• Title/Summary/Keyword: Euler 방정식

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Transient Response Analysis of Locally Nonlinear Structures Using Substructure-Based-State Equations (부분구조의 상태방정식을 이용한 국부 비선형계의 과도응답해석)

  • 김형근;박윤식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.10
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    • pp.2457-2466
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    • 1993
  • A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

Stability Analysis of Wakes with Chemical Reaction (연소 반응을 가지는 후류 유동의 불안정성)

  • 신동신;홍성제
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 1998.04a
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    • pp.17-17
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    • 1998
  • 연소반응을 가지는 후류(wake)는 가스터빈 연소실의 flame holder 등에서 발생한다. 후류유동의 안정성 혹은 불안정성은 이러한 유동에 있어서 많은 영향을 끼치므로 상당히 중요하다. 본 연구는 위와 같이 연소 반응에 의한 밀도구배를 가지는 후류유동에 대하여 불안정성 해석을 수행하였다. 교란에 대한 지배방정식은 Navier-Stokes 방정식에서 점성항을 제외한 Euler 방정식을 고려하였다. 충류유동의 압력은 일정하다고 가정하였다. 교란 방정식을 유도하기 위하여 충류 유동이 평행하여 유동 방향에 수직한 방향의 구배만이 존재한다고 가정하였다. 모든 변수들은 충류 유동의 값과 움직이는 파장의 형태를 가지는 작은 교란의 합으로 생각하여 압력에 대한 교란방정식을 구하며, shooting법과 Newton-Raphson법에 근거를 두는 반복법을 사용하여 풀었다. 불안정성 해석을 수행하는 기본 유동의 속도장 및 온도장은 불안정성 해석을 수행하는 기본 유동의 속도장 및 온도장은 비압축성의 경우 우선 Gaussian Profile 가정함과 동시에 연소반응을 포함하는 유동장을 보다 정확히 구하기 위하여 Navier-Stokes 방정식으로부터 구한 결과를 사용하였다. 연소반응을 포함하는 유동장을 구할 때에는 해석상 편의를 위해 예혼합물질은 이상기체로, 화학반응은 1단계의 비가역반응으로 가정하였으며, 반응열로 인한 부력의 효과는 무시하였다. 위와 같은 유동장을 가지고 불안정성 해석을 수행한 결과 후류유동은 두 개의 변곡점을 가지며 sinuous 모드와 varicose모드의 두 개의 불안정성 모드가 있음을 보였다. 밀도 변화가 있는 경우나 밀도 변화가 없는 경우 모두 sinuous 모드의 가장 불안정한 모드가 varicose 모드의 가장 불안정한 모드보다 더 불안정함을 보여주어 후류 유동은 자유 유동에 가까운 위상 속도를 가지는 sinuous 모드에 의해 지배될 것임을 예측할 수 있다. 연소반응이 완전연소에 가까울수록 그리고 압축성 효과가 클수록 유동내부의 온도가 증가하고 점성 또한 증가하여 후류유동은 안정됨을 알 수 있었다 유동변수들의 contour로부터 유동의 특성을 예측한 결과 baroclinic 항이 dilatational 항보다 상대적으로 크며, 중심선 상하에 생기는 vortex를 더욱 성장시킬 것으로 생각된다.

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Vibration Control of a Robot Manipulator with a Parallel Drive Mechanism (평행구동방식 로봇 조작기의 진동제어)

  • 최승철;하영균;박영필
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.15 no.6
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    • pp.2015-2025
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    • 1991
  • A long and light-weight forearm of the vertical 2 DOF robot manipulator with a heavy payload driven by parallel drive mechanism is modelled as a Euler-Bernoulli beam with a tip mass subjected to a high speed rotation. Governing equation is obtained by Hamilton's principle and represented as state variable form using the perturbed variables which describe the perturbed errors at the manipulator's final configuration. Digitial optimal control and observer theory are used to suppress the forearm vibration and control the positions of the joint angles with measured/estimated state feedback. Computer simulations and experimental results are obtained and compared each other.

Aerodynamic Noise Analysis Using the Permeable Surface for UH-1H Rotor Blade in Hovering Flight Condition (UH-1H 로터 블레이드의 제자리 비행 시 투과면을 이용한 원방 소음 해석)

  • Kim, Ki Ro;Park, Min Jun;Park, Soo Hyung;Lee, Duck Joo;Park, Nam Eun;Im, Dong Kyun
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.46 no.5
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    • pp.376-384
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    • 2018
  • The aerodynamic far-field noise was computed by an acoustic analogy code using the permeable surface for the UH-1H rotor blade in hover. The permeable surface surrounding the blade was constructed to include the thickness noise, the loading noise, and the flow noise generated from the shock waves and the tip vortices. The computation was performed with compressible three-dimensional Euler's equations and Navier-Stokes equations. The high speed impulsive noise was predicted and validated according to the permeable surface locations. It is confirmed that the noise source caused by shock waves generated on the blade surface is a dominant factor in the far-field noise prediction.

