This paper discusses several modelling aspects that are important for the performance predictions of a ducted propulsor with a low-order Panel Method. The aspects discussed are the alignment of the wake geometry, the influence of the duct boundary layer on the wake pitch, and the influence of a transpiration velocity through the gap. The analysis is carried out for propeller Ka4-70 operating without and inside a modified duct 19A, in which the rounded trailing edge is replaced by a sharp trailing edge. Experimental data for the thrust and torque are used to validate the numerical results. The pitch of the tip vortex is found to have a strong influence on the propeller and duct loads. A good agreement with the measurements is achieved when the wake alignment is corrected for the presence of the duct boundary layer.

A low order potential based panel code is used to analyze the flow around the blades of a horizontal axis marine current turbine. An empirical vortex model is assumed for the turbine wake, which includes the variation of pitch of the helicoidal vortices trailing behind the blades. The analysis is carried out for uniform inflow conditions in steady flow for a turbine with controllable pitch for two different pitch settings in a wide range of tip-speed-ratios. Grid convergence studies carried out to verify the accuracy of predicted pressure distributions and integrated forces show a fast convergence with grid refinement for this geometry. The effect of the helicoidal wake model parameters used in the analysis is found to have a strong influence in the performance curves. The results are compared with experimental data from literature and with the lifting line theory. A discussion of viscous effects is also provided to help explaining the main discrepancies with the data.

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A formal error analysis of the order of approximation of a potential based boundary element method (BEM) for two-dimensional flows is performed in order to derive consistent approximations for the potential integrals. Two higher-order approaches satisfying consistency requirements to attain second and third order convergence in the potential are selected for numerical implementation. From the formal local expansions of the potential integrals the influence coefficients are derived and evaluated analytically. In order to assess the methods accuracy, the low and higher-order methods are applied to two-dimensional steady flows around analytical foils. A numerical error analysis is done and a comparison between their theoretical and numerical asymptotic order of accuracy performed. IntroductionBoundary element methods (BEM) have been used successfully for many years in the solution of compressible and incompressible inviscid flows around complex configurations, [8]. In the aerodynamic and hydrodynamic fields, these methods, also known as panel methods, have matured to a level which allows their use as design tools on a routine basis. In spite of the success achieved in many hydrodynamic applications, there are situations where BEM computations may still pose considerable challenges, both from the modelling and the computational points of view. This appears to be the case in the non-linear computations of partial and super-cavitating flows on hydrofoils and marine propellers, e.g. [10,12]. From the computational point of view, BEM solutions of such flow problems require the use of accurate and efficient numerical algorithms which need to be applied on considerably fine grids. Maskew, [13], has shown that the low-order potential based BEM, [9,15], was able to provide solutions for the pressure distribution with accuracy comparable to higher-order methods for a small number of panels. However, in non-linear computations of cavity flows on foils accurate solutions may only be obtained with a large number of elements, especially in regions of high geometry curvature, such as the leading edge and the cavity closure region, [2,5]. This still involves large computation times in the three-dimensional flow case, which makes its application in design studies rather time consuming. In such situations higher-order methods may become attractive to further reduce computation times.In the present paper, we concentrate on the application of higher-order boundary element methods to the twodimensional case of the steady incompressible potential flow around foils in the absence of cavitation. The work of Kinnas and Hsin [11] showed that the rate of convergence of the low-order BEM on foils is slow due to the effect of the local error on the sharp trailing edge. Therefore, significant improvements are expected from higher-order BEM formulations. Such improvements may turn out to be of practical relevance in the application of the method to the computation of 2D unsteady cavitating flows needed for design purposes. Our objective is to inv...

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SUMMARY This paper discusses the estimation of discretization errors on the basis of power series expansions for grid sets that are not geometrically similar, that is, grids not exhibiting a constant grid refinement ratio for the entire computational domain. Simple test cases with structured and unstructured grids are used to demonstrate that reliable error estimates on the basis of power series expansions can be made if the grids are refined systematically. However, if the grid refinement ratio is not constant in the complete domain, the definition of the typical cell size is not obvious, and the observed order of accuracy may not be equal to the expected theoretical order of the discretization. Some alternatives for the definition of the typical cell size are tested. In these tests, the error estimation does not show a significant effect of the definition of the typical cell size even for some cases with data sets clearly outside the ‘asymptotic range’. For non‐geometrically similar grids, the best estimates of the observed order of accuracy are obtained with the typical cell size on the basis of the mode of the cell size (the cell size that occurs more often in a given grid). Copyright © 2012 John Wiley & Sons, Ltd.

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