I think we’re gonna need a bigger boat
When you ask anyone to name a famous ship, the answer is usually “the Titanic.” Sure, there are other contenders depending on what part of the world you come from, but none left their mark on the wider public’s consciousness - or indeed continues to hold it - some 105 years since she sunk this coming April 15. In conversation with some colleagues the question was posed “I wonder if anyone’s ever really looked into simulating the Titanic?” There are computer animations, but this is not simulation. From a brief scan of the internet it seemed that this perhaps wasn’t the case. There are quite a few attempts at hand calcs to work out the physics involved, and plenty of debate about the precise nature of what happened with the propeller cavitation or the rudder being too small. But with the current set of computational tools available to engineers these days, specifically computational fluid dynamics (CFD), I thought it would be interesting to look back on the most famous ship of all time in STAR-CCM+ and what I learned was not exactly what I was expecting, but more on that later.
So where to start creating a digital twin of the Titanic? Thankfully, the availability of drawings of the Titanic are plentiful so recreating a 3D model in CAD is a luxury that we almost take for granted in 2017 that some 100 years ago engineers, designers and draughtsmen would have dreamed for. So obtaining a replica of the Titanic is straightforward enough. The first step in getting the Titanic to sail for the first time in 105 years (albeit digitally) is to set up a simple sink and trim simulation of the hull and rudder at a 10m draft (the height of the waterline is from the base of the keel) at 22.5 knots, the approximate speed she was last sailing at. This way STAR-CCM+ will calculate the precise way the fluid forces acting on the Titanic from the water passing around it made her change how she behaved in the ocean at speed by modeling the Dynamic Fluid Body Interaction (DFBI). This will provide us with some initial information on the amount of thrust required by the propellers to overcome the resistance of the hull in the water and the shape of the wave pattern around the Titanic.
Figure 1: Titanic Free Surface (wave pattern) at 22.5 knots
The wave generated from the Titanic passing through still ocean is something that has not been seen for well over a century. However, thanks to the EHP (Estimated Hull Performance) toolset within STAR-CCM+, finally in figure 1 we are now able to get an idea of the bow and stern waves and the ripple effect these made through the ocean. This simulation also gives us an idea of the drag force (approximately 2,600,000 N) which has to be balanced by the three propellers at the rear.
Figure 2: The Titanic’s propellers looking forward from the stern as the ship was going ahead, with (contra-rotating) "outward" rotating wing propellers and a right-handed central one.
While section views of the Titanic’s structure are available, the sections of the propeller design are less so. This required a few days of “forensic engineering” based off of the limited number of photographs of the original propellers (see figure 2) and getting these into 3D CAD, testing them at several different rpm and then reconfiguring them in order to get the three propellers to each generate the right amount of thrust to balance the drag previously calculated. With what limited information there was on operating rpm, I eventually got the CFD model to balance with 60 rpm for each of the three bladed wing propellers and 160 rpm for the four-bladed central propeller, and ended up being pretty close to some eventual information I found! As the animation shows, there is a passing frequency for each blade as it either passes the wings of the outer propellers, or the keel for the central propeller. Causing spikes in the thrust which would also contribute to significant noise, but probably only for the 3rd class passengers.
Animation: Propellers in action
So now joining the two of these simulations together - the hull and rudder as well as the propellers and the operating rpm - we can set up a full model in STAR-CCM+ in one of two ways:
The complete model with the correct CAD of the propellers rotating, which is very precise but very computationally intensive.
Using the propeller models in an “open water test” to generate performance curve data so that a “virtual disc” approach will generate the relevant source terms in the propeller region to rotate the water and provide the same thrust.
Either of the choices of these will act as a further refinement step towards the full ship's hydrodynamic performance as the effects of the hull and propeller combined will change the behavior of each. I’ve chosen the first one so stay tuned for an eventual update!
In order to gain a little bit of initial insight, and perhaps assist in the debate of the actual maneuver around the iceberg which ultimately ruptured enough of the side of the Titanic's hull to sink her, it was relatively easy to use the stand alone propeller model and rotate the rudder 35 degrees - the approximate angle at which it was steered, I’ve read both 30 degrees and 40 degrees on this. With the propellers running at their full rpm for 22.5 knots and then reversed (at 50 percent of the 22.5 knots ahead rpm). The resulting low pressure behind the propellers, as shown in figure 3, yields a 30 percent reduction in the amount of side force the rudder can generate, the deep dark red pressure contour on the rudder gives way to mostly yellow. The velocity plane of the sea acting through the propeller is very slow (dark blue) when the propellers are reversed and the pressure on the downstream side of the propeller is <-0.1 MPa (almost black on the separate hull and propeller scalar contour). Although cavitation is not modeled here, it's doubtful that even with a larger rudder that it still would have been able to steer enough away from the iceberg that claimed her.
Figure 3: (Top) Full ahead and (Bottom) 50 percent in reverse, both with rudder at 35 degrees
So some initial results show how the Titanic is able to digitally sail once more and hint at the potential hydrodynamic issues with the rudder, which I hope to address in the future. But what of my earlier statement about the things I learned that I wasn’t expecting? These were more philosophical ones, such that in order to look to the future sometimes it's worth looking to the past to appreciate your direction. Currently we stand at the dawn of the 4th Industrial revolution, and in my study of an icon built at the end of the first it’s clear to see that it’s never been faster, or easier, to design something in our history. My two-day propeller design would be several orders of magnitude faster than the designers of the Titanic devoted. And there is a complacency perhaps in ignoring past technological advances which risk being consumed by the passing of time much like the Atlantic Ocean did to RMS Titanic, simply because they aren’t swathed in carbon fiber. The one constant in all of this are the fundamental forces of nature, of which CFD’s direct purpose is to solve for, and in forging ahead we have to count ourselves fortunate to be in a time of not only faster engineering, but given the right toolset, accessible engineering.