• Title/Summary/Keyword: Rectangular Geometry

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Adaptive time-step control for modal methods to integrate the neutron diffusion equation

  • Carreno, A.;Vidal-Ferrandiz, A.;Ginestar, D.;Verdu, G.
    • Nuclear Engineering and Technology
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    • v.53 no.2
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    • pp.399-413
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    • 2021
  • The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry.

Stability assessment of unlined tunnels with semicircular arch and straight sides in anisotropic clay

  • Bibhash Kumar;Jagdish P. Sahoo
    • Geomechanics and Engineering
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    • v.35 no.2
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    • pp.149-163
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    • 2023
  • This paper presents stability evaluation of unlined tunnels with semi-circular arch and straight sides (SASS) driven in non-homogeneous and anisotropic undrained clay. Numerical analysis has been conducted based on lower bound finite element limit analysis with second order cone programming under plane strain condition. The solutions will be used for the assessment of stability of unlined semi-circular arch tunnels and tunnels in which semi-circular roof is supported over rectangular/square sections. The stability charts have been generated in terms of a non-dimensional factor considering linear variation in undrained anisotropic strength for normally consolidated and lightly over consolidated clay with depth, and constant undrained anisotropic strength for heavily over-consolidated clay across the depth. The effect of normalized surcharge pressure on ground surface, non-homogeneity and anisotropy of clay, tunnel cover to width ratio and height to width ratio of tunnel on the stability factor and associated zone of shear failure at yielding have been examined and discussed. The geometry of tunnel in terms of shape and size, and non-homogeneity and anisotropy in undrained strength of clay has been observed to influence significantly the stability of unlined SASS tunnels.

Detection of a Crack on a Plate by IDT Type Lamb Wave Sensors (IDT형 Lamb 파 센서에 의한 판상의 균열 검출)

  • Kim, Jun-Ho;Roh, Yong-Rae
    • The Journal of the Acoustical Society of Korea
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    • v.29 no.8
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    • pp.483-490
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    • 2010
  • In this paper, an Inter-Digital Transducer (IDT) type Lamb wave sensor is proposed to estimate the geometry and number of cracks on a plate structure, and its validity is checked through experiments. This IDT type sensor is more readily controllable than conventional patch type piezoelectric sensors to modify its operation frequency and directionality by altering its finger patterns. In this work, omni-directional annular IDT and highly directional rectangular IDT sensors are designed and fabricated. The IDT sensors are used to diagnose the length, number and orientation of cracks on an aluminum plate by measuring the amplitude and time of flight of Lamb waves. The results are analyzed to discuss the efficacy of the IDT sensors.

Analysis of 1D and 2D Flows in Open-Channel with FDM and FVM (유한차분법과 유한체적법을 이용한 1차원과 2차원 개수로 흐름해석)

  • Kim, Man Sik;Lee, Jin Hee;Jeong, Chan;Park, Roh Hyuk
    • Journal of Wetlands Research
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    • v.10 no.2
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    • pp.67-79
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    • 2008
  • The one-dimensional (1D) finite-difference method (FDM) with Abbott-Ionescu scheme and the two-dimensional (2D) finite-volume method (FVM) with an approximate Riemann solver (Osher scheme) for unsteady flow calculation in river are described. The two models have been applied to several problems including flow in a straight channel, flow in a slightly meandering channel and a flow in a meandering channel. The uniform rectangular channel was employed for the purpose of comparing results. A comparison is made between the results of computation on 1D and 2D flows including straight channel, slightly meandering channel and meandering channel application. The implementation of the finite-volume method allows complex boundary geometry represented. Agreement between FVM and FDM results regarding the discharge and stage is considered very satisfactory in straight channel application. It was concluded that a 1D analysis is sufficient if the channel is prismatic and remains straight. For curved (meandering) channels, a 2D or 3D model must be used in order to model the flow accurately.

