• International Journal of Fluid Machinery and Systems
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• v.10 no.2
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• pp.119-137
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• 2017

Although the stall stagnation phenomena have often been experienced in site and also analytically in numerical experiments in surges in systems of compressors and flow paths, the fundamental causes have not been identified yet. In order to clarify the situations, behaviours of infinitesimal disturbance waves superposed on a main flow were studied in a simplified one-dimensional flow model. A ratio of the amplifying rate of the system instability to the characteristic slope of the compressor element was surveyed as the instability enhancement factor. Numerical calculations have shown the following tendency of the factor. In the situation where both the sectional area ratio and the length ratio of the delivery flow-path to the suction duct are sufficiently large, the enhancement factors are greater in magnitude, which means occurrence of ordinary deep surges. However, in the situation where the area ratio and/or the length ratio is relatively smaller, the enhancement factor tends to lessen significantly, which situation tends to suppress deep surges for the same value of the characteristic slope. It could result in the stall stagnation condition. In the domain of area ratio vs. length ratio of the delivery duct to the suction duct, contour-lines of the enhancement factor behave qualitatively similar to those of the stall stagnation boundaries of a fan analytically obtained, suggesting that a certain range of the enhancement factor values could specify the stagnation occurrence. The significant decreases in the factors are observed to accompany appearances of phase lags and travelling waves in the wave motions, which macroscopically suggests breaking down of the complete surge actions of filling and emptying of the air in the delivery duct. The strength of the action is deeply related with acoustic interferences and is evaluated in terms of the volume-modified reduced resonance frequency proposed by the author. These observations have shown the fundamental cause and the sequence of the stall stagnation in principle.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.4
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• pp.1489-1498
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• 2013

The monolithically coupled finite element analysis for a deformable unsaturated soil slope is performed to investigate the effect of antecedent rainfall which is assumed by initial conditions varying degree of saturation (36, 51, 77%) in finite element analysis. The distributions of matric suction and deformation on slope surface obtained from numerical simulation show the instability of antecedent rainfall-induced unsaturated soil slope. Moreover, the numerical analysis using Drucker-Prager model can be checked if a soil slope has reached failure (trial failure criterion $f^{tr}$ >0, plastic behavior) or not (trial failure criterion $f^{tr}$ < 0, elastic behavior). It is found that displacement of slope surface layer increases and the matric suction on soil slope decreases with an increase of initial degree of saturation by antecedent rainfall. Especially, the matric suction of the soil slope in dry condition (S=36%) rapidly decreases rather than that in wet condition (S=51%) at the same rainfall duration. The results of the trial failure criterion ($f^{tr}$ > 0) show slope instability in the toe region and surface of the slopes.

• Journal of the Korean Society for Marine Environment & Energy
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• v.19 no.2
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• pp.99-110
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• 2016

When a riser is damaged, the oil spills to sea. Oil spills cause huge economic losses as well as a destruction of the marine environment. To reduce losses, it is needed to predict spilled oil volume from risers and the excursion of the oil. The present paper simulated the oil spill for a damaged riser using open source libraries, called Open-FOAM. To verify numerical methods, jet flow and Rayleigh-Taylor instability were simulated. The oil spill was simulated for various damaged leak size, spilled oil volume rates, damaged vertical locations of a riser, and current speeds. From results, the maximum excursion of the spilled oil at the certain time was predicted, and a forecasting model for various parameters was suggested.

• International Journal of Aeronautical and Space Sciences
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• v.6 no.2
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• pp.84-96
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• 2005

Helical tip vortex is known as stable vortex structure, however the specific frequency component of far wake perturbation induces the vortex pairing in hover and axial flight. It is expected that the tip vortex pairing phenomena may happen in transition flight and very low advance ratio flight so that inflow may be most nonuniform in the low advance ratio flight. The objectives of this paper are that a tip-vortex instability during the transition from hover into very low advance ratio forward flight is numerically predicted to understand a physics by using a time-marching free-wake method. To achieve the objectives, numerical method is firstly validated in typical axial and forward flights cases. Present scheme with trim routine can predict airloads and inflow distribution of forward flight with good accuracy. Then, the transition flight condition is calculated. The rotor used in this wake calculation is a small-scale AH-1G model. By using a tip-vortex trajectory tracking method, the tip-vortex pairing process are clearly observed in transient flight($\mu$=0.03) and disappears at a slightly higher advance ratio($\mu$=0.05). According to the steady flight simulation at $\mu$=0.03, it is confirmed the tip-vortex pairing process is continued in the rear part of rotor disk and not occurs in the front part. Time averaged inflow in this case is predicted as smooth distribution.

