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Why hull appendages are hydrodynamically superimposed on ship motion models

Nobody expects to see fish walking around on land, but many species can do it. The Climbing Perch is one example. No, it doesn’t have any legs. Yet it has the ability to trundle along on the ground with its fins. It isn’t just for fun: they can often get to new bodies of water they couldn’t reach otherwise. But generally, gills don’t work in the air: they are too floppy and collapse, limiting any oxygen transfer the fish need. This usually means most fish can only survive for a few minutes out of the water. So what’s so special about the Climbing Perch?

The key is a special adaptation in their gills that allows direct oxygen transfer from the air. But what’s remarkable is that they aren’t made this way from the start. It’s an adaptation that grows and changes over time, right on top of their existing gill structure. Bumps and ridges form directly on top of their gills. This keeps the gills open while in the air, significantly increasing the amount of oxygen they can absorb when out for a walk. The superposition of these structures unlocks new capabilities.

Superposition is when something is added on top. Sometimes, adding things on top gives you a way to work around a problem and find a new way of doing things. Superposition comes up in ship hydrodynamics, too, and it’s also crucial to unlocking new capabilities. Ship motion prediction models based on potential flow aren’t made to do everything from the start on their own. Potential flow theory can’t handle complex flow effects from hull appendages like bilge keels, fins, and skegs. Yet the hydrodynamic effects of hull appendages can be directly superimposed on the numerical ship motion model. In this article, we’re going to cover how this works and why it’s so advantageous.

The physics of potential flow seakeeping hydrodynamics has crucial gaps

Potential flow theory is helpful because it is very effective in calculating the hydrodynamic interaction of ocean waves with large floating hulls. These wave interaction effects, like wave radiation from hull movement and excitation and diffraction from incident waves in the ocean, are needed to calculate ship motion in a seaway. But there’s a fundamental assumption in all potential flow theory: it completely ignores viscous effects.

This crucial gap of ignoring viscous effects includes the physics of hull appendages

Hull appendages have strong viscous effects, including form drag, skin friction drag, lift, and eddy-making drag. Some systems, like barges, don’t always have hull appendages. Then, potential flow alone can be great for evaluating their hydrodynamics and motion in a seaway. But it’s common for ships to have at least a few hull appendages, like skegs or bilge keels.

Though hull appendages are small, they can significantly affect vessel motion. In fact, they are crucial to controlling ship motion during maneuvering and can strongly influence some critical degrees of freedom, like roll. So, how can you address these viscous hydrodynamic effects that are missing in potential flow models?

The effects of hull appendages can be addressed through superposition

The general idea is that the forces from the hull appendages can be resolved from relatively simple empirical relationships. These forces are then superimposed on all other forces acting on the hull when solving the equations of motion for the ship. These empirical relationships often incorporate the ship’s forward speed and motion, and relative flow from incident waves.

However, there is a catch. The catch is an underlying assumption that appendages don’t significantly affect the flow field. The benefit is that the calculation process is substantially simplified because the potential flow calculations don’t need to be adjusted.

But how can you ignore the effects of the appendages on the flow field?

You can do this because, generally, appendages are too small to have a significant effect on the flow field around the hull. This means the incident wave excitation, diffraction, and radiation effects on the hull don’t change much from the presence of the appendages.

But this assumption does have limits. There’s more uncertainty when appendages are extremely large and more likely to disrupt the flow around the hull. This might be the case with a particularly large skeg, or wing keel on a tug. On top of this, appendages in close proximity to each other might cause a problem. The wake from one appendage might cause enough disturbance in the flow to affect downstream systems. For example, bilge keels and fin stabilizers need careful spacing so they don’t hydrodynamically interfere with each other.

What about wave interaction with appendages themselves?

When hull features are large enough and close enough to the water surface, it might contribute to wave radiation or diffraction interaction effects with the free surface. However, the most common forms of hull appendages are too small and too far from the water surface to cause significant wave diffraction or radiation effects. This means relatively simple empirical lift, drag, and constant added mass relationships can be used to capture the influence of most appendages.

In the ProteusDS ShipMo3D toolset, the BuildShip application lets you adjust the dimensions and locations of hull appendages like bilge keels, skegs, static and active foils, etc. Typically, a seakeeping analysis takes only a minute to compute after this, so you can rapidly see the effects of different hull appendage configurations.

Example time:

Let’s take a closer look with an example. The Generic Frigate has several different kinds of appendages including bilge keels, skegs, and fixed fins. The Stabilizer Generic Frigate is an alternative configuration that incorporates active fin stabilizers, too. So what are the implications of superimposing these appendages, and the viscous effects on the flow field?

Let’s consider one scenario in forward ship motion. In this scenario, the fin stabilizers generate a lot of lift (and a little bit of extra drag) as they operate. Fin stabilizers generate the most lift as long as the flow is well-conditioned and not separated over the wing. This might mean a fin deflection of only a few degrees. And well conditioned flow means there isn’t very much disturbance in the wake of the fin stabilizer, either. So fin stabilizers are a good example of how you can superimpose these viscous effects in the ship motion model without worrying about any errors in the fluid flow.

But what about bilge keels while in forward ship motion? Certainly they will add a bit of extra drag, and generate a wake effect, in this scenario, too. For this reason, it is good practice to have some separation between appendages like fins and bilge keels, to help reduce the chance the wake will interfere with other appendages, like fin stabilizers. But these wakes are generally small enough to fall in the envelope of the appendage itself. Roll motion is a different scenario though.

In roll motion, appendages like bilge keels have a different effect. These structures are specifically added to create as much viscous damping as possible when the ship is rolling. In the figure, the ship rolls counter-clockwise, and the bilge keels generate drag forces and moments that resist this motion.

In this case, these bilge keels act like flat plates, and can generate more intense viscous effects like vortices and a stronger wake. Yet this wake is also still more or less in scale the size of the bilge keels themselves. The fin stabilizers will also make some additional drag, but they tend to cover a small fraction of the length of the ship. As strong as these effects can be on ship roll, they are also a relatively small hydrodynamic effects compared ocean waves. Ocean waves large enough to create motion in a ship like the Generic Frigate are also much larger than the scale of these viscous wakes generated by these appendages. Appendages are also typically far enough from the water surface that there are no significant wave radiation and diffraction effects.

Summary

We covered a few details on hull appendages, and now it’s time to summarize. Potential flow is valuable for modelling floating systems and their interactions with waves. The big problem is the physics of potential flow fundamentally ignores viscous effects. Yet viscous effects are important in hull structures like appendages, and include important effects like life and drag that can have a dramatic influence on some motion in some cases. Fortunately, viscous effects can be superimposed on a numerical ship model using empirical relationships based on local relative flow speeds from ship motion, forward speed, and ocean waves. As long as the hull appendages aren’t too large and close to the water surface to cause significant diffraction and radiation loads, the potential flow calculations don’t need to be adjusted and the resulting ship motion will be accurate.

Superposition is a way of building on top of what’s there to get an advantage. It’s one way of adapting that the Climbing Perch knows well to get a leg up on exploration by going for a walk on land!

Next step

The Stabilizer Generic Frigate is one of the publicly available ProteusDS ShipMo3D toolset sample projects. You can use it to explore the fin stabilizer model and its effect on ship motion performance. Download it from the Documentation section on our website here.