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(9)
“Pure yaw”: The model travels through the tank while it performs a pure yaw motion, where it is forced to follow the tangent of the oscillating path. In terms of velocities this means that v=0, while r and u oscillate harmonically. u oscillates, since the carriage speed in the present set-up is constant. “Yaw and rudder”: Same as “Pure yaw” but the rudder is deflected. “Yaw and drift”: The model travels through the tank, while it performs a pure yaw motion as described in “Pure yaw”. However, a fixed and preset drift angle is overlaid on the motion in order to obtain a drift angle relative to the tangent of the oscillating path. In terms of velocities this means that v≠0, but constant, while r and u oscillate harmonically. For all of the above conditions, the tests were conducted according to FORCE’s standard PMM testing procedures. This means that the model was constrained in all degrees of freedom except for heave and pitch to account for dynamic sinkage and trim. The PMM setup is shown in Figure 1. During the test the model is equipped with propeller and rudder. The propeller RPMs are kept constant at the model’s self propulsion point. The model is shown in Figure 2 and Figure 3, where the sand strips used for turbulence stimulation can also be seen. The PMM test program is carried out for speeds down to 0.35U0 corresponding to a Froude number of 0.091. The test program carried out including the repeat tests for the uncertainty assessment are shown in Table 2. During the test the instantaneous operatingconditions for the ship like speeds, positions etc. aremeasured together with the resultant forces. All forcesare measured in a coordinate system following the ship,meaning that X-components act in the longitudinaldirection of the ship (positive forward) and Y-components perpendicular to this direction (positivestarboard). The yaw moment is taken with respect tothe mid-ship position at ܮ/2. All hydrodynamicforces and moments presented in the present work arenon-dimensionalized by the data reduction equationsshown below. It should be mentioned that for the staticconditions, the hydro dynamic forces and moments areequal to the measured quantities, i.e. (6) ܺᇱ, ܻԢ and ܰԢ are the longitudinal force, the transverse force and the yaw moment, respectively. ߩ is the water density. ܷൌ √ݑଶ ݒଶ is the ship speed, where u and v are the surge and sway velocities respectively. r is the yaw rate. Finally, the dots above the velocity quantities indicate the corresponding accelerations. See Figure 4. ܶ and ܮ are the mean draft and the length between perpendiculars. ܯ and ܫ are the mass and moment of inertia of the model, i.e. of the model itself, the gauges and the ballast weights. ܺீ and ܻீ are the X- and Y-distances from the center of gravity of the model to the point, which the model rotates around. A part of the experimental work also covered assessment of the experimental uncertainty. Following the approach in ITTC 1999a and b and Simonsen 2004 the uncertainty assessment, which covers both precision and bias limits, is based on the data reduction equations for the forces and moments listed above. The uncertainties are expressed as 2 2 2' ' 'X X X P B U (7) 2 2 2' ' 'Y Y YP B U (8) 2 2 2' ' 'N N N P B U (9) B and P are the bias (systematic errors) and precision (random errors) limits, respectively. The bias contributions are found by sensitivity analysis of the data reduction equations and error estimates related to the inpidual components of the measurement system, The bias limits are assessed based on a study of the measuring system. According to ITTC 1999a they can be estimated on the basis of JiJiJi kik k i i i r B B B11112 2 22 (10) where ߠ is the influence coefficient defined by iiXr (11) ܤ is the bias limits in ܺ and ܤ is the correlated bias limits in ܺ and ܺ . Lk i ik B B B1) ( ) ( (12) where ܮ is the number of correlated bias error sources that are common for measurement of variables ܺ and ܺ. The bias error for each variable in the data reduction equation may consist of a number of bias errors, so in order to calculate the combined bias error the root-sum-square is used Jkk i iB B12 2) ( (13) ݅ is the number of the considered variable in the data reduction equation. The precision limits are assessed through repeated tests, which are built into the test program. The model has not been dismounted from the carriage during the test, so in order to “disturb” the system the repeat tests has been mixed with the other test configurations. According to ITTC 1999a the precision limit is estimated from MSP rr2 (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