• Title/Summary/Keyword: Stokes equation

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Dynamic stress, strain and deflection analysis of pipes conveying nanofluid buried in the soil medium considering damping effects subjected to earthquake load

  • Abadi, M. Heydari Nosrat;Darvishi, H. Hassanpour;Nouri, A.R. Zamani
    • Computers and Concrete
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    • v.24 no.5
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    • pp.445-452
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    • 2019
  • In this paper, dynamic stress, strain and deflection analysis of concrete pipes conveying nanoparticles-water under the seismic load are studied. The pipe is buried in the soil which is modeled by spring and damper elements. The Navier-Stokes equation is used for obtaining the force induced by the fluid and the mixture rule is utilized for considering the effect of nanoparticles. Based on refined two variables shear deformation theory of shells, the pipe is simulated and the equations of motion are derived based on energy method. The Galerkin and Newmark methods are utilized for calculating the dynamic stress, strain and deflection of the concrete pipe. The influences of internal fluid, nanoparticles volume percent, soil medium and damping of it as well as length to diameter ratio of the pipe are shown on the dynamic stress, strain and displacement of the pipe. The results show that with enhancing the nanoparticles volume percent, the dynamic stress, strain and deflection decrease.

2-Dimensional Numerical Model for Sediment Transport considering the Impact of Helical Flow (Helical Flow의 영향을 고려한 2차원 하상변동모의)

  • Kim, Mujong;Lee, Seonmin;Choi, Sung-Uk
    • Proceedings of the Korea Water Resources Association Conference
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    • 2016.05a
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    • pp.64-64
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    • 2016
  • 하천은 인간에게 용수의 이용 및 하천호안의 휴식처로써의 이용을 통해 직접적인 영향을 주고, 하천구조물의 심미적 영향, 랜드마크로써의 역할을 통해 간접적인 영향을 준다. 또한, 하천은 하천생태계에 서식하는 동 식물에게 영향을 준다. 그러나 하천유사로 인해 통수능이 감소하고, 하천구조물 주변에 침식을 야기할 뿐만 아니라, 댐과 저수지에 유사의 퇴적으로 저수용량의 감소시킨다. 그러므로 이를 예측하는 것은 경제적, 환경적으로 중요하다. 하상변동의 모의를 위해 기존의 2차원 모형은 만곡흐름에서 유동의 helical flow를 고려하지 않아 예측이 부정확하였다. 본 연구에서는 천수방정식을 이용한 하상변동 수치모의에 helical flow의 영향을 고려하였다. 하천과 같은 천수영역에서의 흐름 및 하상변동을 해석하기 위하여 수심평균 된 Navier-Stokes equations인 천수방정식을 이용하였다. 지배방정식은 곡선 좌표계에서 유한체적법으로 차분하였고, 비엇갈림격자를 사용하였다. 지배방정식의 닫힘 문제를 해결하기위해 0-방정식 난류모형을 사용하였고, "time marching" 기법의 적용을 위해 계산단계분할 방법을 이용하였다. 비엇갈림격자의 사용으로 인해 검사체적의 면에서의 유속이 필요하여 pressure-velocity coupling을 사용하여 유속의 진동을 줄였다. 또한, 만곡부의 helical flow를 모의하기위해 helical flow intensity model을 도입하였다. 앞에서 계산한 흐름을 바탕으로 유사량 산정공식과 Exner 방정식을 이용하여 하상변동을 모의하였다. 흐름의 검증, helical flow의 영향에 대한 확인, 하상변동의 적용을 위해 선행연구의 실험이 사용되었다.

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The Effect of Slip on the Convective Instability Characteristics of the Stagnation Point Flow Over a Rough Rotating Disk

  • Mukherjee, Dip;Sahoo, Bikash
    • Kyungpook Mathematical Journal
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    • v.61 no.4
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    • pp.831-843
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    • 2021
  • In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.

Numerical Analysis on the Flow Distribution in Ondol Flue Channel (산고래 온돌연도내의 유동분포에 관한 수치해석)

  • Man Man-Ki;Lee Seung Woo
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.12 no.4
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    • pp.264-274
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    • 1983
  • Two-dimensional jet flows into a couple of confined rectangular enclosures such as an Ondol flue channel and their flow distributions were analyzed by numerical graphics : rectangular space in one enclosure is vacated and the other has 8 rectangular small posts. Both enclosures have a protruded inlet nozzle and on outlet on its center line. Steady state incompressible laminar viscous flow was assumed. The primitive forms of Navier-Stokes equations and continuity equation in a cartesian coordinate system were solved numerically by the Marker and Cell method for Reynolds numbers of 5, 10, 20, 30 and 40. From the numerical graphics it was found that the flow regions in both enclosures were devided into tow parts ; one part was the jet flow localized in a narrow center region of the enclosure and the other part was the very slow recirculating flow occupying the rest of the flow region in the enclosures. However there were a little differences in the shapes of jet flow in both enclosures for Reynolds numbers of 5 and 10 and also in the shapes of recirculating flows in both enclosures for all Reynolds number. Also it was found that waving flow appeared right before the outlet at Reynolds number of 20 and more.

