• Title/Summary/Keyword: triangular net

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A variational nodal formulation for multi-dimensional unstructured neutron diffusion problems

  • Qizheng Sun ;Wei Xiao;Xiangyue Li ;Han Yin;Tengfei Zhang ;Xiaojing Liu
    • Nuclear Engineering and Technology
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    • v.55 no.6
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    • pp.2172-2194
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    • 2023
  • A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (keff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

The hydrodynamic characteristics of the canvas kite - 2. The characteristics of the triangular canvas kite - (캔버스 카이트의 유체역학적 특성에 관한 연구 - 2. 삼각형 캔버스 카이트의 특성 -)

  • Bae, Bong-Seong;Bae, Jae-Hyun;An, Heui-Chun;Lee, Ju-Hee;Shin, Jung-Wook
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.40 no.3
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    • pp.206-213
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    • 2004
  • As far as an opening device of fishing gears is concerned, applications of a kite are under development around the world. The typical examples are found in the opening device of the stow net on anchor and the buoyancy material of the trawl. While the stow net on anchor has proved its capability for the past 20 years, the trawl has not been wildly used since it has been first introduced for the commercial use only without sufficient studies and thus has revealed many drawbacks. Therefore, the fundamental hydrodynamics of the kite itself need to ne studied further. Models of plate and canvas kite were deployed in the circulating water tank for the mechanical test. For this situation lift and drag tests were performed considering a change in the shape of objects, which resulted in a different aspect ratio of rectangle and trapezoid. The results obtained from the above approaches are summarized as follows, where aspect ratio, attack angle, lift coefficient and maximum lift coefficient are denoted as A, B, $C_L$ and $C_{Lmax}$ respectively : 1. Given the triangular plate, $C_{Lmax}$ was produced as 1.26${\sim}$1.32 with A${\leq}$1 and 38$^{\circ}$B${\leq}$42$^{\circ}$. And when A${\geq}$1.5 and 20$^{\circ}$${\leq}$B${\leq}$50$^{\circ}$, $C_L$ was around 0.85. Given the inverted triangular plate, $C_{Lmax}$ was 1.46${\sim}$1.56 with A${\leq}$1 and 36$^{\circ}$B${\leq}$38$^{\circ}$. And When A${\geq}$1.5 and 22$^{\circ}$B${\leq}$26$^{\circ}$, $C_{Lmax}$ was 1.05${\sim}$1.21. Given the triangular kite, $C_{Lmax}$ was produced as 1.67${\sim}$1.77 with A${\leq}$1 and 46$^{\circ}$B${\leq}$48$^{\circ}$. And when A${\geq}$1.5 and 20$^{\circ}$B${\leq}$50$^{\circ}$, $C_L$ was around 1.10. Given the inverted triangular kite, $C_{Lmax}$ was 1.44${\sim}$1.68 with A${\leq}$1 and 28$^{\circ}$B${\leq}$32$^{\circ}$. And when A${\geq}$1.5 and 18$^{\circ}$B${\leq}$24$^{\circ}$, $C_{Lmax}$ was 1.03${\sim}$1.18. 2. For a model with A=1/2, an increase in B caused an increase in $C_L$ until $C_L$ has reached the maximum. Then there was a tendency of a very gradual decrease or no change in the value of $C_L$. For a model with A=2/3, the tendency of $C_L$ was similar to the case of a model with A=1/2. For a model with A=1, an increase in B caused an increase in $C_L$ until $C_L$ has reached the maximum. And the tendency of $C_L$ didn't change dramatically. For a model with A=1.5, the tendency of $C_L$ as a function of B was changed very small as 0.75${\sim}$1.22 with 20$^{\circ}$B${\leq}$50$^{\circ}$. For a model with A=2, the tendency of $C_L$ as a function of B was almost the same in the triangular model. There was no considerable change in the models with 20$^{\circ}$B${\leq}$50$^{\circ}$. 3. The inverted model's $C_L$ as a function of increase of B reached the maximum rapidly, then decreased gradually compared to the non-inverted models. Others were decreased dramatically. 4. The action point of dynamic pressure in accordance with the attack angle was close to the rear area of the model with small attack angle, and with large attack angle, the action point was close to the front part of the model. 5. There was camber vertex in the position in which the fluid pressure was generated, and the triangular canvas had large value of camber vertex when the aspect ratio was high, while the inverted triangular canvas was versa. 6. All canvas kite had larger camber ratio when the aspect ratio was high, and the triangular canvas had larger one when the attack angle was high, while the inverted triangluar canvas was versa.

