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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 482 CONCLUSIONS A numerical procedure for the prediction of the forces and moments of a tab assisted control surface has been developed. The procedure is based on solving the incompressible Reynolds-averaged Navier-Stokes equations coupled with a -ω, turbulence model. Computed results of lift, flap, and tab torque coefficients were compared with the measured data at a Reynolds number of 9.7x105 based on the mean chordlength. Three meshes with grid size of 65K, one half million, and 1.6 millions were used to investigate the grid independent solution. A grid independent solution was achieved in most of the cases except for some cases with high flap and tab deflections. The trend of the changes in the forces and moments due to the variations in the angle of attack of the stabilizer and the deflection of the flap and tab has been completely captured. In most cases investigated, the predictions are within 10% of the measurements. Some exceptions are the tab torque coefficients at high tab deflections and the slopes of the lift and flap torque coefficients near zero tab deflection. It is suggested that both the turbulence model and the grid resolution need to be improved. The fact that even with a grid as large as 1.6 million cells, a grid independent solution can only be achieved in most, but not all cases, indicates that more efficient numerical schemes and turbulence models are urgently needed. Despite all these limitations, the predictive procedure presented here is already a useful tool for the design of efficient control surfaces. ACKNOWLEDGMENTS This work is funded by the Office of Naval Research, Code 333, under the Mechanics and Energy Conversion Science and Technology Division (PE0602121). Dr Patrick Purtell is the technical monitor of this program. Dr. Nguyen Thang is the monitor at David Taylor Model Basin. Helpful discussions of experiment and measured data with Mr. David Bochinski at David Taylor Model Basin are gratefully acknowledged. Computer resources provided by the Department of Defense High Performance Computing Modernization Office (DOD-HPCMC) at NAVO and the Arctic Region Supercompting Center in Fairbank, AK are also gratefully acknowledged. REFERENCES 1. AGARD Conference Proceedings 515 on “High-Lift System Aerodynamics”, September, 1993. 2. Richard I.Sears and Robert B.Liddel, “Wind-Tunnel investigation of Conrol-Surface Characteristics, VI—A 3 Percent-Chord Plain Flap On the NACA 0015 Airfoil”. NACA Wartime Report 454, June 1942. 3. Whicker, L.Folger and Leo F.Fehlner, “Free-Stream Characteristics of a Family of Low-Aspect Ratio, All-Movable Control Surfaces For Application to Ship Design”, David Taylor Model Basin Report 933, December 1958. 4. Bowers, Allen, “Wind Tunnel Investigation of the Characteristics of a Flapped Control Surface Mounted on a Simulated Submarine Hull”, University of Maryland Wind Tunnel Report No. 259, June, 1959. 5. Kerwin, Justine E., Philip Mandel and S.Dean Lewis, “An Experimental Study of a Series of Flapped Rudders”, Journal of Ship Research, December, 1972 6. Goodrich, G.J. and A.F.Molland, “Wind Tunnel Investigation of Semi-Balanced Ship Skeg-Rudders”, The Royal Institute of Naval Architects, pp. 285–307, 1979. 7. Soding, H., “Limits of Potential Theory in Rudder Flow Predictions”, Twenty-Second Symposium on Naval Hydrodynamics, Washington, D.C., pp. 264–276, August 9–14, 1998. 8. Chau, Shiu-Wu, “Computation of Rudder Force and Moments in Uniform Flow”, Ship Technology Research Vol. 45, pp. 3–13, 1998. 9. Gowing, Scott, Thang Nguyen and David Bochinski, “T.A.C. Test Static Results in the 24” Water Tunnel”, NSWC, CD, not yet published, 1999. 