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Development of Two-dimensional Finite Volume Model Applicable to Mixed Meshes (혼합격자의 적용이 가능한 2차원 유한체적모형의 개발)

  • Kim, Byung-Hyun;Han, Kun-Yeon;Son, Ah-Long
    • Journal of Korea Water Resources Association
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    • v.44 no.2
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    • pp.109-123
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    • 2011
  • In this study, 2D finite volume model, which can apply to the mixed meshes that is effective to treat the complicated topography such as a natural river, is developed. To do so, an algorithm for finding the neighbouring cell of a computational cell is introduced, and fluxes are computed using the HLLC approximate Riemann solver at each interface between a computational cell and it's neighbouring cells. Moreover, in order to numerically treat the bed slope which has important effect on the balance between flux gradients and sourte terms, different formula to compute the bed slope for rectangular and triangular mesh are applied. The developed model is applied to analyze dam-break in an experimental channel with $90^{\circ}$ bend and Malpasset dam-break in France. The two cases consist of mixed meshes and the suggested method is validated for the experimental channel and natural channel by comparison with the experimental data, field data and computed results.

Validation of 3D discrete fracture network model focusing on areal sampling methods-a case study on the powerhouse cavern of Rudbar Lorestan pumped storage power plant, Iran

  • Bandpey, Abbas Kamali;Shahriar, Kourush;Sharifzadeh, Mostafa;Marefvand, Parviz
    • Geomechanics and Engineering
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    • v.16 no.1
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    • pp.21-34
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    • 2018
  • Discontinuities considerably affect the mechanical and hydraulic properties of rock mass. These properties of the rock mass are influenced by the geometry of the discontinuities to a great extent. This paper aims to render an account of the geometrical parameters of several discontinuity sets related to the surrounding rock mass of Rudbar Lorestan Pumped Storage Power Plant powerhouse cavern making use of the linear and areal (circular and rectangular) sampling methods. Taking into consideration quite a large quantity of scanline and the window samplings used in this research, it was realized that the areal sampling methods are more time consuming and cost-effective than the linear methods. Having corrected the biases of the geometrical properties of the discontinuities, density (areal and volumetric) as well as the linear, areal and volumetric intensity accompanied by the other properties related to four sets of discontinuities were computed. There is an acceptable difference among the mean trace lengths measured using two linear and areal methods for the two joint sets. A 3D discrete fracture network generation code (3DFAM) has been developed to model the fracture network based on the mapped data. The code has been validated on the basis of numerous geometrical characteristics computed by use of the linear, areal sampling methods and volumetric method. Results of the linear sampling method have significant variations. So, the areal and volumetric methods are more efficient than the linear method and they are more appropriate for validation of 3D DFN (Discrete Fracture Network) codes.

Effects of Rotation Speed on Heat Transfer and Flow in a Coolant Passage with Turning Region (II) - Parallel Ribbed Duct - (곡관부를 가지는 내부 냉각유로에서 회전수 변화에 따른 열전달 및 유동 특성 (II) - 평행한 요철배열 덕트 -)

  • Kim Kyung Min;Kim Yun Young;Lee Dong Hyun;Cho Hyung Hee
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.29 no.8 s.239
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    • pp.911-920
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    • 2005
  • The present study investigates heat/mass transfer and flow characteristics in a ribbed rotating passage with turning region. The duct has an aspect ratio (W/H) of 0.5 and a hydraulic diameter ($D_h$) of 26.67 mm. Rib turbulators are attached in the parallel arrangement on the leading and trailing surfaces of the passage. The ribs have a rectangular cross section of 2 m (e) $\times$ 3 m (w) and an attack angle of $70^{\circ}$. The pitch-to-rib height ratio (p/e) is 7.5, and the rib height-to-hydraulic diameter ratio (e/$D_h$) is 0.075. The rotation number ranges from 0.0 to 0.20 while the Reynolds number is constant at 10,000. To verify the heat/mass transfer augmentation, internal flow structures are calculated for the same conditions using a commercial code FLUENT 6.1. The results show that a pair of vortex cells are generated due to the symmetric geometry of the rib arrangement, and heat/mass transfer is augmented up to $Sh/Sh_0=2.9$ averagely, which is higher than that of the cross-ribbed case presented in the previous study for the stationary case. With the passage rotation, the main flow in the first-pass deflects toward the trailing surface and the heat transfer is enhanced on the trailing surface. In the second-pass, the flow enlarges the vortex cell close to the leading surface, and the small vortex cell on the trailing surface side contracts to disappear as the passage rotates faster. At the highest rotation number ($R_O=0.20$), the turn-induced single vortex cell becomes identical regardless of the rib configuration so that similar local heat/mass transfer distributions are observed in the fuming region for the cross- and parallel-ribbed case.

