• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.17 no.3
• /
• pp.166-177
• /
• 2005

This study developed the jet integral model to analyze the behavior of the wastewater discharge in the near field using the fourth order Runge-Kutta method in order to numerically solve the problems of six ordinary differential equations and six unknowns. This jet integral model used the entrainment hypothesis and the manipulation of sonle shape constant. This study also conducted the hydraulic experiments fnr single horizontal buoyant Jet using LIF through the calibration procedure. The results calculated by the previous models, CORMIX 1 and VISJET, and the proposed jet integral model were compared to the hydraulic experimental results. The centerline trajectories predicted by the proposed model were in good agreements with the experimental results in the transition region whereas the trajectories calculated by the VISJET model agreed well with the measured data in the momentum and buoyancy-dominated regions. The centerline dilution calculated by the proposed model agreed generally with the measured dilution in the intial and transition regions while the centerline dilution predicted by the CORMIX 1 was in good agreements with the experimental results in the momentum and buoyancy-dominated regions.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.38 no.10
• /
• pp.973-978
• /
• 2010

In this paper, we studied the shimmy phenomena of an aircraft nose landing gear considering free-play. Shimmy is a self-excited vibration in lateral and torsional directions of a landing gear during either the take-off or landing. This phenomena is caused by a couple of conditions such as low torsional stiffness of the strut, friction and free-play in the gear, wheel imbalance, or worn parts, and it may make an aircraft unstable. Free-play non-linearity is linearized by the described function for a stability analysis in a frequency domain, and time marching is performed using the fourth-order Runge-Kutta method. We performed the numerical simulation of the nose landing gear shimmy and investigated its linear and nonlinear characteristics. From the numerical results, we found limit-cycle-oscillations at the speed under linear shimmy speed for the case considering free-play and it can be concluded that the shimmy stability can be decreased by free-play.

• Journal of Energy Engineering
• /
• v.26 no.2
• /
• pp.64-72
• /
• 2017

The performance analysis of the 70 W class LED lighting system suitable for the Middle East environment was performed using the lumped parameter model. The LED light is composed of a heating substrate, a heat pipe, and a heat sink. We divided the LED lights into four objects and applied energy equilibrium to each of them to establish four lumped nonlinear differential equations. The solution of the simultaneous equations was obtained by the Runge-Kutta method. Convective heat transfer coefficients of the lumped model were obtained by multidimensional CFD analysis. As a result of comparison with experiment, it was found that the heating substrate had an error of $1.5^{\circ}C$ and the upper heat sink had an error of $1.8^{\circ}C$ and the relative error was about 0.6 %. Using this model, temperature distribution analysis was performed for normal operating conditions with an ambient temperature of $55^{\circ}C$, with sunlight only, with abnormal operating conditions with sunlight, and without an upper heat sink.

• Journal of Astronomy and Space Sciences
• /
• v.2 no.1
• /
• pp.19-33
• /
• 1985

The singularities of differential Newtonian equation of motion in three body problem cause the loss of accuracy and the considerable increase of the computer time. These singularities could be eliminated during the process of regularization to transform the independent variables and the coordinate of Newtonian equations of motion. In this study, we calculated the positions and velocities of three body along the time scale to find out the unique solution of regularized Newtonian equations of motion with the $5^{th}$ order Runge-Kutta method by assuming the suitable initial velocities and positions. As the results of these calculations it is shown that the tripe stellar system eventually distintegrated, two of them formed a binary, and the last one escaped from this system with a hyperbolic orbit. This may suggest one possible explanation for the binary formation.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.13 no.12
• /
• pp.5689-5695
• /
• 2012

