• Title/Summary/Keyword: Euler equation

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Effect of Tunnel Entrance Shape of High Speed Train on Aerodynamic Characteristics and Entry Compression Wave (고속전철의 터널입구 형상이 공력특성 및 터널입구 압축파에 미치는 영향)

  • Jeong, Soo-Jin;Kim, Woo-Seung;Zhu, Ming
    • Transactions of the Korean Society of Automotive Engineers
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    • v.12 no.6
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    • pp.111-118
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    • 2004
  • The work presented in this paper concerns the aerodynamic characteristics and compression wave generated in a tunnel when a high speed train enters it. A large number of solutions have been proposed to reduce the amplitude of the pressure gradient in tunnels and some of the most efficient solutions consist of (a) addition ofa blind hood, (b) addition of inclined part at the entrance, and (c) holes in the ceiling of the tunnel. These are numerically studied by using the three-dimensional unsteady compressible Euler equation solver with ALE, CFD code, based on FEM method. Computational results showed that the smaller inclined angle leads to the lower pressure gradient of compression wave front. This study indicated that the most efficient slant angle is in the range from $30^{\circ}$ to $50^{\circ}$. The maximum pressure gradient is reduced by $26.81\%$ for the inclined angle of $30^{\circ}$ as compared to vertical entry. Results also showed that maximum pressure gradient can be reduced by $15.94\%$ in blind hood entry as compared to $30^{\circ}$ inclined tunnel entry. Furthermore, the present analysis showed that inclined slant angle has little effect on aerodynamic drag. Comparison of the pressure gradient between the inclined tunnel hood and the vertical entry with air vent holes indicated that the optimum inclined tunnel hood is much more effective way in reducing pressure gradient and increasing the pressure rise time.

Unscented KALMAN Filtering for Spacecraft Attitude and Rate Determination Using Magnetometer

  • Kim, Sung-Woo;Abdelrahman, Mohammad;Park, Sang-Young;Choi, Kyu-Hong
    • Journal of Astronomy and Space Sciences
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    • v.26 no.1
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    • pp.31-46
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    • 2009
  • An Unscented Kalman Filter (UKF) for estimation of the attitude and rate of a spacecraft using only magnetometer vector measurement is developed. The attitude dynamics used in the estimation is the nonlinear Euler's rotational equation which is augmented with the quaternion kinematics to construct a process model. The filter is designed for small satellite in low Earth orbit, so the disturbance torques include gravity-gradient torque, magnetic disturbance torque, and aerodynamic drag torque. The magnetometer measurements are simulated based on time-varying position of the spacecraft. The filter has been tested not only in the standby mode but also in the detumbling mode. Two types of actuators have been modeled and applied in the simulation. The PD controller is used for the two types of actuators (reaction wheels and thrusters) to detumble the spacecraft. The estimation error converged to within 5 deg for attitude and 0.1 deg/s for rate respectively when the two types of actuators were used. A joint state parameter estimation has been tested and the effect of the process noise covariance on the parameter estimation has been indicated. Also, Monte-Carlo simulations have been performed to test the capability of the filter to converge with the initial conditions sampled from a uniform distribution. Finally, the UKF performance has been compared to that of the EKF and it demonstrates that UKF slightly outperforms EKF. The developed algorithm can be applied to any type of small satellites that are actuated by magnetic torquers, reaction wheels or thrusters with a capability of magnetometer vector measurements for attitude and rate estimation.

Development of a Submerged Propeller Turbine for Micro Hydro Power

  • Kim, Byung-Kon
    • The KSFM Journal of Fluid Machinery
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    • v.18 no.6
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    • pp.45-56
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    • 2015
  • This paper aims to develop a submerged propeller turbine for micro hydropower plant which allows to sustain high values of efficiency in a broad range of hydrological conditions (H=2~6 m, $Q=0.15{\sim}0.39m^3/s$). The two aspects to be considered in this development are mechanical simplicity and high-efficiency operation. Unlike conventional turbines that have spiral casing and gear box, this is directing driving and no spiral casing. A 10 kW class turbine which has the most high potential of the power generation has been developed. The most important element in the design of turbine is the runner blade. The initial blade is designed using inverse design method and then the runner geometry is modified by classical hydraulic method. The design process is carried out in two steps. First, the blade shape is fix and then other components of submerged propeller turbine are designed. Computational fluid dynamics analyses based on the Navier-Stokes equations have been used to obtain overall performance data for the blade and the full turbine, respectively. The results generated by performance parameters(head, guide vane opening angle and rotational speed) variations are theoretically analysed. The evaluation criteria for the blade and the turbine performances are the pressure distribution and flow's behavior on the runner blades and turbine. The results of simulation reveals an efficiency of 91.5% and power generation of 10.5kW at the best efficiency point at the head of 4m and a discharge of $0.3m^3/s$.

Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method

  • Yesilce, Yusuf;Catal, Seval
    • Structural Engineering and Mechanics
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    • v.31 no.4
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    • pp.453-475
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    • 2009
  • The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko beams on elastic soil is plenty, but the free vibration analysis of Reddy-Bickford beams on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded Reddy-Bickford beam on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of one end fixed and the other end simply supported Reddy-Bickford beam on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the mode shapes are presented in graphs.

Nonlinear numerical modelling for the effects of surface explosions on buried reinforced concrete structures

  • Nagy, N.;Mohamed, M.;Boot, J.C.
    • Geomechanics and Engineering
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    • v.2 no.1
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    • pp.1-18
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    • 2010
  • The analysis of structure response and design of buried structures subjected to dynamic destructive loads have been receiving increasing interest due to recent severe damage caused by strong earthquakes and terrorist attacks. For a comprehensive design of buried structures subjected to blast loads to be conducted, the whole system behaviour including simulation of the explosion, propagation of shock waves through the soil medium, the interaction of the soil with the buried structure and the structure response needs to be simulated in a single model. Such a model will enable more realistic simulation of the fundamental physical behaviour. This paper presents a complete model simulating the whole system using the finite element package ABAQUS/Explicit. The Arbitrary Lagrange Euler Coupling formulation is used to model the explosive charge and the soil region near the explosion to eliminate the distortion of the mesh under high deformation, while the conventional finite element method is used to model the rest of the system. The elasto-plastic Drucker-Prager Cap model is used to model the soil behaviour. The explosion process is simulated using the Jones-Wilkens-Lee equation of state. The Concrete Damage Plasticity model is used to simulate the behaviour of concrete with the reinforcement considered as an elasto-plastic material. The contact interface between soil and structure is simulated using the general Mohr-Coulomb friction concept, which allows for sliding, separation and rebound between the buried structure surface and the surrounding soil. The behaviour of the whole system is evaluated using a numerical example which shows that the proposed model is capable of producing a realistic simulation of the physical system behaviour in a smooth numerical process.

Design of a Propeller Type Rim-Driven Axial-Flow Turbine for a Micro-Hydropower System (마이크로 수력 발전을 위한 프로펠러형 림구동 축류 터빈 설계)

  • Oh, Jin-An;Bang, Deok-Je;Jung, Rho-Taek;Lee, Su-Min;Lee, Jin-Tae
    • Journal of the Society of Naval Architects of Korea
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    • v.59 no.3
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    • pp.183-191
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    • 2022
  • A design method for a propeller type rim-driven axial-flow turbine for a micro-hydropower system is presented. The turbine consists of pre-stator, impeller and post-stator, where the pre-stator plays a role as a guide vane to provide circumferential velocity to the on-coming flow, and the impeller as a rotational power generator by absorbing angular momentum of the flow. BEM(Blade Element Method), which is based on the turbine Euler equation, is employed to design the pre-stator and impeller blades. NACA 66 thickness form and a=0.8 mean camber line, which is widely accepted as a marine propeller blade section, is used for the pre-stator and turbine blade section. A CFD method, derived from the discretization of the RANS equations, is applied for the analysis of the designed turbine system. The design conditions of the turbine is confirmed by the CFD calculation. Turbine characteristic curve is calculated by the CFD method, in order to provide the performance characteristics at off-design operation conditions. The proposed procedures for the design of a propeller type rim-driven axial-flow turbine are established and confirmed by the CFD analysis.

Parametric study of the wave dispersion in the hydro-elastic system consisting of an inhomogeneously prestressed hollow cylinder containing compressible inviscid fluid

  • Surkay D. Akbarov;Gurbaneli J. Veliyev
    • Coupled systems mechanics
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    • v.12 no.1
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    • pp.41-68
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    • 2023
  • The present work is concerned with the study of the influence of inhomogeneous initial stresses in a hollow cylinder containing a compressible inviscid fluid on the propagation of axisymmetric longitudinal waves propagating in this cylinder. The study is carried out using the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses to describe the motion of the cylinder and using the linearized Euler equations to describe the flow of the compressible inviscid fluid. It is assumed that the inhomogeneous initial stresses in the cylinder are caused by the internal pressure of the fluid. To solve the corresponding eigenvalue problem, the discrete-analytic solution method is applied and the corresponding dispersion equation is obtained, which is solved numerically, after which the corresponding dispersion curves are constructed and analyzed. To obtain these dispersion curves, parameters characterizing the magnitude of the internal pressure, the ratio of the sound velocities in the cylinder material and in the fluid, and the ratio of the material densities of the fluid and the cylinder are introduced. Based on these parameters, the influence of the inhomogeneous initial stresses in the cylinder on the dispersion of the above-mentioned waves in the considered hydro-elastic system is investigated. Moreover, based on these results, appropriate conclusions about this influence are drawn. In particular, it is found that the character of the influence depends on the wavelength. Accordingly, the inhomogeneous initial stresses before (after) a certain value of the wavelength lead to a decrease (increase) of the wave propagation velocity in the zeroth and first modes.

