• Journal of Environmental Science International
• /
• v.6 no.4
• /
• pp.399-407
• /
• 1997

The pyrolysis reactions of atomic hydrogen with chloroform were studied In a 4 cm 1.6. tubular flow reactor with low flow velocity 1518 cm/sec and a 2.6 cm 1.4. tubular flow reactor with high flow velocity (1227 cm/sec). The hydrogen atom concentration was measured by chemiluminescence titration with nitrogen dioxide, and the chloroform concentrations were determined using a gas chromatography. The chloroform conversion efficiency depended on both the chloroform flow rate and linear flow velocity, but 416 not depend on the flow rate of hydrogen atom. A computer model was employed to estimate a rate constant for the initial reaction of atomic hydrogen with chloroform. The model consisted of a scheme for chloroform-hydrogen atom reaction, Runge-Kutta 4th-order method for Integration of first-order differential equations describing the time dependence of the concentrations of various chemical species, and Rosenbrock method for optimization to match model and experimental results. The scheme for chloroform-hydrogen atom reaction Included 22 elementary reactions. The rate constant estimated using the data obtained from the 2.6 cm 1.4. reactor was to be 8.1 $\times$ $10^{-14}$ $cm^3$/molecule-sec and 3.8 $\times$ $10^{-15}$ cms/molecule-sec, and the deviations of computer model from experimental results were 9% and 12% , for the each reaction time of 0.028 sec and 0.072 sec, respectively.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.145-155
• /
• 1998

A computer code has been developed for the computation of the viscous flow around a ship model with the free surface. In this code, the incompressible Reynolds-averaged Navier-Stokes equations are solved numerically by a finite difference method which employes second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration of the governing equations. For the turbulence closure, a modified version of the Baldwin-Lomax model is exploited. The location of the free surface is determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and the boundary-fitted grid is generated at each time step so that one of the grid surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition is applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method and the computer code developed in the present study, the numerical computations are carried out for both Wigley parabolic hull and Series 60 $C_B=0.6$ ship model and the computational results are compared with the experimental data.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.13 no.6
• /
• pp.88-98
• /
• 2014

A moving mass on a skewed linear guideway model to analyze the friction-induced stick-slip behavior of ball-screw-driven slides is proposed. To describe the friction force, a friction coefficient function is modelled as a third-order polynomial of the relative velocity between the slide mass and a guideway. A nonlinear differential equation of motion is derived and an approximate solution is obtained using a perturbation method for the amplitudes and base frequencies of both pure-slip and stick-slip oscillations. The results are presented with time responses, phase plots, and amplitude plots, which are compared adequately with those obtained by Runge Kutta 4th-order numerical integration, as long as the difference between the static and kinematic friction coefficients is small. However, errors in the results by the approximate solution increase and are not negligible if the difference between the friction coefficients exceeds approximately 40% of the static friction coefficient.

• Journal of Mechanical Science and Technology
• /
• v.17 no.1
• /
• pp.85-96
• /
• 2003

In the present investigation, the nonlinear dynamic buckling of a curved plate subjected to sinusoidal loading is examined. By the theoretical analyses, a highly nonlinear snap-through motion of a clamped-free-clamped-free plate and its effect on the overall vibration response are investigated. The problem is reduced to that of a single degree of freedom system with the Rayleigh-Ritz procedure. The resulting nonlinear governing equation is solved using Runge-Kutta (RK-4) numerical integration method. The snap-through boundaries, which vary with different damping coefficient and linear circular frequency of the flat plate are studied and given in terms of force and displacement. The relationships between static and dynamic responses at the start of a snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. 1) small oscillation about the buckled position-softening spring type motion, 2) chaotic motion of intermittent snap-through, and 3) large oscillation of continuous snap-through motion crossing the two buckled positions-hardening spring type. The responses of buckled plate were found to be greatly affected by the snap-through motion. Therefore, better understanding of the snap-through motion is needed to predict the full dynamic response of a curved plate.

• Advances in aircraft and spacecraft science
• /
• v.9 no.2
• /
• pp.95-102
• /
• 2022

The paper investigates the process of pulsation of a spherical cavity (bubble) in a liquid under the influence of a source of ultrasonic vibrations. The process of pulsation of a cavitation pocket in liquid is investigated. The Kirkwood-Bethe model was used to describe the motion. A numerical solution algorithm based on the Runge-Kutta-Felberg method of 4-5th order with adaptive selection of the integration step has been developed and implemented. It was revealed that if the initial bubble radius exceeds a certain value, then the bubble will perform several pulsations until the moment of collapse. The same applies to the case of exceeding the amplitude of ultrasonic vibrations of a certain value. The proposed algorithm makes it possible to fully describe the process of cavitation pulsations, to carry out comprehensive parametric studies and to evaluate the influence of various process parameters on the intensity of cavitation.

