Cavitation and hydrodynamic performance are critical aspects of ABB Dynafin™, ABB’s high-efficiency ship propulsion system, that have been investigated at the VTT Technical Research Centre of Finland via computational fluid dynamics (CFD) [1]. These methods deliver insights that lead to improved designs.

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_{Ville Viitanen, Antonio Sánchez-Caja, Jussi Martio, Ilkka Perälä VTT Technical Research Centre of Finland Ltd. Espoo, Finland

Mika Nuutinen ABB Marine and Ports Helsinki, Finland mika.nuutinen@ abb.fi.com}

The innovative ABB Dynafin is a marine propulsion system that generates thrust by means of blades that project outward from the bottom of the ship. The blades rotate around their own axis and around the axis of the rotatable wheel upon which they are all mounted. The ABB Dynafin can achieve very high hydrodynamic efficiencies and change thrust direction almost instantaneously, giving far better maneuverability than an azimuthing thruster, where a conventional propeller is rotated about a vertical axis to direct thrust.

The ABB Dynafin concept is essentially a cycloidal propeller with individually controlled blades following a trochoidal path →01. (A trochoid is the curve generated by a point on the radius of a circle as the circle rolls on a fixed straight line.) Trochoidal propellers have been studied before, but until now, technology constraints have prevented them from being commercialized and introduced to the market.

Cavitation

Cavitation describes the formation of small vapor-filled cavities, such as bubbles, in a liquid. Cavitation can occur when local static pressure falls below the liquid’s vapor pressure. This undesirable phenomenon often causes noise plus propeller erosion and damage.

Accordingly, to gain a detailed understanding of ABB Dynafin’s hydrodynamic and cavitation performance in a ship-scale context, the VTT Technical Research Centre of Finland and ABB collaborated on a numerical study to investigate a full-scale trochoidal propeller in wetted and cavitating conditions. The analyses are based on transient viscous-flow CFD simulations using both open-source OpenFOAM and the commercial STAR-CCM+ software tools. Cavitation modeling is done using volume-of-fluid (VOF)-based homogeneous multiphase mixture flow models with standard Reynolds-averaged Navier–Stokes (RANS) and hybrid RANS large eddy simulation (RANS-LES) turbulence modeling approaches.

Flow based on Navier-Stokes equations

The homogeneous flow model used is based on the Navier-Stokes equations for two incompressible, isothermal and immiscible fluids with phase change accounted for by mass-transfer models. Liquid flows around an ABB Dynafin blade are turbulent and this situation has to be taken into account. For this task, the popular k – ω shear stress transport (SST) base turbulence model is used [2]. The study also uses a scale-adaptive simulation (SAS), which is a hybrid RANS-LES turbulence modeling method that functions with the SST model [4]. The SAS method has the advantage that it adjusts the turbulent length scale based on local flow.

Mass transfer models

Cavitation is modeled using a mass transport equation for the liquid phase volume fraction. Different mass transfer models can be employed to account for local effects in the flow. Several cavitation mass-transfer models have been developed and typically, the mass-transfer rate is proportional to a pressure difference from saturation pressure. A number of mass-transfer models are available in OpenFOAM and STAR-CCM+ for homogeneous mixture modeling. For the present work, the model described in [5] is used with both solvers.

The flow equations are discretized with a collocated finite volume method. Time-accurate simulations are carried out to resolve the flow field. In the case of OpenFOAM simulations, a first-order implicit scheme is applied for time derivatives, with a time step determined by a maximum Courant number of 1 in the vicinity of the blades. (The Courant number indicates an appropriate size of the time step for a given velocity flow speed range.) In practice, this resulted in physical time steps corresponding to 0.1 to 0.5 ° of the main wheel’s rotation. For STAR-CCM+ simulations, a second-order, three-level implicit scheme is applied for time derivatives. The used time step size corresponded to 1 ° of revolution of the main wheel. For both solvers, all flow variables are discretized using second-order spatial schemes with upwind-biased methods applied for convective terms.

Validate then test

To ensure the validity of the numerical methods, they are tested against two cases for which experimental data and numerical analysis are available:

A four-bladed trochoidal propeller. Here, previous open-water and self-propulsion experiments have been carried out at the VTT towing tank and numerical analysis was performed [6].
A five-bladed cycloidal propeller, for which experimental results are available.

Once it is shown that the methods work in these two cases, the five-bladed ABB Dynafin concept can then be investigated under wetted and cavitating conditions using the same methods. The validation cases were analyzed in model-scale conditions, whereas the five-bladed ABB -Dynafin concept was studied in fullscale conditions. The diameter of the ABB Dynafin device is 3 m, the span of the blades is 3.5 m and a symmetrical blade profile is used.

Results of the validation cases

For the simulations, boundary conditions were set, for example:

The devices were modeled as if inside a rectangular cavitation tunnel.
Flow speed was specified at the inlet and pressure at the outlet.
A no-slip condition was used for the tunnel ceiling and a no-slip moving wall boundary condition was used for the blades.
The sides and bottom of the rectangular domain were modeled as slip walls.

→02 shows simulated hydrodynamic efficiency values for the four-bladed trochoidal device based on three different grid resolutions, together with FLUENT simulations [6] and the model-scale experimental result. The latter two correspond well. The case is pure trochoidal motion with λ = 1.6. The simulations converge monotonically toward the experimental result and the fine grid result is within 0.2 percent of the reference experimental value. The deviation of the medium grid result is roughly 1.5 percent and the coarse grid result is a bit less than 8 percent.

→03 illustrates the instantaneous flow field from fine grid simulations of the four-bladed device. Accelerated flow near the blades and in the middle of the device, as well as individual blade wakes, are clearly visible. Resolution of wake flow features is sustained in the slipstream. Blade wakes interact with succeeding blades at the aft part of the device, as well as farther downstream.

