• Title/Summary/Keyword: nonlinear heat equation

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Pressure Wave Propagation Phenomena in Water Containing Uniformly Distributed Gas Bubbles (소량의 기포를 함유한 이상유체 내에서의 압력파의 전파현상)

  • Kim, D.-H.
    • The Journal of the Acoustical Society of Korea
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    • v.8 no.1
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    • pp.23-30
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    • 1989
  • Propagation phenomena of nonlinear pressure waves in a bubbly mixture are studied. The governing equations for a bubbly mixture are derived heuristically and energy equation is incorporated with other governing equations to take thermal effects into consideration inside the bubble. This non-isothermal condition of the bubble inside is especially important when high amplitude pressure waves are treated. Keller's equation is adapted for the bubble dynamics as practical problem. Some numerical simulations are carried out for the shock tube problem using a computer program based on the above model. A comparison with experimental results of Noordzij and van Wijngaarden shows that the structure of the wave in the shock tube experiment seems to be much more significantly affected 요 the complex heat transfer phenomena inside the bubbles than by the relative translational motion between bubbles and surrounding liquid.

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A Study on Improvement of Wegmann's method by Low Frequency pass Filter (저주파 필터를 이용한 Wegmann 방법의 개량에 관한 연구)

  • Song, Eun-Jee
    • The KIPS Transactions:PartA
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    • v.8A no.4
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    • pp.503-508
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    • 2001
  • Conformal mapping is useful to solve problems in heat conduction, electrostatic potential and fluid flow involving Laplace's equation in two independent variables. Determinations of conformal maps from the unit disk onto a Jordan region eventually requires solving the Theodorsen equation which is in general nonlinear with respect to the boundary correspondence function. H bner's method which has been well known for the efficient method among the many suggestions for the Theodorsen equation, was improved in early study[1, 2]. In this paper Wegmann's method is treated that is more efficient in computation cost rather than H bner's. But we found that a question which is divergent in some difficult problems by numerical experiment of Wegmann's iteration. We analyze theoretically the cause of divergence and propose an improved method by applying a low frequency filter to the Wegmann's method. Numerical experiments by our improved method show convergence for all divergent problems by Wegmann's method.

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Minimization of consumption energy for a manipulator with nonlinear friction in PPT motion

  • Izumi, T.;Takase, K.
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.95-99
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    • 1994
  • Robot engineering is developed mainly in the field of intelligibility such as a manipulation. Considering the popularization of robots in the future, however, a robot should be studied from a viewpoint of saving energy because a robot is a kind of machine with a energy conversion. This paper deals with minimizing an energy consumption of a manipulator which is driven in a point-to-point control method. When a manipulator carries a heavy payload toward gravitation or the links are de-accelerated for positioning, the motors at joints generate electric energy. Since this energy can be regenerated to the source by using a chopper, the energy consumption of a manipulator is only heat loss by an electric and a frictional resistance of the motors. The minimization of the sum of these losses is reduced Lo a two-points boundary-value problem of an non-linear differential equation. The solutions are obtained by the generalized Newton-Raphson method in this paper. The energy consumption due to the optimum angular velocity patterns of two joints of a two-links manipulator is compared with conventional velocity patterns such as quadratic and trapezoid.

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Deterioration of Structural Capacity of Fire-Damaged Reinforced Concrete Column (화해를 입은 철근콘크리트 기둥의 구조성능 저하)

  • 이차돈;신영수;홍성걸;이승환
    • Proceedings of the Korea Concrete Institute Conference
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    • 2003.11a
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    • pp.371-374
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    • 2003
  • The degree of changes in mechanical properties of fire-damaged reinforced concrete column depends mostly on sectional geometry, duration exposed to fire, and moisture containment. In order to reasonably assess the deterioration of structural capacity of fire-damaged reinforced concrete column, it is necessary to develop a theoretical model predicting column behavior based on nonlinear heat transfer equation in addition to the traditional mechanics. This research focuses on the development of theoretical model to predict moment-curvature relations of fire-damaged reinforced column. The model is used for the assessment of structural capacity of fire-damaged column in terms of moment-curvature relations and PM interaction curves.

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A Low-Reynolds-Number 4-Equation Model for Turbulent Separated and Reattaching Flows (난류박리 및 재부착 유동의 해석을 위한 저레이놀즈수 4-방정식 난류모형의 개발)

  • 이광훈;성형진
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.8
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    • pp.2039-2050
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    • 1995
  • The nonlinear low-Reynolds-number k..epsilon. model of park and Sung is extended to predict the turbulent heat transports in separated and reattaching flows. The equations of the temperature variance( $k_{\theta}$ and its dissipation rate(.epsilon.$_{\theta}$ are solved, in concert with the equations of the turbulent kinetic energy(k) and its dissiation rate(.epsilon). In the present model, the near-wall effect and the non-equilibrium effect are fully taken into consideration. The validation of the model is then applied to the turbulent flow behind a backward-facing step and the flow over a blunt body. The predicted results of the present model are compared and evaluated with the relevant experiments.