Aerodynamic Shape Optimization of Helicopter Rotor Blades in Hover Using a Continuous Adjoint Method on Unstructured Meshes (비정렬 격자계에서 연속 Adjoint 방법을 이용한 헬리콥터 로터 블레이드의 제자리 비행 공력 형상 최적설계)

  • Lee, S.-W.;Kwon, O.-J.
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.1
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    • pp.1-10
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    • 2005
  • An aerodynamic shape optimization technique has been developed for helicopter rotor blades in hover based on a continuous adjoint method on unstructured meshes. The Euler flow solver and the continuous adjoint sensitivity analysis were formulated on the rotating frame of reference for hovering rotor blades. In order to handle the repeated evaluation of the design cycle efficiently, the flow and adjoint solvers were parallelized using a domain decomposition strategy. A solution-adaptive mesh refinement technique was adopted for the accurate capturing of the tip vortex. Applications were made for the aerodynamic shape optimization of Caradonna-Tung rotor blades and UH60 rotor blades in hover. The results showed that the present method is an effective tool to determine optimum aerodynamic shapes of rotor blades requiring less torque while maintaining the desired thrust level.

An Analysis of the Springing Phenomenon of a Ship Advancing in Waves (파랑 중에 전진하는 선박에 대한 스프링잉 현상 해석)

  • H.Y. Lee;H. Shin;H.S. Park;J.H. Park
    • Journal of the Society of Naval Architects of Korea
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    • v.38 no.3
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    • pp.41-46
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    • 2001
  • The very large vessels like VLCC and container ship have been built recently and those vessels have smaller structural strength in comparison with the other convectional skips. As a result the fatigue destruction of upper deck occurs a frequently due to the springing phenomenon at the encountering frequencies. In this study, the hydrodynamic loads are calculated by three-dimensional source distribution method with the translating and pulsating Green function. A ship is longitudinally divided into 23 sections and the added mass, damping and hydrodynamic force of each section is calculated. focusing only on the vertical motion. Stiffness matrix is calculated by the Euler beam theory. The calculation is carried out for Esso Osaka.

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PERFORMANCE OF LIMITERS IN MODAL DISCONTINUOUS GALERKIN METHODS FOR 1-D EULER EQUATIONS (1-D 오일러 방정식에 관한 Modal 불연속 갤러킨 기법에서의 Limiter 성능 비교)

  • Karchani, A.;Myong, R.S.
    • Journal of computational fluids engineering
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    • v.21 no.2
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    • pp.1-11
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    • 2016
  • Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($p^1$, $p^2$, and $p^3$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.

A Study on Tunnel Entry Design Considering the Booming Noise Resulting from Micro-Pressure Wave (미기압파에 의한 터널 출구 소음 저감을 위한 고속철도 터널 형상 개선에 관한 연구)

  • 목재균;최강윤;유재석
    • Journal of KSNVE
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    • v.7 no.6
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    • pp.959-966
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    • 1997
  • In general, the booming noise intensity at tunnel exit is strongly related to the gradient of the compression wave front created by high speed train entering the tunnel. This paper presents some results in relation with the compression wave front produced when the high speed train enters a tunnel. Four kinds of tunnel entrance shape with real dimensions were studied to investigate the formation of compression wave front inside tunnel by train entering tunnel. Computations were carried out using three-dimensional compressible Euler equation with vanishing viscosity and conductivity of fluid. According to the results, the flow disturbances occured at tunnel entrance were eliminated by tunnel hood with same cross sectional area. The compression wave front is formed completely at 30-40m from tunnel entrance. The maximum pressure gradient of compression wave front is reduced by 29.8% for the inclined tunnel hood and reduced by 21.5% for the tunnel hood with holes at the top face with tunnel without hood. The length of the inclined hood is 15m and the length of the hood with holes is 20m.

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A study on tunnel entry design considering the booming noise resulting from micro-pressure wave (미기압파에 의한 터널출구소음저감을 위한 고속철도 터널형상개선에 관한 연구)

  • 목재균;최강윤
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1997.04a
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    • pp.627-635
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    • 1997
  • In general, the booming noise intensity at tunnel exit is strongly related to the gradient of the compression wave front created by high speed train entering the tunnel. This paper presents some results in relation with the compression wave front produced when the high speed train enters a tunnel. Four kinds of tunnel entrance shape with real dimensions were studied to investigate the formation of compression wave front inside tunnel by train entering tunnel. Computations were carried out using three-dimensional compressible Euler equation with vanishing viscosity and conductivity of fluid. According to the reslts, the flow disturbance occured at tunnel entrance were eliminated by tunnel hood with same cross sectional area. The compression wave front is formed completely at 30-40m from tunnel entrance. The maximum pressure gradient of compression wave front is reduced by 29.8% for the inclined tunnel hood and reduced by 21.5% for the tunnel hood with holes at the top face with tunnel without hood. The length of the inclined hood is 15m and the length of the hood with holes is 20m.

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A Numerical Study on the Supersonic Separation of Air-launching Rocket from the Mother Plane (초음속 공중발사 로켓의 모선분리 현상에 관한 수치적 연구)

  • Ji, Young-Moo;Kim, Young-Shin;Lee, Jae-Woo;Park, Jun-Sang
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.8
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    • pp.18-25
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    • 2005
  • This paper describes a supersonic separation of air-launching rocket from the mother plane. Three dimensional Euler equations were numerically solved to analyze steady/unsteady state fluid flows. The results of simulation clearly demonstrate effect of shock-expansion wave interaction between the rocket and the mother plane. Moreover, important influential factors at separating stage of the rocket were extracted with a comprehensive analysis. Finally, from the consideration of supersonic-separation, a guideline to safety-separation is given to the design of supersonic air-launching rocket.