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(5)
(23) where Gestp is the limiting or theoretical accuracy of the applied numerical method, is close to unity, the solutions are close to the asymptotic range. In this case the sign of the error is known, so the numerical error,*SN , benchmark, C S and uncertainty, GC U can be calculated from ) 1 *( *1 G RE G SN C (24) *SN C S S (25) 125 . 0 1 , 1125 . 0 1 , ) 1 . 0 ) 1 ( 4 . 2 (** 211G RE GG RE GGCC CC CUGG (26) If the correction factor is away from unity only the numerical uncertainty is calculated 125 . 0 1 , ) 1 1 2 (125 . 0 1 , ) 1 . 1 ) 1 ( 6 . 9 (** 211G RE GG RE GGC CC CUGG (27) Table 6: % change in non-dim forces and moments between grids. % Change X’ Y’ N’ 3 to 2 -2.74 -4.74 1.14 2 to 1 1.28 -2.12 -0.97 Table 7: Estimated order of accuracy and grid uncertainty. Quantity G p G U G U % 1 S X’ Oscill. 0.00029 1.4 Y’ 2.3 0.00372 2.5 N’ Oscill. 0.00026 0.6 Table 6 shows the change in quantities between grids. It is seen that all quantities are converging as the grid is refined, but both X’ and N’ show oscillatory convergence, i.e. the order of accuracy cannot be estimated. For Y’ Table 7 shows that an order of accuracy of 2.3 is achieved. This is close to the theoretical order of accuracy of 2. Finally, Table 7 also shows the estimated grid uncertainty, which ranges from 0.6 to 1.4 % of the fine grid solution. It should be noted that if the solution for Y’ is corrected with the numerical error, the grid uncertainty can be reduced to 2.3%. In order to validate the computations against measurements, the measured data shown in Table 8 are used. No specific uncertainty assessment was made for the un-propelled 20 degrees static drift case, so the uncertainty estimates from the propelled 8 degrees drift case is applied, by assuming that the percentage in Table 3 is representative for the un-propelled case. Table 8: Measured values and data uncertainty Quantity D D U D U % D X’ -0.0220 0.00094 4.26 Y’ 0.1551 0.00326 2.10 N’ 0.0434 0.00099 2.28 Table 9: Validation investigation. Quantity E=D-S V U E % D X’ 0.00086 0.00098 3.90 Y’ -0.00779 0.00494 5.03 N’ 0.00167 0.00102 3.84 To finally check if Validation has been obtained it is necessary to check if the absolute comparison error E is smaller than the validation uncertainty calculated as2 2D G V U U U , i.e. if the comparison error is within the combined noise from the CFD simulation and the experiments. From Table 9 it is seen that the computation agrees with the measurement within approximately maximum 5%, so the agreement is pretty good taking into account that it is a pretty complex flow field at 20 degrees drift angle. However, in spite of this it is only X´ that is validated. Taking into account that going from medium to fine grids will only change the results with approximately 2% while the computational time will be more than doubled, it was judged that the medium mesh was sufficient for the present study, which has much focus on computation of large data sets for practical application. It should also be mentioned that later in the project it was necessary to increase the mesh size a little in order to have a mesh that work for non-zero rudder angles. Therefore, the final mesh used for the production runs contains app. 3.57 million cells, which is a little finer than the initial medium mesh. It was designed to give a Y+ of maximum 75.5 and an average over the hull of 23.5. After the verification and validation work, all the production runs for the static maneuvers to be used in the simulator model were made. The figures below show comparisons between CFD and EFD for all the computed cases, which cover static drift, static rudder and the combined static drift and rudder conditions. As mentioned earlier only static CFD data will be used as input for the simulator, as the dynamic computations are not finalized at the present time of writing. Figure 8 to Figure 10 show the computed and measured non-dimensionalized forces and moments, X´, Y´and N´ as function of the rudder angle for three different speeds. For X´ it is seen to be close to 0 and negative for the highest speed, whereas it increases to larger positive values as the speed is reduced. This means that the propeller is over-thrusting at the lower speeds. However, based on the applied constant RPM approach, where the propeller RPMs are kept constant at service speed self-propulsion point, the propeller will deliver too much thrust at the lower speeds giving the observed behavior. It is seen that the CFD computations generally predicts X´ fairly well. The slightly larger deviations at large negative rudder angles are probably related to the simplified propeller model not being able to capture the rudder propeller interaction.