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Performance assessment of pitch-type wave energy converter in irregular wave conditions on the basis of numerical investigation

  • Poguluri, Sunny Kumar;Kim, Dongeun;Bae, Yoon Hyeok
    • Ocean Systems Engineering
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    • v.12 no.1
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    • pp.23-38
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    • 2022
  • In this paper, a pitch-type wave energy converter (WEC-rotor) is investigated in irregular wave conditions for the real sea testing at the west coast of Jeju Island, South Korea. The present research builds on and extends our previous work on regular waves to irregular waves. The hydrodynamic characteristics of the WEC-rotor are assessed by establishing a quasi-two-dimensional numerical wave tank using computational fluid dynamics by solving the Reynolds-averaged Navier-Stokes equation. The numerical solution is validated with physical experiments, and the comparison shows good agreement. Furthermore, the hydrodynamic performance of the WEC-rotor is explored by investigating the effect of the power take-off (PTO) loading torque by one-way and two-way systems, the wave height, the wave period, operational and high sea wave conditions. Irrespective of the sea wave conditions, the absorbed power is quadratic in nature with the one-way and two-way PTO loading systems. The power absorption increases with the wave height, and the increment is rapid and mild in the two-way and one-way PTO loading torques, respectively. The pitch response amplitude operator increases as the wave period increases until the maximum value and then decreases. For a fixed PTO loading, the power and efficiency are higher in the two-way PTO loading system than in the one-way PTO loading system at different wave periods.

Newton's Method to Determine Fourier Coefficients and Wave Properties for Deep Water Waves

  • JangRyong Shin
    • Journal of Ocean Engineering and Technology
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    • v.37 no.2
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    • pp.49-57
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    • 2023
  • Since Chappelear developed a Fourier approximation method, considerable research efforts have been made. On the other hand, Fourier approximations are unsuitable for deep water waves. The purpose of this study is to provide a Fourier approximation suitable even for deep water waves and a numerical method to determine the Fourier coefficients and the wave properties. In addition, the convergence of the solution was tested in terms of its order. This paper presents a velocity potential satisfying the Laplace equation and the bottom boundary condition (BBC) with a truncated Fourier series. Two wave profiles were derived by applying the potential to the kinematic free surface boundary condition (KFSBC) and the dynamic free surface boundary condition (DFSBC). A set of nonlinear equations was represented to determine the Fourier coefficients, which were derived so that the two profiles are identical at specified phases. The set of equations was solved using Newton's method. This study proved that there is a limit to the series order, i.e., the maximum series order is N=12, and that there is a height limitation of this method which is slightly lower than the Michell theory. The reason why the other Fourier approximations are not suitable for deep water waves is discussed.

Development of Non-Invasive Pressure Estimation Using 3D Multi-Path Line Integration Method from Magnetic Resonance Velocimetry (MRV) (자기공명유속계 (MRV) 에서 3차원 다중경로 선적분법을 활용한 비침습적 압력예측 방법 개발)

  • Ilhoon Jang;Muhammad Hafidz Ariffudin;Simon Song
    • Journal of the Korean Society of Visualization
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    • v.21 no.2
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    • pp.14-23
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    • 2023
  • The pressure difference across stenotic blood vessels is a commonly used clinical metric for diagnosing many cardiovascular diseases. At present, most clinical pressure measurements rely solely on invasive catheterization. In this study, we propose a novel method for non-invasive pressure estimation using the incompressible Navier-Stokes equations and a 3D multi-path integration approach. We verify spatio-temporal convergence on an in-silico dataset of a cylindrical straight pipe phantom with steady and pulsatile flow fields. We then evaluate the proposed method on an in vitro dataset of reconstructed control, pre-operative, and post-operative carotid artery cases acquired from 4D flow MRI. The performance of our method is compared to existing approaches based on the pressure Poisson equation and work-energy relative pressure. The results demonstrate the proposed method's high accuracy, robustness to spatio-temporal subsampling, and reduced sensitivity to noise, highlighting its great potential for non-invasive pressure estimation.

