• Title/Summary/Keyword: time integration scheme

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Effects of Characteristic Condition Number on Convergence in Calculating Low Mach Number Flows, I : Euler Equations (저속 유동 계산의 수렴성에 미치는 특성 조건수의 영향 I : 오일러 방정식)

  • Lee, Sang-Hyeon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.2
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    • pp.115-122
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    • 2008
  • The effects of characteristic condition number on the convergence of preconditioned Euler equations were investigated. The two-dimensional preconditioned Euler equations adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Euler equations are strongly affected by the characteristic condition number, and there is an optimal characteristic condition number for a problem. The optimal characteristic condition numbers for the Choi and Merkle's preconditioning and temperature preconditioning are different.

Effects of Characteristic Condition Number on Convergence in Calculating Low Mach Number Flows, II : Navier-Stokes Equations (저속 유동 계산의 수렴성에 미치는 특성 조건수의 영향 II : 나비어스톡스 방정식)

  • Lee, Sang-Hyeon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.2
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    • pp.123-130
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    • 2008
  • The effects of characteristic condition number on the convergence of preconditioned Navier-Stokes equations were investigated. The two-dimensional preconditioned Navier-Stokes adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Navier-Stokes equations are strongly affected by the characteristic condition number. Also it is shown that the optimal characteristic condition numbers for viscous flows are larger than that in inviscid flows.

Numerical simulation of fully nonlinear sloshing waves in three-dimensional tank under random excitation

  • Xu, Gang;Hamouda, A.M.S.;Khoo, B.C.
    • Ocean Systems Engineering
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    • v.1 no.4
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    • pp.355-372
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    • 2011
  • Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.

A Study on the Participation of Virtual Power Plant Based Technology Utilizing Distributed Generation Resources in Electricity Market (분산발전자원을 활용한 가상발전소 기반 기술의 전력시장 참여 방안에 대한 연구)

  • Lee, Yun-Hwan
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.65 no.2
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    • pp.94-100
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    • 2016
  • A virtual power plant (VPP) technology is a cluster of distributed generation installations. VPP system is that integrates several types of distributed generation sources, so as to give a reliable overall power supply. Virtual power plant systems play a key role in the smart grids concept and the move towards alternative sources of energy. They ensure improved integration of the renewable energy generation into the grids and the electricity market. VPPs not only deal with the supply side, but also help manage demand and ensure reliability of grid functions through demand response (DR) and other load shifting approaches in real time. In this paper, utilizing a variety of distributed generation resources(such as emergency generator, commercial generator, energy storage device), activation scheme of the virtual power plant technology. In addition, through the analysis of the domestic electricity market, it describes a scheme that can be a virtual power plant to participate in electricity market. It attempts to derive the policy support recommendation in order to obtain the basics to the prepared in position of power generation companies for the commercialization of virtual power plant.

Code Development for Computation of Turbulent Flow around a Ship Model with Free-Surface (자유표면을 포함한 선체주위 난류유동 해석 코드 개발)

  • Kim J.J.;Kim H.T.;Van S.H.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.05a
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    • pp.145-155
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    • 1998
  • A computer code has been developed for the computation of the viscous flow around a ship model with the free surface. In this code, the incompressible Reynolds-averaged Navier-Stokes equations are solved numerically by a finite difference method which employes second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration of the governing equations. For the turbulence closure, a modified version of the Baldwin-Lomax model is exploited. The location of the free surface is determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and the boundary-fitted grid is generated at each time step so that one of the grid surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition is applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method and the computer code developed in the present study, the numerical computations are carried out for both Wigley parabolic hull and Series 60 $C_B=0.6$ ship model and the computational results are compared with the experimental data.

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Numerical Investigation on the Mechanism of Mode Transition in Axi-symmetric Supersonic Jet Screech (축대칭 초음속 제트에서 스크리치 모드 전이현상의 수치적 연구)

  • Bin, Jong-Hoon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.8
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    • pp.790-797
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    • 2010
  • Mode transition of the axi-symmetric screech tone in the low supersonic Mach number range from 1.0 to 1.20 is numerically analyzed. The axi-symmetric Navier-Stokes equations and the k-e turbulence model are solved in the cylindrical coordinate system. The dispersion-relation-preserving(DRP) scheme is applied for space discretization and the optimized four levels marching method are used for time integration. At low supersonic Mach numbers with an axi-symmetric A1 mode in the simulation, it is shown that acoustic propagation due to the nonlinear effects is seen in the lateral direction and the screech tone frequency is the same as the vortex passing frequency due to the generation of intense large-scale vortical motions.

