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Figure 11: Wave profile along the plate for incresing Froude number (top to bottom). Normalized wave height η=h/(αFr), α=4.5°. Navier-Stokes simulation: two-block O-O grid 40×24×16.

Figure 12: Wave profile along the plate for incresing Froude number (top to bottom). Normalized wave height η=h/(αFr), α=9.0°. Navier-Stokes simulation: two-block O-O grid 40×24×16.

means of the inviscid model with respect to the experiments and to the Navier-Stokes calculation is not clear at the present stage. In more details, the gap between the two predictions seems not to be due to the separation bubble at the leading edge, otherwise the same problem would be observed when computing double model flows. Moreover, it is unlikely to be caused by geometrical linearization of the free surface, because the same condition has very little effects on the forces when applied to the Navier-Stokes calculation.

Therefore, a possible reason of such a behaviour must be sought in the nonlinear terms in the free surface boundary conditions, neglected in our inviscid computations. Another possible cause could be related to the Kutta condition imposed at the trailing edge. In fact, this condition implies continuity of the total pressure, and therefore it does not allow a free surface jump across the vortex layer. Future investigations will try to clarify the question.

References

[1] Baldwin, B.S., Lomax, H. “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows”, AIAA Paper 78–257, 1978.

[2] Bassanini P., Casciola C., Lancia M.R., Piva R., “A Boundary Integral Formulation for the Kinetic Field in Aerodynamics ”, Eur. J. Mech., B/Fluids, vol 10, 605–627, 1991; vol 11, 69–92, 1992.

[3] Belotserkovskii, S.M. ( 1969). “Calculation of the flow around wings of arbitrary planforms in a wide range of angles of attack”. NASA TT F-12.

[4] Brandt A., “Multigrid Techniques: 1984 Guide with Application to Fluid Dynamics ”, The Weizmann Institute of Science, Rehovot (Israel), 1984.

[5] Brard R., “A Vortex theories for bodies moving in water”, 9th Symp. on Naval Hydrodynamics, R.Brard and A.Castera Eds, Washington, U. S.Gov. Printing Office, 1187–1284.

[6] Burcher R.K., “The prediction of the manoeuvring characteristics of vessels” Phil. Trans. R. Soc. Lond., A, 334, 265–279, 1991.

[7] Lamar, J.E. ( 1974). “Extension of leading-edge suction analogy to wings with separated flow around the side edges at subsonic speeds”. NASA TR R-428.



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