• Title/Summary/Keyword: Courant number

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A Study of Interpolation Methods for the Water Hammer Analysis using the Method of Characteristics (특성선 방법을 이용한 관망 수격현상 해석의 보간방법연구)

  • Jung, Bong Seog;Kim, Chu In;Kim, Sang Hyun;Park, Nam Sik
    • Journal of Korean Society of Environmental Engineers
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    • v.22 no.2
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    • pp.363-373
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    • 2000
  • It is necessary to employ the interpolation technique to resolve problems, which are associated with the characteristic locus in time-distance space, in the unsteady analysis of pipe flow. Various interpolation methods such as linear timeline interpolation, linear spaceline interpolation, wave speed adjustment, cubic spaceline interpolation and cubic timeline interpolation have been suggested and tested to investigate the interpolation error. Performance of various interpolation techniques was evaluated both a single pipeline and a complex one. The range of error was calculated as the courant number varied between 0 and 1 in a single pipeline. Reorganization of computational element and proper selection of interpolation method are found to be prerequisites for the effective computation of unsteady analysis.

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Analysis of optimum grid determination of water quality model with 3-D hydrodynamic model using environmental fluid dynamics code (EFDC)

  • Yin, Zhenhao;Seo, Dongil
    • Environmental Engineering Research
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    • v.21 no.2
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    • pp.171-179
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    • 2016
  • This study analyzes guidelines to select optimum number of grids to represent behavior of a given water system appropriately. The EFDC model was chosen as a 3-D hydrodynamic and water quality model and salt was chosen as a surrogate variable of pollutant. The model is applied to an artificial canal that receives salt water from coastal area and fresh water from a river from respective gate according to previously developed gate operation rule. Grids are subdivided in vertical and horizontal (longitudinal) directions, respectively until no significant changes are found in salinity concentrations. The optimum grid size was determined by comparing errors in average salt concentrations between a test grid systems against the most complicated grid system. MSE (mean squared error) and MAE (mean absolute error) are used to compare errors. The CFL (Courant-Friedrichs-Lewy) number was used to determine the optimum number of grid systems for the study site though it can be used when explicit numerical method is applied only. This study suggests errors seem acceptable when both MSE and MAE are less than unity approximately.

A Study on the Structure of Instantaneous Flow Fields of a Small-Size Axial Fan by Large Eddy Simulation (대규모 와 모사에 의한 소형축류홴의 순간유동장 구조에 대한 연구)

  • Kim, Jang-Kweon;Oh, Seok-Hyung
    • Journal of Power System Engineering
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    • v.22 no.6
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    • pp.28-35
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    • 2018
  • The large-eddy simulation (LES) was carried out to evaluate the instantaneous vector and vorticity profiles of a small-size axial fan (SSAF) at the operating point of full-flowrate. The downstream flow of the SSAF exhibits a shorter axial flow when not fully developed, especially the stronger vortex appears at the edge near the flow end. On the other hand, the downstream flow of the SSAF exhibits a longer axial flow, and the weaker vortex appears at the edge near the flow end when the flow is sufficiently developed. Moreover, in the downstream of the SSAF, a periodic and intermittent flow pattern appears at the edge showing the axial flow, and the instantaneous vorticity contour lines showing the form of a circle group are distributed at specific intervals from the downstream region of the blade tip, which is considered to be the result of the intermittency phenomenon influenced by the number of blades and the number of revolutions.

A Study on the Structure of Turbulent Flow Fields According to the Operating Loads of Three-Dimensional Small-Size Axial Fan by Large Eddy Simulation (대규모와 모사에 의한 3차원 소형축류홴의 운전부하에 따른 난류유동장 구조에 대한 연구)

  • Kim, Jang-Kweon;Oh, Seok-Hyung
    • Journal of Power System Engineering
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    • v.19 no.5
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    • pp.80-85
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    • 2015
  • The unsteady-state, incompressible and three-dimensional large eddy simulation(LES) was carried out to analyze the structure of turbulent flow fields according to the operating loads of three-dimensional small-size axial fan(SSAF). LES shows the best prediction performance in comparison with any other Reynolds averaged Navier-Stokes(RANS) method because static pressure coefficients analysed by LES show a little bit larger than measurements including all flow coefficients. Also, it can be known that the wake of SSAF is divided into from axial flow to radial flow before and behind stall region according to the increase of static pressure through LES analysis.

Large Eddy Simulation on the Vorticity Characteristics of Three-Dimensional Small-Size Axial Fan with Different Operating Points (운전점에 따른 3차원 소형축류홴의 와도 특성에 대한 대규모 와 모사)

  • Kim, Jang-Kweon;Oh, Seok-Hyung
    • Journal of Power System Engineering
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    • v.20 no.6
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    • pp.64-70
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    • 2016
  • The unsteady-state, incompressible and three-dimensional large-eddy simulation(LES) was carried out to evaluate the vorticity distribution of a small-size axial fan(SSAF). The X-component vorticity profiles developed around blade tips turn from axial to radial, and diminish the density of distribution according to the increase of static pressure. Otherwise, the Z-component vorticity profiles evenly develop at the region larger than the half radial distance of blade at the operating points of A and B, partly at the trailing-edge region of blade and radially over bellmouth according to the increase of static pressure.

