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Validation data

This chapter contains useful references for extracting data about the lift and drag on different wind propulsion devices, that, for instance, can be used to validate a simulation setup. The most relevant comparison data are from methods that can be considered to be higher fidelity than the methods in Stormbird. In other words, the articles below mostly contain data from either CFD, experiments, or some type of processing of full-scale measurements.

Wing sails

Relevant papers

Rotor sails

The flow around rotor sails is defined by very high lift coefficients and therefore strong tip vortices. They often come with end-plates to specifically reduce the tip losses, and thereby increase lift and reduce drag forces. CFD simulations done on rotor sails in the KSP WIND project indicate that the exact features of the tip-geometry can have large impact on the final results. For instance, the foundation geometry can have a large impact on the forces. These types of geometric details will not be part of a simplified line model of a rotor sail directly. As such, it is generally necessary to tune the models to achieve the right combination of lift and drag.

Tuning the lift can generally be done by adjusting the lift parameters in the sectional model, as the 3D lift is generally very close to the 2D lift for a rotor sail. This is because the lift is not dependent on the angle of attack, in the same way as for a wing sail or suction sail.

The recommended practice when modeling rotor sails is to first adjust the model of a single sail by comparing it to some high-fidelity data source, and then use the Stormbird library when, for instance, interaction effects are of interest.

Relevant papers

  • Application of the Magnus effect to the wind propulsion of ships (1926), by L. Prandtl. One of the first papers about rotor sails. The text mainly consists of a general discussion about the concept and the history of the first ship using rotor sails for propulsion, namely The Buckau. However, there are also results from one of the first experiments of rotor sails in the appendix of the paper.
  • Experiments on a Flettner rotor at critical and supercritical Reynolds numbers (2019), by G. Bordogna and more. Contains results from experiments where lift, drag and power coefficients on rotor sails were measured at different Reynolds numbers and spin ratios. Note: the experiments are performed in a wind tunnel where the rotor extends from the floor to the roof, which indicate that the force measurements should be interpreted as two-dimensional. However, it is mentioned in the article that there might be three-dimensional effects due to the boundary layer along the walls. The measured drag is also so large that there seem to be some three-dimensional effects present. The results are therefore probably most useful as a comparison for lift and power, while the drag values are a bit hard to interpret.
  • Design, operation and analysis of wind-assisted cargo ships (2020), by F. Tillig and more. A paper about methods to set up empirical modeling of wind powered ships. One of the empirical methods presented is for the lift, drag and power consumption of rotor sails, tuned based on full-scale measurements.
  • Retrofitting of Flettner Rotors – Results From Sea Trials of the General Cargo Ship “Fehn Pollux (2020), by M. Vahs. A paper that really is about how to analyze sea-trial data from a ship equipped with rotor sails. A part of the paper also contains wind tunnel measurements that originates from a bachelor thesis (original source not found), which gives lift and drag as a function of spin ratio.
  • Levelling the Playing Field: A Numerical Platform for the Fair Comparison of Wind Propulsion Systems (2022), by F. C. Gerhardt and more. A paper mostly about the need to have independent analysis of wind propulsion devices. As part of explaining the rotor sail models, CFD results of lift and drag as a function of spin ratio are presented. This presentation also includes a comparison against other available data sources.
  • Calculation of Flettner rotor forces using lifting line and CFD methods (2023), by A. Östman and more. A paper that compares lifting line simulations against CFD simulations for rotor sails. As part of this, there is both two- and three-dimensional data for lift and drag. The default parameters in the rotating cylinder sectional model in Stormbird are fitted to the two-dimensional data from this paper.
  • Aerodynamics of the Flettner rotor at high Reynolds number (2024), by F. Deybach and more. Note: not yet publicly available. Part of the RINA conference on wind propulsion in 2024. Contains experimental results, where a rotor sail is tested in a wind tunnel at different Reynolds numbers and spin ratios, as well as with different end plate configurations. Concludes that the lift is not very sensitive to the Reynolds number.