A Experimental Study on Gas Explosions by Variations L/D ratio in a Partially Confined Geometry (부분 밀폐 공간에서의 L/D비 변화에 따른 가스 폭발의 실험적 연구)

  • Lee, Young-Soon;Park, Dal-Jae;Ahan, Jeong-Jin;Ahan, Sung-Joon;Oh, Shin-Kyu
    • Journal of the Korean Society of Safety
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    • v.21 no.2 s.74
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    • pp.29-34
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    • 2006
  • It is revealed that these are correlated with the height of chamber deciding the turbulence extent. In the first experiment, It was examined about the effects of different multiple obstacles such as circular, triangular and square things with the rig that the dimension of original experimental rig was $700{\times}700{\times}200mm{\wedge}3$. Then the heights of chamber were increased from 200 to 1000mm. The dimensions of each obstacle were $70{\times}700{\times}{\wedge}2$ and rectangular vent area were $210{\times}700{\times}{\wedge}2$. In the second one, we performed to see the effects of locations of different multiple obstacles in 200, 500 and 800mm height from the bottom. The results are : The multiple triangular obstacles caused the highest overpressure while the lowest one was the multiple circle bars. Then, the triangular bars caused the highest flame acceleration while the circular obstacles was lowest too. The results showed that the critical height was 800mm due to the formation of turbulence. And the lesser $Av/V^{2/3}$ were small, the more pressure and pressure acceleration rate were increased.

Analysis of Turbulent Velocity Fluctuations of Rectangular Shape of the Surface Roughness Change (직사각형 형상의 표면조도 변화에 의한 난류변동분 해석)

  • Oh, Dae-Kyun;Oh, Woo-Jun;Kim, Do-Jung;Lee, Gyoung-Woo
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.17 no.2
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    • pp.167-172
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    • 2011
  • In physical engineering, the turbulent flow on the surface roughness is very important. With the welding, design and paint, the hull surface roughness at each stage in the various aspects are important factors to be considered. In this study, the hull surface roughness geometry that was generalized to the PIV was applied to the tank test. The roughness of the surface changed the distance of the interval. Experimental velocity is Re = $1.1{\times}10^4$, Re = $2.0{\times}10^4$ and Re = $2.9{\times}10^4$. The turbulent intensity at the time-average were examined The roughness coefficient occurred with increasing turbulence intensities was stronger. The turbulence intensity away from the roughness in the shape was zero. The variation of turbulence intensity at the experimental flow conditions change was not affected.

Natural Frequency Analysis of Cantilever Plates with Added Mass (부가수 질량을 고려한 외팔판의 고유진동 해석)

  • Jang, Hyun-Gil;Nho, In Sik;Hong, Chang-Ho;Lee, Chang-Sup
    • Journal of the Society of Naval Architects of Korea
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    • v.50 no.1
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    • pp.1-7
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    • 2013
  • The high-skewed and/or composite propellers of current interests to reduce the ship vibration and to increase the acoustic performance are likely to be exposed to the unexpected structural problems. One typical example is that the added mass effect on the propellers working in the non-uniform wake field reduces the natural frequency of the propeller leading to the resonance with the low-frequency excitation of the external forces. To avoid this resonance problem during the design stage, the technique of fluid-structure interaction has been developed, but the higher-order effect of the blade geometry deformation is not yet considered in evaluating the added mass effects. In this paper the fluid boundary-value problem is formulated by the potential-based panel method in the inviscid fluid region with the velocity inflow due to the body deformation, and the structural response of the solid body under the hydrodynamic loading is solved by applying the finite element method which implements the 20-node iso-parametric element model. The fluid-structure problem is solved iteratively. A basic fluid-sturcture interaction study is performed with the simple rectangular plates of thin thickness with various planform submerged in the water of infinite extent. The computations show good correlation with the experimental results of Linholm, et al. (1965).