Andy: Over the past few weeks, we have been discussing your concept of using a pneumatic spring as part of the power take-off for the wave/buoy project that MBARI is developing. The motivation for using the pneumatic spring is that it provides the desired force constant and stroke in a much simpler package than standard elastic materials. The analyses that suggest that the pneumatic spring will be effective have assumed that the two volumes of gas do not lose or gain heat during the process. Prior to construction of a prototype device, you are interested in evaluating the effect of this adiabatic assumption on the performance of the pneumatic spring. This email contains a proposal from Airflow Sciences Corporation (ASC) to use CFD modeling to provide this analysis. Goals - To assess the force vs. distance characteristics of the proposed pneumatic spring under a given sinusoidal motion profile with heat transfer between the gas volumes and the surrounding sea water. Approach - While the motion of the gases is expected to be of little interest, the volume/pressure/temperature variations that occur due to the piston motion and the heat transfer through the unit can be readily simulated with standard CFD techniques. The geometry of the pneumatic spring is largely axisymmetric, with the only exception being a ported support at one end of the inner tube. In order to be able to run the model with an axisymmetric assumption, you have suggested adding a small bump to the inside of the outer tube in order to provide the same average open area. The other option is to apply a porous jump resistance at that plane to provide the equivalent pressure drop. The gases will be diatomic with a ratio of specific heats of 1.4. At the neutral position, the upper pressure will be 60 PSI, while the lower pressure will be 150 PSI. The exterior water temperature will be 12 C, and a suitable convective heat transfer coefficient will be assumed. Two motion profiles have been suggested - 40" total stroke at a 12 second period, and 20" total stroke with an 8 second period. Transient models will be run for sufficient periods until the behavior falls into a repeating pattern. Data will be collected and reported for a single period of the repeating pattern. Output from the model will include animations showing piston motion, gas velocity, gas temperature, and gas pressure, force vs. displacement data, and heat flux rates through the various surfaces. A brief report will be prepared. Scope of Work - 1. Construct a CFD model of the pneumatic spring according to the drawings provided. Include material thicknesses and properties for the cylinder walls, etc. 2. Simulate the performance of the pneumatic spring with a 40" amplitude and 12 second period. 3. Prepare a brief report, including comparison with adiabatic assumption results. Discuss results with MBARI. 4. Simulate the pneumatic spring with a 20" amplitude and 8 second period. 5. Document the results as for the first case. Commercial Proposal - ASC's price to perform the analysis listed above is $7,000 for the first case, and $3,000 for additional cases. Invoices will be prepared monthly for partial completion of projects. Terms are Net 30 Days. The expected duration of the project is 1-2 weeks for the first analysis, and less than a week for subsequent analyses. The prices contained in this proposal will remain valid through 1 June 2010. + + + + + Let us know if you have any questions or concerns regarding this proposal. We look forward to assisting in this aspect of the wave/buoy project. Best regards, Andrew Andrew L. Banka, P.E. Airflow Sciences Corporation 12190 Hubbard St. Livonia, MI 48150, USA Phone: (734) 525-0300 x203 Cell: (734) 834-5331 Fax: (734) 525-0303 www.airflowsciences.com