• Title/Summary/Keyword: lagrangian

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Level Set Based Shape Optimization of Linear Structures using Topological Derivatives (위상민감도를 이용한 선형구조물의 레벨셋 기반 형상 최적설계)

  • Yoon, Minho;Ha, Seung-Hyun;Kim, Min-Geun;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.1
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    • pp.9-16
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    • 2014
  • Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The "Hamilton-Jacobi(H-J)" equation and computationally robust numerical technique of "up-wind scheme" lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H-J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes are not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

Improved Calculation of the Advection Term in the Semi-Lagrange Method for Realistic Smoke Simulation (사실적 연기 시뮬레이션을 위한 Semi-Lagrange 방법에서의 이류항 계산방법 개선)

  • Park, Su-Wan;Chang, Mun-Hee;Ki, Eun-Ju;Ryu, Kwan-Woo
    • The KIPS Transactions:PartA
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    • v.14A no.4
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    • pp.191-196
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    • 2007
  • In the field of computer graphics, Navier-Stokes equations would be used for realistic simulations of smokes and currents. However, implementations derived from these equations are hard to achieve for real-time simulations, mainly due to its massive and complex calculations. Thus, there have been various attempts to approximate these equations for real-time simulation of smokes and others. When the advection terms of the equations are approximated by the Semi-Lagrange methods, the fluid density can be rapidly reduced and small-scale vorticity phenomena are easy to be missed, mainly due to the numerical losses over time. In this paper, we propose an improved numerical method to approximately calculate the advection terms, and thus eliminate these problems. To calculate the advection terms, our method starts to set critical regions around the target grid points. Then, among the grid points in a specific critical region, we search for a grid point which will be advected to the target grid point, and use the velocity of this grid point as its advection vector. This method would reduce the numerical losses in the calculation of densities and vorticity phenomena, and finally can implement more realistic smoke simulations. We also improve the overall efficiency of vector calculations and related operations through GPU-based implementation techniques, and thus finally achieve the real-time simulation.

Investigation of dust particle removal efficiency of self-priming venturi scrubber using computational fluid dynamics

  • Ahmed, Sarim;Mohsin, Hassan;Qureshi, Kamran;Shah, Ajmal;Siddique, Waseem;Waheed, Khalid;Irfan, Naseem;Ahmad, Masroor;Farooq, Amjad
    • Nuclear Engineering and Technology
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    • v.50 no.5
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    • pp.665-672
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    • 2018
  • A venturi scrubber is an important element of Filtered Containment Venting System (FCVS) for the removal of aerosols in contaminated air. The present work involves computational fluid dynamics (CFD) study of dust particle removal efficiency of a venturi scrubber operating in self-priming mode using ANSYS CFX. Titanium oxide ($TiO_2$) particles having sizes of 1 micron have been taken as dust particles. CFD methodology to simulate the venturi scrubber has been first developed. The cascade atomization and breakup (CAB) model has been used to predict deformation of water droplets, whereas the Eulerian-Lagrangian approach has been used to handle multiphase flow involving air, dust, and water. The developed methodology has been applied to simulate venturi scrubber geometry taken from the literature. Dust particle removal efficiency has been calculated for forced feed operation of venturi scrubber and found to be in good agreement with the results available in the literature. In the second part, venturi scrubber along with a tank has been modeled in CFX, and transient simulations have been performed to study self-priming phenomenon. Self-priming has been observed by plotting the velocity vector fields of water. Suction of water in the venturi scrubber occurred due to the difference between static pressure in the venturi scrubber and the hydrostatic pressure of water inside the tank. Dust particle removal efficiency has been calculated for inlet air velocities of 1 m/s and 3 m/s. It has been observed that removal efficiency is higher in case of higher inlet air velocity.

Characteristics of Static Shift in 3-D MT Inversion (3차원 MT 역산에서 정적효과의 특성 고찰)

  • Lee Tae Jong;Uchida Toshihiro;Sasaki Yutaka;Song Yoonho
    • Geophysics and Geophysical Exploration
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    • v.6 no.4
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    • pp.199-206
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    • 2003
  • Characteristics of the static shift are discussed by comparing the three-dimensional MT inversion with/without static shift parameterization. The galvanic distortion by small-scale shallow feature often leads severe distortion in inverted resistivity structures. The new inversion algorithm is applied to four numerical data sets contaminated by different amount of static shift. In real field data interpretations, we generally do not have any a-priori information about how much the data contains the static shift. In this study, we developed an algorithm for finding both Lagrangian multiplier for smoothness and the trade-off parameter for static shift, simultaneously in 3-D MT inversion. Applications of this inversion routine for the numerical data sets showed quite reasonable estimation of static shift parameters without any a-priori information. The inversion scheme is successfully applied to all the four data sets, even when the static shift does not obey the Gaussian distribution. Allowing the static shift parameters have non-zero degree of freedom to the inversion, we could get more accurate block resistivities as well as static shifts in the data. When inversion does not consider the static shift as inversion parameters (conventional MT inversion), the block resistivities on the surface are modified considerably to match possible static shift. The inhomogeneous blocks on the surface can generate the static shift at low frequencies. By those mechanisms, the conventional 3-D MT inversion can reconstruct the resistivity structures to some extent in the deeper parts even when moderate static shifts are in the data. As frequency increased, however, the galvanic distortion is not frequency independent any more, and thus the conventional inversion failed to fit the apparent resistivity and phase, especially when strong static shift is added. Even in such case, however, reasonable estimation of block resistivity as well as static shift parameters were obtained by 3-D MT inversion with static shift parameterization.

