• Title/Summary/Keyword: second order difference equations

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A Computational Study on Turbulent Flow Characteristics around Full-form Tankers

  • Van, Suak-Ho;Kim, Hyoung-Tae
    • Journal of Hydrospace Technology
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    • v.2 no.2
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    • pp.1-13
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    • 1996
  • This paper presents the result of a computational study on the wake characteristics of two tanker models, i.e. HSVA and Mystery hull forms. The focus of the study is on the distributions of axial, radial and tangential velocities of the two hull forms in way of the propeller, especially over the propeller disk. The effect of bilge vortices on the velocity distribution is also concerned. For the computation of stern and wake flows of the two hull farms, the incompressible Reynolds-Averaged Wavier-Stokes(RANS) equations are numerically solved by the second order finite difference method, which employs a four stage Runge-Kutta scheme with a residual averaging technique and the Baldwin-Lomax model. The calculated pressure distributions on the hull surface and the axial, radial and tangential velocity distributions over the propeller disk are presented for the two hull forms. Finally, the result of wake analysis for the computed wake distribution over the propeller disk is given in comparison with those for the experimental wake distribution fur the both hull forms.

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Passive Control of the Condensation Shock Wave Using Bleed Slots

  • Kim, H.D.;Lee, K.H.;Setoguchi, T.
    • Proceedings of the KSME Conference
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    • 2001.06e
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    • pp.299-304
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    • 2001
  • The current study describes experimental and computational work on the passive control of the steady and unsteady condensation shock waves, which are generated in a transonic nozzle. The bleed slots are installed on the contoured wall of the transonic nozzle in order to control the magnitude of the condensation shock wave and its oscillations. For computations, a droplet growth equation is incorporated into the two-dimensional Navier-Stokes equation systems. Computations are carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order tractional time step. Baldwin-Lomax turbulence model is employed to close the governing equations. An experiment using an indraft transonic wind tunnel is made to validate the computational results. The current computations represented well the experimental flows. From both the experimental and computational results it is found that the magnitude of the condensation shock wave in the bleed slotted nozzle is significantly reduced, compared with no passive control of solid wall. The oscillations of the condensation shock wave are successfully suppressed by a bleed slot system.

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Passive Control of the Condensation Shock Wave Using Bleed Slots (Bleed Slot을 사용한 응축충격파의 피동제어)

  • Baek, Seung-Cheol;Kwon, Soon-Bum;Kim, Heuy-Dong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.7
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    • pp.997-1004
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    • 2002
  • The current study describes experimental and computational works on the passive control of the steady and unsteady condensation shock waves, which are generated in a transonic nozzle. The bleed slots are installed on the contoured wall of the transonic nozzle in order 10 control the magnitude of the condensation shock wave and its oscillations. For computations, a droplet growth equation is copuled with two-dimensional Navier-Stokes equation systems. Computations are carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order fractional time step. Baldwin-Lomax turbulence model is employed to close the governing equations. An experiment using an indrafi transonic wind tunnel is made to validate the computational results. The current computations represented well the experimental flows. From both the experimental and computational results it is found that the magnitude of the condensation shock wave in the bleed slotted nozzle is signi ficantly reduced, compared with no passive control of solid wall. The oscillations of the condensation shock wave are successfully suppressed by a bleed slot system.

Development of Ingrowth Estimation Equations for Pinus densiflora in Korea Derived from National Forest Inventory Data (국가산림자원조사 자료를 이용한 소나무의 진계생장 추정식 개발)

  • Moon, Ga Hyun;Yim, Jong Su;Shin, Man Yong
    • Journal of Korean Society of Forest Science
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    • v.107 no.4
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    • pp.402-411
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    • 2018
  • This study was conducted to develop ingrowth estimation equations on Pinus densiflora found in Gangwon Province and in the center of Korean Peninsula, based on the National Forest Inventory (NFI)'s permanent sampling plot data. For this study, identical sampling plots in $5^{th}$ and $6^{th}$ NFI data were collected in order to identify ingrowth amounts for the last 5 years. Following two-stage approaches in developing the ingrowth estimation equations, the logistic regression model was used in the first stage to estimate the ingrowth probability. In the second stage, regression analysis on sampling plots with ingrowth occurrence was used to estimate the ingrowth amount. A candidate model was finally selected as an optimal model after a verification based on three evaluation statistics which include mean difference (MD), standard deviation of difference (SDD) and standard error of difference (SED). In results, a logistic regression model based on the number of sampling plot which did not result in ingrowth (model VI), was selected for an ingrowth probability estimation equation and exponential function including the species composition (SC) variable was optimal for an ingrowth estimation equation (model VII). The ingrowth estimation equations developed in this study also evaluated the estimation ability in various forest stand conditions, and no particular issue in fitness or applicability was observed.

Comparison of Numerical Methods for Two-dimensional Wave Breaker on a Plane Beach of Constant Slope (2차원 Beach에서 쇄파의 시뮬레이션을 위한 수치계산기법의 비교)

  • Jeong K. L.;Lee Y.-G.
    • 한국전산유체공학회:학술대회논문집
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    • 2004.03a
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    • pp.119-125
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    • 2004
  • Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory and solitary wave theory are employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with each other. The marker-density method is better then the hybrid method. Also they are compared with other existing experimental results. The Agreement between the experimental data and the computation results is good.