Definition of Ship Hull using $GC^1$ Surface ([$GC^1$] 곡면을 이용한 선형의 표현)

  • J.S. Park;D.J. Kim
    • Journal of the Society of Naval Architects of Korea
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    • v.31 no.4
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    • pp.32-40
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    • 1994
  • This paper describes a smooth surface interpolating method of ship hull using a three-dimensional currie net that comes from the mesh curve fairing process. Geometric continuity(($GC^1$) is preserved across the boundary curve between patches. The three-dimensional curve net can have nonrectangular topologies, such as triangular and pentagonal topology. Among the boundary curve interpolation methods, Hermite blended Coons patch, Convex combination, and Gregory patch interpolation method are used to generate the ship hull surface. To check the fairness of the surface, the numerical method of surface/surface intersection problem is adopted. An application to an actual ship hull is given as an example.

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A cosmic ray muons tomography system with triangular bar plastic scintillator detectors and improved 3D image reconstruction algorithm: A simulation study

  • Yanwei Zhao;Xujia Luo;Kemian Qin;Guorui Liu;Daiyuan Chen;R.S. Augusto;Weixiong Zhang;Xiaogang Luo;Chunxian Liu;Juntao Liu;Zhiyi Liu
    • Nuclear Engineering and Technology
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    • v.55 no.2
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    • pp.681-689
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    • 2023
  • Purpose: Muons are characterized by a strong penetrating ability and can travel through thousands of meters of rock, making them ideal to image large volumes and substances typically impenetrable to, for example, electrons and photons. The feasibility of 3D image reconstruction and material identification based on a cosmic ray muons tomography (MT) system with triangular bar plastic scintillator detectors has been verified in this paper. Our prototype shows potential application value and the authors wish to apply this prototype system to 3D imaging. In addition, an MT experiment with the same detector system is also in progress. Methods: A simulation based on GEANT4 was developed to study cosmic ray muons' physical processes and motion trails. The yield and transportation of optical photons scintillated in each triangular bar of the detector system were reproduced. An image reconstruction algorithm and correction method based on muon scattering, which differs from the conventional PoCA algorithm, has been developed based on simulation data and verified by experimental data. Results: According to the simulation result, the detector system's position resolution is below 1 ~ mm in simulation and 2 mm in the experiment. A relatively legible 3D image of lead bricks in size of 20 cm × 5 cm × 10 cm used our inversion algorithm can be presented below 1× 104 effective events, which takes 16 h of acquisition time experimentally. Conclusion: The proposed method is a potential candidate to monitor the cosmic ray MT accurately. Monte Carlo simulations have been performed to discuss the application of the detector and the simulation results have indicated that the detector can be used in cosmic ray MT. The cosmic ray MT experiment is currently underway. Furthermore, the proposal also has the potential to scan the earth, buildings, and other structures of interest including for instance computerized imaging in an archaeological framework.

FINITE ELEMENT BASED FORMULATION OF THE LATTICE BOLTZMANN EQUATION

  • Jo, Jong-Chull;Roh, Kyung-Wan;Kwon, Young-W.
    • Nuclear Engineering and Technology
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    • v.41 no.5
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    • pp.649-654
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    • 2009
  • The finite element based lattice Boltzmann method (FELBM) has been developed to model complex fluid domain shapes, which is essential for studying fluid-structure interaction problems in commercial nuclear power systems, for example. The present study addresses a new finite element formulation of the lattice Boltzmann equation using a general weighted residual technique. Among the weighted residual formulations, the collocation method, Galerkin method, and method of moments are used for finite element based Lattice Boltzmann solutions. Different finite element geometries, such as triangular, quadrilateral, and general six-sided solids, were used in this work. Some examples using the FELBM are studied. The results were compared with both analytical and computational fluid dynamics solutions.

Delaunay triangulation for efficient reduction of measured point data (측정데이터의 효율적 감소를 위한 De Iaunay 삼각형 분할의 적용)

  • 허성민;김호찬;이석희
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2001.04a
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    • pp.53-56
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    • 2001
  • Reverse engineering has been widely used for the shape reconstruction of an object without CAD data and it includes some steps such as scanning of a clay or wood model, and generating some manufacturing data in an STL file. A new approach to remove point data with Delaunay triangulation is introduced to deal with the size problems of STL file and the difficulties in the operation of RP process. This approach can be used to reduce a number of measuring data from laser scanner within a specified tolerance, thus it can avoid the time for handing point data during modeling process and the time for verifying and slicing STL model during RP process. Developed software enables the user to specify the criteria for the selection of group of triangles either by the angle between triangles or the percentage of triangles reduced, and thus RP models with accuracy will be helpful to automated process.