Analytical solution of a two-dimensional thermoelastic problem subjected to laser pulse

  • Abbas, Ibrahim A.;Alzahrani, Faris S.
    • Steel and Composite Structures
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    • v.21 no.4
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    • pp.791-803
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    • 2016
  • In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.

Analysis of payload compartment venting of satellite launch vehicle

  • Mehta, R.C.
    • Advances in aircraft and spacecraft science
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    • v.4 no.4
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    • pp.437-448
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    • 2017
  • The problem of flow through the vent is formulated as an unsteady, nonlinear, ordinary differential equation and solved using Runge-Kutta method to obtain pressure inside payload faring. An inverse problem for prediction of the discharge coefficient is presented employing measured internal pressure of the payload fairing during the ascent phase of a satellite launch vehicle. A controlled random search method is used to estimate the discharge coefficient from the measured transient pressure history during the ascent period of the launch vehicle. The algorithm predicts the discharge coefficient stepwise with function of Mach number. The estimated values of the discharge coefficients are in good agreement with differential pressure measured during the flight of typical satellite launch vehicle.

A Three-Dimensional Numerical Model of Circulation and Heat Transport in Coastal Region (연안 해수유동 및 온배수 확산에 관한 3차원 수치모형)

  • 정태성;이길성
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.6 no.3
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    • pp.245-259
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    • 1994
  • This paper is concerned with the development of a three-dimensional numerical model for coastal circulation and heat transport with improved prediction ability. The model uses fully nonlinear, time-dependent three-dimensional, $\sigma$-transformed equations of motion and equation of heat transport The model was verified with experimental data for wind-driven current in a one-dimensional channel and thermal jets flowing into stagnant waters and applied for unsteady flow induced by tide and thermal jets in coastal waters around Kori nuclear power plant. The model results were in good agreements with experimental data sets for wind-driven current and thermal jet, and field observed data sets in coastal waters. This study has shown that the $\kappa$-$\varepsilon$ turbulence model is applicable to various coastal conditions without any modification of turbulence constants.

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Eddy-Resolving Simulations for the Asian Marginal Seas and Kuroshio Using Nonlinear Terrain-Following Coordinate Model

  • Song, Y.-Tony;Tang, Tao
    • Journal of the korean society of oceanography
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    • v.37 no.3
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    • pp.169-177
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    • 2002
  • An eddy-resolving free-surface primitive-equation model with nonlinear terrain-following coordinates is established to study the exchange of water masses among the Asian marginal seas and their adjacent waters. A curvilinear coordinate system is used to generate the horizontal grid with a variable resolution for the regional oceans from $5^{\circ}$S to $45^{\circ}$N and $100^{\circ}$E to $155^{\circ}$E. The higher resolution region has about a 10 km by 10 km grid covering the complex geometry of the coastal marginal seas, while the lower resolution region has about a 30 km by 30 km grid covering the eastern Pacific. The model is initialized by the Levitus annual climitology and forced by the monthly mean air-sea fluxes of momentum, heat, and freshwater derived from the Comprehensive Ocean-Atmosphere Data Set. High-resolution and low-viscosity are identified as the key factors for a better representation of the exchange of waters through narrow straits and passages between the marginal seas and their adjacent waters. The dynamics of the loop currents and eddies in the South China Sea and Celebes Sea are examined in detail. It has found that the anticyclonic loop and detached eddies from the Kuroshio through the Luzon Strait play an important role in transporting warm and salty water into the South China Sea, while the cyclonic circulation of the Mindanao Current in the Celebes Sea plays a role in contributing cold water to the Indonesian throughflow. The deep undercurrent of the western Pacific is shown to provide fresher water to the South China Sea and Celebes Sea. These modeling results suggest that the exchange processes via the narrow straits and passages are of fundamental importance to the maintenance of water masses for the marginal sea region.

Analysis of Temperature distribution in a BSCCO-2223 tape stacked current lead (고온초전도 선재를 이용한 전류도입선의 열분포 해석)

  • Choi, Se-Yong;Nah, Wan-Soo;Joo, Jin-Ho;Yoo, Jai-Moo;Kim, Kye-Soo
    • 한국초전도학회:학술대회논문집
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    • v.9
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    • pp.275-279
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    • 1999
  • It is well known that HTS current lead minimizes helium vaporizations much less than the conventional current lead. To estimate the helium vaporizations in the design step, we need to compute the exact the temperature distributions on the lead. Unfortunately, the thermal parameters such as thermal conductivity and electrical resistivity depend strongly on the temperature. That is, heat equation itself has a nonlinear characteristics in the current lead. Furthermore, the uncertainties of helium vaporizations make it more difficult to estimate the boundary values. So far, numerical analyses using constant parameters in finite intervals have been used. In this paper, we calculate the temperature distribution in the current lead in considerations of temperature dependent parameters. The results showed self consistencies.

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