Development and Application of Two-Dimensional Numerical Tank using Desingularized Indirect Boundary Integral Equation Method (비특이화 간접경계적분방정식방법을 이용한 2차원 수치수조 개발 및 적용)

  • Oh, Seunghoon;Cho, Seok-kyu;Jung, Dongho;Sung, Hong Gun
    • Journal of Ocean Engineering and Technology
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    • v.32 no.6
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    • pp.447-457
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    • 2018
  • In this study, a two-dimensional fully nonlinear transient wave numerical tank was developed using a desingularized indirect boundary integral equation method. The desingularized indirect boundary integral equation method is simpler and faster than the conventional boundary element method because special treatment is not required to compute the boundary integral. Numerical simulations were carried out in the time domain using the fourth order Runge-Kutta method. A mixed Eulerian-Lagrangian approach was adapted to reconstruct the free surface at each time step. A numerical damping zone was used to minimize the reflective wave in the downstream region. The interpolating method of a Gaussian radial basis function-type artificial neural network was used to calculate the gradient of the free surface elevation without element connectivity. The desingularized indirect boundary integral equation using an isolated point source and radial basis function has no need for information about the element connectivity and is a meshless method that is numerically more flexible. In order to validate the accuracy of the numerical wave tank based on the desingularized indirect boundary integral equation method and meshless technique, several numerical simulations were carried out. First, a comparison with numerical results according to the type of desingularized source was carried out and confirmed that continuous line sources can be replaced by simply isolated sources. In addition, a propagation simulation of a $2^{nd}$-order Stokes wave was carried out and compared with an analytical solution. Finally, simulations of propagating waves in shallow water and propagating waves over a submerged bar were also carried and compared with published data.

Assessment of Structural Soundness and Joint Load of the Rotorcraft External Fuel Tank by Sloshing Movement (슬로싱 운동에 의한 회전익항공기 외부연료탱크 체결부 하중 및 구조건전성 평가)

  • Kim, Hyun-Gi;Kim, Sung Chan
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.20 no.5
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    • pp.605-611
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    • 2019
  • The fuel sloshing due to the rapid manoeuvre of the aircraft causes significant loads on internal components, which may break components or piping. In particular, a significant load is applied to the joint of the external fuel tank by sloshing movement, which may affect the safety of the aircraft when the joint of the external fuel tank is damaged. Therefore, in order to improve the survivability of aircraft and crew members, the design of external fuel tanks, and joints should be performed after evaluating the sloshing load through a numerical analysis of the fuel sloshing conditions. In this paper, a numerical analysis was performed on the sloshing test of the external fuel tank for rotorcraft. ALE (Arbitrary Lagrangian Eulerian) technique was used, and the test conditions specified in the U.S. Military Specification (MIL-DTL-27422D) was applied as the conditions for numerical analysis. As a result of the numerical analysis, the load on the joint of the external fuel tank was calculated. Moreover, the effects of sloshing movement on structural soundness were assessed through analysis of stress levels and margin of safety on metal fittings and composite containers.

Numerical Study on the Effects of Air Decking in Half Charge Blasting Using AUTODYN (AUTODYN을 이용한 하프장전 발파공법의 에어데크 효과에 대한 수치해석적 연구)

  • Baluch, Khaqan;Kim, Jung-Kyu;Kim, Seung-Jun;Jin, Guochen;Jung, Seung-Won;Yang, Hyung-Sik;Kim, Nam-Soo;Kim, Jong-Gwan
    • Explosives and Blasting
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    • v.36 no.4
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    • pp.1-8
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    • 2018
  • This numerical study was intended to evaluate the applicability of the half charge blasting to mining and tunnelling. The half charge blasting is a method that two separate rounds are sequentially blasted for the rock burdens in which long blast holes have already been drilled at one operation. The aim of the method is to decrease the construction cost and period in mining and tunnelling projects as well as to increase the blasting efficiency. Several numerical analyses were conducted by using the Euler-Lagrange solver on ANSYS AUTODYN to identify the effects of the suggested method on the blasting results in underground excavations. The overall performance of the suggested method was also compared to an ordinary blasting method. The analysis model was comprised of the Eulerian parts (explosive, air, and stemming materials) and the Lagrangian parts (rock material). As a result, it was found that, owing to the air decks formed in the bottom parts of the long blast holes, the first round of the suggested method presented a higher shock pressure and particle velocities in the vicinity of the blast holes compared to the ordinary blasting method.

