• Journal of the Society of Naval Architects of Korea
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• v.51 no.4
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• pp.328-333
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• 2014

A hybrid particle-mesh method based on the vorticity-velocity formulation for solving the incompressible Navier-Stokes equations is a combination of the Vortex-In-Cell(VIC) method for convection and the penalization method for diffusion. The key feature of the numerical methods is to determine velocity and vorticity fields around a solid body on a temporary grid, and then the time evolution of the flow is computed by tracing the convection of each vortex element using the Lagrangian approach. Assuming that the vorticity and velocity fields are to be computed in time domain analysis, pressure fields are estimated through a complete set of solutions at present time step. It is possible to obtain vorticity and velocity fields prior to any pressure calculation since the pressure term is eliminated in the vorticity-velocity formulation. Therefore, pressure field is explicitly treated by solving a suitable Poisson equation. In this paper, we propose a simple way to numerically implement the vorticity-velocity-pressure formulation including a penalty term. For validation of the proposed numerical scheme, we illustrate the early development of viscous flows around an impulsive started circular cylinder for Reynolds number of 9500.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.44-48
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• 2009

In this study, a vortex visualization method based on the vorticity magnitude is developed. One of the simplest models for a vortex is a vortex filament with the maximum vorticity on its center. The proposed method is based on the observation of this ideal distribution of vorticity magnitude. Laplacian and Hessian matrix of vorticity magnitude are tested for detecting the local maximum of vorticity magnitude. These ideas were applied to wake flow past a sphere. It was found that the Laplacian method is not able to distinguish vortices from the underlying shear layer clearly, while the Hessian matrix method does not suffer from this problem.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.4
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• pp.1-10
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• 1998

This paper presents a vorticity-based numerical method for analyzing an incompressible Newtonian viscous flow around an impulsively started cylinder. The Navier-Stockes equations have a natural Helmholtz decomposition. The vorticity transport equation and the pressure equation are derived from this decoupled form. The associated boundary conditions are dynamic for the vorticity and pressure variables representing the coupling relation between them and the force balance on the wall. The various numerical treatments for solving the governing equations are introduced. According to Wu et al.(1994), the boundary conditions are decoupled, keeping the dynamic relation between vorticity and pressure. The vorticity transport equation is formulated by FVM and TVD(Total Variation Diminishing) scheme is used for the convection term. An integral approach similar to the panel method is used to obtain the velocity field for a given vorticity field and the pressure field, instead of the conventional differential approaches. In the numerical process, the structured grid is generated. The results are compared to existing numerical and analytic results for the validity of the present method.

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.47-52
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• 2002

We present an improved Lagrangian vortex method in 2-D incompressible unsteady viscous flows, which is based on a mesh-free integral approach of the velocity-vorticity formulation. Vorticity fields are represented by discrete vortex blobs that are updated by the Lagrangian vorticity transport with the particle strength exchange scheme. Velocity fields are expressed in a form of the Helmholtz decomposition, which are calculated by a fast algorithm of the Biot-Savart integration with a smoothed kernel and by a well-established panel method. No-slip condition is enforced through viscous diffusion of vorticity from a solid body into field. The vorticity flux is determined in such a way that spurious slip velocity vanishes. Through the comparison with the existing finite volume scheme for the transient vortical flows around an impulsively started cylinder at Reynolds number Re=550, we would obtain a more accurate scheme for vortex methods in complicated flows.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.11-21
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• 1998

A vorticity-based method for the numerical solution of the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations for vorticity, velocity and pressure variables are expressed in an integro-differential form. The global coupling between the vorticity and the pressure boundary conditions is fully considered in an iterative procedure when numerical schemes are employed. The finite volume method of the second order TVD scheme is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition. The velocity field is obtained by using the Biot-Savart integral. The Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well established for potential flow analysis. The present formulation is validated by comparison with data from the literature for the two-dimensional cavity flow driven by shear in a square cavity. We take two types of the cavity now: (ⅰ) driven by non-uniform shear on top lid and body forces for which the exact solution exists, and (ⅱ) driven only by uniform shear (of the classical type).

• Journal of the Korea Institute of Military Science and Technology
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• v.17 no.4
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• pp.551-559
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• 2014

The influence of the battle damage hole on the velocity and vorticity flow field have been studied by using particle image velocimetry. Time averaged velocity and vorticity vector fields in the vicinity of jet are presented. The perforated damage hole on a wing created from a hit by anti-air artillery was modeled as a 10% chord size hole which positioned at quarter chord. At low angles of attack, the vorticity in the forward side of the jet is cancelled due to mixing with the wing surface boundary layer. Stretching of vorticity in the backside of the jet generates a semi-cylindrical vortical layer that enclosing a domain with slow moving reverse flow. Conversely, at higher the angles of attack, the jet vorticity advected away from the wing surface and remains mostly confined to the jet. The mean flow behind the jet has a wake-like structure.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.15-28
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• 1998

As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.9
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• pp.1032-1041
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• 2004

In this study we decompose the 3-dimensional velocity field of isotropic turbulent flow into the coherent and the incoherent structure using the discrete wavelet. It is shown that the coherent structure, 3% wavelet modes, has 98% energy and 88% enstrophy and its statistical characteristics are almost same as the original turbulence structure. And it is confirmed that the role of the coherent structure is that it produces the turbulent kinetic energy at the inertia range then transfers energy to the dissipation range. The incoherent structure, with residual wavelet modes, is uncorrelated and has the Gaussian probability density function but it dissipates the kinetic energy in dissipation range. On the procedure, we propose a new but easy way to get the threshold by applying the energy partition percentage concept about coherent structure. The vorticity field extracted from the wavelet-decomposed velocity field has the same structure as the result of the precedent studies which decomposed vorticity field directly using wavelet. Therefore it has been shown that velocity and vorticity field are on the interactive condition.

• Journal of Ocean Engineering and Technology
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• v.22 no.3
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• pp.24-33
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• 2008

In this study, flow and creation and dissipation of vorticity around rectangular floating breakwater is investigated both experimentally and numerically. The PIV system(Particle image velocimetry) is employed to obtain the velocity field in the vorticity of rectangular structure. The numerical model, combined with ${\kappa}-{\varepsilon}$ turbulence model and the VOF method based on RANS equation, is used to analyze the turbulence structure. In the results of this study, the vorticity is found around conner of rectangular structure at all time domain, and creation and dissipation of vorticity are closely related to wave period. Separation points of phase of vortex due to flow separation for longer period waves are faster then for shorter period waves.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1601-1606
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.