• 제목/요약/키워드: navier method

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PENALIZED APPROACH AND ANALYSIS OF AN OPTIMAL SHAPE CONTROL PROBLEM FOR THE STATIONARY NAVIER-STOKES EQUATIONS

  • Kim, Hong-Chul
    • 대한수학회지
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    • 제38권1호
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    • pp.1-23
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    • 2001
  • This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. by introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. The existence of optima solutions for the penalized problem will be shown. Next, by employing Lagrange multipliers method and the material derivatives, we derive the shape gradient for the minimization problem of the shape functional which represents the viscous drag.

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정익과 동익의 상호작용을 고려한 익렬의 공력 최적 설계 (Optimization Design of Cascade with Rotor-Stator Interaction Effects)

  • 조장근;정영래;박원규
    • 유체기계공업학회:학술대회논문집
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    • 유체기계공업학회 2001년도 유체기계 연구개발 발표회 논문집
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    • pp.293-299
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    • 2001
  • Since the previous cut-and-try design algorithm require much cost and time, it has recently been concerned the automatic design technique using the CFD and optimum design algorithm. In this study, the Navier-Stokes equations is solved to consider the more detail viscous flow informations of cascade interaction and O-H multiblock grid system is generated to impose an accurate boundary condition. The cubic-spline interpolation is applied to handle a relative motion of a rotor to the stator. To validate present procedure, the time averaged aerodynamic loads are compared with experiment and good agreement obtained. Once the N-S equations have been solved, the computed aerodynamic loads may be used to computed the sensitivities of the aerodynamic objective function. The Modified Method of feasible Direction(MMFD) is usef to compute the

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Upwind Navier-Stokes 방정식을 이용한 무딘 물체 주위의 유동장 해석 (A Numerical Analysis of High Speed Flow over Blunt Body Using Upwind Navier-Stokes Method)

  • 권창오;김상덕;송동주
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 1995년도 추계 학술대회논문집
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    • pp.203-212
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    • 1995
  • In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone($5^{\circ}$) geometry. The effective gamma($\bar{r}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30Km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about $3\sim5$ percent. The skin friction coefficient and heat transfer coefficient were also calculated.

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Flow Field Analysis on the Stagnation Streamline of a Blunt Body

  • Lee, Chang-Ho
    • International Journal of Aeronautical and Space Sciences
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    • 제17권2호
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    • pp.149-156
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    • 2016
  • The hypersonic flow on the stagnation streamline of a blunt body is analyzed with quasi one-dimensional (1-D) Navier-Stokes equations approximated by adopting the local similarity to the two-dimensional (2-D)/axisymmetric Navier-Stokes equations. The governing equations are solved using the implicit finite volume method. The computational domain is confined from the stagnation point to the shock wave, and the shock fitting method is used to find the shock position. We propose a boundary condition at the shock, which employs the shock wave angle in the vicinity of the stagnation streamline using the shock shape correlation. As a result of numerical computation conducted for the hypersonic flow over a sphere, the proposed boundary condition is shown to improve the accuracy of the prediction of the shock standoff distance. The quasi 1-D Navier-Stokes code is efficient in computing time and is reliable for the flow analysis along the stagnation streamline and the prediction of heat flux at the stagnation point in the hypersonic blunt body flow.

날개꼴의 형상 최적화를 위한 유동방정식 영향 연구 (Influence of Flow Solvers On Airfoil Shape Optimization)

  • 정희택;류병석
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 1999년도 춘계 학술대회논문집
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    • pp.171-176
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    • 1999
  • In the present paper, three types of the flow solvers were used to investigate the influence on the airfoil shape optimization. The adopted equations, i.e., Euler , thin layer Navier- Stokes and full Navier-Stokes ones, are solved using implicit LU-ADI decomposition scheme. The feasible direction algorithm with the sinusoidal function was used as an optimization algorithm. The present numerical method was applied to the drag minimization problems under the initial shape of NACA0012 airfoils.