Large Eddy Simulation on the Drag and Static Pressure Acting on the Blade Surface of Three-Dimensional Small-Size Axial Fan with Different Operating Loads (운전부하에 따른 3차원 소형축류홴 날개표면에 작용하는 정압과 항력에 대한 대규모와 모사)

  • Kim, Jang-Kweon;Oh, Seok-Hyung
    • Journal of Power System Engineering
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    • v.21 no.2
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    • pp.57-63
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    • 2017
  • The large-eddy simulation(LES) was carried out to evaluate the drag and static pressure acting on the blade surface of a small-size axial fan(SSAF) under the condition of unsteady-state, incompressible fluid and three-dimensional coordination. The axial component of drag coefficient increases with the increase of operating load, but the radial components have negligible sizes regardless of operating loads. Otherwise, the static pressures acting on the blade surfaces of SSAF show different distributions around the operating point of D equivalent to the stall. Also, with the increase of operating load, the static pressures acting on the pressure and suction surfaces of blade concentrate at the tips and leading-edges as a whole.

An Investigation on Turbulent Flow Characteristics According to the Operating Loads of Three-Dimensional Small-Size Axial Fan by Large Eddy Simulation (대규모 와 모사에 의한 3차원 소형축류홴의 운전부하에 따른 난류유동 특성치 고찰)

  • Kim, Jang-Kweon;Oh, Seok-Hyung
    • Journal of Power System Engineering
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    • v.20 no.1
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    • pp.50-56
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    • 2016
  • This paper handled an investigation on the turbulent flow characteristics of three-dimensional small-size axial fan(SSAF) according to operating loads. Also, it was carried out by unsteady-state, incompressible and three-dimensional large eddy simulation(LES). The downstream flow type of SSAF is changed from axial flow to radial flow around the beginning of stall region at the aerodynamic performance curve. Axial mean velocity component largely grows around blade tip at the operating point of A to D, but transverse and vertical mean velocity components as well as Reynolds shear stresses highly develop around blade tip at the operating point of E to H. On the other hand, the peak value of turbulent kinetic energy developed around blade tip shows the highest at the operating point of E.

Modeling and Simulation for PIG Flow Control in Natural Gas Pipeline

  • Nguyen, Tan-Tien;Kim, Sang-Bong;Yoo, Hui-Ryong;Park, Yong-Woo
    • Journal of Mechanical Science and Technology
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    • v.15 no.8
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    • pp.1165-1173
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    • 2001
  • This paper deals with dynamic analysis of Pipeline Inspection Gauge (PIG) flow control in natural gas pipelines. The dynamic behaviour of PIG depends on the pressure differential generated by injected gas flow behind the tail of the PIG and expelled gas flow in front of its nose. To analyze dynamic behaviour characteristics (e.g. gas flow, the PIG position and velocity) mathematical models are derived. Tow types of nonlinear hyperbolic partial differential equations are developed for unsteady flow analysis of the PIG driving and expelled gas. Also, a non-homogeneous differential equation for dynamic analysis of the PIG is given. The nonlinear equations are solved by method of characteristics (MOC) with a regular rectangular grid under appropriate initial and boundary conditions. Runge-Kutta method is used for solving the steady flow equations to get the initial flow values and for solving the dynamic equation of the PIG. The upstream and downstream regions are divided into a number of elements of equal length. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. Simulation is performed with a pipeline segment in the Korea gas corporation (KOGAS) low pressure system. Ueijungboo-Sangye line. The simulation results show that the derived mathematical models and the proposed computational scheme are effective for estimating the position and velocity of the PIG with a given operational condition of pipeline.

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Transient Analysis and Leakage Detection Algorithm using GA and HS algorithm for a Pipeline System

  • Kim Sang-Hyun;Yoo Wan-Suk;Oh Kwang-Jung;Hwang In-Sung;Oh Jeong-Eun
    • Journal of Mechanical Science and Technology
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    • v.20 no.3
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    • pp.426-434
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    • 2006
  • The impact of leakage was incorporated into the transfer functions of the complex head and discharge. The impedance transfer functions for the various leaking pipeline systems were also derived. Hydraulic transients could be efficiently analyzed by the developed method. The simulation of normalized pressure variation using the method of characteristics and the impulse response method shows good agreement to the condition of turbulent flow. The leak calibration could be performed by incorporation of the impulse response method with Genetic Algorithm (GA) and Harmony Search (HS). The objective functions for the leakage detection can be made using the pressure-head response at the valve, or the pressure-head or the flow response at a certain point of the pipeline located upstream from the valve. The proposed method is not constrained by the Courant number to control the numerical dissipation of the method of characteristics. The limitations associated with the discreteness of the pipeline system in the inverse transient analysis can be neglected in the proposed method.

Modelling and Simulation for PIG Flow Control in Natural Gas Pipeline

  • Nguyen, Tan-Tien;Yoo, Hui-Ryong;Park, Yong-Woo;Kim, Sang-Bong
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.448-448
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    • 2000
  • This paper deals with dynamic behaviour analysis for pipeline inspection gauge (PIG) flow control in natural gas pipeline. The dynamic behaviour of the PIG is depending on the different Pressure between the rear and nose parts, which is generated by injected gas flow behind PIG's tail and expelled gas flow in front of its nose. To analyze the dynamic behaviour characteristics such as gas flow in pipeline, and the PIG's position and velocity, mathematical model is derived as two types of a nonlinear hyperbolic partial differential equation for unsteady flow analysis of the PIG driving and expelled gas, and nonhomogeneous differential equation for dynamic analysis of PIG. The nonlinear equation is solved by method of characteristics (MOC) with the regular rectangular grid under appropriate initial and boundary conditions. The Runge-Kuta method is used when we solve the steady flow equations to get initial flow values and the dynamic equation of PIG. The gas upstream and downstream of PIG are divided into a number of elements of equal length. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. The simulation is performed with a pipeline segment in the Korea Gas Corporation (KOGAS) low pressure system, Ueijungboo-Sangye line. The simulation results show us that the derived mathematical model and the proposed computational scheme are effective for estimating the position and velocity of PIG with different operational conditions of pipeline.

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