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Tag: CFD

Rudder Simulations

While designing the thrust/steering module for the AUV, I figured I should determine how much torque the rudder will require (for motor selection) and what forces it will result (for eventual control development). The rudder itself is a fairly simple plane with an airfoil type profile, with the rotational axis a quarter of the way from the front to the rear, making it what’s known as a balanced rudder. More on this later.

Balanced Rudder

I set up an Open Foam case to calculate the forces and torque, and made a script to run it through 0 to 50-degree steering in 5-degree increments. I opted to just use an isolated rudder for the initial tests, although in reality there will be interaction between the body and the rudder, especially since the rudders will be located in the region where flow is beginning to separate from the AUV hull. Note that in earlier CAD models, I had shown the rudder being only a portion of a fin — in order to simplify things, and balance the rudder, I opted to make the rudder consist of the entire fin.

The simulated results I got are shown in the chart below. I only ran simulations up to 2 m/s, as I don’t expect the AUV to go much faster than that operationally.

Rudder torque vs deflection angle, with rudder rotational axis 25% back from leading edge of mean chord

Although there appears to be an outlier at 30 degrees deflection (Either due to some real hydrodynamic effect or errors in the simulation), this result is actually what’s expected for a balanced (or partially balanced) rudder. If the rotational axis was at the front edge of the rudder, all the forces would be acting on one side of the rotational axis which would result in significant torque requirements to move the rudder. By locating the pivot point near the rudder foil’s center of pressure, the forces in front of and behind the rotational axis negate each other resulting in reduced torque requirements.

With the balanced rudder, the forces start off minimal while the flow is laminar. Once the rudder’s foil begins to stall, the torque will actually invert and go the other direction. To illustrate this, some renderings of the results from Open Foam are shown below. Note that the streamline colours represent particle velocity, but the colour scales are slightly different between all images.

 

10-Degree deflection. Flow is laminar.

In the first case above, with 10 degrees deflection, the flow is still smooth around the rudder’s foil. While the torque value at this point is very low (hence why it’s “balanced”), using the right-hand rule to interpret the torque around the Z-axis, it appears that the torque is actually wanting the rudder to keep deflecting!

20-Degree deflection. Flow is starting to separate.

At 20-degrees separation, per the plotted results, the rudder foil is around the stall point. At this point, the torque around the rotational axis is neutral. Any further deflection wants to push the rudder back towards the forward position.

40-Degree deflection. The rudder is stalled. Note the turbulence behind.

Throwing the rudder even further, to 40-degrees, we can see that it’s now clearly stalled. You can see the turbulent flow behind the rudder. The streamlines make for a really cool graphic!

For curiosity’s sake, I ran a couple of extra simulations, varying the location of the rudder’s pivot axis 4mm forward and 4mm back from the 1/4 chord position (this turned out to be 6.6% of the mean chord). A plot of the results below. I still have some optimization to do in terms of rudder profile and mounting point, but these give me a good order of magnitude understanding of the rudder torque for initial design work.

Varying the location of the rudder’s rotational axis effects the torque.

In terms of motors to drive the rudders, I’m currently planning a geared down brushless motors, as I want to have fairly fine and smooth control over the mechanism (reduce noise, vibrations, improve fine control over hobby servos).

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Doppler Velocity Log Acoustic Windows

Although I haven’t posted anything in the past month, I have been working away at the AUV here and there between work and some much-needed vacation. I’m making some decent progress in design and setting up for manufacture. A couple of the big things I’m working on are some detailed design work on an acoustic modem, and putting some finishing touches on my CNC machines to start building some of the mechanical components for this project. I’ll post an update on those topics when I have some more substantial progress.

In the meantime, I was digging for some files and came across some earlier CFD results, specifically pertaining to the Doppler Velocity Log (DVL) and the flow of water around it. A DVL works by sending sonar pulses out at multiple off-nadir angles and measuring the doppler shift in the return signal. If the AUV is stationary, there is no Doppler shift, but if there is motion a Doppler shift is induced which can be measured to determine the motion of the AUV underwater in lieu of not being able to get a GPS lock.

Water flow around the DVL Pockets.
Water flow around the DVL Pockets.

Due to the relatively small diameter of the AUV, and the size of the DVL transducers, they needed to be pocketed in the hull. I ran some simulations to determine the way water would flow, and as expected there is some recirculation induced by the pockets. This not only adds drag but potentially increases flow noise on the transducer itself.

As such, I’ve modified the design slightly and will attempt to put a LDPE window to hopefully improve the flow. LDPE is a type of plastic which has an acoustic impedance fairly close to water, so should be mostly transparent to the sonar wave. Modeling the shape proved an interesting challenge, but haveing done so will enable to me to fairly easily cut out the shape from flat sheet using the CNC.

