• 한국추진공학회지
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• 제10권2호
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• pp.1-14
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• 2006

본 논문은 약한 불안정 데토네이션 영역부터 강한 불안정 데토네이션 영역까지 여러 영역에 걸친 데토네이션 파 셀 구조 모사에 대한 수치적 문제점들을 살펴보았다. 비열 비 값이 변하는 점성 유체 역학 방정식 및 1단계 Arrhenius 반응 모델 해석을 위하여 MUSCL-type TVD 기법을 이용한 공간 차분과 4차 정확도의 Runge-Kutta 시간 적분을 이용하였다. 일련의 수치해석 연구는 여러 반응 상수 및 격자 해상도에 따른 데토네이션 셀 구조를 해석하기 위하여 요구되는 계산 조건을 구하기 위하여 다양한 데토네이션 현상 영역에서 수행되었다. 다른 영역의 데토네이션 현상에서 셀 구조를 포착하기 위한 계산 영역의 크기와 최소 격자 해상도를 찾아내기 위하여 정상 1차원 ZND 해석 결과와 전산 해석 결과를 비교 검토하였다.

• 한국수자원학회논문집
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• 제38권6호
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• pp.429-438
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• 2005

본 연구에서는 Boussinesq 방정식을 이용하여, 불규칙 파랑의 직접적인 해석이 가능한 한 쌍의 상미분방정식을 유도하였다. 입사파랑은 TMA(TEXEL storm, MARSEN, ARSLOE) 천해 스펙트럼을 이용하여 재현하였으며, 지배방정식은 4차 Runge-Kutta 법을 이용하여 적분하였다. 새로 유도된 파랑 방정식을 이용하여, 일정 수심을 진행하는 파랑의 비선형 에너지 교환효과를 계산하였다. 또한, 일정 경사면의 정현파형 지형을 통과하는 불규칙파랑의 특성에 관해 수치적으로 검토하였다. 비선형성이 불규칙파랑의 통과와 반사에 큰 영향을 주었다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 추계 학술대회논문집
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• pp.235-238
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• 2005

The unsteady supersonic flow over two- and three-Dimensional cavities has been analyzed by the integration of unsteady Reynolds-Averaged Navier-Stokes(RANS) with the k - w turbulence model. The unsteady flow is characterized by the periodicity due to the mutual relation between the shear layer and the internal flow in cavities. Numerical method is upwind TVD scheme based on the flux vector split with the Van Leer limiters, and time accuracy is used explicit 4th stage Runge-Kutta scheme. Cavity flows are Comparison of two- and three-dimensional. The cavity has a L/D ratio of 3 for two-dimensional case. and same L/D and W/D ratio is 1 for three-dimensional case. The Mach and Reynolds numbers are held constant at 1.5 and 450000 respectively. For the three-dimensional case, the flow field is observed to oscillate in the 'shear layer mode' with a feedback mechanism that follow Rossiter's formula. On the other hand, the self-sustained oscillating flow transitions to a 'wake mode' for the two-dimensional simulation, with more violent fluctuations inside the cavity.

• Tribology and Lubricants
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• 제33권6호
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• pp.309-314
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• 2017

This paper presents a theoretical investigation of the dynamic characteristics of externally pressurized air pad bearings with closed loop grooves. These grooves are made on the surface of bearings to reduce the number of supply holes so that manufacturing costs can be reduced. The semi-implicit method is applied to calculate the time varying pressure profile on the air bearing surface owing to the advantages of numerical stability and fast time tracing characteristics. The static pressure of the groove bearings is much higher than that without grooves, so the groove bearings can provide high load carrying capacity. The equation of motion considering vertical motion and tilting motion are also solved using the Runge-Kutta 4th order method. By combining the semi-implicit method and the Runge-Kutta method, fast calculations of the dynamic behavior of the air bearing can be achieved. The variations of bearing reaction force, air film reaction moment, height, and tilting angle are investigated for the step force input, which is 20% higher than the bearing reaction, when the nominal clearance is 6 mm. The effect of the groove width and the groove depth are investigated by calculating the dynamic behavior. The possibility of the air hammering with the depth of the groove is found and discussed.

• 해양환경안전학회지
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• 제1권1호
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• pp.27-38
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• 1995

In this paper, a program for the calculation of GZ curve for a ship in waves is developed and GZ curves for a ferry in the still water and in waves are calculated. And the added mass, damping, restoring forces and wave exciting forces are calculated by using the strip theory given by Salvesen, Tuck, Faltinsen. Capsizing simulations are perfoned in consideration if the nonlinear restoring forces of the ship in waves by using the Runge-Kutta 4-th method.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1997년도 제25회 춘계학술대회
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• pp.204-209
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• 1997

This paper reports on the theoretical study of the vane motions in a positive displacement vane pump. Vane detachment cause the pressure fluctuation, noise, wear in cam ring, and decrease the volumetric efficiency. Dynamic equation of vane motion and flow continuity equation have been modeled and solved simultaneously using 4th order Runge-Kutta method. As results of analysis, vane detachment occurs due to pressure overshoot by excess compression in the pumping chamber. Amount of vane detachment has been reduced by decreasing the pressure overshoot.