• Steel and Composite Structures
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• v.39 no.5
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• pp.615-630
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• 2021

The main purpose of the present work was to study the dynamic instability of a three-layered, thick composite sandwich beam with the functionally graded (FG) flexible core subjected to an axial compressive follower force. Flutter instability of a sandwich cantilever beam was analyzed using the high-order theory of sandwich beams, for the first time. The governing equations in general for sandwich beams with an FG core were extracted and could be used for all types of sandwich beams with any types of face sheets and cores. A polynomial function is considered for the vertical distribution of the displacement field in the core layer along the thickness, based on the results of the first Frosting's higher order model. The governing partial differential equations and the equations of boundary conditions of the dynamic system are derived using Hamilton's principle. By applying the boundary conditions and numerical solution methods of squares quadrature, the beam flutter phenomenon is studied. In addition, the effects of different geometrical and material parameters on the flutter threshold were investigated. The results showed that the responses of the dynamic instability of the system were influenced by the follower force, the coefficients of FGs and the geometrical parameters like the core thickness. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory. The results showed that the follower force of the flutter phenomenon threshold for long beams tends to the corresponding results in the Timoshenko beam.

• 한국방재학회:학술대회논문집
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• 2007.02a
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• pp.181-185
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• 2007

A free-surface correction(FSC) method is presented to solve the 3-D shallow water equations. Using the mode splitting process, FSC method can simulate shallow water flows under the hydrostatic assumption. For the hydrostatic pressure calculation, the momentum equations are firstly discretized using a semi-implicit scheme over the vertical direction leading to the tri-diagonal matrix systems. A semi-implicit scheme has been adopted to reduce the numerical instability caused by relatively small vertical length scale compare to horizontal one. and, as the free surface correction step the final horizontal velocity fields are corrected after the final surface elevations are obtained. Finally, the vertical final velocity fields can be calculated from the continuity equation. The numerical model is applied to the calculation of the simulation of flow fields in a rectangular open channel with the tidal influence. The comparisons with the analytical solutions show overall good agreements between the numerical results and analytical solutions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.195-199
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• 1993

In the analysis of metal forming processes by the finite element method, there are many numerical instabilities such as element locking, hourglass mode, shear locking. These instabilities may have a bad effect upon accuracy and convergence. The present work is concerned with improvement of stability and efficiency in two dimensional rigid-plastic finite element method using various type of elements and numerical integration schemes. AS metal forming examples, upsetting and backward extrusion are taken for comparison among the methods : various element types and numerical integration schemes. comparison is made in terms of stability and efficiency. As a result, it has been shown that the finite element computation is stabilized from the viewpoint of computational time, convergency, and numerical instability.

• Journal of Mechanical Science and Technology
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• v.16 no.3
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• pp.395-402
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• 2002

This paper shows how to formulate the transient analysis of 2-dimensional Hagen-Poiseuille flow using smoothed particle hydrodynamics (SPH). Treatments of viscosity, particle approximation and boundary conditions are explained. Numerical tests are calculated to examine effects caused by the number of particles, the number of particles per smoothing length, artificial viscosity and time increments for 2-dimensional Hagen-Poiseuille flow. Artificial viscosity for reducing the numerical instability directly affects the velocity of the flow, though effects of the other parameters do not produce as much effect as artificial viscosity. Numerical solutions using SPH show close agreement with the exact ones for the model flow, but SPH parameter must be chosen carefully Numerical solutions indicate that SPH is also an effective method for the analysis of 2-dimensional Hagen-Poiseuille flow.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.528-531
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• 2004

For a simple one-dimensional ignition problem a mathematical model is described to investigate the difficulties in numerical simulations. Some computation results are obtained and comparison is made with analytical solution. Discussions are made on topics such as 1) coordinate transformation, 2) gas-phase and solid-phase analysis; (divergence form of the governing system, a finite-volume discretization, implicit time integration, upwind split flux, spatial accuracy improvement are described. Mass, reagent mass, and energy conservations are solved.), and 3) method to determine quantities on the burning surface (matching). Results obtained for small values of the non-dimensional pressure show a steady-combustion and good agreement with the analytical solution. Numerical instability appeared for larger values of the pressure, discussion on the cause of the problem is made. This effort is a part of a study of flame spread phenomena on solid propellant surface.

• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.1095-1099
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• 2017

A fission source can act as a stabilization element in coupled Monte Carlo simulations. We have observed this while studying numerical instabilities in nonlinear steady-state simulations performed by a Monte Carlo criticality solver that is coupled to a xenon feedback solver via fixed-point iteration. While fixed-point iteration is known to be numerically unstable for some problems, resulting in large spatial oscillations of the neutron flux distribution, we show that it is possible to stabilize it by reducing the number of Monte Carlo criticality cycles simulated within each iteration step. While global convergence is ensured, development of any possible numerical instability is prevented by not allowing the fission source to converge fully within a single iteration step, which is achieved by setting a small number of criticality cycles per iteration step. Moreover, under these conditions, the fission source may converge even faster than in criticality calculations with no feedback, as we demonstrate in our numerical test simulations.