• Title/Summary/Keyword: hyperbolic function

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STUDY ON THE DEFORMATION OF DROPLETS IN A TWO-DIMENSIONAL CHANNEL FLOW (2차원 채널유동에서의 액적 변형에 대한 수치해석적 연구)

  • Jung, S.R.;Cho, M.H.;Choi, H.G.;Yoo, J.Y.
    • 한국전산유체공학회:학술대회논문집
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    • 2011.05a
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    • pp.6-9
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    • 2011
  • In this study, the two-phase incompressible flow in two-dimensional channel considering the effect of surface tension is simulated using an improved level-set method. Quadratic element is used for solving the continuity and Navier-Stokes equations to avoid using an additional pressure equation, and Crank-Nicholson scheme and linear element are used for solving the advection equation of the level set function. Direct approach method using geometric information is implemented instead of the hyperbolic-type partial differential equation for the reinitializing the level set function. The benchmark test case considers various arrays of defomable droplets under different flow conditions in straight channel. The deformation and migration of the droplets are computed and the results are compared very well with the existing studies.

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Two-dimensional Model Analysis on Cochlear Basilar Membrane Motion (코클리어 기저막 운동의 2차원 모델 해석)

  • Yu, Seon-Guk;Baek, Seung-Hwa;Park, Sang-Hui
    • Journal of Biomedical Engineering Research
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    • v.5 no.2
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    • pp.161-166
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    • 1984
  • In this paper, we describe an effective technique for computing the steady-state motion in a two-dimensional cochlear model. With the cochlear fluid assumed incompressible and invisid, the problem reduces to solving an integral equation for a region with yielding boundary. Using the conformal mapping, Jacobian elliptic function and hyperbolic function, a pair of second-order differential equation is derived. What we will show in this paper is that by appropriately transforming integral equation, the same computation can be performed with comparable accuracy in a short time.

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Control of Damping Coefficients for the Shear Mode MR Dampers Using Inverse Model (역모델을 이용한 MR 댐퍼의 감쇠계수 제어)

  • Na, Uhn Joo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.23 no.5
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    • pp.445-455
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    • 2013
  • A new linearization model for MR dampers is analyzed. The nonlinear hysteretic damping force model of MR damper can be modeled as a hyperbolic tangent function of currents, positions, and velicities, which is an algebraic function with constant parameters. Model parameters can be identified with numerical method using experimental force-velocity-position data obtained from various operating conditions. The nonlinear hysteretic damping force can be linearized with a given slope of damping coefficient if there exist corresponding currents to compensate for the nonlinearity. The corresponding currents can be calculated from the inverse model when the given linear damping force is set equal to the nonlinear hysteretic damping force. The linearization controller is realized in a DSP controller such that the corresponding currents to satisfy a given damping coefficient should be calculated. Experiments show that the current inputs to the MR damper produce linearized damping force with a given slope of the damping coefficient.

Phase Doppler Measurements and Probability Density Functions in Liquid Fuel Spray (연료분무의 위상도플러 측정과 확률밀도함수의 도출)

  • 구자예
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.4
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    • pp.1039-1049
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    • 1994
  • The intermitternt and transient fuel spray have been investigated from the simultaneous measurement of droplet sizes and velocities by using Phase/Doppler Particle Analyzer(PDPA). Measurement have been done on the spray axis and at the edge of the spray near nozzle at various gas-to-liquid density ratios(.rho./sub g//.rho./sub l/) that ranges from those found in free atmospheric jets to conditions typical of diesel engines. Probability density distributions of the droplet size and velocity were obtained from raw data and mathematical probability density functions which can fit the experimental distribations were extracted using the principle of maximum likelihood. In the near nozzle region on the spray axis, droplet sizes ranged from the lower limit of the measurement system to the order of nozzle diameter for all (.rho./sub g/ /.rho./sub l/) and droplet sizes tended to be small on the spray edge. At the edge of spray, average droplet velocity peaked during needle opening and needle closing. The rms intensity is greatly incresed as the radial distance from the nozzle is increased. The probability density function which can best fit the physical breakage process such as breakup of fuel drops is exponecially decreasing log-hypebolic function with 4 parameters.

Study on the direct approach to reinitialization in using level set method for simulating incompressible two-phase flows (비압축성 2 상유동의 모사를 위한 level set 방법에서의 reinitialization 직접 접근법에 관한 연구)

  • Cho, Myung-H.;Choi, Hyoung-G.;Yoo, Jung-Y.
    • 한국전산유체공학회:학술대회논문집
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    • 2008.03b
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    • pp.568-571
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    • 2008
  • The computation of moving interface by the level set method typically requires reinitializations of level set function. An inaccurate estimation of level set function ${\phi}$ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, accurate and robust reinitialization process is essential to the free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates directly level set function ${\phi}$ using a normal vector in the interface without solving the re-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1splitting FEM are adopted to discretize advection equation of the level set function and the Navier-Stokes equation, respectively. Advection equation of free surface and re-initialization process are validated with benchmark problems, i.e., a broken dam flow and time-reversed single vortex flow. The simulation results are in good agreement with the existing results.

