MBARI is currently working on a project to develop a power generation system for ocean buoy station-keeping that is based on a flapping foil concept.  Development and optimization of the flapping foil will be through computer simulations of both the surface and submerged portions of the system.  You have developed a Matlab-based simulation for the surface portion and would like Airflow Sciences Corporation (ASC) to develop/perform the simulations for the submerged portion.

In order to test out the Matlab simulation, you have calculated the flapping foil forces based on published airfoil data and a quasi-static assumption.  Previous flapping foil studies that Jim Paul found show that vortices that form near the foil while at high angles of attack affect the foil performance when rotated to lower angles of attack for at least some combinations of velocity and pitch rate.  The question for the station-keeping project is whether the pitch rates of the foil are such that a quasi-static assumption is valid or if a transient simulation (or some other technique) is required.

As a test of that question, we have discussed performing a simulation in which the foil motions that you have predicted with your quasi-static assumption are applied to a foil in a transient CFD simulation.  While the actual foil motions may be different than those predicted with the quasi-static assumption, they are expected to be close enough to actual motions to allow for an assessment of the difference in forces between a transient simulation and the quasi-static approach.  

Approach -

The key elements of the simulation approach are outlined below:

- The simulation will be 2D.

- Foil motion (XY) and pitch will be defined by MBARI.

- The domain will include a sufficiently large region around the foil.

- The foil will remain stationary in the domain, but a moving reference frame (both translation and rotation) will be applied to the domain.

- The parameters of the moving reference frame will be adjusted for each time step in the simulation.

- Constant pressure boundaries will be used on the periphery of the domain.

- The duration of the simulation will be 600 seconds, representing about 50 periods of foil motion.

- The initial condition of the water will be stationary.  

- The main output of the simulation will be force and moment data over time and animations of the flow field around the foil.

Comparisons will be made between the forces and moments predicted from the CFD simulation and those calculated with the quasi-static assumption.  A brief report will be prepared.

Commercial Proposal -

ASC's price to perform the initial 2D transient foil simulation outlined above is $8,000.  Invoices will be prepared monthly for partial completion of this task.  Terms are Net 30 Days.  The expected duration of this task is 2-3 weeks.  The quoted price will remain valid through 30 December 2009.

ASC expects that this initial transient simulation will provide considerable insight into the simulation techniques needed to provide an accurate representation of the behavior of the submerged, flapping foil.  As with any new simulation effort, the first case requires greater resources than subsequent efforts.  ASC estimates that additional flapping foil simulations with prescribed motions could be performed for about $4,000.

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Please let us know if you have any questions or concerns regarding this proposal.  We look forward to continuing our work with you on this project.

Best regards,

Andrew