• Journal of Ocean Engineering and Technology
• /
• v.34 no.6
• /
• pp.406-418
• /
• 2020

In this study, a nonlinear wave simulation code is developed using a higher-order spectral (HOS) method. The HOS method is very efficient because it can determine the solution of the boundary value problem using fast Fourier transform (FFT) without matrix operation. Based on the HOS order, the vertical velocity of the free surface boundary was estimated and applied to the nonlinear free surface boundary condition. Time integration was carried out using the fourth order Runge-Kutta method, which is known to be stable for nonlinear free-surface problems. Numerical stability against the aliasing effect was guaranteed by using the zero-padding method. In addition to simulating the initial wave field distribution, a nonlinear adjusted region for wave generation and a damping region for wave absorption were introduced for wave generation simulation. To validate the developed simulation code, the adjusted simulation was carried out and its results were compared to the eighth order Stokes theory. Long-time simulations were carried out on the irregular wave field distribution, and nonlinear wave propagation characteristics were observed from the results of the simulations. Nonlinear adjusted and damping regions were introduced to implement a numerical wave tank that successfully generated nonlinear regular waves. According to the variation in the mean wave steepness, irregular wave simulations were carried out in the numerical wave tank. The simulation results indicated an increase in the nonlinear interaction between the wave components, which was numerically verified as the mean wave steepness. The results of this study demonstrate that the HOS method is an accurate and efficient method for predicting the nonlinear interaction between waves, which increases with wave steepness.

• Journal of Ocean Engineering and Technology
• /
• v.33 no.5
• /
• pp.400-410
• /
• 2019

In this study, the numerical code for the 3D nonlinear dynamic analysis of an SLWR (Steel Lazy Wave Riser) was developed using the lumped mass line model in a FORTRAN environment. Because the lumped mass line model is an explicit method, there is no matrix operation. Thus, the numerical algorithm is simple and fast. In the lumped mass line model, the equations of motion for the riser were derived by applying the various forces acting on each node of the line. The applied forces at the node of the riser consisted of the tension, shear force due to the bending moment, gravitational force, buoyancy force, riser/ground contact force, and hydrodynamic force based on the Morison equation. Time integration was carried out using a Runge-Kutta fourth-order method, which is known to be stable and accurate. To validate the accuracy of the developed numerical code, simulations using the commercial software OrcaFlex were carried out simultaneously and compared with the results of the developed numerical code. To understand the nonlinear dynamic characteristics of an SLWR, dynamic simulations of SLWRs excited at the hang-off point and of SLWRs in regular waves were carried out. From the results of these dynamic simulations, the displacements at the maximum bending moments at important points of the design, like the hang-off point, sagging point, hogging points, and touch-down point, were observed and analyzed.

• Journal of the Korean Society of Fisheries and Ocean Technology
• /
• v.29 no.3
• /
• pp.214-219
• /
• 1993

Counter balance valve is used as one part of hydraulic motor brake system. The function of this valve is to protect over-run or free falling of inertia load. But occasionally the brake system with counter balance valve makes some undesirable problems such as pressure surges or vibrations. These problems may hurt system safety and driver's conformability. Nevertheless, studies on dynamic characteristics of hydraulic system including counter balance valve are very rare, so further accumulation of research results are required. In this study, for the purpose of easy estimation about dynamic characteristics of hydraulic system including counter balance valve, precise formulation describing fluid dynamics and valve dynamics under various boundary conditions were made. The equations obtained in the preceding process include some parameters that must be got experimentally. Flow coefficients of valve and choke are the most significant ones among the parameters. So these parameters are obtained experimentally in this study, and experimental equations obtained from the experimental data were used for numerical calculation. The equations were analysed by numerical integration using Runge-Kutta method, because the equations contain various nonlinear terms. From the numerical analysis, it was verified that the dynamic response of counter balance valve and pressure variation at each elements can be estimated very easily. So the analysing method developed in this study enabled very easy estimating the relation between the performances of counter balance valve and various physical parameters related to the valve. Conclusively, it is said that the results obtained in this study can be used very usefully to develop a new type counter balance valve or to apply the valve to actual hydraulic system for various industrial equipments.

• Structural Engineering and Mechanics
• /
• v.24 no.6
• /
• pp.709-725
• /
• 2006

In this paper the buckling and post-buckling behavior of slender bars under self-weight are studied. In order to study the post-buckling behavior of the bar, a geometrically exact formulation for the non-linear analysis of uni-directional structural elements is presented, considering arbitrary load distribution and boundary conditions. From this formulation one obtains a set of first-order coupled nonlinear equations which, together with the boundary conditions at the bar ends, form a two-point boundary value problem. This problem is solved by the simultaneous use of the Runge-Kutta integration scheme and the Newton-Raphson method. By virtue of a continuation algorithm, accurate solutions can be obtained for a variety of stability problems exhibiting either limit point or bifurcational-type buckling. Using this formulation, a detailed parametric analysis is conducted in order to study the buckling and post-buckling behavior of slender bars under self-weight, including the influence of boundary conditions on the stability and large deflection behavior of the bar. In order to evaluate the quality and accuracy of the results, an experimental analysis was conducted considering a clamped-free thin-walled metal bar. As this kind of structure presents a high index of slenderness, its answers could be affected by the introduction of conventional sensors. In this paper, an experimental methodology was developed, allowing the measurement of static or dynamic displacements without making contact with the structure, using digital image processing techniques. The proposed experimental procedure can be used to a wide class of problems involving large deflections and deformations. The experimental buckling and post-buckling behavior compared favorably with the theoretical and numerical results.

• Advances in aircraft and spacecraft science
• /
• v.8 no.4
• /
• pp.345-372
• /
• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.