Other data sources

The KSP WIND project (the project funding the development of Stormbird) has performed CFD simulations of rotor sails as part of the project. These data are not yet published anywhere, except shown in the plots below. The primary goal of these simulations was to investigate the impact of the foundation on the lift and drag. The results indicate that the foundation can have a huge impact on the forces. A model that does not include the tip vortex on the bottom of the sails can, therefore, be overly optimistic.

Rotor sails
Figure 1: Streamlines from CFD simulations of rotor sails with and without the foundation present, to illustrate the strength of the vortices, and the impact on the bottom tip vortex when the foundation is inclined in the simulation. Each version of the sail is simulated independently, and then the streamlines are combined in post-processing

Plot of data

Three dimensional data

Figure 2: Lift and drag coefficients as a function of spin ratio for three-dimensional rotor sails. The data is from the experiments and CFD simulations listed under relevant papers above, together with the unpublished CFD simulations from the KSP WIND project, with and without the foundation. The data sources use different sail geometries and test conditions, so differences between them are not only due to the method used.

Two-dimensional data

Figure 3: Two-dimensional lift and drag coefficients as a function of spin ratio for rotor sails, from the wind tunnel experiments by Bordogna et al. (2019) and the CFD simulations by Östman et al. (2023). Only the lift is shown for the experiments, as the measured drag is hard to interpret (see the note in the list of relevant papers).

Suction sails

For suction sails there are two aspects to the model that needs tuning. The first is to find good sectional model properties to represent how lift and drag depends on the angle of attack as a function of the fan system settings. This process is largely the same as when tuning a model for a wing sail. The only difference would be that the internal state of the section model changes from a flap angle to typically a non-dimensional suction rate (power coefficient can also be used, but this is a simplification). The second part of the model, which is new, is to find a good correlation between suction rate and power consumed. The last part is typically more challenging to get exact based on published data alone. Below is a list of papers that present some data on the properties of suction sail, although with most focus on the lift and drag, and not really the power consumption.

Relevant papers

Three dimensional data

The figure below shows the lift and drag coefficients for a three-dimensional model of the Turbosail, measured in a wind tunnel for three different suction rates. The suction rate is given as a suction coefficient, \( C_Q \), defined as:

\[ C_Q = \frac{Q}{A V} \]

where \( Q \) is the volume flow through the suction system, \( A \) is the wing area and \( V \) is the wind velocity. The lift is shown as a function of angle of attack, while the drag is shown as a function of the lift. In the original figure, the drag curves for \( C_Q = 0.05 \) and \( C_Q = 0.036 \) are drawn on top of each other for most of the lift range, and are therefore identical in the digitized data.

Figure 4: Three-dimensional lift and drag coefficients for the Turbosail at different suction coefficients, CQ. The data is digitized from the wind tunnel experiments presented in Fondation Cousteau and windship propulsion - 1980 - 1985 (Charrier et al., 1985).

The figure below shows the lift coefficient of the same three-dimensional sail as a function of the power coefficient, \( C_P \), defined as:

\[ C_P = \frac{P}{0.5 \rho A V^3} \]

where \( P \) is the input power to the suction system and \( \rho \) is the air density. The article does not give details about how this data was obtained, for instance at which angle of attack it applies. It should therefore mainly be seen as an example of the power consumption of a suction sail, rather than as accurate data for model tuning.

Figure 5: Three-dimensional lift coefficient for the Turbosail as a function of the power coefficient, CP. The data is digitized from Fondation Cousteau and windship propulsion - 1980 - 1985 (Charrier et al., 1985).

Two dimensional data

The figure below shows two-dimensional lift and drag coefficients for the Turbosail section, for a wider range of suction coefficients. As for the three-dimensional data, the lift is shown as a function of angle of attack and the drag as a function of the lift.

Figure 6: Two-dimensional lift and drag coefficients for the Turbosail at different suction coefficients, CQ. The data is digitized from the wind tunnel experiments presented in Fondation Cousteau and windship propulsion - 1980 - 1985 (Charrier et al., 1985).