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Segmentation of data measured by laser scanning in reverse engineering (역공학에서 레이저스캔 데이터의 분할)

  • 김호찬;허성민;이석희
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1997.10a
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    • pp.129-132
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    • 1997
  • Laser scanning is widely used due to its fast measuring and high precision, and the segmentation of the scanned data is necessary for the fast and efficient surface modelling. But most segmentation techniques are based on the very regular data and the adaptation of previous techniques to the scanned data does not usually produce good result. A new approach to perform the segmentation on the scanned data is introduced to deal with problems during reverse engineering process. The approach is based on the triangulated data and its result is depending on the some user-defined criteria. The result is illustrated to demonstrate its adaptability to the measured data on free-form surface and the each result by different criteria is compared respectively.

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A Study on Local Hole Filling and Smoothing of the Polygon Model (폴리곤모델의 국부적 홀 메움 및 유연화에 관한 연구)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.9 s.186
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    • pp.190-199
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    • 2006
  • A new approach which combines implicit surface scheme and recursive subdivision method is suggested in order to fill the holes with complex shapes in the polygon model. In the method, a base surface is constructed by creating smooth implicit surface from the points selected in the neighborhood of holes. In order to assure C$^1$ continuity between the newly generated surface and the original polygon model, offset points of same number as the selected points are used as the augmented constraint conditions in the calculation of implicit surface. In this paper the well-known recursive subdivision method is used in order to generate the triangular net with good quality using the hole boundary curve and generated base implicit surface. An efficient anisotropic smoothing algorithm is introduced to eliminate the unwanted noise data and improve the quality of polygon model. The effectiveness and validity of the proposed method are demonstrated by performing numerical experiments for the various types of holes and polygon model.

DEVELOPMENT OF AN LES METHODOLOGY FOR COMPLEX GEOMETRIES

  • Merzari, Elia;Ninokata, Hisashi
    • Nuclear Engineering and Technology
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    • v.41 no.7
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    • pp.893-906
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    • 2009
  • The present work presents the development of a Large Eddy Simulation (LES) methodology viable for complex geometries and suitable for the simulation of rod-bundles. The use of LES and Direct Numerical Simulation (DNS) allows for a deeper analysis of the flow field and the use of stochastical tools in order to obtain additional insight into rod-bundle hydrodynamics. Moreover, traditional steady-state CFD simulations fail to accurately predict distributions of velocity and temperature in rod-bundles when the pitch (P) to diameter (D) ratio P/D is smaller than 1.1 for triangular lattices of cylindrical pins. This deficiency is considered to be due to the failure to predict large-scale coherent structures in the region of the gap. The main features of the code include multi-block capability and the use of the fractional step algorithm. As a Sub-Grid-Scale (SGS) model, a Dynamic Smagorinsky model has been used. The code has been tested on plane channel flow and the flow in annular ducts. The results are in excellent agreement with experiments and previous calculations.

Flow-induced instability and nonlinear dynamics of a tube array considering the effect of a clearance gap

  • Lai, Jiang;Sun, Lei;Li, Pengzhou
    • Nuclear Engineering and Technology
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    • v.51 no.6
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    • pp.1650-1657
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    • 2019
  • Fluidelastic instability and nonlinear dynamics of tube bundles is a key issue in a steam generator. Especially, once the post-instability motion of the tube becomes larger than the clearance gap to other tubes, effective contact or impact between the tubes under consideration and the other tube inevitable. There is seldom theoretical analysis to the nonlinear dynamic characteristics of a tube array in two-phase flow. In this paper, experimental and numerical studies were utilized to obtain the critical velocity of the flow-induced instability of a rotated triangular tube array. The calculation results agreed well with the experimental data. To explore the post-instability dynamics of the tube array system, a Runge-Kutta scheme was used to solve the nonlinear governing equations of tube motion. The numerical results indicated that, when the flow pitch velocity is larger than the critical velocity, the tube array system is undergoing a limit cycle motion, and the dynamic characteristics of the tube array are almost similar for different void fractions.