• Journal of computational fluids engineering
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• v.12 no.2
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• pp.53-62
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• 2007

A high resolution numerical method aimed at solving cavitating flow is proposed and applied to gas-liquid two-phase shock tube problem. The present method employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. By applying the homogeneous equilibrium cavitation model, the present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation and large density changes. The speed of sound for gas-liquid two-phase media is derived on the basis of thermodynamic relations and compared with that by eigenvalues. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media at isothermal condition and some data related to computational efficiency are made. Comparisons of predicted results and exact solutions are provided and discussed.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.5
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• pp.8-13
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• 2004

In order to better understand the characteristics of the flow field around the submerged hydrofoil of finite span with high speed and shallow submergence. a numerical code which can solve the flow around a fast lifting body under the free surface was developed and used to obtain various interesting features of the flow. The code was based on the panel method of Hess( 1972), and the free surface condition was linearized to conform with the assumption of the high Froude number. It is shown that the effect of the change of submerged depth. angle of attack and aspect ratio upon the sectional lift coefficient is rather significant for the case of the chosen example wing, which has the rectangular planform. Since Lee(2002)'s theoretical results were for the wing of elliptical planform, the direct comparison of the two results was not possible. It seems that more computational results are in need to compare the theoretical and the numerical prediction in detail.

• Journal of Ocean Engineering and Technology
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• v.9 no.2
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• pp.53-60
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• 1995

A multi-leg spread mooring system for floating offshore structures is important, but the multi-leg static analysis is complicated due to the nonlinear behavior of each line and the effect of current which affects each line differently. The pretensioned position of the multi-leg mooring system obtained from the static equilibrium condition changes into a different position due to external loads and current. In this paper, the new position and the static tension at each line are caculated. The relation between the initial static equilibrium position and the new position due to the external loads is expressed in terms of the Taylor's series expansion. The Runge-Kutta $4^{th}$ method is employed in analyzing the 3-dimensional static cable nonlinear equations.

• Journal of Astronomy and Space Sciences
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• v.5 no.1
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• pp.19-30
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• 1988

The existence of the j-type collision periodic orbit is examined on the condition of mass ratio 0.9878449 and Jacobian constant 2.9∼3.4. Using the Birckhoff's regularization method and the 5th order Runge-Kutta variable step-sized numerical roution introduced by Fehlberg (1968). we test their periodicities. As the results, 4 j-type collision orbits and 5 peculiar orbits are represented. There are good agreements in this collision orbits with the relationship between the period and the shape of orbit proposed by Pinotsis Zikides(1984).

• Journal of Ocean Engineering and Technology
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• v.2 no.1
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• pp.83-89
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• 1988

정지된 유동장에 놓인 반무한 평판이 횡방향으로 갑자기 출발하는 경우에 있어서 평판의 끝에서 발생하는 보텍스의 거동을 해석적 및 수치적 측면에서 검토하였다. 해석적 방법은 단일 보텍스 모델에 근거를 두었으며, 해석결과 순환량은 시간의 1/3승, 보텍스의 중심까지의 거리는 시간의 2/3승에 비례하여 증가함을 알 수 있었다. 룬게.쿠타(Runge-Kutta)방법을 써서 분리 보텍스 모델에 따른 비선형 운동방정식의 해를 수치적으로 구했다. 수치해는 시간의 경과에 따라 해석 해에 접근하였다. 보텍스의 형상에 있어서도 실험결과와 잘 맞았다.

• Journal of the Korean Society of Combustion
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• v.1 no.2
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• pp.41-49
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• 1996

A numerical study is conducted to investigate the periodically unstable shock induced combustion around blunt bodies in stoichiometric hydrogen-air mixtures. Euler equations are spatially discretized by upwind-biased third order scheme and temporally integrated by Runge-Kutta method. Chemistry model used in this study involves 8 elementary kinetics steps and 7 species. At a constant Mach number, the effects of projectile size, inflow pressure and inflow temperature are examined with Lehr#s experimental condition as a reference. In addition to oscillation frequency, characteristic distances and time averaged values are found from the result to find an relation with dimensionless parameters. As a result, it is found that the effects of inflow pressure and body size are very similar and $Damk{\ddot{o}}hler$ number plays an important role in determining the instability characteristics.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.870-875
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• 2003

This paper deals with the free vibrations of horizontally curved beams with the general boundary condition, which consists of translational and rotational springs. The equations of general boundary condition of such beams are derived, while the ordinary differential equations governing free vibrations are adopted from the literature. The parabola as the curved beam's curvilinear shape is considered in numerical examples. For calculating the natural frequencies, the governing equations are solved by numerical methods. The Runge-Kutta and Determinant Search Methods are used for integrating the differential equations and for calculating the natural frequencies, respectively. for validation purpose, the numerical results obtained herein are compared to those obtained from the SAP 2000. With regard to numerical results, the relationships between frequency parameters and various beam parameters are presented in the forms of Table and figures.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.91-97
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• 2014

A high resolution numerical method aimed at solving cavitating flow was proposed and applied to gas-liquid two-phase shock tube problem with arbitrary void fraction. The present method with compressibility effects employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. The Jacobian matrix from the inviscid flux of constitute equation is diagonalized analytically and the speed of sound for the two-phase media is derived by eigenvalues. So that the present method is appropriate for the extension of high order upwind schemes based on the characteristic theory. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results of high speed flow phenomena such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and some data related to computational efficiency are made. Comparisons of predicted results and solutions at isothermal condition are provided and discussed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.155-162
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• 2009

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved numerically. The Runge-Kutta method and shooting method are used to integrate the differential equation and to determine the unknown initial boundary condition of the given beam. In the numerical examples, the simple beams are considered as the end constraint and also, the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data related with the static behaviors, under which static maximum behaviors become to be minimum.

• Laser Solutions
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• v.5 no.1
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• pp.23-31
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• 2002

The uniform metal droplet generation using Nd-YAG laser was studied and experiment was carried out. The shape and volume of developed droplet was measured and the Young-Laplace equation and equilibrium condition of force were applied this model. The differential equation predicting shape of droplet using equilibrium condition of force instead of Navier-stokes equation was induced and numerical solution of differential equation compared with experimentation data. The differential equation was solved by Runge-Kutta method. Surface tension coefficient of droplet was determined with numerical solution relate to experimental result under the statical condition. In case of dynamic vibration, metal droplet shape and detaching critical volume are predicted by recalculating proposed model. The result revealed that this model could reasonably describe the behavior of molten metal droplet on vibration.