DVL Acoustic Windows (Bottom left transducer cavity exposed)
DVL Acoustic Windows (Bottom left transducer cavity exposed)

Hopefully, some more updates will be forthcoming in the next couple of weeks!

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Preliminary CFD Results

This post is jumping into the middle of things, as a huge amount of work has gone into getting the AUV design this far, with several revisions of the design and some background work on the sonar to determine how much AUV I’ll actually need to carry it.

A very preliminary design choice was the dimensions of the AUV. The length will be driven by module and payload lengths, leaving the diameter as something needing a tradeoff between how much I could compact the module electronics vs what I could build. I settled on an outside diameter of 5.5 inches, driven largely by the size parts I can realistically make on my small lathe. I would have preferred a larger diameter, but that’s the way the cookie crumbles. Interestingly, with a 5 inch ID (0.25-inch wall thickness), I can just fit 8x 15AH LiFePO4 cells for a 24 volt, 360 Watt-hour battery.

Why imperial units for the diameter when most of the rest of the design is metric? That’s driven by the availability of stock acrylic and aluminum tubing to be used as the main pressure hull body components. (Flooded modules will likely just be fiberglass). Mixing imperial and metric is just a necessary part of life up in Canada. Sometimes with poor results.

Initial Hull Shape
Initial Hull Shape

Knowing the basic dimensions, I’ve been working on detailed 3D CAD models of the entire AUV design, refining the shape and design of the critical components including the Doppler Velocity Log (DVL), drive section, and the universal bulkhead rings (more on those later). The end result is a rough shape of what the AUV will look like in the end. This design will be refined significantly, but is good enough as a starting point, and is shown above. (Note that the antenna on the top wasn’t exported into the flow simulations)

I set up some simulations in OpenFOAM to estimate the drag and flow around the AUV — The goal being to determine enough information to optimize the propulsion design. I’ve been experimenting with both the simpleFoam and pimpleFoam solver. The computational requirements to get a fine enough mesh  to resolve the features properly proved difficult on my home laptop, so I stood up a server on AWS to handle the simulations — After much experimentation with setting up OpenFOAM cases, the AUV hull design, boundary conditions, and meshing, I finally got things set up well enough to run at a high level of detail with a configuration I felt I could trust. 48 hours later, I had a result. I probably could have introduced larger timesteps into the pimpleFoam solver (the maximum Courant number was set to 25), so I’ll experiment with that on future runs.

 

 

 

 

 

The plot above shows the flow over the stern of the AUV. The Reynolds number is fairly high in this design, leading to turbulent flow, and some strange flow along the stern, where you can see it circulating near the surface. The drag pressures appear to settle within 0.4 or so seconds, with a total simulation time of 1 second. The time-steps were dynamic, so prior to settling were very short to avoid the solution diverging. Curiously, the viscous drag remains steady, but the pressure drag is somewhat unsteady.

Plot of the viscous and pressure forces converging over successive iterations.
Plot of the viscous and pressure forces converging over successive iterations.

Previous results had already led me to reduce the tail angle in an attempt to reduce the wake, but ultimately I think this will have to do as narrowing the tail angle too much will result in other design challenges in terms of length of the thrust module.

Streamlines and pressure distribution along hull
Streamlines and pressure distribution along hull

Apart from estimating the drag on the hull, the really cool thing is I can determine the inflow velocity at the propeller disc. Since the hull inevitably has a negative impact on the water speed, designing a propeller for a water flow equal to the vehicle velocity won’t produce an optimal design. The simulation allowed me to extract the velocity profile, which I can feed into propeller design to further optimize the design. If time allows I may optimize the nozzle (it’s currently a vanilla Kort nozzle). However, the purpose of the nozzle in this design isn’t just to attempt to improve the performance, but also to provide a safety guard to protect wildlife and support divers during testing, as well as to reduce the probability of entanglement.

From the results, the hull has a significant impact on the inflow. The Kort nozzle does increase the speed a bit around the propeller tips, but closing into the propeller hub the velocity drops sharply.

Axial velocity through propeller disc
Axial velocity through propeller disc

Interestingly, the horizontal tangential (y-axis) velocity is low but produces an interesting plot showing that the flow is not perfectly axial, but slightly canted inwards. Note that the scale of this image is different than above. This is mostly included because I believed it was a cool picture.

Horizontal tangential flow
Horizontal tangential flow

Of course, I’m not a CFD expert and am learning things as I go, so I need to take these results with a grain of salt. The results seem to be within the order of magnitude of what I can find in literature, so they’re good enough for the next steps in the design process.

Next steps in the CFD work will be verifying the control surface size is sufficient enough to provide good control authority, and to size the motors required to turn them. So far the control surfaces have just been eyeballed, so I’ll have to do some initial calculations to determine what’s required, adjust the design, and simulate.

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