Influence of Mesh in Open Water Propeller Blade CFD

Figure 1: Structured multiblock grid for Potsdam propeller blade.

1700 words / 8 minutes read

Introduction

In the previous article on open water propeller blade, we covered aspects of the domain, zones, and interfaces, boundaries conditions, grid refinement, in particular the wake, blade tip refinement to capture the cavitation vortices. In this final article in the series, we try to address aspects of grid influences on the solution flow field, including, grid uncertainty analysis for wetted vs cavitating flows conditions, mesh refinement studies using both sequential grids and adaptively refined grids and lastly model vs full-scale propeller blade performance.

Video 2: Cavitation CFD simulation using MARIN ReFRESCO solver.

Uncertainty Analysis of Wetted vs Cavitation Flows

Overall, the grid uncertainty levels of both wetted and cavitating results are low and is less than 1 percent. But the main difference between them is in the order of convergence of performance coefficients, which is low for the cavitating case than wetted flow. In wetted flow conditions, since grid sensitivities mainly occur around the blade tip, the thrust converges more slowly than torque. Figure 2 shows the radial distribution of thrust coefficient for the two cases.

Radial thrust loads in wetted and cavitating conditions — **Figure 2: a**. Comparision of radial thrust loads in wetted condition on various grids. b. Comparison between radial thrust loading for wetted and cavitating conditions. Image source ref [4].

Radial thrust loading prediction improves with grid refinement for wetted flow case, with the main differences observed closer to the blade tip. With refinement, the leading edge vortex resolution improves thereby modifying the pressure distribution and radial loading distribution. But after the level 3 grid, the improvement is marginal. For the cavitation case, the influence of grid refinement is even less, resulting in slightly lower uncertainty numbers.

Figures 2a and 2b show the comparison for the two cases. The reduction in tip loading for the cavitating case is quite evident. This is mainly because of the presence of sheet cavitation which lowers the suction peak strength and leading-edge vortex. Interestingly, even though the suction peak close to the tip is absent compared to the wetted flow condition, a larger lower pressure area exists due to the cavity.

Grid Refinement Study ( GCS and AGR)

**Figure 3:** Cavitation observed in the experimental setup. Image source ref [4].

Grid sensitivity studies have shown a steady convergence in prediction accuracy with grid refinement. The results predicted by coarse grids emphasize the importance of grid density and refinement. Refinement can be done globally by generating a sequence of grids, while it can be done locally by applying adaptive grid refinement.

One region which shows remarkable improvement with grid refinement is the tip vortex region, where the cavity extensions are visibly significant with successive grids. One noteworthy aspect is that, even though the cavity extent is limited by the increasing eddy viscosity when using RANS, adaptive grid refinement aids in better capturing of tip vortex cavitation with lesser total cell count.

In fact, one researcher concludes in a paper that, the grid resolution is more important than cavitation modeling parameters when predicting the inception of tip vortex cavitation.

Cavity extents for three different grids visualised using isosurfaces of the vapour volume fraction — **Figure 4:** Cavity extents for three different grids visualized using isosurfaces of the vapour volume fraction. Image source ref [4].

Vapour Volume Uncertainty Analysis

This analysis helps to examine the effect of grid refinement on cavitation flow prediction. Figure 4 shows the cavity extents for 3 different grids refined at a rate of 1.5, visualized using iso-surfaces of vapour volume fraction.

From Figure 4, it can be observed that the form of the sheet cavity is less sensitive to grid refinement. This is somewhat expected, as given the low grid uncertainty of the thrust, which is directly related to the pressure distribution on the blade.

However, the tip vortex cavity shows a large grid dependency. For the first grid, there is no noticeable tip vortex cavitation. For the second refined grid, the tip vortex begins to cavitate. For the third refined grid, the cavity extension increases. On the finest grid, one can observe that the vortex rolls-up and form the characteristic ‘necked’ appearance.

Propeller - contour of vapour volume fraction near blade tip — **Figure 5:** Contour of vapour volume fraction. Image source ref [4].

Analysis of the Cavitating Flow Field

Even though the predicted sheet cavity shape did not appear to vary significantly with grid refinement, the variation on a 2D slice shows more subtle differences as shown in Figure 5. Here, the liquid-vapour interface and re-entrant jet resolution become sharper with refinement.

Propeller vapour volume fraction distribution — **Figure 6:** Vapour volume fraction. Image source ref [4].

Propeller pressure coefficient distribution — **Figure 7:** Pressure coefficient. Image source ref [4].

propeller eddy viscosity ratio distribution — **Figure 8:** Eddy viscosity ratio. Image source ref [4].

Further analysis of the effect of grid refinement on the cavitating tip vortex is made in Figure 6-8, where slices of the vapour volume fraction, pressure coefficient, and normalized eddy viscosity are shown at an axial station in the propeller blade wake, 0.05D downstream of the propeller plane. As anticipated, grid refinement brings remarkable improvement in predicting tip vortex cavitation. As seen in Figure 7, the minimum pressure inside the vortex gets reduced significantly with refinement. Just a grid refinement ratio of 2.4 was good enough to develop a much-extended tip vortex.