In this study, vibration properties of seat and human body are analyzed through test and numerical analysis methods by taking into account the viscoelastic characteristics of polyurethane foam as seat material which is applied for vehicle. These viscoelastic characteristics which show nonlinear and quasi-static behavior are obtained by compression test. In addition, the viscous elastic property of polyurethane foam is modelled mathematically by using convolution integral and nonlinear stiffness model. In order to analyze the performance on ride comfort of seat, vertical vibration model is established by using dynamic model of seat and vertical vibration model of human body at ISO5982, and so the related motion equations are derived. A numerical analysis simulation is applied by using the nonlinear motion equation with Runge-Kutta integral method. The dynamic responses of seat and human body on the input of vibration acceleration measured at the floor of the railway vehicle are examined. The variation of the index value at ride comfort on seat design parameters is analyzed and the methodology on seat design is suggested.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.6 no.3
• /
• pp.1-9
• /
• 1986

Dynamic stability of parabolic shallow arches, which are supported by hinges at both ends, is investigated. The Runge-Kutta method is used to perform time integrations of the differential equations of motion with proper boundary conditions. Based on Budiansky-Roth criterion, dynamic critical load combinations are evaluated numerically for cases of step loads of infinite duration and impulse loads, individually. The results are plotted to get interaction curves. The loci of the dynamic critical loads, which are obtained in this study, are proposed as boundaries between the dynamic stability and instability regions for the parabolic shallow arches. The results for the parabolic shallow arches are also compared with those for sinusoidal arches of the same arch rises. According to the investigation, the dynamic stability regions for the parabolic arches are larger than those for the sinusoidal arches. However, it is shown that the arch rise is the more governing factor than the shape.

• Membrane Journal
• /
• v.16 no.3
• /
• pp.204-212
• /
• 2006

A numerical analysis was carried out for separation of carbon dioxide from carbon dioxide/nitrogen gas mixture by a polyethersulfone hollow fiber membrane which has shown a good stability against plasticization by carbon dioxide and an excellent separation efficiency fur carbon dioxide from its gas mixture. A computer program for carbon dioxide separation was developed using the Compaq Visual Fortran 6.6 software. Governing module equations were thought to be an initial-value problem and the nonlinear ordinary differential equations were simultaneously solved using the Runge-Kutta-Verner fifth-order method. From results of numerical analysis, the carbon dioxide partial pressure of the feed stream, the pressure ratio of the feed side to the permeate side and the feed gas residence time at the inside of a membrane were found to be very important factors to affect the permeation characteristics of carbon dioxide.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.44 no.4
• /
• pp.281-289
• /
• 2016

Accurate prediction of the trajectory and time of a time-varying mass parachute system remains essential in the mission requiring a precision airdrop to the ground. In this study, we investigate the altitude-varying behavior of a cross-type parachute system designed to deliver a time-varying mass object like flare. The dynamics of the descending parachute system was analyzed based on the Runge-Kutta method of the ordinary differential system. The drag coefficients of the cross-type parachute and flare were calculated by a CFD code based on the incompressible Navier-Stokes equation. Finally, by using a simplified gust wind model in troposphere, the combined effects of gust wind and time-varying mass were examined in detail.

• Journal of Convergence for Information Technology
• /
• v.10 no.7
• /
• pp.131-137
• /
• 2020

The characteristics of forced vibration with excited sinusoidal force was introduced. Also, numerical analyses and FRF in frequency domain were performed in detail. In this regard, the responses of displacement, velocity and acceleration were investigated in a forced vibration model. The FRF characteristics in real and imaginary part around natural frequency are also discussed. This response approach of forced vibration in time domain is used for the identification and monitoring of sinusoidal forced vibration. For acquiring a displacement, velocity and acceleration, a numerical technique of Runge-Kutta-Gill method was performed. For the FRF(frequency response function), These responses are used. Also, the FRF can represent the intrinsic characteristics of the forced vibration. These performed results and analysis are successful in each damped condition for the forced vibration model. After numerical analysis of the different mass, damping and stiffness, the forced vibration response characteristics with sinusoidal force was discriminated considering its amplitude and frequency simultaneously.

• Structural Engineering and Mechanics
• /
• v.12 no.6
• /
• pp.657-668
• /
• 2001

Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.