• Title/Summary/Keyword: Symmetric condition

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An Application of the Localized Finite Element Method to Two-dimensional Free Surface Wave Problems (2차원 자유표면파 문제에서의 국소 유한요소법의 응용)

  • Hyun-Kwon,Kil;K.J.,Bai
    • Bulletin of the Society of Naval Architects of Korea
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    • v.22 no.3
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    • pp.9-18
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    • 1985
  • The numerical calculation for solving boundary-value problem related to potential flows with a free surface is carried out by application of the localized finite element method. Only forced motion of 2-D body in infinitely deep fluid is considered, although this schemes is equally applicable to any first order time-harmonic problems of similar nature. The infinite domain of the fluid is separated into the inner flow field and the outer flow field with common inter-surface boundary. The finite element method is applied to obtain the solution in the inner flow field and the Green functions are utilized to represent the solution in the outer flow field. At the inter-surface boundary, the continuity of the value of potential and the normal derivative of the potential(i.e. matching condition) is conserved. The present method has better computational efficiency than the previous LFEM and the integral equation method of Frank. This enhanced computational efficiency is presumably due to the fact that the present method gives a symmetric coefficient matrix and requires less computational time in calculating the influence coefficient matrix of Green function than the integral equation method. And the irregular frequency desen't exist because the uniqueness of the solution is assured by the such that the exact free surface condition is satisfied on the boundary of the localized finite element region(i.e. inner region). As an example of the above method, the hydrodynamic forces for the circular cylinder and the rectangular cylinders are calculated. In the computed results, the small number of singularity distribution segments($3{\sim}6$) give good result relative to Ursell's and Vugts'.

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Study of the semi-segregation algorithms of the incompressible Navier-Stokes equations using P2P1 finite element formulation (P2P1 유한요소 공식을 이용한 비압축성 Navier-Stokes 방정식의 반-분리 해법에 관한 연구)

  • Cho, Myung-H.;Choi, Hyoung-G.;Yoo, Jung-Y.;Park, Jae-I.
    • 유체기계공업학회:학술대회논문집
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    • 2006.08a
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    • pp.349-352
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    • 2006
  • The conventional segregated finite element formulation produces a small and simple matrix at each step than in an integrated formulation. And the memory and cost requirements of computations are significantly reduced because the pressure equation for the mass conservation of the Navier-Stokes equations is constructed only once if the mesh is fixed. However, segregated finite element formulation solves Poisson equation of elliptic type so that it always needs a pressure boundary condition along a boundary even when physical information on pressure is not provided. On the other hand, the conventional integrated finite element formulation in which the governing equations are simultaneously treated has an advantage over a segregated formulation in the sense that it can give a more robust convergence behavior because all variables are implicitly combined. Further it needs a very small number of iterations to achieve convergence. However, the saddle-paint-type matrix (SPTM) in the integrated formulation is assembled and preconditioned every time step, so that it needs a large memory and computing time. Therefore, we newly proposed the P2PI semi-segregation formulation. In order to utilize the fact that the pressure equation is assembled and preconditioned only once in the segregated finite element formulation, a fixed symmetric SPTM has been obtained for the continuity constraint of the present semi-segregation finite element formulation. The momentum equation in the semi-segregation finite element formulation will be separated from the continuity equation so that the saddle-point-type matrix is assembled and preconditioned only once during the whole computation as long as the mesh does not change. For a comparison of the CPU time, accuracy and condition number between the two methods, they have been applied to the well-known benchmark problem. It is shown that the newly proposed semi-segregation finite element formulation performs better than the conventional integrated finite element formulation in terms of the computation time.

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Enzymatic synthesis of asymmetric structured lipids containing 1,2-disaturated-3-unsaturated glycerol using acyl migration (효소적 Acyl migration을 이용한 비대칭형 재구성지질(1,2-disaturated-3-unsaturated glycerol)의 합성 및 분석)

