• Title/Summary/Keyword: Euler 방정식

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Numerical Simulation of Shock-Induced Combustion on Adaptive Mesh (적응격자를 이용한 충격파 유도 연소장 해석)

  • Kim, Sang-Hoon;Choi, Jeong-Yeol;Oh, Se-Jomg
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2010.05a
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    • pp.397-400
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    • 2010
  • Unstructured adaptive grid flow simulation is applied to the calculation of high speed compressible flow of inert and reactive gas mixtures. Computational results are presented for the case of premixed hydrogen-air supersonic flow over a 2-D wedge. In such a configuration, combustion may be triggered behind the oblique shock wave and transition to an oblique detonation wave is eventually obtained. It is shown that the solution adaptive procedure implemented is able to correctly define the important wave front.

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An Experimental Study on Nozzle Damping Characteristics for Combustion Instability Suppression (노즐감쇠 실험을 통한 연소 불안정 억제 연구)

  • Ryoo, Seunghyun;Kim, Junseong;Kim, Hakchul;Moon, Heejang;Lee, Dohyung
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2017.05a
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    • pp.724-729
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    • 2017
  • The interaction between the flow of the nozzle and the acoustic motion in the combustion chamber acts as an important factor in suppressing combustion instability where nozzle damping effect can be evaluated by nozzle admittance. In this study, Modified Impedance Tube experiment is implemented to predict the acoustic nozzle damping effect. The experimental admittances are compared to numerical admittances values which are calculated from one-dimensional linearized Euler equation of Crocco's theory. As a result, it was possible to identify qualitatively the tendency between increasing and decreasing parts. Also, Efficient frequency bands of nozzle attenuation can be predicted.

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Dynamic Analysis of Constrained Mechanical System Moving on a Flexible Beam Structure(II) : Application (유연한 보 구조물 위를 이동하는 구속 기계계의 동력학 해석(II) : 응용)

  • Park, Chan-Jong;Park, Tae-Won
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.11
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    • pp.176-184
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    • 2000
  • Recently, it becomes a very important issue to consider the mechanical systems such as high-speed vehicle and railway train moving on a flexible beam structure. Using general approach proposed in the first part of this paper, it tis possible to predict planar motion of constrained mechanical system and elastic structure with various kinds of foundation supporting condition. Combined differential-algebraic equations of motion derived from both multibody dynamics theory and Finite Element Method can be analyzed numerically using generalized coordinate partitioning algorithm. To verify the validity of this approach, results from simply supported elastic beam subjected to a moving load are compared with exact solution from a reference. Finally, parameter study is conducted for a moving vehicle model on a simply supported 3-span bridge.

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Vehicle-Bridge Interaction Analysis of Railway Bridges by Using Conventional Trains (기존선 철도차량을 이용한 철도교의 상호작용해석)

  • Cho, Eun Sang;Kim, Hee Ju;Hwang, Won Sup
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.1A
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    • pp.31-43
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    • 2009
  • In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations of motion. The coupled equations of motion for the vehicle-bridge interaction are solved by the Newmark ${\beta}$ of a direct integration method, and by composing the effective stiffness matrix and the effective force vector according to a analysis step, those can be solved with the same manner of the solving procedure of equilibrium equations in static analysis. Also, the effective stiffness matrix is reconstructed by the Skyline method for increasing the analysis effectiveness. The Cholesky's matrix decomposition scheme is applied to the analysis procedure for minimizing the numerical errors that can be generated in directly calculating the inverse matrix. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 16 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by the PSD functions of the Federal Railroad Administration (FRA). The results of the vehicle-bridge interaction analysis are verified by the experimental results for the railway plate girder bridges of a span length with 12 m, 18 m, and the experimental and analytical data are applied to the low pass filtering scheme, and the basis frequency of the filtering is a 2 times of the 1st fundamental frequency of a bridge bending.

Three-Dimensional Vibration Analysis of Deep, Nonlinearly Tapered Rods and Beams with Circular Cross-Section (원형단면의 깊은 비선형 테이퍼 봉과 보의 3차원 진동해석)

  • 심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.3
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    • pp.251-260
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    • 2003
  • A three dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of deep, tapered rods and beams with circular cross section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sup r/, u/sub θ/ and u/sub z/, in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler-Bernoulli beam theory.

Study on the Applicability of a New Multi-body Dynamics Program Through the Application to the Heave Compensation System (상하동요 감쇠장치 적용을 통한 새로운 다물체동역학 프로그램의 적용성 검토)

  • Ku, Nam-Kug;Ha, Sol;Roh, Myung-Il
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.4
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    • pp.247-254
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    • 2013
  • In this paper, dynamic response analysis of a heave compensation system is performed for offshore drilling operations based on multibody dynamics. With this simulation, the efficiency of the heave compensation system can be virtually confirmed before it is applied to drilling operations. The heave compensation system installed on a semi-submersible platform consists of a passive and an active heave compensator. The passive and active heave compensator are composed of several bodies that are connected to each other with various types of joints. Therefore, to carry out the dynamic response analysis, the dynamics kernel was developed based on mutibody dynamics. To construct the equations of motion of the multibody system and to determine the unknown accelerations and constraint forces, the recursive Newton-Euler formulation was adapted. Functions of the developed dynamics kernel were verified by comparing them with other commercial dynamics kernels. The hydrostatic force with nonlinear effects, the linearized hydrodynamic force, and the pneumatic and hydraulic control forces were considered as the external forces that act on the platform of the semi-submersible rig and the heave compensation system. The dynamic simulation of the heave compensation system of the semi-submersible rig, which is available for drilling operations with a 3,600m water depth, was carried out. From the results of the simulation, the efficiency of the heave compensation system were evaluated before they were applied to the offshore drilling operations. Moreover, the calculated constraint forces could serve as reference data for the design of the mechanical system.