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Study on the Solution of Reinitialization Equation for Level Set Method in the Simulation of Incompressible Two-Phase Flows (비압축성 2 상유동의 모사를 위한 Level Set 방법의 Reinitialization 방정식의 해법에 관한 연구)

  • Cho, Myung-Hwan;Choi, Hyoung-Gwon;Yoo, Jung-Yul
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.32 no.10
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    • pp.754-760
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    • 2008
  • Computation of moving interface by the level set method typically requires the reinitialization of level set function. An inaccurate estimation of level set function $\phi$ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, an accurate and robust reinitialization process is essential to the simulation of free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates level set function directly using a normal vector on the interface without solving there-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1 splitting/SUPG (Streamline Upwind Petrov-Galerkin) FEM are adopted to discretize advection equation of the level set function and the incompressible Navier-Stokes equation, respectively. Advection equation and re-initialization process of free surface capturing are validated with benchmark problems, i.e., a broken dam flow and timereversed single vortex flow. The simulation results are in good agreement with the existing results.

A Visual Programming Environment for Medical Image Processing (의료영상처리를 위한 시각 프로그래밍 환경)

  • Sung, Chong-Won;Kim, Jin-Ho;Kim, Jee-In
    • The Transactions of the Korea Information Processing Society
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    • v.7 no.8
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    • pp.2349-2360
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    • 2000
  • In medical image processing, if new technologies arc developed, they arc applied to real clinical cases. The results are to be analyzed by doctors to improve the new technologies. So, it is important for doctors to have a tool that helps the doctors in applying the new technologies to clinical cases and analyzing the clinical results. In this paper, we design and implement a visual programming environment where non-programming experts, such as medical doctors, can easily compose a medical image processing application program. A set of image processing functions are implemented and represented as icons. Thc user selects functions by clicking correslxmding icons. The users can easily find necessary' functions from the visualized library. A user selects a function from the visualized library and [Jut the function node into a canvas of Visual Programming Interface. The user connects nodes to compose a dataflow diagram. The connected dataflow diagram shows the now of the program. Hyperbolic Tree is helpful in visualizing a set of function icons in a single screen because it provides both the whole stmcture of the function Iihrary and the details of the focused functions at the same time. We also developed a CUI builder where the user interfaces of the medical image processing applications are composed. Therefore. non'programming experts such as physicians can apply new medical image processing algorithms to clinical cases without performing complex computer programming procedures.

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Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory

  • El-Hassar, Sidi Mohamed;Benyoucef, Samir;Heireche, Houari;Tounsi, Abdelouahed
    • Geomechanics and Engineering
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    • v.10 no.3
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    • pp.357-386
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    • 2016
  • In this research work, an exact analytical solution for thermal stability of solar functionally graded rectangular plates subjected to uniform, linear and non-linear temperature rises across the thickness direction is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the efficient hyperbolic plate theory based on exact neutral surface position is employed to derive the governing stability equations. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the quadratic distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Just four unknown displacement functions are used in the present theory against five unknown displacement functions used in the corresponding ones. The non-linear strain-displacement relations are also taken into consideration. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the present theory, demonstrating its importance and accuracy in comparison to other theories.

Free vibration of FGM plates with porosity by a shear deformation theory with four variables

  • Yousfi, Mahfoud;Atmane, Hassen Ait;Meradjah, Mustapha;Tounsi, Abdelouahed;Bennai, Riadh
    • Structural Engineering and Mechanics
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    • v.66 no.3
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    • pp.353-368
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    • 2018
  • In this work, a high order hyperbolic shear deformation theory with four variables is presented to study the vibratory behavior of functionally graduated plates. The field of displacement of the theory used in this work is introduced indeterminate integral variables. In addition, the effect of porosity is studied. It is assumed that the material characteristics of the porous FGM plate, varies continuously in the direction of thickness as a function of the power law model in terms of volume fractions of constituents taken into account the homogeneous distribution of porosity. The equations of motion are obtained using the principle of virtual work. An analytical solution of the Navier type for free vibration analysis is obtained for a FGM plate for simply supported boundary conditions. A comparison of the results obtained with those of the literature is made to verify the accuracy and efficiency of the present theory. It can be concluded from his results that the current theory is not only accurate but also simple for the presentation of the response of free vibration and the effect of porosity on the latter.

Application of Artificial Neural Network to Flamelet Library for Gaseous Hydrogen/Liquid Oxygen Combustion at Supercritical Pressure (초임계 압력조건에서 기체수소-액체산소 연소해석의 층류화염편 라이브러리에 대한 인공신경망 학습 적용)

  • Jeon, Tae Jun;Park, Tae Seon
    • Journal of the Korean Society of Propulsion Engineers
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    • v.25 no.6
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    • pp.1-11
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    • 2021
  • To develop an efficient procedure related to the flamelet library, the machine learning process based on artificial neural network(ANN) is applied for the gaseous hydrogen/liquid oxygen combustor under a supercritical pressure condition. For hidden layers, 25 combinations based on Rectified Linear Unit(ReLU) and hyperbolic tangent are adopted to find an optimum architecture in terms of the computational efficiency and the training performance. For activation functions, the hyperbolic tangent is proper to get the high learning performance for accurate properties. A transformation learning data is proposed to improve the training performance. When the optimal node is arranged for the 4 hidden layers, it is found to be the most efficient in terms of training performance and computational cost. Compared to the interpolation procedure, the ANN procedure reduces computational time and system memory by 37% and 99.98%, respectively.