• 대한전기학회논문지
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• 제39권5호
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• pp.516-518
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• 1990

We have derived the equation which involves the variation of electron energy with time in a lowly ionized plasma when a low alternating electric field is applied. We consider only elastic collisions between electrons and neutral atoms. This equation is solved using the 4th-order Runge-Kutta method, and applied to argon gas discharge which is driven by source frequency of 100, 1K, 10K, 100K, and 1M (Hz). The results show that the variation of electron energy becomes flat with higher frequencies.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 PARALLEL CFD 2006
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• pp.311-314
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• 2006

The supersonic flow around tandem cavities was investigated by three- dimensional numerical simulations using the Reynolds-Averaged Navier-Stokes(RANS) equation with the $\kappa-\omega$ thrbulence model. The flow around a cavity is characterized as unsteady flow because of the formation and dissipation of vortices due to the interaction between the freestream shear layer and cavity internal flow, the generation of shock and expansion waves, and the acoustic effect transmitted from wake flow to upstream. The upwind TVD scheme based on the flux vector split using van Leer's limiter was used as the numerical method. Numerical calculations were performed by the parallel processing with time discretizations carried out by the 4th-order Runge-Kutta method. The aspect ratio of cavities are 3 for the first cavity and 1 for the second cavity. The ratio of cavity interval to depth is 1. The ratio of cavity width to depth is 1 in the case of three dimensional flow. The Mach number and the Reynolds number were 1.5 and $4.5{\times}10^5$, respectively. The characteristics of the dominant frequency between two-dimensional and three-dimensional flows were compared, and the characteristics of the second cavity flow due to the fire cavity flow cavity flow was analyzed. Both two dimensional and three dimensional flow oscillations were in the 'shear layer mode', which is based on the feedback mechanism of Rossiter's formula. However, three dimensional flow was much less turbulent than two dimensional flow, depending on whether it could inflow and outflow laterally. The dominant frequencies of the two dimensional flow and three dimensional flows coincided with Rossiter's 2nd mode frequency. The another dominant frequency of the three dimensional flow corresponded to Rossiter's 1st mode frequency.

• Journal of Mechanical Science and Technology
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• 제20권8호
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• pp.1256-1265
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• 2006

The supersonic flows around tandem cavities were investigated by two-dimensional and three-dimensional numerical simulations using the Reynolds-Averaged Navier-Stokes (RANS) equation with the k- ω turbulence model. The flow around a cavity is characterized as unsteady flow because of the formation and dissipation of vortices due to the interaction between the freestream shear layer and cavity internal flow, the generation of shock and expansion waves, and the acoustic effect transmitted from wake flow to upstream. The upwind TVD scheme based on the flux vector split with van Leer's limiter was used as the numerical method. Numerical calculations were performed by the parallel processing with time discretizations carried out by the 4th-order Runge- Kutta method. The aspect ratios of cavities are 3 for the first cavity and 1 for the second cavity. The ratio of cavity interval to depth is 1. The ratio of cavity width to depth is 1 in the case of three dimensional flow. The Mach number and the Reynolds number were 1.5 and $4.5{\times}10^5$, respectively. The characteristics of the dominant frequency between two- dimensional and three-dimensional flows were compared, and the characteristics of the second cavity flow due to the first cavity flow was analyzed. Both two dimensional and three dimensional flow oscillations were in the 'shear layer mode', which is based on the feedback mechanism of Rossiter's formula. However, three dimensional flow was much less turbulent than two dimensional flow, depending on whether it could inflow and outflow laterally. The dominant frequencies of the two dimensional flow and three dimensional flows coincided with Rossiter's 2nd mode frequency. The another dominant frequency of the three dimensional flow corresponded to Rossiter's 1st mode frequency.

• 대한기계학회논문집B
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• 제21권2호
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• pp.202-212
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• 1997

In this study, performance of the multi-stage explicit methods for numerical computation of the unsteady Navier-Stokes equations is investigated. Three methods under consideration are 1 st-, 2 nd-, and 4 th-order Runge-Kutta (R-K) methods. Compared in this estimation is stability, accuracy, and CPU time of each method. The computational codes developed are applied to the two-dimensional flow in a square cavity driven by an oscillating lid. It turned out that at Reynolds number 400, the 1 st-order R-K method is the best, while at 3200 the 2 nd-order R-K is recommended. At higher Reynolds numbers, it is conjectured that the 4 th-order R-K method will be the best algorithm among three due to its highest stability.