14:00
Linear and non-linear waves I
Chair: Jun Ding
14:00
30 mins
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OSCILLATING SOURCES IN A SHEAR FLOW WITH A FREE SURFACE
Simen Å. Ellingsen, Peder A. Tyvand
Abstract: In the domain of potential theory, oscillating line and point sources form the building blocks of the Green function theory which describes how immersed bodies interact with surface waves (e.g., [1]). The solutions are well established and in routine use when irrotational flow may be assumed. In the presence of a shear flow, however, the behaviour of free surface flow in the presence of point singularities remains relatively unexplored, although other 3D surface flow phenomena have recently been solved [2,3].
We report on progress on the free surface flow in the presence of submerged oscillating line sources (2D) or point sources (3D) when a simple shear flow is present varying linearly with depth. In both cases the Euler equations are solved to linear order in perturbation quantities using standard Fourier transform techniques. The sources are held at rest with respect to the surface for simplicity.
Both in 2D and 3D an new type of solution appears compared to irrotational case, which we identify as a critical layer, whose surface manifestation (“wave”) drifts downstream from the source at the velocity of the flow at the source depth. A previous 2D solutions based on a potential theory [4] fails to capture this effect. We provide a simple physical argument why a critical layer is a necessary consequence of Kelvin’s circulation theorem.
For the flow around a point source in 3D, no potential theory can exist. Again, critical layer-type solutions are found to drift downstream of the source. We provide, for the first time, illustrations of the velocity field downstream of the source to illustrate the shape of the critical layer flow structures. Our results all indicate that the formulation of a Green function theory able to describe bodies in a shear flow will be much complicated by the presence of critical layer solutions.
REFERENCES
[1] J. N. Newman, Marine Hydrodynamics (MIT Press, 1977)
[2] S. Å. Ellingsen, “Initial surface disturbance on a shear current: The Cuahcy-Poisson problem with a twist” Phys. Fluids Vol. 26, 082104 (2014).
[3] S. Å. Ellingsen, “Ship waves in the presence of uniform vorticity” J. Fluid Mech. Vol 742, R2 (2014)
[4] P. A. Tyvand and M. E. Lepperød, “Oscillatory line source for water waves in shear flow” Wave Motion Vol 51, 505-516 (2014)
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14:30
30 mins
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THE MDO SOLUTION OF A SHIP HYDRODYNAMIC DESIGN
Lei Yang, Xi-Zhong Wei, Feng Zhao
Abstract: As the design of ship hydrodynamic requires complex analysis in multiple disciplines，the ignore of handling the interactions between the disciplines will keep optimization away from the system optimal solutions. The Multidisciplinary Design Optimization (MDO) which focuses on solving the couples and coordination among disciplines could overcome this deficiency. So, an effected MDO algorithm called Collaborative Optimization (CO) was applied for a surface ship hydrodynamic design in this paper.
According to the structure of the ship hydrodynamic design environment, the whole system was decomposed into a system level optimization and three disciplinary optimizations; a three-objective functions optimization for a three-discipline design problem which including powering, seakeeping and manoeuvrability was devised. The role of the system level optimization was to improve the design of the whole system using information provided by disciplinary optimization, and the disciplinary optimization could take into all important influence factors account. So, the whole system could be optimized collaboratively and a so-called reality system optimal solution would be got.
At the present stage, the work involves modelling, development and implementation in the framework of the CO approach. Based on the obtained results, the optimization cycle was successful, and reductions of all the objective functions have been finally reached. Further development of this work may rely on the improvement of the discipline analysis models, some high fidelity models, such as simpler flow solvers, RANS solver, may be applied. Meanwhile, dealing with time-consuming CPU codes, a trade-off between efficiency of the optimizer and total CPU time is unavoidable, so a variable-fidelity strategy could be applied; all this work has been in progress.
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15:00
30 mins
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GENERATING AND ABSORBING BOUNDARY CONDITIONS FOR COMBINED WAVE-CURRENT SIMULATIONS
Xing Chang, Ido Akkerman, Rene Huijsmans, Arthur Veldman
Abstract: The CFD simulation tool ComFLOW is extended to investigate the characteristics of wave motions in the presence of steady uniform currents. Initially, the inflow boundary is the superposition of waves and current. Effect of the latter on the former is resolved by solving Navier-Stokes equations within the domain as a next step. A Generating and Absorbing Boundary Condition (GABC) with currents is introduced that allows the simulation of a combined wave-current environment in truncated domain. This GABC is characterized by a rational function approximation of dispersion relation, based on Sommerfeld condition and irrotational wave model.
The artificial boundaries where GABC with current is applied are transparent to incoming and outgoing waves and currents simultaneously. The absorption properties of the GABC for various waves and currents are analysed. The temporal and spatial differences of free surface elevation between the small domain and large domain turn out to be small, i.e. the GABC prevents the reflection from the boundaries well. The large domain here is arranged in such a way that the reflected waves and currents will not reach the outflow boundary of the small domain within the simulation time. The behaviour of GABC in 3D domain is also investigated, where waves and currents are traveling under an angle of incidence colinearly.
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