FD生成的PMM数据在初步设计阶段进行评估英文文献和中文翻译(3)
(14) where ܯ is the number of repeats and the factor of 2 is applied for ܯ10. ܵ is the standard deviation defined as ½121) ( MkkrMr rS (15) Here ݎ is the value from each repeat test and ݎ is the mean value of all the quantities from the repeat tests. ݎ is defined as Mkk rM r11 (16) Table 3. Uncertainties for “static drift”, β=8°, Fr=0.201. X’ Y’ N’ ܤ´0.000736 0.000798 0.000285 ܲ´ 0.000214 0.000246 0.000047 ܷ´ 0.000766 0.000836 0.000289 ܦ´ 0.0180 0.0397 0.0127 ܷ݅݊%ܦ´ 4.26 2.10 2.28 The uncertainty assessment procedure is very extensive and is not described here. It has only been done for a few conditions as spot checks of the uncertainty level. It is described in details in Larsen (2012). Table 3 and Table 4 show the results of the uncertainty assessment for the “static drift” case with ߚൌ8, and “static rudder” case with ߜൌ10, respectively at model speed of 1.318m/s, i.e. 0.775U0. Table 4. Uncertainties for “static rudder”, δ=10°, Fr=0.201. X’ Y’ N’ ܤ´0.000724 0.000705 0.000228 ܲ´0.000160 0.000408 0.000218 ܷ´ 0.000742 0.000815 0.000316 ܦ´ 0.0165 0.0150 -0.0077 ܷ݅݊%ܦ´ 4.50 5.45 4.11 29th Symposium on Naval Hydrodynamics Gothenburg, Sweden, 26-31 August 2012 The level of the uncertainties is higher than for a resistance test, but this is to be expected since the PMM test is conducted with a two-gauge system, which typically gives higher uncertainties than a single gauge system. The uncertainty level seems reasonable and the level is comparable to other to PMM tests in Benedetti et al. (2006), Yoon (2009) and Simonsen (2004). With respect to the measured data, examples are shown in Figure 8 to Figure 19 in the section below, in connection with the discussion of the comparison between computed and measured PMM data. Data generation based on CFD computations The CFD computations in the present work are supposed to replace both dynamic and static PMM conditions. However, at present time of writing the dynamic conditions are not completed, so only results for static cases are covered. Computational method The computations are performed with the Reynolds Averaged Navier-Stokes (RANS) solver STAR-CCM+ from CD-adapco. The code solves the RANS and continuity equations on integral form on an unstructured mesh by means of the finite volume technique. Both steady state and transient calculations are considered depending on the considered test condition. For the steady state calculations the temporal discretization is based on a first order Euler difference, while a second order difference is used for transient calculations. Spatial discretization is performed with second order schemes for both convective and viscous terms. The pressure and the velocities are coupled by means of the SIMPLE method. Closure of the Reynolds stress problem is achieved by means of the isotropic blended k-ε/k-ω SST turbulence model with an all Y+ wall treatment, which depending on the Y+ value selects the near wall treatment. The rotating propeller is not modelled directly, as this requires very long computational times that are not realistic when computing a large number of cases. Therefore, a prescribed body force propeller is applied instead as is commonly done for this type of simulations. The propeller model is based on a radial varying body force field, which follows the variation of a theoretically derived circulation distribution. It is prescribed by means of the ship speed based advance coefficient ܬ௩ and the propeller coefficients ܥ் and ܭொ. The model is integrated in the CFD-code, where the axial and tangential force components are given by h*h* *θ θ* *X Xr r rr rA fb , r r A fb ) 1 (11 (17) Where the non-dimensional propeller and hub radii are defined by ) 1 ( ) ( h h*r / r r r and p h h /R R r . With ∆ݔ being the longitudinal extension of the disk pided by the ship length, the coefficients ܣ௫ and ܣఏ are defined by h hThxr r x ΔC A 1 3 4 16105 (18) h h VQθr r π J x ΔKA 1 3 41052