• Title/Summary/Keyword: numerical formulation

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Numerical Study of Rocket Exhaust Plume with Equilibrium Chemical Reaction and Thermal Radiation (평형화학반응과 복사열전달을 고려한 로켓 플룸 유동 해석)

  • Shin J.-R.;Choi J.-Y.;Choi H.-S.
    • 한국전산유체공학회:학술대회논문집
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    • 2004.03a
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    • pp.146-153
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    • 2004
  • The Numerical study has been carried out to investigate the effects of chemical reaction and thermal radiation on the rocket plume flow-field at various altitudes. The theoretical formulation is based on the Navier-Stokes equations for compressible flows along with the infinitely fast chemistry and thermal radiation. The governing equations were solved by a finite volume fully-implicit TVD(Total Variation Diminishing) code which uses Roe's approximate Riemann solver and MUSCL(Monotone Upstream-centered Schemes for Conservation Laws) scheme. LU-SGS (Lower Upper Symmetric Gauss Seidel) method is used for the implicit solution strategy. An equilibrium chemistry module for hydrocarbon mixture with detailed thermo-chemical properties and a thermal radiation module for optically thin media were incorporated with the fluid dynamics code. In this study, kerosene-fueled rocket was assumed operating at O/F ratio of 2.34 with a nozzle expansion ratio of 6.14. Flight conditions considered were Mach number zero at ground level, Mach number 1.16 at altitude 5.06km and Mach number 2.9 at altitude 17.34km. Numerical results gave the understandings on the detailed plume structures at different altitude conditions. The diffusive effect of the thermal radiation on temperature field and the effect of chemical recombination during the expansion process could be also understood. By comparing the results from frozen flow and infinitely fast chemistry assumptions, the excess temperature of the exhaust gas resulting from the chemical recombination seems to be significant and cannot be neglected in the view point of performance, thermal protection and flow physics.

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A Study on Describing Uninterrupted Traffic Flows using Macroscopic Models (연속교통류 재현을 위한 거시적 모형의 비교 연구)

  • 임성만;김대호;김영찬
    • Journal of Korean Society of Transportation
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    • v.20 no.3
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    • pp.69-82
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    • 2002
  • The objective of this study is to evaluate the performance of macroscopic traffic flow models with the analytical and field data. Five candidate models were selected as follows ; Lax Method Model, Upwind Scheme Model, Hilliges'Model, Papageorgiou's Model, and Cell-Transmission Model. In the analytical test scenario, the traffic condition was assumed that could cause the building and dissipation of queue, and each model was compared with analytical solutions and the numerical results. An analytical test indicated that both simple continuum and high order continuum models are able to reproduce queue building and dissipating behavior in a reasonable way A field test has shown that Upwind and Papageorgiou's model show similar performances. Considering the simplicity in model formulation and numerical computation, we firstly recommend Upwind scheme model , and secondly Papageorgiou's model that performed will to represent traffic flow in tests as candidate models for further development of simulation model for Naebu expressway in Seoul.

An Elasto-Plastic Constitutive Law for Modeling the Shear Behavior of Rough Rock Joints (거친 절리면의 전단거동 해석을 위한 탄소성 구성법칙)

  • 이연규;이정인
    • Tunnel and Underground Space
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    • v.8 no.3
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    • pp.234-248
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    • 1998
  • This paper presents a new constitutive model for numerical modeling the shear behaviour of rough rock joints. The model incorporates the dilatancy of joints on the basis of elasto-plastic theory. Barton's empirical shear strength formular are adopted in the formulation process. The mobilized JRC concept is evoked to address the shear strength hardening and sofrening phenomena. The mobilized JRC in the pre- and post-peak range is approximated by assuming that the variation of JRC is a function of tangential plastic work. Discrete finite joint element is used to implement the proposed constitutive model. The model is validated by the numerical direct shear test on a single joint which is subjected to different boundary conditions. The test results are in good agreement with the experimental observations reported by other authors. The numerical tests also exhibit that the proposed model can simulate the salient features envisaged in the behaviour of rough rock joints.

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Analytical and higher order finite element hybrid approach for an efficient simulation of ultrasonic guided waves I: 2D-analysis

  • Vivar-Perez, Juan M.;Duczek, Sascha;Gabbert, Ulrich
    • Smart Structures and Systems
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    • v.13 no.4
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    • pp.587-614
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    • 2014
  • In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.

Homogenization of Elastic Cracks in Hoek-Brown Rock (Hoek-Brown 암석에서 발생된 탄성균열의 균질화)

  • Lee, Youn-Kyou;Jeon, Seok-Won
    • Tunnel and Underground Space
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    • v.19 no.2
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    • pp.158-166
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    • 2009
  • As a basic study for investigating the development of the stress-induced crack in Hoek-Brown rock, a homogenization technique of elastic cracks is proposed. The onset of crack is monitored by Hoek-Brown empirical criterion, while the orientation of the crack is determined by the critical plane approach. The concept of volume averaging in stress and strain component was invoked to homogenize the representative rock volume which consists of intact rock and cracks. The formulation results in the constitutive relations for the homogenized equivalent anisotropic material. The homogenization model was implemented in the standard FEM code COSMOSM. The numerical uniaxial tests were performed under plane strain condition to check the validity of the propose numerical model. The effect of friction between the loading plate and the rock sample on the mode of deformation and fracturing was examined by assuming two different contact conditions. The numerical simulation revealed that the homogenized model is able to capture the salient features of deformation and fracturing which are observed commonly in the uniaxial compression test.