Cavitation performance of the ABB Dynafin

For the cavitation performance of the ABB Dynafin, calculations were performed based on a cavitation number, σVeff, ranging from 1 to 5 – that is, from wetted or non-cavitating (high cavitation number) to fully cavitating conditions (low cavitation number). Most conditions were analyzed with OpenFOAM and a comparison at a selected operating point was carried out with OpenFOAM and STAR-CCM+ solvers. A λ of 1.6 was used for all cases. In addition to a pure trochoidal trajectory, an optimized pitch function was also analyzed. Optimization, in this case, was based on further improving the efficiency and cavitation performance of the device. Results at different cavitation numbers, in terms of the global performance coefficients, are given in →04. The table shows the coefficients for the trochoidal trajectory used and the optimized trajectory. The results shown in the table are also shown in →05 to compare performance coefficients for trochoidal and optimized blade trajectories.

A high open-water efficiency of 0.77 is reached with the trochoidal motion and an even better 0.8 is obtained with the optimized trajectory. The performance and thrust remain high with little variation until below σVeff ≈ 1.7 with the optimized blade trajectory. For pure trochoidal trajectory, a breakdown of thrust occurs slightly earlier, and after that condition, there is a decrease in the efficiency curve. Comparing the results from OpenFOAM and STAR-CCM+ CFD solvers, there are slight differences in the predicted thrust and torque coefficients, the coefficients being smaller in the STAR-CCM+ solution. Deviation in torque coefficients is slightly larger than in the thrust coefficients. These differences may be partly attributed to dissimilar temporal and grid resolutions applied, especially in the boundary layers of the blades. Still, predicted hydro- dynamic efficiencies are very close to those of the CFD solvers.

The thrust coefficient for a single blade from OpenFOAM and STAR-CCM+ simulations during one revolution of the main wheel is shown in →06. The evolution of vapor volume for a single blade is shown in →07: As the blades rotate in the fore part of the device (θ 315 ° to 45 °) and go downward, cavitation starts to form first near the root, then grows spanwise to cover a thin region near the blade leading edge. A cavitation-free region is followed by a two-peaked pattern of increasing vapor volume at around θ ≈160 ° and θ ≈ 200 °. Greatest vapor formation takes place at the aft part of the device, that is, after the blade has passed θ ≈ 180 °. Between roughly 240 ° and 315 °, a cavitation-free region appears. The applied homogeneous-mixture CFD methods predict mainly sheet-type cavities on the blades.

Overall, the thrust and gas volume values have similar forms for each CFD solver for most of the wheel’s rotation. Differences arise mainly when the blade passes through the wake generated by the other blades as the main wheel rotates – for example, near θ = 180 °. →08 shows the scaled, non-dimensional flow speed (U/Uinflow) at a middle z-plane of the device, illustrating that wakes of individual blades are more distinctly resolved in OpenFOAM simulations and as a blade passes through the wake of another blade, the wake’s effects are more pronounced in the blade’s force time history. Note that there is a slight deviation in shapes of vapor time evolution close to θ ≈ 45 ° – ie, when the rotating blades meet an undisturbed flow. Possible causes of this discrepancy require further investigation. In addition to differences in grid resolutions, the time step used in the STAR-CCM+ simulations was a bit larger, which may increase numerical diffusion in the flow solution. The shorter time step applied in the OpenFOAM solution can also result in a more resolved vapor field.

Simulation matches reality

This VTT and ABB collaborative study shows that the performance of the ABB Dynafin with a purely trochoidal motion of the blades is good, with efficiencies near 0.8. Under the conditions considered, performance remains excellent up to relatively low cavitation numbers. Cavitation and hydrodynamic performance can be further enhanced with an optimized blade pitch function, which leads to improvement over the pure trochoidal motion.

OpenFOAM simulation results compared well with available experimental and reference simulation data. Overall, the CFD methods applied to the ABB Dynafin device produce similar results. Differences in the flow field and time evolution of the vapor volume were observed and discussed. More operating points should be investigated to obtain more precise data about the onset of cavitation and the trend of the performance coefficients. A detailed description of the study described in this article can be found in [1].

Future work includes a numerical uncertainty assessment with respect to grid resolution. Further, the implementation of scale-resolving turbulence modeling techniques could allow for a more thorough investigation of cavitation dynamics and multiphase flow. Moreover, to supplement current mixture multiphase flow models, the application of two-fluid methods could ensure cavitation features and types are represented more completely.

_{References

[1] V. Viitanen et al., “Cavitation analyses of trochoidal propellers,” presented at ISOPE – 2024, The International Society of Offshore and Polar Engineers Conference, Rhodes, Greece, June 2024.

[2] F. R. Menter et al., “Ten years of industrial experience with the SST turbulence model,” Turbulence, heat and mass transfer, 4(1), pp. 625 – 632, 2003.

[3] B. E. Launder and B. Spalding, “The numerical computation of turbulent flows,” Computer methods in applied mechanics and engineering, 3, pp. 269 – 289, 1974.

[4] Y. Egorov and F. R. Menter, “Development and application of SST– SAS model in the DESIDER project,” Advances in Hybrid RANS–LES Modelling. Notes on Numerical Fluid Mechanics, pp. 261 – 270, 2008.

[5] G.H.Schnerr et al., “Physical and numerical modelling of unsteady cavitation dynamics,” Fourth international conference on multiphase flow, vol. 1. ICMF New Orleans, 2001

[6] J. Salminen, “Three-dimensional computational fluid dynamics analysis of cyclorotor propulsion system,” Master’s thesis, Aalto University. School of Engineering, 2023.}

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