fit through the experimental values, the filled symbols the ReFRESCO (RANS) results and the open symbols the PROCAL (BEM) results.
Verification and validation Since the use of any numerical method requires a thorough analysis of the numerical errors involved, an example of the estimation of the numerical error and uncertainty is here presented. The uncertainty of a numerical calculation can be addressed using well-established procedures
for
verification [7]. There are also modern validation procedures [7], with permit quantitative comparisons between numerical and experimental data. Tese are also here applied. For the E779A propeller an uncertainty
analysis has been performed at the design point for which a range of geometrically similar grids with varying grid densities was required. Te variation of thrust, torque and open-water efficiency for the different grids, ranging from 1.5 to 24 million grid cells, is presented in Figure 2. Te corresponding
Figure 3: Flow field analysis of E779A (top), skewed (bottom left) and ducted (bottom right) propeller. For the E779A propeller the development of vortices in the numerical domain is visualised. For the skewed and ducted propeller the limiting streamlines and pressure distribution, respectively, are shown.
values of uncertainty for different open-water characteristics follow from the numerical uncertainty procedure and are in the order of 3-5% for the design condition. From Figure 2 it follows that for different
grid densities a considerable variation in thrust and torque characteristics was found, especially for the torque on coarse grids. For practical purposes a grid of about 10 million cells (full propeller) was chosen for evaluation of the open-water diagram. Te open-water characteristics differ only slightly compared with the results for the finest grid, but the computational effort is greatly reduced. The simulation can be considered
validated when the difference between experimental and numerical result is within their combined uncertainty. Te uncertainty
Figure 2: Variation of thrust (KT), torque (KQ) and open water efficiency (η0) with number of grid cells Ncells in (M)illions. The variation for different grids is used to determine the numerical uncertainty (U).
The Naval Architect July/August 2011
of the experimental results is assumed to be 1.5% in thrust and torque, based on in-house studies taking into account the reproducibility of different test runs, manufacturing tolerances and uncertainties of the sensors. The deviation between ReFRESCO and experimental results for the design condition was in the order of 1-4% for the open-water quantities, see Figure 2. Tis is within the combined uncertainty, therefore, validating the numerical solution for this condition. Considering a similar level of uncertainty for the other advance ratios, the open-water results are validated for the major part of the open-water diagram.
Flow field analysis A great benefit of CFD is the amount of detailed flow data available from the numerical simulations. Next to propeller pressure distributions and field velocities, viscous-flow related phenomena, such as separation areas and the development of vortices can be visualised and studied.
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