10. Wilcox, D.C., Turbulence Modeling for CFD, DCW Industries, Inc. CA, 1993 11. Speziale, Charles G., “Comparison of Explicit and Traditional Algebraic Stress Models of Turbulence”, AIAA Journal vol. 35, No. 9, September 1997. 12. Chorin, A.J., “A Numerical Method for Solving Incompressible Viscous Flow Problem”, Journal of Computational Physics, vol. 2, 275, 1967. 13. Turkel, E., “Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations”, Journal of Computational Physics, vol. 72, 277, 1987. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 483 14. Yee, H.C., “A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods”, NASA Technical Memorandum 101088, February, 1989. 15. James on, A., “Time Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wings”, AIAA 91–1596, June 1991. 16. Liu, C., X.Zheng and C.H.Sung, “Preconditioned Multigrid Methods for Unsteady Incompressible Flows”, Journal of Computational Physics, vol. 139, 35–57, 1998. 17. Brandt, A., “Multigrid Techniques: 1984 Guide, with Applications to Fluid Dynamics”, 1984, 191 pages, ISBN-3–88457–081–1; GMD-Studien Nr 85; Available from GMD-AIW, Postfach 1316, D-53731, St. Augustin 1, Germany, 1984. 18. Jameson, A., “Multigrid Algorithms for Compressible Flow Calculations”, Lecture Notes in Mathematics, No. 1228, Proceedings of the Second European Conference on Multigrid Methods, Cologne, pp. 166–201, October 1–4, 1985. 19. Brandt, A., “Barriers to Achieving Textbook Multigrid Efficiency (TME) in CFD”, NASA/CR-1998–207647, ICASE Interim Report No. 32, April 1998. 20. Hedstrom, G.W., “Nonreflecting Boundary Conditions for Nonlinear Hyperbolic System”, Journal of Computational Physics, vol. 30, pp. 222–237, 1979. 21. Rudy, D.H., and J.C.Strikwerda, “Boundary Conditions for Subsonic Compressible Navier-Stokes Equations”, Computers and Fluids, vol. 9, pp. 327–338, 1981. 22. Sung, C.H., “An Explicit Runge-Kutta Method for 3D Incompressible Turbulent Flows”, DTNSRDC/SH—1244–01, July 1987. 23. Jameson, A. and L.Martinelli, “Mesh Refinement and Modeling Errors in Fluid Simulation”, AIAA Journal vol. 36, No. 5, May 1998. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line VALIDATION OF TAB ASSISTED CONTROL SURFACE COMPUTATION 484 DISCUSSION Y.Tahara Oskaka Prefecture University Japan In your computation, laminar-to-turbulent flow transition was not considered, although your experimental condition (i.e., Re≈106) apparently implies that there exists laminar-flow region on the wing (stabilizer in your definition) surface. Inclusion of the effects is generally essential for accurate prediction of hydrodynamic forces especially for drag component [Tahara et al., 1998, 2000]. In addition, the conventional two equation model used in your work may not be suitable for the purpose. REFERENCES: Tahara, Y., et al., “An Application of RaNS Equation Method to Strut/Bulb Configuration of America's Cup Sailing Yacht and Comparison with Experiments,” J. Kansai Society of Naval Architects, No. 230, 1998, pp. 163–171. Tahara, Y., et al., “Development of Ballast Bulb for IACC Sailing Yacht—Especially for Investigation on Basic Low Drag Form,” J. Kansai Society of Naval Architects, No. 234, 2000, pp. 51–59 AUTHOR'S REPLY Due to a relatively high turbulence level in a water tunnel, early experimental tests indicated that the flow was turbulent at a Reynolds number of about one million based on a mean chordlength of 9.53 inches. For this reason, computations were made assuming the flow was completely turbulent. Transition from laminar to turbulence was not considered. Admittedly, turbulence models are not perfect for a complex flow such as the one investigated here. However, the −ω turbulence model used here worked quite satisfactorily in our opinion. It is believed that further improvement of accuracy can be made by increasing the grid size, particularly in the leeward side of the flow region. This will be investigated in the future. the authoritative version for attribution.