rudder which had a small displacement effect was used in the computation. Of course, the interactive method using a invicid propeller theory is preferred and the body force should be the function of ~ for the with rudder condition.
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From page 745... ...
4. COMPUTATIONAL RESULTS AND DISCUSSION Axial velocity contours and cross flow vectors of half domain computation for the with and without rudder conditions are shown in Fig.ll and Fig.12, respectively.
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From page 746... ...
At the rudder trailing edge, x=1.23, high velocity region has similar shape as the experimental high velocity region except near the Nat plate. Near the flat plate, the cross plane velocity is small due to the laminar boundary layer and the present computation resolution.
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From page 747... ...
The numerical method and the computational results for the flat plate rudder behind the propeller which represented by body force distribution are also presented. Although the Reynolds number of the computation is small and the number of grid is limited, the salient feature of the flow field for the time-averaged flow field has been predicted by present approach.
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From page 748... ...
Suzuki,H., Toda,Y., and Suzuki,T.: "Numerical Simulation of a Flow Field Around a Flat Plate Rudder in Propeller Slipstream'', Journal of the Kansai Society of Naval Architects' Japan, No.219, 1993 (in Japanese) Table 1.
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From page 749... ...
PROPELLER 330mm l <~_ OPEN BOAT . ; ~ ~ 66mm CIRCULATING WATER CHANNEL Fig.2 Experimental set 749 .
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From page 750... ...
c) 9.00Dp behind propeller Fig.4 Measured axial and C1OSS MOW velocity distributions (Witllout ruclcler)
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From page 751... ...
./, ... '~7' ~ .1.'.( · I ~ / Fig.6 Axial and cross flow velocity distribution at x=0.125 (without propeller and rudder)
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From page 752... ...
VA = 0.63 (mlS) _7.16 (r.n.~.1 Fig.8 Flow visualization of the propeller tip vorticities using air bubblesS 752
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From page 753... ...
. ~ 50 100 150 200 Fig.10 Body force distribution 753
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From page 754... ...
I\ Alp= I'' a) Just behind!
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From page 755... ...
2.13Dp behind propeller Fig.12 Computed axial and cross flow velocity distribution Calf domain computation; with rudder)
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From page 756... ...
r ~ i l J J ~ ~ ~1 c) 2.13Dp behind propeller Fig.13 Computed axial and cross flow velocity distributio (Full domain computation; without rudder)
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From page 757... ...
1 .0 L 1 4 4 ~Y t Y r r r ~· ~L 4 4 ~Y 7 Y V r / ~ ~; ~· ~4 ~4 · · 4 4 ~t Y ~, 4 4 d · ~L t · ~r Y Y ~L ~, ~ 4 4 ~ L L L ~ ~ ~ ~ ~ ~ ~ ~ ~ r t Y ~ 4 ~ ~ ~ ~ c) 2.13Dp behind propeller Fig.14 Computed axial and ClOSS ~OW velocit,~ rlistributio (F~lll domaiIl computation; with 1~clder)
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From page 759... ...
of 3 ~ ~: z= 0545 ~ ~.
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From page 760... ...
r/Rp=O.9 Looking upward Fig.17 Computed streakline of a propeller slipstream (without rudder) 1 4=,~;~ W~to,~O OF · ° O 0 0 0 003 Looking starboard side ~O6~;: {~,~o~;~0;~0~io Looking upward t - Looking starboard side ° O O ~ Looking upstream a)
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From page 761... ...
is 0.3 Fig. 19 Limiting stream line on the rudder surface 761 X
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From page 763... ...
inflow, and r-axis coincident with first blade generatrix. 763 Main Symbols b CL CTh D A Geometric influence coefficient matrix a Radius vector P-S Panel boundary vector Lift coefficient Thrust loading coefficient Propeller diameter Propeller advance coefficient Number of control points Rudder chord length Propeller rate of turn Field point vector Propeller radius Vortex point vector J m p z R S UOO Velocity of uniform parallel inflow Vind Induced velocity Number of propeller blades Hydrodynamic induced pitch angle pi r Circulation Circulation density Acp Load distribution normalized by stagnation pressure of uniform inflow _ _ ~ Vortex segment Si+1 -Si A: Axial separation of helical vortices Rudder angle of attack relative to UOO Velocity potential Aspect ratio Dipole moment density Radius of asymptotic vortex cylinder Mass density of fluid A p p
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From page 764... ...