A Study on Dynamic Characteristics of Hydraulic Motor Brake System with Counter Balance Valve (카운터 밸런스 밸브를 내장한 유압 모터 브레이크 시스템의 동특성)

  • Yun, So-Nam;Lee, Ill-Yeong
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.29 no.3
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    • pp.214-219
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    • 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.

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Numerical Evaluation of the Influence of Joint Roughness on the Deformation Behavior of Jointed Rock Masses (절리면의 거칠기 특성이 정리암반의 거동에 미치는 영향에 대한 수치해석적 연구)

  • 이연규
    • Tunnel and Underground Space
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    • v.11 no.3
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    • pp.225-236
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    • 2001
  • The roughness of rock joint is one of the most important parameters in developing the shear resistance and the tendency of dilation. Due to the damage accumulated with shearing displacement, the roughness angle is lowered continuously. It is known that dilation, shear strength hardening, and softening are directly related to the degradation of asperities. Much effort has been directed to incorporate the complicated damage mechanism of asperities into a constitutive model fur rock joints. This study presents an elasto-plastic formulation of joint behavior including elastic deformability, dilatancy and asperity surface damage. It is postulated that the plastic portion of incremental displacement 7an be decomposed into contributions from both sliding along the asperity surface and damage of asperity. Numerical cyclic shear tests are presented to illustrate th? performance of the derived incremental stress-displacement relation. A laboratory cyclic shear test is also simulated. Numerical examples reveal that the elasto-plastic joints model is promising.

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A Study of Numerical Method for Analysis of the 3-Dimensional Nonlinear Wave-Making Problems (3차원 비선형 조파문제 해석을 위한 수치해법 연구)

  • Ha, Y.R.;An, N.H.
    • Journal of Power System Engineering
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    • v.16 no.5
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    • pp.40-46
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    • 2012
  • For free surface flow problem, a high-order spectral/boundary element method is adapted as an efficient numerical tool. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated and hydrodynamic forces also can be calculated in time domain. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved by using the high-order spectral method and body potential is solved by using the high-order boundary element method. Using the combination of these two methods, the free surface flow problems of a submerged moving body are solved in time domain. In the present study, lifting surface theory is added to the former work to include effects of lift force. Therefore, a new formulation for the basic mathematical theory is introduced to contain the lift body in calculation.

Development of Three-Dimensional Fracture Strain Surface in Average Stress Triaxiaility and Average Normalized Lode Parameter Domain for Arctic High Tensile Steel: Part II Formulation of Fracture Strain Surface (극한지용 고장력강의 평균 응력 삼축비 및 평균 정규 로드 파라메터를 고려한 3차원 파단 변형률 평면 개발: 제2부 파단 변형률 평면의 정식화)

  • Chong, Joonmo;Park, Sung-Ju;Kim, Younghun
    • Journal of Ocean Engineering and Technology
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    • v.29 no.6
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    • pp.454-462
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    • 2015
  • An extended study was conducted on the fracture criterion by Choung et al. (2011; 2012) and Choung and Nam (2013), and the results are presented in two parts. The theoretical background of the fracture and the results of new experimental studies were reported in Part I, and three-dimensional fracture surface formulations and verifications are reported in Part II. How the corrected true stress can be processed from the extrapolated true stress is first introduced. Numerical simulations using the corrected true stress were conducted for pure shear, shear-tension, and pure compression tests. The numerical results perfectly coincided with test results, except for the pure shear simulations, where volume locking appeared to prevent a load reduction. The average stress triaxialities, average normalized lode parameters, and equivalent plastic strain at fracture initiation were extracted from numerical simulations to formulate a new three-dimensional fracture strain surface. A series of extra tests with asymmetric notch specimens was performed to check the validity of the newly developed fracture strain surface. Then, a new user-subroutine was developed to calculate and transfer the two fracture parameters to commercial finite element code. Simulation results based on the user-subroutine were in good agreement with the test results.

On Numerical Modeling of Kerosene/Liquid Oxygen Coaxial Swirl Injectors (케로신/액체산소 동축 와류형 분사기에 대한 수치해석 모델 고찰)

  • Kim, Seong-Ku;Choi, Hwan-Seok
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2010.11a
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    • pp.729-732
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    • 2010
  • The present study has been motivated by the development of a reliable numerical methodology for simulation of kerosene/LOx coaxial swirl injectors. To deal with thermodynamic non-ideality and anomalies of transport properties pronounced at supercritical pressures, a set of subroutine libraries has been constructed based on the cubic equations of state, and applied to an existing flamelet analysis code. For computational efficiency, two-dimensional axisymmetric RANS formulation with swirl was adopted and validated successfully against an isothermal coaxial swirling jet. For the actual problem with high pressure combustion, however, numerical results show that the RANS models yield excessive production of turbulence probably due to high density gradient magnitude in the vicinity of mixing layer of swirling film flow, and imply strongly further improvement of the turbulence models.

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