In the past, one way to calculate how much power a submarine needs was to put a scale model of it into a test tank flowing with water and measure the model’s resistance to the flow stream. But thanks to advancements in computational-fluid-dynamics (CFD) software, this task can now take place in an engineering office. We used CFdesign from **Blue Ridge Numerics** (the company has since been purchased by **Autodesk**, San Rafael, Calif.) to help characterize a small sub’s power requirements.

In this example, the sub was designed to fit into a standard high-cube 40-ft-long shipping container. But the shipping container size limited the sub’s maximum dimensions, which, in turn, limited the vessel’s battery capacity.

Battery capacity is one of the most critical design parameters in a small submersible. The amount of power available determines sub speed and range. By far, the most energy-intensive requirement is the power propelling the submersible through the water. So it’s important to predict the horsepower required at various underwater velocities.

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**Submerged velocity and drive-motor power**

The analytical test tank or water tunnel for the CFD model was a 1,000-in.-long pipe with a 249-in. ID. The software test tunnel was filled with room-temperature water moving through at 1 to 7 knots.

Two calculations are necessary for this problem. The first is a calibration CFD run. The submersible hull is basically a cylinder 76 in. in diameter by 400-in. long. We substituted for this geometry a simple 76-in.-diameter sphere inside the flow field for calibration. CFD calculated the sphere’s pressure drop for midrange flow rates of 6 knots, where they matched classical pressure drop calculations. The classical methods are found in any good fluid-dynamics textbook.

The second calculation involved placing a CAD model of the actual submersible into the virtual test tank and measuring the new pressure drop as a function of flow rate. Pressure drops measured across the water tunnel were then used to directly calculate the necessary drive-motor horsepower. The CFD performance aligned with classical results after calibrating for the differences in geometry.

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**Calculation results**

To double check results, it’s customary to perform calculations with actual numbers. The first step is to calculate the Reynolds number as 6 × 106 for the water-flow stream at 6 knots using the spherical diameter as the significant dimension in the Reynolds equation. Now use the spherical drag coefficient Cd = 0.2, taken from a typical immersed body drag plot. The actual drag of the sphere is calculated as 627 lbf.

The calculation method presented here is a simple approximation for determining low-speed motive power requirements of bluff-bowed fully immersed objects moving through water.

Autodesk Inc. | Patriot Engineering Co. | “Elementary Fluid Mechanics,” 5th Edition, by John Vennard and Robert Street, John Wiley & Sons, 1975. | © 2012 Penton Media, Inc.