  • Hyeon, Jin-Woo;Lee, Ki-Teak
    • Korean Journal of Agricultural Science
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    • v.40 no.4
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    • pp.367-375
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    • 2013
  • The enzymatic interesterification was performed to produce structured lipids (SLs) with palm mid fraction (PMF) and stearic ethyl ester (STEE) for 1, 3, 6, 9, 12 and 15 hr at $80^{\circ}C$. The reaction was catalyzed by Lipozyme TLIM (immobilized lipase from Thermomyces lanuginosus, amount of 20% by weight of total substrates) in a shaking water bath set at 180 rpm. The optimum condition for synthesis of asymmetric SLs were: substrate molar ratio 1:0.5 (PMF:STEE, by weight), reaction time 6 hr, enzyme 20% (wt%, water activity=0.085) of total substrate and reaction temperature $80^{\circ}C$. After reaction at optimized condition, triacylglycerols (symmetrical and asymmetrical TAGs) from reactants were isolated. POP/PPO (1,3-palmitoyl-2-oleoyl glycerol or 1,2-palmitoyl-3-oleoyl glycerol), POS/PSO (palmitoyl-oleoyl-stearoyl glycerol or palmitoyl-stearoyl-oleoyl glycerol), SOS/SSO (1,3-stearoyl-2-oleoyl glycerol or 1,2-stearoyl-3-oleoyl glycerol) were obtained by solvent fractionation. Finally, refined SLs contained stearic acid of 16.91%. Solid fat index and thermogram of the refined SLs were obtained using differential scanning calorimetry. The degree of asymmetric triacylglycerol in the refined SLs was analyzed by Ag-HPLC equipped with evaporated light scattering detector (ELSD). The refined SLs consisted of symmetric TAG of 41.15 area% and asymmetric TAG of 58.85 area%.

A rational estimating method of the earth pressure on a shaft wall considering the shape ratio (벽체형상비의 영향을 합리적으로 고려한 원형수직구 벽체에 작용하는 토압산정방법)

  • Shin, Young-Wan;SaGong, Myung
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.9 no.2
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    • pp.143-155
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    • 2007
  • The earth pressure acting on a circular shaft wall is smaller than that acting on the wall in plane strain condition due to the three dimensional axi-symmetric arching effect. Accurate estimation of the earth pressure is required for the design of the shaft wall. In this study, the stress model considering the decrease of earth pressure due to the horizontal and vertical arching effect and the influence of shape ratio (shaft height/radius) is proposed. In addition, model test on the sandy soil is conducted and a comparison is made between the stress model and the test results. The comparison shows that the proposed stress model is in agreement with test results; decrease of shape ratio (increase of radius) leads to stress state equal to the plane strain condition and approximate stress distribution is found between stress model and model test results.

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Super-Cavitating Flow Problems about Two-Dimensional Symmetric Strut (2차원 대칭 스트럿 주위의 초월 공동 유동 문제의 해석)

  • Y.G.,Kim;C.S.,Lee
    • Bulletin of the Society of Naval Architects of Korea
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    • v.27 no.4
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    • pp.15-26
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    • 1990
  • This paper describes a potential-baoed panel method formulated for the analysis cf a supercavitating two-dimensional symmetri strut. The method employs normal dipoles and sources distributed on the foil and cavity surfaces to represent the potential flow around the cavitating hydrofoil. The kinematic boundary condition on the wetted portion of the foil surface is satisfied by requiring that the total potential vanish in the fictitious inner flow region of the foil, and the dynamic boundary condition on the cavity surface is satisfied by requiring that the potential vary linearly, i.e., the tangential velocity be constant. Green's theorem then results in a potential-based integral equation rather than the usual velocity-based formulation of Hess & Smith type, With the singularities distributed on the exact hydrofoil surface, the pressure distributions are predicted with improved accuracy compared to those of the linearized lifting surface theory, especially near the leading edge. The theory then predicts the cavity shape and cavitation number for an assumed cavity length. To improve the accuracy, the sources and dipoles on the cavity surface are moved to the newly computed cavity surface, where the boundary conditions are satisfied again. This iteration process is repeated until the results are converged.

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Experimental Investigation of Sonic Jet Flows for Wing/Nacelle Integration

  • Kwon, Eui-Yong;Roger Leblanc;Garem, Jean-Henri
    • Journal of Mechanical Science and Technology
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    • v.15 no.4
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    • pp.522-530
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    • 2001
  • An experimental study of compressible jet flows has been undertaken in a small transonic wind tunnel. The aim of this investigation was to realize a jet simulator in the framework of wing/nacelle integration research and to characterize the jet flow behavior. First, free jet configuration, and subsequently jet flow in co-flowing air stream configuration were analyzed. Flow conditions were those encountered in a typical flight condition of a generic transport aircraft, i.e. fully expanded sonic jet flows interacting with a compressible external flowfield. Conventional experimental techniques were used to investigate the jet flows-Schlieren visualization and two-component Laser Doppler Velocimetry (LDV). The mean and fluctuating properties were measured along the jet centerline and in the symmetric plane at various downstream locations. The results of two configurations show remarkable differences in the mean and fluctuating components and agree well with the trend observed by other investigators. Moreover, these experiments enrich the database for such flow conditions and verify the feasibility of its application in future aerodynamic research of wing/nacelle interactions.

