Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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A Potential Based Panel Method for the Unsteady Flow Around Open and Ducted Propellers
A Potential Based Panel Method for the Unsteady Flow Around Open and Ducted Propellers
Pages 667-686
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From page 667... ...
It combines an unsteady lifting surface method for the propeller with a potential based panel metl~od for the duct. The propeller is essentially treated with an existing time marching vortex lattice scheme which has been developed for open propellers, with the effects of the duct being accounted for via the generalized images of the propeller singularities with respect to the duct.
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From page 668... ...
The nun~erica,1 method is also shown to be consistent with existing analytic solutions as well as with an unsteady lifting surface method. Finally, a hybrid lifting surface / potential leased panel method is developed for the analysis of unsteady flows around ducted propellers.
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From page 669... ...
The panels in the wake start from the blade trailing edge and their edges are located on the prescribed wale surface at equal angular spacing AOltr, which is related to the time step At as follows: ~61~,~.' = wAt.
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, are taken equal to those on the key blade at an earlier time step, when the blade It' was at the place of the key blade. This scheme, already used in an unsteady propeller lifting surface vortex lattice method [19]
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Instead of inverting the system of equations 25 at each time step, the following technique of base problems is developed and implemented: 2For a discretization with N = 40 and llI = 20 the computing time on an IRIS 4D/25 TO is approximately equal to four hours.
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uniform factor. The resulting spanwise circulation distributions are extra.polated to zero thicl;ness and Glen compared with the results from applying an unsteady lifting surface method to the zero thickness wing (or propeller)
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First, the sensitivity of the method to the size of the time step, i\t, is investigated, when a, constant strength dipole distribution is utilized in the first wake panel. The results, shown in Figure 7, appear to be very de pendent on the ratio of the length of the first wake panel UL\t to the length of the trailing edge panel ~XT.
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0 300. 0 wt Figure 13: Convergence of the unsteady propeller panel method with time step size.
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From page 675... ...
Both the propeller and duct surfaces must be panelled and unsteady wal;es must be shed from the trailing edges of the propeller blades and duct. In the present work, we model the duct with a potential based panel method and the propeller with a lifting surface vortex lattice method which will be described in Section 4.
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From page 676... ...
One way of analyzing the unsteady flow around the ducted propeller is by treating the duct and propeller as one body and by employing a time marching scheme similar to that described in Section 2.2. Instead, in the present work, we only treat the propeller with a time marching lifting surface scheme with the effects of the duct on the unsteady propeller flowfield being a,ccounted for via the generalized images of the propeller singularities with respect to the duct.
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From page 677... ...
Step 3 The unsteady propeller lifting surface method, described in Section 4, is then applied as if the propeller was open, but with the following modifications in order to take into account the duct: · The propeller inflow is taken equal to qD, as computed in Step 1. The propeller to propeller influence coefficients, velocities A, are modified by adding to them the corresponding generalized ima.ge influence coefficients, qi, which were computed in Step 21~.
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has shown that the vortex lattice lifting surface representation of the propeller blades described here follows naturally from the potential-based method described in Section 2. Differentiating equation (3)
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The geometry of the wale sheets is prescribed. The angular extent of the panels is equal to that swept out by the blade in one time step except that the wake panel adjoining the trailing edge is one quarter this size.
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Previous implementations of vortex lattice lifting surface models have obtained blade forces from the "rotating bedspring" analogy (a term coined by J
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4. 2.2 Leading Edge Suction As a consequence of idealizing the propeller blades as zero thickness surfaces we introduce a singularity in pressure at the leading edge.
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5 Conclusions A time marching potential based panel method was presented for the analysis of the unsteady flow around open marine propellers subject to spatially nonuniform inflows. An efficient algorithm is implemented in order to ensure an explicit Rutty condition (i.e.
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From page 683... ...
The method combines an unsteady lifting surface method for the propeller with a potential based panel method for the duct. The propeller is treated with a time marching vortex lattice scheme as if the propeller were open.
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Lee. A potential based panel method for the analysis of marine propellers in steady flow.
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From page 685... ...
Thus, the generalized image coefficients depend only on the geometry of the duct and propeller and do not need to be recomputed for each time step in the propeller solution or for a different inflow. The primary reasons for selecting the generalized image technique as opposed to a direct duct and propeller time marching solver are mentioned in Section 3.1.
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