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단단 축류압축기 유동해석에 대한 k-w 난류모델의 응용 (Application of k-w turbulence model to the analysis of the flow through a single stage axial-flow compressor)

  • 이준석;김광용
    • 유체기계공업학회:학술대회논문집
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    • 유체기계공업학회 1999년도 유체기계 연구개발 발표회 논문집
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    • pp.27-32
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    • 1999
  • A numerical study based on the three-dimensional thin-layer Navier-Stokes solver is carried out to analyze the flowfield through a single stage transonic compressor. Explicit four-step Runge-Kutta scheme with spatially variable time step and implicit residual smoothing is used. The governing equations are discretized with exploit finite difference method. Mixed-out average method is used at the interface between rotor and stator. And, an artificial dissipation model is used to assure the stability of solution. The results with k-$\omega$ turbulence model were compared to the results with Baldwin-Lomax model, and physical phenomena of transonic compressor are presented. The two turbulence models give the results that show reasonably good agreements with experimental data.

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비압축성 Navier-Stokes 방정식에 대한 Krylov 부공간법의 적용 (Application of the Krylov Subspace Method to the Incompressible Navier-Stokes Equations)

  • 맹주성;최일곤;임연우
    • 대한기계학회논문집B
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    • 제24권7호
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    • pp.907-915
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    • 2000
  • The preconditioned Krylov subspace methods were applied to the incompressible Navier-Stoke's equations for convergence acceleration. Three of the Krylov subspace methods combined with the five of the preconditioners were tested to solve the lid-driven cavity flow problem. The MILU preconditioned CG method showed very fast and stable convergency. The combination of GMRES/MILU-CG solver for momentum and pressure correction equations was found less dependency on the number of the grid points among them. A guide line for stopping inner iterations for each equation is offered.

PARALLEL ALGORITHMS FOR INTEGRATION OF NAVIER-STOKES EQUATIONS BASED ON THE ITERATIVE SPACE-MARCHING METHOD

  • Skurin Leonid I.
    • 한국전산유체공학회지
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    • 제10권1호
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    • pp.67-72
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    • 2005
  • This research is based on the iterative space-marching method for incompressible and compressible Navier-Stokes equations[1-4]. A principle of parallel computational schemes construction for steady and unsteady problems is suggested. It is analytically proven that convergence of these schemes is unconditional for incompressible case. When the parallel scheme is used the total volume of computations is the sum of a large number of independent and equal parts. Estimation of the speed-up K shows that K > 1000 in ideal case. First results of using the parallel schemes are presented.

다중 격자 Wavier-Stokes 해석의 수렴성 증진 기법 (Convergence Acceleration Methods for the Multigrid Navier-Stokes Computation)

  • 김윤식;권장혁;최윤호;이승수
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2002년도 학술대회지
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    • pp.35-38
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    • 2002
  • The convergence acceleration methods for the compressible Wavier-Stokes equations are studied ,which are multigrid method and implicit preconditioned multistage time stepping method. In this paper, the performance of implicit preconditioning methods are studied for the full-coarsening multigrid methods on the high Reynolds number compressible flow computations. The effect of numerical flux on the convergence are investigated for the inviscid and viscous calculations.

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스펙트랄요소법(SEM)을 이용한 파랑-조류 상호작용 현상 수치해석 연구 (Numerical Analysis of Wave-Current Interaction Phenomenon Using the Spectral Element Method)

  • 성홍근;홍기용;경조현;홍사영
    • 한국항해항만학회:학술대회논문집
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    • 한국항해항만학회 2006년도 추계학술대회 논문집(제1권)
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    • pp.181-186
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    • 2006
  • 본 논문에서는 Freak Wave의 생성원인에 대하여 간략히 논의하였으며, 이 중 파랑-조류 비선형 상호작용에 대한 이론 및 수치적 해석기법의 역사와 장단점 등을 기술한다. 본 연구에서는 파랑-조류 상호작용에 대한 수치모델링 및 해석 기법을 개발하고 있다. 개발 중인 수치해석 기법은 공간적으로 불균일한 조류와 파랑의 비선형 상호작용을 해석하기 위하여 Navier-Stokes 방정식을 이용하여 유동현상을 모델링하였으며, 이산화를 위하여 스펙트랄요소법(Spectral Element Method; SEM)을 이용하였다. 또한 자유표면의 운동을 효과적으로 기술하기 위하여 ALE(Arbitrary Lagrangian-Eulerian)기법을 사용하였다. 본 연구의 유동 모델과 수치해석기법의 과정과 특성, 그리고 장점 등에 대하여 논의하였으며, 초기적인 수치해석 결과를 제시하였다. 이를 바탕으로 개발된 수치해석기법의 정확성 및 수렴성을 확인할 수 있다.

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