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A numerical study on the optimum operation condition for axial oxygen concentration in 8 inch silicon growth by cusp MCZ (8인치 실리콘성장을 위한 커스프 MCZ계에서 축방향 산소분포에 대한 연구)

  • 이승철;윤종규
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.7 no.3
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    • pp.406-417
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    • 1997
  • A numerical study was conducted on the optimum magnetic field intensity and asymmetric factor for uniform axial oxygen concentration in 8 inch silicon single crystal growing process by magnetic Czochralski method. For constant shape of cusp field, a change of coil and crucible position were compared. In case of symmetric cusp field, magnetic field intensity variation shows concave downward with crystal growing for uniform, axial oxygen concentration. A numerical results show similar value of standard deviation of average oxygen concentration for uniform oxygen concentration between coil and crucible position change. In case of asymmetric cusp field. asymmetric factor is increased with crystal growing to have uniform oxygen concentration.

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Vibration Analysis of the Rotating Hybrid Cylindrical Shells Laminated with Metal and Composite (회전하는 금속복합재료 혼합적층 원통쉘의 진동해석)

  • Lee, Young-Sin;Kim, Young-Wann
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.3
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    • pp.968-977
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    • 1996
  • The linear/nonlinear vibration response of the rotating hybrid cylindrical shell with simply supported boundary condition is studied. The Ritz-Galerkin method is applied to obtain the nonlinear frequency equation, which excludes in-plane and rotatory inertia but includes bending stretching coupling terms. The bifurcation phenomena for the linear frequency and the frequency ratio(nonlinear/linear frequency ratio) are presented. The hybrid cylindrical shells are composed of composite(GFRP, CFRP) metal(aluminium, steel) with symmetric and antisymmetric stacking sequence. The effects of the Coriolis and centrifugal force are considered The results also present the effects of length-to- radies ratio, radius-to-thickness ratio, the circumferential wave number, the stacking sequence, the material property, the initial excitation amplitude and the rotating speed. The present linear frequency results are compared with those of the available literature.

Electrochromic Properties of Symmetric and Asymmetric Viologens (대칭, 비대칭 Viologen 유도체의 전기변색특성)

  • Kim, Sung Hoon;Bae, Jin Seok;Hwang, Seok Hwan;Gwon, Tae Sun;Do, Myung Ki;Park, Chul
    • Journal of the Korean Chemical Society
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    • v.40 no.11
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    • pp.686-691
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    • 1996
  • Several kind of viologen derivatives were synthesized and the electrochromic property of these compounds was examined by cyclovoltametric and chronoamperometric method, relating to the mechanisum of coloring reaction. The electrochromic properties of 1,1'-diethyl-4,4'-bipyridinium dibromide(EV), 1,1'-dipropyl-4,4'-bipyridinium dibromide(PV), 1,1'-dibuthyl-4,4'-bipyridinium dibromide(BV) and 1-ethyl-1'-butyl-4,4'-bipyridinium dibromide(EBV) are studied by using an propylenecarbonate/methanol solution with $Bu_4NBF_4$ as supporting electrolyte. A monomer-dimer equilibrium was proposed to explain the related observation that EV and EBV cation radical solutions are violet at an applied voltage of 1.7∼3.0V but become blue in open-circuit condition.

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Synthesis of Organic Carbonates with Alkyl/aryl 4,5-dichloro-6-oxopyridazine-1(6H)-carboxylates and ROH/AlCl3 under Ambient Condition

  • Sung, Gi Hyeon;Kim, Bo Ram;Ryu, Ki Eun;Kim, Jeum-Jong;Yoon, Yong-Jin
    • Bulletin of the Korean Chemical Society
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    • v.35 no.9
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    • pp.2758-2764
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    • 2014
  • We demonstrated the synthesis of organic carbonates using alkyl/aryl 4,5-dichloro-6-oxopyridazine-1(6H)-carboxylates and alcohol in the presence of aluminum chloride. Alkyl/aryl 4,5-dichloro-6-oxopyridazine-1(6H)-carboxylates were reacted with alcohol in the presence of $AlCl_3$ in toluene at room temperature to afford the corresponding unsymmetric and symmetric organic carbonates in good to excellent yields. These are efficient and convenient processes. Alkyl/aryl 4,5-dichloro-6-oxopyridazine-1(6H)-carboxylates are solid, stable and non-toxic $CO_2/CO_2R$(Ar) source. It is noteworthy that the reaction is carry out under an ambient and acidic conditions, the easy-to prepare and readily available starting materials and the quantitative isolation of reusable 4,5-dichloropyridazin-3(2H)-one.