• Transactions of the Korean Society of Mechanical Engineers
• /
• v.10 no.1
• /
• pp.102-109
• /
• 1986

Based on the Hartenberg-Denavit symbolic equation, which is one of equations for the kinematic analysis of three dimensional (3-D) linkage, a generalized kinematic motion equation is derived utilizing Euler angles and employing the coordinates transformation. The derived equation can feasibly be used for the motion analysis of any type of 3-D linkages as well as 2-D ones. In order to simulate the general motion of 3-D linkgages on digital computer, the generalized equation is programmed through the process of numerical analysis after converting the equation to the type of Newton-Raphson formula and denoting it in matrix form. The feasibility of theoretically derived equation is experimentally proved by comparing the results from the computer with those from experimental setup of three differrent but generally empolyed 3-D linkages.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.10a
• /
• pp.56-59
• /
• 2007

The screech tone of an underexpanded jet is numerically calculated without any specific modeling for the screech tone itself. A fourth-order optimized compact scheme and fourth-order Runge-Kutta method are used to solve the 2D axisymmetric Euler equation. The Fourier transform of pressure signal at upstream shows the directivity pattern of the screech tone very clearly. Pressure signal is shown to observe the generation of the screech tone. Most importantly, we can simulate the axisymmetric mode change of the screech tone very precisely with the proposed method. It can be concluded that the basic phenomenon of the screech tone including its frequency can be calculated and its mode change can be simulated with inviscid Euler equations.

• Journal of the Society of Naval Architects of Korea
• /
• v.55 no.6
• /
• pp.490-496
• /
• 2018

The consistency of the initially designed waves in the domain is essential for accurate calculation of the added resistance in waves through CFD. In particular, unwanted reflected waves at domain boundaries can cause incorrect numerical solutions due to the superposition with initially designed waves. Euler Overlay Method(EOM) is one of the methods for reducing wave reflections by adding an additional source term to momentum and phase conservation equations, respectively. In this study, we apply the Euler Overlay Method(EOM) to the open-source CFD library, OpenFOAM(R), to simulate the accurate free-surface waves in the domain and the parametric study is performed for efficient implementation of Euler Overlay Method(EOM). Considering that the damping efficiency depends on the selection of the overlay parameter in the added source terms, the size of overlay zone and the wave steepness, the influences of these factors are tested through the wave elevation measured at constant time intervals in the 2D numerical wave tank. Through this process, guidelines for selection of optimal overlay parameter and overlay zone size that can be applied according to the scaling law are finally presented.

• Proceedings of the KSME Conference
• /
• 2002.08a
• /
• pp.165-168
• /
• 2002

This paper describes the dynamics of the weak shock wave propagating inside some kinds of branched pipe bends. Computations are carried out by solving the two-dimensional, compressible, unsteady Euler Equations. The second-order TVD(Total Variation Diminishing) scheme is employed to discretize the governing equations. For computations, two types of branched pipe($90^{\circ}$ branch,$45^{\circ}$ branch) with a diameter of D are used. The incident normal shock wave is assumed at D upstream of the pipe bend entrance, and its Mach number is changed between 1.1 and 2.4. The flow fields are numerically visualized by using the pressure contours and computed schlieren images. The comparison with the experimental data performed for the purpose of validation of computational work. Reflection and diffraction of the propagating shock wave are clarified. The present computations predicted the experimented flow field with a good accuracy.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.881-898
• /
• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• Advances in nano research
• /
• v.12 no.2
• /
• pp.167-183
• /
• 2022

In this paper, the free and forced vibration analysis of rotating cantilever nanoscale cylindrical beams and tubes is investigated under the external dynamic load to examine the nonlocal effect. A couple of nonlocal strain gradient theories with different beams and tubes theories, involving the Euler-Bernoulli, Timoshenko, Reddy beam theory along with the higher-order tube theory, are assumed to the mathematic model of governing equations employing the Hamilton principle in order to derive the nonlocal governing equations related to the local and accurate nonlocal boundary conditions. The two-dimensional functional graded material (2D-FGM), made by the axially functionally graded (AFG) in conjunction with the porosity distribution in the radial direction, is considered material modeling. Finally, the derived Partial Differential Equations (PDE) are solved via a couple of the generalized differential quadrature element methods (GDQEM) with the Newmark-beta techniques for the time-dependent results. It is indicated that the boundary conditions equations play a crucial task in responding to nonlocal effects for the cantilever structures.

• Proceedings of the KSR Conference
• /
• 2010.06a
• /
• pp.1478-1485
• /
• 2010

In this paper, the nonlinear dynamic response of Vehicle-Bridge interaction with the coupled equations of motion including nonlinear Hertzian contact is presented. The moving train model is chosen to have 10 degrees of freedom (DOF). The bridge is modeled as 2D Euler-Bernoulli beam element with 4 DOF for each element, two for rotations and another two for translations. The nonlinear Hertzian contact is used to simulate the interaction between vehicle and bridge. Base on the relationship of wheel displacement of the vehicle and the vertical displacement of the bridge in Hertzian contact, the coupled equations of motion of the whole system is derived. The convenient formulation was encoded into a computer program. The contact forces, contact area and stress of the rail surface were also computed. The accuracy and efficiency of the proposed program are verified and compared with exact analytical solution and other previous studies. Various numerical examples and parametric studies have demonstrated the versatility and applicability of the proposed program.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.98-105
• /
• 1999

The Pressure-based Unstructured-grid Navier-Stokes Solver PUNS-2/3D for incompressible steady and unsteady viscous flows has been developed. It is based on nonstaggered cell-centered finite volume method. Second-order upwind scheme with least-square reconstruction is used for convective fluxes. The SIMPLE method is implemented to couple the pressure and velocity fields. And the time derivatives in the momentum equations are discretised using a second-order Euler backward-differencing scheme. The discretised linear equations are solved by the preconditioned Biconjugate Gradient Stabilized method(Bi-CGSTAB). The developed solver is applied to validation problems using hybrid meshes.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.11
• /
• pp.1157-1169
• /
• 2008

This paper presents spectral element formulation which approximates Lamb wave propagation by PZT transducers bonded on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by a piezoelectric (PZT) layer rigidly bonded on a base plate. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Euler-Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with the electro-mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are obtained through equations of motions converted into frequency domain. Detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through numerical examples.

• Journal of computational fluids engineering
• /
• v.12 no.3
• /
• pp.29-40
• /
• 2007

An implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes. The method can achieve high-order spatial accuracy by using hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. Also, the flows around a 2-D circular cylinder and an NACA0012 airfoil were numerically simulated. The numerical results showed that the implicit discontinuous Galerkin methods couples with a high-order representation of curved solid boundaries can be an efficient method to obtain very accurate numerical solutions on unstructured meshes.