Numerical Requirements for the Simulation of Detonation Cell Structures (데토네이션 셀 구조 모사를 위한 수치적 요구 조건)

  • Choi Jeong-Yeol;Cho Deok-Rae
    • Journal of the Korean Society of Propulsion Engineers
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    • v.10 no.2
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    • pp.1-14
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    • 2006
  • Present study examines the numerical issues of cell structure simulation for various regimes of detonation phenomena ranging from weakly unstable to highly unstable detonations. Inviscid fluid dynamics equations with $variable-{\gamma} $ formulation and one-step Arrhenius reaction model are solved by a MUSCL-type TVD scheme and 4th order accurate Runge-Kutta time integration scheme. A series of numerical studies are carried out for the different regimes of the detonation phenomena to investigate the computational requirements for the simulation of the detonation wave cell structure by varying the reaction constants and grid resolutions. The computational results are investigated by comparing the solution of steady ZND structure to draw out the minimum grid resolutions and the size of the computational domain for the capturing cell structures of the different regimes of the detonation phenomena.

Large Eddy Simulation of Shock-Boundary Layer Interaction

  • Teramoto, Susumu
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2004.03a
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    • pp.426-432
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    • 2004
  • Large-Eddy Simulation (LES) is applied for the simulation of compressible flat plate boundary with Reynolds number up to 5 X 10$^{5}$ . Numerical examples include shock/boundary layer interaction and boundary layer transition, aiming future application to the analysis of transonic fan/compressor cascades. The present LES code uses hybrid com-pact/WENO scheme for the spatial discretization and compact diagonalized implicit scheme for the time integration. The present code successfully predicted the bypass transition of subsonic boundary layer. As for supersonic turbulent boundary layer, mean and fluctuation velocity of the attached boundary, as well as the evolution of the friction coefficient and the displacement thickness both upstream and downstream of the separation region are all in good agreement with experiment. The separation point also agreed with the experiment. In the simulation of the shock/laminar boundary layer interaction, the dependence of the transition upon the shock strength is reproduced qualitatively, but the extent of the separation region is overpredicted. These numerical examples show that LES can predict the behavior of boundary layer including transition and shock interaction, which are hardly managed by the conventional Reynolds-averaged Navier-Stokes approach, although there needs to be more effort before achieving quantitative agreement.

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Adaptive second-order nonsingular terminal sliding mode power-level control for nuclear power plants

  • Hui, Jiuwu;Yuan, Jingqi
    • Nuclear Engineering and Technology
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    • v.54 no.5
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    • pp.1644-1651
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    • 2022
  • This paper focuses on the power-level control of nuclear power plants (NPPs) in the presence of lumped disturbances. An adaptive second-order nonsingular terminal sliding mode control (ASONTSMC) scheme is proposed by resorting to the second-order nonsingular terminal sliding mode. The pre-existing mathematical model of the nuclear reactor system is firstly described based on point-reactor kinetics equations with six delayed neutron groups. Then, a second-order sliding mode control approach is proposed by integrating a proportional-derivative sliding mode (PDSM) manifold with a nonsingular terminal sliding mode (NTSM) manifold. An adaptive mechanism is designed to estimate the unknown upper bound of a lumped uncertain term that is composed of lumped disturbances and system states real-timely. The estimated values are then added to the controller, resulting in the control system capable of compensating the adverse effects of the lumped disturbances efficiently. Since the sign function is contained in the first time derivative of the real control law, the continuous input signal is obtained after integration so that the chattering effects of the conventional sliding mode control are suppressed. The robust stability of the overall control system is demonstrated through Lyapunov stability theory. Finally, the proposed control scheme is validated through simulations and comparisons with a proportional-integral-derivative (PID) controller, a super twisting sliding mode controller (STSMC), and a disturbance observer-based adaptive sliding mode controller (DO-ASMC).

Development of supporting platform for the fine flow characteristics of reactor core

  • Hao Qian;Guangliang Chen;Lei Li;Lixuan Zhang;Xinli Yin;Hanqi Zhang;Shaomin Su
    • Nuclear Engineering and Technology
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    • v.56 no.5
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    • pp.1687-1697
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    • 2024
  • This study presents the Supporting platform for reactor fine flow characteristics calculation and analysis (Cilian platform), a user-friendly tool that supports the analysis and optimization of pressurized water reactor (PWR) cores with mixing vanes using computational fluid dynamics (CFD) computing. The Cilian platform allows for easy creation and optimization of PWR's main CFD calculation schemes and autonomously manages CFD calculation and analysis of PWR cores, reducing the need for human and computational resources. The platform's key features enable efficient simulation, rapid solution design, automatic calculation of core scheme options, and streamlined data extraction and processing techniques. The Cilian platform's capability to call external CFD software reduces the development time and cost while improving the accuracy and reliability of the results. In conclusion, the Cilian platform exemplifies an innovative solution for efficient computational fluid dynamics analysis of pressurized water reactor (PWR) cores. It holds great promise for driving advancements in nuclear power technology, enhancing the safety, efficiency, and cost-effectiveness of nuclear reactors. The platform adopts a modular design methodology, enabling the swift and accurate computation and analysis of diverse flow regions within core components. This design approach facilitates the seamless integration of multiple computational modules across various reactor types, providing a high degree of flexibility and reusability.