Moreover, it is assumed that the effect of the propeller slipstream on the rudder, which amounts to a slowly time-varying inflow in the rudder-fixed reference system, can be approximated by discrete quasi-steady steps. For solving the potential equation, dipole singularities are distributed on the rudder center-plane and on the shear layer in the wake emanating from the side edges and the trailing edge; the propeller slipstream is idealized by discrete vortex lines.
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From page 765... ...
The problem becomes considerably more complex if the rudder is located in a propeller slipstream rather than in a uniform parallel inflow. The special case of a rudder in a nozzle was treated by Andrich (1989, 1990, 1991~; however, the structure of free vortices shed by the propeller was prescribed on the basis of experimental observations (LDV measurements)
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From page 766... ...
Thus the free vortex surface is effectively modeled by vortex lines of constant strength which are at the same time also streamlines. Only the bound vortex surface comprises closed vortex rings, each of constant strength, whereby the side edge and trailing edge vortex rings extend to infinity, see Schroder (1979~.
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From page 767... ...
Induced Velocity Field of Vortex Line Basis of a numerical solution in the vortexlattice method is the discretization of curved vortex lines into straight vortices. Each vortex line is replaced by a finite number of straight-line segments so that the integral equation reduces to a summation equation.
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From page 768... ...
For estimating the borderline between near field and far field the entire bound and free vortex sheet can be replaced by a horseshoe vortex since the free vortex sheet rolls up downstream into two tip vortices of equal but opposite circulation. For reasons of symmetry the two free vortex lines of the horseshoe vortex form at infinity a pair of straightlines lying in a plane at an angle to the uniform parallel inflow which is less than the rudder angle of mclc once.
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From page 769... ...
Closed vortex rings on the bound vortex sheet comprise just four panel edge vortex segments, whereas the boundary panels comprise three bound vortex segments and two chains of free vortex segments extending downstream to infinity. In other words, boundary panels are represented by horseshoe vortices.
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From page 770... ...
Computed bounded and free vortex sheets of a rectangular rudder in uniform parallel inflow (A = 0.966; ~ = 15 de")
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From page 771... ...
In the near field discrete vortex lines are aligned to the resultant velocity field. For numerical reasons curved free vortex lines are approximated by straight vortex segments.
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From page 772... ...
thrust loading coefficient CTh, and normalized velocity error bound Far,VC |aF vc| = R ~ CTh (4.6) In the iterative no-force alignment of the free vortex segments of propeller wake a transition range |aTra~ls VC| ahead of the vortex cylinders is specially considered.
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From page 773... ...
(4.8) ETrans,VC This means that every individual vortex line must be continued as a chain of discrete vortex segments over an axial range ~aTra'2s vc~ between the end of the near field and the beginning of the far field.
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From page 774... ...
The basic flow now includes an angular component so that during the iterative alignment of free vortices in the near field the displacement vector from old to new vortex location cannot simply be superimposed onto the remaining downstream vortex segments. The length of the vortex segment remains unchanged during all corrections in the near field.
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From page 775... ...
Their free vortex lines are discretized as chains of straight vortex segments the last of which is semi-infinite. The propeller wake is simulated by helical blade tip and root vortices ending in semi-infinite Figure 11.
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From page 776... ...
In this integral method the rudder skeleton surface and the shear layer separating from the side edges as well as from the trailing edge 776 are discretized in quadrilateral panels. Each panel carries a closed vortex ring of constant circulation.