Evaluation of high-velocity impact welding's interfacial morphology between Cu and CP-Ti using SPH numerical analysis method (SPH 해석기법을 이용한 Cu와 CP-Ti 고속 충돌 접합 단면의 형상학적 평가)

  • Park, Ki Hwan;Kang, Beom Soo;Kim, Jeong
    • Journal of Aerospace System Engineering
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    • v.13 no.2
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    • pp.34-42
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    • 2019
  • The existence of different thermodynamic properties results in various undesirable effects, such as thermal deformation and residual stress, in heat-welding processes. The solid-state junction, by using explosive or electromagnetic forces, i.e., high-velocity impact welding without employing heat is advantageous in joining materials with different thermodynamic properties. In the solid-state junction, the joining is performed within a short time, a high velocity and large deformations are accompanied by interfacial surfaces. The numerical analysis models play an important role in the understanding of the mechanism of high-velocity impact welding. However, in the analysis of high velocity and large deformations, the conventional Lagrangian method has low reliability due to the occurrence of entanglements. In this study, high-velocity impact welding between Cu and CP-Ti with different thermodynamic properties was performed using a un-gridded numerical method, SPH (Smoothed Particle Hydrodynamics), and interfacial morphology occurred. As a result of the analysis, the interfacial morphology was confirmed and the compared degree of shape (straight, vortex), period, length, and so on appeared differently depending on the relationship between the parameters (impact angle and speed).

Conservation for the Seismic Models of Intake Tower with Nonlinear Behaviors and Fluid Structure Interaction (비선형거동과 구조물유체상호작용을 고려한 취수탑 내진모델의 보수성평가)

  • Lee, Gye-Hee;Lee, Myoung-Kyu;Hong, Kwan-Young
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.24 no.6
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    • pp.17-24
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    • 2020
  • In this study, series of nonlinear seismic analysis were performed on a reinforced concrete intake tower surrounded by water. To consider the fluid effect around the structure, analysis models were composed using an added mass and CEL approach. At this time, the implicit method was used for the added mass model, and the explicit method was used for the fluid structure interaction model. The input motions were scaled to correspond to 500, 1000, and 2400 years return period of the same artificial earthquake. To estimate the counteractivity of the fluid coupled model, models without fluid effect were constructed and used as a reference. The material models of concrete and reinforcement were selected to consider the nonlinear behavior after yielding, and analysis were performed by ABAQUS. As results, in the acceleration response spectrum of the structure, it was found that the influence of the surrounding fluid reducing the peak frequency and magnitude corresponding to the fundamental frequency of the structure. However, the added mass model did not affect the peak value corresponding to the higher mode. The sectional moments were increased significantly in the case of the added mass model than those of the reference model. Especially, this amplification occurred largely for a small-sized earthquake response in which linear behavior is dominant. In the fluid structure interaction model, the sectional moment with a low frequency component amplifies compared to that of the reference model, but the sectional moment with a high requency component was not amplified. Based in these results, it was evaluated that the counteractivity of the additive mass model was greater than that of the fluid structure interaction model.

Active Fault Tolerant Control of Quadrotor Based on Multiple Sliding Surface Control Method (다중 슬라이딩 표면 제어 기법에 기반한 쿼드로터의 능동 결함 허용 제어)

  • Hwang, Nam-Eung;Kim, Byung-Soo
    • The Journal of the Korea institute of electronic communication sciences
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    • v.17 no.1
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    • pp.59-70
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    • 2022
  • In this paper, we proposed an active fault tolerant control (AFTC) method for the position control of a quadrotor with complete loss of effectiveness of one motor. We obtained the dynamics of a quadrotor using Lagrangian equation without small angle assumption. For detecting the fault on a motor, we designed a fault detection module, which consists of the fault detection and diagnosis (FDD) module and the fault detection and isolation (FDI) module. For the FDD module, we designed a nonlinear observer that observes the states of a quadrotor based on the obtained dynamics. Using the observed states of a quadrotor, we designed residual signals and set the appropriate threshold values of residual signals to detect the fault. Also, we designed an FDI module to identify the fault location using the designed additional conditions. To make a quadrotor track the desired path after detecting the fault of a motor, we designed a fault tolerant controller based on the multiple sliding surface control (MSSC) technique. Finally, through simulations, we verified the effectiveness of the proposed AFTC method for a quadrotor with complete loss of effectiveness of one motor.