Adaptively refined grids for propeller — **Figure 9:** Views of the adapted grid. The helix shown represents cells refined during the third refinement stage. Image source ref [4].

Adaptive Grid Refinement

Improvement in predicting tip vortex cavitation can be done using adaptive grid refinement with fewer grid cells.

By comparing Figure 10 and Figure 4 with Figure 3, one can appreciate the differences between computations with and without adaptive grid refinement. The tip vortex cavity extension in the L1 adaptive grid is of similar length to that obtained on the finest grid in the sequential family (Figure 10a). With further increase in local refinement, not only does the tip vortex cavitation becomes longer, but the roll-up of the tip vortex also gets better resolved (Figure 10b,10c).

**Figure 10:** Cavity extents for different combinations of adapted grid. Cavity visualized using isosurfaces of the vapour volume fraction. Image source ref [4].

Interestingly, with more and more refined grid cells inside the tip vortex, the eddy viscosity increases significantly with RANS solvers. This has a negative impact on the predicted cavity extent and hence many researchers conclude that RANS is not suitable for tip vortex prediction especially when the focus is on the dynamics.

Model vs Full-Scale Performance

Contrary to intuition, solutions obtained on a model scale cannot be extrapolated to the real-life full-scale propeller model. This is rightly so because with increase in geometry dimensions the Reynolds number at which computations are done increases and as a consequence, the flow patterns also change significantly. The numerical predictions performed at the model scale are more challenging than those at full scale due to the simultaneous cohabitation of laminar and turbulent flow regimes and the subsequent difficulty in the accurate prediction of the transition from laminar to turbulence in the computations.

Also, the propeller blade performance characteristics vary between the model and a full-scale geometry. Analysis of the results shows that the full-scale simulations yield a bit higher thrust coefficient, a slightly lower torque coefficient and consequently a higher open-water efficiency. It is interesting to note that, just like the model-scale, full-scale propeller efficiency does not show a great dependency on the grid density and the performance characteristics converge monotonically towards the experimental values.

**Figure 11:** Comparison of near-blade cavitation results with different grid densities. Image source [10].

Just like the solutions from the model scale cannot be extrapolated to the full-scale models, the model scale grid also cannot be scaled to fit full-scale geometry. Though the surface mesh and outer volume mesh can be scaled, the boundary layer needs to be regenerated as the Reynolds number perceived by the full model is much higher. At higher Reynolds number, the total thickness of the boundary layer reduces and so also the first spacing.

Figures 11, 12 show the near-blade and overall cavitation predicted on different grid densities for both model and full-scaled propeller blade. As can be observed from Figure 11, near-blade cavitation is quite similar to each other on various grids. On all grids, sheet cavitation develops at the leading edge which then transforms to tip vortex cavitation. The root cavitation also grows in extent with increase in grid resolution but only marginally. Looking at Figure 11, it will be safe to say that the near-blade cavitation is mostly independent of the utilized grid densities.

Comparison of cavitation patterns for the PPTC propeller with different grid densities — **Figure 12:** Comparison of cavitation patterns for the PPTC propeller blade with different grid densities. On the left: model-scale simulations. On the right: full-scale simulations. Image source [10].

However, visible big differences in the prediction between different grids can be observed in the propeller blade wake as shown in Figure 12. On a coarse grid, very limited vortex cavitation is seen, with the tip vortex cavitation seizing just after the blade trailing edge. In the medium grid, the tip vortex cavitation extends more than in the coarse grid but is less than one diameter in the axial direction and the modal shapes are barely distinguishable. Fine grids predict a well-established vortex cavity extension with proper modal shapes.

However, we do not see such a clear grid density influence in hub vortex cavitation. The hub vortex predicted by the medium grid matches very well with fine grid results and experiments.

**Figure 13:** Pressure coefficient in the track of the tip vortex with different grid densities. The figure on the left shows the fine grid simulations and the track as a dashed line along which the Cp is evaluated. Image source ref [10].

Figure 13 shows the pressure coefficient (Cp) comparison on various grids in the wake at the track of the tip vortex. The pressure minima is greater for the coarse and medium grids as the axial distance from the propeller increases. The Cp in the first vortex core for the coarse grid is significantly less than the vapor pressure and therefore the tip vortex cavitation terminates just after the blades. For the medium grid, the first tip vortex core on the curve maintains a low Cp level and a cavitation vortex as seen in Figure 12b develops. Beyond this point, the Cp decreases and the tip vortex cavitation disappears.

Parting Thoughts

As these results emphasize, local refined grids bring in a significant improvement in flow feature prediction and which in turn makes the flow parameter prediction more accurate and compares well with the experimental results. Whether the refinement is through sequential grids or by adaptive grid refinement, the benefits of such an exercise are quite evident as underscored in this article.

References

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10. “Cavitation on Model- and Full-Scale Marine Propellers: Steady and Transient Viscous Flow Simulations at Different Reynolds Numbers”, Ville Viitanen et al, Journal of Marine Science and Engineering, 2020, 8, 141.

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