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From page 777... ...
at the location of the rudder. The effect of propeller slipstream on the rudder load distribution is found by superimposing the 777 vortex models of the rudder and of the propeller wake.
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From page 778... ...
Lift characteristic of rectangular rudder (A = 0.966) in propeller slipstream (Wageningen B4.55R: PID = 0.8; c Th = 2.44~.
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From page 779... ...
Principal results indicate strong unsteady viscous effects with massive flow separation and intensive vertical structures as a result of the leading and trailing edge separation and the further flow evolution. A dynamic stall may occur for some foil motions.
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From page 780... ...
These effects include leading edge separation initiated by the dynamic adverse pressure gradient, massive separation with a strong viscous-inviscid interaction, trailing edge separation and wake distortion. They could be hardly simulated properly by a inviscid model, whose affects on the foil performance might be remarkable.
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From page 781... ...
For the present stucly these factors are the foil motions and some preliminary knowledge for the general flow features which have to be properly modeled. Foil Motion According to the stated objectives, the hydrofoil is allowed to perform ah 2D transient motions; pitching, heaving (plunging)
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From page 782... ...
yl pivot; point location \ ~ Uoo [0 ~ \ To Fig. 1: Coordinate systems definition limited to the laminar 2D flows, highly unsteadiness such as the dynamic changes of the effective incidence angle, strong separation and viscous-inviscid interaction may be expected.
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From page 783... ...
The Fourier transform method is used to solve the stream function equation by a direct approach. The vorticity and stream function equations are solved sequentially.
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From page 784... ...
The simulated flows by the two grid systems are qualitatively identical, although qualitative discrepancies are observed around the leading and trailing edges. The coarse grid system am.
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From page 785... ...
, it appears that we can not proceed with the computations regardless how fine the time step is. For a bit smaller values of parameters of the foil motion, high frequency oscillations in the vorticity field are observed around the leading and trailing edges of the foil.
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From page 786... ...
, the separation over the upper side of foil propagates upstream, while the front stagnation point rolls down (Fig.7 all. Leading edge separation appears long after the effective incidence angle (Jeff)
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From page 787... ...
. Small foil acceleration can not delay the leading edge separation.
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From page 789... ...
(Fig.ll coy. The leading edge vortex formed during the downstroke is finally shed and improves the circulation around the foil to cause a better propulsion.
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From page 790... ...
In this case, leading edge separation is prevented almost completely. However, large trailing edge separation is generated which induces an increase of the drag.
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From page 791... ...
As the frequency of oscillations increases, the inertial terms play a more significant role. Trailing edge separation decreases rapidly when the leading edge separation is negligible (Fig.17~.
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From page 792... ...
Soon after the motion has begun, very small separation bubble formed earlier near the leading edge and a weak trailing edge sep :/;K} \~ Fig. 19: Streamlines in a moving frame (rp = -0.5, k = 3.0, MA = 15°, I*
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From page 793... ...
The trailing edge vortex is shed when the bubble separates in two smaller structures which travel into downstream over the foil.
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From page 794... ...
Its reatt achment leads to a trailing edge vortex. When the foil approaches the position of the maximum amplitude, the case of C4 has a worse efficiency.
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From page 795... ...
Leading edge separation appears earlier and forms a series of vortices (Fig.24 elf. The mean value of the ratio Cx/Cy is very high.
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From page 796... ...
In the case of Re = 1.0 x 103, the leading edge separation vanishes but the trailing edge separation is much stronger. For Re = Lox 104 the leading edge separation is stronger, but the scale is smaller and more intensive.
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From page 797... ...
The foil acceleration is revealed as a major physical parameter for the unsteady and viscous effects. · The ability of an oscillating foil to pro(luce forward thrust is in direct connection with the foil motion and resulted flow.
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From page 798... ...
flow from a general symmetrical motion of a flexible flat plate normal to itself," Journal Fluid Mechanics, Vol.
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