Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Modeling 3D Unsteady Sheet Cavities Using a Coupled UnRANS-BEM code
Modeling 3D Unsteady Sheet Cavities Using a Coupled UnRANS-BEM code
Pages 670-686
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From page 670... ...
dynaflow-inc . com ABSTRACT The flow field of a propeller blade subjected to sheet and cloud cavitation includes several complex and strongly interacting features: flow separation, turbulence, presence of vertical structures, deforming and moving free surfaces, free surface instability, and cavity break-up.
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From page 671... ...
The potential part is solved using the BEM code, which is modified to account for the vertical components, both in the time stepping procedure and in the boundary conditions. The Helmholtz decomposition is carried into the momentum equation, which results in a modified Bernoulli equation involving the vertical and viscous terms.
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From page 672... ...
timesteps (one for each of the methods) , ad th ough a g id "overl y" of The results of one medhod onto the other UnRANS Approach for the Liquid Behavior In turbulent flows a wide spech m of eddy sizes wish a corresponding spectrum of fluctuation frequencies exist he largest eddies have sizes on the same order of magnitude as the flow domain, have low frequencies, ad are affected by The boundaries ad the mea flow he smallest eddies, on the ocher h Ed, are detemmined by the viscosity of the fluid ad have high frequency fluct ations As the Rey olds m mber of a given flow increases, The width of the spectr m, or the difference between The largest ad smallest eddies more As he large eddies exhort kinetic energy from the mea motion Ed feed it to the large scale turbulent motion Energy is passed dow The cascade to smaller ad smaller eddies mtil viscosity cases the dissipation of the eddies he rate of energy dissipated is determined by the large Dale motion although dissipation occurs at the smallest scales it is impo tat to note that viscosity does not detemmine the amo mt of dissipated energy, but only The scale at which dissipation occurs, ad that away f om boundaries much of the physics of t rbulence is effectively mviscid Direct mmmerical simulations ENS)
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From page 673... ...
: at 0~ :s s,~Ow, where s is the distance normal to He solid surface This eddy s-iscosiries~ mug ~ ~ are in turn written m terms of average flow characteristics i yolvmg the local vorticity ad the law of He wall coordinates, y+ The UNCLE code is based on the artificial compressibility method m which a time derivatiy of the pressure is added to She contimmity equation to couple it with the moment m equations As a consequence, a hyperbolic system of equations is formed md cm be sold d using a timemarching scheme The method can be marched in pseud.ntime to reach a steady state solution when a din regency free y lociy field is obtained To obtain a t me acurate solution, a sub-iteratiy procedure with pseudo-time steps is performed at each physical time step UnRANS Free Surface Conditions When coupling the NarienStokes computation with the bo mdary element code 3DYNAFS, He Nayier-Stokes flow sold r mu t be ale to handle gas liquid mte face ad moving bo mdaries We have implemented in UNCLE a generali:osd free surface bo mdary conditions that e force zero shear stress ad normal shess balm e on He bubble surface For He curvilinear coordinate system with orthogonal bo mdaries, the bo mdary condition can be w itten as follows: · V 733tg ..
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From page 674... ...
Multi-block "ridding used in the modified UnRANS code UNCLE for the sheet cavitation problem treatment. difference method on the simple computational domain.
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provides an expression for f / t needed to update f at the following time step. Dual Reciprocity BEM To update the nodal values of f at the free surface at successive time steps we need to solve in an efficient way the Poisson equation for .
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From page 676... ...
An adaptive time stepping selects a time step proportional to the ratio of the smallest internodal distance to the largest nodal velocity. Wake and Tip Vortex Modeling in the BEM In order to properly describe the pressure and the lift _ <~ .~ distribution on the foil it is necessary with an inviscid method, to introduce additional singularity distributions to account for real fluid effects that are not directly recovered by the irrotational model.
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From page 677... ...
and of a dipole distribution at N+1 of intensity, fN ~ fN f:. The modified BEM procedure is then to obtain at each time step: a)
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The figure compares the results of the Navier Stokes code with those of the BEM code when the Kutta condition is and is not accounted for. Near the trailing edge, a separation area exists for this high incidence angle, that is captured by the RANS code (see Figure 9)
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From page 679... ...
Numerical results were then obtained using the BEM code 3DYNAFS alone, the modified UnRANS code UNCLE alone and the BEM/UnRANS coupled code that is still being developed. The mesh of the foil was chosen to be at the beginning of the calculation denser close to the leading edge, where the cavitation inception takes place, and coarser near the trailing edge.
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From page 680... ...
Sheet cavity volume versus time at different incidence angles obtained with the modified UnRANS code reentrant jet in collapsing bubbles (Zhang et al, 199* , Chahine et al, 19964.
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and with the UnRANS code (bottom)
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The change in the pressure distribution as the sheet cavity develops can be seen in Figure 24. Finally Figure 25 shows the difference in the cavity shape and in the flow field pressure distribution at a selected time and at various span locations over the foil.
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This development involves mainly definition of adequate grid generation procedures. From our numerical results it appear that there are three schemes for cavity shape oscillations at various flow conditions.
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From page 684... ...
and Chahine, G L., "Numerical Simulation of Unsteady Sheet Cavitation on a 3D Hydrofoil," Third International Symposium on Cavitation, Grenoble France, April, 1998.
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From page 685... ...
ad Brebbia, C A, ad Wrobel, L C, ' he dual reciprocity bo mdary element method," Computational mechaics publications, Soubhampton, Elsevier, London, 1991 29 Pellone, C, Maibe, T Bria omMarjollet, L, 'Partially Cavitating Hydkofoils: E perimental adN merical Analysis','Jou~nalofShipRerear h, Vol.
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From page 686... ...
DISCUSSION C Song University of Minnesota, USA Assuming you can overcome the simu ation of re-entraut jet, how wou d t y to simu ate the very small cavities generated in the cloud cavity?
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