Numerical Investigation on detonation combustion waves of hydrogen-air mixture in pulse detonation combustor with blockage

  • Pinku Debnath;K.M. Pandey
    • Advances in aircraft and spacecraft science
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    • v.10 no.3
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    • pp.203-222
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    • 2023
  • The detonation combustion is a supersonic combustion process follows on shock wave oscillations in detonation tube. In this paper numerical studies are carried out combined effect of blockage ratio and spacing of obstacle on detonation wave propagation of hydrogen-air mixture in pulse detonation combustor. The deflagration to detonation transition of stoichiometric (ϕ=1)fuel-air mixture in channel has been analyzed for effect of blockage ratio (BR)=0.39, 0.51, 0.59, 0.71 with spacing of 2D and 3D. The reactive Navier-Stokes equation is used to solve the detonation wave propagation mechanism in Ansys Fluent platform. The result shows that fully developed detonation wave initiation regime is observed near smaller vortex generator ratio of BR=0.39 inside the combustor. The turbulent rate of reaction has also a great significance role for shock wave structure. However, vortices of rapid detonation wave are appears near thin boundary layer of each obstacle. Finally, detonation combustor demonstrates the superiority of pressure gain combustor with turbulent rate of reaction of 0.6 kg mol/m3 -s inside the detonation tube with obstacle spacing of 12 cm, this blockage enhanced the turbulence intensity and propulsive thrust. The successful detonation wave propagation speed is achieved in shortest possible time of 0.031s with a significance magnitude of 2349 m/s, which is higher than Chapman-Jouguet (C-J) velocity of 1848 m/s. Furthermore, stronger propulsive thrust force of 36.82 N is generated in pulse time of 0.031s.

Development of a High Performance Ocean Model using Julia Language (줄리아 언어를 이용한 고성능 해양모델의 개발)

  • KWON, MIN-SUN;KIM, JONG GU
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.24 no.2
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    • pp.187-207
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    • 2019
  • In order to develop a high performance ocean model, we used Julia, a Just-In-Time compile language, and to obtain the solution of the momentum equation, we made the code to solve the Poisson equation by the Successive Over-Relaxation method. And then we made two models to test Julia calculation codes. First, a simple channel form is modeled to test constant source/sink conditions. Second, the simplified Yellow Sea was modeled to test tidal forcing, Coriolis forces, and the effect of vertical eddy diffusivity coefficients. The model has been tested with a total of eight cases in the two scenarios. As a result of the test, the depth-averaged current speed of the three cases in Scenario 1 converged perfectly to the theoretical value, and that showed well a vertical flow velocity gradient due to the bottom friction. Also, the result of Scenario 2 represented well the amphidromic points of Yellow Sea and the tidal characteristics of mid-western and southwestern coast of Korea. Therefore, it is considered that the ocean model using Julia language has developed successfully, this suggests that the ocean model has come to the stage of successful transition from a classical compile language to a Just-In-Time compile language.

Numerical Modeling of Flow Characteristics within the Hyporheic Zones in a Pool-riffle Sequences (여울-소 구조에서 지표수-지하수 혼합대의 흐름 특성 분석에 관한 수치모의 연구)

  • Lee, Du-Han;Kim, Young-Joo;Lee, Sam-Hee
    • Journal of Wetlands Research
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    • v.14 no.1
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    • pp.75-87
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    • 2012
  • Hyporheic zone is a region beneath and alongside a stream, river, or lake bed, where there is mixing of shallow groundwater and surfacewater. Hyporheic exchange controls a variety of physical, biogeochemical and thermal processes, and provides unique ecotones in a aquatic ecosystem. Field and experimental observations, and modeling studies indicate that hyporheic exchange is mainly in response to pressure gradients driven by the geomorphological features of stream beds. In the reach scale of a stream, pool-riffle structures dominate the exchange patterns. Flow over a pool-riffle sequence develops recirculation zones and stagnation points, and this flow structures make irregular pressure gradient which is driving force of the hyporheic exchange. In this study, 3 D hydro-dynamic model solves the Reynolds-averaged Navier-Stokes equations for the surface water and Darcy's Law and the continuity equation for ground water. The two sets of equations are coupled via the pressure distribution along the interface. Simulation results show that recirculation zones and stagnation points in the pool-riffle structures dominantly control the upwelling and downwelling patterns. With decrease of recirculation zones, length of donwelling zone formed in front of riffles is reduced and position of maximum downwelling point moves downward. The numerical simulation could successfully predict the behavior of hyporheic exchange and contribute the field study, river management and restoration.