Study of the Flush Air Data Sensing System for Subsonic and Supersonic Flows (아음속 및 초음속 유동의 플러시 대기자료 측정장치 연구)

  • Lee, Chang-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.47 no.12
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    • pp.831-840
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    • 2019
  • Flush Air Data Sensing system (FADS) estimates air data states using pressure data measured at the surface of flight vehicles. The FADS system does not require intrusive probes, so it is suitable for high performance aircrafts, stealth vehicles, and hypersonic flight vehicles. In this study, calibration procedures and solution algorithms of the FADS for a sphere-cone shape vehicle are presented for the prediction of air data from subsonic to supersonic flights. Five flush pressure ports are arranged on the surface of nose section in order to measure surface pressure data. The algorithm selects the concept of separation for the prediction of flow angles and the prediction of pressure related variables, and it uses the pressure model which combines the potential flow solution for a subsonic flow with the modified Newtonian flow theory for a hypersonic flow. The CFD code which solves Euler equations is developed and used for the construction of calibration pressure data in the Mach number range of 0.5~3.0. Tests are conducted with various flight conditions for flight Mach numbers in the range of 0.6~3.0 and flow angles in the range of -10°~+10°. Air data such as angle of attack, angle of sideslip, Mach number, and freestream static pressure are predicted and their accuracies are analyzed by comparing predicted data with reference data.

Total Dynamic Analysis of Deep-Seabed Integrated Mining System (심해저 광물자원 채광시스템의 통합거동 해석)

  • Kim, Hyung-Woo;Hong, Sup;Lee, Chang-Ho;Choi, Jong-Su;Yeu, Tae-Kyeong
    • Journal of Navigation and Port Research
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    • v.34 no.3
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    • pp.195-203
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    • 2010
  • This paper concerns about total dynamic analysis of integrated mining system. This system consists of vertical steel pipe, intermediate buffer station, flexible pipe and self-propelled miner. The self-propelled miner and buffer are assumed as rigid-body of 6-dof. Discrete models of vertical steel pipe and flexible pipe are adopted, which are obtained by means of lumped-parameter method. The motion of mining vessel is not considered. Instead, the motion of mining vessel is taken into account in form of various boundary conditions (e.g. forced excitation in slow motion and/or fast oscillation and so on). A terramechanics model of extremely cohesive soft soil is applied to the self-propelled miner. Hinged and ball constraints are used to define the connections between sub-systems (vertical steel pipe, buffer, flexible pipe, self-propelled miner). Equations of motion of the coupled model are derived with respect to the each local coordinates system. Four Euler parameters are used to express the orientations of the sub-systems. To solve the equations of motion of the total dynamic model, an incremental-iterative formulation is employed. Newmark-${\beta}$ method is used for time-domain integration. The total dynamic responses of integrated mining system are investigated.

Design Optimization of Transonic Wing/Fuselage System Using Proper Orthogona1 Decomposition (Proper Orthogonal Decomposition을 이용한 천음속 날개/동체 모텔의 최적설계)

  • Park, Kyung-Hyun;Jun, Sang-Ook;Cho, Maeng-Hyo;Lee, Dong-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.5
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    • pp.414-420
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    • 2010
  • This paper presents a validation of the accuracy of a reduced order model(ROM) and the efficiency of the design optimization using a Proper Orthogonal Decomposition(POD) to transonic wing/fuselage system. Three dimensional Euler equations are solved to extrude snapshot data of the full order aerodynamic analysis, and then a set of POD basis vectors reproducing the behavior of flow around the wing/fuselage system is calculated from these snapshots. In this study, reduced order model constructed through this procedure is applied to several validation cases, and then it is confirmed that the ROM has the capability of the prediction of flow field in the space of interest. Additionally, after the design optimization of the wing/fuselage system with the ROM is performed, results of the ROM are compared with results of the design optimization using response surface model(RSM). From these, it can be confirmed that the design optimization with the ROM is more efficient than RSM.

GAS-LIQUID TWO-PHASE HOMOGENEOUS MODEL FOR CAVITATING FLOW -Part II. HIGH SPEED FLOW PHENOMENA IN GAS-LIQUID TWO-PHASE MEDIA (캐비테이션 유동해석을 위한 기- 2상 국소균질 모델 -제2보: 기-액 2상 매체중의 고속유동현상)

  • Shin, B.R.;Park, S.;Rhee, S.H.
    • 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.