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A Numerical Solution. Method for Two-dimensional Nonlinear Water Waves on a Plane Beach of Constant Slope

  • Lee, Young-Gill;Heo, Jae-Kyung;Jeong, Kwang-Leol;Kim, Kang-Sin
    • Journal of Ship and Ocean Technology
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    • v.8 no.2
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    • pp.61-69
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    • 2004
  • Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with other existing experimental results. Agreement between the experimental data and the computation results is good.

Inhomogeneous Helmholtz equation for Water Waves on Variable Depth (비균질 Helmholtz 방정식을 이용한 변동 수심에서의 파랑변형)

  • Kim, Hyo-Seob;Jang, Chang-Hwan
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.13 no.3
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    • pp.174-180
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    • 2010
  • The inhomogeneous Helmholtz equation is introduced for variable water depth and potential function and separation of variables are introduced for the derivation. Only harmonic wave motions are considered. The governing equation composed of the potential function for irrotational flow is directly applied to the still water level, and the inhomogeneous Helmholtz equation for variable water depth is obtained. By introducing the wave amplitude and wave phase gradient the governing equation with complex potential function is transformed into two equations of real variables. The transformed equations are the first and second-order ordinary differential equations, respectively, and can be solved in a forward marching manner when proper boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a side boundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set of equations. The equation set is applied to two test cases, Booij’ inclined plane slope profile, and Bragg’ wavy bed profile. The present equations set is satisfactorily verified against other theories including the full linear equation, Massel's modified mild-slope equation, and Berkhoff's mild-slope equation etc.

A Numerical Study on the Aerodynamic Characteristics of a Bus-Like Bluff Body - Effect of Turbulence Model and Discretisation Scheme - (버스형상 무딘물체의 공력특성에 관한 수치해석적 고찰 - 난류모델과 이산화법의 영향 -)

  • 김민호;국종영;천인범
    • Transactions of the Korean Society of Automotive Engineers
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    • v.11 no.3
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    • pp.115-123
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    • 2003
  • With the advent of high performance computers and more efficient numerical algorithms, computational fluid dynamics(CFD) has come out as a modem alternative for reducing the use of wind tunnels test in automotive engineering. However, in spite of the fact that many competent researchers have made all their talents in developing turbulence model over since the past dozen or more years, it has been an important impediment in using the CFD effectively to design machinery and to diagnose or to improve engineering problems in the industry since the turbulence model has been acting as the Achilles' tendon in aspect of the reliability even to this time. In this study, Reynolds-averaged Wavier-Stokes equations were solved to simulate an incompressible turbulent flow around a bus-like bluff body near ground plane. In order to investigate the effect of the discretisation schemes and turbulence model on the aerodynamic forces several turbulence models with five convective difference schemes are adopted. From the results of this study, it is clear that choice of turbulence model and discretisation scheme profoundly affects the computational outcome. The results also show that the adoption of RNG $k-\varepsilon$ turbulence model and nonlinear quadratic turbulence model with the second order accurate discretisation scheme predicts fairly well the aerodynamic coefficients.

A CFD Analysis of Gas Flow through an Ultrasonic Meter (초음파 유량계를 통하는 기체유동의 CFD 해석)

  • Kim, Jae-Hyung;Kim, Heuy-Dong;Lee, Ho-Joon;Hwang, Shang-Yoon
    • Proceedings of the KSME Conference
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    • 2003.11a
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    • pp.998-1003
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    • 2003
  • Ultrasonic flow metering(UFM) technology is being received much attention from a variety of industrial fields to exactly measure the flow rate. The UFM has much advantage over other conventional flow meter systems, since it has no moving parts, and offers good accuracy and reliability without giving any disturbances to measure the flow rate, thereby not causing pressure losses in the flow fields. In the present study, 3-dimensional, unsteady, compressible Navier-Stokes equations are solved by a finite volume scheme, based upon the second order upwind scheme for spatial derivatives and the multi-stage Runge-Kutta integral method for time derivatives. In order to simulate multi-path ultrasonic flow meter, an excited pressure signal is applied to three different locations upstream, and the pressure signals are received at three different locations downstream. The mean flow velocities are calculated by the time difference between upstream and downstream propagating pressure signals. The obtained results show that the present CFD method simulates successfully ultrasonic meter gas flow and the mean velocity measured along the chord near the wall is considerably influenced by the boundary layers.

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Computation of Turbulent Flow around Wigley Hull Using 4-Stage Runge-Kutta Scheme on Nonstaggered Grid (정규격자계와 4단계 Range-Kutta법을 사용한 Wigley선형 주위의 난류유동계산)

  • Suak-Hp Van;Hyoung-Tae Kim
    • Journal of the Society of Naval Architects of Korea
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    • v.31 no.3
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    • pp.87-99
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    • 1994
  • Reynolds Averaged Navier-Stokes equations are solved numerically for the computation of turbulent flow around a Wigley double model. A second order finite difference method is applied for the spatial discretization on the nonstaggered grid system and 4-stage Runge-Kutta scheme for the numerical integration in time. In order to increase the time step, residual averaging scheme of Jameson is adopted. Pressure field is obtained by solving the pressure-Poisson equation with the appropriate Neumann boundary condition. For the turbulence closure, 0-equation turbulence model of Baldwin-Lomax is used. Numerical computation is carried out for the Reynolds number of 4.5 million. Comparisons of the computed results with the available experimental data show good agreements for the velocity and pressure distributions.

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