Estimating a Precautionary Saving Motive under Consumption Uncertainty (소비의 불확실성에 따른 예비적 저축 동기 추정)

  • Hwang, Jin-tae;Kim, Sung-min
    • Economic Analysis
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    • v.26 no.3
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    • pp.48-70
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    • 2020
  • Using data from the Household Income and Expenditure Survey over the period 1994-2016, we estimate the coefficient of relative prudence in order to capture precautionary saving motive. To do this, we adopt a cohort approach, where we transform such microdata into sample cohort means. Together with initial income involving liquidity constraint, we estimate the relative prudence derived from the Euler equation. The two-stage least-squares (2SLS) between estimate of it obtained from the cohort panel data analysis is too small for the existence of precautionary saving motive, as in previous studies, while the 2SLS random effects estimate is so reasonable. Moreover, the liquidity-constrained cohorts tend to be more sensitive to uncertainty, relative to the unconstrained ones.

Photon Mapping-Based Rendering Technique for Smoke Particles (연기 파티클에 대한 포톤 매핑 기반의 렌더링 기법)

  • Song, Ki-Dong;Ihm, In-Sung
    • Journal of the Korea Computer Graphics Society
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    • v.14 no.4
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    • pp.7-18
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    • 2008
  • To realistically produce fluids such as smoke for the visual effects in the films or animations, we need two main processes: a physics-based modeling of smoke and a rendering of smoke simulation data, based on light transport theory. In the computer graphics community, the physics-based fluids simulation is generally adopted for smoke modeling. Recently, the interest of the particle-based Lagrangian simulation methods is increasing due to the advantages at simulation time, instead of the grid-based Eulerian simulation methods which was widely used. As a result, because the smoke rendering technique depends heavily on the modeling method, the research for rendering of the particle-based smoke data still remains challenging while the research for rendering of the grid-based smoke data is actively in progress. This paper focuses on realistic rendering technique for the smoke particles produced by Lagrangian simulation method. This paper introduces a technique which is called particle map, that is the expansion and modification of photon mapping technique for the particle data. And then, this paper suggests the novel particle map technique and shows the differences and improvements, compared to previous work. In addition, this paper presents irradiance map technique which is the pre-calculation of the multiple scattering term in the volume rendering equation to enhance efficiency at rendering time.

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Kinematic and Dynamic Analyses of Human Arm Motion

  • Kim, Junghee;Cho, Sungho;Lee, Choongho;Han, Jaewoong;Hwang, Heon
    • Journal of Biosystems Engineering
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    • v.38 no.2
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    • pp.138-148
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    • 2013
  • Purpose: Determining an appropriate path is a top priority in order for a robot to maneuver in a dynamically efficient way especially in a pick-and-place task. In a non-standardized work environment, current robot arm executes its motion based on the kinematic displacements of joint variables, though resulting motion is not dynamically optimal. In this research we suggest analyzing and applying motion patterns of the human arm as an alternative to perform near optimum motion trajectory for arbitrary pick-and-place tasks. Methods: Since the motion of a human arm is very complicated and diverse, it was simplified into two links: one from the shoulder to the elbow, and the other from the elbow to the hand. Motion patterns were then divided into horizontal and vertical components and further analyzed using kinematic and dynamic methods. The kinematic analysis was performed based on the D-H parameters and the dynamic analysis was carried out to calculate various parameters such as velocity, acceleration, torque, and energy using the Newton-Euler equation of motion and Lagrange's equation. In an attempt to assess the efficacy of the analyzed human motion pattern it was compared to the virtual motion pattern created by the joint interpolation method. Results: To demonstrate the efficacy of the human arm motion mechanical and dynamical analyses were performed, followed by the comparison with the virtual robot motion path that was created by the joint interpolation method. Consequently, the human arm was observed to be in motion while the elbow was bent. In return this contributed to the increase of the manipulability and decrease of gravity and torque being exerted on the elbow. In addition, the energy required for the motion decreased. Such phenomenon was more apparent under vertical motion than horizontal motion patterns, and in shorter paths than in longer ones. Thus, one can minimize the abrasion of joints by lowering the stress applied to the bones, muscles, and joints. From the perspectives of energy and durability, the robot arm will be able to utilize its motor most effectively by adopting the motion pattern of human arm. Conclusions: By applying the motion pattern of human arm to the robot arm motion, increase in efficiency and durability is expected, which will eventually produce robots capable of moving in an energy-efficient manner.